APPLICABILITY OF WEIGHT-SHIFT MICROLIGHT AIRCRAFT FOR
MEASURING THE TURBULENT EXCHANGE ABOVE COMPLEX TERRAIN
A disse a ion submi ed o he
FACULTY OF BIOLOGY, CHEMISTRY AND GEOSCIENCES
OF THE UNIVERSITY OF BAYREUTH, GERMANY
o a ain he academic deg ee o
DR. RER. NAT.
p esen ed by
STEFAN METZGER
Diplom Geoökologe
bo n Sep embe 13, 1980
in Schwein u , Ba a ia, Ge many
Bay eu h, 2013-04-15
I
APPLICABILITY OF WEIGHT-SHIFT MICROLIGHT AIRCRAFT FOR
MEASURING THE TURBULENT EXCHANGE ABOVE COMPLEX TERRAIN
Supe iso s
P o . D . Thomas Foken
P o . D . Klaus Bu e bach-Bahl
II
Die o liegende A bei wu de in de Zei on Sep embe 2007 bis Ok obe 2012 an de Uni e si ä
Bay eu h am Leh s uhl ü Hyd ologie, Ab eilung Mik ome eo ologie, un e Be euung on P o . D .
Thomas Foken und P o . D . Klaus Bu e bach-Bahl ange e ig .
Volls ändige Abd uck de on de Fakul ä ü Biologie, Chemie und Geowissenscha en de
Uni e si ä Bay eu h genehmig en Disse a ion zu E langung des akademischen G ades eines
Dok o s de Na u wissenscha en (D . e . na .).
P omo ionsgesuch einge eich am: 2012-10-08
Wissenscha liches Kolloquium am: 2013-04-15
P ü ungsausschuss:
P o . D . Thomas Foken (E s gu ach e )
P o . D . Jens Bange (Zwei gu ach e )
P o . D . Be nd Huwe (Vo si zende )
P o . D . Michael Hauhs
P o . D . And eas Held
Dekan: P o . D . Bea e Lohne
III
The p esen disse a ion was conduc ed om Sep embe 2007 o Oc obe 2012, as ex e nal doc o al
candida e o he Uni e si y o Bay eu h, Depa men o Mic ome eo ology, Bay eu h, Ge many.
The esea ch ai c a and he majo i y o he in as uc u e we e p o ided by he Ka ls uhe Ins i u e o
Technology, Ins i u e o Me eo ology and Clima e Resea ch, A mosphe ic En i onmen al Resea ch,
Ga misch-Pa enki chen, Ge many.
The bulk o p epa a ion, implemen a ion and analysis o he expe imen s we e pe o med a he
Chinese Academy o Sciences, Ins i u e o A mosphe ic Physics, S a e Key Labo a o y o
A mosphe ic Bounda y Laye Physics and A mosphe ic Chemis y, Beijing, China.
The doc o al hesis was comple ed while employed a he Na ional Ecological Obse a o y Ne wo k,
Fundamen al Ins umen Uni , Boulde , CO, U.S.A.
This doc o al hesis was pe o med unde s ipend unding by he Ge man Academic Exchange
Se ice, Helmhol z Associa ion o Ge man Resea ch Cen e s, China Schola ship Council and he
Eu opean Union unde he Science and Technology Fellowship China.
The ligh in Inne Mongolia was unded by he Ge man Resea ch Founda ion, esea ch g oup 536
“Ma e luxes in g asslands o Inne Mongolia as in luenced by s ocking a e”, and he Na ional
Na u al Science Founda ion o China (g an numbe 41021004).
The publica ions we e unded by he Ge man Resea ch Founda ion and Open Access Publishing Fund
o he Ka ls uhe Ins i u e o Technology / Helmhol z Associa ion.
This ma e ial is based upon wo k suppo ed by he Na ional Science Founda ion unde he g an DBI-
0752017. Any opinions, indings, and conclusions o ecommenda ions exp essed in his ma e ial a e
hose o he au ho and do no necessa ily e lec he iews o he Na ional Science Founda ion.
IV
Con en s
CONTENTS ......................................................................................................................................... IV
ACKNOWLEDGEMENTS ................................................................................................................... V
LIST OF MANUSCRIPTS .................................................................................................................. VI
SUMMARY ....................................................................................................................................... VIII
ZUSAMMENFASSUNG ...................................................................................................................... X
1INTRODUCTION ......................................................................................................................... 1
1.1The eddy-co a iance me hod ................................................................................................. 1
1.2E ec s o complex e ain ...................................................................................................... 2
1.3Mo i a ion .............................................................................................................................. 3
1.4Objec i es o his hesis ......................................................................................................... 4
2EXPERIMENTS AND DATA ...................................................................................................... 6
2.1The weigh -shi mic oligh ai c a ....................................................................................... 6
2.2Ba a ia, Ge many .................................................................................................................. 8
2.3B andenbu g, Ge many .......................................................................................................... 8
2.4Inne Mongolia, P.R. China ................................................................................................... 9
3RESULTS .................................................................................................................................... 11
3.1Wind measu emen .............................................................................................................. 11
3.2Tu bulen lux measu emen ................................................................................................ 16
3.3Spa ial esolu ion and ex apola ion o u bulen luxes ...................................................... 22
4CONCLUSIONS .......................................................................................................................... 29
NOTATION ......................................................................................................................................... 32
REFERENCES .................................................................................................................................... 35
LIST OF APPENDICES ...................................................................................................................... 43
APPENDIX A: INDIVIDUAL CONTRIBUTIONS TO THE JOINT PUBLICATIONS .................. 44
APPENDIX B: METZGER ET AL. (2011) ........................................................................................ 48
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) ....................................................... 73
APPENDIX D: METZGER ET AL. (2012) ........................................................................................ 87
APPENDIX E: METZGER ET AL. (2013) ....................................................................................... 106
ERKLÄRUNG ................................................................................................................................... 131
V
Acknowledgemen s
In 2007 I se ou on a jou ney o combine my cu iosi y abou he o ien , amily, and en husiasm o
a mosphe ic science… Now, abou i e yea s la e I eel equally a home in Ge many, China and he
U.S., we a e speaking Chinese a home, and I migh soon be a doc o …
I wan o use his oppo uni y o hank he wonde ul pe sons who ha e made possible his
de elopmen . F om he e y s a Benjamin Wol poin ed me o Ga misch-Pa enki chen, and you
always had a sympa he ic ea – hank you! I am much obliged o my supe iso s Thomas Foken and
Klaus Bu e bach-Bahl, o you us in my abili ies, you scien i ic and pe sonal guidance, and he
lexibili y you p o ided me on his pa h. Special ecogni ion goes o Wol gang Junke mann, o you
un ailing pa ience when in oducing he ai c a o me, and you ou s anding pe o mance o he hai -
ising ligh pa e ns. My g a e ulness o Xunhua Zheng o hos ing me and p o iding indispensable
in as uc u e and nego ia ion skills. Fu he I am hank ul o my co-au ho s, F ank Bey ich, Ma hias
Maude , F ank Neidl, Klaus Schä e , Hans-Pe e Schmid, Bal asa T ancon y Widemann, and
Sebas ian Wieneke, o you pi o al s imuli and you con ibu ions o he manusc ip s. My
app ecia ion o many o he indi iduals who ound innume able ways o inspi e and suppo his
jou ney, including; Wol gang Babel, Jens Bange, F auke Ba hold, Tobias Bie mann, Benjamin
Blank, Timo hy B own, Jose -Michael Bu ge , Yimin Cao, Dao Cha uchi ipan, Li ang Chen, Yong
Chen, Michael Dannemann, Jia Deng, F ancesco di Maio, So ia Dos San os Mendes, Elias, Leyla and
Roland Felgen äge , Edwin Haas, Shenghui Han, Jo dan Hixson, Na ascha Kljun, Alexand a
Lehmann, Jens-Pe e Leps, Chunyan Liu, Ronghua Liu, Hen y Loesche , Tiina Ma kkanen, Alan
Page, Raül Ramos, Ma hias Reiche, Jakob Rei be ge , Cha lo e Roehm, Da id Scha a h, Hans-
Eckha Scheel, And eas Schmid le , Clemens Smolde s, Ch is ian Spe be , Raine S einb eche ,
Je ey Taylo , Aline an den K oonenbe g, Ul ich Weisensee, Geo g Wichmann, Hongkai Zhang,
Yuandi Zhu, Rose Zuu bie .
My hea el hanks o my wi e Liang Sun and o ou amilies. You s eady suppo and unswe ing
ai h we e he building blocks on which I could de elop my po en ial.
VI
Lis o manusc ip s
The disse a ion is p esen ed in cumula i e o m. I consis s o h ee indi idual manusc ip s. Two
manusc ip s ha e been published in he pee - e iewed jou nal A mosphe ic Measu emen
Techniques, o which he i s one also includes a 14 page supplemen . A hi d manusc ip has been
published in he pee - e iewed jou nal Biogeosciences.
Published manusc ip s
Me zge , S., Junke mann, W., Bu e bach-Bahl, K., Schmid, H. P., and Foken, T.: Co igendum o
"Measu ing he 3-D wind ec o wi h a weigh -shi mic oligh ai c a " published in A mos. Meas.
Tech., 4, 1421–1444, 2011, A mos. Meas. Tech., 4, 1515-1539, doi:10.5194/am -4-1515-2011, 2011.
Includes one supplemen . Publishe ’s No e: Due o mis akes on he publishe ’s side i was necessa y
o e ise he o iginal a icle A mos. Meas. Tech., 4, 1421–1444, 2011 in his Co igendum. Please
use his Co igendum as he main documen .
Me zge , S., Junke mann, W., Maude , M., Bey ich, F., Bu e bach-Bahl, K., Schmid, H. P., and
Foken, T.: Eddy-co a iance lux measu emen s wi h a weigh -shi mic oligh ai c a , A mos. Meas.
Tech., 5, 1699-1717, doi:10.5194/am -5-1699-2012, 2012.
Me zge , S., Junke mann, W., Maude , M., Bu e bach-Bahl, K., T ancón y Widemann, B., Neidl, F.,
Schä e , K., Wieneke, S., Zheng, X. H., Schmid, H. P., and Foken, T.: Spa ially explici
egionaliza ion o ai bo ne lux measu emen s using en i onmen al esponse unc ions,
Biogeosciences, 10, 2193-2217, doi:10.5194/bg-10-2193-2013, 2013.
Publica ions no included in his hesis
Pee - e iewed
Sun, F., Ma, Y., Li, M., Ma, W., Tian, H., and Me zge , S.: Bounda y laye e ec s abo e a
Himalayan alley nea Moun E e es , Geophys. Res. Le ., 34, L08808, doi:10.1029/2007gl029484,
2007.
Eigenmann, R., Me zge , S., and Foken, T.: Gene a ion o ee con ec ion due o changes o he local
ci cula ion sys em, A mos. Chem. Phys., 9, 8587-8600, doi:10.5194/acp-9-8587-2009, 2009.
VII
No pee - e iewed
Me zge , S., Ma, Y. M., Ma kkanen, T., Göckede, M., Li, M. S., and Foken, T.: Quali y assessmen o
Tibe an Pla eau eddy-co a iance measu emen s u ilizing oo p in modeling, Ad ances in Ea h
Sciences, 21, 1260-1267, 2006.
Me zge , S., and Foken, T.: COPS expe imen – Con ec i e and o og aphically induced p ecipi a ion
s udy, 1 June 2007 – 31 Augus 2007 – Documen a ion, Uni e si ä Bay eu h, Ab eilung
Mik ome eo ologie, Bay eu h, Ge many, 72 pp. ISSN:1614-8924, 2007.
Eigenmann, R., Me zge , S., and Foken, T.: Gene a ion o ee con ec ion due o changes o he local
ci cula ion sys em, A mos. Chem. Phys. Discuss., 9, 11367-11411, doi:10.5194/acpd-9-11367-2009,
2009.
Me zge , S., Junke mann, W., Bu e bach-Bahl, K., Schmid, H. P., and Foken, T.: Measu ing he 3-D
wind ec o wi h a weigh -shi mic oligh ai c a , A mos. Meas. Tech. Discuss., 4, 1303-1370,
doi:10.5194/am d-4-1303-2011, 2011.
B oadwell, I., Jenkins, G., and Me zge , S.: Th ee pe spec i es: ca ee s in China, Phys. Wo ld, 24,
42-43, 2011.
Me zge , S., Junke mann, W., Maude , M., Bey ich, F., Bu e bach-Bahl, K., Schmid, H. P., and
Foken, T.: Eddy-co a iance lux measu emen s wi h a weigh -shi mic oligh ai c a , A mos. Meas.
Tech. Discuss., 5, 2591-2643, doi:10.5194/am d-5-2591-2012, 2012.
2 INTRODUCTION
a e along-, c oss-, and e ical wind speeds wi h espec o he Ca esian coo dina es x, y, and z; is
ime, and z is he measu emen heigh .
Te m I in Eq. (1) ep esen s he endency o s in he e ical column below he senso , i.e. s o age.
Te ms II–IV ep esen he u bulen lux di e gence, and e ms V–VII ep esen ad ec ion h ough
he laye be ween he su ace and senso . Fo low o spa se canopies i is assumed ha his laye is
well-mixed, and ha s eady s a e condi ions p e ail du ing he a e aging pe iod (/0), which
cancels e m I om Eq. (1). Assuming ho izon al homogenei y (/0, /0) implies equal
ho izon al in low and ou low a opposi e aces o a con ol olume (e.g., Finnigan e al., 2003), and
cancels ho izon al lux di e gence ( e ms II–III) and ad ec ion ( e ms V–VI) om Eq. (1).
Fu he mo e, neglec ing la ge-scale subsidence o con ec ion (≡0) cancels e m VII om Eq. (1),
and hence only e m IV emains. Using dimensional analysis and simila i y numbe s i can be shown
ha he eddy co a iance ′
is cons an wi h heigh in he a mosphe ic su ace laye o wi hin
app oxima ely 10% (e.g., Foken, 2008a). When all abo e condi ions hold ue, he o al lux is hen
equal o he EC measu emen ;
′
. (2)
1.2 E ec s o complex e ain
As long as he one-dimensional anspo Eq. (2) is alid, a single g ound-based EC measu emen can
ep esen he spa ially a e aged lux o o om an unde lying ecosys em. In eali y howe e , e e y
ecosys em is inhomogeneous o some ex en , and a g adua ion om less o mo e complex su aces is
much mo e applicable. He e and in he ollowing, complex e e s no only o he s uc u e, unc ion
and spa io- empo al dis ibu ion o he su ace sou ces and sinks, bu also o su ace opog aphy.
Consequen ly, eal-wo ld measu emen condi ions p incipally in alida e he assump ion o one-
dimensional anspo in a ious o ms and deg ees (e.g., Finnigan, 2008; Foken e al., 2011; Leuning
e al., 2012; Mah , 2010; Maude e al., 2007b). Aside om senso limi a ions (e.g., Dellwik e al.,
2010; Kochendo e e al., 2012), i is his o e simpli ica ion ha is held esponsible o he
sys ema ic ene gy imbalance ha is equen ly obse ed ac oss EC senso ne wo ks (e.g., Foken e al.,
2011; Leuning e al., 2012; Wilson e al., 2002). The lack o ag eemen be ween he sum o he
u bulen hea luxes and he a ailable ene gy also challenges he alidi y o EC lux measu emen s o
clima e e ec i e ace gases (Ruppe e al., 2006).
Kaminski e al. (2012) ind ha EC lux measu emen s e icien ly cons ain modeling app oaches o
ela i ely homogeneous si ua ions, bu a e no obus agains unknown complexi y. Failu e o
explici ly conside spa ial ep esen a i eness inc eases he unce ain y in he obse ed spa io- empo al
lux s uc u e o EC senso ne wo ks. This e ec is also known as loca ion bias (Schmid and Lloyd,
1999). Such bias can be in oduced by p e e en ial measu emen loca ions, e.g., on hill ops a he
han in alleys (Finnigan, 2008), o in d ye a he han in mois e a eas (Desja dins e al., 1997).
Also, he sou ce a ea o an EC lux measu emen a ies in space and ime, as a unc ion o
a mosphe ic s abili y and he wind ield. O e complex e ain, he spa ial ep esen a i eness o an EC
measu emen hus a ies om diu nal o e seasonal o in e -annual ime scales (Göckede e al.,
INTRODUCTION 3
2008). Biases a e in oduced when he sou ce a ea changes sys ema ically o e su aces wi h
dis inc ly di e en biophysical p ope ies and sou ce/sink beha io (e.g., Chen e al., 2012).
1.3 Mo i a ion
Da a om EC senso ne wo ks a e being used o pa ame e ize, cons ain and e alua e land su ace
schemes in clima e models (e.g., Williams e al., 2009). In his way biases in EC lux obse a ions
p opaga e di ec ly in o he esul an da a p oduc s (Leuning e al., 2012). Imp o ed cha ac e iza ion o
he unce ain ies in he EC obse a ions would signi ican ly os e ou abili y o unde s and, model,
o ecas and e en ually mi iga e en i onmen al change (Jung e al., 2011). The mo i a ion o his
disse a ion is o p o ide an ai bo ne measu emen pla o m which enables s udying some o he
mechanisms ha lead o sys ema ically biased lux es ima es om EC senso ne wo ks.
Despi e mos EC lux obse a ions a e pe o med a g ound-based si es in he ime domain, much o
u bulence heo y is concep ually o mula ed in he spa ial domain (e.g., Kaimal and Finnigan, 1994;
Lenschow e al., 1980; Mah , 2010; Pano sky and Du on, 1984). As compa ed o ime domain
measu emen s, EC lux measu emen s in he spa ial domain do no ely on he passi e anspo o
a mosphe ic eddies wi h he mean wind (Taylo , 1915). E.g., he speed o a esea ch ai c a is
ypically much as e han he wind speed. Th ough ac i e p opulsion in space, as esponse ai bo ne
measu emen s mo e comple ely cap u e he ue spa ial a ia ion o he u bulen exchange o e
he e ogeneous su aces (e.g., Kus as e al., 2006). Thus, ai bo ne soundings co e a compa a i ely
la ge ange in he s a e space o en i onmen al d i e s and esponses. I su icien measu emen
accu acy is wa an ed, his esul s in a high signal o noise a io in he ai bo ne obse a ions
(Lenschow and Sun, 2007).
Howe e , spa ial sampling does no pe se obsole e he assump ions in he one-dimensional anspo
Eq. (2). Ye , compa ed o hei g ound-based pendan s, ai c a EC measu emen s end o be e ul ill
some o he assump ions ha jus i y cancella ion o he espec i e e ms om Eq. (1). Because o
hei sho du a ion, change in he s o age e m I is likely small (s eady s a e condi ions). I is
hypo hesized ha , du ing uns able s a i ica ion, su ace he e ogenei y induces non-p opaga ing
eddies (NPE, e m VII), which in u n cause ho izon al compensa o y lows ( e ms II–III, V–VI, e.g.,
Foken e al., 2011; Mah , 2010). These NPEs a e explici ly esol ed in a spa ial sample, bu no in a
empo al one. Mo eo e , each o e ms II–III, V–VII is mo e likely app oaching ze o o an
ins an aneous spa ial a e age han o a s a iona y empo al a e age (S ein eld e al., 2007). Las ly,
he e ec o e ical lux di e gence ( e m IV) on he ai bo ne EC measu emen is negligible, as long
as he soundings a e pe o med close o he su ace (e.g., Isaac e al., 2004). I highe ligh al i udes
a e equi ed, e m IV can also be app oxima ed om con ec i e bounda y laye (CBL) scaling (e.g.,
Dea do , 1974), s acked ligh pa e ns (e.g., Be s e al., 1990), o om a conse a ion app oach
(Bange e al., 2006).
Abo e p ope ies make ai bo ne lux da a pa icula ly aluable o he analysis o a mosphe ic
anspo mechanisms (e.g., Hiyama e al., 2007; Maude e al., 2007a; S unin e al., 2004), and
acili a es he de i a ion o scaling laws (e.g., Lenschow and S anko , 1986; Mah , 2000). This
mo i a es using ai c a obse a ions o he su ace-a mosphe e exchange also o sepa a ing
unce ain ies in EC lux measu emen s due o;
4 INTRODUCTION
(i) sampling e o s;
(ii) di ec e ec s o su ace he e ogenei y, such as loca ion bias h ough a iable sou ce/sink
beha io and su ace oughness, and;
(iii) indi ec e ec s o su ace he e ogenei y, such as anspo by NPEs.
Howe e , o da e manned pla o ms, such as ixed wing ai c a and helicop e s, a e expensi e o
ope a e o no applicable in se ings such as emo e a eas beyond he ange o an ai ield. Unmanned
ae ial ehicles on he o he hand p o ide mobili y, ye do no allow a comp ehensi e senso package
due o payload es ic ions (e.g., o e iew in Dias e al., 2012; Egge e al., 2002; Hobbs e al., 2002;
Ma in e al., 2011; Thomas e al., 2012). In o de o enable he ela ion o ai bo ne EC lux
measu emen s o su ace p ope ies, ai c a a e bound o ly a low and cons an al i ude abo e
g ound. To ollow opog aphically s uc u ed e ain, an ai c a mus he e o e possess a high a io o
climb a e o ai speed, which only ew ai bo ne pla o ms p o ide. This disse a ion in ends o make
accessible an al e na i e ai bo ne measu emen pla o m which combines comp ehensi e, e ain-
ollowing obse a ions o e complex e ain wi h a minimal demand in cos , anspo and
in as uc u e. A e success ully applying a weigh -shi mic oligh ai c a (WSMA) o ae osol and
adia ion ans e s udies (e.g., Junke mann, 2001; Junke mann, 2005), i was hypo hesized ha
WSMA can also ul ill abo e equi emen s. The possibili y o low-le el, e ain- ollowing EC lux
measu emen s wi h WSMA is explo ed in his disse a ion, which can p o ide a iable addi ion o
exis ing ai bo ne measu emen pla o ms. Such de elopmen could aid o e coming he lack o
applicable measu emen pla o ms and echniques o s udy hus a poo ly unde s ood CBL p ocesses
o e complex e ain.
1.4 Objec i es o his hesis
The o e a ching goal o his disse a ion is o e alua e he sui abili y o WSMA o gaining new
insigh s in he spa ial a iabili y o hea and mois u e exchange abo e complex e es ial su aces.
Th ee conc e e objec i es a e assigned o his goal;
(i) assessing he sui abili y o WSMA based 3D wind ec o measu emen o EC applica ions;
(ii) quan i ying he unce ain y in WSMA based measu emen s o u bulence s a is ics and EC
lux, and;
(iii) demons a ing he use ulness o WSMA based EC lux measu emen s o spa ially esol e he
land-a mosphe e exchange abo e complex and no eadily accessible e ain.
These objec i es a e add essed by h ee indi idual publica ions as well as supplemen a y ma e ials
p esen ed in Appendices B–E o his hesis.
Me zge e al. (2011, Appendix B) add ess objec i e (i) by de eloping, es ablishing and e alua ing a
gene alized calib a ion s a egy o he wind measu emen om ai bo ne pla o ms. This s a egy
consis s o an expanded algo i hmic desc ip ion o he wind measu emen (Supplemen o Me zge e
al., 2011, Appendix C), in combina ion wi h a speci ic sequence o ligh pa e ns used o calib a ion.
The p incipal aim o his pape is o enable accu a e wind measu emen s e en du ing low-le el,
e ain- ollowing ligh , such as equi ed o EC soundings o e complex e ain. Hence, he
INTRODUCTION 5
possibili y o dynamically o se he e ec o pilo inpu on he wind measu emen is sough . I is
shown ha his can be ealized h ough conside a ion o he li coe icien , i.e. he a io o ai c a
g a i a ional o p opulsion o ces, in he wind compu a ion. All sou ces o unce ain y a e
quan i a i ely p opaga ed h ough he algo i hmic desc ip ion, and he WSMA wind measu emen is
e alua ed agains independen e e ence measu emen s. The indings emphasize ha WSMA a e
capable o accu a ely measu ing he 3D wind ec o . Hence he necessa y basis is p o ided o he
s udy o p ecision and spec al quali y o he wind measu emen , which is p e equisi e o eliable EC
lux measu emen s.
Me zge e al. (2012, Appendix D) add ess objec i e (ii) by, i s o all, quan i ying he p ecision o
he wind measu emen om WSMA, he lynchpin o lux calcula ions om ai c a . F om he e, he
smalles esol able changes in ic ion eloci y, and sensible- (H) and la en (LE) hea lux a e
es ima ed. Secondly, measu emen s o wind, empe a u e, humidi y and espec i e luxes a e
compa ed be ween independen g ound-based e e ence ins alla ions and he WSMA. Some
di e ences a e obse ed, which could be ela ed o inconsis encies in he g ound-based ins alla ions,
and o hei di e en abili ies o cap u e lux con ibu ions om NPEs. These indings encou age he
use o WSMA as a low cos and highly e sa ile lux measu emen pla o m. In combina ion wi h i s
high anspo abili y and unique ligh cha ac e is ics, he WSMA is hus well sui ed o s udy land-
a mosphe e in e ac ions abo e complex e ain.
The objec i e (iii) is add essed in Me zge e al. (2013, Appendix E). In his pape , low-le el EC
measu emen s om WSMA a e used o cha ac e ize he exchange o hea and mois u e o e a
complex landscape in Inne Mongolia, P.R. China. F om CBL scaling i is ound ha he e ical lux
g adien s below he e ain- ollowing ligh s sa is y he su ace laye de ini ion. Consequen ly he
WSMA based EC measu emen s can be in e p e ed as su ace luxes. Wa ele decomposi ion o he
WSMA u bulence da a is hen combined wi h oo p in modeling and a machine lea ning echnique
o in e en i onmen al esponse unc ions. F om hese esponse unc ions high esolu ion maps o he
hea and mois u e exchange o e he en i e Xilin Ri e Ca chmen a e ex apola ed. These maps a e
hen summa ized o each land co e ype, p o iding in o ma ion on he indi idual sou ce s eng h
and spa ial a iabili y. This s udy emphasizes he po en ial o WSMA based EC lux measu emen s
abo e complex e ain o (a) p o ide high- esolu ion in en o ies o he land-a mosphe e exchange, (b)
ad ancing he loca ion bias ea men o g ound-based lux measu emen s om diagnos ic assessmen
(e.g., Chen e al., 2011) o p ognos ic ans e unc ions, and consequen ly (c) sepa a ing he e ec s o
sampling e o s and su ace he e ogenei y in long- e m senso ne wo ks.
The algo i hms de eloped in he cou se o his hesis a e in ended o u u e use beyond he da a
collec ed and analyzed he e. Fo his pu pose all algo i hms a e implemen ed in a so wa e package in
he R p og amming language (R De elopmen Co e Team, 2012). This so wa e package is cu en ly
a ailable upon eques , and will be eleased o The Comp ehensi e R A chi e Ne wo k (h p://c an. -
p ojec .o g/) in he nea u u e.
6 EXPERIMENTS AND DATA
2 Expe imen s and da a
The esul s p esen ed in his hesis a e based on h ee ex ensi e ligh campaigns wi h he WSMA. In
Sec . 2.1 he WSMA and i s scien i ic equipmen a e b ie ly in oduced. The publica ions p esen ed in
Appendices B and C a e based on da a ha we e collec ed du ing wo ligh campaigns in Ge many
(Sec s. 2.1, 2.3). These campaigns we e conduc ed wi h he sole pu pose o explo e he possibili y o
wind and EC lux measu emen s wi h he WSMA. The da ase used o he publica ion in Appendix D
was collec ed du ing a hi d ligh campaign in China (Sec . 2.4). This campaign was pe o med as
in eg al pa o he Sino-Ge man esea ch collabo a ion MAGIM (DFG esea ch g oup 536). All
ligh campaigns we e ini ia ed by K. Bu e bach-Bahl, I de eloped he measu emen s a egies, and
W. Junke mann pe o med he majo i y o he esea ch ligh s.
2.1 The weigh -shi mic oligh ai c a
Acco ding o he sa e y and egula o y s anda ds o he Eu opean Ci il A ia ion Con e ence,
mic oligh ai c a a e de ined as ai c a wi h a maximum s all speed o 65 km h−1 and a ake-o
mass o no mo e han 450 kg. Figu e 1 shows he weigh -shi mic oligh esea ch ai c a D–MIFU.
I consis s o wo dis inc pa s, he wing and he ike ( he uni hung below he wing, con aining pilo ,
engine and he majo i y o he scien i ic equipmen ). The weigh -shi con ol sys em is enabled by
he pilo ’s di ec applica ion o pi ching o olling momen s o he wing ia he baseba .
Coun e balance is p o ided by he mass o he ike uni suspended below he wing. Simple
p ocedu es o ce i ica ion o ins alla ions on an open ai c a allow a wide spec um o applica ions
as well as he lexible ins alla ion o scien i ic equipmen . A an ope a ional ai speed o ≈100 km h−1,
D–MIFU can ca y a maximum o 80 kg scien i ic payload om 15 m a.g.l. (abo e g ound le el) o
4000 m a.s.l. (abo e sea le el). The ull pe o mance cha ac e is ics can be ound in Junke mann
(2001), and addi ional echnical de ail is p o ided in Me zge e al. (2011, Appendix B).
The s uc u e o a WSMA di e s om common ixed-wing ai c a , which p o ides excep ional
anspo abili y and climb a e, and quali ies i o applica ions in complex and inaccessible e ain.
Howe e , hese s uc u al ea u es migh also expose he ike-based wind measu emen o a iable
dis o ion in he low ield a ound he wing. Fi s ly, he ike, i.e. he u bulence measu emen
pla o m, is ee o o a e in pi ch and oll agains he wing. Secondly, he wing de o ms
ae oelas ically wi h ai c a im, which changes i s ae odynamic p ope ies. These cha ac e is ics
complica e he accu a e and p ecise measu emen o he ue 3D wind ec o , and consequen ly he
dependable measu emen o EC luxes.
EXPERIMENTS AND DATA 7
Fig. 1. Weigh -shi mic oligh esea ch ai c a D-MIFU, ai c a s uc u al ea u es a e highligh ed
by dash-do ed lines. Senso loca ions o wind-measu ing i e hole p obe (5HP), ine ial measu emen
and global posi ioning sys em (IGS, inside ai c a nose) and uni e sal lase al i ude senso (ULS,
below pilo sea ) a e indica ed. Figu e modi ied a e Me zge e al. (2011, Appendix B).
The WSMA is equipped wi h as esponse ins umen s ha enable cap u ing he u bulen scales o
a mosphe ic mo ion. A de ailed desc ip ion o he ins alla ion poin s, models and cha ac e is ics o he
deployed senso s and da a acquisi ion is gi en in Me zge e al. (2011, Appendix B). In sho , mos
a iables a e sampled a 100 Hz and a e block-a e aged and s o ed a 10 Hz, yielding a ho izon al
esolu ion o app oxima ely 2.5 m. To conduc as wind measu emen s, he WSMA is ou i ed wi h
a combina ion o ine ial measu emen and global posi ioning sys em (IGS, RT3102, Ox o d
Technical Solu ions, Uppe Hey o d, England), and a i e-hole p essu e p obe (5HP, in-house
de elopmen ). The p inciple is o esol e he me eo ological wind ec o om he ec o di e ence
o he ai c a ’s ine ial eloci y (cap u ed by he IGS) and he wind ec o ela i e o he ai c a
(cap u ed by he 5HP, Supplemen o Me zge e al., 2011, Appendix C). Addi ional accele a ion
measu emen s (ADXL330, Analog De ices, Inc., No wood, U.S.A.) we e ins alled in he hang poin
o ike and wing, and in he 5HP. These enable in es iga ing po en ial in luences on he wind
measu emen om WSMA engine o p opelle esonance, o om he na u al equencies o he ike
and he wing. On he unde side o he 5HP, ai empe a u e is measu ed wi h a 50 μm he mocouple
(CHAL-002, OMEGA Enginee ing, Inc. S am o d, U.S.A.). An open pa h in a ed gas analyze
(IRGA, OP2, ADC Bioscien i ic, G ea Amwell, UK) o he po side o he 5HP is used o measu e
8 EXPERIMENTS AND DATA
he concen a ion o wa e apo . The ins umen esponse o bo h he he mocouple and he IRGA is
50 Hz. In addi ion, a slow (2 Hz ins umen esponse) humidi y e e ence om a TP3 dew poin
mi o (Me eolabo AG, We zikon, Swi ze land) is s o ed a ≤0.1 Hz. A hi d-o de Sa i zky-Golay
complemen a y il e (Chen e al., 2004) is used o co ec d i o he IRGA due o p essu e changes
wi h al i ude. This il e bases he humidi y luc ua ions measu ed by he IRGA on he slow dew poin
mi o e e ence. A il e window size o 13.9 s o ≈350 m maximizes he in eg al o e he humidi y
powe spec um, and is used o co ec he measu emen s. Addi ional slow measu emen s (≤0.1 Hz)
o su ace empe a u e (CT in a ed he mome e , Op is GmbH, Be lin, Ge many) and downwelling
sho wa e adia ion (LI–200 SZ, LI–COR Inc., Lincoln, Neb aska) a e used in his hesis.
2.2 Ba a ia, Ge many
The i s ligh campaign ook place om 19 June o 11 July 2008 o e Lake S a nbe g, Ge many
(47.9°N, 11.3°E). The lake is loca ed in he o eland o he Ge man Alps, which is a sligh ly olling
landscape (600–800m a.s.l.) and mainly consis s o g assland wi h pa ches o o es . The campaign
was designed o acqui e he necessa y da ase s o de eloping and calib a ing a WSMA wind
compu a ion algo i hm which enables o dynamically o se he e ec s o pilo inpu . Fo his pu pose
31 ligh s o 8 speci ic pa e ns we e pe o med in he ee a mosphe e abo e Lake S a nbe g. O
hese, 10 ideal ealiza ions o hese pa e ns a e used in Me zge e al. (2011, Appendix B). Aside
om he WSMA, no addi ional scien i ic equipmen was deployed. This campaign was unded and
implemen ed solely unde he Ka ls uhe Ins i u e o Technology.
2.3 B andenbu g, Ge many
An e alua ion o he WSMA wind and EC lux measu emen s agains g ound-based e e ence
measu emen s was ca ied ou du ing he second ligh campaign be ween 14 and 21 Oc obe 2008.
This expe imen was pe o med a ound he bounda y laye ield si e Falkenbe g (52.2°N, 14.1°E) o
he Ge man Me eo ological Se ice (DWD), Richa d-Aßmann Obse a o y, Lindenbe g, Ge many.
This ield si e lies in he basically la No h Ge man Plain, and he e ain heigh a ies be ween 40 m
and 130 m a.s.l. wi hin an a ea o 20×20 km2. The land co e is domina ed by ag icul u e and o es s,
in e spe sed by equal amoun s o lakes, meadows and se lemen s. This campaign was unded by he
Ka ls uhe Ins i u e o Technology, and implemen ed in close collabo a ion wi h he DWD.
To e alua e he accu acy o he WSMA wind measu emen , Me zge e al. (2011, Appendix B) use
da a om an ins umen ed 99 m owe and om sonic de ec ion and anging (SODAR, PCS-2000/64,
Me ek GmbH, Elmsho n, Ge many). The 99 m owe p o ided cup measu emen s o wind speed a
ou le els (40, 60, 80, and 98 m a.g.l., Wind Senso Classic, Adol Thies GmbH, Gö ingen,
Ge many). The wind di ec ion was measu ed wi h anes a heigh s o 40 and 98 m a.g.l. (Wind
Di ec ion Senso Classic, Adol Thies GmbH, Gö ingen, Ge many), and a s a ic p essu e e e ence
was p o ided a 1 m a.g.l. (PTB220A, Vaisala Oy, Helsinki, Finland, 10 min a e ages). Towe p o ile
and p essu e da a we e a e aged and s o ed in 10 min in e als. Sonic anemome e s (USA-1, Me ek
GmbH, Elmsho n, Ge many) p o ided wind ec o measu emen s a a a e o 20 Hz a 50 and 90 m
a.g.l. The SODAR wind ec o p o iles (15 min a e ages) eached, a inc emen s o 20 m, om 40 o
240 m a.g.l. 17 c oss-shaped ligh pa e ns wi h legs o 3 km leng h we e pe o med wi h hei cen e
EXPERIMENTS AND DATA 9
be ween he 99 m owe and he SODAR. The ligh s we e ca ied ou a he app oxima e sounding
le els o he 99 m owe and he SODAR (50, 100, 150, 200 and 250 m a.g.l.). This enables he di ec
compa ison o he wind componen s be ween he WSMA and he g ound-based measu emen s.
Mo eo e , Me zge e al. (2012, Appendix D) compa e u bulence s a is ics, EC luxes and powe
spec a be ween he WSMA and g ound-based measu emen s. Fo his pu pose addi ional da a om
ins alla ions on he 99 m owe , an EC su ace lux measu emen , a la ge-ape u e scin illome e
(LAS), a wind p o ile , and om adio soundings a e used. In combina ion wi h he sonic
anemome e s, open pa h IRGAs (LI-7500, LI-COR Biosciences, Lincoln, U.S.A.) a 50 m and 90 m
a.g.l. enable he compa ison o u bulence s a is ics, EC luxes and powe spec a be ween WSMA
and owe . The 99 m owe was u he equipped wi h p o ile measu emen s o empe a u e (HMP-45,
Vaisala Oy, Helsinki, Finland) and humidi y (F ankenbe ge Psych ome e , Theodo F ied ichs
GmbH, Hambu g, Ge many) a 40, 60, 80, and 98 m a.g.l (10 min a e ages). The p o iles a e
in e pola ed o he heigh s o he EC ins alla ions and a e used o compa e a e age empe a u e and
humidi y measu emen s be ween WSMA and owe . The wo lowes le els o he c oss-shaped ligh
pa e ns we e pe o med a he app oxima e heigh o he owe EC ins alla ions, and p o ided 36
indi idual ligh legs o his compa ison. Iden ical ins umen a ion as on he owe was used o an
addi ional EC su ace lux measu emen upwind (sou h) o he owe base, a 2.4 m a.g.l. Also 10 min
a ea-a e aged su ace sensible hea luxes we e de i ed om he LAS. Fu he mo e, hou ly es ima es
o he CBL dep h we e de i ed om SODAR and wind p o ile da a, and om six-hou ly ou ine
adio soundings pe o med by he DWD. The su ace sensible hea luxes measu ed a he 2.4 m EC
and he LAS a e used in conjunc ion wi h he CBL dep hs o app oxima e e ical lux p o iles. On
wo days, simul aneous owe and WSMA measu emen s o he sensible hea lux a e compa ed o
hese lux p o iles.
2.4 Inne Mongolia, P.R. China
The hi d ligh campaign was pe o med om 23 June o 4 Augus 2009 o e he emo e s eppe o
he Mongolian Pla eau. The hilly in es iga ion a ea sou h o he p o incial capi al Xilinho , Inne
Mongolia, China (43.6°N, 116.7°E, 1000–1400 m a.s.l.) is co e ed by semi-a id g assland,
in e sec ed by a dune bel . The land co e in he in es iga ion a ea a ies dis inc ly in space and ime
(Ke ze e al., 2008; Scha a h e al., 2011). On he small scale landscape posi ion e ec s soil
mois u e a ailabili y. On la ge scales managemen p ac ices such as haymaking, g azing o i iga ed
ag icul u e a e suspec ed o cause a as he e ogenei y in he hea and mois u e luxes be ween
su ace and a mosphe e. As in eg al pa o he Sino-Ge man esea ch collabo a ion MAGIM (Ma e
luxes in g asslands o Inne Mongolia as in luenced by s ocking a e), he goal o his ligh
campaign was o suppo long- e m g ound-based measu emen s h ough gaining new insigh s in he
spa ial dis ibu ion o luxes on he egional scale. In addi ion o he WSMA measu emen s, Me zge
e al. (2013, Appendix E) deployed a ceilome e (LD40 – Vaisala Oy, Helsinki, Finland) o his
pu pose. The ceilome e p o ided 10 min e ical p o iles o he a mosphe ic lase adia ion
backsca e in ensi y. The dep h o he con ec i e bounda y laye (CBL) was in e ed om his da a
using he maximum g adien me hod (Emeis e al., 2008) in combina ion wi h semi-daily adiosonde
ascends in nea by Xilin Ho (Wo ld Me eo ological O ganiza ion s a ion 54102,
h p://wea he .uwyo.edu/uppe ai /sounding.h ml). The CBL dep h is used o cha ac e ize he
10 EXPERIMENTS AND DATA
ho izon al mixing be ween su ace and ligh le el and o de e mine he sou ce a ea o he WSMA
based EC lux measu emen s. EC measu emen s wi h he WSMA we e pe o med along 14 indi idual
s aigh line ligh pa e ns, which ollowed he e ain a ≈50 m a.g.l. Two ligh lines pe pendicula
o he p e ailing wind di ec ion we e chosen on a daily basis, and epea ed un il a minimum o 40 km
o da a was acqui ed. This esul ed in a o al o 35 WSMA soundings du ing he ligh campaign, o
which Me zge e al. (2013, Appendix E) selec ed 12 ligh s o analysis wi h s a iona i y o he sola
i adiance being he selec ion c i e ia. This ligh campaign was unded by he Ge man Resea ch
Founda ion, and was implemen ed in collabo a ion be ween he Ka ls uhe Ins i u e o Technology and
he Chinese Academy o Sciences.
RESULTS 11
3 Resul s
In he ollowing, he esul s o he de elopmen and applica ion o WSMA based EC lux
measu emen a e ou lined and ela ed o he co esponding publica ions in Appendices B–E. This
de elopmen p ocess s a s wi h he wind measu emen (Sec . 3.1), con inues o he u bulen lux
measu emen (Sec . 3.2) and concludes wi h a sample applica ion o he WSMA based EC lux
measu emen o e complex and p e iously inaccessible e ain (Sec . 3.3).
3.1 Wind measu emen
The EC echnique elies upon he p ecise measu emen o luc ua ions o a mosphe ic quan i ies,
based on negligible senso d i h oughou an a e aging pe iod. Measu ed om ai c a , he
de e mina ion o he wind ec o equi es a sequence o he modynamic and igonome ic equa ions
(Supplemen o Me zge e al., 2011, Appendix C). These equa ions p opaga e a ious sou ces o
e o , and a e consequen ly he lynchpin o EC lux measu emen s om ai c a . An abundance o
me hods exis s o calib a ing hese algo i hms o he indi idual ae odynamic p ope ies o a wide
ange o ixed-wing ai c a (e.g., Tje ns öm and F iehe, 1991; an den K oonenbe g e al., 2008;
Williams and Ma co e, 2000). Howe e , none o he exis ing me hods is capable o ea ing WSMA
speci ic e ec s on he wind measu emen , o igina ing om ike o a ion and wing de o ma ion.
Hence, Me zge e al. (2011, Appendix B) ad ance he exis ing wind calib a ion p ocedu es wi h
ocus on (i) c ea ing a o mal calib a ion amewo k, (ii) e aining applicabili y o ixed-wing ai c a ,
and (iii) o se ing WSMA speci ic e ec s on he wind measu emen . The esul is a bo om-up
calib a ion p ocedu e in h ee s ages;
(i) basic calib a ion o empe a u e and p essu e senso s;
(ii) gene al in- ligh calib a ion o low angle measu emen s, and;
(iii) WSMA speci ic in- ligh calib a ion o low angle measu emen s.
These h ee s ages a e composed o a sequence o se en calib a ion s eps A–G, which is shown in
Fig. 2. Each s ep a ge s one o mo e a iables in he wind ec o compu a ion, u ilizes expe imen al
da a unde de ined en i onmen al condi ions, and esul s in inc emen ally e ined sys em
pe o mance. Addi ional in o ma ion on he ligh maneu e s used o his pu pose as well as a iable
de ini ions is p o ided in Me zge e al. (2011, Appendix B).
18 RESULTS
because i is he axis o plug- and socke connec ion be ween IGS and 5HP, i.e. he axis wi h he leas
ma gin o esonance. No emnan s o his scale disc epancy a e e iden in he wind measu emen s, in
pa icula be ween 1‒5 Hz (Me zge e al., 2012, Fig. 3, Appendix D). This leads o he conclusions
ha (i) he wind ec o compu a ion co ec ly accoun s o he displacemen o 5HP and IGS, and (ii)
he cause o enhanced 5HP accele a ion measu emen s (especially longi udinal o he body) lies in he
ix u e o he accele a ion senso in he 5HP, a he han in he moun ing o he 5HP agains he IGS.
The spec al beha io o he wing accele a ion measu emen s is di e en o hose o he ike. I
displays a dis inc peak a ound 0.7 Hz, which is only p esen in he ans e se componen o he ike
measu emen s. I can be unde s ood as he wing's na u al equency, i.e. i s ine ia.
Fig. 5. Smoo hed powe spec a o accele a ion measu emen s in he WSMA ike coo dina e sys em.
The dashed e ical line indica es he −3 dB equency (20 Hz) o he Bu e wo h low-pass il e in
he wind ec o da a acquisi ion sys em. Figu e modi ied a e Me zge e al. (2012, Appendix D).
Subsequen ly, Me zge e al. (2012, Appendix D) quan i y he impac o WSMA spec al p ope ies
on he wind- and EC lux measu emen . Fo his pu pose a as Fou ie ans o ma ion is applied o
he 36 owe and WSMA as esponse da a se ies du ing he compa ison ligh s. Each indi idual
ans o m is no malized o a sum o uni y. To educe sca e , he no malized ans o ms o all owe
and WSMA measu emen s, espec i ely, a e hen binned in o equency bands and ensemble-
RESULTS 19
a e aged. He e, only he esul s o he cospec a a e discussed. In Fig. 6 ensemble cospec a (Co) a e
p esen ed as unc ion o he no malized equency n= ·z/U¯, wi h being he sampling equency, z
being he measu emen heigh , and U¯ being he ho izon al wind speed o he owe and he ue
ai speed o he WSMA, espec i ely. Also shown is he e e ence cospec um o Massman and
Clemen (2004), wi h he spec al maximum a n=0.1 o uns able s a i ica ion (Kaimal and Finnigan,
1994, 24 ou o 36 ligh s). The momen um lux a he owe exhibi s la ge sca e in he indi idual
cospec a a bo h ins alla ion heigh s, and he ensemble cospec um is no calcula ed. The sca e
migh esul om he wind di ec ion dependen co ela ion o he ho izon al- and e ical wind
componen s a he USA‒1 sonic anemome e s (e.g., Maude e al., 2007c). All analyzed ensemble
cospec a app oxima ely ollow he e e ence cospec um, and o he hea luxes he peak o he
owe cospec a coincide wi h n=0.1 o he e e ence cospec um. The cospec al peaks o he WSMA
measu emen s a e ma ginally shi ed owa ds highe equencies a ound n=0.2. Me zge e al. (2012,
Sec . 3.3.3, Appendix D) associa e inc eased a iance in he WSMA wind componen s wi h spec al
a i ac s esul ing om he ea men o he ne low dis o ion in he ime-, bu no in he equency
domain (Me zge e al., 2011, Appendix B). In o de o quan i y he impac on he WSMA lux
measu emen , all indi idual cospec a a e compa ed be ween he WSMA and he e e ence
cospec um in he ange o he wing’s na u al equency (0.4≤ ≤2 Hz). To accoun o he in luence o
s a i ica ion, he peaks o he e e ence cospec a a e calcula ed using he o ms o Kaimal e al.
(1972). Rela i e o he en i e equency ange he spec al a i ac s lead o a sys ema ic de ia ion in
he luxes o momen um, sensible- and la en hea o 3±6%, −1±6% and 1±3% (median di e ences),
espec i ely.
Fig. 6. A e age cospec a o all measu emen s be ween owe and WSMA. Also shown is he
e e ence cospec um o Massman and Clemen (2004, dashed line). Figu e om Me zge e al. (2012,
Appendix D).
The WSMA wind and lux measu emen s a e co ec ed o his spec al inconsis ency be o e
compa ing hem o g ound based measu emen s. The app op ia e co ec ion ac o s a e es ima ed
om he compa ison o measu ed spec a and cospec a o modeled ones (Me zge e al., 2012, Sec s.
3.3.3, 3.3.4, Appendix D). A maximum likelihood unc ional ela ionship (MLFR, Ripley and
20 RESULTS
Thompson, 1987), which conside s he andom e o in he da a, is used o compa e owe and
WSMA measu emen s. Fo his pu pose he s a is ical andom e o
an is calcula ed a e Lenschow
and S anko (1986) and Lenschow e al. (1994), and consolida ed a e Mah (1998) o he ensemble
o all measu emen s (
ens). A e ages o along-wind componen u, empe a u e T and absolu e
humidi y a ag ee e y well be ween owe and WSMA (Table 1). The MLFRs o s anda d de ia ions
(2‒34%) and luxes (17‒21%) indica e highe es ima es o he ai bo ne measu emen s compa ed o
he owe . Conside ing he 99.5% con idence in e als he obse ed di e ences a e no signi ican ,
wi h excep ion o he empe a u e s anda d de ia ions. I mus be no ed ha he magni ude o he low
dis o ion co ec ion o he USA‒1 sonic anemome e s a he owe alone is in he o de o he
obse ed di e ences be ween he owe and he WSMA. Mo eo e , he ampli ude esolu ion es by
Vicke s and Mah (1997) would ejec 28 ou o 36 owe sonic empe a u e da a se s. The p oblem is
ela ed o he insu icien sonic empe a u e esolu ion (0.01 K) o he USA‒1, which appea s as
addi ional spec al ene gy in he o m o high equency whi e noise. Consequen ly he USA‒1
measu emen s canno be ega ded as eliable e e ence o he empe a u e s anda d de ia ions, and
he applied spec al co ec ion ac o s and esul ing MLFRs mus be in e p e ed wi h cau ion. The
Table 1. Resul s o he maximum likelihood unc ional ela ionships be ween owe and WSMA
measu emen s. Shown a e he MLFR slope and i s s anda d e o Slope±
, weigh ed coe icien o
de e mina ion R2, esidual s anda d e o
es, he a e age s a is ical andom e o
an and he
ensemble andom e o
ens. Table om Me zge e al. (2012, Appendix D).
Va iable Slope± R2
es
an
ens
A e ages
u 0.99±0.02 1.00 9% 15% 3%
T 1.00±0.00 1.00 0% 0% 0%
a 0.99±0.00 1.00 1% 2% 0%
S anda d de ia ions
u 1.15±0.05 0.99 21% 9% 2%
1.02±0.05 0.98 20% 8% 1%
w 1.10±0.03 0.99 9% 5% 1%
T 1.34±0.07 0.98 17% 7% 1%
a 1.17±0.08 0.98 23% 9% 1%
Fluxes
u* 1.21±0.07 0.98 13% 25% 5%
H 1.17±0.08 0.98 10% 29% 8%
LE 1.17±0.10 0.96 25% 34% 7%
RESULTS 21
p oblem is less p onounced o he sensible hea lux. The whi e noise in he USA‒1 sonic
empe a u e measu emen does no a ec he measu emen o , o he co ela ion wi h, he e ical
wind measu emen . The esul is a modes unde es ima ion o −3% o he owe sensible hea lux due
o educed cohe ence o sonic empe a u e and e ical wind a high equencies.
(iii) Subsequen ly Me zge e al. (2012, Appendix D) in es iga e whe he he di e ences be ween
WSMA and owe measu emen s can be ela ed o hei di e en spa ial ep esen a i eness. Fo his
pu pose a c oss-wind dis ibu ed oo p in pa ame e iza ion is used oge he wi h Co ine Land Co e
2006 da a (Ve sion 13, Eu opean En i onmen Agency, 2010, 100 m ho izon al esolu ion). The
spa ial con ex o he pla o ms ag ees well when conside ing he a e age oo p in con ibu ions o e
all owe -WSMA compa ison measu emen s. Fo bo h pla o ms mos o he oo p in co e s a able
land (95‒97%). Con ibu ions om he emaining land co e s a e sub-pe cen excep o o es (2‒
3%), and meadows do no con ibu e a all. Taking a close look a he indi idual, simul aneous
measu emen s he sou ce a eas can howe e di e conside ably. O e all simul aneous measu emen s
he ac ual o e lap anges om 12‒68% o he oo p in weigh s, wi h a median o 35±17%. Howe e
a ying o e lap did no sys ema ically al e he di e ences in he lux measu emen s be ween owe
and WSMA (R2≤0.07). Hence, spa ial ep esen a i eness canno explain he emaining di e ences
be ween WSMA and owe measu emen s.
(i ) Las ly, Me zge e al. (2012, Appendix D) assess he po en ial impac o p incipal di e ences o
spa ial a e aging (LAS, WSMA) and empo al a e aging ( owe EC) on he measu ed luxes. Fo his
pu pose simul aneous measu emen s o he sensible hea lux on wo days a e in e -compa ed
be ween he measu emen pla o ms using bounda y laye scaling. Any H measu ed by owe EC and
ex apola ed o ligh al i ude is lowe by 25‒40% compa ed o he LAS. A he same ime H
measu ed by he WSMA is ≤25% lowe compa ed o he LAS, bu 15‒25% highe compa ed o he
owe EC. The oo p in s o all measu emen s is domina ed by >90% con ibu ions om a able land.
Consequen ly di e ing sou ce a eas o he measu emen s do no quali y as po en ial eason o he
obse ed di e ences. Foken (2008b) and Mah (2010) sugges ha he ene gy balance non-closu e
equen ly obse ed om owe EC measu emen s is connec ed o he in e ac ion o e ain
he e ogenei y and u bulen scales. Following hei hypo hesis, he owe EC canno adequa ely
cap u e lux con ibu ions om NPEs due o i s inabili y o spa ial sampling. On he o he hand a
LAS cap u es NPEs up o he dimension o i s pa h leng h, wi h inc easing sensi i i y owa ds he
cen e o i s op ical pa h (Foken e al., 2010). Also ai bo ne EC is capable o spa ial sampling and
cap u es some o he associa ed lux, depending on he ho izon al ex en o he NPEs and he ligh
pa h. The p esence o NPEs in he s udy a ea has been shown (S ein eld e al., 2007; Uhlenb ock e
al., 2004), and can hus be conside ed a po en ial explana ion o he de ia ion o he owe EC esul s
om he WSMA, and e en mo e so om he LAS esul s.
Me zge e al. (2012, Appendix D) show ha u bulence measu emen s om WSMA can be achie ed
wi h su icien p ecision and accu acy o enable EC lux calcula ion. Di e ences in he o de o 15‒
25% emain be ween he luxes measu ed by he g ound based ins umen s and he WSMA. Howe e ,
he 99.5% con idence in e als in he compa ison be ween owe and WSMA indica e ha he
di e ences a e insigni ican and he WSMA lux measu emen is unbiased. The p ecision o he
WSMA lux measu emen can be quan i ied o ≤10% (1 MLFR slope e o ).
22 RESULTS
3.3 Spa ial esolu ion and ex apola ion o u bulen luxes
The o e a ching goal o ai bo ne eddy-co a iance lux measu emen s is o b idge he gap be ween
obse a ions and da a assimila ion app oaches on di e en spa ial scales. Me zge e al. (2013,
Appendix E) de elop a p ocedu e ha aids his pu pose by ‘mining‘ he in o ma ion con en o EC
lux obse a ions. Th ough accomplishmen o ou subsequen s eps his LTFM p ocedu e ex ac s
quan i a i e esponse unc ions wi h en i onmen al d i e s;
(i) low le el EC lux ligh s;
(ii) ime- equency analysis o he lux obse a ions;
(iii) composi ion o con inuous biophysical su ace p ope ies in he lux oo p in , and;
(i ) en i onmen al esponse unc ion om non-pa ame ic machine lea ning echniques.
In de eloping he LTFM p ocedu e, he objec i e o Me zge e al. (2013, Appendix E) is o spa ially
explici ly cha ac e ize he exchange o sensible- and la en hea o e he he e ogeneous s eppe
landscape o he Xilin Ri e Ca chmen (XRC), Inne Mongolia, P.R. China (Sec . 2.4).
(i) The LTFM p ocedu e equi es he ela ion o he ai bo ne measu ed luxes o land co e
p ope ies. To enable his equi emen an ai c a is bound o measu e close o he su ace, whe e
cha ac e is ic luxes om di e en land co e s a e no ye ully homogenized (o blended, Mason,
1988; Wood and Mason, 1991). Mo eo e he lux mus be measu ed a a cons an al i ude abo e
g ound, so as o a oid a i icial lux con ibu ions h ough al i ude luc ua ions along e ical
g adien s (Vicke s and Mah , 1997). Howe e in es iga ion a eas a e seldom ideally la , and
opog aphy can a y signi ican ly ac oss a domain. To sa ely ollow e ain con ou s a a low and
cons an al i ude abo e g ound, he ai c a mus possess a low a io o ue ai speed o climb a e.
The WSMA ul ills his equi emen , and e ain- ollowing EC lux measu emen s wi h he WSMA
we e conduc ed a 50 m a.g.l. in he XRC. F om bounda y laye scaling i is ound ha he e ical
lux g adien s below he ligh le el sa is y he su ace laye de ini ion (cons an wi hin |5–10%|).
Hence measu ed H and E can be in e p e ed as su ace luxes.
(ii) Me zge e al. (2013, Appendix E) use he wa ele c oss-scalog am echnique o enable a high
spa ial disc e iza ion o u bulen lux measu emen s, wi hou neglec ing lux con ibu ions om long
wa eleng hs. Fo each indi idual 10 Hz obse a ion he wa ele c oss-scalog am ep esen s he
measu ed u bulen lux as con ibu ions om di e en a mosphe ic anspo scales. Theo e ically,
his enables a spa ial esolu ion o ≈2.5 m o he WSMA lux measu emen . Howe e , o an
indi idual sample he andom e o is excessi ely la ge, bu dec eases in e sely p opo ional o he
squa e oo o he sample size (e.g., Lenschow and S anko , 1986). In sea ch o a sui able sample
size, a comp omise mus be ound be ween andom e o (high esolu ion) and smea ing (low
esolu ion) o he esul ing lux es ima es. Me zge e al. (2013, Appendix E) ind ha he ypical
leng h scale o su ace he e ogenei y is in he o de o 1000 m. Thus, a ligh pa h leng h o 1000 m is
a physically meaning ul window o he compu a ion o u bulence s a is ics and luxes. Hence, while
e aining a spa ial disc e iza ion o 90 m, he wa ele c oss-scalog am is in eg a ed o e cen e ed
subin e als o 1000 m leng h. Compa ed o an in eg a ion leng h o 90 m his esul s in a dec ease o
he ensemble andom e o (Mah , 1998) o ≈70% o a ligh line o 20 km leng h. This p ocedu e
RESULTS 23
yields a high numbe o lux obse a ions along a ligh line, which p o ides p e iously unachie able
esolu ion and co e age o he en i onmen al s a e space. The downside o he low- equency suppo
o wa ele s is ha edge e ec s due o he ini e o e all da a se inc ease wi h scale. To ence and
Compo (1998) de ine he cone o in luence as he bounda y whe e he powe o edge- ela ed a i ac s
is damped by a ac o o e-2. In gene al, mo e ce ain lux con ibu ions below he cone o in luence
include anspo scales up o ≈⅓ o he ligh leng h. Fo he ligh s in he XRC he less ce ain lux
con ibu ions abo e he cone o in luence a e small (−15% o −4% median di e ences o all ligh s).
These con ibu ions a e included in he analysis, o ensu e inclusion o iden ical anspo scales close
o he s a o end, and a he cen e o a da ase , and o p ese e he global co a iance.
(iii) The spa ial a ia ion o empe a u e and p ecipi a ion in he XRC ollows al i udinal and
la i udinal ends (Aue swald e al., 2009; Wi me e al., 2010). To esol e he e ec i e s a e o
biophysical su ace p ope ies o e ime, Me zge e al. (2013, Appendix E) use Mode a e Resolu ion
Imaging Spec o adiome e (MODIS) da a. He e, 8-day composi es o he land su ace empe a u e
(LST, MOD11A2.5, 1 km esolu ion), and 16-day composi es o he enhanced ege a ion index (EVI,
MOD13Q1, MYD13Q1, 250 m esolu ion) a e used. The LST and EVI da ase s a e bi-linea ly
in e pola ed o he 90 m esolu ion o an exis ing land co e classi ica ion, and linea ly in e pola ed in
ime o yield an indi idual map o each ligh day. Tu bulence s a is ics o each 1000 m subin e al
o e a wa ele scalog am is used o e alua e he 2D oo p in model desc ibed in Me zge e al.
(2012, Appendix D). An indi idual e alua ion is ca ied ou o each o e lown cell o he land co e ,
LST and EVI g ids (i.e., e e y 90 m along he ligh pa h). Wi h he o e lown g id cell as base poin ,
and he oo p in weigh s wxy
1
xy
w o each g id cell wi h posi ion x, y, ela i e o he base
poin , he oo p in composi ion is calcula ed;
,
xy
xyxy LSTwLST (5)
,
xy
xyxy EVIwEVI (6)
wi h he land su ace empe a u e and enhanced ege a ion index o each g id cell, LSTxy and EVIxy,
espec i ely. Fo g aphical ep esen a ion he oo p in weigh s o all e alua ions along a ligh line
a e supe imposed and no malized o a sum o uni y. In Fig. 7 LST and EVI gene ally ollow he land
co e pa e ns, e.g. lowe empe a u e and highe g eenness o i iga ed ag icul u e and ma shland.
Howe e , i is also e iden ha he s a ic land co e classi ica ion canno e lec he cu en su ace
condi ions. E.g., he ma shland in he no h-wes e n quad an appea s d ied-ou (high LST and low
EVI), while he s eppe a ea in he no h-eas e n quad an shows la ge a ia ions in LST. I.e., he land
co e classi ica ion ep esen s he long- e m e ec s o ege a ion, clima e, soil and opog aphy.
Howe e , biophysical su ace p ope ies also a y signi ican ly wi hin land co e classes. This is
likely as a unc ion o geomo phological p ope ies such as aspec , slope and soil ype, bu also due o
he la ge a iabili y o con ec i e ain all e en s ac oss he s udy a ea (e.g., Scha a h e al., 2011).
24 RESULTS
Fig. 7. Fligh along pa e n O12 on 8 July 2009, 12:16–12:24 Chinese s anda d ime (UTC+8 h, whi e
dashed line). The composi e lux oo p in along he ligh line (30%, 60%, 90% con ou lines) is
supe imposed o e maps o land co e (uppe le panel), land su ace empe a u e (LST, uppe igh
panel), and enhanced ege a ion index (EVI, lowe le panel). The land co e colo codes a e
abb e ia ed o ba e soil (Ba e), ma shland (Ma sh), gene ic s eppe (S eppe), i iga ed ag icul u e
(I iga ed), and ain ed ag icul u e (A able). Figu e om Me zge e al. (2013, Appendix E).
(i ) En i onmen al esponse unc ions (ERF, Desja dins e al., 1994) a e an app oach o u ilize
quan i a i e in o ma ion abou he EC measu emen ’s spa ial con ex . The gene al idea is o es ablish
a unc ional ela ionship be ween spa ially o empo ally esol ed lux obse a ions ( esponses) and
RESULTS 25
co esponding en i onmen al d i e s. Me zge e al. (2013, Appendix E) base he de elopmen o a
ca chmen -speci ic ERF on he wo ks o Chen e al. (1999), Hu jes e al. (2010) and Ogunjemiyo e
al. (2003). The LTFM p ocedu e ad ances hese app oaches;
(a) Thus a , a sui able numbe o lux obse a ions was ob ained by ei he sho ening he ime-
domain EC a e aging in e al (Chen e al., 1999; Ogunjemiyo e al., 2003), o by s a i ying
epea ed obse a ions along he same ligh line on di e en days (Hu jes e al., 2010). The
inhe en d awbacks a e he neglec o ei he long wa eleng h con ibu ions o he lux
measu emen , o in e -day a iabili y o ecosys em d i e s. Bo h a e o e come using he
wa ele c oss-scalog am echnique;
(b) P e iously, he de elopmen o ERFs has solely ocused on d i e s in he oo p in o he lux
obse a ions, namely disc e e land co e classi ica ions. This p ocedu e igno es wi hin-class
a iabili y ac oss a ca chmen , e.g. along clima ic o al i udinal g adien s, which is o e come
by using con inuous a iables such as LST and EVI ins ead. Also, subs i u ing disc e e wi h
con inuous a iables enables he use o mo e ad anced scaling algo i hms. In addi ion, he
p esen app oach conside s me eo ological d i e s such as downwelling sho wa e adia ion
(S↓), mixing a io (MR), and po en ial empe a u e (θ). This a oids he need o s a i y o p e-
selec da a, and enables cons uc ing a single ERF ha is alid o he obse a ion pe iod and,
wi hin in ange o he measu ed a iables, ac oss a ca chmen o in e es .
(c) Hi he o, ERFs we e de e mined as he in e se o a linea mixing ma ix, using ei he
nume ical (Chen e al., 1999) o eg ession me hods (Hu jes e al., 2010; Ogunjemiyo e al.,
2003). Such p ocedu e assumes a linea ela ionship be ween d i e s and esponses, which is
subjec o on-going discussion and esea ch (e.g., Raupach and Finnigan, 1995). Ins ead, he
p esen app oach uses boos ed eg ession ees (BRT), a non-pa ame ic machine lea ning
echnique, o es ablish an ERF be ween d i e s and esponses. In con as o pa ame ic
app oaches, BRT does no assume a p ede e mined o m o he esponse, bu cons uc s an
ERF acco ding o in o ma ion in he da a. BRT can i complex nonlinea ela ionships,
au oma ically handle in e ac ions be ween d i e s, and p o ide p edic i e pe o mance ha is
supe io o mos adi ional modeling me hods (e.g., Hu e al., 2010).
Me zge e al. (2013, Appendix E) apply BRTs o N=8446 obse a ions du ing 35 ligh s in he XRC
(Sec . 2.4). The pu pose is o ex ac he ela ionships be ween H, LE and land co e (LST, EVI) and
me eo ological (S↓, MR, and θ) a iables. In Fig. 8 he BRTs o H a e summa ized as pa ial
dependence plo s. These show he e ec o each indi idual a iable on he esponse a e sub ac ion
o he o se (161 W m−2), and a e accoun ing o he a e age e ec s o all o he a iables in he
model. The pa ial dependence plo s in Fig. 8 a e so ed in o de o he ela i e impo ance o he
esponse a iables (F iedman, 2001). The mos impo an esponses o H a e non-linea (LST, θ),
ollowed by linea esponses (S↓, MR, and EVI). Wi h he excep ion o MR and EVI he indi idual
esponses a e posi i e in sign.
26 RESULTS
Fig. 8. Boos ed eg ession ee pa ial esponse plo s o H o all i e s a e a iables in o de o hei
ela i e impo ance (in b aces). The i ed unc ion (black) shows he a iable esponse o he BRT
o e he ange o one indi idual s a e a iable, while he emaining s a e a iables a e held a an
a e age, cons an alue. The ed dashed line is a smoo hed ep esen a ion o he i ed unc ion
(locally weigh ed polynomial eg ession). Figu e om Me zge e al. (2013, Appendix E).
To e alua e he pe o mance o he BRT models, MLFRs a e es ablished be ween BRT i ed alues
o H and LE and he obse ed luxes. Fo bo h, H and LE he ag eemen be ween he BRT i ed
alues and he obse ed luxes is excellen , wi h app oxima ely uni y slope and ≤1% median absolu e
de ia ion in he esiduals. Fo he du a ion o each ligh pa e n, he ained BRT models a e used o
ex apola e H and LE ac oss he XRC. Fo his pu pose he median me eo ological s a e a iables
du ing each ligh pa e n as well as opical g ids o MODIS LST and EVI da a a e used. G id cells
ha exceed he s a e space o he BRT aining da a se a e excluded om ex apola ion. Fig. 9 shows
he esul ing lux g ids o h ee di e en days, wi h a spa ial co e age o ≥92%. Despi e he land
co e classi ica ion was ne e used du ing he ex apola ion p ocess, se e al landscape uni s a e
clea ly ecognizable in he lux maps. Fo ins ance bo h, he Xilin i e alley o he wes , as well as
he moun ainous headwa e a ea o he eas display low sensible- and high la en hea luxes. On he
con a y, he non- ege a ed basin on he no he n ip shows consis en ly low e apo anspi a ion.
RESULTS 27
Fig. 9. Maps o LTFM p edic ed luxes o sensible hea (H, op) and la en hea (LE, bo om) on 13,
17 and 26 July 2009 (le o igh ). Pe cen ages in b aces a e he ligh iden i ie (O8, O7, C2)
indica e he spa ial co e age o he p edic ion h oughou he ca chmen . Me eo ological s a e
a iables om he supe imposed ligh lines a e used in he espec i e LTFM p edic ion. Figu e aken
om Me zge e al. (2013, Appendix E).
To assess he eliabili y o he LTFM me hod o spa ially esol ing and ex apola ing u bulen
luxes, Me zge e al. (2013, Appendix E) es ablish an unce ain y budge (Table 2);
(a) Me zge e al. (2012, Appendix D) ha e shown ha u bulen lux measu emen s wi h he
WSMA pla o m and ins umen a ion a e unbiased, and p ecise o ≤10%;
(b) Fo a single lux measu emen he sys ema ic and andom componen s o he unce ain y due
o he limi ed sampling size o u bulen eddies a e <1±57% o H and <1±121% o LE,
espec i ely;
(c) Small median esiduals o 0±5% o H and 0±6% o LE be ween i ed and obse ed alues
emphasize ha he BRT i ing echnique is unbiased;
(d) Howe e , po en ial biases in he LTFM p ocedu e can esul om using non-linea BRT
esponse unc ions o p edic ion. E.g., de ia ions om he ue alue o LST o simila
magni ude bu opposi e sign do no cancel ou in he p edic ions. Me zge e al. (2013,
Appendix E) quan i y he esul ing bias o h ee di e en es cases (Table 2: Spa io-
empo al analysis, BRT esponse unc ion, BRT s a e a iables). The sys ema ic di e ences
34 NOTATION
Pa ame e s and a iables
α A ack an
g
le [ ad]
β
Sidesli
p
an
g
le [ ad]
ρ
Ai densi
y
[k
g
m
−3]
θ Po en ial em
p
e a u e [K]
a Absolu e humidi
y
[
g
m
−3]
CL Li coe icien
[-]
e Eule ’s numbe
(
≈2.71828
)
[-]
E
V
I
Enhanced e
g
e a ion index [-]
Measu emen e
q
uenc
y
[Hz]
H
Sensible hea lux [W
m
−2]
L Li
[N]
LE La en hea lux [W
m
−2]
LS
T
Land su ace em
p
e a u e [K]
M
R Mixin
g
a io [
g
k
g
−1]
n No malized e
q
uenc
y
[-]
N
Sam
p
le size [-]
R
2 Wei
g
h ed coe icien o de e mina ion [-]
s
Scala
q
uan i
y
(
wildca d
)
[-]
S
Su ace a ea o win
g
[
m
2]
S
↓ Downwellin
g
sho wa e adia ion [W
m
−2]
u* F ic ion eloci
y
[
m
s−1]
Time [s]
T
Ai em
p
e a u e [K]
u Alon
g
-wind s
p
eed [
m
s−1]
U
¯
Ho izon al wind s
p
eed o he owe and he ue ai s
p
eed o he WSMA [
m
s−1]
C oss-wind s
p
eed [
m
s−1]
as T ue ai s
p
eed [
m
s−1]
wu
p
w
U
p
wash eloci
y
[
m
s−1]
w Foo
p
in wei
g
h
[-]
w Ve ical wind s
p
eed [
m
s−1]
x
,
y
,
z
Ca esian coo dina es [-]
z
Measu emen hei
g
h
[m]
REFERENCES 35
Re e ences
Ande son, M. C., Kus as, W. P., Al ie i, J. G., Gao, F., Hain, C., P uege , J. H., E e , S., Colaizzi, P.,
Howell, T., and Chá ez, J. L.: Mapping daily e apo anspi a ion a Landsa spa ial scales du ing he
BEAREX’08 ield campaign, Ad . Wa e Res., 50, 162-177, doi:10.1016/j.ad wa es.2012.06.005,
2012.
Aubine , M., Vesala, T., and Papale, D., (Eds.): Eddy co a iance: A p ac ical guide o measu emen
and da a analysis, Sp inge , Do d ech , Heidelbe g, London, New Yo k, 438 pp., 2012.
Aue swald, K., Wi me , M. H. O. M., Männel, T. T., Bai, Y. F., Schäu ele, R., and Schnyde , H.:
La ge egional-scale a ia ion in C3/C4 dis ibu ion pa e n o Inne Mongolia s eppe is e ealed by
g aze wool ca bon iso ope composi ion, Biogeosciences, 6, 795-805, doi:10.5194/bg-6-795-2009,
2009.
Baldocchi, D., Falge, E., Gu, L., Olson, R., Hollinge , D., Running, S., An honi, P., Be nho e , C.,
Da is, K., E ans, R., Fuen es, J., Golds ein, A., Ka ul, G., Law, B., Lee, X., Malhi, Y., Meye s, T.,
Munge , W., Oechel, W., U, K., Pilegaa d, K., Schmid, H., Valen ini, R., Ve ma, S., Vesala, T.,
Wilson, K., and Wo sy, S.: FLUXNET: A new ool o s udy he empo al and spa ial a iabili y o
ecosys em-scale ca bon dioxide, wa e apo , and ene gy lux densi ies, Bull. Am. Me eo ol. Soc., 82,
2415-2434, doi:10.1175/1520-0477(2001)082<2415:FANTTS>2.3.CO;2, 2001.
Bange, J., Zi el, P., Spiess, T., Uhlenb ock, J., and Bey ich, F.: A new me hod o he de e mina ion
o a ea-a e aged u bulen su ace luxes om low-le el ligh s using in e se models, Bounda y
Laye Me eo ol., 119, 527-561, doi:10.1007/s10546-005-9040-6, 2006.
Ba nha , B. L., Eichinge , W. E., and P uege , J. H.: In oducing an Ogi e me hod o discon inuous
da a, Ag ic. Fo . Me eo ol., 162–163, 58-62, doi:10.1016/j.ag o me .2012.04.003, 2012.
Be s, A. K., Desja dins, R. L., Macphe son, J. I., and Kelly, R. D.: Bounda y-laye hea and mois u e
budge s om FIFE, Bounda y Laye Me eo ol., 50, 109-138, doi: 10.1007/BF00120520, 1990.
Chen, B., Coops, N. C., Fu, D., Ma golis, H. A., Ami o, B. D., Ba , A. G., Black, T. A., A ain, M.
A., Bou que, C. P. A., Flanagan, L. B., La leu , P. M., McCaughey, J. H., and Wo sy, S. C.:
Assessing eddy-co a iance lux owe loca ion bias ac oss he Fluxne -Canada Resea ch Ne wo k
based on emo e sensing and oo p in modelling, Ag ic. Fo . Me eo ol., 151, 87-100,
10.1016/j.ag o me .2010.09.005, 2011.
Chen, B., Coops, N. C., Fu, D., Ma golis, H. A., Ami o, B. D., Black, T. A., A ain, M. A., Ba , A.
G., Bou que, C. P. A., Flanagan, L. B., La leu , P. M., McCaughey, J. H., and Wo sy, S. C.:
Cha ac e izing spa ial ep esen a i eness o lux owe eddy-co a iance measu emen s ac oss he
Canadian Ca bon P og am Ne wo k using emo e sensing and oo p in analysis, Remo e Sens.
En i on., 124, 742-755, doi:10.1016/j. se.2012.06.007, 2012.
Chen, J., Jonsson, P., Tamu a, M., Gu, Z. H., Ma sushi a, B., and Eklundh, L.: A simple me hod o
econs uc ing a high-quali y NDVI ime-se ies da a se based on he Sa i zky-Golay il e , Remo e
Sens. En i on., 91, 332-344, doi:10.1016/j. se.2004.03.014, 2004.
Chen, J. M., Leblanc, S. G., Cihla , J., Desja dins, R. L., and MacPhe son, J. I.: Ex ending ai c a -
and owe -based CO2 lux measu emen s o a bo eal egion using a Landsa hema ic mappe land
co e map, J. Geophys. Res. A mos., 104, 16859-16877, doi:10.1029/1999JD900129, 1999.
C aw o d, T., Dobosy, R., and Dumas, E.: Ai c a wind measu emen conside ing li -induced
upwash, Bounda y Laye Me eo ol., 80, 79-94, doi:10.1007/BF00119012, 1996.
Dea do , J. W.: Th ee-dimensional nume ical s udy o u bulence in an en aining mixed laye ,
Bounda y Laye Me eo ol., 7, 199-226, doi:10.1007/b 00227913, 1974.
36 REFERENCES
Dellwik, E., Mann, J., and La sen, K. S.: Flow il angles nea o es edges – Pa 1: Sonic
anemome y, Biogeosciences, 7, 1745-1757, doi:10.5194/bg-7-1745-2010, 2010.
Desja dins, R. L., MacPhe son, J. I., Schuepp, P. H., and Hayhoe, H. N.: Ai bo ne lux measu emen s
o CO2, sensible, and la en hea o e he Hudson Bay lowland, J. Geophys. Res. A mos., 99, 1551-
1561, doi:10.1029/93JD01296, 1994.
Desja dins, R. L., MacPhe son, J. I., Mah , L., Schuepp, P., Pa ey, E., Neumann, H., Baldocchi, D.,
Wo sy, S., Fi zja ald, D., McCaughey, H., and Joine , D. W.: Scaling up lux measu emen s o he
bo eal o es using ai c a - owe combina ions, J. Geophys. Res. A mos., 102, 29125-29133,
doi:10.1029/97JD00278, 1997.
Dias, N., Gonçal es, J., F ei e, L., Hasegawa, T., and Malhei os, A.: Ob aining po en ial i ual
empe a u e p o iles, en ainmen luxes, and spec a om mini unmanned ae ial ehicle da a,
Bounda y Laye Me eo ol., 145, 93-111, doi:10.1007/s10546-011-9693-2, 2012.
Egge , J., Baj achaya, S., Hein ich, R., Kolb, P., Lammlein, S., Mech, M., Reude , J., Schape , W.,
Shakya, P., Schween, J., and Wend , H.: Diu nal winds in he Himalayan Kali Gandaki alley. Pa 3:
Remo ely pilo ed ai c a soundings, Mon hly Wea he Re iew, 130, 2042-2058, doi:10.1175/1520-
0493(2002)130<2042:DWITHK>2.0.CO;2, 2002.
Emeis, S., Schä e , K., and Münkel, C.: Su ace-based emo e sensing o he mixing-laye heigh - a
e iew, Me eo ol. Z., 17, 621-630, doi:10.1127/0941-2948/2008/0312, 2008.
Fan, L., Liu, S., Be nho e , C., Liu, H., and Be ge , F. H.: Regional land su ace ene gy luxes by
sa elli e emo e sensing in he Uppe Xilin Ri e Wa e shed (Inne Mongolia, China), Theo . Appl.
Clima ol., 88, 231-245, doi:10.1007/s00704-006-0241-9, 2007.
Finnigan, J.: An in oduc ion o lux measu emen s in di icul condi ions, Ecological Applica ions,
18, 1340-1350, doi:10.1890/07-2105.1, 2008.
Finnigan, J. J., Clemen , R., Malhi, Y., Leuning, R., and Cleugh, H. A.: A e-e alua ion o long- e m
lux measu emen echniques. Pa 1: A e aging and coo dina e o a ion, Bounda y Laye Me eo ol.,
107, 1-48, doi:10.1023/A:1021554900225, 2003.
Foken, T.: Mic ome eo ology, Sp inge , Be lin, Heidelbe g, 306 pp., 2008a.
Foken, T.: The ene gy balance closu e p oblem: An o e iew, Ecological Applica ions, 18, 1351-
1367, doi:10.1890/06-0922.1, 2008b.
Foken, T., Maude , M., Liebe hal, C., Wimme , F., Bey ich, F., Leps, J.-P., Raasch, S., DeB uin, H.
A. R., Meijninge , W. M. L., and Bange, J.: Ene gy balance closu e o he LITFASS-2003
expe imen , Theo . Appl. Clima ol., 101, 149-160, doi:10.1007/s00704-009-0216-8, 2010.
Foken, T., Aubine , M., Finnigan, J. J., Lecle c, M. Y., Maude , M., and Paw U, K. T.: Resul s o a
panel discussion abou he ene gy balance closu e co ec ion o ace gases, Bull. Am. Me eo ol.
Soc., 92, ES13-ES18, doi:10.1175/2011bams3130.1, 2011.
Foken, T., Aubine , M., and Leuning, R.: The eddy-co a iance me hod, in: Eddy co a iance: A
p ac ical guide o measu emen and da a analysis, edi ed by: Aubine , M., Vesala, T., and Papale, D.,
Sp inge , Do d ech , Heidelbe g, London, New Yo k, 1-19, 2012.
F iedman, J. H.: G eedy unc ion app oxima ion: A g adien boos ing machine, Ann S a , 29, 1189-
1232, doi:10.1214/aos/1013203451, 2001.
Ga man, K. E., Hill, K. A., Wyss, P., Ca lsen, M., Zimme man, J. R., S i m, B. H., Ca ney, T. Q.,
San ini, R., and Shepson, P. B.: An ai bo ne and wind unnel e alua ion o a wind u bulence
measu emen sys em o ai c a -based lux measu emen s, J. A mos. Oceanic Technol., 23, 1696-
1708, doi:10.1175/JTECH1940.1, 2006.
REFERENCES 37
Ga man, K. E., Wyss, P., Ca lsen, M., Zimme man, J. R., S i m, B. H., Ca ney, T. Q., San ini, R., and
Shepson, P. B.: The con ibu ion o a iabili y o li -induced upwash o he unce ain y in e ical
winds de e mined om an ai c a pla o m, Bounda y Laye Me eo ol., 126, 461-476,
doi:10.1007/s10546-007-9237-y, 2008.
Göckede, M., Foken, T., Aubine , M., Au ela, M., Banza, J., Be nho e , C., Bonne ond, J. M., B une ,
Y., Ca a a, A., Clemen , R., Dellwik, E., Elbe s, J., Eugs e , W., Fuh e , J., G anie , A., G uenwald,
T., Heinesch, B., Janssens, I. A., Knohl, A., Koeble, R., Lau ila, T., Longdoz, B., Manca, G., Ma ek,
M., Ma kkanen, T., Ma eus, J., Ma eucci, G., Maude , M., Miglia acca, M., Mine bi, S., Monc ie ,
J., Mon agnani, L., Moo s, E., Ou ci al, J. M., Papale, D., Pe ei a, J., Pilegaa d, K., Pi a, G., Rambal,
S., Rebmann, C., Rod igues, A., Ro enbe g, E., Sanz, M. J., Sedlak, P., Seu e , G., Siebicke, L.,
Soussana, J. F., Valen ini, R., Vesala, T., Ve beeck, H., and Yaki , D.: Quali y con ol o
Ca boEu ope lux da a - Pa 1: Coupling oo p in analyses wi h lux da a quali y assessmen o
e alua e si es in o es ecosys ems, Biogeosciences, 5, 433-450, doi:10.5194/bg-5-433-2008, 2008.
Hiyama, T., S unin, M. A., Tanaka, H., and Oh a, T.: The de elopmen o local ci cula ions a ound
he Lena Ri e and hei e ec on owe -obse ed ene gy imbalance, Hyd ol. P ocesses, 21, 2038-
2048, doi:10.1002/hyp.6705, 2007.
Hobbs, S., Dye , D., Cou aul , D., Olioso, A., Lagoua de, J. P., Ke , Y., McAneney, J., and
Bonne ond, J.: Su ace laye p o iles o ai empe a u e and humidi y measu ed om unmanned
ai c a , Ag onomie, 22, 635-640, doi:10.1051/ag o:2002050, 2002.
Hopkin, M.: Ecology: Spying on na u e, Na u e, 444, 420-421, doi:10.1038/444420a, 2006.
Hsieh, C.-I., and Ka ul, G.: The Lag angian s ochas ic model o es ima ing oo p in and wa e apo
luxes o e inhomogeneous su aces, In . J. Biome eo ol., 53, 87-100, doi:10.1007/s00484-008-0193-
0, 2009.
Hu, F. S., Higue a, P. E., Walsh, J. E., Chapman, W. L., Du y, P. A., B ubake , L. B., and Chipman,
M. L.: Tund a bu ning in Alaska: Linkages o clima ic change and sea ice e ea , J. Geophys. Res.,
115, G04002, doi:10.1029/2009jg001270, 2010.
Hu jes, R. W. A., Vellinga, O. S., Gioli, B., and Miglie a, F.: Dis-agg ega ion o ai bo ne lux
measu emen s using oo p in analysis, Ag ic. Fo . Me eo ol., 150, 966-983,
doi:10.1016/j.ag o me .2010.03.004, 2010.
IPCC: Clima e change 1990 - Scien i ic assessmen o clima e change, con ibu ion o wo king g oup
1 o he i s assessmen epo o he In e go e nmen al Panel on Clima e Change, In e go e nmen al
Panel on Clima e Change, Camb idge, Uni ed Kingdom, 410 pp., 1990.
IPCC: Clima e change 1995 - The science o clima e change, con ibu ion o wo king g oup 1 o he
second assessmen epo o he In e go e nmen al Panel on Clima e Change, In e go e nmen al
Panel on Clima e Change, Camb idge, Uni ed Kingdom, 588 pp., 1995.
IPCC: Clima e change 2001 - The scien i ic basis, con ibu ion o wo king g oup 1 o he hi d
assessmen epo o he In e go e nmen al Panel on Clima e Change, In e go e nmen al Panel on
Clima e Change, Camb idge, Uni ed Kingdom, 881 pp., 2001.
IPCC: Clima e change 2007 - The physical science basis, con ibu ion o wo king g oup 1 o he
ou h assessmen epo o he In e go e nmen al Panel on Clima e Change, In e go e nmen al Panel
on Clima e Change, Camb idge, Uni ed Kingdom, 996 pp., 2007.
Isaac, P. R., McAneney, J., Leuning, R., and Hacke , J. M.: Compa ison o ai c a and g ound-based
lux measu emen s du ing OASIS95, Bounda y Laye Me eo ol., 110, 39-67,
doi:10.1023/A:1026002301152, 2004.
38 REFERENCES
Jung, M., Reichs ein, M., Ma golis, H. A., Cesca i, A., Richa dson, A. D., A ain, M. A., A ne h, A.,
Be nho e , C., Bonal, D., Chen, J. Q., Gianelle, D., Gob on, N., Kiely, G., Ku sch, W., Lasslop, G.,
Law, B. E., Lind o h, A., Me bold, L., Mon agnani, L., Moo s, E. J., Papale, D., So oco nola, M.,
Vacca i, F., and Williams, C.: Global pa e ns o land-a mosphe e luxes o ca bon dioxide, la en
hea , and sensible hea de i ed om eddy co a iance, sa elli e, and me eo ological obse a ions, J.
Geophys. Res. Biogeosci., 116, G00J07, doi:10.1029/2010jg001566, 2011.
Junke mann, W.: An ul aligh ai c a as pla o m o esea ch in he lowe oposphe e: Sys em
pe o mance and i s esul s om adia ion ans e s udies in s a i o m ae osol laye s and b oken
cloud condi ions, J. A mos. Oceanic Technol., 18, 934-946, doi:10.1175/1520-
0426(2001)018<0934:AUAAPF>2.0.CO;2, 2001.
Junke mann, W.: The ac inic UV- adia ion budge du ing he ESCOMPTE campaign 2001: Resul s o
ai bo ne measu emen s wi h he mic oligh esea ch ai c a D-MIFU, A mos. Res., 74, 461-475,
doi:10.1016/j.a mos es.2004.06.009, 2005.
Kaimal, J. C., Wyngaa d, J. C., Izumi, Y., and Co é, O. R.: Spec al cha ac e is ics o su ace-laye
u bulence, Q. J. R. Me eo olog. Soc., 98, 563-589, doi:10.1002/qj.49709841707, 1972.
Kaimal, J. C., and Finnigan, J. J.: A mosphe ic bounda y laye lows: Thei s uc u e and
measu emen , Ox o d Uni e si y P ess, New Yo k, 289 pp., 1994.
Kalogi os, J. A., and Wang, Q.: Calib a ion o a adome-di e en ial GPS sys em on a Twin O e
esea ch ai c a o u bulence measu emen s, J. A mos. Oceanic Technol., 19, 159-171,
doi:10.1175/1520-0426(2002)019%3C0159:COARDG%3E2.0.CO;2, 2002a.
Kalogi os, J. A., and Wang, Q.: Ae odynamic e ec s on wind u bulence measu emen s wi h esea ch
ai c a , J. A mos. Oceanic Technol., 19, 1567-1576, doi:10.1175/1520-
0426(2002)019<1567:AEOWTM>2.0.CO;2, 2002b.
Kaminski, T., Rayne , P. J., Voßbeck, M., Scholze, M., and Ko i, E.: Obse ing he con inen al-scale
ca bon balance: Assessmen o sampling complemen a i y and edundancy in a e es ial assimila ion
sys em by means o quan i a i e ne wo k design, A mos. Chem. Phys., 12, 7867-7879,
doi:10.5194/acp-12-7867-2012, 2012.
Ke ze , B., Liu, H., and Be nho e , C.: Su ace cha ac e is ics o g asslands in Inne Mongolia as
de ec ed by mic ome eo ological measu emen s, In . J. Biome eo ol., 52, 563-574,
doi:10.1007/s00484-008-0148-5, 2008.
Kheli , D., Bu ns, S. P., and F iehe, C. A.: Imp o ed wind measu emen s on esea ch ai c a , J.
A mos. Oceanic Technol., 16, 860-875, doi:10.1175/1520-
0426(1999)016<0860:IWMORA>2.0.CO;2, 1999.
Kochendo e , J., Meye s, T. P., F ank, J., Massman, W. J., and Heue , M. W.: How well can we
measu e he e ical wind speed? Implica ions o luxes o ene gy and mass, Bounda y Laye
Me eo ol., in p ess, doi:10.1007/s10546-012-9738-1, 2012.
Kus as, W. P., Ande son, M. C., F ench, A. N., and Vicke s, D.: Using a emo e sensing ield
expe imen o in es iga e lux- oo p in ela ions and lux sampling dis ibu ions o owe and
ai c a -based obse a ions, Ad . Wa e Res., 29, 355-368, doi:10.1016/j.ad wa es.2005.05.003,
2006.
Lenschow, D., and Sun, J.: The spec al composi ion o luxes and a iances o e land and sea ou o
he mesoscale, Bounda y Laye Me eo ol., 125, 63-84, doi:10.1007/s10546-007-9191-8, 2007.
Lenschow, D. H., Wyngaa d, J. C., and Pennell, W. T.: Mean- ield and second-momen budge s in a
ba oclinic, con ec i e bounda y laye , Jou nal o he A mosphe ic Sciences, 37, 1313-1326,
doi:10.1175/1520-0469(1980)037<1313:m asmb>2.0.co;2, 1980.
REFERENCES 39
Lenschow, D. H., and S anko , B. B.: Leng h scales in he con ec i e bounda y laye , Jou nal O The
A mosphe ic Sciences, 43, 1198-1209, doi:10.1175/1520-0469(1986)043<1198:LSITCB>2.0.CO;2,
1986.
Lenschow, D. H., Mann, J., and K is ensen, L.: How long is long enough when measu ing luxes and
o he u bulence s a is ics?, J. A mos. Oceanic Technol., 11, 661-673, doi:10.1175/1520-
0426(1994)011<0661:HLILEW>2.0.CO;2, 1994.
Leuning, R., an Go sel, E., Massman, W. J., and Isaac, P. R.: Re lec ions on he su ace ene gy
imbalance p oblem, Ag ic. Fo . Me eo ol., 156, 65-74, doi:10.1016/j.ag o me .2011.12.002, 2012.
Mah , L.: Flux sampling e o s o ai c a and owe s, J. A mos. Oceanic Technol., 15, 416-429,
doi:10.1175/1520-0426(1998)015<0416:FSEFAA>2.0.CO;2, 1998.
Mah , L.: Su ace he e ogenei y and e ical s uc u e o he bounda y laye , Bounda y Laye
Me eo ol., 96, 33-62, doi:10.1023/a:1002482332477, 2000.
Mah , L.: Compu ing u bulen luxes nea he su ace: Needed imp o emen s, Ag ic. Fo . Me eo ol.,
150, 501-509, doi:10.1016/j.ag o me .2010.01.015, 2010.
Ma kkanen, T., S ein eld, G., Kljun, N., Raasch, S., and Foken, T.: A nume ical case s udy on
oo p in model pe o mance unde inhomogeneous low condi ions, Me eo ol. Z., 19, 539-547,
doi:10.1127/0941-2948/2010/0488, 2010.
Ma in, S., Bange, J., and Bey ich, F.: Me eo ological p o iling o he lowe oposphe e using he
esea ch UAV "M2AV Ca olo", A mos. Meas. Tech., 4, 705-716, doi:10.5194/am -4-705-2011, 2011.
Mason, P. J.: The o ma ion o a eally-a e aged oughness leng hs, Q. J. R. Me eo olog. Soc., 114,
399-420, doi:10.1002/qj.49711448007, 1988.
Massman, W. J., and Clemen , R.: Unce ain y in eddy co a iance lux es ima es esul ing om
spec al a enua ion, in: Handbook o mic ome eo ology: A guide o su ace lux measu emen and
analysis, 1 ed., edi ed by: Lee, X., Law, B., and Massman, W., Sp inge , Do d ech , 67-100, 2004.
Ma oss, D. M., And ews, A., Pa hma he an, M., Ge big, C., Lin, J. C., Wo sy, S. C., Daube, B. C.,
Go lieb, E. W., Chow, V. Y., Lee, J. T., Zhao, C., Bakwin, P. S., Munge , J. W., and Hollinge , D.
Y.: Es ima ing egional ca bon exchange in New England and Quebec by combining a mosphe ic,
g ound-based and sa elli e da a, Tellus B, 58, 344-358, doi:10.1111/j.1600-0889.2006.00206.x, 2011.
Maude , M., Desja dins, R. L., and MacPhe son, I.: Scale analysis o ai bo ne lux measu emen s
o e he e ogeneous e ain in a bo eal ecosys em, J. Geophys. Res. A mos., 112, D13112,
doi:10.1029/2006JD008133, 2007a.
Maude , M., Jegede, O. O., Okogbue, E. C., Wimme , F., and Foken, T.: Su ace ene gy balance
measu emen s a a opical si e in Wes A ica du ing he ansi ion om d y o we season, Theo .
Appl. Clima ol., 89, 171-183, doi:10.1007/s00704-006-0252-6, 2007b.
Maude , M., Oncley, S., Vog , R., Weidinge , T., Ribei o, L., Be nho e , C., Foken, T., Kohsiek, W.,
De B uin, H., and Liu, H.: The ene gy balance expe imen EBEX-2000. Pa II: In e compa ison o
eddy-co a iance senso s and pos - ield da a p ocessing me hods, Bounda y Laye Me eo ol., 123, 29-
54, doi:10.1007/s10546-006-9139-4, 2007c.
Me zge , S., Junke mann, W., Bu e bach-Bahl, K., Schmid, H. P., and Foken, T.: Co igendum o
"Measu ing he 3-D wind ec o wi h a weigh -shi mic oligh ai c a " published in A mos. Meas.
Tech., 4, 1421–1444, 2011, A mos. Meas. Tech., 4, 1515-1539, doi:10.5194/am -4-1515-2011, 2011.
Me zge , S., Junke mann, W., Maude , M., Bey ich, F., Bu e bach-Bahl, K., Schmid, H. P., and
Foken, T.: Eddy-co a iance lux measu emen s wi h a weigh -shi mic oligh ai c a , A mos. Meas.
Tech., 5, 1699-1717, doi:10.5194/am -5-1699-2012, 2012.
40 REFERENCES
Me zge , S., Junke mann, W., Maude , M., Bu e bach-Bahl, K., T ancón y Widemann, B., Neidl, F.,
Schä e , K., Wieneke, S., Zheng, X. H., Schmid, H. P., and Foken, T.: Spa ially explici
egionaliza ion o ai bo ne lux measu emen s using en i onmen al esponse unc ions,
Biogeosciences, 10, 2193-2217, doi:10.5194/bg-10-2193-2013, 2013.
Ogunjemiyo, S. O., Kaha aba a, S. K., Schuepp, P. H., MacPhe son, I. J., Desja dins, R. L., and
Robe s, D. A.: Me hods o es ima ing CO2, la en hea and sensible hea luxes om es ima es o
land co e ac ions in he lux oo p in , Ag ic. Fo . Me eo ol., 117, 125-144, doi:10.1016/S0168-
1923(03)00061-3, 2003.
Pano sky, H. A., and Du on, J. A.: A mosphe ic u bulence: Models and me hods o enginee ing
applica ions, John Wiley & Sons, New Yo k, Chiches e , B isbane, To on o, Singapo e, 397 pp.,
1984.
R De elopmen Co e Team: R: A language and en i onmen o s a is ical compu ing, R Founda ion
o S a is ical Compu ing, Vienna, Aus ia, 2012.
Raupach, M. R., and Finnigan, J. J.: Scale issues in bounda y-laye me eo ology: Su ace ene gy
balances in he e ogeneous e ain, Hyd ol. P ocesses, 9, 589-612, doi:10.1002/hyp.3360090509,
1995.
Ripley, B. D., and Thompson, M.: Reg ession echniques o he de ec ion o analy ical bias, Analys ,
112, 377-383, doi:10.1039/an9871200377, 1987.
Ruppe , J., Thomas, C., and Foken, T.: Scala simila i y o elaxed eddy accumula ion me hods,
Bounda y Laye Me eo ol., 120, 39-63, doi:10.1007/s10546-005-9043-3, 2006.
Scha a h, D., Ba hold, F., and Be nho e , C.: Spa io empo al a iabili y o g assland ege a ion
co e in a ca chmen in Inne Mongolia, China, de i ed om MODIS da a p oduc s, Plan and Soil,
340, 181-198, doi:10.1007/s11104-010-0465-4, 2011.
Schmid, H. P., and Lloyd, C. R.: Spa ial ep esen a i eness and he loca ion bias o lux oo p in s
o e inhomogeneous a eas, Ag ic. Fo . Me eo ol., 93, 195-209, doi:10.1016/s0168-1923(98)00119-1,
1999.
Sogache , A., and Lloyd, J.: Using a one-and-a-hal o de closu e model o he a mosphe ic bounda y
laye o su ace lux oo p in es ima ion, Bounda y Laye Me eo ol., 112, 467-502,
doi:10.1023/B:BOUN.0000030664.52282.ee, 2004.
S ein eld, G., Le zel, M. O., Raasch, S., Kanda, M., and Inagaki, A.: Spa ial ep esen a i eness o
single owe measu emen s and he imbalance p oblem wi h eddy-co a iance luxes: Resul s o a
la ge-eddy simula ion s udy, Bounda y Laye Me eo ol., 123, 77-98, doi:10.1007/s10546-006-9133-
x, 2007.
S unin, M. A., Hiyama, T., Asanuma, J., and Oha a, T.: Ai c a obse a ions o he de elopmen o
he mal in e nal bounda y laye s and scaling o he con ec i e bounda y laye o e non-homogeneous
land su aces, Bounda y Laye Me eo ol., 111, 491-522,
doi:10.1023/B:BOUN.0000016542.72958.e9, 2004.
S ull, R. B.: An In oduc ion o Bounda y Laye Me eo ology, Kluwe Academic Publishe s,
Do d ech , 670 pp., 1988.
Taylo , G. I.: Eddy mo ion in he a mosphe e, Philosophical T ansac ions o he Royal Socie y o
London, A 215, 1-26, doi:10.1098/ s a.1915.0001, 1915.
Thomas, R. M., Lehmann, K., Nguyen, H., Jackson, D. L., Wol e, D., and Ramana han, V.:
Measu emen o u bulen wa e apo luxes using a ligh weigh unmanned ae ial ehicle sys em,
A mos. Meas. Tech., 5, 243-257, doi:10.5194/am -5-243-2012, 2012.
REFERENCES 41
Tje ns öm, M., and F iehe, C. A.: Analysis o a adome ai -mo ion sys em on a win-je ai c a o
bounda y-laye esea ch, J. A mos. Oceanic Technol., 8, 19-40, doi:10.1175/1520-
0426(1991)008%3C0019:AOARAM%3E2.0.CO;2, 1991.
To ence, C., and Compo, G. P.: A p ac ical guide o wa ele analysis, Bull. Am. Me eo ol. Soc., 79,
61-78, doi:10.1175/1520-0477(1998)079<0061:apg wa>2.0.co;2, 1998.
Uhlenb ock, J., Raasch, S., Hennemu h, B., Zi el, P., and Meijninge , W. M. L.: E ec s o land
su ace he e ogenei ies on he bounda y s uc u e and u bulence du ing LITFASS-2003: La ge-eddy
simula ions in compa ison wi h u bulence measu emen s, 16 h AMS Symposium on Bounda y Laye s
and Tu bulence, Po land, U.S.A., 8-13 Augus , 2004.
an den K oonenbe g, A., Ma in, T., Buschmann, M., Bange, J., and Vo smann, P.: Measu ing he
wind ec o using he au onomous mini ae ial ehicle M2AV, J. A mos. Oceanic Technol., 25, 1969-
1982, doi:10.1175/2008JTECHA1114.1, 2008.
Ve e , S., Scha a h, D., and Be nho e , C.: Spa ial simula ion o e apo anspi a ion o semi-a id
Inne Mongolian g assland based on MODIS and eddy co a iance da a, En i onmen al Ea h
Sciences, 65, 1567-1574, doi:10.1007/s12665-011-1187-5, 2012.
Vicke s, D., and Mah , L.: Quali y con ol and lux sampling p oblems o owe and ai c a da a, J.
A mos. Oceanic Technol., 14, 512-526, doi:10.1175/1520-0426(1997)014<0512:QCAFSP>2.0.CO;2,
1997.
Wang, W., and Ro ach, M. W.: Flux oo p in s o e an undula ing su ace, Bounda y Laye
Me eo ol., 136, 325-340, doi:10.1007/s10546-010-9498-8, 2010.
Williams, A., and Ma co e, D.: Wind measu emen s on a maneu e ing win-engine u bop op ai c a
accoun ing o low dis o ion, J. A mos. Oceanic Technol., 17, 795-810, doi:10.1175/1520-
0426(2000)017%3C0795:WMOAMT%3E2.0.CO;2, 2000.
Williams, M., Richa dson, A. D., Reichs ein, M., S oy, P. C., Peylin, P., Ve beeck, H., Ca alhais, N.,
Jung, M., Hollinge , D. Y., Ka ge, J., Leuning, R., Luo, Y., Tomelle i, E., T udinge , C. M., and
Wang, Y. P.: Imp o ing land su ace models wi h FLUXNET da a, Biogeosciences, 6, 1341-1359,
doi:10.5194/bg-6-1341-2009, 2009.
Wilson, K., Golds ein, A., Falge, E., Aubine , M., Baldocchi, D., Be bigie , P., Be nho e , C.,
Ceulemans, R., Dolman, H., Field, C., G elle, A., Ib om, A., Law, B. E., Kowalski, A., Meye s, T.,
Monc ie , J., Monson, R., Oechel, W., Tenhunen, J., Valen ini, R., and Ve ma, S.: Ene gy balance
closu e a FLUXNET si es, Ag ic. Fo . Me eo ol., 113, 223-243, doi:10.1016/s0168-1923(02)00109-
0, 2002.
Wi me , M. H. O. M., Aue swald, K., Bai, Y., Schäu ele, R., and Schnyde , H.: Changes in he
abundance o C3/C4 species o Inne Mongolia g assland: E idence om iso opic composi ion o soil
and ege a ion, Global Change Biol., 16, 605-616, doi:10.1111/j.1365-2486.2009.02033.x, 2010.
Wood, N., and Mason, P.: The in luence o s a ic s abili y on he e ec i e oughness leng hs o
momen um and hea ans e , Q. J. R. Me eo olog. Soc., 117, 1025-1056,
doi:10.1002/qj.49711750108, 1991.
Yang, F., Ichii, K., Whi e, M. A., Hashimo o, H., Michaelis, A. R., Vo a a, P., Zhu, A. X., Hue e, A.,
Running, S. W., and Nemani, R. R.: De eloping a con inen al-scale measu e o g oss p ima y
p oduc ion by combining MODIS and Ame iFlux da a h ough suppo ec o machine app oach,
Remo e Sens. En i on., 110, 109-122, doi:10.1016/j. se.2007.02.016, 2007.
Yu, G.-R., Wen, X.-F., Sun, X.-M., Tanne , B. D., Lee, X., and Chen, J.-Y.: O e iew o
ChinaFLUX and e alua ion o i s eddy co a iance measu emen , Ag ic. Fo . Me eo ol., 137, 125-137,
doi:10.1016/j.ag o me .2006.02.011, 2006.
42 REFERENCES
Ziehn, T., Kno , W., and Scholze, M.: In es iga ing spa ial di e en ia ion o model pa ame e s in a
ca bon cycle da a assimila ion sys em, Global Biogeochem. Cycles, 25, GB2021,
doi:10.1029/2010gb003886, 2011.
LIST OF APPENDICES 43
Lis o Appendices
LIST OF APPENDICES ...................................................................................................................... 43
APPENDIX A: INDIVIDUAL CONTRIBUTIONS TO THE JOINT PUBLICATIONS ................... 44
APPENDIX B: METZGER ET AL. (2011) ......................................................................................... 48
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) ........................................................ 73
APPENDIX D: METZGER ET AL. (2012) ......................................................................................... 87
APPENDIX E: METZGER ET AL. (2013) ....................................................................................... 106
50 APPENDIX B: METZGER ET AL. (2011)
Fig. 1. Weigh -shi mic oligh esea ch ai c a D-MIFU, ai c a s uc u al ea u es a e highligh ed by dash-do ed lines. Senso loca ions
o he i e hole p obe (5HP), ine ial na iga ion sys em (INS, inside ai c a nose) and uni e sal lase senso (ULS, below pilo sea ) a e
indica ed. Fo de ails on he espec i e ins alla ions see Sec . 2.2 and Table 2. Figu e 3 de ails he layou o he i e hole p obe.
The ull pe o mance cha ac e is ics can be ound in Junke -
mann (2001).
D-MIFU consis s o a KISS 450 cambe ed wing by Ai
C ea ion, F ance, and he ENDURO-1150 ike manu ac-
u ed by Ul aleich lug Schmid le , Ge many. Owing o i s
ae oelas ici y, he ailless del a wing is e med a lex-wing,
con ibu ing ≈15 % o he ai c a weigh . The p ima y pa s
o he wing s uc u e a e he leading edges joined a he nose
o he keel ube, which uns he oo leng h o he wing
(Fig. 1). S e ched o e uppe and lowe su ace is a high
s eng h polyes e sail. A a span o 9.8 m and keel leng h o
2.1 m, he wing p o ides a su ace (S) o 15.1 m2. I is pu
unde conside able in e nal loads du ing igging, i ’s o m
and igidi y being ensu ed by c oss- ubes, ods and a wi ing
sys em. The baseba in on o he pilo sea is linked o
he keel ia wo up igh s and ensioned lying wi es. I p o-
ides ansmission o pi ch and oll o ces and is he p i-
ma y ligh con ol (G a on, 2001). In he hangpoin on he
wing keel he ike is a ached o he wing. Since he ike
is ee o o a e in pi ch and oll wi hou hind ance, he e is
no pendula s abili y. In his ega d he ela ionship o ike
o wing is simila o he ela ionship o a ailing bomb o
i s ca ie (e.g. HELIPOD, Bange and Ro h, 1999). How-
e e ike and wing a e ixed in hei longi udinal axis, i.e. in
he heading di ec ion. The ike does no con ibu e signi -
ican ly o he WSMA’s li , bu ep esen s a la ge po ion
o weigh (≈85 %), d ag, and p o ides all h us h ough
a 73 kW pushe engine-p opelle combina ion. Fligh s abil-
i y in h ee axes is based on he o se o o ques appea ing a
di e en loca ions on he wing (Cook, 1994). To ques esul
om wing ae odynamical e ec s, which sum nea es o neu-
al (sligh nose-down o que o cambe ed wings) in one
poin along he wing’s cho d line, e med he wing’s cen e
o p essu e (Fig. 2). The cen e o g a i y, as a as he wing
is conce ned, is loca ed in he hangpoin . The ne ae ody-
namical o que is o se by a longi udinal le e a m be ween
he cen es o p essu e and by a longi udinal -g a i y, de e -
mining he ai c a ’s im speed ( he ai speed a which he
ai c a will ly s eadily wi hou pilo inpu ). Mo eo e in-
c easing ai speed will esul in an ae oelas ical la ening o
he wing, which is in con as o FWA. This in u n can al-
e he balance o o sional loads and wi h i he ci cula ion
abou he wing (Cook and Spo iswoode, 2006).
2.1 Physical p ope ies
The need o adap wind calib a ion p ocedu es designed o
ixed-wing ai c a is mainly caused by wo s uc u al ea-
u es o he WSMA. The ike, i.e. he u bulence measu e-
men pla o m, is mobile o pi ching and olling mo emen s
below he wing. The e o e he ike-based low- and a i-
ude angles mus be measu ed wi h high esolu ion, p eci-
sion and accu acy. Mo eo e , wing ae odynamics depends
on i s ae oelas ici y wi h ai speed, and a ying low dis o -
ion in on o he wing mus be conside ed. The e ec s
o hese WSMA ea u es a e no necessa ily independen o
each o he , and may ha e a di e en impac on he wind mea-
su emen depending on he ai c a dynamics a a pa icula
ime. The e o e he WSMA was equipped wi h mo ion sen-
so s. On he ike hese we e placed in he uselage (Ine ial
APPENDIX B: METZGER ET AL. (2011) 51
Fig. 2. Geome ical ea u es o he weigh -shi mic oligh ai c a
and coo dina e sys ems wi h axes X, Y, and Z used o compu e he
wind ec o . The supe sc ip s a, b, g, m and w ep esen , espec-
i ely, he ae odynamic-, body-, geode ic-, me eo ological and wing
coo dina e sys ems (Supplemen A). (A) S a boa d iew: Angle o
a ack (α), pi ch angle (), no malized adius (n), wing upwash di-
ec ion (ξ), cen e o g a i y and cen e o p essu e. (B) Rea iew:
Roll angle (); (C) Top iew: Sideslip angle (β) and ue heading
().
Na iga ion Sys em, INS) and he wind measu ing p essu e
p obe (3-D accele a ion), ex ending ≈0.7 m and ≈3.5 m o -
wa d om uselage and a -moun ed p opelle , espec i ely
(Figs. 1 and 2). Fu he , he wing was equipped wi h mo ion
senso s in he hangpoin (3-D accele a ion) and a op he wing
(3-D a i ude). The INS is he mos eliable mo ion senso
(Table 2), since i in eg a es he complemen a y cha ac e is-
ics o global posi ioning sys em (unbiased) and ine ial mea-
su emen (p ecise). Posi ion and eloci y a e calcula ed om
ine ial measu emen s o 3-D accele a ion and 3-D angula
a e, and ma ched wi h da a om wo global posi ioning uni s
using a Kalman il e . The INS ou pu s 3-D ec o s o posi-
ion, a i ude, eloci y, angula a es and accele a ion.
Ai bo ne wind measu emen s a e suscep ible o dis o ion,
since he ai c a i sel is (a) a low ba ie and (b) mus p o-
duce li o emain ai bo ne (Wyngaa d, 1981; Coope and
Roge s, 1991). The ai c a ’s p opelle , ike, and wing can
be sou ces o low dis o ion. Only li le dis o ion om
ike s uc u al ea u es is expec ed ans e se o he p essu e
p obe: he ike body is symme ic on i s po and s a boa d
side, and he p essu e p obe, p opelle and pilo a e cen ed
on i s longi udinal axis (Figs. 1 and 2). In con as he body is
asymme ic on i s upside and unde side, and he p opelle lo-
ca ion is 0.8 m highe han he p essu e p obe. This sugges s
symme ic lows in ans e se, and asymme ic lows in lon-
gi udinal and e ical di ec ions. All o which a e expec ed o
ca y con inuously h ough he p essu e p obe loca ion, since
he p obe is igidly ixed o he ike. This howe e is no he
case o dis o ion om he WSMA wing. While he wind
measu emen encoun e s li -induced upwash om he wing
(C aw o d e al., 1996; Ga man e al., 2008), he ike, and
wi h i he p essu e p obe, has o a ional eedom in pi ch
and oll owa ds he WSMA wing. In he ollowing we will
ou line he dependences o upwash gene a ion om he wing.
The amoun o li (L) gene a ed by he wing equals he ai -
c a ’s sum o o ces pe pendicula o he ai s eam:
L=ma
g,z,(1)
wi h he ai c a mass (m) and he e ical accele a ion (ag,z)
in he geode ic coo dina e sys em (GCS, supe sc ip g, pos-
i i e no hwa d, eas wa d and downwa d) a he wing’s cen-
e o g a i y (measu ed a , o disloca ed o he hangpoin ).
Fo simplici y he accele a ion pe pendicula o he ai s eam
was app oxima ed by he e ical accele a ion in he GCS.
The maximum de ia ion du ing se e e e ical manoeu ing
(only used o e alua ion) does no exceed ±1%. Also
he ai c a con ol o ces applied by he pilo mee in he
hangpoin . Du ing ABL measu emen s hese a e p ima ily
changes in powe se ing and wing pi ch o adjus he ai -
c a al i ude. Fo le el, unaccele a ed ligh , li essen ially
equals he ai c a ’s weigh o ce, bu is opposi e in sign. The
loading ac o (LF) du ing e ically accele a ed ligh is hen
LF = L
mg , he a io o li - o weigh o ce wi h g= 9.81 m s−2.
No malizing L o he ai s eam’s dynamic p essu e (pq)and
52 APPENDIX B: METZGER ET AL. (2011)
Fig. 3. Layou o he i e hole p obe, wi h le e s indica ing senso loca ions. (A) The hal sphe e ip o he i e hole p obe, wi h po s o
o al- and di e en ial p essu e measu emen s. (B) Po s o s a ic p essu e measu emen downs eam o he hal sphe e. (C) The mocouple
and po o he capaci i e humidi y measu emen . (D) Loca ion o i e hole p obe 3-D accele a ion senso . Addi ional in o ma ion is gi en
in Sec . 2.2.
he wing’s su ace a ea (S) yields he uni - ee li coe icien
(CL):
CL =1
pq
L
S
=2
ρ 2
as
L
S,(2)
wi h wing loading (L
S). Mo eo e pqin Eq. (2) can be
subs i u ed by ai densi y (ρ) and ue ai speed ( as). In
CL he wing’s abili y o gene a e li is de e mined o be
app oxima ely linea wi h wing pi ch. As a consequence
o li gene a ion ai ises in on o he wing, which is
de ined as upwash. C aw o d e al. (1996) p o ide he
ollowing pa ame iza ion o calcula e he upwash eloci y
( w
up) o FWA:
w
up =1
π2n as CL
=1
π2n
as
pq
L
S,wi h
δ
as
p
q
δ as ≈−0.3hPa
−1.(3)
He e w
up is de ined as he angen on a ci cle wi h no mal-
ized adius n. The eby nis he sepa a ion dis ance om
he wing’s cen e o p essu e o he posi ion o he p essu e
p obe, no malized by he e ec i e wing cho d (Fig. 2). The
wing upwash di ec ion ξis hen enclosed by nand he ike
body axis Xb. Since he wing is ee o o a e in pi ch and
oll, w
up ca ies he o ien a ion o he wing coo dina e sys-
em (WCS, supe sc ip w, posi i e o wa d, s a boa d, and
downwa d). In Eq. (3) w
up a ies in e sely wi h n. Fu -
he mo e w
up can be exp essed ei he di ec ly p opo ional o
as and CL, o di ec ly p opo ional o ela i e ai speed (
as
p
q
)
and L
S. Based on he unc ional ela ion be ween li and up-
wash gene a ion a ea men o he wind measu emen om
WSMA is de i ed in Sec . 4.1.
2.2 Ins umen a ion and da a p ocessing
Wind measu emen by ai bo ne sys ems is challenging. High
esolu ion senso s a e needed o de e mine he a i ude, posi-
ion, and eloci y o he ai c a ela i e o he ea h, as well
as he ai low in on o he uselage. The ins umen a ion
in ol ed in he wind measu emen and da a acquisi ion, in-
cluding he espec i e manu ac u e s, is summa ized in Ta-
ble 1. A mo e de ailed desc ip ion o senso cha ac e is ics
and unce ain ies is p o ided in Table 2, while espec i e lo-
ca ions a e displayed in Figs. 1 and 3.
The p inciple is o esol e he me eo ological wind ec-
o om he ec o di e ence o he ai c a ’s ine ial eloc-
i y ( eco ded by he ine ial na iga ion sys em) and he wind
ec o ela i e o he ai c a . To de e mine he la e , he
ai c a was ou i ed wi h a specially designed ligh weigh
i e hole hal sphe e p essu e p obe (5HP, e.g. C aw o d and
Dobosy, 1992; Leise and Mas e s, 1993). Figu e 3a shows
he hal sphe e ip o he 5HP, wi h a o al p essu e (p ) po
a i s cen e. Two addi ional p essu e po s on each, he
e ical (p1,p3) and he ho izon al axis (p2,p4), su ound
he cen al po a an angle o τ=45
◦. These di e en ial
APPENDIX B: METZGER ET AL. (2011) 53
Table 1. O e iew o senso s and elec onic ins umen a ion used o he wind measu emen .
Componen Model Manu ac u e Add ess
Bu e wo h low pass il e AF40-4BU TP E.S.F. elec onic G¨
o ingen, Ge many
Elec onic compass module TCM2-20 PNI Senso Co po a ion San a Rosa, USA
Humidi y senso SHT75 Sensi ion AG S ae a, Swi ze land
Indus ial compu e PR-Z32-EA-ST Diamond Sys ems Co po a ion Newa k, USA
Ine ial na iga ion sys em RT3102 Ox o d Technical Solu ions Uppe Hey o d, England
Di e en ial p essu e senso PCLA12X5D Senso echnics GmbH Puchheim, Ge many
S a is ic p essu e senso SP82AL Cap o As. Ho en, No way
The mocouple CHAL-002 OMEGA Enginee ing, Inc. S am o d, USA
Th ee-axis accele ome e ADXL330 Analog De ices, Inc. No wood, USA
Uni e sal lase senso ULS (Second edi ion) Lase Technology, Inc. Cen ennial, USA
Ope a ing sys em Minix 2.0 And ew S ua Tanenbaum Ams e dam, Ne he lands
p essu e eadings a e used o de e mine a ack angle (α)and
sideslip angle (β), espec i ely, a ows indica e he di ec ion
o posi i e angula measu emen . Polye he ke one ubings
o ≤80 mm leng h and 1 mm inne diame e a e used o con-
nec hese po s o 1.5 mm diame e o hei espec i e p es-
su e ansduce s. Addi ional (unnumbe ed) p essu e po s a
45◦inc emen s a e no used in his s udy. Six p essu e po s
a e loca ed downs eam o he hal sphe e (Fig. 3b). These
a e ing-compensa ed a ound he ci cum e ence o he i e
hole p obe o low angle independen s a ic p essu e (ps)
measu emen . Figu e 3c shows he eely suspended 50 μm
ype K he mocouple o as empe a u e (Ts) measu emen
and he 10 mm po o a capaci i e humidi y measu emen
(e). Time cons an s o he mocouple and humidi y senso a e
<0.02 s and <5s a as =27ms
−1, espec i ely. Humidi y
eadings a e solely used o p o ide he ai densi y co ec ion
(Eq. A10) o he as compu a ion. A a ypical ue ai speed
o 28 m s−1only abou 30 % and 15 % o he dynamic- and
di e en ial p essu e ansduce s’ ange is exploi ed, espec-
i ely.Thishowe e enables he5HP obeusedalsoon as e
ai c a such as mo o ized glide s, e.g. o in e -compa ison
measu emen s. Plug- and-socke connec o s wi h loca ing
pins insu e a epea able loca ion o he 5HP wi h espec o
he INS wi hin <0.1◦. The whole ins alla ion weigh s in a
350 g.
100 Hz empe a u e and p essu e signals pass h ough
ha dwa e (analogue) ou -pole Bu e wo h il e s wi h 20 Hz
cu -o equency o il e high- equency noise. Fil e slope
and equency we e chosen o allow minia u iza ion and
comply wi h he sys em’s 15 Hz bo leneck il e equency
o he in a- ed gas analyse o EC lux calcula ion (no used
in his s udy). The il e leads o a phase shi in he signal o
≈20 ms, and he ampli ude o a 10 Hz sine signal is educed
by <1 %. The INS da a a e s o ed in a s andalone sys em
a a a e o 100 s−1. Remaining da a s eams o he wind
compu a ion a e s o ed cen ally a a a e o 10 s−1by an
in-house de eloped da a acquisi ion sys em (embedded Ins i-
u e o Me eo ology and Clima e Resea ch da a acquisi ion
sys em, EIDAS). EIDAS is based on a uggedized indus ial
compu e and a eal- ime UNIX-like ope a ing sys em. 5 V
analogue signals a ≥10 Hz pass h ough a mul iplexe and
A/D con e e a a esolu ion o 16 bi s. Fo o e sampled
a iables (100 Hz) he esul ing signal is block a e aged.
The INS has a la ency ime o in e nal calcula ions o
≈4 ms. Ye INS and EIDAS da a s eams ha e o be me ged
o calcula e he ambien wind, and la e u bulen luxes.
The e o e he esul ing ime lag be ween INS and 5HP o
≈16 ms has o be conside ed. The app op ia e ime shi
o one o wo 100 Hz inc emen s is de e mined ia lagged
co ela ion. Du ing pos -p ocessing he 100 Hz INS da a se
is hen shi ed by his inc emen be o e block a e aging o
10 Hz. A spike es e ealed ≈7 % missing alues in he
wing a i ude da a, which we e illed ia linea in e pola ion.
To enable angula a e aging o in e pola ion, heading angles
we e ans o med om pola o Ca esian coo dina es.
3 Wind ec o
App oaches o compu e he wind ec o om ixed-wing
ai c a a e o en simila in p inciple, hough di e con-
side ably in de ail (e.g., Tje ns ¨
om and F iehe, 1991;
Williams and Ma co e, 2000; an den K oonenbe g e al.,
2008). The e o e we p o ide a supplemen o his s udy a
h p://www.baycee .uni-bay eu h.de. Supplemen A de ails
he speci ic implemen a ion ha was ound sui able o he
wind measu emen wi h ou weigh -shi mic oligh ai c a .
A model o p opaga e unce ain y h ough he wind ec o
equa ions is p o ided in Supplemen B. Rele an no a ion
and abb e ia ions a e lis ed in Supplemen C.
The sys em’s calib a ion was a anged bo om-up,
i.e. om single ins umen o collec i e applica ion. The
p ocedu e s a s wi h he labo a o y calib a ion o he indi-
idual senso s, con inues wi h he cha ac e iza ion o low
a ound he 5HP, and concludes wi h he ea men o WSMA
speci ic e ec s on he wind measu emen . Finally h ee
54 APPENDIX B: METZGER ET AL. (2011)
Table 2. Lis o measu ed a iables, senso cha ac e is ics, signal p ocessing and da a acquisi ion. Indi idual senso loca ions a e desc ibed
in Sec . 2.2 and displayed in Figs. 1 and 3. Resolu ion e e s o he smalles change egis e ed by he da a acquisi ion (DAQ) uni s. σis he
o e all senso unce ain y p o ided by he manu ac u e in o m o one s anda d de ia ion. Signal a es a e displayed o sampling, il e ing
and s o ing (Signal SFS). Da a acquisi ion akes place in wo o ms, s andalone (SA) and on he cen al DAQ uni EIDAS. Fo non SA
de ices signal o wa ding ia A/D con e e , ecommended s anda d 232 (RS232) o se ial pe iphe al in e ace (SPI) is indica ed (In e ace
DAQ).
Quan i y Va iable Senso Range Resolu ion σSignal SFS [s−1]In e ace DAQ
Ai ame mo ion
La i ude/longi ude RT3102 ±89.9◦/±180◦6×10−15◦1.1 m 100 100 SA
Al i ude sea le el RT3102 <18 000 m 0.001 m 2.7 m 100 100 SA
Al i ude g ound le el ULS 0.15–500 m 0.001 m 0.04 m 10 10 RS232 EIDAS
Heading, body bRT3102 0–360◦0.00006◦0.1◦100 100 SA
Heading, wing wTCM2-20 0–360◦0.1◦0.5◦16 10 RS232 EIDAS
Pi ch/ oll, body b/bRT3102 ±90◦/±180◦0.00006◦0.06◦100 100 SA
Pi ch/ oll, wing w/wTCM2-20 ±20◦0.1◦0.2◦16 10 RS232 EIDAS
3-D eloci y, body m
gs RT3102 0–515 m s−10.0001 m s−10.02 m s−1100 100 SA
3-D ang. a ., body bRT3102 ±100◦s−10.0006◦s−10.01◦s−1100 100 SA
3-D accel., body abRT3102 ±10 g 0.00001 g 0.001 g 100 100 SA
3-D accel., wing ADXL330 ±3 g 0.0003 g 0.01 g 100 100 A/D EIDAS
3-D accel., 5HP ADXL330 ±3 g 0.0003 g 0.01 g 100 100 A/D EIDAS
Rela i e ai mo ion
S a ic p essu e ps,ASP82AL 0–1000 hPa 0.02 hPa 0.1 hPa 100 20 10 A/D EIDAS
Dynamic p essu e pq,APCLA12X5D ±12.5 hPa 0.0005 hPa 0.06 hPa 100 20 10 A/D EIDAS
A ack p essu e pαPCLA12X5D ±12.5 hPa 0.0005 hPa 0.06 hPa 100 20 10 A/D EIDAS
Sideslip p essu e pβPCLA12X5D ±12.5 hPa 0.0005 hPa 0.06 hPa 100 20 10 A/D EIDAS
Fas emp. TsCHAL-002 −20–60 ◦C 0.0015 K 0.5 K 100 20 10 A/D EIDAS
Humidi y, 5HP eSHT75 0–70 hPa 0.07 hPa 0.3 hPa 10 10 SPI EIDAS
independen lines o analysis a e used o quan i y he o e all
sys em unce ain y: (a) unce ain y p opaga ion h ough e-
spec i e equa ions, (b) in- ligh es ing and (c) compa ison o
he measu ed wind ec o wi h g ound based measu emen s.
3.1 Wind unnel s udy
P io oin- ligh use, he i e hole p obe was es ed in an open
wind unnel a he Technical Uni e si y o Munich, Ge many,
Ins i u e o Fluid Mechanics. Objec i es we e o (a) con-
i m he applicabili y o ans o ma ion Eqs. (A5)–(A7) and
(b) de e mine he 5HP’s unce ain y in he ope a ional ange
o he WSMA. The 5HP was moun ed on D-MIFU’s nose-
cap and measu ing occu ed a ai low eloci ies anging
om 20 o 32 m s−1(equi alen o 2–6 hPa wind unnel dy-
namic p essu e). The dynamic p essu e a he design s ag-
na ion poin (i.e. he wind unnel angles o a ack ˜α=0
◦and
sideslip ˜
β=0
◦) was measu ed a ai low eloci y inc emen s
o 1 m s−1. A inc emen s o 2 m s−1a o al o 570 pe mu a-
ions o 10 p ede ined angles ˜αand ˜
β, each anging om
0◦ o +20◦, we e measu ed. In addi ion one-dimensional
symme y es s we e pe o med o six p ede ined angles ˜α
and ˜
β anging om −20◦ o +20◦a an ai low eloci y
o 30 m s−1. Fo he WSMA ope a ional ue ai speed o
28 m s−1(o 4.5 hPa dynamic p essu e du ing ligh ) he un-
ce ain y o he wind unnel ai low eloci y was 0.7 % o
σ= 0.03 hPa dynamic p essu e. The ai low angles we e a -
ied by a calib a ion obo , he unce ain y in he wind unnel
angles was σ˜α, ˜
β<0.1◦(equal o he alignmen epea abil-
i y be ween 5HP and INS). The wind unnel angles ˜α,˜
βa e
ela ed o he ai low angles αand βused o he wind calcu-
la ion (Boi ie , 1998):
α=˜α,
β=a c an an ˜
β
cos ˜α.(4)
The wind ec o calcula ed om ai bo ne measu emen s is
e y sensi i e o unce ain ies in i s inpu a iables. Calib a-
ion in labo a o y and assessmen in wind unnel yield he ba-
sic senso se up. Howe e he e ec o senso and alignmen
unce ain ies on he wind ec o is no s aigh o wa d, and
in ol es nume ous igonome ic unc ions (Supplemen A).
To make he in luence o indi idual measu ed quan i ies
on he wind ec o anspa en , linea unce ain y p opaga-
ion models we e used (Supplemen B). The in en ion is o
in es iga e he wind measu emen ’s unce ain y cons ain by
senso se up and wind model desc ip ion unde con olled
APPENDIX B: METZGER ET AL. (2011) 55
Table 3. Fligh campaign summa y o loca ions Lake S a nbe g (ST), Lindenbe g (LI), and Xilinho (XI). An icyclonic and cyclonic
condi ions a e indica ed by a and c, espec i ely. Fo he ligh pa e ns ace ack (RACE), wind squa e (SQUA), a iance op imiza ion
(VARI), e ical wind speci ic ligh s (VW1–VW3) and he compa ison o g ound based measu emen s (COMP) he numbe o a ailable
da ase s o each da e is gi en oge he wi h espec i e ack leng h (km) in pa en hesis. Addi ional in o ma ion is gi en in Sec . 3.2.
Da e 19 Jun 24 Jun 25 Jun 11 Jul 15 Oc 16 Oc 18 Oc 20 Oc 21 Oc 31 Jul
2008 2008 2008 2008 2008 2008 2008 2008 2008 2009
Loca ion STSTSTSTLILILILILIXI
CYC 950 hPa a a c c a c a a c a
CYC 500 hPa a a a a a c a a a a
p[hPa] 1019 1021 1020 1015 1017 1008 1020 1018 1012 1010
Tmax [◦C]22.4 21.6 27.7 27.8 14.8 14.3 13.1 16.5 21.7 31.1
Cloud co e 5/8 4/8 4/8 4/8 8/8 8/8 5/8 4/8 4/8 7/8
RACE 2 (10) 4 (10) 4 (10) 4 (10)
SQUA 5 (12) 1 (12)
VAR I 6 (20) 4 (20) 2 (80)
VW1 1 (4)
VW2 1 (11) 1 (11)
VW3 1 (9)
COMP 6 (12) 5 (12) 6 (12)
bounda y condi ions. Because o low dis o ion e ec s
(Sec . 2.1) he bounda y condi ions du ing ligh howe e a e
less well known and migh be signi ican ly di e en om he
labo a o y. The e o e a me hodology o in- ligh calib a ion
and e alua ion was de i ed. I consis s o a WSMA speci ic
calib a ion model and - ligh pa e ns.
3.2 Fligh campaigns
These pa e ns we e ca ied ou du ing h ee ligh campaigns
a di e en si es, each wi h i s cha ac e is ic landscape and
me eo ological o cing:
3.2.1 Lake S a nbe g, Ge many
The i s ligh campaign ook place om 19 June o
11 July 2008 o e Lake S a nbe g (47.9◦N, 11.3◦E). The
lake is loca ed in he o eland o he Ge man Alps, ha is
a sligh ly olling landscape (600–800 m a.s.l.) and mainly
consis s o g assland wi h pa ches o o es . The campaign
ocused on ea ly mo ning soundings in he ee a mosphe e
abo e Lake S a nbe g.
3.2.2 Lindenbe g, Ge many
In a second campaign om 14–21 Oc obe 2008 com-
pa ison ligh s we e ca ied ou a he bounda y laye
measu emen ield o he Ge man Me eo ological Se ice,
Richa d-Aßmann-Obse a o y, nea Lindenbe g (52.2◦N,
14.1◦E). The a ea lies in he la No h Ge man Plain (40–
100 m a.s.l.), whe e land-use in he icini y is domina ed
by an equal amoun o ag icul u e and o es s, in e spe sed
by lakes. Fligh s in he a mosphe ic bounda y laye we e
conduc ed unde nea -neu al s a i ica ion (s abili y pa ame-
e |z
L|≤0.2).
3.2.3 Xilinho , China
To ex end he ope a ional ange, an addi ional da ase un-
de condi ions app oaching ee con ec ion ( z
L−0.2) was
included in his s udy: F om 23 June o 4 Augus 2009
an Eddy-Co a iance lux campaign was pe o med o e he
s eppe o he Mongolian Pla eau. The hilly in es iga ion
a ea sou h o he p o incial capi al Xilinho , Inne Mongo-
lia, China (43.6◦N, 116.7◦E, 1000–1400 m a.s.l.) is co e ed
by semi-a id g assland, in e sec ed by a dune bel .
A summa y o all ligh s as well as an o e iew o he
synop ic wea he condi ions is p o ided in Table 3. Synop ic
wind di ec ion and cyclonali y (CYC) we e e ie ed om
he objec i e wea he ype da a base o he Ge man Me eo o-
logical Se ice (Bissolli and Di mann, 2001). The XI ligh
on 31 July 2009 was supplemen ed wi h publicly a ailable
da a om he US Na ional Cen e o En i onmen al P edic-
ion. P e ailing wind di ec ion h oughou all ligh days was
sou h-wes . Sea le el p essu e (p), 2 m a.g.l. maximum em-
pe a u e (Tmax) and cloud co e age a e 24 h obse a ions o
he closes na ional me eo ological se ice s a ion on he e-
spec i e day.
3.3 Fligh pa e ns
In he ollowing, he s a egies o he indi idual ligh pa -
e ns a hese h ee si es a e ca ego ized in i e classes and
b ie ly ou lined. The i s ou o hem se e o isola e
independen pa ame e s o he low dis o ion co ec ion,
56 APPENDIX B: METZGER ET AL. (2011)
while he las one is used o compa e ai c a o g ound based
measu emen s. The pa e ns a e used o he ac ual calib a-
ion and e alua ion o he wind measu emen in Sec . 4.
3.3.1 Race ack pa e n
The i s ype o ligh pa e n consis s o wo legs pa allel
o he mean wind di ec ion a cons an al i ude (one pai ),
one ups eam leg (subsc ip +) and one downs eam leg (sub-
sc ip −). The legs a e sui ably aligned wi h he mean wind
when ha ing opposi e acks o iden ical ai c a se ings.
Fo any ace ack pai lown a cons an ue ai speed ( as),
he (assumed homogeneous and s a iona y) mean wind ( m)
cancels ou (Leise and Mas e s, 1993; Williams and Ma -
co e, 2000):
| m
gs|=1
2(| m
gs,+|+| m
gs,−|)
=1
2( as,++ | m|)+( as,−− | m|)
= as.(5)
In his way he INS measu ed g ound speed (| m
gs|) can be
used o minimize he di e ence || m
gs|− as|by i e a i ely
adjus ing dynamic p essu e in Eq. (A8). This yields an in-
e se e e ence o dynamic p essu e, which is solely based
on INS da a. Since he empe a u e and s a ic p essu e sen-
si i i ies o Eq. (A8) a e wo o de s o magni ude lowe han
ha o he dynamic p essu e (Table 5), he in e se e e ence
can now be used o adjus he 5HP measu ed dynamic p es-
su e o in- ligh condi ions. A o al o 14 ace ack pai s a
ai speeds anging om 21 o 32 m s−1we e conduc ed in he
calm and s eady a mosphe e abo e he ABL (Table 3).
3.3.2 Wind squa e pa e n
The second ype o ligh pa e n consis s o ou legs lown
a cons an al i ude and cons an as in he ca dinal di ec-
ions (no h (N), eas (E), sou h (S), wes (W)). Assuming
ha he ligh s we e ca ied ou in a homogeneous and s a-
iona y wind ield, he measu ed ho izon al wind componen s
( m
u, m
) should be independen o ai c a heading, i.e. con-
s an a each side o he wind squa e. Wi h i a po en ial
o se in βcan be de e mined: The o se in βis changed i -
e a i ely, un il he s anda d de ia ion o m
uand m
h ough-
ou a wind squa e is minimized. Fo ligh s abo e he ABL,
in addi ion he e ical wind componen can be expec ed o
be negligible. A po en ial o se in αcan be de e mined
in a simila ashion o β, howe e , unde he cons ain o
minimizing he absolu e alue o he e ical wind compo-
nen ( m
w). The wind squa e pa e n u he allows o es i-
ma e he unce ain ies o as and β: Since he ligh legs
a e aligned in he ca dinal di ec ions, along- ack wind com-
ponen s ( m
u(N, S), m
(E, W)) a e p edominan ly sensi i e
o e o s in as. C oss- ack wind componen s ( m
(N, S),
m
u(E, W)) a e p edominan ly sensi i e o e o s in β. Thus,
e o s in as and βcan be es ima ed as:
σ
u , as
=1
2
m
u
(N)−
m
u
(S)
2
+
m
(E)−
m
(W)
2
σ
u ,β
=1
2
m
(N)−
m
(S)
2
+
m
u
(E)−
m
u
(W)
2
.(6)
Six wind squa es we e lown abo e he ABL a ai speeds
om 23 o 29 m s−1(Table 3).
3.3.3 Va iance op imiza ion pa e n
The hi d ype o ligh pa e n is a s aigh and le el ABL
sounding, in ended o EC lux measu emen . The assump-
ion made he e is ha e o s in he low angles inc ease he
wind a iance. In con as o he p e ious wo pa e ns, his
me hod does no imply homogenei y o s a iona i y. I can
he e o e be applied e en in he p esence o he mal u bu-
lence, i.e. in he con ec i e ABL (Tje ns ¨
om and F iehe,
1991; Kheli e al., 1999; Kalogi os and Wang, 2002a). O -
se s and slopes o αand βwe e compu ed o minimize
(a) he sum o he wind componen s a iances plus (b) he
absolu e alue o he mean e ical wind. He e i is expec ed
ha m
wapp oaches ze o o a su icien ly high numbe o
da ase s abo e app oxima ely le el e ain. Twel e s aigh
and le el ABL soundings (o 360 km o ligh da a, Table 3)
a ai speeds om 24 o 28 m s−1be ween 50 and 160 m abo e
g ound we e used o his a iance op imiza ion.
3.3.4 Ve ical wind speci ic pa e ns
The ou h ype o ligh pa e n speci ically add esses e -
o s in m
w, he wind componen c ucial o EC lux applica-
ions. Based on Lenschow (1986) s aigh - ligh calib a ion
pa e ns we e pe o med abo e he ABL. These a e in ended
o assess and minimize he possible in luence o ai c a (in
ou case WSMA) li and im on m
w. A ai speeds anging
om 21 o 32 m s−1 i e e ical wind (VW) speci ic ligh s,
di ided in o h ee sub-pa e ns, we e u ilized in his s udy
(Table 3):
–VW1 – (Le el accele a ion – decele a ion): whils he
engine’s powe se ing was g adually a ied, he wing
pi ch (and wi h i li coe icien ) was adjus ed o main-
ain ligh al i ude. Wi h his pa e n he in luence o
ai c a im on m
wcan be de e mined.
–VW2 – (Smoo h oscilla ion): s a ing om le el ligh
he powe se ing was slowly a ied, while he wing
pi ch was adjus ed o main ain cons an as. In con-
sequence, he ai c a ascended and descended abou
he mean heigh , while CL emained app oxima ely un-
changed. VW2 was used o assess he in luence o wing
pi ch and ai c a e ical eloci y on m
w.
APPENDIX B: METZGER ET AL. (2011) 57
–VW3 – (Fo ced oscilla ion): s a ing om le el ligh
he wing pi ch was o cibly al e na ed. The ai c a as-
cended and descended a ound he mean heigh , while
powe se ing emained unchanged. In esponse ai -
c a accele a ions and eloci ies, and wi h i he ai low
a ound he ai c a , changed. VW3 was used o assess
he in eg al in luence o e ically accele a ed ligh on
m
w, as e.g. du ing e ain ollowing ligh s in he ABL
(see Sec . 4.1, S ep G6).
3.3.5 Compa ison o g ound based e e ence
measu emen s
The i h and las ype o ligh pa e n is a se ies o com-
pa ison measu emen s be ween WSMA and g ound based
measu emen s. These we e ca ied ou a he bounda y laye
measu emen ield o he Ge man Me eo ological Se ice,
Richa d-Aßmann-Obse a o y, nea Lindenbe g. The lowe
pa o he ABL was p obed by a 99-m owe and a SODAR
wi h hei base a 73 m a.s.l. The 99-m owe p o ided cup
measu emen s (10 min a e ages) o wind speed a ou le els
(40, 60, 80, and 98 m a.g.l.), he wind di ec ion was measu ed
wi h anes a heigh s o 40 and 98 m a.g.l. (10 min a e ages).
Sonic anemome e s moun ed a he owe p o ided u bulen
wind ec o measu emen s a 50 and 90 m a.g.l. The SODAR
wind ec o p o iles (15 min a e ages) eached, a inc emen s
o 20 m, om 40 o 240 m a.g.l. In addi ion a e e ence o
s a ic p essu e was p o ided a 1 m a.g.l. 17 c oss-shaped pa -
e ns ( an den K oonenbe g e al., 2008), wi h ligh legs o
3 km cen ed be ween owe and SODAR, we e pe o med a
24 and 27 m s−1ai speed (Table 3). The ligh s we e ca -
ied ou a he app oxima e sounding le els o owe and
SODAR (50, 100, 150, 200 and 250 m a.g.l.). This allows
a di ec compa ison o WSMA and g ound based measu ed
wind componen s. Ai c a and sonic wind measu emen s
we e il e ed using he s a iona i y es o wind measu e-
men s by Foken and Wichu a (1996). SODAR, cup and ane
da a we e s a i ied o he bes quali y a ing assigned by he
Ge man Me eo ological Se ice. Simul aneous wind da a o
WSMA and g ound based measu emen s we e accep ed o
compa ison only i hey ag eed o wi hin ±20 m heigh abo e
g ound (which equals ≈2σo a ia ions in WSMA al i ude).
This da a sc eening esul ed in a o al o 20 da a couples (be-
ween WSMA and cups/ anes, sonics and SODAR) o m
u ,
and 19 da a couples o m
w. Compa ed o cups/ anes, sonics
and SODAR, he WSMA soundings we e on a e age highe
abo e g ound by 0.1 ±5.5, 8.7 ±5.6, and 0.5 ±5.3 m, e-
spec i ely.
4 Applica ion o weigh -shi mic oligh ai c a
To unde s and ope a ional equi emen s o se up and cal-
ib a ion o he wind ec o measu emen , ai c a a -
i ude and dynamics we e assessed o a s aigh and
le el bounda y laye ligh (Table 3, a iance op imiza ion
ligh on 31 July 2009). His og ams o ai c a p ope -
ies we e calcula ed om ≈3×104da a poin s sampled
≈50 m a.g.l. (Fig. 4). Va ia ions in ue ai speed and ai c a
e ical mo emen we e esul ing om ai c a manoeu es
o ollow he e ain con ou s as well as he mal u bulence
(labile s a i ica ion, s abili y pa ame e z
L≈−0.9). A i ude
angles (b,b) indica e cons an upwa d pi ching and an i-
clockwise oll o he ike, espec i ely. Pi ching as well as
olling inc ease in magni ude wi h as, i.e. powe se ing
o he engine. The pi ching momen can be unde s ood as
he dynamic balance wi h as be ween p opelle h us and
he d ag di e ence be ween he ike (low) and he wing
(high). This is con i med by an es ima e o he a ack angle
(α), which shows ewe a ia ion due o alignmen wi h he
s eamlines, hough alike binc eases wi h as (≈0.4◦pe
ms
−1). The olling momen can be unde s ood as coun e -
balance o he clockwise o a ing p opelle o que. In ad-
di ion side-slipping o he ike o e i s po side was de-
ec ed om an es ima e o he sideslip angle (β), inc easing
a a a e o ≈−0.6◦pe m s−1wi h as. The ope a ional
ange in αand βes ima es we e ound ≈|15◦|, a e aging
o 6.0 ±1.8◦and −5.5 ±3.2◦, espec i ely (Fig. 4). Fol-
lowing he li Eq. (2), wing pi ch dec eases wi h as. Tha
is, wi h inc easing as he noses o wing and ike app oach
each o he . Wing oll does no display dependence on as,
i.e. no coun e eac ion on p opelle o que o ike oll. The
wing loading ac o (LF) was ound o a y wi hin a ange o
σ≈0.1 g (Fig. 4), om which he upwash a ia ion in on
o he wing can be assessed.
Using i e hole p obe measu ed as in Eq. (3) he up-
wash eloci y ( w
up) a 5HP loca ion was de e mined o
1.52 ±0.19 m s−1. D-MIFU is a elling a low ai speed and
has a small ela i e sepa a ion (n) be ween wing and 5HP.
Bo h ac o s lead o an inc ease in w
up. Va ious esea ch ai -
c a ha e been assessed wi h ega d o upwash gene a ion
(C aw o d e al., 1996), compa ed o which D-MIFU anges
mid- able. This can be asc ibed o he low wing loading,
whichisa ac iono hoseo ixed-wing ai c a , and de-
c eases w
up. Wing loading, and wi h i w
up, a e di ec ly p o-
po ional o e ical accele a ion and ai c a mass in Eq. (1).
Hence σ≈10 % a ia ion in LF (Fig. 4) accoun s o mos o
he a iance in w
up. In addi ion ai c a mass can a y du ing
he ligh due o uel consump ion (±4 %) and among mea-
su emen s due o weigh di e ences o pilo s (±2 %). Due o
he ike’s o a ional eedom, upwash abou he wing’s cen-
e o p essu e can pa ially ansla e in o along- and side-
wash (longi udinal and ans e se o he ike body, espec-
i ely) a he 5HP loca ion in he ike body coo dina e sys-
em (BCS). Mean ae odynamic cho d heo y yields he cen-
e o p essu e’s posi ion o he wing wi hin 0.2 m o <10 %
cho d leng h o he cen e o g a i y. Assuming he cen es o
p essu e and g a i y o coincide, he pi ch di e ence be ween
wing and ike can be neglec ed, and w
up is easily ans o med
58 APPENDIX B: METZGER ET AL. (2011)
Fig. 4. His og ams o ai c a p ope ies de i ed o he ligh on 31 July 2009 (Table 3). Componen densi y is scaled so ha he his og ams
ha e a o al a ea o one. Red e ical lines indica e dis ibu ion a e age (solid) and s anda d de ia ion (dashed). The black dashed bell cu e
displays a e e ence no mal dis ibu ion: T ue ai speed ( as), a ack angle (αA), sideslip angle (βA), ai c a e ical eloci y ( m,z
gs ), ike
pi ch- (b) and oll (b) angles, loading ac o (LF, he a io o li - o weigh o ce), as well as wing pi ch- (w) and oll (w) angles.
in o he BCS: he ans o ma ion Eq. (A13) was ca ied ou
abou ze o heading di e ence, he wing upwash di ec ion
(ξ=−41.9 ±0.3◦), and he oll di e ence be ween wing and
ike. Wing upwash ne e ec a he 5HP loca ion was hen
di ec ed o wa d, igh and upwa d wi h 1.01 ±0.13 m s−1,
0.12 ±0.13 m s−1,and−1.12 ±0.14 m s−1in ike body co-
o dina es (Fig. 5).
4.1 Wind measu emen calib a ion
The sensi i i y o he wind model desc ip ion was analysed
by linea unce ain y p opaga ion models (Supplemen B).
The i s model in Eq. (B1) pe mi s o exp ess he sensi i -
i y o he wind compu a ion as a unc ion o a i ude angles,
low angles and ue ai speed. I was ca ied ou o wo e -
e ence ligh s a es a as =27ms
−1. In S a e 1 a i ude and
low angles we e assumed small (1◦), as i would be yp-
ical o calm a mosphe ic condi ions. This allows o he
small-angle app oxima ion in Eq. (B1), esul ing in unce -
ain ies o he wind componen s ( m
u w) as a unc ion o
he heading angle (). In S a e 2 a i ude (10◦)and low
angles (−15◦) we e app oxima ely inc eased o hei 95 %
con idence in e als du ing soundings in he con ec i e ABL
(Fig. 4). Consequen ly he ull o m o Eq. (B1) mus be
used o S a e 2. I allows o calcula e he maximum un-
ce ain y in he wind componen s (| m
u w|) o e all ,as
well as o compa e hese be ween bo h ligh s a es. Bo h
s a es we e in e ed unce ain ies o 1◦and 0.5 m s−1 o
APPENDIX B: METZGER ET AL. (2011) 59
Table 4. Inpu unce ain y (IU) om he linea unce ain y p opaga ion model Eq. (B1). Fo he sensi i i y analysis he model was o ced
wi h wo di e en e e ence s a es, S a e 1 wi h small and S a e 2 wi h enhanced low (α,β) and a i ude (b,b,b,) angles. Bo h s a es
we e in e ed simila unce ain y quan i ies iin α,β,b,b,b, and ue ai speed ( as). A e calib a ion S ep B he e e ence S a e 2
was used o he unce ain y p opaga ion: he ac ual unce ain ies in (a) he low compu a ion (α,βand as, Table 5), and (b) he senso
alignmen (b,b,b) we e in e ed. Addi ional in o ma ion is gi en in Sec . 4.1.
Va iable αβ
bbb as IU
Model o cing
S a e 1 1◦1◦1◦1◦0...360◦27 m s−1
S a e 2 −15◦−15◦10◦10◦0...360◦27 m s−1
i,sensi i i y 1◦1◦1◦1◦1◦0.5 m s−1
i,p opaga ion 0.76◦0.76◦0.1◦0.1◦0.1◦0.34 m s−1
Resul s S a e 1 – sensi i i y
m
u[ms
−1]<0.01 0.47cos<0.01 <0.01 0.47cos0.50 1.08
m
[ms
−1]<0.01 −0.47sin<0.01 <0.01 −0.47sin0.50 1.08
m
w[ms
−1]0.47 <0.01 −0.47 <0.01 <0.01 <0.01 0.95
| m
u |[ms
−1]0.01 0.47 <0.01 0.01 0.47 0.5 1.08
| m
w|[ms
−1]0.47 0.01 0.48 0.01 0.00 <0.01 0.97
Resul s S a e 2 – sensi i i y
| m
u |[ms
−1]0.21 0.47 0.21 0.14 0.42 0.45 1.34
| m
w|[ms
−1]0.41 0.05 0.32 0.14 0.00 0.22 1.14
Resul s S a e 2 – p opaga ion
| m
|[ms
−1]0.16 0.36 0.02 0.01 0.04 0.30 0.64
| m
w|[ms
−1]0.31 0.04 0.03 0.01 0.00 0.15 0.55
Fig. 5. His og ams o wing-gene a ed alongwash, sidewash and upwash a he i e hole p obe loca ion. Resul s a e calcula ed om wing
p ope ies in Eqs. (1)–(3) and hen o a ed om wing- in o ike body coo dina es (Fig. 2) using Eq. (A13). P esen ed is he same da ase and
in he same manne as in Fig. 4.
angula - and as measu emen s, espec i ely. F om S a e 1
i can be seen ha he majo unce ain y in he ho izon al
wind componen s ( m
u ) o igina es om as, sideslip angle
(β) and heading angle (), whe e βand ca y simila
sign and sensi i i y (Table 4). On he con a y, he e ical
wind componen ( m
w) is simila ly sensi i e o a ack angle
(α) and pi ch angle (), ye wi h e e sed sign. As com-
pa ed o S a e 1, in S a e 2 he absolu e unce ain ies in he
ho izon al (| m
u |) and e ical (| m
w|) wind componen s
a e inc eased by 24 % and 18 %, espec i ely. The inc ease
howe e does no o igina e om he mos sensi i e e ms,
bu om o me ly negligible e ms such as ike oll (b).
66 APPENDIX B: METZGER ET AL. (2011)
Fig. 10. Smoo h oscilla ion ligh s (VW2) on 24 June 2008 (le ) and 25 June 2008 ( igh ). In addi ion o he a iables explained in Fig. 8
he e ical ai c a eloci y ( m,z
gs ) is shown. Addi ional in o ma ion is gi en in Sec . 4.1 S ep G3.
independence o m
w om as, he de ec ed BIAS depends on
αup,o in Eq. (7). Bo h, αup,o and αupw,slo we e de e mined
using he VW1 ligh on 25 June 2008 du ing ambiguous cy-
clonali y a op and below measu emen al i ude (Table 3). In
Fig. 9 he de e mina ion o αupw,slo depends on he change o
CL, while he o se αup,o depends on he ambien e ical
wind. Du ing he in e se e e ence p ocedu e m
wwas o ced
o ze o while, e.g. in an an icyclone, subsidence occu s. In
such a si ua ion αup,o would be unde es ima ed. Du ing he
VW ligh s on 24 and 25 June 2008, cyclonali y and BIAS
in m
wbo h changed. While αupw,slo is insensi i e, no con-
s an αup,o could be de e mined om he VW ligh s. A
his poin he a iance op imiza ion ligh s in he ABL a e o
impo ance. Assuming cons an ABL heigh (app oxima ely
ul illed o noon ime EC soundings) he second op imali y
c i e ia s a es ha due o mass conse a ion m
wapp oaches
ze o o a su icien ly high numbe o da ase s. Wi h i αup,o
was de e mined di ec ly om ABL ligh s. Using he i s
a iance op imiza ion op imali y c i e ia, i.e. he minimiza-
ion o he wind a iance, also αand βslopes we e es ed.
S ep G5 – I e a i e ea men o c oss dependences
An app oach simila o Eq. (7), he explana ion o upwash in
α, was used o explain sidewash in β:
β∞=βA−βupw,o +βupw,sloCL,(8)
using he calib a ion c i e ia o he wind squa e ligh s o
pa ame iza ion. Acco ding o Eq. (A11) c oss dependence
occu s be ween he pa ame iza ions in αand β. This p ob-
lem was sol ed by i e a ing he op imali y c i e ia o wind
squa e, e ical wind, and a iance op imiza ion ligh s in se-
quence. The o de o his sequence, i.e. i s op imizing o
he ho izon al wind componen s ( m
u ), hen o he e ical
wind componen ( m
w), was chosen due o hei di e en o de
o magni ude and impo ance o EC applica ion. Spu ious
con amina ion wi h m
wwould change m
u only by a ac ion.
The o he way a ound howe e would esul in conside ably
highe con amina ion in m
w.The inal calib a ion coe icien s
a e summa ized in Table 6.
Compa ed o he upwash pa ame iza ion, sidewash was
ound o be modes (βupw,o =−0.004 ad) and less sensi i e
ega ding CL (βupw,slo =−0.010 ad, Table 6). This is in line
wi h he ini ial a emp o esol e he ci cula ion a ound he
wing and he ike mo emen explici ly (Fig. 5). The indings
also con i m ou ini ial hypo hesis ha low ans e se o he
p essu e p obe equi es less co ec ion han in he e ical
di ec ion (Sec . 2.1): lea ing dynamic conside a ions aside
(i.e. li coe icien is ze o), he magni ude o he sideslip an-
gle co ec ion is one o de o magni ude lowe han he a ack
angle co ec ion (0.039 ad, o se s in Table 6). Fo a ue
ai speed o 30 m s−1 his a ec s he wind measu emen o
app oxima ely −0.1 m s−1and 1.2 m s−1, espec i ely. The
ans e se dis o ions inc ease and he e ical dis o ions de-
c ease a a a io o ≈1:3, when conside ing in e ac ions wi h
p opelle and wing (i.e. non-ze o li coe icien , slopes in
Table 6).
S ep G6 – Applica ion o e ain ollowing ligh
The unce ain y o he co ec ion du ing e ain ollow-
ing ligh can be assessed om he eg ession e o s,
e.g. in he upwash a ack angle o he e ical wind. In
S ep G3 he le el accele a ion-decele a ion ligh was used
o calib a e he eg ession slope. This slope did no di -
e signi ican ly compa ed o he o ced oscilla ion ligh ,
wi h −0.027 ±0.002 and −0.024 ±0.002, espec i ely. In
S ep G4 we used 12 ABL ligh s o 360 km o ligh da a o
APPENDIX B: METZGER ET AL. (2011) 67
pa ame ize he eg ession o se (0.039 ±0.003). The com-
bined e o s in slope and in e cep we e applied o he e ain
ollowing ligh on 31 July 2009. The esul ing unce ain y in
he e ical wind measu emen is wi hin 0.1 m s−1(RMSE)
o he mean and 1 % o he a iance. This compa es o
he magni ude o he co ec ion, which is in he o de o
0.5 m s−1 o he mean and 3 % o he a iance, espec i ely.
Many a iables in he ABL scale wi h dis ance om he
exchange su ace (e.g. Mah , 2000; Mah e al., 2001). In-
e p e able esul s can be achie ed by lying a app oxima ely
cons an al i ude abo e g ound (e.g. Be s e al., 1990; Vick-
e s and Mah , 1997). Ye many e es ial su aces a e no
ideally la . Du ing e ain ollowing measu emen s we o-
cus on mos ly ho izon al ligh acks be ween 40 and 80 km
ex end. Typical al i ude g adien s du ing such ligh pa e ns
a e 100 m e ical on 10 km ho izon al, and a ely each ±5◦
climb angle. In o de o adjus ai c a al i ude, he pilo an-
icipa es he e ain con ou s a a scale o kilome es. A ypi-
cal ai speeds his co esponds o an adjus men o powe se -
ing and wing pi ch h ough he pilo a equencies <0.1 Hz.
In addi ion o he low equency con ol o ces, also ex e nal
o ces due o a mosphe ic u bulence and mesoscale mo ions
mee in he hangpoin . An inc ease in he e ical wind a i-
ance in he o de o 1 % would esul when applying he co -
ec ion o low equency pilo ac ions o he en i e equency
spec um. Consequen ly he co ec ion is only applied o e-
quencies <0.1 Hz. This is achie ed by calcula ing Eqs. (7),
(8) h ough a hi d o de Sa i zky-Golay complemen a y il-
e (e.g. Chen e al., 2004). The ea men leads o a dec ease
in he e ical wind a iance in he o de o −3 %. This is
expec ed since he impac o he low equency pilo ac ions
on he wind measu emen is emo ed.
Low equency a mosphe ic mo ions, such as u bulen o -
ganized s uc u es, o e lap wi h pilo ac ions in equency
space. The e ec o low equency a mosphe ic mo ions
on he co ec ion can be es ima ed wi h a simple exam-
ple. In a la ge-scale downd a o eloci y wdan ai c a
o mass mand ai speed as has o p oduce he o al li
L=mag,z(1+wd/ as), see Eq. (1). As compa ed o ze o
e ical wind condi ions he li , and wi h i he li coe -
icien in Eq. (2), is changed by he a io o wd/ as.Fo
he ligh on 31 July 2009 a a io o ±1 % is equi alen
o wd=±0.27 m s−1, a ypical alue o u bulen o ganized
s uc u es in he ABL (e.g., S ein eld e al., 2007). To es he
in luence on he co ec ion a sinusoidal signal wi h ampli ude
1 % and equency 0.01 Hz was added o he measu ed li co-
e icien . The maximum de ia ion om he undis u bed mea-
su emen is wi hin ±3 %, o sub cen ime e. The a iance o
he e ical wind is changed by <0.01 %. We conclude ha
he co ec ion can be applied o he en i e equency ange
≤0.1 Hz wi hou in oducing signi ican unce ain y o he
wind measu emen .
4.2 Wind measu emen e alua ion
A e comple ing all calib a ion s eps, he wind measu e-
men wi h he WSMA was e alua ed. The e alua ion was
ca ied ou in h ee lines o analysis, (a) unce ain y p opa-
ga ion, (b) wind squa e ligh s, and (c) compa ison o g ound
based wind measu emen s. Fo a ue ai speed o 27 m s−1
he p opaga ion o unce ain ies in senso s ( low angle di -
e en ial p essu es, dynamic- and s a ic p essu es, s a ic em-
pe a u e, and wa e apou p essu e), hei basic calib a ion
and wind model desc ip ion yield an unce ain y (σ) o 0.76◦,
0.76◦, and 0.34 m s−1in a ack angle (α), sideslip angle (β)
and ue ai speed, espec i ely (Table 5). Feeding he inpu
unce ain y Eq. (B1) wi h hese quan i ies ex ends he unce -
ain y p opaga ion o he wind componen s (Table 4). The
inpu e o is o mula ed wo s case, and pa ame ized o
he 95 % con idence in e als o he a i ude and low angles.
In addi ion he unce ain y o he ine ial na iga ion sys em
(0.02 m s−1) was conside ed in he wind ec o Eq. (A1).
This allows o es ima e he maximum po en ial unce ain y
by senso se up and wind model desc ip ion. The esul s
o he maximum o e all unce ain y bounds a e 0.66 and
0.57 m s−1 o he ho izon al ( m
u ) and e ical ( m
w)wind
componen s, espec i ely.
Figu e 11 shows he esul s o all wind squa e ligh s. Fo
wind eloci ies >2ms
−1 m
u de e mined o indi idual legs
de ia e less han 10 % om he a e age o he en i e squa e.
The esiduals did no scale wi h he a e age wind eloci y, o
a g ea e deg ee hey a e likely o esul om an incomple e
emo al o wind ield inhomogenei ies o e he 12 km long
ligh pa hs. The e o e a ho izon al wind eloci y o 2 m s−1
can no be conside ed as a de ec ion limi o wind measu e-
men s om WSMA. Also no sys ema ic de ia ion o ai c a
o ien a ion could be de ec ed. Howe e m
wshows a sligh
sensi i i y o −0.05 on as (R2= 0.46). Using he ca dinal
di ec ion e alua ion c i e ia Eq. (6), RMSE in α∞,β∞and
| m
as|we e compu ed o 0.31, 0.33 and 0.26 m s−1, espec-
i ely. These compa e well o he esul s om he unce ain y
p opaga ion (Tables 4 and 5), which amoun o 0.31, 0.36 and
0.34 m s−1 o αA,βAand as, espec i ely.
Figu e 12 shows a quali a i e compa ison o WSMA and
g ound based wind measu emen s o he ligh on 15 Oc-
obe 2008. The e ical p o ile shows an equal numbe o
ligh s a 24 and 27 m s−1 ue ai speed. Despi e one ou lie
in m
and m
wa 120 m a.g.l., no dis inc di e ences in a -
e age wind eloci ies be ween g ound based measu emen s
and WSMA a e appa en . The compa abili y o WSMA and
g ound based wind measu emen was u he quan i ied by
calcula ing RMSE and BIAS o all measu emen s accep ed
o he compa ison (Table 3). The impac o calib a ion
S eps C–G on hese measu es is displayed in Fig. 13. The
measu emen o he ho izon al wind componen s ( m
u )was
mainly imp o ed (14 %, ela i e o he ini ial unce ain y) by
means o he in- ligh dynamic p essu e co ec ion (S ep D).
A e he wind squa e analysis (S ep E) he measu emen
68 APPENDIX B: METZGER ET AL. (2011)
Fig. 11. Resul s om he wind squa e ligh s. Fo he ho izon al wind componen s ( m
u ) he x-axis displays he esiduals (leg a e age–squa e
a e age), while he y-axis shows he wind magni ude. In con as he e ical wind componen ( m
w) is plo ed agains he ue ai speed.
Fligh legs a e depic ed wi h di e en symbols acco ding o hei posi ion in he squa e pa e n. Dashed lines indica e a 10 % c i e ia o m
u ,
and he ze o line o m
w.
was no u he imp o ed no de e io a ed. Ye he e ical
wind measu emen ( m
w) ecei es i s g ea es imp o emen
(31 %) du ing S eps F–G, i.e. a iance op imiza ion and e -
ical wind speci ic pa e ns: Du ing hese s eps BIAS and
dBIAS, i.e. i s dependence on as, we e educed. In con as
o he indings om he wind squa e analysis, wi h a sensi i -
i y o ≈+0.05 a sligh posi i e dependence o all wind com-
ponen s on as emained. Conside ing all da a couples be-
ween WSMA and g ound based measu emen s, RMSE and
BIAS amoun o 0.50 and −0.07 m s−1 o m
u and 0.37 and
−0.10 m s−1 o m
w, espec i ely. In addi ion o he abo e
men ioned ou lie , wo mo e suspec s we e iden i ied o he
ligh on 18 Oc obe 2008, again concu en o m
and m
w.
A possible explana ion is he inc eased land su ace he e o-
genei y sensed by he ai c a while a elling h ough he
wind ield. On he no he n and wes e n limbs o he ai c a
c oss pa e n, o es pa ches o ≥200 m edge leng h in e up
he la a able land immedia ely upwind. The e o e WSMA
measu emen s can include u bulence and wake e ec s gen-
e a ed a he o es edges. In con as owe measu emen s
a e no subjec o compa able oughness changes un il ≈2km
in upwind di ec ion. Omi ing he h ee ou lie s om he
s a is ics, RMSE and BIAS be ween WSMA and g ound
based measu emen s imp o e o 0.39 and −0.11 m s−1 o
m
u and 0.27 and −0.10 m s−1 o m
w, espec i ely.
4.3 Discussion
Dis o ions o he wind measu emen o igina ing om he
in e ac ions o he ae oelas ic wing, p opelle and ike
s uc u al ea u es we e success ully co ec ed o condi ions
app oxima ing s aigh , e ain ollowing ligh . Ye he ea -
men s in eg al o Eqs. (A7), (7) and (8) lea e oom o im-
p o emen : Compa ed o g ound based measu emen s he
ai c a unde es ima ed he wind componen s ≈−0.1 m s−1.
A possible eason could be he disca ded o se du ing he dy-
namic p essu e (pq)in- ligh calib a ion (Sec . 4.1, S ep D).
Ra he o cing he linea i o ze o would sligh ly enhance
he slope o pqand wi h i compliance o he ai c a ’s ine -
ial speed.
Du ing he wind squa e and compa ison ligh s con adic-
o y sensi i i ies ( eg ession slope −0.05 e sus +0.05) o he
wind componen s on he ue ai speed we e ound. Fo he
a iabili y in as du ing a he mally u bulen ligh in he
a mosphe ic bounda y laye (σ= 1.24 m s−1, Fig. 4) his co -
esponds o ±0.06 m s−1de ia ion in he wind componen s.
Since his de ia ion is one o de o magni ude lowe han he
sys em’s inpu unce ain y, i was no u he ea ed.
The li coe icien is used as sole explana o y a iable
o he obse ed ne upwash in he linea calib a ion mod-
els Eqs. (7) and (8). This ea s he in luence o ai c a
im (i.e. dynamic p essu e) and li (i.e. loading ac o ) on
APPENDIX B: METZGER ET AL. (2011) 69
Fig. 12. Ve ical p o iles o ho izon al ( m
u ) and e ical ( m
w) wind componen s o simul aneous g ound based and weigh -shi mic oligh
ai c a measu emen s on 15 Oc obe 2008, 14:50–16:00 CET. Di e en symbols indica e he di e en wind senso s. Black ci cles ep esen
ai c a measu emen s a 24 m s−1 ue ai speed, while g ey ci cles ep esen measu emen s a 27 m s−1 ue ai speed. Ve ical e o ba s
indica e one s anda d de ia ion o he ai c a al i ude.
he wind measu emen wi h simila sensi i i y. The s udy by
Visbal and Shang (1989) howe e shows ha he low ield
esponse o ai oils o pi ch oscilla ions depends on he ex-
ci a ion equency. Wi h he Fou ie me hod p oposed by
Kalogi os and Wang (2002b) he equency dependence o
he wing induced upwash can be modelled o FWA. The
dis inc di e ence om ime domain me hods is an ampli-
ied (≈20 %) upwash co ec ion in he ine ial sub ange o
a mosphe ic u bulence compa ed o lowe equencies. Due
o li le con ibu ions o he ine ial sub ange, he e ec on
he eddy lux measu emen a ligh al i ude (≤4%) ishow-
e e ela i ely small. A he same ime a ans o ma ion om
he wing o he ike coo dina e sys em would be equi ed,
ca ying a po en ially a iable phase di e ence. Mo eo e
he in e ac ions wi h p opelle and ike, esul ing in he ne
low dis o ion, emain un ea ed. Isola ing hese in e ac ions
would equi e conside ably mo e in- ligh da a and analy ical
e o . In e u n such p ocedu e could add ess o enamed de-
pendence o he wind componen s on as and addi ionally
allow o supe io wind measu emen s du ing u ning ma-
noeu es.
5 Conclusions
We ha e shown ha ca e ully compu ed wind ec o mea-
su emen s using a weigh -shi mic oligh ai c a a e no in-
e io o hose om o he ai bo ne pla o ms. A 10 % limi o
con amina ion o he wind componen s by he ai c a mo e-
men , as used by he US Na ional Cen e o A mosphe ic
Resea ch, was ul illed e en du ing se e e e ical manoeu-
ing. Fo ligh s including ising and sinking o he ai -
c a , such as du ing e ain ollowing Eddy-Co a iance ap-
plica ions, h ee independen lines o analysis yield compa-
able unce ain y. This con e gence is ema kable and em-
phasizes he in eg i y o sensing elemen s and wind model
desc ip ion. The p ocedu e u he enables o quan i y he
o e all ope a ional unce ain y ( oo mean squa e e o ) o
0.4 m s−1 o he ho izon al and 0.3 m s−1 o he e ical
wind componen s.
Independen conside a ion o ike mo emen and wing
ci cula ion acco ding o he ixed-wing ai c a heo y was
no success ul. Ins ead low dis o ion o uselage, p opelle
and wing we e minimized by an app oach in eg a ed in he
dynamic p essu e and low angle compu a ions. The mag-
ni ude o dis o ion was ea ed as slope co ec ion in he
dynamic p essu e compu a ion. The dis o ion’s dis ibu-
ion in componen s longi udinal, ans e se and e ical o
he wind measu emen was subsequen ly pa ame ized in he
a ack- and sideslip angle compu a ions. The li coe icien
70 APPENDIX B: METZGER ET AL. (2011)
Fig. 13. In luence o he calib a ion S eps C–G on oo mean squa e
e o (RMSE) and bias (BIAS) be ween weigh -shi mic oligh ai -
c a and all simul aneous g ound based measu emen s o he ho -
izon al ( m
u ) and he e ical ( m
w) wind componen s. dBIAS in-
dica es he di e ence in BIAS be ween measu emen s a 27 and
24 m s−1 ue ai speed.
was success ully used as sole a iable explaining he up-
wash dis ibu ion, con aining in i he e ec s o ai c a im
and li . A e he ea men an inconclusi e dependence
o he e ical wind measu emen on he ai c a ’s ue ai -
speed emained. In- ligh es s ela e his dependence o an
unce ain y o 0.06 m s−1in he e ical wind measu emen .
As compa ed o g ound based measu emen s he inal wind
componen s we e ma ginally unde es ima ed by he ai c a
(≈−0.1 m s−1).
Ou indings emphasize ha he 3-D wind ec o can be
measu ed eliably om a highly anspo able and low-cos
weigh -shi mic oligh ai c a . Hence he necessa y basis is
p o ided o he s udy o p ecision and spec al quali y o he
wind measu emen , which is p e equisi e o eliable Eddy-
Co a iance lux measu emen s. This b ings he weigh -shi
mic oligh ai c a pla o m an impo an s ep close owa ds
a ull ea u ed en i onmen al esea ch ai c a .
Supplemen a y ma e ial ela ed o his
a icle is a ailable online a :
h p://www.a mos-meas- ech.ne /4/1515/2011/
am -4-1515-2011-supplemen .pd .
Acknowledgemen s. Special ecogni ion has o be gi en o
Jose -Michael Bu ge , Ma hias Maude , F ank Neidl, Raine S ein-
b eche and Rose Zuu bie a he Ka ls uhe Ins i u e o Technology,
Ins i u e o Me eo ology and Clima e Resea ch. Bu ge and
Zuu bie ca ied ou he bulk o he wind- unnel measu emen s,
whe eas Maude con ibu ed his mic ome eo ological ad ise. Neidl
p og ammed and con inuously main ained he da a acquisi ion
sys em, while S einb eche ini ia ed wind- and lux measu emen s
wi h he weigh -shi mic oligh ai c a in he i s place. Ou
g a e ulness o Xunhua Zheng and he wo k-g oup a he Chinese
Academy o Sciences, Ins i u e o A mosphe ic Physics, who was
hos ing ou p ojec and p o iding indispensable in as uc u e. We
a e much obliged o F ank Bey ich o he Ge man Me eo ological
Se ice, Richa d-Aßmann-Obse a o y, who pe mi ed us o ca y
ou he e alua ion ligh s and p o ided us wi h he co esponding
SODAR- and owe da a o his s udy. Ou hanks o Jens Bange
and Aline an den K oonenbe g o he Technical Uni e si y o
B aunschweig, Ins i u e o Ae ospace Sys ems (now Ebe ha d
Ka ls Uni e si y o T¨
ubingen, Ins i u e o Geoscience), o
hei i eless ad ise. S ipend unding by he Ge man Academic
Exchange Se ice, Helmhol z Associa ion o Ge man Resea ch
Cen e s, China Schola ship Council and he Eu opean Union unde
he Science and Technology Fellowship China is acknowledged.
The ligh in Inne Mongolia was unded by he Ge man Resea ch
Founda ion, esea ch g oup 536 “Ma e luxes in g asslands o
Inne Mongolia as in luenced by s ocking a e”. The publica ion
was unded by he Ge man Resea ch Founda ion and Open Access
Publishing Fund o he Ka ls uhe Ins i u e o Technology. We
hank John Kalogi os and an anonymous e iewe o hei aluable
commen s and de ailed eedback.
Edi ed by: J.-P. Pomme eau
Re e ences
Baldocchi, D., Falge, E., Gu, L., Olson, R., Hollinge , D., Run-
ning, S., An honi, P., Be nho e , C., Da is, K., E ans, R.,
Fuen es, J., Golds ein, A., Ka ul, G., Law, B., Lee, X., Malhi, Y.,
Meye s, T., Munge , W., Oechel, W. U. K., Pilegaa d, K.,
Schmid, H., Valen ini, R., Ve ma, S., Vesala, T., Wilson, K.,
and Wo sy, S.: FLUXNET: A new ool o s udy he empo al
and spa ial a iabili y o ecosys em-scale ca bon dioxide, wa e
apou , and ene gy lux densi ies, B. Am. Me eo ol. Soc., 82,
2415–2434, 2001.
Bange, J. and Ro h, R.: Helicop e -bo ne lux measu emen s in he
noc u nal bounda y laye o e land – a case s udy, Bound.-Lay.
Me eo ol., 92, 295–325, 1999.
Be s, A. K., Desja dins, R. L., Macphe son, J. I., and Kelly, R. D.:
Bounda y-laye hea and mois u e budge s om FIFE, Bound.-
Lay. Me eo ol., 50, 109–138, 1990.
Bey ich, F., Leps, J. P., Maude , M., Bange, J., Foken, T.,
Huneke, S., Lohse, H., Ludi, A., Meijninge , W. M. L.,
Mi ono , D., Weisensee, U., and Zi el, P.: A ea-a e aged su -
ace luxes o e he LITFASS egion based on Eddy-Co a iance
measu emen s, Bound.-Lay. Me eo ol., 121, 33–65, 2006.
Bissolli, P. and Di mann, E.: The objec i e wea he ype classi-
ica ion o he Ge man Wea he Se ice and i s possibili ies o
applica ion o en i onmen al and me eo ological in es iga ions,
Me eo ol. Z., 10, 253–260, 2001.
APPENDIX B: METZGER ET AL. (2011) 71
Bohn, D. and Simon, H.: Meh pa ame ige App oxima ion de
Eich ¨
aume und Eich l¨
achen on Un e schall- bzw. ¨
Ube schall-
5-Loch-Sonden, A chi ¨
u Technisches Messen und Meß ech-
nische P axis, 470, 31–37, 1975.
Boi ie , J.-L.: The Dynamics o Fligh : The Equa ions, Wiley,
1998.
B own, E. N., F iehe, C. A., and Lenschow, D. H.: The use o
p essu e- luc ua ions on he nose o an ai c a o measu ing ai
mo ion, J. Clim. Appl. Me eo ol., 22, 171–180, 1983.
Chen, J., Jonsson, P., Tamu a, M., Gu, Z. H., Ma sushi a, B., and
Eklundh, L.: A simple me hod o econs uc ing a high-quali y
NDVI ime-se ies da a se based on he Sa i zky-Golay il e , Re-
mo e Sens. En i on., 91, 332–344, 2004.
Cook, M. V.: The heo y o he longi udinal s a ic s abili y o he
hang-glide , Ae onau . J., 98, 292–304, 1994.
Cook, M. V. and Spo iswoode, M.: Modelling he ligh dynamics
o he hang glide , Ae onau . J., 110, 1–20, 2006.
Coope , W. A. and Roge s, D.: E ec s o ai - low ajec o ies
a ound ai c a on measu emen s o scala luxes, J. A mos.
Ocean. Tech., 8, 66–77, 1991.
C aw o d, T. L. and Dobosy, R. J.: A sensi i e as - esponse p obe
o measu e u bulence and hea - lux om any ai plane, Bound.-
Lay. Me eo ol., 59, 257–278, 1992.
C aw o d, T., Dobosy, R., and Dumas, E.: Ai c a wind measu e-
men conside ing li -induced upwash, Bound.-Lay. Me eo ol.,
80, 79–94, 1996.
Desja dins, R. L., MacPhe son, J. I., Mah , L., Schuepp, P., Pa -
ey, E., Neumann, H., Baldocchi, D., Wo sy, S., Fi zja ald, D.,
McCaughey, H., and Joine , D. W.: Scaling up lux measu e-
men s o he bo eal o es using ai c a - owe combina ions, J.
Geophys. Res., 102, 29125–29133, 1997.
Egge , J., Baj achaya, S., Hein ich, R., Kolb, P., Lammlein, S.,
Mech, M., Reude , J., Schape , W., Shakya, P., Schween, J., and
Wend , H.: Diu nal winds in he Himalayan Kali Gandaki al-
ley, Pa III: Remo ely pilo ed ai c a soundings, Mon. Wea he
Re ., 130, 2042–2058, 2002.
Foken, T.: Tempe a u messungen mi d¨
unnen Pla ind ¨
ah en, Z. Me-
eo ol., 29, 299–307, 1979.
Foken, T. and Wichu a, B.: Tools o quali y assessmen o su ace-
based lux measu emen s, Ag . Fo es Me eo ol., 78, 83–105,
1996.
Ga man, K. E., Hill, K. A., Wyss, P., Ca lsen, M., Zimme -
man, J. R., S i m, B. H., Ca ney, T. Q., San ini, R., and Shep-
son, P. B.: An ai bo ne and wind unnel e alua ion o a wind
u bulence measu emen sys em o ai c a -based lux measu e-
men s, J. A mos. Ocean. Tech., 23, 1696–1708, 2006.
Ga man, K. E., Wyss, P., Ca lsen, M., Zimme man, J. R.,
S i m, B. H., Ca ney, T. Q., San ini, R., and Shepson, P. B.:
The con ibu ion o a iabili y o li -induced upwash o he un-
ce ain y in e ical winds de e mined om an ai c a pla o m,
Bound.-Lay. Me eo ol., 126, 461–476, 2008.
G a on, G. B.: The weigh shi -con olled mic oligh ae oplane,
P oceedings o he Ins i u ion o Mechanical Enginee s Pa G,
J. Ae ospace Eng., 215, 147–154, 2001.
Hobbs, S., Dye , D., Cou aul , D., Olioso, A., Lagoua de, J. P.,
Ke , Y., McAneney, J., and Bonne ond, J.: Su ace laye p o-
iles o ai empe a u e and humidi y measu ed om unmanned
ai c a , Ag onomie, 22, 635–640, 2002.
Junke mann, W.: An ul aligh ai c a as pla o m o esea ch in
he lowe oposphe e: sys em pe o mance and i s esul s om
adia ion ans e s udies in s a i o m ae osol laye s and b oken
cloud condi ions, J. A mos. Ocean. Tech., 18, 934–946, 2001.
Junke mann, W.: The ac inic UV- adia ion budge du ing he ES-
COMPTE campaign 2001: esul s o ai bo ne measu emen s
wi h he mic oligh esea ch ai c a D-MIFU, A mos. Res., 74,
461–475, 2005.
Kaimal, J. and Finnigan, J.: A mosphe ic Bounda y Laye Flows:
Thei S uc u e and Measu emen , Ox o d Uni e si y P ess,
1994.
Kalogi os, J. A. and Wang, Q.: Calib a ion o a adome-di e en ial
GPS sys em on a win o e esea ch ai c a o u bulence mea-
su emen s, J. A mos. Ocean. Tech., 19, 159–171, 2002a.
Kalogi os, J. A. and Wang, Q.: Ae odynamic e ec s on wind u -
bulence measu emen s wi h esea ch ai c a , J. A mos. Ocean.
Tech., 19, 1567–1576, 2002b.
Kheli , D., Bu ns, S. P., and F iehe, C. A.: Imp o ed wind measu e-
men s on esea ch ai c a , J. A mos. Ocean. Tech., 16, 860–875,
1999.
Leise, J. A. and Mas e s, J. M.: Wind measu emen om ai c a ,
Tech. ep., Uni ed S a es Depa men o Comme ce, Na ional
Oceanic and A mosphe ic Adminis a ion, Ai c a Ope a ions
Cen e , MacDill Ai Fo ce Base, 1993.
Lenschow, D. H.: Ai c a measu emen s in he bounda y laye , in:
P obing he A mosphe ic Bounda y Laye , Ame ican Me eo o-
logical Socie y, Bos on, Massachuse s, USA, 39–55, 1986.
Mah , L.: Su ace He e ogenei y and Ve ical S uc u e o he
Bounda y Laye , Bound.-Lay. Me eo ol., 96, 33–62, 2000.
Mah , L., Vicke s, D., and Sun, J.: Spa ial a ia ions o su ace
mois u e lux om ai c a da a, Ad . Wa e Res., 24, 1133–
1141, 2001.
Maude , M., Desja dins, R. L., and MacPhe son, I.: C ea ing su -
ace lux maps om ai bo ne measu emen s: applica ion o he
Mackenzie a ea GEWEX s udy MAGS 1999, Bound.-Lay. Me-
eo ol., 129, 431–450, 2008.
S ein eld, G., Le zel, M. O., Raasch, S., Kanda, M., and Inagaki, A:
Spa ial ep esen a i eness o single owe measu emen s and he
imbalance p oblem wi h eddy-co a iance luxes: esul s o a
la ge-eddy simula ion s udy, Bound.-Lay. Me eo ol., 123, 77–98,
2007.
Tje ns ¨
om, M. and F iehe, C. A.: Analysis o a adome ai -mo ion
sys em on a win-je ai c a o bounda y-laye esea ch, J. A -
mos. Ocean. Tech., 8, 19–40, 1991.
T enkle, F. and Reinha d , M.: In- ligh empe a u e measu emen s,
ol. 2 o Ad iso y G oup o Ae ospace Resea ch and De elop-
men : Fligh Tes Ins umen a ion Se ies, No h A lan ic T ea y
O ganiza ion, Neuilly-su -Seine, F ance, 1973.
an den K oonenbe g, A., Ma in, T., Buschmann, M., Bange, J.,
and Vo smann, P.: Measu ing he wind ec o using he au-
onomous mini ae ial ehicle M2AV, J. A mos. Ocean. Tech., 25,
1969–1982, 2008.
Vicke s, D. and Mah , L.: Quali y con ol and lux sampling p ob-
lems o owe and ai c a da a, J. A mos. Ocean. Tech., 14, 512–
526, 1997.
Visbal,M.R.andShang,J.S.: In es iga iono he low s uc u e
a ound a apidly pi ching ai oil, AIAA J., 27, 1044–1051, 1989.
72 APPENDIX B: METZGER ET AL. (2011)
Williams, A. and Ma co e, D.: Wind measu emen s on a maneu e -
ing win-engine u bop op ai c a accoun ing o low dis o ion,
J. A mos. Ocean. Tech., 17, 795–810, 2000.
Wyngaa d, J. C.: The e ec s o p obe-induced low dis o ion on
a mosphe ic- u bulence measu emen s, J. Appl. Me eo ol., 20,
784–794, 1981.
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) 73
Appendix C: Supplemen o Me zge e al. (2011)
Supplemen o
Me zge , S., Junke mann, W., Bu e bach-Bahl, K., Schmid, H. P., and Foken, T.:
Measu ing he 3-D wind ec o wi h a weigh -shi mic oligh ai c a
I is he in en ion o his supplemen o make anspa en he p ocedu es in he main a icle,
and o guide he eade h ough he ele an calcula ions. Supplemen A p o ides he o mula y
necessa y o compu e he wind ec o om a weigh -shi mic oligh ai c a . A model o p op-
aga e unce ain y h ough he wind ec o equa ions is p o ided in Supplemen B1. Rele an
no a ion and abb e ia ions a e lis ed in Supplemen C. Re e ences o li e a u e a e gi en a he
end o he documen .
Supplemen A Wind measu emen ans o ma ion equa ions
The wind measu emen om ai c a equi es se e al coo dina e sys ems, as well as angles o
ans o m be ween hem (Fig. 2). We define he wind ec o m=( m
u, m
, m
w) in he s anda d
me eo ological coo dina e sys em (MCS, supe sc ip m, posi i e eas wa d, no hwa d, and up-
wa d). Then mcan be calcula ed om na iga ion, flow and a i ude measu emen s: In he
MCS mis exp essed as he ec o di e ence be ween he ai c a ’s g ound speed ec o ( m
gs),
di ec ly measu ed by he ine ial na iga ion sys em (INS), and he ue ai speed ec o ( as
m
),
essen ially measu ed by he fi e hole p obe (5HP, Williams and Ma co e, 2000):
m= m
gs − m
as
= m
gs −Mbm ×Mab(− as)+ b
le .(A1)
Ye he quan i y di ec ly measu ed by he 5HP is he ue ai speed scala as. The second, de-
composed o m o he wind ec o Eq. (A1) indica es ha se e al calcula ion s eps a e necessa y
o a i e a he desi ed ec o quan i y m
as.
74 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011)
In he ollowing we will walk h ough hese successi e s eps, s a ing wi h he 5HP measu e-
men s. F om he po s o he 5HP (Fig. 3) h ee di e en ial p essu es we e measu ed:
pq,A=p −ps,(A2)
pα=p3−p1,and (A3)
pβ=p4−p2.(A4)
Measu ed dynamic p essu e pq,A(subsc ip uppe -case le e s A–G indica e calib a ion s age),
and a ack- and sideslip di e en ial p essu es pα,pβwe e used o calcula e he ai flow angles
(Williams and Ma co e, 2000):
αA=2
9sin(2τ)
pα
pq,A
,and (A5)
βA=2
9sin(2τ)
pβ
pq,A
.(A6)
He e τ=45
◦is he angle be ween he cen al po p and he o he po s p1 h ough p4on he
5HP hal sphe e. Defining he no maliza ion ac o D=1+ an2αA+ an2βA he measu ed
dynamic p essu e pq,Acan be co ec ed o he p essu e d op occu ing a ele a ed ai flow
angles:
pq,B=pq,A9−5D2
4D2−1
.(A7)
Now we can de i e as om he he modynamic measu emen s o he 5HP: Due o s agna ion
a he ip o he 5HP ambien ai is hea ed om i s in insic empe a u e (Ts) o o al empe a u e
(T ). Assuming adiaba ic hea ing, Be noulli’s equa ion
2
as =2cp,h(T −Ts)
=2cp,hTsps
ps+pq−κ
−1,(A8)
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) 75
gi es as as a unc ion o he empe a u e di e ence (Leise and Mas e s, 1993). Since T can
no be measu ed di ec ly, i is subs i u ed in Eq. (A8) by he adiaba ic p ocess ( am ise)
T =Tsps
ps+pq−κ
,(A9)
wi h he Poisson numbe κ=1−c
,h
c
p,h
. Fu he mo e he wind measu emen should be inde-
penden o ai humidi y (subsc ip h). The e o e he specific hea s unde cons an p essu e
(subsc ip p) cp,ho cons an olume (subsc ip ) c ,ho mois ai ha e o be de i ed om
he specific hea cons an s o d y ai (subsc ip d) and wa e apou (subsc ip w), cp,d=
1005 Jkg
−1K−1,cp,w= 1846 Jkg
−1K−1,c ,d= 718 Jkg
−1K−1, and c ,w= 1384 Jkg
−1K−1
(Kheli e al., 1999):
cp,h=cp,d1+qcp,w
cp,d
−1,
c ,h=c ,d1+qc ,w
c ,d
−1,wi h specific humidi y being
q=εe
ps+e(ε−1),(A10)
whe e ε=0.622 is he a io o molecula weigh o wa e apou o ha o d y ai , and eis he
5HP measu ed wa e apou p essu e.
Once de i ed, he scala quan i y as has o be ans o med in o a ec o quan i y. This can
be achie ed by defining he ae odynamic coo dina e sys em (ACS, supe sc ip a, posi i e o -
wa d, s a boa d, and downwa d), which has i s o igin a he 5HP ip. In his coo dina e sys em
he ue ai speed ec o has he componen s a
as =(− as,0,0). Since he ACS is aligned wi h
he s eamlines i s o ien a ion howe e a ies in ime. The e o e a
as is ans o med in o a fixed
coo dina e sys em, ha is he ike body coo dina e sys em (BCS, supe sc ip b, posi i e o -
wa d, s a boa d, and downwa d) wi h i s o igin in he INS. This is accomplished by successi e
o a ions abou he e ical axis Zaand he ans e se axis Ya. Following Lenschow (1986) he
82 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011)
qSpecific humidi y
RRe e ence measu emen
RMSE Roo mean squa e e o
SWing su ace a ea
TTempe a u e
Veloci y scala o ec o componen
Veloci y ec o
x, y, z Dis ances on espec i e coo dina e axes
z
LS abili y pa ame e
αAngle o a ack
βAngle o sideslip
εRa io o molecula masses
ΘPi ch
κPoisson numbe
ΦRoll
ξWing upwash di ec ion
πPe ime e cons an
ρAi densi y
σS anda d de ia ion, RMSE
τAngle be ween cen al and su ounding po s on hal -sphe e
ΨHeading
ΩBody a e
C3 Subsc ip s – supe sc ip s
1–4 P essu e po s
∞F ee ai s eam
+,−In o wind, wi h wind
˜Wind unnel
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) 83
a Ae odynamic coo dina e sys em,
posi i e o wa d, s a boa d, and downwa d
A–G Calib a ion s eps
b Body coo dina e sys em, posi i e o wa d, s a boa d and downwa d
d D y ai
g Geode ic coo dina e sys em, posi i e no hwa d, eas wa d and downwa d
gau Gaussian unce ain y p opaga ion
gs G ound speed
h Humid ai
le Le e a m
m Me eo ological coo dina e sys em,
posi i e eas wa d, no hwa d and upwa d
o O se
q Dynamic-
In e se e e ence
s S a ic-
slo Slope
To al-
as T ue ai speed
u, , w Wind componen s in x, y, z di ec ions
up Upwash
w Wa e apou ; Wing coo dina e sys em,
posi i e o wa d, s a boa d and downwa d
x, y, z S anda d Ca esian coo dina e axes
αAngle o a ack
βAngle o sideslip
84 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011)
C4 Abb e ia ions
5HP Fi e hole p obe
ABL A mosphe ic bounda y laye
ACS Ae odynamic coo dina e sys em,
posi i e o wa d, s a boa d, and downwa d
a.g.l. Abo e g ound le el
a.s.l. Abo e sea le el
BCS Body coo dina e sys em, posi i e o wa d, s a boa d and downwa d
D-MIFU Name o ai c a
DAQ Da a acquisi ion
E Eas
EC Eddy co a iance
EIDAS Embedded Ins i u e o Me eo ology and
Clima e Resea ch da a acquisi ion sys em
FWA Fixed-wing ai c a
GCS Geode ic coo dina e sys em,
posi i e no hwa d, eas wa d and downwa d
INS Ine ial na iga ion sys em
IU Inpu unce ain y
LI Lindenbe g
MCS Me eo ological coo dina e sys em,
posi i e eas wa d, no hwa d and upwa d
N No h
S Sou h
ST Lake S a nbe g
ULS Uni e sal lase senso
VW1–VW3 Ve ical wind specific fligh pa e ns
W Wes
APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011) 85
WCS Wing coo dina e sys em,
posi i e o wa d, s a boa d and downwa d
WSMA Weigh -shi mic oligh ai c a
XI Xilinho
86 APPENDIX C: SUPPLEMENT TO METZGER ET AL. (2011)
Re e ences
ISO: S a is ics – ocabula y and symbols – Pa 1: P obabili y and gene al s a is ical e ms, ol. ISO
3534-1, In e na ional O ganiza ion o S anda diza ion, Gene a, Swi ze land, 1993.
Kheli , D., Bu ns, S. P., and F iehe, C. A.: Imp o ed wind measu emen s on esea ch ai c a , J. A mos.
Ocean. Tech., 16, 860–875, 1999.
Leise, J. A. and Mas e s, J. M.: Wind measu emen om ai c a , Tech. ep., Uni ed S a es Depa men o
Comme ce, Na ional Oceanic and A mosphe ic Adminis a ion, Ai c a Ope a ions Cen e , MacDill
Ai Fo ce Base, 1993.
Lenschow, D. H.: Ai c a measu emen s in he bounda y laye , in: P obing he A mosphe ic Bounda y
Laye , Ame ican Me eo ological Socie y, Bos on, Massachuse s, USA, 39–55, 1986.
Maude , M., Liebe hal, C., G¨
ockede, M., Leps, J. P., Bey ich, F., and Foken, T.: P ocessing and quali y
con ol o flux da a du ing LITFASS-2003, Bound.-Lay. Me eo ol., 121, 67–88, 2006.
Taylo , J. R.: An In oduc ion o E o Analysis: he S udy o Unce ain ies in Physical Measu emen s,
Uni e si y Science Books, Mill Valley, Cali o nia, USA, 2nd edn., 1997.
Vog , S. and Thomas, P.: Soda – a use ul emo e sounde o measu e wind and u bulence, J. Wind Eng.
Ind. Ae od., 54, 163–172, 1995.
V¨
o smann, P.: Ein Bei ag zu Bo dau onomen Windmessung, Ph.D. hesis, Technische Uni e si ¨
a
B aunschweig, 1985.
Williams, A. and Ma co e, D.: Wind measu emen s on a maneu e ing win-engine u bop op ai c a
accoun ing o flow dis o ion, J. A mos. Ocean. Tech., 17, 795–810, 2000.
APPENDIX D: METZGER ET AL. (2012) 87
Appendix D: Me zge e al. (2012)
A mos. Meas. Tech., 5, 1699–1717, 2012
www.a mos-meas- ech.ne /5/1699/2012/
doi:10.5194/am -5-1699-2012
© Au ho (s) 2012. CC A ibu ion 3.0 License.
A mosphe ic
Measu emen
Techniques
Eddy-co a iance lux measu emen s wi h a weigh -shi
mic oligh ai c a
S. Me zge 1,2,3,W.Junke mann
1,M.Maude
1, F. Bey ich4, K. Bu e bach-Bahl1,H.P.Schmid
1,andT.Foken
5
1Ka ls uhe Ins i u e o Technology, Ins i u e o Me eo ology and Clima e Resea ch, A mosphe ic En i onmen al Resea ch,
Ga misch-Pa enki chen, Ge many
2Chinese Academy o Sciences, Ins i u e o A mosphe ic Physics, S a e Key Labo a o y o A mosphe ic Bounda y Laye
Physics and A mosphe ic Chemis y, Beijing, China
3Na ional Ecological Obse a o y Ne wo k, Fundamen al Ins umen Uni , Boulde , USA
4Ge man Me eo ological Se ice, Richa d-Aßmann-Obse a o y, Lindenbe g, Ge many
5Uni e si y o Bay eu h, Depa men o Mic ome eo ology, Bay eu h, Ge many
Co espondence o: W. Junke mann (w[email p o ec ed])
Recei ed: 18 Feb ua y 2012 – Published in A mos. Meas. Tech. Discuss.: 30 Ma ch 2012
Re ised: 17 June 2012 – Accep ed: 18 June 2012 – Published: 19 July 2012
Abs ac . The objec i e o his s udy is o assess he ea-
sibili y and quali y o eddy-co a iance lux measu emen s
om a weigh -shi mic oligh ai c a (WSMA). Fi s ly,
we in es iga e he p ecision o he wind measu emen
(σu, ≤0.09 m s−1,σw=0.04 ms−1), he lynchpin o lux
calcula ions om ai c a . F om he e, he smalles esol -
able changes in ic ion eloci y (0.02 m s−1), and sensible-
(5 W m−2) and la en (3 W m−2) hea lux a e es ima ed.
Secondly, a se en-day ligh campaign was pe o med nea
Lindenbe g (Ge many). He e we compa e measu emen s o
wind, empe a u e, humidi y and espec i e luxes be ween
a all owe and he WSMA. The maximum likelihood unc-
ional ela ionship (MLFR) be ween owe and WSMA mea-
su emen s conside s he andom e o in he da a, and shows
e y good ag eemen o he scala a e ages. The MLFRs o
s anda d de ia ions (SDs, 2–34 %) and luxes (17–21 %) in-
dica e highe es ima es o he ai bo ne measu emen s com-
pa ed o he owe . Conside ing he 99.5 % con idence in e -
als, he obse ed di e ences a e no signi ican , wi h excep-
ion o he empe a u e SD. The compa ison wi h a la ge-
ape u e scin illome e e eals lowe sensible hea lux es-
ima es a bo h owe (−40 o −25 %) and WSMA (−25–
0 %). We ela e he obse ed di e ences o (i) inconsis en-
cies in he empe a u e and wind measu emen a he owe
and (ii) he measu emen pla o ms’ di e ing abili ies o cap-
u e con ibu ions om non-p opaga ing eddies. These ind-
ings encou age he use o WSMA as a low cos and highly
e sa ile lux measu emen pla o m.
1 In oduc ion
Ene gy and ma e luxes be ween he Ea h’s su ace and
he a mosphe e can be de e mined using he eddy-co a iance
(EC) me hod. This me hod is based on he Reynolds de-
composi ion o he Na ie -S okes equa ion, and i assumes
s eady s a e condi ions and ho izon al homogenei y (e.g.
Kaimal and Finnigan, 1994). Ne e heless, he EC me hod
is equen ly used in complex e ain, o which applicabil-
i y is subjec o on-going esea ch (e.g. Foken e al., 2010;
G¨
ockede e al., 2008). In pa icula , i is assumed ha he
mean e ical wind app oaches ze o o a su icien ly long
a e aging in e al. This equi emen is mo e likely ul illed
by spa ial han by empo al measu emen s, because spa ial
measu emen s enable egis e ing a mosphe ic mo ions on
la ge scales (e.g. Mah , 2010). Unde condi ions o negli-
gible ad ec ion and ho izon al lux di e gence, he o al e -
ical lux is hen in e ed om he co a iance be ween he
e ical wind and he scala o in e es (e.g. empe a u e, hu-
midi y).
G ound-based measu emen s o u bulen luxes a e o lo-
cal cha ac e and a e he e o e no necessa ily ep esen a-
i e o hei g ea e su oundings, especially in complex e -
ain (e.g. Desja dins e al., 1997; Isaac e al., 2004b; Mah ,
2010). The spa ial gap be ween in-si u obse a ions, sa el-
li e obse a ions and modelled da a needs o be conside ed
as one plausible explana ion o hei equen ly obse ed
misma ch (e.g. Kanda e al., 2004; Lu e al., 2005). He e
88 APPENDIX D: METZGER ET AL. (2012)
p ocess s udies wi h ai bo ne pla o ms p o ide a aluable
link o unde s and and b idge scale disc epancies (e.g. Bange
e al., 2002; Da is e al., 1992; Hiyama e al., 2007; Isaac
e al., 2004a). A he same ime, ixed-wing ai c a and heli-
cop e s a e expensi e o ope a e o no applicable in se ings
such as emo e a eas beyond he ange o an ai ield. Un-
manned ae ial ehicles on he o he hand p o ide mobili y,
ye do no allow a comp ehensi e senso package due o pay-
load es ic ions (e.g. Egge e al., 2002; Hobbs e al., 2002;
Ma in e al., 2011; Thomas e al., 2012). He e he weigh -
shi mic oligh ai c a (WSMA) can p o ide an al e na i e
a low cos -, anspo - and in as uc u al demand. A e suc-
cess ully applying a WSMA o ae osol and adia ion ans-
e s udies (Junke mann, 2001, 2005), Me zge e al. (2011)
showed ha ca e ully compu ed wind measu emen s om
WSMA a e no in e io o hose om o he ai bo ne pla -
o ms. On his basis, he easibili y o EC lux measu emen s
om WSMA in he a mosphe ic bounda y laye (ABL) is ex-
plo ed in his s udy. The o e a ching pe spec i e is o wo k
owa ds an ai bo ne pla o m ha allows cha ac e ising com-
plex e ain in emo e a eas, including he measu emen o
egional u bulen luxes.
Con ibu ions o he EC lux measu emen o igina e om
u bulen a mosphe ic mo ions on a a ie y o wa eleng hs
and ampli udes. In o de o eliably es ima e he o al lux,
he luc ua ions o he e ical wind and he scala s mus
be measu ed wi h high accu acy and p ecision. Fu he mo e,
he ins umen a ion and da a acquisi ion mus possess a sui -
able equency esponse and sampling a e. In he case o
ai bo ne measu emen s, he ca ie can addi ionally in lu-
ence he spec al quali y o he measu emen . The e o e,
he p esen s udy commences wi h (i) an assessmen o he
measu emen e o s. To e alua e he sys em pe o mance,
we (ii) compa e spec al p ope ies, a e ages, de ia ions and
luxes be ween WSMA and owe -based EC measu emen s.
The analysis con inues wi h (iii) a s udy o he measu e-
men s’ spa ial con ex , which is in e ed om oo p in mod-
elling. The (i ) compa ison o a la ge-ape u e scin illome-
e (LAS) b ings o a en ion he e ec o la ge -scale a mo-
sphe ic mo ions on he esul s and comple es he s udy.
2 Ma e ials and me hods
2.1 The weigh -shi mic oligh ai c a
The s uc u e o a WSMA di e s om common ixed-wing
ai c a : i consis s o wo dis inc pa s, he wing and he
ike, which hangs below he wing and con ains he pilo , en-
gine and he majo i y o he scien i ic equipmen . This pa -
icula s uc u e p o ides he WSMA wi h excep ional ans-
po abili y and climb a e, which quali ies i o applica ions
in complex and inaccessible e ain. A de ailed desc ip ion
o he physical p ope ies o he WSMA used in his s udy
as well as cha ac e is ics and manu ac u e s o senso s and
da a acquisi ion is gi en in Me zge e al. (2011). In sho ,
mos a iables a e sampled a 100 Hz and a e block-a e aged
and s o ed a 10 Hz, yielding a ho izon al esolu ion o ap-
p oxima ely 2.5 m. To conduc as wind measu emen s, he
WSMA is ou i ed wi h a combina ion o global posi ion-
ing sys em and ine ial measu emen uni (GPS/IMU), and a
i e-hole p essu e p obe (5HP). The p inciple is o esol e
he me eo ological wind ec o om he ec o di e ence
o he ai c a ’s ine ial eloci y (cap u ed by he GPS/IMU)
and he wind ec o ela i e o he ai c a (cap u ed by he
5HP). The s uc u al ea u es o he WSMA also in luence
he wind measu emen : (i) he wing de o ms ae oelas ically
wi h ai c a im, and (ii) he ike is ee o o a e in pi ch
and oll agains he wing. Me zge e al. (2011) p esen a ime
domain p ocedu e which ea s he impac o he WSMA’s
s uc u al ea u es as well as pilo inpu on he wind mea-
su emen . The emaining maximum de ia ion o he e i-
cal wind componen is 0.15 m s
−1
du ing se e e e ical ma-
noeu es. A ypical ai speeds be ween 23–30 m s
−1
, simul-
aneous wind measu emen s om WSMA and g ound-based
ins umen a ion ag ee wi hin 0.3 m s
−1
o he e ical and
wi hin 0.4 m s
−1
o he ho izon al componen s ( oo mean
squa e e o ). The p esen s udy in es iga es he po en ial in-
luence o esonance om he WSMA’s engine o p opelle ,
o om he na u al equencies o ike and wing, on he wind
measu emen . Fo his pu pose, accele a ion measu emen s
in he hang poin o ike and wing, in he global posi ioning
sys em/ine ial measu emen uni and in he i e-hole p obe,
a e used. The accele a ion measu emen in he hang poin is
ans o med o he ike coo dina e sys em. A 100 Hz da ase
consis ing o ≈3×10
5
da a poin s sampled du ing a le el
long-dis ance ligh on 31 July 2009 (Me zge e al., 2011,
Table 3) is used o he assessmen .
Ai empe a u e is measu ed wi h a 50 μm he mocouple.
The empe a u e e o in oduced by in e mi en sola adi-
a ion a he unshielded he mocouple is <0.05 K a nomi-
nal ue ai speed (Me zge e al., 2011). An OP2 in a ed gas
analyse (IRGA, ADC Bioscien i ic, G ea Amwell, UK) is
used o measu e he concen a ion o wa e apou . The in-
s umen esponse o bo h he he mocouple and he IRGA
is 50 Hz. In addi ion, a slow (2 Hz ins umen esponse) hu-
midi y e e ence om a TP3 dew poin mi o (Me eolabo
AG, We zikon, Swi ze land) is s o ed a ≥0.1 Hz. Ve ical
p o ile ligh s e ealed a dependence o he IRGA measu e-
men s on ligh al i ude. This dependence was ela ed o a
mal unc ioning empe a u e compensa ion o he ligh sou ce
as well as ai pe meabili y o he ligh chambe . F om mea-
su emen s o calib a ion gases in a clima e chambe , he em-
pe a u e compensa ion is upda ed in pos -p ocessing. Simila
measu emen s we e conduc ed in a p essu e chambe o de-
e mine he ime cons an o he ligh chambe pe meabili y
(≈60 s o 1500 m o ho izon al ligh ). In o de o co ec
he pe meabili y e ec , a hi d-o de Sa i zky-Golay com-
plemen a y il e (Chen e al., 2004) is used. The complemen-
a y il e co ec s o he IRGA’s d i by basing he humidi y
APPENDIX D: METZGER ET AL. (2012) 89
luc ua ions measu ed by he IRGA on he slow dew poin
mi o e e ence. A window size o 13.9 s o ≈350 m max-
imises he in eg al o e he humidi y powe spec um, and is
used o co ec he measu emen s.
In he p esen s udy, also he in luence o measu emen
p ecision on he eddy-co a iance lux esul s is in es iga ed.
Fo his pu pose, we ollow Ga man e al. (2006) and de ine
measu emen p ecision as 1 σ epea abili y. The p ecision o
all a iables en e ing he EC lux calcula ion is p esen ed in
Table 1. In he case o he GPS/IMU, p ecision o igina es
om Kalman il e ou pu s, and in he case o he 5HP, i
is calcula ed om labo a o y and wind unnel measu emen s
(Me zge e al., 2011).
2.2 Field campaign
A compa ison be ween he ai bo ne WSMA and g ound-
based measu emen s was ca ied ou du ing a ligh cam-
paign be ween 14 and 21 Oc obe 2008. This expe imen was
pe o med a ound he bounda y laye ield si e Falkenbe g
(52.2
◦
N, 14.1
◦
E) o he Ge man Me eo ological Se ice
(DWD), Richa d-Aßmann Obse a o y, Lindenbe g, Ge -
many. This ield si e lies in he basically la No h Ge -
man Plain, and he e ain heigh a ies be ween 40 m and
130 m abo e sea le el (a.s.l.) wi hin an a ea o 20 ×20 km
2
.
To cha ac e ize su ace he e ogenei y, we use he Co ine
Land Co e 2006 da a wi h a ho izon al esolu ion o 100 m
(Ve sion 13, Eu opean En i onmen Agency, 2010). The
a able land was ha es ed be o e he s udy pe iod, and, con-
sequen ly, he su ace p ope ies di e ed mainly be ween
bu no wi hin landscape uni s. We hus eg ouped he 28
Co ine Land Co e ac ions in he s udy a ea in o i e land-
scape uni s, he eby educing unnecessa y sca e (Figs. 7
and 9). The esul ing ep esen a ion o he landscape a ound
he Falkenbe g si e (20 ×20 km
2
) is domina ed by ag icul-
u e (47 %) and o es s (38 %), in e spe sed by equal amoun s
(5 %) o lakes, meadows and se lemen s.
A ull cha ac e isa ion o he Falkenbe g si e and i s in-
s umen a ion is p esen ed by Bey ich and Adam (2007).
Da a om an ins umen ed 99 m owe a e used o he com-
pa ison o he WSMA measu emen s. Sonic anemome e s
(USA-1 – Me ek GmbH, Elmsho n, Ge many) as well as
open pa h IRGAs (LI-7500 – LI-COR Biosciences, Lincoln,
USA) we e ins alled a 50 m and 90 m abo e g ound le el
(a.g.l.). These ins umen s sampled he wind ec o , sonic
empe a u e and humidi y a a a e o 20 Hz, enabling EC
lux compu a ion. Fo he USA-1, he manu ac u e ’s 2-D
low dis o ion co ec ion was ope a ionally applied o he
wind ec o measu emen . These da a a e used o he com-
pa ison o he a e age wind as well as a iances, co a iances
and powe spec a be ween he WSMA and he owe . The
owe was u he equipped wi h p o ile measu emen s o
empe a u e (HMP-45 – Vaisala Oy, Helsinki, Finland) and
humidi y (F ankenbe ge Psych ome e – Theodo F ied ichs
GmbH, Hambu g, Ge many) a 40, 60, 80, and 98 m a.g.l.
Table 1. Measu emen p ecision o global posi ioning sys-
em/ine ial measu emen uni (GPS/IMU), i e-hole p obe (5HP),
he mocouple, and in a ed gas analyze (IRGA).
Quan i y P ecision
Heading (GPS/IMU) 0.1
◦
Pi ch, Roll (GPS/IMU) 0.04
◦
3-D eloci y (GPS/IMU) 0.02 m s
−1
3-D angula a e (GPS/IMU) 0.01
◦
s
−1
3-D accele a ion (GPS/IMU) 0.01 m s
−2
A ack angle (5HP) 0.08
◦
Sideslip angle (5HP) 0.18
◦
T ue ai speed (5HP) 0.05 m s
−1
Tempe a u e ( he mocouple) 0.04 K
Humidi y (IRGA) 0.005 g m
−3
The p o iles a e in e pola ed o he heigh s o he EC in-
s alla ions and a e used o compa e a e age empe a u e
and humidi y be ween owe and WSMA. A s a ic p essu e
measu emen (PTB220A – Vaisala Oy, Helsinki, Finland) a
74 m a.s.l. is ex apola ed o he heigh s o he owe EC in-
s alla ions using he hypsome ic equa ion. I is used o he
con e sion o he owe EC luxes om kinema ic uni s o
uni s o ene gy. Towe p o ile and p essu e da a we e a e -
aged and s o ed in 10 min in e als.
Iden ical ins umen a ion as on he owe was used o an
addi ional EC su ace lux measu emen upwind (sou h) o
he owe base, a 2.4 m a.g.l. The hal -hou ly sensible hea
lux was de e mined om his measu emen as an ope a-
ional p oduc o he DWD. Global adia ion was measu ed
a 2 m using a CM24 py anome e /albedome e (Kipp and
Zonen, Del , The Ne he lands) and s o ed as 10 min a e -
ages. Also 10 min a ea-a e aged su ace sensible hea luxes
we e de i ed om a la ge-ape u e scin illome e . A an e -
ec i e beam heigh o 43 m a.g.l., he nea -in a ed LAS uns
along a pa h leng h o 4.7 km (Fig. 9). The LAS was de el-
oped and buil by he Me eo ology and Ai Quali y G oup o
he Wageningen Uni e si y; echnical de ails a e p esen ed
in Meijninge e al. (2006). Fu he mo e, hou ly es ima es o
he ABL dep h we e de i ed om sonic de ec ion and ang-
ing and wind p o ile da a, and om six-hou ly ou ine adio
soundings pe o med by he DWD. The su ace sensible hea
luxes measu ed a he 2.4 m EC and he LAS a e used in con-
junc ion wi h he ABL dep hs o app oxima e e ical lux
p o iles. Simul aneous WSMA measu emen s o he sensible
hea lux a e compa ed o hese lux p o iles.
In he cou se o he ligh campaign, he a mosphe ic con-
di ions changed om e y weak o s ong u bulen mixing.
The cloud co e (09:00 o 15:00 UTC) dec eased om 8/8 o
4/8, and he maximum a ailable global adia ion inc eased
om 280 W m
−2
a he beginning o 460 W m
−2
a he end
o he campaign. Also he wind speed inc eased om 2 m s
−1
o 10 m s
−1
a he 50 m owe le el, wi h he wind di ec ion
90 APPENDIX D: METZGER ET AL. (2012)
changing om wes o sou h. The anges o he su ace
sensible and he la en hea luxes we e 0–100 W m
−2
and
0–200 W m
−2
, espec i ely. The sensible hea lux sligh ly
inc eased in he cou se o he campaign, while he la en
hea lux emained app oxima ely compa able h oughou he
ligh days. Also he maximum ABL dep h inc eased om
250 m o 1150 m in he cou se o he campaign. The a mo-
sphe ic s a i ica ion was neu al o uns able, wi h he median
o he s abili y pa ame e z/L =−0.18 ±0.21 om WSMA
and −0.14 ±0.29 om owe measu emen s.
2.3 Da a p ocessing
Eddy-co a iance da a we e pos -p ocessed analogously o
he 99 m owe and o he WSMA u bulence measu emen s.
The so wa e package TK3 (Maude and Foken, 2011) was
used o p ocess he owe EC da a, applying he aw da a
ea men s and lux co ec ions as pu o wa d in Foken
e al. (2012). (i) The aw da a we e sc eened o spikes us-
ing he algo i hm o Hojs up (1993). Visual inspec ion e-
ealed ha neighbou ing spikes in he IRGA da a we e no
de ec ed by he algo i hm. The o iginal algo i hm uses a -
e age and s anda d de ia ion c i e ia wi h low b eak down
poin s o small sample sizes (Rousseeuw and Ve bo en,
2002). A e subs i u ing he c i e ia wi h he median and
he median absolu e de ia ion, he spikes we e e icien ly e-
mo ed. (ii) The ime delay due o sepa a ion be ween he e -
ical wind measu emen and adjacen senso s was de e mined
and co ec ed by maximizing hei lagged co ela ion. (iii) To
co ec o po en ial misalignmen , he USA-1 wind mea-
su emen was o a ed in o he s eamline coo dina e sys em
using he plana - i me hod by Wilczak e al. (2001). (i ) The
empe a u e a iance as well as he sensible hea lux was cal-
cula ed using he c osswind co ec ion by Liu e al. (2001).
( ) The o mula ions by Webb e al. (1980) we e used o co -
ec he la en hea lux o densi y luc ua ions.
To handle he WSMA da a, an analysis package wi h sim-
ila p ocessing s eps was de eloped in GNU R e sion 2.13
(R De elopmen Co e Team, 2011), which is a ailable upon
eques . Se e al o enamed co ec ions a e no applicable o
he WSMA measu emen and we e omi ed: (iii) he ai c a
e ical wind is al eady de ined in geode ic no mal, which is
pe pendicula o he spa ial a e age o he s eamlines, and
(i ) he ai empe a u e is di ec ly measu ed by he he mo-
couple. The sensi i i y o he WSMA measu ed luxes on
he emaining co ec ions was es ed o a ligh in he con-
ec i e bounda y laye (z/L =−0.8) a 50 m a.g.l. No spikes
we e p esen in his da ase , and consequen ly he spike elim-
ina ion (i) had no in luence on he esul s. The co ec ions
o ime delay (ii), high equency spec al loss (Moo e,
1986) and densi y luc ua ions ( ) only a ec ed he la en
hea lux. The median di e ences be ween applying and ne-
glec ing hese co ec ions we e in he o de o 5 %, 1 % and
20 %, espec i ely, which is in ag eemen wi h he indings o
Maude and Foken (2006). In he ollowing, he co ec ion
o high equency loss due o senso sepa a ion is no ap-
plied because i s in luence is negligible a measu ing heigh s
≥50 m. The luxes compu ed om bo h so wa e packages
we e compa ed using eg ession analysis and showed pe ec
ag eemen wi h uni y slope. Consequen ly, compa abili y is
ensu ed when calcula ing luxes om owe and WSMA pla -
o ms wi h hei espec i e so wa e packages.
2.4 E alua ion s a egy
2.4.1 P opaga ion o senso e o s
The eddy-co a iance echnique elies upon he p ecise mea-
su emen o luc ua ions o a mosphe ic quan i ies, based on
negligible senso d i h oughou an a e aging pe iod. Ou
in en ion is o e alua e whe he senso p ecision and d i a-
cili a e he use o he weigh -shi mic oligh ai c a as u -
bulence measu emen pla o m. Measu ed om ai c a , he
de e mina ion o he wind ec o equi es a sequence o he -
modynamic and igonome ic equa ions (e.g. Me zge e al.,
2011). These equa ions p opaga e a ious sou ces o e o ,
and a e consequen ly he lynchpin o EC lux measu emen s
om ai c a . He e we p opaga e known senso p ecisions
o a mosphe ic quan i ies, which yields he minimum esol -
able change in he associa ed luxes. The ea e , he maxi-
mum achie able a e aging pe iod o he lux calcula ion is
de e mined as a unc ion o senso d i .
2.4.2 Spec al p ope ies o he ai c a
As opposed o g ound-based measu emen s, he weigh -shi
mic oligh ai c a is subjec o se e al simul aneous mo-
ions, such as locomo ion, engine and p opelle o a ion. Ou
in en ion is o assess i and o wha ex en he WSMA’s mo-
ions in luence he wind measu emen . Fo his pu pose, a
spec al analysis was ca ied ou by as Fou ie ans o ma-
ion o accele a ion measu emen s in he hang poin o ike
and wing, in he global posi ioning sys em/ine ial measu e-
men uni and in he i e-hole p obe. We p esen powe spec-
a ep esen a i e o hese s uc u al pa s o he WSMA and
in e p e he spec al beha iou in he con ex o he wind
measu emen .
2.4.3 Compa ison be ween owe and ai c a
measu emen s
Measu emen s wi h he weigh -shi mic oligh ai c a we e
conduc ed along a c oss-shaped pa e n wi hin 1.5 km ho i-
zon al dis ance o he all owe om 15 o 18 Oc obe 2008
(Fig. 7). A o al o 36 ligh s o 3 km leng h o ≈120 s du a-
ion a e compa ed o simul aneous owe measu emen s. The
WSMA was a elling a wo di e en ai speeds, 24 m s
−1
and 27 m s
−1
, and was lying wi hin 0.5±5.3 m al i ude o
he co esponding ins alla ions on he owe . The WSMA
empe a u e and densi ies we e ans o med o po en ial
quan i ies a he espec i e owe heigh . The objec i e o he
APPENDIX D: METZGER ET AL. (2012) 91
compa ison is o assess he quali y o he WSMA measu e-
men , wi h ocus on he EC lux. The objec i e is no o quan-
i y he ac ual exchange be ween su ace and a mosphe e.
The compa a i ely sho ligh legs a e he e o e a comp o-
miseo samplesize(≈1200 da a poin s om WSMA) and
icini y o he measu emen pla o ms.
Di e ing spec al con ibu ions can lead o a sys ema ic
bias in he lux es ima es be ween he pla o ms. To ensu e
equal con ibu ions om he long wa e pa o he spec um,
we cons ain he a e aging pe iods o he same no malized
equency. The owe a e aging pe iod τ
ow
=τ
ai
·
as
/|u w|
hen esul s om he ligh du a ion o one leg τ
ai
and he
a io o ai speed
as
o he module o he wind ec o |u w|.
Fo τ
ai
≈120 s and he a io
as
/|u w|≈5, he app op ia e
owe a e aging pe iod is τ
ow
≈600 s o 10 min. Using his
a e aging pe iod, he owe esul s we e calcula ed a inc e-
men s o 1 min. The WSMA was mo e equen ly a elling
upwind (180 ±720 m median di e ence) han downwind o
he owe .Inawindowo ±10 inc emen s, he owe esul
was chosen ha minimized he sca e ( oo mean squa e e -
o ) be ween all lux measu emen s o bo h pla o ms. This
allows aking in o accoun ad ec ion be ween he pla o ms,
as well as po en ial iming di e ences o he da a acqui-
si ion sys ems. Bes ag eemen was eached o a shi o
2±6 inc emen s, co esponding o an upwind dis ance o
600 ±1800 m o an ai mass a elling a 5 m s
−1
.
In o de o de ec sys ema ic di e ences be ween owe
and WSMA measu emen s, a eg ession-like analysis was
applied o all 36 ligh s. Simple leas -squa es eg ession is
s ic ly applicable only when one measu emen is wi hou
e o (Lindley, 1947). This howe e is no he case o he
measu emen s in ou s udy, which a e subjec o unce ain ies
such as andom s a is ical e o . Ins ead, we use maximum-
likelihood i ing o a unc ional ela ionship (MLFR, Ripley
and Thompson, 1987). This me hod assigns a weigh o each
da a couple in he ela ionship, which is in e sely p opo -
ional o i s e o a iances. In ou case, he squa ed andom
s a is ical e o s in he owe and WSMA measu emen s a e
used, which app ecia es eliable da a and dep ecia es unce -
ain da a couples. These e o s a e in e ed om he in eg al
leng h scales o he WSMA measu emen s (Appendix A),
and de ine an inne and an ou e scale o con idence in he
compa ison. The e o s in he MLFR coe icien s a e de e -
mined om a jackkni e es ima o (Quenouille, 1956; Tukey,
1958). Since he eg ession in e cep s we e no signi ican ,
he ela ionships we e o ced h ough he o igin, and con i-
dence in e als we e de e mined om he slope e o . The
coe icien o de e mina ion R
2
was calcula ed in analogy
o weigh ed leas -squa es eg ession (K alse h, 1985; Wil-
le and Singe , 1988). I is he p opo ion o a ia ion in
weigh ed Y ha can be accoun ed o by weigh ed X. Finally,
he esidual s anda d e o is de e mined using Eq. (A4).
2.4.4 Spa ial analysis
We use oo p in modelling in o de o assess he spa ial con-
ex o measu emen s. Fo his pu pose, he along-wind oo -
p in pa ame e iza ion o Kljun e al. (2004) was combined
wi h a sui able c osswind dis ibu ion (Appendix B). The e-
sul ing model is compu a ionally as , conside s 3-D dispe -
sion and is applicable beyond he a mosphe ic su ace laye .
We compa e he o e lap o he owe and WSMA oo p in s
as well as he con ibu ion o di e en land co e s o he mea-
su emen s.
2.4.5 Compa ison wi h la ge-ape u e scin illome e
In addi ion o owe - and ai c a -based eddy-co a iance
measu emen s, we also include sensible hea lux es ima es
om he la ge-ape u e scin illome e in he compa ison. On
seasonal a e age, LAS measu es 10–20 % highe alues o
he sensible hea lux compa ed o owe EC measu emen s
(e.g. Liu e al., 2011; Meijninge e al., 2006). In pa icu-
la abo e he e ogeneous e ain, he cap u e o ele a ed, non-
p opaga ing eddies (NPE) by he LAS, bu no by he owe
EC, is discussed as a po en ial eason o he obse ed di -
e ences (Foken e al., 2010). In his espec , he spa ially a -
e aged EC measu emen om WSMA is simila o he LAS.
Consequen ly, he objec i e o he compa ison wi h LAS is
o aid he in e p e a ion o sys ema ic di e ences be ween
he spa ially (ai c a ) and empo ally ( owe ) a e aged EC
measu emen s. On 20 and 21 Oc obe 2008, wo ligh s o
4.7 km leng h o ≈150 s du a ion we e conduc ed ≈1km o
he eas o , and pa allel o he LAS measu ing pa h (Fig. 9).
The du a ion o he WSMA ligh ansla es o ≈750 s o
12.5 min a e aging in e al a he 50 m and 90 m le els o he
owe . Ne e heless, he owe lux measu emen s a e a e -
aged o e 10 min, iden ical o Sec . 2.4.3. Fo longe a e ag-
ing in e als, he ime se ies became inc easingly ins a ion-
a yon21Oc obe 2008,and he lux magni ude dec eased.
WSMA empe a u e and densi y measu emen s we e ans-
o med o po en ial quan i ies a he mean ligh al i ude, i.e.
108 m and 119 m a.g.l. on 20 and 21 Oc obe 2008, espec-
i ely. Using bounda y laye scaling, he esul s om LAS
and WSMA a e compa ed o simul aneous owe EC mea-
su emen s a 2.4 m, 50 m and 90 m a.g.l., which a e loca ed
a he LAS ansmi e si e.
3Resul s
3.1 P opaga ion o senso e o s
In he i s pa o his sec ion, we assess he WSMA’s mea-
su emen p ecision and i s impac on EC lux measu emen s
o e sho ligh legs. In he second pa , we e alua e he max-
imum lux a e aging pe iod acili a ed by he d i (accu acy)
o he senso s.
98 APPENDIX D: METZGER ET AL. (2012)
Fig. 8. Ve ical p o ile o he sensible hea lux du ing wo ligh s:
20 Oc obe 2008, 10:53–10:55 UTC ( ed) and 21 Oc obe 2008,
09:56–09:59 UTC (blue). Hea luxes a e compa ed be ween la ge-
ape u e scin illome e (LAS), owe eddy co a iance a 2.4 m, 50 m
and 90 m (TOW02, TOW50, TOW90) and he weigh -shi mic o-
ligh ai c a (WSMA). Whe e a ailable, e o ba s show he an-
dom s a is ical e o and he al i ude s anda d de ia ion. Addi ional
in o ma ion is gi en in he ex .
4 Discussion
The p opaga ion o senso e o s enables de ining he mini-
mum change in an a mosphe ic quan i y ha can be eliably
esol ed by he WSMA measu emen s o espec i e a i-
ables. Fo he wind measu emen , his coincides wi h he
lowe ma gin o he s anda d de ia ions obse ed a bo h
owe and WSMA (Fig. 4). We hus conclude ha he p e-
cision o he wind measu emen wa an s eddy-co a iance
lux measu emen s unde uns able o sligh ly s able s a i i-
ca ions. The p ecision o he e ical wind is be e by a ac-
o o wo compa ed o he ho izon al wind componen s. This
can be aced back o he be e p ecision o he a ack- and
pi ch (≤0.08
◦
) angles compa ed o he sideslip- and head-
ing (≤0.18
◦
) angles. F om he assessmen o senso accu a-
cies, we ound ha he wind and scala measu emen s acili-
a e he signal le els equi ed o he esolu ion o mesoscale
ABL s uc u es. This enables ex ending a e aging in e als
and spec al analyses up o a scale o ens o kilome es.
The ocus o his s udy is on he compa ison o u bu-
lence s a is ics be ween weigh -shi mic oligh ai c a and
owe measu emen s. A po en ial sou ce o unce ain y is
he low dis o ion co ec ion o he USA-1 sonic anemome-
e s used a he all owe . Two di e en co ec ions a e p o-
ided by he manu ac u e , o which he “milde ” 2-D e sion
was used in he ope a ional se up o he DWD. A pos p o-
cessing compa ison o he p esen ed owe da a shows ha
he 3-D e sion would lead o a sys ema ic inc ease in he
wind SDs by ≈35 %, and in he luxes by ≈15 %. F om in-
s umen compa ison, he 2-D co ec ion seems o be mo e
Fig. 9. Foo p in e ec le els o he measu emen s om Fig. 8 on
20 Oc obe 2008 (A) and 21 Oc obe 2008 (B), p esen ed simila ly
o Fig. 7. In addi ion, he weigh ed oo p in along he LAS pa h
is shown ( ed), and he oo p in s om he owe measu emen s a
50 m (black) and 90 m (yellow) a e dis inguished.
app op ia e. Howe e , i mus be no ed ha he magni ude o
his co ec ion alone is in he o de o he di e ences in he
wind SDs and he luxes obse ed be ween he owe and he
WSMA. Longe a e aging in e als a he owe o de end-
ing o he WSMA da a did no change he gene al beha iou ,
bu inc eased he sca e in he compa ison. Mo eo e , e i-
cal lux di e gence can be uled ou as po en ial e o sou ce,
since he measu emen s we e conduc ed a app oxima ely he
same al i ude abo e g ound. Also, al i ude luc ua ions by he
WSMA we e accoun ed o by using po en ial quan i ies o
empe a u e and densi ies a he owe p essu e le el. In he
ollowing, we consequen ly ocus on he e ec s o spec al
a i ac s and su ace he e ogenei y.
Du ing he in es iga ion o he WSMA spec al p ope ies,
a scale disc epancy was de ec ed be ween accele a ions ac -
ing a he i e-hole p obe and hei accoun ing in he global
posi ioning sys em/ine ial measu emen uni , i.e. he wind
compu a ion (Fig. 1). No emnan s o his scale disc epancy
a e e iden in he wind measu emen s, in pa icula be ween
1–5 Hz. This leads o he conclusions ha (i) he wind ec o
compu a ion co ec ly accoun s o he displacemen o 5HP
and GPS/IMU, and (ii) he cause o enhanced 5HP accele a-
ion measu emen s (especially longi udinal o he body) lies
in he ix u e o he accele a ion senso in he 5HP, a he
han in he moun ing o he 5HP agains he GPS/IMU. The
spec al peak in he WSMA e ical and s eamwise wind
componen s (Fig. 3) coincides wi h he wing’s na u al e-
quency a ound 0.7 Hz (Sec . 3.2). A less p onounced peak
be ween 0.15–0.4 Hz in he ans e se wind componen co-
incides only wi h a peak in e ical accele a ions (Fig. 1).
Bo h spec al ea u es can po en ially be associa ed wi h he
ea men o wing upwash in he ime domain, bu no in
he equency domain (Me zge e al., 2011). The WSMA
wind and lux measu emen s we e co ec ed o his spec al
inconsis ency be o e compa ing hem o g ound-based mea-
su emen s. The app op ia e co ec ion ac o s we e es ima ed
APPENDIX D: METZGER ET AL. (2012) 99
om he compa ison o measu ed spec a and cospec a o
modelled ones.
Because o la ge sca e in he momen um lux cospec a
a he owe , no ensemble was calcula ed. We specula e ha
he sca e o igina es om he wind di ec ion-dependen co -
ela ion o he ho izon al and e ical wind componen s a
he USA-1 sonic anemome e s (e.g. Maude e al., 2007b).
The e oneous sonic empe a u e spec um indica es p ob-
lems wi h he measu emen o he empe a u e SD and he
sensible hea lux a he owe . The ampli ude esolu ion
es by Vicke s and Mah (1997) would ejec 28 ou o 36
owe sonic empe a u e da a se s. The p oblem was ela ed
o he insu icien sonic empe a u e esolu ion (0.01 K) o
he USA-1, which appea s as supe icial spec al ene gy in
he o m o high- equency whi e noise. Spec al co ec ion
ac o s analogous o he WSMA measu emen s we e used in
an a emp o co ec he sys ema ic o e es ima ion o he
empe a u e SD. Such a p ocedu e changes he maximum
likelihood unc ional ela ionship be ween owe and ai c a
empe a u e SD om −9 % unde es ima ion o 34 % o e -
es ima ion o he WSMA measu emen . A he same ime,
he esidual s anda d e o in he MLFR inc eases om 9 %
o 17 %. The sca e ing can be supp essed by ejec ing da a
poin s wi h weak empe a u e SD (<0.05 K), esul ing in a
educed o e es ima ion o 15 % o he WSMA measu emen .
Consequen ly, he USA-1 measu emen s canno be ega ded
as eliable e e ence o he empe a u e SD, and he spec-
al co ec ion ac o s mus be in e p e ed wi h cau ion. The
p oblem is less p onounced o he sensible hea lux. The
whi e noise in he USA-1 sonic empe a u e measu emen
does no a ec he measu emen o , o he co ela ion wi h,
he e ical wind measu emen . The esul is a modes un-
de es ima ion o −3 % o he owe sensible hea lux due o
educed cohe ence o sonic empe a u e and e ical wind a
high equencies. The humidi y measu emen s ag ee well be-
ween he pla o ms in he ime and in he equency domain.
Se e al ou lie s in he WSMA la en hea lux measu emen
coincide wi h WSMA ligh s wes o he all owe , which
a e close o a o es edge. Inc eased mechanical u bulence
downwind o he o es edge is a po en ial explana ion o in-
c eased u bulen luxes. This inding howe e does no hold
o he sensible hea lux and he ic ion eloci y, which is in
con adic ion o scala simila i y.
As a po en ial sou ce o he obse ed di e ences, we as-
sess he spa ial con ex o he owe and ai c a measu e-
men s. The oo p in esul s illus a e ha he land co e con-
ibu ions a e e y simila o bo h pla o ms. P o ided he
land co e da a a e a sui able p oxy o he land-a mosphe e
exchange, di e ences be ween owe and WSMA measu e-
men s canno be a ibu ed o di e en land co e con i-
bu ions alone. Howe e , he oo p in analysis also e eals
ha he sou ce a eas only sha e a ac ional o e lap. Con-
sequen ly, he obse ed di e ences can po en ially o igina e
om he pla o ms’ p incipally di e en sampling s a egies.
Foken (2008) and Mah (2010) conclude ha he ene gy
balance non-closu e equen ly obse ed om owe EC
measu emen s is connec ed o he in e ac ion o e ain he -
e ogenei y and u bulen scales. Fo his pu pose, he ans-
e o hea be ween su ace and a mosphe e is conside ed
sepa a ely o smalle , andom eddies and o la ge , non-
p opaga ing eddies. The eo , he ans e by he small, an-
dom eddies is measu ed by he owe EC. Howe e , an ad-
di ional ans e componen is suspec ed o occu a signi -
ican su ace he e ogenei ies, leading o he gene a ion o
non-uni o mly dis ibu ed NPEs. Based on in ensi e mea-
su emen campaigns and modelling e o s, he p esence o
NPEs in he s udy a ea has been shown (Uhlenb ock e al.,
2004). A 100 m measu ing heigh , he esul ing a e age ho -
izon al imbalance o he sensible hea lux is in he o de
o 4–19 % (S ein eld e al., 2007). In he same s udy a ea,
Bey ich e al. (2006) ound compa able di e ences be ween
su ace lux es ima es om ai c a and owe o 11 % o
he sensible hea and 23 % o he la en hea . Fu he mo e,
a endency was shown o close he ene gy balance on he e-
gional scale wi h spa ially a e aging me hods (Maude e al.,
2007a). This sugges s ha he owe EC canno adequa ely
cap u e all lux con ibu ions due o i s inabili y o spa ial
sampling. On he o he hand, a la ge-ape u e scin illome e
cap u es NPEs up o he dimension o i s pa h leng h, wi h
inc easing sensi i i y owa ds he cen e o he pa h (Foken
e al., 2010). Also ai bo ne EC is capable o spa ial sampling
and cap u es some o he associa ed lux, depending on he
ho izon al ex en o he NPEs and he ligh pa h. The e o e,
he p esence o NPEs in he s udy a ea can be conside ed a
po en ial explana ion o he de ia ion o he owe EC e-
sul s om he WSMA, and e en mo e so om he LAS e-
sul s. In o de o u he adjus esul s om owe and ai -
bo ne EC measu emen s, he aw da a could be high-pass il-
e ed, which es ic s low- equency lux con ibu ion o an
iden ical h eshold (e.g. Thomas e al., 2012).
This s udy combines se e al p inciples and me hods o
he pu pose o quan i ying: (i) he sui abili y o ai bo ne in-
s umen a ion o EC measu emen s, (ii) he complex eed-
back o WSMA mo ions on he EC measu emen , and
(iii) he di ec in e compa ison o measu emen pla o ms
wi h di e ing spa ial ep esen a i eness. The applied ech-
niques a e no es ic ed o use wi h he WSMA, bu a e gen-
e al enough o be used o he de elopmen and assessmen
o o he ai bo ne pla o ms.
5 Conclusions
We ha e shown ha u bulence measu emen s om a
weigh -shi mic oligh ai c a can be achie ed wi h su i-
cien p ecision o enable eddy-co a iance lux calcula ion.
Fu he mo e, a coo dina ed se up o all owe , la ge-ape u e
scin illome e and weigh -shi mic oligh ai c a measu e-
men s a oids ypical e o s due o a e aging in e als and
e ical lux di e gence (e.g. Be s e al., 1990). Di e ences
100 APPENDIX D: METZGER ET AL. (2012)
on he o de o 15–25 % emain be ween he luxes measu ed
by he g ound-based ins umen s and he WSMA. A ha ,
he LAS gene ally measu ed he highes lux magni ude, ol-
lowed by he WSMA and he owe . Howe e , he 99.5 %
con idence in e als o he maximum likelihood unc ional
ela ionships be ween owe and WSMA include uni y slope.
Consequen ly, he obse ed di e ences can be conside ed in-
signi ican , and he accu acy o he WSMA lux measu e-
men is quan i ied o ≤10 % (1 σslope e o ).
Ne e heless, se e al po en ial easons o he disag ee-
men o he esul s be ween he measu emen pla o ms a e
in es iga ed. (i) The WSMA wind and lux measu emen is
subjec o spec al a i ac s o igina ing om i s wing, and he
esul s a e co ec ed p io o he compa ison. (ii) The low
dis o ion co ec ion and he empe a u e esolu ion a he
owe sonic anemome e measu emen alone can explain he
ull magni ude o he disag eemen . (iii) A oo p in analysis
allows excluding di e ences in he su ace a eas as he p i-
ma y eason o he disag eemen . (i ) P incipal di e ences
be ween spa ially and empo ally a e aging lux measu e-
men s may also explain he obse ed di e ences. In pa ic-
ula , ene gy ans e by non-p opaga ing eddies abo e he -
e ogeneous e ain is discussed as a po en ial eason.
We conclude ha he WSMA is a sui able ool o p omo e
he on-going esea ch o su ace-a mosphe e in e ac ions in
he e ogeneous landscapes. The lux measu emen is su i-
cien ly accu a e o co e he equi ed ligh ansec leng h
(10–100 km). Mo eo e , he WSMA’s low a io o ue ai -
speed o climb a e is well sui ed o e ain- ollowing ligh
o e complex e ain. Using e.g. wa ele analysis, he e-
gional u bulen exchange measu ed om he ai c a can be
loca ed in space and in spec al scale (Maude e al., 2007a;
S unin and Hiyama, 2004). All o he abo e ea u es a e ben-
e icial o he s udy o ye poo ly unde s ood exchange mech-
anisms be ween he Ea h’s su ace and he a mosphe e. This
u he subs an ia es he e sa ili y o he WSMA as a low
cos and widely applicable en i onmen al esea ch ai c a .
Appendix A
In eg al leng h scales and s a is ical e o
The in eg al leng h scale λcan be in e p e ed as he ypical
size o he mos ene gy- anspo ing eddies. I is calcula ed
by in eg a ion o he au oco ela ion unc ion om ze o lag
o he i s c ossing wi h ze o a lag
0
(Bange e al., 2002;
Lenschow and S anko , 1986):
λ=
0
0
(x)
(x + )
(x)
2
d . (A1)
He e ep esen s a u bulen quan i y c(scala s o wind
componen s), bu also combina ions o hese wi h he e ical
wind (x)=w
(x) ·c
(x) (Bange, 2007). Hence, he in eg al
scales o he u bulen luxes we e di ec ly calcula ed om
he da a o he weigh -shi mic oligh ai c a . The ans o -
ma ion in o he in eg al ime scale τo simul aneous owe
measu emen s is ca ied ou by di ision o λwi h he mean
ho izon al wind speed a he owe . This assumes ha Tay-
lo ’s hypo hesis o ozen u bulence is alid (Taylo , 1915).
The andom s a is ical e o o he sample a e age ¯
is sim-
ply he squa e oo o i s a iance (
)
2
. Howe e , he e -
o s in he a iance Vo , o he co a iance Fo i s combi-
na ions, a e unc ions o he in eg al scales λ,τ. The andom
s a is ical e o s σ
V
and σ
F
we e de e mined a e Lenschow
and S anko (1986); Lenschow e al. (1994):
σ
2
V
=2·V
2
·λ
L,(A2)
σ
2
F
=2·F
2
·λ
L·1+
2
wc
2
wc
,(A3)
wi h he a e aging leng h Land he co ela ion coe icien
be ween e ical wind and he u bulen quan i y
wc
.I isas-
sumed ha λL,and ha wand ca e Gaussian dis ibu ed.
The momen um lux consis s o wo o hogonal componen s,
u
w
and
w
, wi h he wind componen s u, and w.The
calcula ion o i s andom e o is ob ained om Gaussian e -
o ep oduc ion o he e o s in i s componen s (Bange e al.,
2002). The indi idual andom e o s o he WSMA and he
owe measu emen , σ
ai
and σ
ow
, espec i ely, we e summa-
ized o each a iable o e all ligh legs:
σ
an
=
n
ai
σ
ai
+
n
ow
σ
ow
2n−1,(A4)
esul ing in he a e age andom e o in he da a couples σ
an
wi h he sample size n. The ensemble andom e o σ
ens
con-
side s he educ ion o he andom e o wi h he sample size
(Mah , 1998):
σ
ens
=σ
an
√n,(A5)
wi h ze o expec ed alue σ
ens
and he s anda d de ia ion σ
an
o he popula ion. While σ
an
is a measu e o he a e age
dispe sion o he da a couples, σ
ens
quan i ies he le el o
con idence we can expec om compa ing he en i e da ase
be ween he wo pla o ms. To use Eqs. (A4)–(A5) o da a
ob ained du ing di e en ligh days, we use no malized e -
o es ima es. Ye , he no malized e o s a e excessi ely la ge
when he denomina o , i.e. he measu emen quan i y, ap-
p oaches ze o. Fo u bulen luxes, his is usually he case
unde s able condi ions, whe e e.g. in e mi en u bulence
can iola e he assump ions in he in eg al leng h scales. Con-
sequen ly, we cons ain he calcula ion o σ
an
and σ
ens
o he
luxes o alues o u
∗
>0.2ms
−1
and H,E>20 W m
−2
,
esul ing in N=28, 15 and 24 samples, espec i ely.
APPENDIX D: METZGER ET AL. (2012) 101
Fig. B1. C oss-wind and along-wind in eg a ed dis ibu ions o he
oo p in s o case 2, z=100 m om Ma kkanen e al. (2009). Up-
pe and lowe panels display longi udinal and c oss-sec ions, e-
spec i ely. The oo p in weigh dis ibu ions a e shown on he le
side, and he cumula i e dis ibu ions a e shown on he igh side.
Appendix B
Foo p in modelling
The oo p in - o sou ce weigh unc ion quan i ies he spa ial
con ibu ions o each measu emen (Schmid, 2002; Vesala
e al., 2008). Analy ical oo p in models a e o en limi ed,
e.g. ega ding s abili y egimes o measu emen heigh s (e.g.
Ko mann and Meixne , 2001, subsequen ly e e ed o wi h
KM01). Lag angian oo p in models o e come hese lim-
i a ions and addi ionally conside 3-D dispe sion, bu a e
compu a ionally expensi e. The oo p in model o Kljun
e al. (2004, KL04) is a pa ame e iza ion o he backwa d
Lag angian model o Kljun e al. (2002, KL02) in he ange
−200 ≤z/L ≤1, u
∗
≥0.2ms
−1
,and1m≤z≤z
i
, wi h he
bounda y laye dep h z
i
. Thus, i combines li le compu a-
ional e o wi h b oad applicabili y. The pa ame e iza ion
depends upon ic ion eloci y u
∗
, measu emen heigh z,
s anda d de ia ion o he e ical wind σ
w
and he ae ody-
namic oughness leng h z
0
,o whichu
∗
,zand σ
w
a e mea-
su ed di ec ly. The oughness leng h is in e ed using he log-
a i hmic wind p o ile wi h he in eg a ed uni e sal unc ion
o momen um exchange a e Businge e al. (1971) in he
o m o H¨
ogs ¨
om (1988). The KL04 is a c oss-wind in e-
g a ed oo p in model, i.e. i does no esol e he dis ibu ion
pe pendicula o he main wind di ec ion. In o de o accoun
o c oss-wind dispe sion, he KL04 was combined wi h
Table B1. Median pe o mance o he oo p in pa ame e iza ions
KL04+ and KM01 compa ed o he e e ence Lag angian model o
Kljun e al. (2002). Unce ain y measu es NMSE, MAD and a e
explained in he ex .
Di ec ion Along-wind C oss-wind
Model KL04+ KM01 KL04+ KM01
NMSE 0.34 ±0.05 0.95 ±0.48 0.34 ±0.05 0.33 ±0.36
MAD [%] 0.43 ±0.10 0.63 ±0.28 0.08 ±0.05 0.12 ±0.14
0.91 ±0.00 0.66 ±0.12 0.99 ±0.01 0.99 ±0.01
a Gaussian c oss-wind dis ibu ion unc ion (Kljun e al.,
2012). The combina ion o KL04 wi h his c oss-wind dis i-
bu ion esul s in a compu a ionally as oo p in pa ame e i-
za ion which conside s 3-D dispe sion and is no cons ained
o applica ions in he su ace laye . In he ollowing, we e e
o his model as KL04+.
To e alua e model pe o mance, KM01 and KL04+ we e
compa ed o he e e ence Lag angian model KL02. Fo his
pu pose, ou exis ing ealiza ions o he KL02 model we e
used om Ma kkanen e al. (2009, Table 1, case 1 (L=
−32 m, u
∗
=0.27 m s
−1
) and case 2 (L=−76.6m, u
∗
=
0.295 m s
−1
), z=50 m and 100 m). Ma kkanen e al. (2009)
adop ed case 1 om Lecle c e al. (1997), and e e enced
he esul s o la ge eddy simula ions (Raasch and Sch ¨
o e ,
2001). The abo e pa ame e se s do no include σ
and σ
w
,
which we e de i ed using he in eg al u bulence cha ac e is-
ics p oposed by Lumley and Pano sky (1964) and Pano sky
e al. (1977), espec i ely. The compu ed oo p in weigh s
we e summa ized o each cell o a g id wi h 100 m ho i-
zon al spacing and subsequen ly in eg a ed o e c oss-wind
and along-wind di ec ion, espec i ely (Fig. B1). In bo h
di ec ions, KL04+ assigns mo e weigh o he close ange
compa ed o KM01 (Fig. B1 le panels). This is consis-
en h oughou he ange o he es ed a mosphe ic condi-
ions (no shown). In along-wind di ec ion, KL04+ ep o-
duces KL02 e y well un il he cumula i e dis ibu ion ac-
coun s o app oxima ely 80 % o he oo p in (Fig. B1 uppe
igh panel). Con ibu ions om below he measu emen lo-
ca ion due o along-wind dispe sion a e sligh ly p onounced
by KL04+, and neglec ed by KM01. The c oss-wind dis ibu-
ions o bo h KL04+ and KM01 ag ee easonably well wi h
KL02.
To quan i y he model compa ison, no malized mean
squa e e o (NMSE, Hanna and Paine, 1989), median abso-
lu e de ia ion (MAD, Rousseeuw and Ve bo en, 2002) and
Pea son’s coe icien o co ela ion ( ) a e used. The NMSE
is based on a iance s a is ics and is hus sensi i e o he ew
la ges de ia ions in he da ase . In con as , he MAD is he
middle alue o he e o dis ibu ion, and is mo e sensi i e
o he e o equency. We use NMSE and MAD o assess
he model pe o mance a ound he peak and he ail o he
oo p in , espec i ely. The co ela ion coe icien p o ides
in o ma ion on he deg ee o simila i y be ween he models’
dis ibu ions. Table B1 summa izes he esul s o he model
102 APPENDIX D: METZGER ET AL. (2012)
compa ison. In bo h along-wind and c oss-wind di ec ions,
he simila i y be ween KL04+ and KL02 is as good o be -
e han be ween KM01 and KL02 ( ). In along-wind di-
ec ion, KL04+ is conside ably close o KL02 in he close
ange (NMSE) and he a ange (MAD) compa ed o KM01.
A simila de ia ion be ween KM01 and KL02 has been e-
po ed by Kljun e al. (2003). In c oss-wind di ec ion, bo h
KL04+ and KM01 ag ee equally well wi h KL02. Fo all
me ics, he s anda d e o s o e he ou pa ame e se s a e
smalle o he KL04+ model, poin ing ou i s eliabili y.
Acknowledgemen s. Recogni ion has o be gi en o F ank Neidl
and Raine S einb eche a he Ka ls uhe Ins i u e o Technol-
ogy, Ins i u e o Me eo ology and Clima e Resea ch. Neidl
p og ammed and con inuously main ained he da a acquisi ion
sys em, while S einb eche ini ia ed wind- and lux measu emen s
wi h he weigh -shi mic oligh ai c a in he i s place. Thanks
go o Ul ich Weisensee and Jens-Pe e Leps a he Ge man
Me eo ological Se ice, Richa d-Aßmann-Obse a o y Lindenbe g
o pe o ming he owe u bulence measu emen s. We a e obliged
o Xunhua Zheng and he wo kg oup a he Chinese Academy o
Sciences, Ins i u e o A mosphe ic Physics, which was hos ing ou
p ojec and p o iding indispensable in as uc u e. Ou hanks o
Jens Bange a he Ebe ha d Ka ls Uni e si y o T¨
ubingen, Ins i u e
o Geoscience, o his ad ice ega ding he ligh campaign
design. The au ho s wish o hank Hen y Loesche a he Na ional
Ecological Obse a o y Ne wo k, Fundamen al Ins umen Uni o
his con inued suppo . S ipend unding by he Ge man Academic
Exchange Se ice, Helmhol z Associa ion o Ge man Resea ch
Cen es, China Schola ship Council and he Eu opean Union unde
he Science and Technology Fellowship China is acknowledged.
The Na ional Ecological Obse a o y Ne wo k is a p ojec spon-
so ed by he Na ional Science Founda ion and managed unde
coope a i e ag eemen by NEON, Inc. This ma e ial is based upon
wo k suppo ed by he Na ional Science Founda ion unde he
g an DBI-0752017. Any opinions, indings, and conclusions o
ecommenda ions exp essed in his ma e ial a e hose o he au ho s
and do no necessa ily e lec he iews o he Na ional Science
Founda ion.
Edi ed by: S. Malinowski
Re e ences
Bange, J.: Ai bo ne Measu emen o Tu bulen Ene gy Exchange
Be ween he Ea h Su ace and he A mosphe e, Facul y o
Enginee ing, B aunschweig Uni e si y o Technology, B aun-
schweig, Ge many, 2007.
Bange, J., Bey ich, F., and Engelba , D. A. M.: Ai bo ne mea-
su emen s o u bulen luxes du ing LITFASS-98: Compa i-
son wi h g ound measu emen s and emo e sensing in a case
s udy, Theo . Appl. Clima ol., 73, 35–51, doi:10.1007/s00704-
002-0692-6, 2002.
Be s, A. K., Desja dins, R. L., Macphe son, J. I., and Kelly, R. D.:
Bounda y-laye hea and mois u e budge s om FIFE, Bound.-
Lay. Me eo ol., 50, 109–138, doi:10.1007/BF00120520, 1990.
Bey ich, F. and Adam, W. K.: Si e and da a epo o he Linden-
be g e e ence si e in CEOP – phase I, Be ich e des Deu schen
We e diens es, 55 pp., 2007.
Bey ich, F., Leps, J. P., Maude , M., Bange, J., Foken, T.,
Huneke, S., Lohse, H., Ludi, A., Meijninge , W. M. L.,
Mi ono , D., Weisensee, U., and Zi el, P.: A ea-a e aged
su ace luxes o e he LITFASS egion based on eddy-
co a iance measu emen s, Bound.-Lay. Me eo ol., 121, 33–65,
doi:10.1007/s10546-006-9052-x, 2006.
Businge , J. A., Wyngaa d, J. C., Izumi, Y., and B adley, E. F.:
Flux-p o ile ela ionships in he a mosphe ic su ace
laye , J. A mos. Sci., 28, 181–189, doi:10.1175/1520-
0469(1971)028<0181:FPRITA>2.0.CO;2, 1971.
Chen, J., Jonsson, P., Tamu a, M., Gu, Z. H., Ma sushi a, B.,
and Eklundh, L.: A simple me hod o econs uc ing
a high-quali y NDVI ime-se ies da a se based on he
Sa i zky-Golay il e , Remo e Sens. En i on., 91, 332–344,
doi:10.1016/j. se.2004.03.014, 2004.
Da is, F. W., Schimel, D. S., F iedl, M. A., Michaelsen, J. C.,
Ki el, T. G. F., Dubayah, R., and Dozie , J.: Co a iance o
biophysical da a wi h digi al opog aphic and land use maps
o e he FIFE si e, J. Geophys. Res.-A mos., 97, 19009–19021,
doi:10.1029/92jd01345, 1992.
Dea do , J. W.: Th ee-dimensional nume ical s udy o u bulence
in an en aining mixed laye , Bound.-Lay. Me eo ol., 7, 199–226,
doi:10.1007/b 00227913, 1974.
Desja dins, R. L., MacPhe son, J. I., Schuepp, P. H., and Ka anja, F.:
An e alua ion o ai c a lux measu emen s o CO
2
, wa e
apo and sensible hea , Bound.-Lay. Me eo ol., 47, 55–69,
doi:10.1007/BF00122322, 1989.
Desja dins, R. L., MacPhe son, J. I., Mah , L., Schuepp, P., Pa -
ey, E., Neumann, H., Baldocchi, D., Wo sy, S., Fi zja ald, D.,
McCaughey, H., and Joine , D. W.: Scaling up lux measu emen s
o he bo eal o es using ai c a - owe combina ions, J. Geo-
phys. Res.-A mos., 102, 29125–29133, doi:10.1029/97JD00278,
1997.
Egge , J., Baj achaya, S., Hein ich, R., Kolb, P., Lammlein, S.,
Mech, M., Reude , J., Schape , W., Shakya, P., Schween, J.,
and Wend , H.: Diu nal winds in he Himalayan Kali Gan-
daki alley. Pa III: Remo ely pilo ed ai c a soundings,
Mon h. Wea he Re ., 130, 2042–2058, doi:10.1175/1520-
0493(2002)130<2042:DWITHK>2.0.CO;2, 2002.
Foken, T.: The ene gy balance closu e p oblem: an o e iew, Ecol.
Appl., 18, 1351–1367, doi:10.1890/06-0922.1, 2008.
Foken, T., G¨
ockede, M., Maude , M., Mah , L., Ami o, B., and
Munge , W.: Pos - ield Da a Quali y Coni ol, in: Handbook o
Mic ome eo ology: A Guide o Su ace Flux Measu emen and
Analysis, 1s Edn., edi ed by: Lee, X., Law, B., and Mass-
man, W., Sp inge Ne he lands, Do d ech , The Ne he lands,
264 pp., 2004.
Foken, T., Maude , M., Liebe hal, C., Wimme , F., Bey ich, F.,
Leps, J.-P., Raasch, S., DeB uin, H. A. R., Meijninge , W. M. L.,
and Bange, J.: Ene gy balance closu e o he LITFASS-
2003 expe imen , Theo . Appl. Clima ol., 101, 149–160,
doi:10.1007/s00704-009-0216-8, 2010.
Foken, T., Leuning, R., Oncley, S. P., Maude , M., and Aubine , M.:
Co ec ions and da a quali y, in: Eddy Co a iance: A P ac i-
cal Guide o Measu emen and Da a Analysis, edi ed by: Aubi-
ne , M., Vesala, T., and Papale, D., Sp inge , Do d ech , Heidel-
APPENDIX D: METZGER ET AL. (2012) 103
be g, London, New Yo k, 85–131, 2012.
Ga man, K. E., Hill, K. A., Wyss, P., Ca lsen, M., Zimme man, J. R.,
S i m, B. H., Ca ney, T. Q., San ini, R., and Shepson, P. B.: An
ai bo ne and wind unnel e alua ion o a wind u bulence mea-
su emen sys em o ai c a -based lux measu emen s, J. A mos.
Ocean. Tech., 23, 1696–1708, doi:10.1175/JTECH1940.1, 2006.
G¨
ockede, M., Foken, T., Aubine , M., Au ela, M., Banza, J., Be n-
ho e , C., Bonne ond, J. M., B une , Y., Ca a a, A., Clemen ,
R., Dellwik, E., Elbe s, J., Eugs e , W., Fuh e , J., G anie , A.,
G ¨
unwald, T., Heinesch, B., Janssens, I. A., Knohl, A., Koeble,
R., Lau ila, T., Longdoz, B., Manca, G., Ma ek, M., Ma kka-
nen, T., Ma eus, J., Ma eucci, G., Maude , M., Miglia acca, M.,
Mine bi, S., Monc ie , J., Mon agnani, L., Moo s, E., Ou ci al,
J.-M., Papale, D., Pe ei a, J., Pilegaa d, K., Pi a, G., Rambal, S.,
Rebmann, C., Rod igues, A., Ro enbe g, E., Sanz, M. J., Sed-
lak, P., Seu e , G., Siebicke, L., Soussana, J. F., Valen ini, R.,
Vesala, T., Ve beeck, H., and Yaki , D.: Quali y con ol o Ca -
boEu ope lux da a – Pa 1: Coupling oo p in analyses wi h
lux da a quali y assessmen o e alua e si es in o es ecosys-
ems, Biogeosciences, 5, 433–450, doi:10.5194/bg-5-433-2008,
2008.
Hanna, S. R. and Paine, R. J.: Hyb id Plume Dispe -
sion Model (HPDM) de elopmen and e alua ion,
J. Appl. Me eo ol., 28, 206–224, doi:10.1175/1520-
0450(1989)028<0206:HPDMDA>2.0.CO;2, 1989.
Hiyama, T., S unin, M. A., Tanaka, H., and Oh a, T.: The de el-
opmen o local ci cula ions a ound he Lena Ri e and hei e -
ec on owe -obse ed ene gy imbalance, Hyd ol. P ocess., 21,
2038–2048, doi:10.1002/hyp.6705, 2007.
Hobbs, S., Dye , D., Cou aul , D., Olioso, A., Lagoua de, J. P.,
Ke , Y., McAneney, J., and Bonne ond, J.: Su ace laye p o-
iles o ai empe a u e and humidi y measu ed om unmanned
ai c a , Ag onomie, 22, 635–640, doi:10.1051/ag o:2002050,
2002.
H¨
ogs ¨
om, U.: Non-dimensional wind and empe a u e p o iles in
he a mosphe ic su ace laye : A e-e alua ion, Bound.-Lay. Me-
eo ol., 42, 55–78, doi:10.1007/BF00119875, 1988.
Hojs up, J.: A s a is ical da a sc eening p ocedu e, Meas. Sci. Tech-
nol., 4, 153–157, doi:10.1088/0957-0233/4/2/003, 1993.
Isaac, P. R., Leuning, R., Hacke , J. M., Cleugh, H. A., Cop-
pin, P. A., Denmead, O. T., and Raupach, M. R.: Es ima-
ion o egional e apo anspi a ion by combining ai c a and
g ound-based measu emen s, Bound.-Lay. Me eo ol., 110, 69–
98, doi:10.1023/A:1026054317990, 2004a.
Isaac, P. R., McAneney, J., Leuning, R., and Hacke , J. M.:
Compa ison o ai c a and g ound-based lux measu e-
men s du ing OASIS95, Bound.-Lay. Me eo ol., 110, 39–67,
doi:10.1023/A:1026002301152, 2004b.
Junke mann, W.: An ul aligh ai c a as pla o m o esea ch
in he lowe oposphe e: Sys em pe o mance and i s esul s
om adia ion ans e s udies in s a i o m ae osol laye s and
b oken cloud condi ions, J. A mos. Ocean. Tech., 18, 934–946,
doi:10.1175/1520-0426(2001)018<0934:AUAAPF>2.0.CO;2,
2001.
Junke mann, W.: The ac inic UV- adia ion budge du ing he ES-
COMPTE campaign 2001: esul s o ai bo ne measu emen s
wi h he mic oligh esea ch ai c a D-MIFU, A mos. Res., 74,
461–475, doi:10.1016/j.a mos es.2004.06.009, 2005.
Kaimal, J. C. and Finnigan, J. J.: A mosphe ic Bounda y Laye
Flows: Thei S uc u e and Measu emen , Ox o d Uni e si y
P ess, 289 pp., New Yo k, USA, 1994.
Kaimal, J. C., Wyngaa d, J. C., Izumi, Y., and Co ´
e, O. R.: Spec al
cha ac e is ics o su ace-laye u bulence, Q. J. Roy. Me eo ol.
Soc., 98, 563–589, doi:10.1002/qj.49709841707, 1972.
Kanda, M., Inagaki, A., Le zel, M. O., Raasch, S., and Wa an-
abe, T.: LES s udy o he ene gy imbalance p oblem wi h
Eddy co a iance luxes, Bound.-Lay. Me eo ol., 110, 381–404,
doi:10.1023/B:BOUN.0000007225.45548.7a, 2004.
Kljun, N., Ro ach, M. W., and Schmid, H. P.: A h ee-dimensional
backwa d lag angian oo p in model o a wide ange o
bounda y-laye s a i ica ions, Bound.-Lay. Me eo ol., 103, 205–
226, doi:10.1023/A:1014556300021, 2002.
Kljun, N., Ko mann, R., Ro ach, M. W., and Meixe , F. X.: Compa -
ison o he Lang angian oo p in model LPDM-B wi h an ana-
ly ical oo p in model, Bound.-Lay. Me eo ol., 106, 349–355,
doi:10.1023/A:1021141223386, 2003.
Kljun, N., Calanca, P., Ro ach, M. W., and Schmid, H. P.:
A simple pa ame e isa ion o lux oo p in p e-
dic ions, Bound.-Lay. Me eo ol., 112, 503–523,
doi:10.1023/B:BOUN.0000030653.71031.96, 2004.
Kljun, N., Ro ach, M. W., and Schmid, H. P.: A Simple Pa ame-
e isa ion o Two-dimensional Flux Foo p in s, in p epa a ion,
2012.
Kolmogo o , A. N.: Lokalnaja s uk u a u bulen nos i
nesch schimaemoi schidkos i p i o schen bolschich schislach
Reynoldsa (The local s uc u e o u bulence in incomp essible
iscous luid o e y la ge Reynolds numbe s), P oceedings o
he USSR Academy o Sciences, 30, 299–303, 1941.
Ko mann, R. and Meixne , F. X.: An analy ical oo p in model o
non-neu al s a i ica ion, Bound.-Lay. Me eo ol., 99, 207–224,
doi:10.1023/A:1018991015119, 2001.
K alse h, T. O.: Cau iona y no e abou R
2
, Am. S a ., 39, 279–285,
1985.
Lecle c, M. Y., Shen, S., and Lamb, B.: Obse a ions and la ge-
eddy simula ion modeling o oo p in s in he lowe con ec-
i e bounda y laye , J. Geophys. Res.-A mos., 102, 9323–9334,
doi:10.1029/96JD03984, 1997.
Lenschow, D. H. and S anko , B. B.: Leng h Scales in he
Con ec i e Bounda y Laye , J. A mos. Sci., 43, 1198–1209,
doi:10.1175/1520-0469(1986)043<1198:LSITCB>2.0.CO;2,
1986.
Lenschow, D. and Sun, J.: The spec al composi ion o luxes and
a iances o e land and sea ou o he mesoscale, Bound.-Lay.
Me eo ol., 125, 63–84, doi:10.1007/s10546-007-9191-8, 2007.
Lenschow, D. H., Mann, J., and K is ensen, L.: How long is
long enough when measu ing luxes and o he u bulence s a is-
ics?, J. A mos. Ocean. Tech., 11, 661–673, doi:10.1175/1520-
0426(1994)011<0661:HLILEW>2.0.CO;2, 1994.
Lindley, D. V.: Reg ession lines and he linea unc ional ela ion-
ship, Supplemen , J. R. S a . Soc., 9, 218–244, 1947.
Liu, H. P., Pe e s, G., and Foken, T.: New equa ions o sonic em-
pe a u e a iance and buoyancy hea lux wi h an omnidi ec-
ional sonic anemome e , Bound.-Lay. Me eo ol., 100, 459–468,
doi:10.1023/A:1019207031397, 2001.
Liu, S. M., Xu, Z. W., Wang, W. Z., Jia, Z. Z., Zhu, M. J., Bai, J., and
Wang, J. M.: A compa ison o eddy-co a iance and la ge ape -
u e scin illome e measu emen s wi h espec o he ene gy bal-
104 APPENDIX D: METZGER ET AL. (2012)
ance closu e p oblem, Hyd ol. Ea h Sys . Sci., 15, 1291–1306,
doi:10.5194/hess-15-1291-2011, 2011.
Lu, L., Denning, A. S., da Sil a-Dias, M. A., da Sil a-Dias, P.,
Longo, M., F ei as, S. R., and Saa chi, S.: Mesoscale ci -
cula ions and a mosphe ic CO
2
a ia ions in he Tapajos
Region, Pa a, B azil, J. Geophys. Res.-A mos., 110, 1–17,
doi:10.1029/2004JD005757, 2005.
Lumley, J. L. and Pano sky, H. A.: The S uc u e o A mosphe ic
Tu bulence, In e science Publishe s, New Yo k, 1964.
Mah , L.: Flux sampling e o s o ai c a and owe s,
J. A mos. Ocean. Tech., 15, 416–429, doi:10.1175/1520-
0426(1998)015<0416:FSEFAA>2.0.CO;2, 1998.
Mah , L.: Compu ing u bulen luxes nea he su ace:
needed imp o emen s, Ag . Fo es Me eo ol., 150, 501–509,
doi:10.1016/j.ag o me .2010.01.015, 2010.
Ma kkanen, T., S ein eld, G., Kljun, N., Raasch, S., and Foken,
T.: Compa ison o con en ional Lag angian s ochas ic oo p in
models agains LES d i en oo p in es ima es, A mos. Chem.
Phys., 9, 5575–5586, doi:10.5194/acp-9-5575-2009, 2009.
Ma in, S., Bange, J., and Bey ich, F.: Me eo ological p o iling o
he lowe oposphe e using he esea ch UAV “M
2
AV Ca olo”,
A mos. Meas. Tech., 4, 705–716, doi:10.5194/am -4-705-2011,
2011.
Massman, W. J. and Clemen , R.: Unce ain y in Eddy Co a iance
lux es ima es esul ing om spec al a enua ion, in: Handbook
o Mic ome eo ology: A Guide o Su ace Flux Measu emen
and Analysis, 1s Edn., edi ed by: Lee, X., Law, B., and Mass-
man, W., Sp inge Ne he lands, Do d ech , The Ne he lands,
264 pp., 2004.
Maude , M. and Foken, T.: Impac o pos - ield da a p ocessing on
eddy co a iance lux es ima es and ene gy balance closu e, Me e-
o ol. Z., 15, 597–609, doi:10.1127/0941-2948/2006/0167, 2006.
Maude , M. and Foken, T.: Documen a ion and Ins uc ion Man-
ual o he Eddy-Co a iance So wa e Package TK3, Uni-
e si ¨
a sbiblio hek Bay eu h, Uni e si ¨
a Bay eu h, Ab eilung
Mik ome eo ologie, Bay eu h, Ge many, 2011.
Maude , M., Desja dins, R. L., and MacPhe son, I.: Scale anal-
ysis o ai bo ne lux measu emen s o e he e ogeneous e ain
in a bo eal ecosys em, J. Geophys. Res.-A mos., 112, D13112,
doi:10.1029/2006JD008133, 2007a.
Maude , M., Oncley, S. P., Vog , R., Weidinge , T., Ribei o, L.,
Be nho e , C., Foken, T., Kohsiek, W., De B uin, H. A. R., and
Liu, H.: The ene gy balance expe imen EBEX-2000. Pa II:
In e compa ison o eddy-co a iance senso s and pos - ield da a
p ocessing me hods, Bound.-Lay. Me eo ol., 123, 29–54, 2007b.
Meijninge , W. M. L., Ha ogensis, O. K., Kohsiek, W., Hoed-
jes, J. C. B., Zuu bie , R. M., and De B uin, H. A. R.:
De e mina ion o a ea-a e aged sensible hea luxes wi h a
la ge ape u e scin illome e o e a he e ogeneous su ace –
Fle oland ield expe imen , Bound.-Lay. Me eo ol., 105, 37–62,
doi:10.1023/a:1019647732027, 2002.
Meijninge , W. M. L., Bey ich, F., L¨
udi, A., Kohsiek, W., and
De B uin, H. A. R.: Scin illome e -based u bulen luxes o sen-
sible and la en hea o e a he e ogeneous land su ace – a con i-
bu ion o LITFASS-2003, Bound.-Lay. Me eo ol., 121, 89–110,
doi:10.1007/s10546-005-9022-8, 2006.
Me zge , S., Junke mann, W., Bu e bach-Bahl, K., Schmid, H. P.,
and Foken, T.: Measu ing he 3-D wind ec o wi h a weigh -
shi mic oligh ai c a , A mos. Meas. Tech., 4, 1421–1444,
doi:10.5194/am -4-1421-2011, 2011.
Moo e, C. J.: F equency- esponse co ec ions o Eddy-
co ela ion sys ems, Bound.-Lay. Me eo ol., 37, 17–35,
doi:10.1007/BF00122754, 1986.
Pano sky, H., Tennekes, H., Lenschow, D., and Wyngaa d, J.: The
cha ac e is ics o u bulen eloci y componen s in he su ace
laye unde con ec i e condi ions, Bound.-Lay. Me eo ol., 11,
355–361, doi:10.1007/b 02186086, 1977.
Quenouille, M. H.: No es on bias in es ima ion, Biome ika, 43,
353–360, doi:10.1093/biome /43.3-4.353, 1956.
R De elopmen Co e Team: A Language and En i onmen o S a-
is ical Compu ing, R Founda ion o S a is ical Compu ing, Vi-
enna, Aus ia, 2011.
Raasch, S. and Sch ¨
o e , M.: PALM – A la ge-eddy simula ion
model pe o ming on massi ely pa allel compu e s, Me eo ol. Z.,
10, 363–372, doi:10.1127/0941-2948/2001/0010-0363, 2001.
Ripley, B. D. and Thompson, M.: Reg ession echniques o
he de ec ion o analy ical bias, Analys , 112, 377–383,
doi:10.1039/an9871200377, 1987.
Rousseeuw, P. J. and Ve bo en, S.: Robus es ima ion in
e y small samples, Compu . S a . Da a An., 40, 741–758,
doi:10.1016/S0167-9473(02)00078-6, 2002.
Schmid, H. P.: Foo p in modeling o ege a ion a mosphe e ex-
change s udies: a e iew and pe spec i e, Ag . Fo es Me eo ol.,
113, 159–183, doi:10.1016/S0168-1923(02)00107-7, 2002.
So bjan, Z.: S a is ics o scala ields in he a mosphe ic bounda y
laye based on la ge-Eddy simula ions. Pa II: Fo ced con ec-
ion, Bound.-Lay. Me eo ol., 119, 57–79, doi:10.1007/s10546-
005-9014-8, 2006.
S ein eld, G., Le zel, M. O., Raasch, S., Kanda, M., and Inagaki, A.:
Spa ial ep esen a i eness o single owe measu emen s and he
imbalance p oblem wi h eddy-co a iance luxes: esul s o a
la ge-eddy simula ion s udy, Bound.-Lay. Me eo ol., 123, 77–98,
doi:10.1007/s10546-006-9133-x, 2007.
S unin, M. A. and Hiyama, T.: Applying wa ele ans o ms o
analyse ai c a -measu ed u bulence and u bulen luxes in he
a mosphe ic bounda y laye o e Eas e n Sibe ia, Hyd ol. P o-
cess., 18, 3081–3098, doi:10.1002/hyp.5750, 2004.
Taylo , G. I.: Eddy mo ion in he a mosphe e, Philos. T. R. Soc.
Lond., 215, 1–26, doi:10.1098/ s a.1915.0001, 1915.
Thomas, R. M., Lehmann, K., Nguyen, H., Jackson, D. L., Wol e,
D., and Ramana han, V.: Measu emen o u bulen wa e a-
po luxes using a ligh weigh unmanned ae ial ehicle sys em,
A mos. Meas. Tech., 5, 243–257, doi:10.5194/am -5-243-2012,
2012.
Tukey, J. W.: Bias and con idence in no -qui e la ge samples, Ann.
Ma h. S a ., 29, p. 614, 1958.
Uhlenb ock, J., Raasch, S., Hennemu h, B., Zi el, P., and Mei-
jninge , W. M. L.: E ec s o land su ace he e ogenei ies on he
bounda y s uc u e and u bulence du ing LITFASS-2003: la ge-
eddy simula ions in compa ison wi h u bulence measu emen s,
16 h AMS Symposium on Bounda y Laye s and Tu bulence,
Po land, USA, Abs ac No. 9.3, 8–13 Augus , 2004.
Vesala, T., Kljun, N., Rannik, U., Rinne, J., Sogache , A., Ma kka-
nen, T., Sabel eld, K., Foken, T., and Lecle c, M. Y.: Flux and
concen a ion oo p in modelling: S a e o he a , En i on. Pol-
lu ., 152, 653–666, doi:10.1016/j.en pol.2007.06.070, 2008.
Vicke s, D. and Mah , L.: Quali y con ol and lux sam-
pling p oblems o owe and ai c a da a, J. A -
APPENDIX D: METZGER ET AL. (2012) 105
mos. Ocean. Tech., 14, 512–526, doi:10.1175/1520-
0426(1997)014<0512:QCAFSP>2.0.CO;2, 1997.
Wang, T. I., Ochs, G. R., and Cli o d, S. F.: A sa u a ion- esis an
op ical scin illome e o measu e C
2
n
, J. Op . Soc. Am., 68, 334–
338, doi:10.1364/JOSA.68.000334, 1978.
Webb, E. K., Pea man, G. I., and Leuning, R.: Co ec ion o
lux measu emen s o densi y e ec s due o hea and wa-
e apou ans e , Q. J. Roy. Me eo ol. Soc., 106, 85–100,
doi:10.1002/qj.49710644707, 1980.
Wilczak, J. M., Oncley, S. P., and S age, S. A.: Sonic anemome e
il co ec ion algo i hms, Bound.-Lay. Me eo ol., 99, 127–150,
doi:10.1023/A:1018966204465, 2001.
Wille , J. B. and Singe , J. D.: Ano he cau iona y no e abou R
2
:
i s use in weigh ed leas -squa es eg ession analysis, Am. S a .,
42, 236–238, 1988.
106 APPENDIX E: METZGER ET AL. (2013)
Appendix E: Me zge e al. (2013)
APPENDIX E: METZGER ET AL. (2013) 107
2194 S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s
Fig. 1. Loca ion o he Xilin Ri e ca chmen in he Inne Mongolia
Au onomous Region, China (modi ied a e S e ens e al., 2008).
small a eas a ound he immedia e measu emen loca ions
(e.g. Kaha aba a e al., 1997; Schuepp e al., 1992). On he
o he hand ai c a -based measu emen s can p o ide lux in-
o ma ion a egional scales (e.g. Desja dins e al., 1995) bu
a e es ic ed o sho pe iods o ime. Thus he empo al
and spa ial cha ac e is ics o g ound-based and ai bo ne mea-
su emen s complemen each o he (Gioli e al., 2004; Maude
e al., 2007). I is desi able o in eg a e bo h app oaches in an
e o o p o ide sui able da ase s o he design, cons ain ,
and e alua ion o mass and ene gy exchange models a si e
as well as a egional scales (Chen e al., 1999; Desja dins
e al., 1997). In he ollowing we b ie ly e iew he equi e-
men s o spa ial scaling o ai bo ne EC measu emen s, and
he applicabili y o ai bo ne EC measu emen s o e complex
e ain.
Agg ega ion app oaches enable es ima ing he exchange
o e en i e landscapes, p o ided luxes o cha ac e is ic land
co e ea u es o domains a e known (Bey ich e al., 2006).
Fligh pa h segmen a ion can be a use ul ool o di ec ly e-
la e ai bo ne EC measu emen s o landscape uni s (e.g. Des-
ja dins e al., 1994; Vellinga e al., 2010). I is also possi-
ble o unc ionally ela e hese measu emen s o land co e
p ope ies, which hen e lec he e ec s o ege a ion, cli-
ma e, soil and opog aphy on he lux s eng h. Fo exam-
ple, Ki by e al. (2008) p opose a me hod o disce ning in-
di idual luxes in a he e ogeneous landscape based on sub-
se s o “pu e” lux agmen s. Ano he app oach is o u ilize
quan i a i e in o ma ion abou he EC measu emen ’s spa ial
con ex , on which basis en i onmen al esponse unc ions
(ERFs, Desja dins e al., 1994) can be de i ed. The gene al
idea o ERFs is o es ablish a ela ionship be ween spa ially
o empo ally esol ed lux obse a ions ( esponses) and co -
esponding en i onmen al d i e s. Hence ERFs a e a quan i-
a i e mechanism o ex ac ela ionships om, and o con-
dense he in o ma ion con en in a da ase . I su icien ly ac-
cu a e, he ex ac ed ela ionships can hen be used, e.g. o
b idge obse a ional scales o o adjus he spa ial ep esen-
a i eness o g ound-based lux measu emen s. In addi ion,
cu en me hods o spa ially esol e su ace luxes a e mainly
ocused on emo e sensing algo i hms (e.g. Fan e al., 2007)
and p ocess-based land su ace models (e.g. Ve e e al.,
2012). These p ocedu es o en demand a - eaching assump-
ions, such as he closu e o he ene gy and wa e balances
(e.g. Ande son e al., 2012), o a e challenging wi h espec
o he equi ed da a basis (e.g. Kaminski e al., 2012; Ziehn
e al., 2011). In con as , accu a e ERFs enable in e ing
high- esolu ion su ace lux maps di ec ly om obse a ional
da a wi h minimal, quan i iable assump ions. Howe e , ERFs
canno p o ide insigh s, e.g. in o ecosys em pools. Conse-
quen ly, ERFs migh be sui able o complemen ing da a as-
simila ion and emo e sensing app oaches, e.g. h ough con-
ibu ing o he design, cons ain and e alua ion o lux al-
go i hms.
The o enamed applica ions equi e he ela ion o he ai -
bo ne measu ed luxes o land co e p ope ies. To enable
his equi emen an ai c a is bound o measu e close o he
su ace, whe e cha ac e is ic luxes om di e en land co -
e s a e no ye ully homogenized (o blended, Mason, 1988;
Wood and Mason, 1991). Mo eo e , he lux mus be mea-
su ed a a cons an al i ude abo e g ound, so as o a oid a -
i icial lux con ibu ions h ough al i ude luc ua ions along
e ical g adien s (Vicke s and Mah , 1997). Howe e in-
es iga ion a eas a e seldom ideally la , and opog aphy can
a y signi ican ly h oughou a domain. To sa ely ollow e -
ain con ou s a a low and cons an al i ude abo e g ound,
he ai c a mus possess a low a io o ue ai speed o climb
a e. Only a ew ai bo ne pla o ms ul il his equi emen
(e.g. Bange e al., 2006; Gioli e al., 2004; Thomas e al.,
2012), wi h he weigh -shi mic oligh ai c a (WSMA) be-
ing one o hem (Me zge e al., 2011, 2012). In o enamed
s udies we desc ibe a WSMA ha enables ai bo ne EC lux
measu emen s in emo e se ings a easonable cos and min-
imal in as uc u al demand. The objec i es o he p esen
s udy a e o in es iga e he possibili ies o (i) de i ing mean-
ing ul EC luxes om WSMA measu emen s o e complex
e ain, and (ii) scaling he esul s o a domain o in e es .
We applied he WSMA o e he undula ing s eppe o
he Xilin Ri e ca chmen (XRC), Inne Mongolia, China
(Fig. 1). On 21 days in he summe o 2009, ligh s along line
ansec s we e conduc ed a 50–100 m a.g.l. F om bounda y
laye scaling i is ound ha he e ical lux g adien s below
he ligh le el sa is y he su ace laye de ini ion (cons an
wi hin 5–10%). Hence measu ed sensible (H) and la en hea
lux (LE) can be in e p e ed as su ace luxes (Sec . 3.1). Be-
cause o i s clima e and managemen p ac ices ypical o
semia id g asslands o China (Bu e bach-Bahl e al., 2011),
in ensi e ecological esea ch commenced in he XRC in he
la e 1970s (Jiang, 1985). Besides Tibe , Inne Mongolia is
Biogeosciences, 10, 2193–2217, 2013 www.biogeosciences.ne /10/2193/2013/
114 APPENDIX E: METZGER ET AL. (2013)
S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s 2201
Fig. 5. Flow cha showing how inpu and epo ed da a s eams a e p ocessed along he ou p incipal s eps o he LTFM me hod. Addi ional
de ail is p o ided in Sec s. 2.4.4 and 4, and a summa y o all no a ion can be ound in Appendix A.
2.4.4 En i onmen al esponse unc ion
We base he de elopmen o a ca chmen -speci ic ERF on
he wo ks o Chen e al. (1999), Hu jes e al. (2010) and
Ogunjemiyo e al. (2003). The gene al idea is o es ablish
a unc ional ela ionship be ween spa ially o empo ally e-
sol ed lux obse a ions ( esponses) and co esponding en i-
onmen al d i e s. Figu e 5 p o ides an o e iew o he no el
app oach o ERF p esen ed in he ollowing.
Thus a , a sui able numbe o lux obse a ions was ob-
ained by ei he sho ening he ime-domain EC a e aging
in e al (Chen e al., 1999; Ogunjemiyo e al., 2003), o by
s a i ying epea ed obse a ion along he same ligh line
on di e en days (Hu jes e al., 2010). The inhe en d aw-
backs a e he neglec o ei he long wa eleng h con ibu ions
o he lux measu emen , o in e -day a iabili y o ecosys-
em d i e s. Bo h a e o e come using he wa ele c oss-
scalog am echnique (Sec . 2.4.2).
P e iously, he de elopmen o ERFs has solely ocused
on d i e s in he oo p in o he lux obse a ions, namely
disc e e land co e classi ica ions. This p ocedu e igno es
wi hin-class a iabili y ac oss a ca chmen , e.g. along cli-
ma ic o al i udinal g adien s, which can be o e come by us-
ing con inuous a iables such as LST and EVI ins ead. In
addi ion, he p esen app oach conside s he me eo ological
d i e s S↓, mixing a io (MR), and po en ial empe a u e
(θ). This a oids he need o s a i ying o p e-selec ing da a,
and enables cons uc ing a single ERF ha is alid o he en-
i e obse a ion pe iod and, wi hin he ange o he measu ed
a iables, h oughou a ca chmen o in e es .
Hi he o, ERFs we e de e mined as he in e se o a linea
mixing ma ix, using ei he nume ical (Chen e al., 1999) o
eg ession me hods (Hu jes e al., 2010; Ogunjemiyo e al.,
2003). Such a p ocedu e assumes a linea ela ionship be-
ween d i e s and esponses, which is subjec o on-going
discussion and esea ch (e.g. Raupach and Finnigan, 1995).
Ins ead, he p esen app oach uses boos ed eg ession ees
(BRTs), a non-pa ame ic machine lea ning echnique, o es-
ablish an ERF be ween d i e s and esponses. In con as
o pa ame ic app oaches, BRTs do no assume a p ede e -
mined o m o he esponse, bu cons uc an ERF acco d-
ing o he in o ma ion in he da a. I is o his eason ha
no he absolu e alues o he land su ace and me eo olog-
ical d i e s a e impo an , bu a he hei spa ial a iabil-
i y and cohe ence. In case o he land su ace d i e s o
example, he only assump ion made he e is ha he spa ial
pa e ns o LST and EVI app oxima e he spa ial pa e ns
o sou ce s eng h in Hand LE (e.g. Holmes, 1970; Oke,
1987). This is a much weake assump ion han a mechanis-
ic link, and adds powe o he me hod. BRTs can i com-
plex nonlinea ela ionships, au oma ically handle in e ac-
ions be ween d i e s, and p o ide p edic i e pe o mance
ha is supe io o mos adi ional modelling me hods (e.g.
Hu e al., 2010). He e we use he BRT wo k package by Eli h
e al. (2008), which builds upon he GBM lib a y by Ridge-
way (2012). To iden i y he op imal choice o pa ame e s and
a iables o he BRTs, a sensi i i y analysis was conduc ed
www.biogeosciences.ne /10/2193/2013/ Biogeosciences, 10, 2193–2217, 2013
APPENDIX E: METZGER ET AL. (2013) 115
2202 S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s
Fig. 6. Fligh along pa e n O12 on 8 July 2009, 12:16–12:24 CST (whi e dashed line). The composi e lux oo p in along he ligh line
(30 %, 60 %, 90 % con ou lines) is supe imposed o e maps o land co e (le panel), land su ace empe a u e (LST, cen e panel), and
enhanced ege a ion index (EVI, igh panel). The land co e colou code and co esponding abb e ia ions a e iden ical wi h Fig. 2.
using he c oss- alida ion (CV) p ocedu e desc ibed in Eli h
e al. (2008). Du ing c oss alida ion all a ailable da a a e
di ided in o 10 andom combina ions o aining (90 %) and
e alua ion (10 %) ac ions, which allows assessing and op i-
mising model pe o mance. The pa ame e se ings ha mini-
mized p edic i e de iance o he p esen da ase we e ound
o be: absolu e (Laplace) e o s uc u e, bag ac ion (0.7),
ee complexi y (5), lea ning a e (0.1), and numbe o ees
(104). The ini ial se o a iables also included ime o he
day, MODIS albedo, a mosphe ic p essu e, land co e , z,
zi,u,u∗,z0, i ual po en ial empe a u e, as well as ele-
a ion, opog aphic we ness index, aspec , and slope o he
oo p in modelled sou ce a ea. We use he a iable d op-
ping algo i hm by Eli h e al. (2008) o each a comp omise
be ween p edic i e de iance and model pa simony. This al-
go i hm (i) i s a BRT model, (ii) pe o ms a 10- old CV,
(iii) d ops he leas impo an p edic o (de e mined om he
imp o emen o he model and he numbe o spli s, F ied-
man, 2001), and (i ) epea s his sequence un il a s opping
c i e ion is eached. The mean CV de iance can be used o
decide how many a iables can be emo ed wi hou signi i-
can ly a ec ing p edic i e pe o mance. He e, we se an up-
pe h eshold o 30 W m−2 o he mean CV de iance, which
equals ≤1/2 he andom sampling e o in he lux obse a-
ions (Table 4). The d opping o a iables i s s opped o
LE a 29.2 W m−2mean CV de iance, yielding a se o he
i e mos impo an p edic o s (LST, EVI, S↓, MR, and θ).
Fo H he same p edic o se yields a mean CV de iance o
only 22.6 W m−2. Rema kably, a mosphe ic p essu e, z,and
ziwe e no signi ican p edic o s o he obse ed luxes. This
indica es ha he chosen ligh /analysis s a egy e ec i ely
minimizes c oss-con amina ion o he lux obse a ions by
e ical lux/p essu e g adien s. Analogously he algo i hm
d opped ele a ion, aspec , and slope o he oo p in mod-
elled sou ce a ea as p edic o s. This shows ha slope-induced
e ec s on adia i e ans e o u bulence gene a ion do no
signi ican ly impac he lux obse a ions. Consequen ly, he
inal BRT model is i ing an ERF o Hand LE as unc ion
o only he i e mos impo an p edic o s. This ERF is hen
used o p edic Hand LE h oughou he XRC, as a unc ion
o LST and EVI o each g id cell, and he median S↓,MR,
and θ o he du a ion o a ligh .
In he ollowing we will use he e m LTFM o e-
e o he o e all p ocedu e consis ing o Low le el
ligh s, Time– equency-, Foo p in -, and Machine
lea ning analyses (Fig. 5).
2.5 Unce ain y
Th oughou he p esen s udy, we use he median and he me-
dian absolu e de ia ion as p e e ed measu e o loca ion and
scale, espec i ely (C oux and Rousseeuw, 1992; Rousseeuw
and Ve bo en, 2002). All esul ing unce ain y es ima es a e
ep esen a i e o one s anda d de ia ion. Fo he pu pose o
de ec ing sys ema ic di e ences be ween obse a ions and
p edic ions, we use he maximum-likelihood i ing o a unc-
ional ela ionship (MLFR, Ripley and Thompson, 1987).
This me hod assigns a weigh o each da a couple in he e-
la ionship, which is in e sely p opo ional o i s e o a i-
ances. In ou case, he squa ed andom lux e o s in he
obse a ions, and he esiduals in he BRT c oss- alida ion
ensemble a e used. This app ecia es eliable da a and dep e-
cia es unce ain da a couples. The e o s in he MLFR co-
e icien s a e de e mined om a jackkni e es ima o (Que-
nouille, 1956; Tukey, 1958). I he eg ession in e cep s we e
no signi ican , he ela ionships we e o ced h ough he o i-
gin, and con idence in e als we e de e mined om he slope
e o . The coe icien o de e mina ion R2was calcula ed
in analogy o weigh ed leas -squa es eg ession (K alse h,
1985; Wille and Singe , 1988). I is he p opo ion o a ia-
ion in he weigh ed dependen a iable ha can be accoun ed
o by he weigh ed independen a iable.
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116 APPENDIX E: METZGER ET AL. (2013)
S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s 2203
Unce ain y in he LTFM up-scaling p ocedu e o igina es
om di e en sou ces du ing measu emen and da a analy-
sis. Pa o hese unce ain y e ms exhibi andom cha ac e -
is ics; i.e. hey end o cease wi h sample size. Ano he pa
howe e will sys ema ically bias he esul s, independen o
sample size. An unce ain y budge o he andom and sys-
ema ic unce ain ies in he LTFM p ocedu e will consis o
unce ain y e ms o (i) ins umen a ion and ha dwa e, (ii)
u bulence sampling, (iii) spa io- empo al analysis, (i ) BRT
esiduals, ( ) BRT esponse unc ion, and ( i) BRT s a e a i-
ables. While unce ain y e ms (i), (ii), and (i ) can be quan-
i ied wi h eadily a ailable p ocedu es (Sec s. 2.4, 3.3), in
eh ollowing we desc ibe se e al echniques o assess e ms
(iii), ( ) and ( i).
2.5.1 Spa io- empo al analysis in he e ogeneous e ain
Unde he umb ella o spa io- empo al analysis, we quan i y
in he ollowing he unce ain y con ibu ion om wa ele
analysis, oo p in modelling, and he assump ion o linea
mixing. The luxes de i ed om he wa ele c oss-scalog am
we e adjus ed o ma ch he leg-a e aged luxes om ime-
se ies EC, which a oids bias be ween bo h echniques. Also
a eas abo e he wa ele c oss-scalog am COI we e used in
he lux calcula ion o ensu e including all scales o u bulen
anspo along he en i e ansec . Howe e , alues abo e he
COI a e po en ially dis o ed due o edge e ec s, in pa icula
close o he beginning and he end o each ansec . These
a e ac s p opaga e in he esul ing a iances and luxes, and
consequen ly in o he oo p in es ima es. Addi ional spa ial
unce ain y e ms esul om he use o an “o line” oo -
p in model ha does no conside he ac ual low ield, as
well as om he MODIS EVI and LST da a. The use o
BRTs does no expec a linea esponse be ween he s a e
a iables and he lux signal. Howe e , LTFM s ill assumes
he linea mixing o he lux signal wi h espec o he con-
ibu ing su ace pa ches wi h di e en biophysical p ope -
ies and sou ce s eng hs.
To quan i y he e o inhe en in he abo e analysis s eps,
we compa e maps o LTFM p edic ed luxes o ai bo ne lux
obse a ions. (i) The BRT is ained wi h all a ailable ob-
se a ions (N=8466). (ii) Using he median s a e a iables
along each ligh leg (N=42), he BRTs esponse unc ion
is used o p edic a simila numbe o lux maps (Fig. 11).
(iii) The LTFM oo p in s a e supe imposed o e hese lux
maps. (i ) Fo each lux obse a ion, a p edic ed lux is cal-
cula ed as he oo p in -weigh ed a e age o all con ibu ing
cells, and ( ) p edic ions and obse a ions a e compa ed.
2.5.2 Response unc ion
BRTs a e a non-pa ame ic machine lea ning echnique in
which a esponse unc ion is cons uc ed acco ding o he
cohe encies in he aining da a. As a di ec consequence he
p edic i e pe o mance o BRTs depends on how comple e
he combina ions o s a e a iables in he e alua ion da a a e
ep esen ed in he aining da a. He e we assess he suscep-
ibili y o he BRT esponse unc ion and p edic i e pe o -
mance o missing s a e a iable combina ions in he ain-
ing da a. Fo his pu pose, 12 incomple e aining da ase s
a e c ea ed, each o which omi ing a di e en ligh ou o
he o al o 12 ligh s in Table 1. Fo each incomple e ain-
ing da ase , (i) he BRT is ained, (ii) he esul ing esponse
unc ion is used wi h he s a e a iables along he omi ed
ligh o p edic ion, and (iii) p edic ions and obse a ions
a e compa ed.
2.5.3 S a e a iables
He e, we conside he unce ain y esul ing om dis ega d-
ing pa o he na u al a iabili y in he s a e a iables ha
a e used o spa ially and empo ally explici BRT p edic-
ions. Fo his pu pose we quan i y he dis ega ded pa s o
he na u al a iabili y in each s a e a iable and p opaga e i
h ough he ull BRT model. While explici in ime, he me e-
o ological a iables measu ed by he ai c a do no co e he
en i e ca chmen . We es ima e a measu e o spa ial a iabili y
om all subsequen pai s o ligh s ha a e loca ed in di e -
en a eas o he ca chmen (Table 1, Fig. 2). The median di -
e ences h oughou he ca chmen o S↓(−6±12 W m−2),
θ(−1.1±1.1K),andMR(−0.5±0.3gkg
−1) a e no signi -
ican (Wilcoxon ank-sum es , p≥0.18). On he con a y,
MODIS EVI and LST a e explici in space, bu no con in-
uous in ime. The 8-day ends om one scene o he nex
a e accoun ed o in he BRT p ocedu e h ough empo al
in e pola ion be ween he MODIS scenes (Sec . 2.2). How-
e e , p ocesses o sho e du a ion, such as equen e en s o
small-scale con ec i e p ecipi a ion, go unaccoun ed. Hence
we es ima e a measu e o he na u al a iabili y be ween
wo MODIS scenes. Fo his pu pose we calcula e he me-
dian change o all g id cells be ween all subsequen MODIS
scenes, amoun ing o 0.01 ±0.05 o EVI and −0.5±6.2K
o LST. The andom pa o EVI and LST na u al a iabil-
i y by a exceeds he MODIS da a p oduc unce ain y o
≈0.015 (Xiang e al., 2003) and ≈1 K (Wan and Li, 2008),
espec i ely. Hence MODIS da a p oduc unce ain y was no
conside ed sepa a ely.
The co ela ion ma ix be ween he s a e a iables was
calcula ed using all 8446 ai c a obse a ions. A a iance-
co a iance ma ix was calcula ed om his co ela ion ma ix
and he andom pa o he s a e a iables’ na u al a iabili y.
P ese ing he a iance-co a iance ela ionship, 1000 sam-
ples we e d awn om a mul i a ia e no mal dis ibu ion wi h
ze o mean. These ep esen 1000 combina ions o co-exis ing
na u al a iabili y in he s a e space o he BRT model. The
p opaga ion h ough he BRT model was pe o med indi idu-
ally o each combina ion by (i) supe imposing he es ima ed
na u al a iabili y o e he measu ed s a e a iables o all
8446 obse a ions, (ii) pe o ming a BRT p edic ion, and (iii)
compa ing he esul s o he undis u bed p edic ions.
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APPENDIX E: METZGER ET AL. (2013) 117
2204 S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s
3 Resul s and discussion
In he i s pa o his sec ion, we assess he su ace–
a mosphe e mixing egimes. F om he e wa ele analysis,
oo p in modelling and BRTs a e used o in e ERFs be-
ween land su ace p ope ies and he lux measu emen s.
Las ly, unce ain ies in he LTFM up-scaling p ocedu e a e
analysed and discussed.
3.1 Ho izon al mixing be ween su ace and ligh le el
On spa ial a e age ene gy conse a ion equi es ha he
e ical p o iles o Hand LE app oach hei espec i e
en ainmen lux a he op o he CBL (e.g. Dea do ,
1974; So bjan, 2006). The linea e ical lux g adien o
H h oughou he CBL was calcula ed (−0.21 W m−2m−1
–−0.06 W m−2m−1), assuming ha Hceases a he s a i-
cally s able en ainmen zone a ound 0.8 CBL. Howe e , he
en ainmen lux o Eis unknown. Hence we canno es ima e
he e ical lux g adien o E, bu assume a compa able o -
de o magni ude as o H. The esul ing e ec o he e -
ical lux g adien below he ligh le el is −5±2% o H,
which alls well wi hin he su ace laye de ini ion (e.g. Rau-
pach and Finnigan, 1995; S ull, 1988, lux cons an wi hin
5−10%). Thus, i is easible o assume ha Hand Emea-
su ed a ligh le el a e ep esen a i e o su ace luxes.
The cha ac e is ic leng h scale o su ace he e ogenei y is
on he o de o se e al hund ed o housand me e s, wi h
an a e age o LH=1012 ±715 m (Table 2). Along iden i-
cal ligh pa hs LHis compa able be ween days wi h di e -
en me eo ological se ings (e.g. 15 and 17 July 2009, 26 and
30 July 2009). This con i ms he use ulness o he su ace
empe a u e measu emen as a p oxy o su ace he e ogene-
i y. Only he longe ligh pa hs C1 and C2 c oss he dune
bel in he cen e o he ca chmen (Fig. 2). The dune bel
is he la ges con inuous land co e a e s eppe, and con-
sequen ly he au oco ela ion unc ion o Tses ima es la ge
alues o LH(1458–2615 m). Du ing all ligh s, LHwas
small compa ed o he Raupach leng h (LR=1532–5214 m),
and hus he in luence o he su ace he e ogenei y is con-
ined wi hin he CBL (zi=1100–2500 m). He e we use he
he mal blending heigh (zTB1 =40 ±29 m) as an es ima e
o he e ical le el whe e quasi-equilib ium o he u bulen
exchange be ween land su ace and a mosphe e is eached.
A all imes he ligh le el (z=48–102 m) is abo e zTB1
and below ≈10 % o he CBL dep h, a common es ima e
o he dep h o he a mosphe ic su ace laye (e.g. Raupach
and Finnigan, 1995; S ull, 1988). Hence i is easible o as-
sume ha he u bulence measu emen a ligh le el is ep-
esen a i e o he land su ace in he lux oo p in . The in-
e p e a ion o he lux obse a ions migh be mo e compli-
ca ed o measu emen heigh s below he he mal blending
heigh (limi ed spa ial ep esen a i eness) o abo e he su -
ace laye ( e ical lux g adien ). The blending leng h o -
mula ions LTB1 (1660±723) and LTB2 (957±441) a e used
o assess he minimum size o su ace he e ogenei y ha sig-
ni ican ly in luences he low a ligh le el. He e we use
255 m <L
TB2 <1852 m as a guideline, because LTB2 is also
ep esen a i e o he magni ude o su ace he e ogenei y. The
na i e esolu ion o he EVI da a (230 m) and he land co e
da a (90 m) is equal o o be e han LTB2, and hus su icien
o ep oduce he a iabili y o he land co e . In compa ison,
he na i e esolu ion o he LST da a (1000 m) is coa se, po-
en ially leading o an a enua ion o he ERFs.
Using he wa ele c oss-scalog am, long wa eleng h con-
ibu ions o he lux do no cons ain he spa ial esolu ion
o he lux compu a ion along he ligh pa h. Ne e heless,
he andom lux e o is in e sely p opo ional o he squa e
oo o he a e aging leng h (e.g. Lenschow and S anko ,
1986), and p opaga es di ec ly in o he compu a ion o he
ERFs. Hence, we conside a ade-o be ween andom e o
(high esolu ion) and smea ing (low esolu ion) o he esul -
ing lux es ima es. The upwind dis ance (pe pendicula o he
WSMA ligh pa h) whe e 80 % o he lux con ibu ions a e
included in he oo p in , L80% =1171±314 m, is compa a-
ble in magni ude o LH. Thus, a ligh pa h leng h o simila
ex en (1000 m) is a physically meaning ul window o he
compu a ion o u bulence s a is ics and luxes, because (i)
changes in he u bulen lux ( esponse) a e esol ed a he
same spa ial scale as he cha ac e is ic su ace he e ogenei y
(d i e ); (ii) he u bulence s a is ics used o oo p in calcu-
la ions a e ep esen a i e on he same spa ial scale as he up-
wind ex en ; and (iii) he andom e o o each lux es ima e
dec eases by ≈70 % compa ed o a window leng h o 90 m.
The (ae odynamic) oughness leng h is usually below
1 m, wi h excep ion o he low wind speed si ua ion on
17 July 2009, pa e n O11, and he highe ligh le els (z≥
97 m) on 26 July 2009 (Table 2).
3.2 Flux un-mixing
The p esen a ion o he lux un-mixing esul s ollows
he sequence o he LTFM analysis s eps. In Sec . 3.2.1
he spa ially esol ed lux obse a ions om he wa ele
c oss-scalog am a e illus a ed. Subsequen ly, oo p in mod-
elling is used o in e he biophysical su ace p ope ies in
he sou ce a ea o each lux obse a ion (Sec . 3.2.2). In
Sec . 3.2.3 he ERFs be ween lux obse a ions and me eo o-
logical and land su ace d i e s a e es ablished. These ERFs
a e hen used o p edic he su ace luxes h oughou he
XRC, which a e inally summa ized o di e en land co -
e s (Sec . 3.2.4).
3.2.1 Spa ially esol ed lux measu emen
He e and in he ollowing we use a ligh along pa e n
O12 o illus a ion, which ollows a shallow ele a ion g a-
dien (Fig. 4 bo om panel). This ligh pa e n is pa icu-
la ly sui able o his pu pose because o i s ma ked land
co e changes o e a ela i ely sho dis ance. The wa ele
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118 APPENDIX E: METZGER ET AL. (2013)
S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s 2205
Table 2. Mean leng h scales ±SD be ween epe i ions du ing he WSMA ligh s selec ed o analysis. Shown a e CBL dep h zi, ae odynamic
oughness leng h z0, ligh al i ude z, he mal blending heigh zTB1, leng h scale o su ace he e ogenei y LH, Raupach leng h LR, he he mal
blending leng hs LTB1 and LTB2, and he upwind dis ance om he WSMA L80%, whe e 80 % o he lux con ibu ions a e included in he
lux oo p in .
Da e Time (CST) ID z
i
(m) z
0
(m) z(m) z
TB1
(m) L
H
(m) L
R
(m) L
TB1
(m) L
TB2
(m) L
80%
(m)
8 Jul 2009 10:20–10:50 O10 1100 0.21 ±0.13 59 ±445±7 802 ±192 1532 ±105 1046 ±171 255 ±5931±52
12:00–12:50 O12 1800 0.07 ±0.05 72 ±624±2 700 ±58 4093 ±164 2160 ±263 628 ±39 1574 ±147
13 Jul 2009 11:30–12:10 O8 1900 0.04 ±0.05 51 ±041±4 1055 ±5 4770 ±3 1330 ±122 999 ±12 1440 ±127
12:40–13:10 O3 2100 0.05 ±0.07 51 ±238±5 858 ±95 4292 ±236 1134 ±45 1108 ±220 1305 ±64
15 Jul 2009 11:30–12:20 O11 2200 0.06 ±0.04 55 ±411±2 370 ±54 5214 ±508 1950 ±223 1368 ±304 1470 ±168
12:30–13:00 O7 2100 0.26 ±0.19 57 ±717±6 298 ±76 3507 ±82 984 ±117 1207 ±132 1081 ±128
17 Jul 2009 11:00–11:30 O11 1400 1.13 ±0.81 48 ±122±0 366 ±37 1589 ±65 788 ±74 440 ±28 720 ±74
12:20–13:00 O7 1400 0.05 ±0.06 52 ±219±8 507 ±219 3136 ±169 1381 ±54 950 ±159 1296 ±150
26 Jul 2009 12:50–15:30 C1 2500 1.75 ±1.91 97 ±485±68 1458 ±913 2626 ±284 1974 ±562 752 ±196 991 ±331
13:10–15:10 C2 2500 2.30 ±2.12 102 ±583±51 1459 ±632 2430 ±382 1921 ±325 916 ±310 945 ±191
30 Jul 2009 11:00–13:30 C1 1600 0.48 ±0.34 56 ±346±21 1653 ±161 3097 ±340 2403 ±1438 1015 ±22 1042 ±100
11:10–13:20 C2 1600 0.11 ±0.01 54 ±051±13 2615 ±84 3798 ±735 2853 ±601 1852 ±51 1206 ±0
c oss-scalog am allows a high spa ial disc e iza ion o u -
bulen lux measu emen s. A he same ime i includes
lux con ibu ions om wa eleng h ha a e signi ican ly
longe han he 1000 m subin e al o each lux obse a-
ion (Fig. 4). The esul ing high numbe o lux obse a ions
along a ligh line leads o p e iously unachie able esolu-
ion and co e age o he s a e space. Spa ially cohe en lux
con ibu ions a e de ec ed on anspo scales (eddy sizes) o
500–2000 m, ha is o simila size as he ex en o homo-
geneous su ace pa ches LH. S ong local lux con ibu ions
a e con ined o scales <500 m, and app oxima ely decay
wi hin he lowe h eshold o he obse ed blending leng hs
LTB1 and LTB2. This con i ms a close coupling be ween a -
mosphe ic u bulence s uc u es wi h su ace pa chiness, and
consolida es he in e p e a ion o he leng h-scale app oach.
The less ce ain lux con ibu ions abo e he wa ele COI a e
small (−15 o −4 % median di e ences o all ligh s). In he
p esen example he COI is con ined o ela i ely small scales
(≤4 km), which is a di ec esul o he compa a i ely sho
ligh . In gene al, mo e ce ain lux con ibu ions below he
COI include anspo scales up o ≈1/3o he ligh leng h,
and can each ≈16 km o ligh pa e ns C1 and C2. How-
e e , his also implies ha he maximum conside ed anspo
scale di e s be ween he ligh pa e ns, jus as i would be
he case o he ime-domain EC me hod. The wa ele c oss-
scalog am e eals s ong u bulen anspo in he second
and ou h qua e o he ligh o H, and in he i s and
hi d qua e o LE (Fig. 4). When in eg a ed o e all ans-
po scales o each o e lown 90 m cell o he land co e
g id, hese pa e ns co espond o s ong upwa d luxes.
3.2.2 Land co e
In Sec . 3.2.1, u bulence s a is ics and luxes we e in eg a ed
o each o e lown 90 m cell o he land co e g id. In he
ollowing we expand he in eg a ion window o o e lapping
subin e als o 1000 m leng h, while e aining a spa ial dis-
c e iza ion o 90 m. Such a p ocedu e signi ican ly educes
he andom sampling e o (Sec . 3.1), hough a he cos o
dec easing he numbe o esul ing obse a ions by one win-
dow size (dN≈10). The esul ing u bulence s a is ics a e
used o calcula e he sou ce a ea o each indi idual lux ob-
se a ion along he ligh line, which a e supe imposed o e
he land co e g ids. Figu e 6 shows ha in gene al LST and
EVI ollow he land co e pa e ns, e.g. lowe empe a u e
and highe g eenness o i iga ed ag icul u e and ma shland.
Howe e , i is also e iden ha he s a ic land co e clas-
si ica ion canno e lec he cu en su ace condi ions. Fo
example, he ma shland in he no h-wes e n quad an ap-
pea s d ied-ou (high LST and low EVI), while he s eppe
a ea in he no h-eas e n quad an shows la ge a ia ions in
LST. Hence, biophysical su ace p ope ies also a y signi i-
can ly wi hin he land co e classes. This is likely a unc ion
o geomo phological p ope ies such as aspec , slope and soil
ype, bu also due o he la ge a iabili y o con ec i e ain-
all e en s ac oss he s udy a ea (e.g. Scha a h e al., 2011).
Following supe imposi ion o he oo p in s o e he land
co e da a, he spa ial con ibu ions o di e en su ace p op-
e ies o each lux obse a ion can be quan i ied (Fig. 7). I is
e iden ha measu ed Bo changes in co espondence wi h
he domina ing land co e , i.e. low Bo o ma shland and
i iga ed ag icul u e, and high Bo o ba e soil and s eppe.
LST and EVI a e s a i ied be ween he land co e s, al-
hough in di e en sequence compa ed o he egional a -
e age (Fig. 3). The a iabili y o LST and EVI wi hin he
land co e classes is equal o o la ge han he be ween-class
a iabili y, in pa icula o ma shland, i iga ed and ain ed
ag icul u e. While LST and EVI beha e in e sely o all na -
u al land co e s (−0.78 < <−0.10), he con a y is ue
o i iga ed ( =0.92) and ain ed ( =0.30) ag icul u e.
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APPENDIX E: METZGER ET AL. (2013) 119
2206 S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s
The la e inding appea s coun e -in ui i e, bu can be ex-
plained by illage a ming in he low-le el plains wi h c ops
ha a e no adap ed o he semia id clima e, such as po a-
oes. The albedo o hese densely ege a ed c ops can be
lowe compa ed o he spa sely ege a ed s eppe land co e
(α≈0.2, Ke ze e al., 2008), esul ing in highe oliage
empe a u es. Only wo na u al land co e s, ma shland and
moun ain meadow, exhibi simila ly high EVI alues as he
ield c ops (Figs. 2, 3). Ne e heless, he LST o hese land
co e s is compa a i ely low. In case o he ma shland his can
be explained by wa e -sa u a ed soils wi h high hea capac-
i y. Con e sely, lowe empe a u es in acco dance wi h he
adiaba ic empe a u e g adien a e expec ed o he moun ain
meadows a highe al i udes.
In Fig. 8 Hand LE obse a ions along he ligh line
a e shown oge he wi h he LST and EVI in he espec-
i e sou ce a ea. Because o he 1000 m in eg a ion win-
dow o e he wa ele c oss-scalog am, he esul s appea
smoo he compa ed o Fig. 4, whe e a 90 m in eg a ion win-
dow is used. I is appa en ha Hand LE bo h sys ema i-
cally change wi h LST ( H=0.64, LE =−0.84) and EVI
( H=−0.62, LE =0.73). Howe e , peaks in H(3 km and
9 km in Fig. 8) and in LE (0 km and 7 km) do no mani es
when hei espec i e land su ace d i e s in he oo p in a e
maximal. Ins ead hey seem o ollow a ade-o unc ion be-
ween LST and EVI.
3.2.3 En i onmen al esponse unc ions
Thus a ou indings indica e ha he in e ac ions be ween
land su ace and a mosphe e a e mul i- ace ed and po en-
ially non-linea . Hence we use LST and EVI as opical,
spa io- empo al p oxies o he sou ce s eng h o Hand
LE, a he han using he land co e classi ica ion di ec ly.
In compa ison o ea lie lux un-mixing s udies (Chen e al.,
1999; Hu jes e al., 2010; Ogunjemiyo e al., 2003), his has
he bene i o (i) p o iding indi idual sou ce s eng h ep-
esen a ions o he e ec s o su ace mois u e and empe -
a u e, and (ii) ep esen ing he land su ace by con inuous
(LST, EVI) a he han disc e e a iables (land co e classes),
hus enabling he use o mo e ad anced scaling algo i hms.
He e, we use BRTs o ex ac he ela ionships be ween all
(N=8446) lux obse a ions and land co e (LST, EVI) and
me eo ological (S↓, MR, and θ) a iables. While BRTs a e
capable o ep oducing complex in e ac ions h ough mul i-
laye ed b anching, he i ed unc ion can be summa ized,
e.g. as pa ial dependence plo s (Fig. 9). These show he e -
ec o each indi idual a iable on he esponse a e (i) sub-
ac ion o he o se (H0=161 W m−2,LE
0=176 W m−2),
and (ii) accoun ing o he a e age e ec s o all o he a i-
ables in he model. The pa ial dependence plo s in Fig. 9
a e so ed in o de o he ela i e impo ance o he esponse
a iables (F iedman, 2001). The mos impo an esponses
o Ha e non-linea (LST, θ), ollowed by linea esponses
(S↓, MR, and EVI). Wi h he excep ion o MR and EVI, he
indi idual esponses a e posi i e in sign. The o de o he e-
sponses o LE is pa ially di e en (MR, LST, θ,S↓,and
EVI), and only he esponses on S↓and EVI a e app oxi-
ma ely linea (no shown). Wi h excep ion o MR (conca e,
maximal esponse a ound 10 g kg−1) and LST (con ex, min-
imal esponse a ound ≈310 K), he signs o he esponses
o LE a e posi i e. I appea s su p ising ha Hand LE a e
only weakly ela ed o S↓. This can be explained by using
only noon ime ligh s in he p esen s udy, whe e S↓mainly
ul ils he pu pose o accoun ing o a ying cloud/ adia ion
condi ions be ween di e en measu emen days. In addi ion,
du ing indi idual ligh s S↓was usually cons an o wi hin
≤10 % (Table B1). Howe e , when using ERFs o ep oduce
a diu nal cycle, a much la ge dependence o Hand LE on
S↓would be expec ed.
In Fig. 10 MLFRs a e es ablished be ween BRT i ed
alues o Hand LE and he obse ed luxes (N=8446).
He e we use he BRT c oss- alida ion esiduals and he an-
dom sampling e o s in he obse a ions o de e mine he
MLFR weigh s o each da a poin . Unce ain y e ms (i),
(iii), ( ) and ( i) (Sec . 2.5) canno be quan i ied indi idu-
ally o each obse a ion. Hence hese e ms a e no consid-
e ed he e, bu in he inal unce ain y budge (Tables 3 and
4). Fo bo h Hand LE he ag eemen be ween he BRT i -
ed alues and he obse ed luxes is excellen . Con a y o
ou ini ial an icipa ion, he ERFs a e no a enua ed by he
ela i ely coa se MODIS LST esolu ion, as indica ed by ap-
p oxima ely ze o MLFR o se and uni y slope. The median
absolu e de ia ion in he esiduals is small (≤1 %). How-
e e , se e al ou lie s a e ound o mode a e o high luxes
o H(N=41) and LE (N=133), o which he BRTs un-
de es ima e he obse ed alue by −150 Wm−2o mo e.
The majo i y o hese cases occu du ing he ligh s O8 on
13 July 2009 and C1 on 26 July 2009, espec i ely. On
bo h da es he ou lie s concu wi h highly in e mi en so-
la i adiance (200 <S↓<1200 W m−2) along a sho sec-
ion o he ligh pa hs. Fo ins ance an in e mi en cloud
co e can dis up he unc ional ela ion be ween he i adi-
ance (d i e ) and he lux ( esponse) obse a ions, because,
(i) a a ligh le el o 50–100 m a.g.l., he ai c a i adiance
measu emen does no ep esen S↓in he sou ce a eas o
Hand LE, and (ii) he plan physiological esponse can a y
subs an ially on spa io- empo al scales ha a e small com-
pa ed o a mosphe ic anspo p ocesses be ween he land
su ace and he ai c a .
Ou choice o land su ace and me eo ological d i e s ap-
pea s o wo k well o desc ibing he noon ime su ace–
a mosphe e exchange o hea and wa e apou o e a
mois u e-limi ed landscape. Howe e , i is impo an o no e
ha app op ia ely desc ibing exchange p ocesses o e longe
pe iods o ime, o di e en landscapes o scala s migh e-
qui e inding an en i ely di e en se o p edic o s.
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120 APPENDIX E: METZGER ET AL. (2013)
S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s 2207
Fig. 7. Biophysical su ace p ope ies in he oo p in o each obse a ion (N=124) along he ligh pa e n O12 on 8 July 2009, 12:16–
12:24 CST, summa ized by land co e . Shown a e (clockwise om op igh panel) land su ace empe a u e, enhanced ege a ion index,
Bowen a io, and he land co e ac ion in he oo p in . The dashed lines a e land co e a e ages o LST and EVI, and he spa ial end o
Bo. The land co e colou code and co esponding abb e ia ions a e iden ical wi h Fig. 2.
Fig. 8. Sensible hea lux (le panels) and la en hea lux ( igh panels) along he ligh pa e n O12 on 8 July 2009, 12:16–12:24 CST. Also
shown is he andom sampling e o (e o ba s) o each obse a ion (N=124), and he spa ial end (dashed line). The op and bo om
panels show he land su ace empe a u e and he enhanced ege a ion index in he oo p in o each obse a ion, espec i ely.
3.2.4 Ex apola ion and summa iza ion
Fo he du a ion o each ligh pa e n, he ained BRT mod-
els a e used o ex apola e Hand LE h oughou he XRC.
Fo his pu pose he median me eo ological s a e a iables
du ing each ligh pa e n as well as opical g ids o MODIS
LST and EVI da a a e used. G id cells ha exceed he s a e
space o he BRT aining da ase (N=8446) a e excluded
om ex apola ion. Fig. 11 shows he esul ing lux g ids o
h ee di e en days, wi h a spa ial co e age o ≥92 %. Be-
cause o he iden ical s a e space anges o BRT aining
and p edic ion, also he anges o he ex apola ed u bulen
luxes a e wi hin limi s o he obse a ions. Despi e ha he
land co e classi ica ion was ne e used du ing he ex apo-
la ion p ocess, se e al landscape uni s a e clea ly ecogniz-
able in he lux maps. Fo ins ance bo , he Xilin Ri e alley
and he moun ainous headwa e a ea o he eas display low
Hand LE. On he con a y, he non- ege a ed basin on he
no he n ip shows consis en ly low e apo anspi a ion.
Fo a gi en me eo ological bounda y condi ion (MR, θ,
S↓), he hea luxes wi hin se e al hou s o sola zeni h
can be exp essed as a unc ion o LST and EVI (Fig. 9). In
u n, hese biophysical su ace p ope ies a e cha ac e is ic
wi hin a land co e class (Fig. 3). He e, we agg ega e all
g id cells o he lux maps acco ding o land co e class,
esul ing in sample dis ibu ions o Hand LE. This allows
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APPENDIX E: METZGER ET AL. (2013) 121
2208 S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s
Table 3. Median land co e speci ic lux es ima es o Hand LE om he LTFM p ocedu e o e all ligh pa e ns ±median spa ial a iabili y
wi hin he espec i e land co e . Also shown a e he co esponding median ensemble andom unce ain ies σens(H), σens(LE) and land co e
speci icsamplesizeN.
Land co e H(Wm−2)LE(Wm
−2)σens(H) σens(LE) N
Ba e soil 193 ±32 136 ±38 1 % 1 % 22049
Sand dunes 188 ±37 144 ±55 1 % 1 % 43424
Ma shland 125 ±55 230 ±59 1 % 1 % 20722
S eppe 202 ±40 138 ±46 <1% <1 % 321956
Moun ain meadow 114 ±47 260 ±69 1 % 1 % 25175
Se lemen s 172 ±40 155 ±46 3 % 5 % 1404
Rain ed ag icul u e 183 ±35 147 ±40 1 % 1 % 17024
I iga ed ag icul u e 116 ±32 224 ±41 5 % 5 % 1068
Table 4. Median sys ema ic- and andom unce ain y e ms (in
pa en heses) o a single lux obse a ion o g id cell h oughou
he LTFM p ocedu e.
Sou ce HLE
Ins umen a ion and ha dwa e 0 % (8 %) 0 % (7 %)
Tu bulence sampling 0 % (57 %) 0 % (121 %)
Spa io- empo al analysis 2 % (40 %) 4 % (47 %)
BRT esiduals 0 % (5 %) 0 % (6 %)
BRT esponse unc ion 11 % (69 %) 18 % (77 %)
BRT s a e a iables 13 % (77 %) 14 % (75 %)
a o mal ansi ion om a mosaic- o a ile ep esen a ion
o Hand LE o e he XRC o he du a ion o each ligh
pa e n (Mengelkamp e al., 2006). These sample dis ibu-
ions hen enable he analysis o land co e speci ic sou ce
s eng hs (36 W m−2<H <364 W m−2,46Wm
−2<LE <
425 W m−2), as well as he spa ial a iabili y wi hin a land
co e (11 W m−2<σ
H<169 W m−2,14Wm
−2<σ
LE <
152 W m−2). Table 3 gi es an o e iew o he median land
co e speci icHandLEo e all ligh pa e ns, and hei
median spa ial a iabili y. These esul s all well wi hin
he ange o summe ime ensemble a e age luxes du ing
sola noon obse ed by g ound-based EC measu emen s
o e di e en land co e s in his egion (100 Wm−2<H<
310 W m−2and 100 Wm−2<LE <480 W m−2; Gao e al.,
2009; Hao e al., 2007; Hao e al., 2008; Shao e al., 2008).
In compa ison, he ligh -line a e age hea luxes a e in
he ange o 71 Wm−2<H<310 W m−2and 46 Wm−2<
LE <300 W m−2(Table B2).
Howe e , he magni udes o Hand LE a e no only unc-
ions o land co e , bu also p opo ional o he a ailable en-
e gy. The a ailable ene gy changes wi hin, bu in pa icula
be ween ligh days. To alle ia e his e ec and o enable
he compa ison be ween di e en ligh s, we calcula e he
Bowen a io Bo =H/LE be ween he sample dis ibu ions.
Despi e di e ences in he me eo ological d i e s (MR, θ,
S↓), he median land co e speci ic Bo ag ees well be ween
subsequen ligh pa e ns on all measu emen days (Fig. 12).
Fig. 9. Boos ed eg ession ee pa ial esponse plo s o H o all
i e s a e a iables in o de o hei ela i e impo ance (in b aces).
The i ed unc ion (black) shows he a iable esponse o he BRT
o e he ange o one indi idual s a e a iable, while he emain-
ing s a e a iables a e held a an a e age, cons an alue. The ed
dashed line is a smoo hed ep esen a ion o he i ed unc ion (lo-
cally weigh ed polynomial eg ession).
Du ing he a e noon ligh s, 12 ±9 % highe Bo alues a e
obse ed compa ed o he mo ning ligh s, as expec ed om
a land su ace ha desicca es in he cou se o he day. Ne e -
heless, he 99.9 % con idence in e al includes uni y slope.
Hence, o se e al hou s wi hin sola zeni h Bo does no
change signi ican ly, and can be in e p e ed as a cha ac e -
is ic land su ace p ope y. On his basis we summa ize he
egional lux es ima es o he du a ion o he ligh campaign
as ime se ies o land co e speci ic Bo a ios (Fig. 12). The
o de o Bo be ween he land co e s ollows he o de o he
land co e speci ic EVI app oxima ely in e sely, while he
empo al pa e n ollows he pa e n o he land co e speci ic
LST (Fig. 3). High Bo alues un il mid-campaign indica e
ha he land su ace d ies ou . This end is e e sed owa d
he end o he campaign, when he app oach o humid ai
masses leads o conside able p ecipi a ion. The median daily
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122 APPENDIX E: METZGER ET AL. (2013)
S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s 2209
Fig. 10. Maximum likelihood unc ional ela ionships be ween N=8446 ai c a obse a ion and LTFM p edic ions o sensible hea lux
(le ) and la en hea lux ( igh ). The weigh o each da a poin in he ela ionship is ep esen ed by he size o he ci cles. The e o ba s
show he c oss- alida ion esiduals o he LTFM p edic ions, and he ensemble andom sampling e o o he ai c a measu emen . The
99.9 % con idence in e als a e oo na ow o be displayed p ope ly.
Fig. 11. Maps o he LTFM p edic ed luxes o sensible hea (H, op) and la en hea (LE, bo om) on 13, 17 and 26 July 2009 (le o igh ).
The colou g adien om blue o e g ey o ed ep esen s alues ha a e lowe , equal o, o g ea e han he a e age o he alues, espec i ely
(see legend). Pe cen ages in b aces a e he ligh ID indica e he spa ial co e age o he p edic ion h oughou he ca chmen . Me eo ological
s a e a iables om he supe imposed ligh lines a e used in he espec i e LTFM p edic ion (illus a ion iden ical wi h Fig. 2).
na u al a iabili y o Bo wi hin he land co e s anges om
48 % ( ain ed ag icul u e) o 79 % (ma shland). Wa e ab-
so bs s ongly in he nea in a ed, leading o nega i e EVI
alues ha a e no indica i e o ege a ion g eenness. Hence
EVI alues o wa e su aces a e disca ded, and he land
co e “wa e ” canno be modelled by he p esen ERFs.
3.3 Unce ain y
Me zge e al. (2012) ha e shown ha u bulen lux mea-
su emen s wi h he WSMA pla o m and ins umen a ion a e
unbiased, and p ecise o wi hin 8 %. Unce ain y due o he
limi ed sampling size o u bulen eddies is es ima ed using
he me hods o Lenschow and S anko (1986) and Lenschow
e al. (1994). De ails on he implemen a ion can be ound
in Me zge e al. (2012). Fo a single lux measu emen , he
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APPENDIX E: METZGER ET AL. (2013) 123
2210 S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s
Fig. 12. Le : MLFR o Bowen a io be ween he i s and he second ligh pa e n on e e y measu emen day. The weigh o each da a poin
in he ela ionship is ep esen ed by he size o he ci cles. Righ : ime se ies o Bo o di e en land co e s h oughou he measu emen
campaign. In bo h images he e o ba s ep esen he Gaussian sum o he na u al a iabili y in each land co e class and he ensemble
andom e o in he LTFM p ocedu e. The land co e colou code and co esponding abb e ia ions a e iden ical wi h Fig. 2.
Fig. 13. MLFRs o median obse ed and p edic ed luxes along 42 ligh lines. The e o ba s co espond o he a iabili y o he luxes along
he ligh line, and he weigh o each da a poin in he ela ionship is ep esen ed by he size o he ci cles.
sys ema ic (and andom) componen s o his sampling unce -
ain y ange om <1 % (57 %) o H o <1 % (121 %) o
LE. Table 4 summa izes abo e unce ain y sou ces, as well
as addi ional sou ces which a e discussed in he ollowing.
In o de o assess he unce ain y a ising om he spa io-
empo al analyses (Sec . 2.5.1), we compa e he median ob-
se ed and p edic ed luxes along all ligh legs (Fig. 13).
The LTFM p edic ions sligh ly o e es ima e he obse ed
luxes (H=5%, LE=5 %), bu in bo h cases he 99.9 %
con idence in e als include uni y slope. The median di -
e ences o dH=2 % (40 %), and dLE =4 % (47 %) ag ee
ma ginally mo e closely. Mo eo e , he median esiduals be-
ween i ed and obse ed alues emphasize ha he BRT i -
ing echnique is unbiased (Table 4).
Subsequen ly, we assess he p edic i e pe o mance o he
BRT esponse unc ion in ligh o missing s a e a iable
combina ions in he aining da a. Fo his pu pose one
ligh a a ime was omi ed om he aining da a, and
he incomple ely ained BRT model was used o p edic
he missing da a. The esul ing median di e ences amoun
o 11 % (69 %, N=7311) o Hand 18 % (77 %, N=
7265) o LE. Du ing p edic ion, cases whe e one o mo e
s a e a iables exceed hei espec i e ange du ing aining
we e excluded. As a consequence he sample size is ≈14 %
smalle han he o al numbe o obse a ions (N=8466).
Las ly, we conside he unce ain y esul ing om dis e-
ga ding pa o he spa io- empo al a iabili y in he s a e
a iables du ing BRT p edic ions. Fo his pu pose we
quan i y he dis ega ded pa s o he na u al a iabili y, and
p opaga e i h ough he ull BRT model. The esul ing me-
dian di e ences amoun o 13 % (77 %) and 14 % (75 %)
o Hand LE, espec i ely, and a e domina ed by he e ec
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130 APPENDIX E: METZGER ET AL. (2013)
S. Me zge e al.: Spa ially explici egionaliza ion o ai bo ne lux measu emen s 2217
Scha a h, D., Ba hold, F., and Be nho e , C.: Spa io empo al a i-
abili y o g assland ege a ion co e in a ca chmen in Inne
Mongolia, China, de i ed om MODIS da a p oduc s, Plan Soil,
340, 181–198, doi:10.1007/s11104-010-0465-4, 2011.
Schmid, H. P.: Foo p in modeling o ege a ion a mosphe e ex-
change s udies: A e iew and pe spec i e, Ag . Fo es . Me eo ol.,
113, 159–183, doi:10.1016/S0168-1923(02)00107-7, 2002.
Schuepp, P. H., MacPhe son, J. I., and Desja dins, R. L.: Ad-
jus men o oo p in co ec ion o ai bo ne lux mapping o e
he FIFE si e, J. Geophys. Res. A mos., 97, 18455–18466,
doi:10.1029/92JD00884, 1992.
Shao, C., Chen, J., Li, L., Xu, W., Chen, S., Gwen, T., Xu, J., and
Zhang, W.: Spa ial a iabili y in soil hea lux a h ee Inne Mon-
golia s eppe ecosys ems, Ag ic. Fo . Me eo ol., 148, 1433–1443,
doi:10.1016/j.ag o me .2008.04.008,2008.
Sogache , A. and Lloyd, J.: Using a one-and-a-hal o de closu e
model o he a mosphe ic bounda y laye o su ace lux oo -
p in es ima ion, Bound.-Lay. Me eo ol., 112, 467–502, 2004.
So bjan, Z.: S a is ics o scala ields in he a mosphe ic bounda y
laye based on la ge-eddy simula ions. Pa 2: Fo ced con ec-
ion, Bound.-Lay. Me eo ol., 119, 57–79, doi:10.1007/s10546-
005-9014-8, 2006.
S e ens, M., K¨
olbl, A., To sche, K. U., and K¨
ogel-Knabne , I.:
G azing e ec s on soil chemical and physical p ope ies in
a semia id s eppe o Inne Mongolia (China), Geode ma, 143,
63–72, doi:10.1016/j.geode ma.2007.09.004, 2008.
S unin, M. A. and Hiyama, T.: Applying wa ele ans o ms o
analyse ai c a -measu ed u bulence and u bulen luxes in he
a mosphe ic bounda y laye o e Eas e n Sibe ia, Hyd ol. P o-
cess., 18, 3081–3098, doi:10.1002/hyp.5750, 2004.
S unin, M. A., Hiyama, T., Asanuma, J., and Oha a, T.: Ai c a
obse a ions o he de elopmen o he mal in e nal bounda y
laye s and scaling o he con ec i e bounda y laye o e non-
homogeneous land su aces, Bound.-Lay. Me eo ol., 111, 491–
522, 2004.
S ull, R. B.: An In oduc ion o Bounda y Laye Me eo ology,
Kluwe Academic Publishe s, Do d ech , 670 pp., 1988.
Thomas, R. M., Lehmann, K., Nguyen, H., Jackson, D. L., Wol e,
D., and Ramana han, V.: Measu emen o u bulen wa e a-
po luxes using a ligh weigh unmanned ae ial ehicle sys em,
A mos. Meas. Tech., 5, 243–257, doi:10.5194/am -5-243-2012,
2012.
To ence, C. and Compo, G. P.: A p ac ical guide o wa ele anal-
ysis, Bull. Am. Me eo ol. Soc., 79, 61–78, doi:10.1175/1520-
0477(1998)079<0061:apg wa>2.0.co;2, 1998.
Tukey, J. W.: Bias and con idence in no -qui e la ge samples, Ann.
Ma h. S a ., 29, 614, 1958.
Van Kes e en, B., Ha ogensis, O. K., an Din he , D., Moene, A. F.,
and De B uin, H. A. R.: Measu ing H2O and CO2 luxes
a ield scales wi h scin illome y: Pa 1 – In oduc ion and
alida ion o ou me hods, Ag ic. Fo . Me eo ol., in p ess,
doi:10.1016/j.ag o me .2012.09.013, 2013.
Vellinga, O. S., Gioli, B., Elbe s, J. A., Hol slag, A. A. M., Kaba ,
P., and Hu jes, R. W. A.: Regional ca bon dioxide and ene gy
luxes om ai bo ne obse a ions using ligh -pa h segmen a ion
based on landscape cha ac e is ics, Biogeosciences, 7, 1307–
1321, doi:10.5194/bg-7-1307-2010, 2010.
Vesala, T., Kljun, N., Rannik, U., Rinne, J., Sogache , A., Ma kka-
nen, T., Sabel eld, K., Foken, T., and Lecle c, M. Y.: Flux and
concen a ion oo p in modelling: S a e o he a , En i on. Pol-
lu ., 152, 653–666, doi:10.1016/j.en pol.2007.06.070, 2008.
Ve e , S., Scha a h, D., and Be nho e , C.: Spa ial simula ion o
e apo anspi a ion o semi-a id Inne Mongolian g assland based
on MODIS and eddy co a iance da a, En i on. Ea h Sci., 65,
1567–1574, doi:10.1007/s12665-011-1187-5, 2012.
Vicke s, D. and Mah , L.: Quali y con ol and lux sam-
pling p oblems o owe and ai c a da a, J. A mos.
Oceanic Technol., 14, 512–526, doi:10.1175/1520-
0426(1997)014<0512:QCAFSP>2.0.CO;2, 1997.
Wan, Z. and Li, Z. L.: Radiance-based alida ion o he V5 MODIS
land-su ace empe a u e p oduc , In . J. Remo e Sens., 29,
5373–5395, doi:10.1080/01431160802036565, 2008.
Wang, W. and Ro ach, M. W.: Flux oo p in s o e an
undula ing su ace, Bound.-Lay. Me eo ol., 136, 325–340,
doi:10.1007/s10546-010-9498-8, 2010.
Webb, E. K., Pea man, G. I., and Leuning, R.: Co ec ion o
lux measu emen s o densi y e ec s due o hea and wa-
e apou ans e , Q. J. R. Me eo olog. Soc., 106, 85–100,
doi:10.1002/qj.49710644707, 1980.
Weil, J., Sulli an, P., Pa on, E., and Moeng, C.-H.: S a is ical a i-
abili y o dispe sion in he con ec i e bounda y laye : Ensembles
o simula ions and obse a ions, Bound.-Lay. Me eo ol., 145,
185–210, doi:10.1007/s10546-012-9704-y, 2012.
Wiesmeie , M., Ba hold, F., Blank, B., and K¨
ogel-Knabne , I.: Dig-
i al mapping o soil o ganic ma e s ocks using andom o es
modeling in a semi-a id s eppe ecosys em, Plan Soil, 340, 7–24,
doi:10.1007/s11104-010-0425-z, 2011.
Wille , J. B. and Singe , J. D.: Ano he cau iona y no e abou R2:
I s use in weigh ed leas -squa es eg ession analysis, Am. S a .,
42, 236–238, 1988.
Wi me , M. H. O. M., Aue swald, K., Bai, Y., Sch¨
au ele, R.,
and Schnyde , H.: Changes in he abundance o C3/C4 species
o Inne Mongolia g assland: E idence om iso opic composi-
ion o soil and ege a ion, Global Change Biol., 16, 605–616,
doi:10.1111/j.1365-2486.2009.02033.x, 2010.
Wood, N. and Mason, P.: The in luence o s a ic s abil-
i y on he e ec i e oughness leng hs o momen um and
hea ans e , Q. J. R. Me eo olog. Soc., 117, 1025–1056,
doi:10.1002/qj.49711750108, 1991.
Xiang, G., Hue e, A. R., and Didan, K.: Mul isenso compa isons
and alida ion o MODIS ege a ion indices a he semia id Jo -
nada expe imen al ange, IEEE T ans. Geosci. Remo e Sens., 41,
2368–2381, doi:10.1109/ g s.2003.813840, 2003.
Yang, F., Ichii, K., Whi e, M. A., Hashimo o, H., Michaelis, A. R.,
Vo a a, P., Zhu, A. X., Hue e, A., Running, S. W., and Ne-
mani, R. R.: De eloping a con inen al-scale measu e o g oss
p ima y p oduc ion by combining MODIS and Ame iFlux da a
h ough suppo ec o machine app oach, Remo e Sens. En i-
on., 110, 109–122, doi:10.1016/j. se.2007.02.016, 2007.
Ziehn, T., Kno , W., and Scholze, M.: In es iga ing spa ial
di e en ia ion o model pa ame e s in a ca bon cycle da a
assimila ion sys em, Global Biogeochem. Cy., 25, GB2021,
doi:10.1029/2010gb003886, 2011.
www.biogeosciences.ne /10/2193/2013/ Biogeosciences, 10, 2193–2217, 2013
ERKLÄRUNG 131
E klä ung
Hie mi e klä e ich, dass ich die A bei selbs ändig e ass und keine ande en als die on mi
angegebenen Quellen und Hil smi el benu z habe.
Fe ne e klä e ich, dass ich ande wei ig mi ode ohne E olg nich e such habe, diese Disse a ion
einzu eichen. Ich habe keine gleicha ige Dok o p ü ung an eine ande en Hochschule endgül ig nich
bes anden.
Bay eu h, 2013-04-15
S e an Me zge
