In eg a ed analysis o ela ionships be ween 3D-s uc u e, lea
pho osyn hesis, and b anch anspi a ion o ma u e
Fagus syl a ica and Que cus pe aea ees
in a mixed o es s and
Disse a ion zu E langung de Dok o wü de (D . e . na .)
de Fakul ä ü Biologie, Chemie und Geowissenscha en
de Uni e si ä Bay eu h
o geleg on
S e an Fleck
aus Hohensolms
Bay eu h, Augus 2001
2
1. Gu ach e : P o . D . J.D. Tenhunen
3
4
5
Danksagung
He n P o . D . John D. Tenhunen danke ich ü die Übe lassung des in e essan en Themas, ü
die Fö de ung und die An egungen zu meine A bei und die gelungene Koo dina ion mi
ande en P ojek en.
Ma kus Schmid sp eche ich meinen he zlichen Dank aus ü die in ensi e und eundscha liche
Zusammena bei im S eige wald, Diskussionen und Un e s ü zung in allen Phasen des P ojek s
sowie die Übe lassung on Messda en.
D . E a Falge, D . Ba ba a Kös ne und D . Ülo Niineme s danke ich ü die s ändige
Diskussionsbe ei scha , ö de nde und k i ische An eilnahme in allen Phasen des P ojek s.
Bei Wol gang Fal in bedanke ich mich ü seine langanhal ende Be ei scha zu koo dinie en
Modellen wicklung und die Un e s ü zung bei Biomassee n en.
D . Alessand o Cesca i, D . Man ed Fo s eu e , P o . D . Yoshi aka Kakuba i, D . Hideyuki
Sai o und D . Jö n S assemeye danke ich ü die ak i e Un e s ü zung in achlichen F agen
und ü die Übe lassung on Messda en
Meine F au Regina Dehmel danke ich he zlich ü die wei eichende Un e sü zung im Zuge de
F eilanda bei en, ü die k i ische Du chsich on Manusk ip en und Li e a u lis e und das
Managemen unse e Familie.
Allen wei e en Mi a bei e n und Hel e n bei F eiland- und Labo a bei en danke ich ü ih e
Ausdaue und Be ei scha zu meis langwie igen Tä igkei en: Anne Bö ne , Liane Chamsai,
Alexand a Hahn, U a Lohwasse , F iede ike Maye , Silke Po has und Ma c Sch oe e - D .
Ma ina Alsheime , D . Bä bel Heindl-Tenhunen, D . Ueli Joss, F iede ike Ro he, Hans-Joachim
Scha enbe g, Anne e Suske und D . Reine Zimme mann gebüh da übe hinaus mein Dank
ü die eundscha liche Au nahme in die A bei sg uppe.
D . Ma kus Reichs ein danke ich ü die in ensi e Du chsich on Manusk ip en und gemeinsam
mi Jens-A ne Subke ü inhal liche Diskussionen.
Bei Ralph Geye bedanke ich mich ü die Lösung zei aubende Ha d- und So wa e-P obleme.
D . Ped o Ge s be ge , D . Alois-Kas ne Ma esch, D . Holge Lange, Ge ha d Mülle und I is
Whelan danke ich ü achliche und p ak ische Un e s ü zung.
Die o liegende A bei wu de am Leh s uhl P lanzenökologie de Uni e si ä Bay eu h im
Rahmen des om Bundesminis e ium ü Fo schung und Technologie ge ö de en P ojek s
PT BEO 51 - 0339476C “En wicklung eines 3-D-Mischbes andesmodells des N-abhängigen
CO
2
- und Wasse aus ausches on Buchen-Mischbes änden in No dbaye n” du chge üh .
6
7
Con en s
1
In oduc ion
..................................................................................................................10
1.1 P oblems in assessmen o gas-exchange o mixed o es s ands
........................10
1.1.1 The ele ance o gas-exchange o mixed o es s ands ..........................................10
1.1.2 S uc u e dependence o mixed s and gas-exchange .............................................11
1.1.3 Unexplo ed e ec s o pa e ns o space cap u e.....................................................12
1.1.4 The complexi y o canopy s uc u e o ma ion.........................................................12
1.1.5 Canopy s uc u e o ma ion is al e ed unde ele a ed CO
2
and ozone....................13
1.1.6 Pa e ns o space cap u e a e he ele an s uc u e in o ma ion o ligh u iliza ion 14
1.1.7 Necessi y o simula ion models o he explana ion o al e ed g ow h pa e ns........14
1.2 Conclusions
.................................................................................................................15
1.2.1 The ele ance o complexi y o s uc u e.................................................................15
1.2.2 Implica ions o ac ual s udies on mixed s and gas-exchange.................................16
1.2.3 Scope and o ganisa ion o his s udy......................................................................17
2 T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea
ees
.......................................................................................................................................18
2.1 Objec i es
....................................................................................................................18
2.2 Ma e ials and Me hods
...............................................................................................19
2.2.1 S and desc ip ions..................................................................................................19
2.2.1.1 Buchenallee.....................................................................................................19
2.2.1.2 G oßebene and S eink euz..............................................................................20
2.2.2 Soil pH and soil C/N a io........................................................................................24
2.2.3 Canopy s uc u e de e mina ion..............................................................................24
2.2.4 Geode ic loca ion measu emen s............................................................................26
2.2.5 Desc ip ion o b anch connec ions..........................................................................27
2.2.6 Lea cloud o ien ed biomass ha es and lea sampling..........................................28
2.2.7 E o es ima ions.....................................................................................................29
2.3 Resul s
.........................................................................................................................30
2.3.1 Allome ic ela ionships o he b anch sys em.........................................................30
2.3.1.1 B anch basal a ea e sus es ima ed sapwood a ea.........................................30
2.3.1.2 Allome ic ela ionships o ami ica ion.............................................................31
2.3.1.3 Allome ic ela ionships be ween basal a ea and lea a ea o lea weigh .........33
2.3.2 Discussion o allome ic ela ionships o he b anch sys em....................................37
2.3.3 Lea a angemen in whole ee c owns..................................................................40
2.3.3.1 3D- ep esen a ion o lea clumping..................................................................40
2.3.3.2 T ee Lea A ea Indices ....................................................................................43
2.3.3.3 A angemen o lea clouds..............................................................................43
2.3.4 Laye o ien ed desc ip ion o lea dis ibu ion in he c own......................................46
2.3.4.1 Lea a ea o heigh laye s................................................................................46
2.3.4.2 Lea a ea densi ies o heigh laye s .................................................................48
2.3.4.3 E ec o gap co ec ion o lea a ea densi ies..................................................50
2.3.4.4 Volume gap ac ions.......................................................................................51
8
2.3.5 Lea cloud o ien ed e alua ion o lea a angemen in he c own.............................53
2.3.5.1 P ope ies o he c own en i onmen o each lea cloud ...................................57
2.3.5.2 Angles o he lea cloud plane ..........................................................................60
2.3.5.3 Main g ow h di ec ions o lea clouds................................................................61
2.3.5.4 Azimu h angles.................................................................................................65
2.3.5.5 Spa ial ex ension o lea clouds........................................................................67
2.3.5.6 Lea a ea densi ies o lea clouds.....................................................................69
2.3.5.7 Wood a ea densi ies o lea clouds...................................................................75
2.4 In e p e a ion o in es iga ions on lea clumping and a angemen
........................75
3 Spa ial dis ibu ion o lea p ope ies in ee c owns
......................................77
3.1 Ma e ials and me hods
................................................................................................77
3.1.1 S uc u al lea pa ame e s.......................................................................................77
3.1.2 Rela i e i adiance...................................................................................................78
3.1.3 Gas-exchange Measu emen s.................................................................................78
3.1.4 E alua ion o A/C
i
-cu es wi h RACCIA...................................................................80
3.1.4.1 The H
ARLEY
/T
ENHUNEN
model o lea pho osyn hesis.......................................81
3.1.4.2 RACCIA ou ine o species-speci ic pa ame e isa ion .....................................83
3.2 Resul s
..........................................................................................................................86
3.2.1 Ligh and heigh dependence o lea p ope ies.......................................................86
3.2.1.1 Rela i e I adiance...........................................................................................86
3.2.1.2 Lea angles ......................................................................................................88
3.2.1.3 Angles o neighbou ing b anches.....................................................................90
3.2.1.4 Lea Fo m.........................................................................................................90
3.2.1.5 Lea mass pe a ea (LMA)................................................................................91
3.2.1.6 Lea ni ogen and ca bon con en s...................................................................94
3.2.2 Pho osyn hesis measu emen s...............................................................................96
3.2.2.1 Compa ison o PAM-2000 and RACCIA es ima es o J
max
................................96
3.2.2.2 Day espi a ion (R
d
)..........................................................................................99
3.2.2.3 Ca boxyla ion capaci y Vc
max
and elec on anspo capaci y J
max
..................101
3.2.2.4 Ni ogen dependence o J
max
and Vc
max
..........................................................104
3.2.2.5 The shape o empe a u e dependence unc ions o J
max
and Vc
max
..............106
3.2.2.6 Ball-Wood ow-Be y-coe icien o s oma al sensi i i y (g
ac
)...........................109
3.2.3 Ni ogen dependen model o lea pho osyn hesis o beech .................................112
3.2.3.1 Model desc ip ion...........................................................................................112
3.2.3.2 Pa ame e isa ion............................................................................................113
3.2.3.3 Valida ion Measu emen s...............................................................................114
3.2.3.4 Model alida ion.............................................................................................117
3.3 Summa y and discussion
..........................................................................................118
4 Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12
and i s s and
......................................................................................................................122
4.1 Me hods
......................................................................................................................122
4.1.1 STANDFLUX-SECTORS.......................................................................................122
4.1.2 Rep esen a ion o 3D-da a wi h CRISTO...............................................................123
4.1.2.1 Rep esen a ion o s and s uc u e wi h c own app oxima ing polyhed ons......124
4.1.2.2 Volume and lea a ea densi y calcula ion o polyhed ons...............................125
4.1.2.3 Segmen a ion o polyhed ons.........................................................................125
9
4.1.3 Pa ame e isa ion o STANDFLUX-SECTORS......................................................128
4.1.3.1 Segmen a ion o lea cloud en eloping polyhed ons......................................128
4.1.3.2 Segmen a ion o c own app oxima ing polyhed ons in he s and G oßebene.128
4.1.3.3 Pa ame e de e mina ion o single compa men s.........................................132
4.1.4 Valida ion o STANDFLUX-SECTORS..................................................................132
4.1.4.1 Ligh and LMA simula ions.............................................................................132
4.1.5 Valida ion da a......................................................................................................133
4.2 Resul s
.......................................................................................................................134
4.2.1 S and S uc u e.....................................................................................................134
4.2.1.1 C own leng h and posi ion o oak and beech ees in he S eige wald s ands 134
4.2.2 LMA-calcula ions ..................................................................................................135
4.2.2.1 Valida ion o he ligh model wi h he LMA/i adiance ela ionship..................135
4.2.2.2 Es ima ion o lea cloud LMA .........................................................................135
4.2.3 Compa ison o clima e and anspi a ion da a.......................................................136
4.2.3.1 Daily cou ses.................................................................................................136
4.2.3.2 Dependence o lea cloud anspi a ion on clima e a iables..........................140
4.2.3.3 Summa ising concep s...................................................................................142
4.3 Summa y and discussion
.........................................................................................142
5 In eg a ing discussion
............................................................................................144
5.1 Cha ac e is ics o oak and beech in he s and G oßebene
...................................144
5.2 Applica ion o Bee ’s law
..........................................................................................146
5.3 Lea mass pe a ea (LMA).................................................................................
147
5.4 Implica ions o gas-exchange modelling
................................................................148
6 Summa y
.....................................................................................................................151
7 Zusammen assung
..................................................................................................153
8 Appendix
.....................................................................................................................156
8.1 Pa ame e de i a ion o chap e 2.3.5
...................................................................156
8.2 Measu ed A/C
i
-cu es
..............................................................................................156
8.2.1 Lea es o beech G 12..........................................................................................157
8.2.2 Lea es o oak G 13 ..............................................................................................158
8.3 Figu es.................................................................................................................
162
9 Li e a u e
.....................................................................................................................169
10 Abb e ia ions
.............................................................................................................182
In oduc ion
16
1.2.2 Implica ions o ac ual s udies on mixed s and gas-exchange
Gi en ha no single s udy can ye p o ide a holis ic syn hesis, a s epwise long- e m s a egy is
equi ed o cope wi h he complexi y o mixed s ands, which s a s wi h in ensi e ine-scale
s uc u al measu emen s and combined gas-exchange measu emen s and ends wi h hei
comple e e alua ion wi h ine-scale models o ligh and gas-exchange. Up-scaling o unc ional
measu emen s along 3D-s uc u es o ee c owns is ine i ably necessa y o achie e his aim
and a comple e e alua ion equi es in he i s place a comple e desc ip ion o s uc u e and
ela ed p ope ies.
Un o una ely, me hods o s uc u al measu emen s in o es canopies did no de elop as apidly
as da a p ocessing by compu e s, so ha he documen a ion o 3D canopy s uc u e o ees is
s ill ime consuming. Though some new measu emen me hods we e es ablished o he
applica ion on smalle plan s (S
INOQUET ET AL
.
1991,
H
IROTA
&
N
AKANO
2000) o o a oughe
desc ip ion o 3D canopy s uc u e (K
OCH
&
R
EIDELSTÜRZ
1998,
L
EFSKY ET AL
.
2000,
T
ANAKA ET
AL
.
1998), 3D s uc u e measu emen s on ma u e ees a e no accele a ed by hese
echniques, when physiological in es iga ions on speci ic pa s o he canopy shall be e e able
o hem. The e o e, unc ion- ela ed measu emen s o 3D s uc u e a e he bo leneck o he
u he de elopmen owa ds a holis ic unde s anding o s uc u e and unc ion o ee canopies.
While a g owing numbe o spa ially explici 3D-models o o es canopy ligh clima e and gas-
exchange exis s (C
ANHAM ET AL
.
1999,
C
ESCATTI
1997,
F
ALGE
1997,
K
NYAZIKHIN ET AL
.
1997,
R
ÖHRIG ET AL
.
1999,
W
ANG
&
J
ARVIS
1990) and u he e inemen s a e unde de elopmen
(F
ALTIN
2001), hei spa ial pa ame e isa ion is mos ly ough o gene al, i.e., ee c owns a e no
segmen ed o a e pa i ioned in o a small numbe o symme ical compa men s. Thus, hei
high po en ial o de ailed up-scaling o lea and b anch le el measu emen s o he canopy is no
ully used, which is simply due o he ime-consuming p ocess o h ee-dimensional s uc u e
measu emen s and he jus as ime-consuming p ocess o ecalcula e hese measu emen s in o
a ine-scale pa ame e isa ion.
The ollowing implica ions o he ac ual s udy we e de i ed:
• Canopy s uc u e measu emen s ha e o be o ganised such, ha hei use ulness o
di e en app oaches o s uc u e ep esen a ion in 3D-models is gua an eed.
• Canopy s uc u e measu emen s need a esolu ion ha is aluable o many di e en kinds
o physiological measu emen s in ee c owns (which is mos ly he b anch scale;
V
ALLADERES
1999) and which is app op ia e o he desc ip ion o ligh -clima e (see 1.1.6).
• Func ional (gas-exchange) measu emen s on di e en scales should be combined wi h
s uc u e measu emen s o enable he analysis o ela ions be ween unc ion and s uc u e
on di e en spa ial le els.
• Co-ope a ion wi h o he esea che s in he same s and is necessa y o b ing he necessa y
in o ma ion oge he .
• As much as possible addi ional in o ma ion abou ac o s in luencing gas-exchange o he
gi en s and should be ga he ed.
• The esul s and samples should be s o ed in a manne ha enables hei u u e e alua ion in
o he ields o esea ch.
In oduc ion
17
• The comple e desc ip ion o all ga he ed da a is impo an o a oid i e ie able losses o
po en ially signi ican in o ma ion, e en when he e alua ion o all ga he ed da a o a gi en
e alua ion le el may be impossible.
• Me hods o au oma ion should be ound and used o educe complexi y and o acili a e
u he s udies on s uc u e- unc ion ela ionships in mixed s ands.
1.2.3 Scope and o ganisa ion o his s udy
The aim o his s udy is o p o ide ield me hods, a da abase, up-scaling ela ionships, and
model sub ou ines o a spa ially explici analysis o mixed s and gas-exchange. The species-
and s and-speci ic esul s ha we e ob ained by applica ion o hese me hods shall indica e
whe e gas-exchange ele an di e ences in s uc u e and physiology o Fagus syl a ica and
Que cus pe aea ees can be expec ed and shall con ibu e o a spa ially explici conside a ion
o pa e ns o space cap u e in he 3D ligh -model STANDFLUX-SECTORS (F
ALGE
1997,
F
ALTIN
2001,
F
LECK ET AL
.
2001).
This equi ed:
1. The de elopmen o pa ially au oma ed me hods o he model-independen desc ip ion o
ee c own s uc u es (lea cloud o ien ed biomass ha es ) and s and s uc u e ( ee c own
o ien ed s and su ey)
2. The de ailed, ligh -clima e o ien ed, and he e o e lea cloud o ien ed 3D-desc ip ion o
c own s uc u es o he wo ee species and desc ip ion o s and s uc u e
3. The in ensi e in es iga ion o ee c own s uc u es o spa ial egula i ies ha enable up-
scaling o a e impo an o ligh -clima e (lea cloud p ope ies)
4. The analysis o easily measu able quan i ies o up-scaling o s uc u e (allome ic
ela ionships be ween b anch o unk basal a ea and lea a ea)
5. Pho osyn hesis measu emen s on lea es on he s anding ees and cha ac e isa ion o hei
ligh -clima e (e alua ion o ish-eye pho os)
6. De elopmen o an op ically con ollable ou ine o A/C
i
-cu es’ au oma ic e alua ion
(RACCIA) o he pa ame e isa ion o Fa quha - ype lea models o gas-exchange.
7. In es iga ions on ligh -clima e ele an p ope ies o lea es (lea -angles)
8. In es iga ion and es ablishmen o ela ionships be ween ligh -clima e, lea mass pe a ea,
lea ni ogen, and lea pho osyn he ic capaci ies o he wo species
9. The de elopmen o a lea ni ogen dependen pho osyn hesis model based on he LEAVES
model (H
ARLEY
&
T
ENHUNEN
1991)
10. The de elopmen o a p og am o op ical con ol and ecalcula ion o s uc u al
measu emen s in o a 3D-pa ame e isa ion, ha can be applied o di e en model
ep esen a ions o 3D-s uc u e (op ically con olled c own in e nal s uc u e ep esen a ion,
CRISTO)
11. The ine-scale pa ame e isa ion o he 3D-ligh model STANDFLUX-SECTORS (F
LECK ET
AL
. 2001), i s e alua ion o b anches, whose sap low was measu ed (M. S
CHMIDT
, Leh s uhl
P lanzenökologie, Uni e si ä Bay eu h, unpublished), and i s alida ion using ela i e ligh
alues om hemisphe ical pic u es
The chap e s epo hese s eps summa ising o di e en spa ial le els:
Chap e 2: T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
18
(le el o boughs and b anches / lea clouds)
Chap e 3: Spa ial dis ibu ion o lea p ope ies in ee c owns (lea le el)
Chap e 4: Rep esen a ion o ee and s and s uc u e wi h CRISTO and applica ion o he
spa ially explici 3D ligh -model STANDFLUX-SECTORS o h ee-dimensional pa e ns o space
cap u e in a mixed s and (s and and ee le el)
2 T ee c own s uc u es o ma u e Fagus syl a ica and Que cus
pe aea ees
2.1 Objec i es
Up-scaling o b anch le el in es iga ions o whole canopies equi es he iden i ica ion o
egula i ies in ee c own s uc u e ha can be exp essed as ma hema ical unc ions and ela ed
o easily measu ed quan i ies. One undamen al assump ion o s uc u al egula i y ha is used
in mos canopy gas exchange models is homogenei y h oughou he olume o h oughou he
heigh ange o ce ain compa men s ( ee c owns, segmen s, o laye s), which enables he up-
scaling o lea -le el pho osyn hesis a es by mul iplica ion wi h lea a ea o he compa men .
This assump ion is only an app oxima ion o he eal si ua ion, and has o be es ed in each
case o co ec ness and u ili y. Because obse a ions o he e ogenei y wi hin single ee c owns
ejec his assump ion, he ollowing hypo heses we e o mula ed:
H1: The lea dis ibu ion in single ee canopies is no homogeneous.
H2: The 3D-a angemen o b anches and associa ed lea clouds in he ee c owns is egula
and i s egula i y is esponsi e o and ele an o ligh in e cep ion.
H3: Di e ences in he egula i y o ee c own s uc u e a e pa ly species-speci ic.
The hope behind hypo heses H2 and H3 is o ind al e na i e egula i ies wi hin ee c owns ha
a e use ul o up-scaling. Two majo implica ions o he e alua ion a ise, when hese
hypo heses a e o be es ed unde na u al condi ions:
- S uc u al egula i y (H2, H3) can ha e many di e en o ms, so ha many di e en
possibili ies mus be explo ed wi h a a ie y o app oaches.
- The necessa y high esolu ion o c own s uc u e measu emen s equi ed in he sea ch o
egula i ies limi s he numbe o ees ha can be in es iga ed, hus p e en ing s a is ical
e alua ion among ees. The esul s, he e o e, canno ini ially be gene alised o o he oaks
and beeches, and canno immedia ely ep esen species-speci ic di e ences (H3). The
esul s mus be conside ed as examples o ee s uc u al p ope ies, ha could simila ly
occu wi h o he oaks and beeches.
Thus, he in es iga ions wi h espec o H2 a e o an explo a i e na u e, while H3 can only be
examined wi h espec o he ee c owns sampled.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
19
Ne e heless, a ull in si u cha ac e isa ion o s uc u al cons ain s in ma u e ee c owns o oak
and beech is achie ed, ha is use ul in u u e conside a ions o ligh and gas-exchange models
o mixed o es s ands.
2.2 Ma e ials and Me hods
2.2.1 S and desc ip ions
Resul s p esen ed in his hesis ely on measu emen s ha ha e been pe o med on h ee
beech domina ed s ands in wo moun ainous egions in no he n Ba a ia. In 1997, s uc u e-
o ien ed in es iga ions we e pe o med in he 120 yea old pu e beech s and “Buchenallee” in
he Fich elgebi ge highlands (50°03‘N, 11°52‘E) a an ele a ion o 905m (Fig. 1).
Rela ionships be ween s uc u e and unc ion we e in es iga ed in 1998 in he 120 yea old
s and “G oßebene” in he S eige wald highlands (49° 52‘N, 10°28‘E) a an ele a ion o 450m.
This s and is sepa a ed by 1.3 km om he main in es iga ion si e “S eink euz” (140 yea s) o
he BITÖK (Bay eu h Ins i u e o Te es ial Ecosys em Resea ch), whe e addi ional s uc u al
and LAI-measu emen s we e aken. G oßebene and S eink euz a e mixed s ands o Fagus
syl a ica and Que cus pe aea. The measu emen s we e ca ied ou a he s ands G oßebene
and Buchenallee due o he a ailabili y o clima e and o he measu emen s a he nea by s ands
S eink euz and Walds ein (G
ERSTBERGER
1997), hei species composi ion, sap low
measu emen s in o he p ojec s on he same ees (M.
S
CHMIDT
,
D
EPT
.
OF
P
LANT
E
COLOGY
,
U
NIVERSITY OF
B
AYREUTH
,
UNPUBLISHED
), and because ee heigh allowed access o dominan
ees wi h he a ailable highli .
2.2.1.1 Buchenallee
The Fich elgebi ge is a moun ainous egion c ea ed by olcanic ac i i y du ing he
Ca boni e ous and Pe mian and has a maximum ele a ion o 1051 m a.s.l. a he Schneebe g
moun ain, which is he highes ele a ion in No he n Ba a ia. Low empe a u es and high
Weissens ad
Bay eu h
10 km
0
F
i
c
h
e
l
-
g
e
b
i
g
e
G
e
m
a
n
y
S ands in he Fich elgebi ge
Walds ein
Buchenallee
Ge many
10 km
0
S ands a he wes e n
edge o he S eige wald
G oßebene
S eink euz
S e i g e -
w a l d
Fig. 1:
Loca ion o he in es iga ed s ands in he S eige wald (le side) and in he Fich elgebi ge
(BITÖK
-
maps c ea ed by
P.
G
ERSTBERGER
)
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
20
p ecipi a ion a e ypical o he clima e in he uppe Fich elgebi ge. Clima e measu emen s a he
Walds ein moun ain (765m a.s.l.) (unpublished da a o he Chai o Mic oclima ology, BITÖK,
Uni e si y o Bay eu h) indica e an annual mean empe a u e o 6 °C. Mean annual p ecipi a ion
a highe ele a ion in he Fich elgebi ge anges om 1100 o 1300 mm and om 950 mm o
1100 mm in hose pa s below 900 m a.s.l. (B
AYERISCHER
K
LIMAFORSCHUNGSVERBUND
1998).
Abou 20% o p ecipi a ion is deposi ed om og du ing 1160 h o oggy wea he du ing he
yea (W
RZESINSKY
&
K
LEMM
2000).
Low soil-pH alues on he mine al poo , silica e ich geological base ma e ial (g ani e) in
combina ion wi h he cold and we clima e in he uppe egion p omo e podzola ion o he soil,
so ha podzolised b own soils and podzolised lep osols (“Ranke ”) co e nea ly he whole
Schneebe g (F
ORSTAMT
W
EISSENSTADT
1989). The in es iga ion a ea “Buchenallee” is loca ed
on he sou h slope o he Schneebe g wi h an inclina ion o 13.5° (measu ed wi h a Suun o
inclinome e ), anging om 900 m o 915 m abo e sea le el. The pa ly podzolised b own ea h
in his a ea has pH
(H2O)
- alues o a ound 4.75 in he uppe 5 cm o he mine al soil. The C/N
a io o he 5.7 cm (on a e age) hick humus laye was ound o be 17.6, which accoun s o
a he good nu ien a ailabili y.
The po en ial na u al climax ege a ion o he Fich elgebi ge should be a beech o es wi h
na u al admix u e o coni e ous ees such as sp uce and i (B
OHN ET AL
.
1999), al hough slow
g ow h and a high occu ence o damage by pa hogens sugges ha beech is a i s al i udinal
limi a he Schneebe g: The oldes beeches a he Buchenallee a e 120 yea s old, bu a e no
highe han 26 m, hus belonging only o yield class 3 (F
ORSTAMT
W
EISSENSTADT
1989). Ten o
20 pe cen o he beeches a e in ec ed wi h di e en pa asi ic ungi, mos ly Fomes omen a ius,
Nec ia di issima, and Fusa ium a enaceum (de e mina ion acco ding o
B
UTIN
1983).
Fu he mo e, he egions abo e 950 m a.s.l. o he compa able adjacen highlands in Thü inge
Wald, E zgebi ge, Böhme wald, and Baye ische Wald ha e moun ainous sp uce o es s as
hei po en ial na u al ege a ion [B
OHN ET AL
.
1999]. Pu e sp uce plan a ions we e a ou ed in
he pas in he Fich elgebi ge o economic easons, so ha oday a ound 90% o he o es is
made up o uni o m and e en-aged No way sp uce s ands (Picea abies (L.) Ka s .).
2.2.1.2 G oßebene and S eink euz
The S eige wald is a hilly egion be ween 200 and 490 m a.s.l., wi h highes ele a ions a i s
s eep wes e n edge which is 200m highe han he adjacen plain o he Main i e (see Fig. 1).
Al i ude dec eases con inuously om he esca pmen owa d he eas , whe e maximum al i udes
o 300m a.s.l. a e a ained. Th ee alleys in eas -wes di ec ion sepa a e he S eige wald in o
ou chains o low moun ains. Clima ic condi ions change in co espondence wi h he ele a ion
g adien : 750 mm o 850 mm p ecipi a ion a e eached in he uplands o he wes e n pa , while
he lowe and he eas e n pa s expe ience only 650 mm o 750 mm (B
AYERISCHER
K
LIMAFORSCHUNGSVERBUND
1998). P ecipi a ion is much lowe and mean annual empe a u e (7
– 8 °C; W
ELSS
1985) is highe han in he Fich elgebi ge, which leads o a id pe iods du ing he
summe ha a e indica ed by less p ecipi a ion (in mm) han wice he empe a u e (in °C)
acco ding o he de ini ion o W
ALTER
&
B
RECKLE
(1999). A id pe iods occu ed e en in he
ela i ely we yea 1998 (see Fig. 2).
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
21
The geological o ma ions o he S eige wald belong mainly o uppe iassic sands ones
(Sands einkeupe ). Blasensands ein, Cobu ge Sands ein and Bu gsands ein build 23-27 m, 5-9
m, and 30 m hick laye s abo e he unde lying, la gely wa e -impe meable, and clayey-sil ic
Leh be g-laye (30 m)
(E
MMERT
1985). The sands one laye s include mul iple in e -bedding o
clay and sands one laye s ha a e usually some dm in hickness (E
MMERT
1985). Sandy b own
ea h soils de elop mainly on Cobu ge Sands ein and Bu gsands ein, while wo-laye -soils wi h
a s ony phase and clayey pelosols occu mainly abo e Blasensands ein- and Leh be g-laye s
(S
EILER
1995,
W
ELSS
1985). Pelosols a e ypically ound on he plains, and wo-laye -soils may
de elop on s eepe slopes by soli luc ion o he Blasensandsein-laye s.
The in es iga ed s ands a e loca ed on he sou h-eas side o he S ollbe g (max. al i ude 475 m
a.s.l.), 2-3 km eas o he wes e n edge o he S eige wald. Sou h slopes on he sou h-wes e n
side o his moun ain a e wa m enough o belong o he mos eas e n a eas o i icul u e in
Ba a ia. The po en ial na u al ege a ion o his egion belongs o he sessile oak / ho nbeam
o es s in wa m-d y a eas wi h li le o no occu ence o beech (B
OHN ET AL
.
1999). Bo h s ands
a e ound on s ongly acidic b own ea h (pH
H2O
= 3.7 in 0-5 cm dep h, measu ed in No embe
2000), which was also ound by C
HANG
(1999) o S eink euz. Ni ogen a ailabili y o bo h
s ands was ound o be good (C/N- a io o he humus laye was 15.2 in bo h s ands). Humus
laye s we e ound o be 1.5 o 3.5 cm hick.
Clima e a iables 1998, Fich elgebi ge
(Walds ein)
-5
20
45
70
95
120
1 3 5 7 9 11
mon h
empe a u e [°C]
-10
40
90
140
190
240
p ecipi a ion [mm]
mean mon hly empe a u e
mon hly sum o p ecipi a ion
Clima e a iables 1998, S eige wald
(Waldklima Eb ach)
-5
20
45
70
95
120
1 3 5 7 9 11
mon h
empe a u e [°C]
-10
40
90
140
190
240
p ecipi a ion [mm]
mean mon hly empe a u e
mon hly sum o p ecipi a ion
Fig. 2:
Annual cou se o clima e a iables a he in es iga ed si es in he yea 1998. A id pe iods a e
indica ed by less p ecipi a ion (in mm) han wice he empe a u e (in °C) (W
ALTER
& B
RECKLE
1999),
i.e., when he empe a u e cu e lies abo e he p ecipi a ion cu e in his diag am.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
22
G oßebene and S eink euz a e mixed s ands o Fagus syl a ica and Que cus pe aea wi h a
high p opo ion o beech, ha we e es ablished by na u al eg ow h a ound 1880 (G oßebene)
and in he pe iod o 1863 o 1872 (S eink euz) (F
ORSTAMT
E
BRACH
2000). The dominance o
beech is s ill suppo ed by na u al eg ow h o seedlings, and his may pa ly be due o he
highe p ecipi a ion a es on he wes e n edge o he S eige wald, whe e d ough esis ance is
no as impo an o compe i ion as i is in he lowe o eas e n pa s. High acidi y is no
necessa ily a disad an age o na u al eg ow h o beech seedlings (L
EUSCHNER ET AL
.
1993).
Ano he eason may be ound in he ac ha oaks in his a ea a e pe iodically in es ed by
insec s o he To ix i idiana communi y. The popula ions o hese insec s may inc ease
eno mously in some yea s and in es ed oaks in he S eige wald may lose hei en i e lea
biomass (S
CHÄFER
1997). While 1995 – 1997 was a pe iod o high pes ac i i y (
HEAD FORESTER
G
EIZ
,
F
ORSTDIENSTSTELLE
O
BERSCHWARZACH
,
PERS
.
COMMUNICATION
), no ob ious insec
damage occu ed o he oaks du ing he in es iga ion yea 1998. Fo es managemen in he
S eige wald gene ally suppo s he g ow h o oaks by selec i e logging o he oak supp essing
beeches (S
CHÄFER
1997).
The main di e ences be ween wo nea ly e en-aged s ands in he S eige wald a e hei heigh
g ow h, hei ee densi y, he igou o oaks, and soil dep h. T ees in S eink euz a e
app oxima ely 10 m highe han in G oßebene and ee densi y is much lowe , causing g ea e
ligh a ailabili y on he g ound and g ea e co e by unde s o ey ege a ion and eg owing ees
Table 1: Main si e ac o s o he h ee in es iga ed s ands o Fagus syl a ica
and Fagus syl a ica mixed wi h Que cus pe aea
S and Buchenallee G oßebene S eink euz
Loca ion
Posi ion 11°51’27-34’’ E,
50°02’30-32’’ N 10°26’43-52’’ E,
49°52’41-48’’ N 10°27’38-44’’ E,
49°52’15-19’’ N
Region Fich elgebi ge S eige wald
Moun ain (maximum
ele a ion) Schneebe g
(1051m a.s.l.) S ollbe g
(475m a.s.l.)
Al i ude 910m a.s.l. 460m a.s.l. 440m a.s.l.
A ea 2424m² *
1
3097m² *
1
12900m² *
2
Inclina ion 13.5° 2° 5,5°
Exposi ion SSW SE SSE
Clima e
Mean annual
p ecipi a ion (long
e m; ’97; ’98)
1100mm - 1300mm
968mm*
3
1299mm*
4
650mm - 800 mm
653mm
807mm
Annual mean
empe a u e (long
e m; ’97; ’98)
-
6.0 °C *
4
5.9°C *
4
7.5°C;
7.1°C;
8.3°C
Range o mon hly
mean empe a u es
(long e m; ’97; ’98)
-
-4.5°C – 17.1°C *
4
-2.5°C – 14.2°C *
4
-1.5°C - 16°C ;
-3.7°C - 15.7°C;
0.0 °C - 16.2°C
Days p.a. wi h mean
empe a u e > 5°C
(long e m; ’97; ‘98)
-
189 *
4
199 *
4
215
185
249
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
23
Soil
Geology Coa se-g ained co e-
g ani e o he
Fich elgebi ge
Middle Keupe (Uppe
T iassic), in e -bedding
o coa se-g ained
sands one
(“Blasensands ein”)
and clayey laye s
Middle Keupe (Uppe
T iassic), in e -bedding
o coa se- o ine-
g ained sands one
(“Blasensands ein,
Cobu ge Sands ein”)
and clayey laye s
Soil ype (FAO-Clas-
si ica ion; S
CHEFFER
&
S
CHACHTSCHABEL
1998)
Loamy-sandy, pa ly
podzolic b own soil
(Dys ic Cambisol)
Loamy-sandy b own
soil wi h s ony phase
(Cambisol)
Sandy b own soil
(Cambisol)
Soil-dep h 30-100cm 5-40cm 50-80cm
Humus-laye 5.7 ± 0.8 cm 2.6 ± 0.9 cm 2.4 ± 0.9cm
Soil-pH
(H2O)
in 0-5cm
4.75 ± 0.13 3.72 ± 0.21 3.65 ± 0.29
C/N o humus laye 17.55 ± 0.45 15.16 ± 2.66 15.15 ± 2.25
Vege a ion
T ee Species
composi ion 99% Fagus syl a ica,
1% Pseudo suga
menziesii
66% Fagus syl a ica,
34% Que cus pe aea 75% Fagus syl a ica,
24% Que cus pe aea
,
1% Ca pinus be ulus
S and age 120a 120a 140a
LAI*
7
8.1 6.1 6.2
Yield class 3 1 1
T ees pe ha 524 526.3 358.1
Max. s and heigh 26m 30m 39m
Unde s o ey co e 2% <1% 5 -10%
Main unde s o ey
species Deschampsia
lexuosa,
Oxalis ace osella,
mosses
Anemone nemo osa,
ee seedlings Luzula albida,
Deschampsia
lexuosa, geophy es,
mosses
Human Impac
Fo es managemen Pe iodic hinning (up
o 30% emo al) Single s em ha es s,
suppo ing g ow h o
oaks
No managemen bu
ecological esea ch
since 1994
Ca
2+
-deposi ion 4.8 (1.6) kg/(ha*a) *
6
10.6 (2.8) kg/(ha*a) *
5
Mg
2+
-deposi ion 2.0 (0.4) kg/(ha*a) *
6
2.8 (0.5) kg/(ha*a) *
5
Na
+
-deposi ion 11.3 (4.5) kg/(ha*a) *
6
7.6 (3.8) (kg/(ha*a) *
5
K
+
-deposi ion 26.1 (2.9) kg/(ha*a) *
6
33.0 (3.1) kg/(ha*a) *
5
Cl
-
-deposi ion 19.1 (6.8) kg/(ha*a) *
6
11.6 (5.1) kg/(ha*a) *
5
SO
42+
-deposi ion 35.1 (9.2) kg/(ha*a) *
6
18.6 (7.6) kg/(ha*a) *
5
NH
4+
-deposi ion 16.7 (7.2) kg/(ha*a) *
6
12.5 (5.5) kg/(ha*a) *
5
NO
3-
-deposi ion 18.5 (6.2) kg/(ha*a) *
6
11.6 (4.8) kg/(ha*a) *
5
*
1
ho izon ally p ojec ed a ea o measu ed ee c own ex ensions
*
2
enced a ea
*
3
Measu emen a DWD-s a ion Bischo sg ün (675m a.s.l)
*
4
Measu emen a Walds ein in es iga ion si e (765m a.s.l.)
*
5
Measu emen in bulk p ecipi a ion (po ion in b acke s), canopy d ip, and s em low a he S eink euz
in es iga ion si e 1996/1996 (L
ISCHEID
&
G
ERSTBERGER
1997)
*
6
Measu emen in bulk p ecipi a ion (po ion in b acke s) and canopy d ip in he No way sp uce s and a
he Walds ein in es iga ion si e 1993-1998 (M
ANDERSCHEID
& A
LEWELL
2000)
*
7
calcula ed om ee diame e s and allome ic ela ionships (Fig. 14) ha we e adjus ed wi h a cons an
ac o based on lea a ea de e mina ions o he ha es ed ees om each s and
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
24
in a sh ubby s age. S eink euz is o much lowe densi y and his canno be due solely o i s
sligh ly g ea e age. The e a da ion o g ow h and de elopmen o he G oßebene s and is
p obably due o i s es ic ed soil dep h which is o en less han 10 cm and a ound 30 cm on
a e age. Thus, oo g ow h a his si e o younge as well as old ees appea s limi ed, as
obse ed om he oo s ock o wind- h own beeches in he s and. Ano he di e ence in he
s ands conce ns he igou o oaks. While oaks in G oßebene a e heal hy and g ea e in heigh
han he beeches (heigh measu ed wi h he o es su ey lase C i e ion 400, Lase Technology
Inc., Englewood, Colo ado), S eink euz oaks appea ou -compe ed by e y all beeches and
hey ha e much less dense c owns.
The in es iga ion yea 1997 was wi h 968 mm p ecipi a ion (DWD-Clima e S a ion Bischo sg ün,
675 m a.s.l.) and a mean empe a u e o 6.0 °C (BITÖK in es iga ion si e Walds ein, 765 m
a.s.l.) in he Fich elgebi ge, and 653 mm and 7.1 °C in he S eige wald (LFW Fo es Clima e
S a ion Eb ach) a ela i ely d y bu no wa m yea wi h a ela i ely sho summe season. The
yea 1998 (1299 mm p ecipi a ion and 5.9 °C a he Walds ein in es iga ion si e and 803 mm /
8.3 °C a he LFW Fo es Clima e S a ion Eb ach) was a e y we yea wi h high empe a u es
and long summe season in he S eige wald (see Fig. 2).
2.2.2 Soil pH and soil C/N a io
Fi e soil co es pe s and we e emo ed in No embe and Decembe 2000 and sepa a ed in o
humus laye and 5cm hick s a i ied samples o he mine al soil (0-5cm, 5-10cm, 10-15cm, 15-
20cm). Thickness o he humus laye (including o ganic laye ) was measu ed in he ield, and
samples we e b ough o he labo a o y. Twen y g am o each sub-sample we e mixed wi h
50ml deionized wa e o 4 – 24 hou s and pH was measu ed wi h a pH-elec ode. The
emainde o he soil samples was sie ed wi h a 2mm sie e and o en-d ied a 90°C o a leas
48 hou s o C and N de e mina ion in a C/N-analyse (CHN-O-Rapid, Foss He aeus GmbH,
Hanau, Ge many).
2.2.3 Canopy s uc u e de e mina ion
Canopy s uc u e o selec ed ees was de e mined in o de o de elop a “lea cloud” o ien ed
desc ip ion o ee c owns o beech and oak. A quan i a i e desc ip ion o oliage clus e ed in
lea clouds (see 2.2.4 o a de ini ion) will allow es ing o up-scaling me hods o gas-exchange
om lea es o canopies by including he in e media e le el o o ganisa ion associa ed wi h
b anches. Thus, canopy s uc u e is iewed om he pe spec i e o gas-exchange as i is
in luenced by he spa ial a angemen o physiologically dis inguished issues (sun lea es,
shade lea es, espi ing o gans) and hei impac on ligh -clima e. Measu emen s included he
geode ic loca ion o b anches and lea clouds inside he c own, he desc ip ion o he b anch
sys em, sampling o lea es o de e mina ion o lea s uc u e, and lea cloud o ien ed biomass
ha es . Geode ic measu emen s we e mos ly done in he lea less s a e in ea ly sp ing, and
lea es we e sampled be ween June and Augus o educe he e ec s o dec easing lea mass
pe a ea (LMA) and ni ogen e ansloca ion on ni ogen issue concen a ions
(D
AY
&
M
ONK
1977,
K
LOEPPEL ET AL
.
1993,
S
CHULTE
1992). Biomass ha es s a ed mid o Augus and was
comple ed in he i s days o Sep embe be o e yellowing o he lea es.
The necessa ily high esolu ion o hese measu emen s limi ed he numbe o ees in es iga ed
o h ee beeches and one oak, hus p e en ing s a is ical e alua ion among ees. The indings,
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
25
he e o e, canno be gene alised o o he oaks and beeches, bu mus be conside ed as
examples o ee s uc u al p ope ies, ha could simila ly occu wi h o he oaks and beeches.
Two beech ees in he Buchenallee s and (Bu38, Bu45) and one beech and one oak a he
G oßebene (G 12, G 13) we e chosen o s udy (see Fig. 3). Thei size and social posi ion we e
selec ed o ob ain lea es in all le els o ligh exposu e. Thus, ees had o be all enough o
p ojec abo e he uppe mos lea -laye o he s and, bu small enough o each wi h he
a ailable highli . Oak and beech in he G oßebene s and we e equi ed o s and adjacen o
each o he . A ypical ees wi h g oss anomalies, such as se e e pa hogen damage, o a ypical
c own a chi ec u e due o ea ly ami ica ion in o wo s ems, o b oken ops, o due o p oximi y
o gaps o oads we e excluded om conside a ion as objec s o his s udy.
G oßebene: Fagus syl a ica
0
1
2
3
4
5
6
7
8
9
10 15 20 25 30 35 40 45 50
maximum DBH [cm]
basal a ea [m²/ha]
0
5
10
15
20
25
30
35
40
ee heigh [m]
cumula ed basal a ea [m²] a e age ee heigh [m]
G oßebene: Que cus pe aea
0
1
2
3
4
5
6
7
8
9
10 15 20 25 30 35 40 45 50
maximum DBH [cm]
basal a ea [m²/ha]
0
5
10
15
20
25
30
35
40
ee heigh [m]
cumula ed basal a ea [m²] a e age ee heigh [m]
S eink euz: Fagus syl a ica
0
1
2
3
4
5
6
7
8
9
10 15 20 25 30 35 40 45 50 55 60 65 70
DBH-class [cm]
basal a ea [m²/ha]
0
5
10
15
20
25
30
35
40
ee heigh [m]
cumula ed basal a ea [m²] a e age ee heigh [m]
S eink euz: Que cus pe aea
0
1
2
3
4
5
6
7
8
9
10 15 20 25 30 35 40 45 50 55 60 65 70
DBH-class [cm]
basal a ea [m²/ha]
0
5
10
15
20
25
30
35
40
ee heigh [m]
cumula ed basal a ea [m²] a e age ee heigh [m]
Buchenallee
0
1
2
3
4
5
6
7
8
9
10 15 20 25 30 35 40 45 50
maximum DBH [cm]
basal a ea [m²/ha]
0
5
10
15
20
25
30
35
40
ee heigh [m]
cumula ed basal a ea [m²] a e age ee heigh [m]
Fig. 3:
In es iga ed ees, DBH and heigh
dis ibu ions in he in es iga ed s ands
Buchenallee, G oßebene, and i s compa ed
neighbou ing s and S eink euz, whe e addi ional
in es iga ions ook place. The diame e classes
o in es iga ed ees a e indica ed by e ical
a ows.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
32
same maximum heigh in oak G 13, while i s lowe boughs we e e y di e en in maximum
heigh . The beech ees showed a mo e con inuous ex ension o boughs h oughou hei
c own’s heigh ange. In he ansi ion zone be ween he a bi a ily classi ied sun and shade
boughs, highe boughs occu ed wi h ex eme sou h ex ension while lowe boughs we e
o ien ed away om he sou h di ec ion (Table 2). Because sou h-ex ended boughs a e likely o
expe ience mo e ligh han no h ex ended boughs, hese boughs we e classi ied as sun
boughs, while he lowe , no h o ien ed boughs we e classi ied as shade boughs.
Table 2: Shade- and Sun-boughs o he in es iga ed ees
Que cus pe aea Fagus syl a ica
G 13 G 12 Bu38 Bu45
B
o
u
g
h
Min. / Max.
heigh [m] Max.
sou h
[m]
B
o
u
g
h
Min. / Max.
heigh [m] Max.
sou h
[m]
B
o
u
g
h
Min. / Max.
heigh [m] Max.
sou h
[m]
B
o
u
g
h
Min. / Max.
heigh [m] Max.
sou h
[m]
G 19.16
19.23
0.92
C
14.45
15.08
4.19
H
16.38
17.63
0.69
C
11.92
12.32
0.61
A 18.41
20.89
4.75
B 15.69
16.35
2.66
D
16.32
17.87
-0.15
A
9.66
14.47
3.54
B 18.89
21.77
-0.14
G
17.4
18.86
1.64
i 17.75
18.81
0.52
F
14.96
15.18
0.75
L 21.48
23.14
0.94
F 17.3
18.92
-1.18
F
15.57
19.9
0.95
I 15.46
15.96
1.38
E 17.44
23.57
5.37
A 14.0
18.96
1.45
Z
18.23
20.19
0.1
B
11.05
15.96
3.45
F 20.92
23.64
4.22
O
18.58
19.77
2.11
J 19.17
20.47
1.1
E
14.35
16.08
3.6
M 23.95
24.74
2.24
N
19.47
20.11
-1.16
C
15.15
21.48
0.07
G
15.47
16.98
1.28
C 16.92
24.75
0.22
Q
20.69
21.12
-1.38
B
14.39
21.82
9.84
N
17.34
17.94
1.72
D 16.92
24.78
3.12
M
20.7
21.31
1.04
A
13.2
22.26
4.63
O
17.92
18.73
2.49
H 20.85
24.90
3.87
L 19.22
21.43
3.35
L 19.49
22.55
1.7
P
18.19
18.84
2.13
N 23.04
25.00
0.89
D
16.74
22.04
1.94
E
15.66
22.57
2.01
Q
18.5
19.03
1.91
K 23.64
25.30
0.98
K 21.14
22.95
1.03
K
18.34
22.59
1.83
M
17.03
19.06
2.07
I 21.91
25.58
2.65
E 15.9
23.22
4.05
J 16.03
19.44
2.26
i 17.97
23.38
3.59
L 16.34
19.66
1.57
H
18.45
23.83
1.45
H
16.27
20.41
3.12
R
21.92
24.08
-2.27
D
13.79
20.59
4.97
T 22.73
24.68
-0.4
U
23.16
24.78
-0.56
P 20.89
25.08
2.91
V 23.09
25.09
0.91
S 21.9
25.5
-0.41
Table 2:
Classi ica ion o boughs as shade boughs (da k colou ed cells) and sun boughs (ligh g ey
colou ed cells) acco ding o he ex ension o hei lea biomass in heigh and owa d he sou h. Boughs in
he able a e so ed by maximum heigh ex ension o he appending lea -biomass. Heigh anks (x = line
numbe s o he able) and maximum heigh ex ensions (y, in me e s) a e isualised in he g aphs below.
The e ical lines in he g aphs indica e he bo de be ween he wo classes and we e d awn a bi a ily,
conside ing he s eep ligh g adien in he uppe c own and be ween sou h and no h side o he c own,
which is especially alid o he Buchenallee ees ha a e s anding on a slope. The di e en ia ion
be ween he lowes sun bough and he highes shade bough was o en acili a ed by he highe maximum
sou h ex ension o he lowes sun bough (see pai s o whi e cells in he able).
18
20
22
24
26
0 5 10
15
17
19
21
23
25
0 5 10 15 20
17
18
19
20
21
22
23
0 5 10
12
14
16
18
20
0 5 10 15
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
33
The ela ionship be ween basal a ea o lea cloud suppo ing b anches and he cumula ed a ea
o he a ilia ed lea cloud b anches ha suppo he second 1m-segmen o he lea cloud was
analysed based on da a o he G oßebene ees. He e b anches wi h a high p opo ion o dead
wood we e excluded. The basal a ea educ ion pe me e was 84% in lea clouds o oak G 13
and 81% in lea clouds o beech G 12 (Fig. 8).
Fig. 8:
Basal a ea ela ionship be ween lea cloud suppo ing b anches and he connec ed b anches in
he second 1m-segmen o he lea cloud
2.3.1.3 Allome ic ela ionships be ween basal a ea and lea a ea o lea weigh
The pipe-model heo y (S
HINOZAKI
1964) i s ad anced he p inciple ha sapwood a ea in ees
is ela ed p opo ionally o oliage biomass (M
ÄKELÄ
1986). The heo y easons ha each uni o
oliage equi es a uni pipeline o wood o conduc wa e om he oo s and o p o ide physical
suppo . As lea a ea is a quan i y ha is in e es ing in e ms o ligh in e cep ion and gas-
exchange, he co ela ions p esen ed he e u ilise lea d y weigh and one-sided lea a ea as key
a iables. Though in he pas , pipe-model ela ions ha e usually exp essed biomass in ela ion
o sapwood a ea, which yields s ong linea co ela ions o lea a ea and lea weigh o se e al
species (G
RIER
&
W
ARING
1974,
K
AUFMANN
&
T
ROENDLE
1981,
R
OGERS
&
H
INCKLEY
1979,
W
ARING ET AL
.
1977) he cu en in es iga ions a e - like some newe publica ions (B
ARTELINK
1997,
S
UMIDA
&
K
OMIYAMA
1997) - based on basal a ea o b anches, boughs and s ems,
because sapwood a ea is di icul o measu e non-des uc i ely and, he e o e, no sui able as
an inpu -pa ame e o up-scaling and modelling pu poses.
In lea clouds o oak G 13, basal a ea o he b anch and appending lea biomass was be e
co ela ed han basal a ea and lea a ea (Fig. 9). The same was ound o beech, when all
beech obse a ions we e pooled: The lea biomass / basal a ea a io was 27.3 wi h an ² o
0.93, while he lea a ea / basal a ea a io o e all beeches (0.364) had a lowe ² o 0.89. The
opposi e was ue i he beeches a e analysed sepa a ely (see Fig. 9). The indi idual di e ences
be ween he beech ees may pa ly be explained by lowe lea biomass and a ea o he
subdominan and in ec ed ee Bu45. In gene al, he concep o cons an a ios be ween lea
a ea o biomass and basal a ea o he espec i e b anch was be e suppo ed o beech lea
clouds han o hose o oak G 13.
Fagus syl a ica
y = 0.8109x
R
2
= 0.9343
0
5
10
15
20
25
30
0 10 20 30
lea cloud basal a ea [cm²]
cumula ed basal a ea o 2nd
1m-segmen s [cm²]
beech G 12
Que cus pe aea
y = 0.8387x
R
2
= 0.9441
0
5
10
15
20
25
30
0 10 20 30
lea cloud basal a ea [cm²]
cumula ed basal a ea o 2nd
1m-segmen s [cm²]
oak G 13
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
34
Fig. 9:
Allome ic ela ionships be ween lea a ea o lea biomass and basal a ea o he associa ed
b anch.
The same ela ionships on he le el o unk connec ed main boughs a e illus a ed in Fig. 10:
Ve y high co ela ions we e ound o he a io o lea a ea o lea biomass o basal a ea o sun-
boughs o oak G 13, while shade-boughs ha e lowe lea a ea and mass. A simila endency
was ound in beeches, whe e he subdominan (shade-) ee Bu45 has less lea es pe basal
a ea han he dominan one (Bu38) o he wo ully ha es ed beeches. Again, co ela ions o
beech a e highe when conside ed on a single ee basis. The a ios o he pooled da a o
beeches a e 0.319 o lea a ea and 0.0196 o lea biomass and bo h ha e a he high
coe icien s o de e mina ion ( ² = 0.896 and 0.904, espec i ely). Coe icien s o de e mina ion
on he spa ial le el o boughs we e, hus, highe han on he le el o lea clouds.
Ra ios o lea a ea o o al basal a ea o boughs a e compa ed o es ima es o lea a ea pe
unk basal a ea in Fig. 11 o in es iga e, i his ela ionship may be ex apola ed: Only he s em
basal a ea o he subdominan beech ee Bu45 is compa ible wi h a linea ex apola ion om
boughs o he s em. The s ems o oak G 13 and beech Bu38 suppo less lea a ea, lea
biomass, and bough basal a ea pe unk basal a ea.
An o e iew o he di e en lea a ea / basal a ea a ios o lea cloud b anches, boughs and
s ems indica es ha he slope o all hese linea eg ession lines dec eases wi h inc easing
basal a ea o he woody elemen o all ees (see Table 3). Thus, an allome ic ela ionship o
all kind o wood om an indi idual ee becomes non-linea , al hough linea eg ession lines
wi h high ² alues may be de e mined on dis inc le els o o ganisa ion.
Fagus syl a ica
y = 0.4384x
R
2
= 0.9155
y = 0.2904x
R
2
= 0.9138
y = 0.3495x
R
2
= 0.9186
0
2
4
6
8
10
12
0 10 20 30
lea -cloud basal a ea [cm²]
lea a ea [m²]
beech Bu38
beech G 12
beech Bu45
Que cus pe aea
y = 0.4129x
R
2
= 0.743
0
2
4
6
8
10
12
0 10 20 30
lea -cloud basal a ea [cm²]
lea a ea [m²]
oak G 13
Fagus syl a ica
y = 27.333x
R
2
= 0.8124
y = 19.126x
R
2
= 0.8469
y = 30.488x
R
2
= 0.8906
0
200
400
600
800
1000
0 10 20 30
lea -cloud basal a ea [cm²]
lea d y weigh [g]
beech Bu38
beech G 12
beech Bu45
Que cus pe aea
y = 32.69x
R
2
= 0.8043
0
200
400
600
800
1000
0 10 20 30
lea -cloud basal a ea [cm²]
lea d y weigh [g]
oak G 13
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
35
Fagus syl a ica
y = 0.1548x
R
2
= 0.952
y = 0.3616x
R
2
= 0.9808
0
20
40
60
80
100
0 50 100 150 200 250
main bough basal a ea [cm²]
lea a ea [m²]
beech Bu38
beech Bu45
Que cus pe aea
y = 0.3756x
R
2
= 0.9539
0
20
40
60
80
100
120
0 100 200 300
main bough basal a ea [cm²]
lea a ea [m²]
sun main boughs shade main boughs
Fagus syl a ica
y = 0.0109x
R
2
= 0.852
y = 0.0218x
R
2
= 0.9656
0
1
2
3
4
5
6
0 50 100 150 200 250
main bough basal a ea [cm²]
lea d y weigh [kg]
beech Bu38
beech Bu45
Que cus pe aea
y = 0.0271x
R
2
= 0.939
0
2
4
6
8
10
0 100 200 300
main bough basal a ea [cm²]
lea d y weigh [kg]
sun main boughs shade main boughs
Que cus pe aea
y = 0.0271x
R
2
= 0.939
0
10
20
30
40
50
0 500 1000 1500
main bough basal a ea [cm²]
lea d y weigh [kg]
sun boughs
unk G 13
Fagus syl a ica
y = 0.0088x
R
2
= 0.9873
y = 0.0218x
R
2
= 0.9656
0
5
10
15
20
25
0 200 400 600 800 1000
main bough basal a ea [cm²]
lea d y weigh [kg]
beech Bu38
beech Bu45
unk Bu45
unk Bu38
Fagus syl a ica
y = 0.1469x
R
2
= 0.9983
y = 0.3616x
R
2
= 0.9808
0
50
100
150
200
250
300
350
0 200 400 600 800 1000
main bough basal a ea [cm²]
lea a ea [m²]
beech Bu38
beech Bu45
unk Bu45
unk Bu38
Que cus pe aea
y = 0.355x
R
2
= 0.8984
0
100
200
300
400
500
600
0 500 1000 1500
main bough basal a ea [cm²]
lea a ea [m²]
oak G 13
unk G 13
Fig. 10:
Allome ic ela ionship be ween lea a ea o biomass and basal a ea o he associa ed bough
Fig. 11:
Compa ison o allome ic ela ionships on he bough le el wi h hose o he unk le el. The
co ela ion o beech Bu45 includes he unk da a
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
36
Table 3: Lea s. woody elemen a ios on di e en spa ial le els
Oak G 13 Beech Bu38 Beech Bu45
Allome ic
ela ionship
Lea clouds
0,4129 32,69 0,4384 30,49 0,2904 19,13
Boughs 0,3756 27,1 0,3616 21,8 0,1548 10,9
S em 0,2433 18,1 0,2216 13,3 0,1464 8,7
The ansi ion om app oxima e linea o non-linea beha iou can be desc ibed wi h a powe
unc ion, which inc eases he o e all coe icien s o de e mina ion. A linea eg ession line o
model is only a special case o a powe unc ion (powe unc ion wi h exponen 1). Indeed ²-
alues inc eased o mo e hen 0.99 when using a powe unc ion o he eg ession. All esul ing
i s ha e exponen s lowe han 1, which indica es he sligh decline o he a io be ween lea
a ea o mass and basal a ea o woody elemen s wi h inc ease in basal a ea as mo e s and
s uc u al complexi y is included. (Fig. 12).
Fig. 12:
Powe unc ion app oxima ion o he a ea- and mass-based allome ic ela ionship be ween basal
a ea (cm²) and lea a ea (m²) o lea d y weigh [kg] o boughs and s ems o he h ee ully ha es ed
ees.
When es ima ing pa ame e s o he powe unc ion eg essions i was ound ha endlines
p oduced by Mic oso Excel a e based on he loga i hmic ans o med da a o bo h a iables
(log-log- ans o ma ion), which is jus i ied only o he special case ha he log-log- ans o med
da a show a be e ag eemen wi h he no mal dis ibu ion han he o iginal da a, because in his
case he po en ial e ec o lacking da a would be conside ed. Because he ag eemen wi h he
no mal dis ibu ion was no es ed sepa a ely in each case, only app oxima ions o he o iginal
da a we e done using he p og amming and calcula ion so wa e Ma hema ica (Wol am
Resea ch, Champaign, Illinois). These app oxima ions gene ally yield he bes i o he
a ailable da a (compa e Fig. 13).
Lea
a ea
H
m²
L
basala ea
H
cm²
L
Lea
biomass
H
g
L
basal a ea
H
cm²
L
400 800 1200 cm²
5
10
15
20
25
30
kg
300 600 900 1200 cm²
5
10
15
kg
200 400 600 800cm²
5
kg
400 800 1200 cm²
200
400
m²
300 600 900 1200 cm²
100
200
m²
200 400 600 cm²
100
m²
cm²
cm²
Oak G 13
Oak G 13
Beech Bu38
Beech Bu38
G 13
Beech Bu45
Beech Bu45
0.68x
0.859
0.048x
0.867
0.074x
0.755
0.016x
0.908
1.27x
0.751
0.17x
0.975
Lea
a ea
H
m²
L
basala ea
H
cm²
L
Lea
a ea
H
m²
L
basala ea
H
cm²
L
Lea
biomass
H
g
L
basal a ea
H
cm²
L
Lea
biomass
H
g
L
basal a ea
H
cm²
L
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
37
A compa ison was made be ween he allome ic ela ionships o 2 beech species, 5 oak species
and 5 addi ional b oad-lea ed ee species o examine, whe he he dec ease in a ios o lea
a ea o o al basal a ea wi h inc easing basal a ea o he s ems may be sys ema ically and
gene ally desc ibed wi h a powe unc ion, and mos da a o his s udy we e aken om
li e a u e. The in es iga ed ee species a e Fagus c ena a (K
AKUBARI
&
M
ARUYAMA
,
UNPUBLISHED
), Fagus syl a ica (B
ARTELINK
1997,
P
ELLINEN
1986,
L
EBAUBE ET AL
.
2000
AND THE
OWN MEASUREMENTS
), Que cus spp. (including Que cus pe aea and Que cus obu , B
URGER
1947
AND THE OWN DATA
), Que cus alba (M
ARTIN ET AL
.
1998,
R
OGERS
&
H
INCKLEY
1979),
Que cus coccinea, Que cus p inus, and Que cus ub a, Ace ub um, Be ula len a, Ca ya spp.
(including Ca ya glab a, Ca ya o a a and Ca ya omen osa), Li iodend on ulipi e a and
Oxydend um a bo eum (M
ARTIN ET AL
.
1998).
The dec ease in s em basal a ea o lea a ea a io a he le el o main unks was ound in 11 o
he 12 ee species, only he da a se o Be ula len a showed a sligh inc ease in his
ela ionship, which seems o be an a e ac due o one da a poin ha ep esen s he la ges
ha es ed Be ula len a ee (see Fig. 14). The powe unc ion app oxima ion o all a ailable ee
da a was 0,463 *
x
0,903
.
2.3.2 Discussion o allome ic ela ionships o he b anch sys em
The in e -indi idually cons an and in e -speci ically simila ela ionship be ween basal a e and
sapwood a ea o a ea o ou e ings o b anches (Fig. 6) s eng hens he hypo hesis, ha bo h
ela ionships desc ibe he same phenomenon. On he one hand, his cons ancy sugges s ha
he dis inguished cen al pa o he c oss-sec ion o b anches g ows in cons an ela ionship o
he whole b anch c oss-sec ion, which in u n indica es physiological changes in he cen al pa
o b anches wi h inc easing diame e , hough hea wood o ma ion has been shown no o ake
place in b anches o se e al di e en species (S
CHWEINGRUBER
1978).
On he o he hand, i shows ha he allome ic ela ionship be ween basal a ea and lea a ea a
he le el o lea cloud suppo ing b anches o bo h species is no in luenced by al e a ions o
sapwood a ea, because a cons an a io be ween basal a ea and sapwood a ea exis s a his
hie a chical le el, bu no on he le el o boughs o unks (Fig. 6, N
AIR
1995).
500 1000 1500
cm²
100
200
300
400
m²
Que cus pe aea
y = 0.533x
0.8769
0
100
200
300
400
0 500 1000 1500
basal a ea [cm²]
lea a ea [m²]
oak G 13
y = 0,68*x
0,859
Fig. 13:
Compa ison o powe unc ion endline (Excel) and powe unc ion app oxima ion
(Ma hema ica) on he same da a se . The sum o squa ed e o s (
χ
²) was 3749,8 o he endline
and 2020.98 o he app oxima ion.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
38
Fig. 14:
Dec ease o a io be ween lea a ea and basal a ea o 11 o 12 in es iga ed ee species wi h
inc easing basal a ea.
Que cus pe aea
and
Que cus obu
a e no dis inguished (“
Que cus spp
.”) and
Ca ya spp
. s ands o
Ca ya glab a
,
Ca ya o a a
and
Ca ya omen osa
.
500 1000 1500 2000 2500cm²
50
100
150
200
250
300
m²
500 1000 1500 2000 2500cm²
20
40
60
80
100
120
m²
500 1000 1500 2000 2500cm²
100
200
300
400
500
600
m²
500 1000 1500 2000 2500cm²
50
100
150
200
250
300
350
m²
500 1000 1500 2000 2500cm²
100
200
300
400
m²
500 1000 1500 2000 2500cm²
50
100
150
200
250
300
m²
500 1000 1500 2000 2500cm²
50
100
150
200
250
m²
500 1000 1500 2000 2500 cm²
50
100
150
200
250
300
m²
1000 2000 3000 4000cm²
200
400
600
800
1000
m²
500 1000 1500 2000 2500 3000 cm²
200
400
600
m²
1000 2000 3000 4000cm²
100
200
300
400
m²
500 1000 1500 2000 2500cm²
100
200
300
400
500
m²
Fagus c ena a
1 Fagus
syl a ic
Que cus
coccinea
Que cus
Que cus alba
Que cus p inus
Que cus ub a Ace ub um
Be ula len a Ca ya spp.
Li iodend on ulipi e a Oxydend um a bo eum
0,542*x
0,749
0,686*
x
0,849
4,878*x
0,542
0,807*x
0,759
1,388*x
0,694
0,526*x
0,825
1,44*x
0,564
0,429*x
0,837
0,068*x
1,16
0,219*x
0,953
1,086*x
0,692
0,942*
x
0,847
Oak G 13
Bu 38
G 12
1000 2000 3000 4000cm²
200
400
600
800
1000
m²
Que cus spp.
0,836*x
0,859
500 1000 1500 2000 2500cm²
100
200
300
400
500
m²
Fagus syl a ica
0,745*x
0,833
Bu45
Bu38
G 12
G 13
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
39
The lea a ea s. basal a ea ela ionship is e y obus (Fig. 9) and, hus, well sui able o up-
scaling o lea a ea along b anch diame e s o a c own. This could educe he necessa y wo k in
biomass ha es s o 10-20% o he lea clouds, as is shown o beech G 12. Ne e heless, he
es ablished ela ionship o oak shows conside able a ia ion ha can no solely be explained
by measu emen e o s. The in e -indi idual di e ences be ween beeches and he sca e
be ween lea clouds may ela e o a ia ion in he egula ion o p ocesses a ec ing wood
o ma ion and di e ing demands placed on hyd aulic conduc i i y acco ding o he o ien a ion,
size and posi ion o he lea cloud on indi idual b anches (M
ATTHECK
1995,
P
ROTZ ET AL
.
2000,
M
AHERALI ET AL
.
1997). The lea a ea / basal a ea a io o boughs may also be use ul o up-
scaling, bu he e di e ences be ween sun- and shade-boughs o oak occu , and he in e -
indi idual di e ences be ween beeches we e la ge han hose obse ed a he b anch le el.
The azimu h di ec ion o g ow h o main boughs om he s em was impo an o s uc u e
o ma ion in he c own, a leas in he case o oak. Also in beech ees Bu38 and G 12, se e al
main boughs each he uppe 1-2m o he c own, while one o wo lowe boughs exhibi ed an
ex eme ex ension o he sou h. This could be in e p e ed as ligh d i en compe i ion be ween
boughs and gi es a hin o he asymme ical dis ibu ion o a ou able condi ions in he ee
c own. The much lowe numbe o li ing shade boughs in he oak c own and he phenomenon
o se e al dead boughs below he li ing c own o oaks con as s o he high numbe o li ing
shade boughs in he h ee beech c owns. This indica es – oge he wi h he low lea a ea / basal
a ea a io o shade boughs o oak - he highe shade ole ance o beech b anches.
Species-speci ic di e ences in hea wood o ma ion occu a he s em and bough le el, bu no
a he le el o lea cloud suppo ing b anches. Ne e heless, allome ic ela ionships o
ami ica ion we e ema kably simila a all h ee spa ial le els o oak G 13 and o beech ees
(Fig. 7 and Fig. 8), which may be due o he common equi emen s in c owns o his size o
s uc u al s abili y.
The a io be ween suppo ed lea a ea and basal a ea o s ems declines in mos species wi h
inc easing basal a ea. This end is also ound in he in es iga ed oak and beech ees,
conside ing he in eg a ion om b anches o boughs and o main s ems. Exponen s lowe han
1 o a powe unc ion ela ionship we e also ound in powe unc ion app oxima ions o s em-
connec ed boughs o Que cus mongolica, Ace sieboldianum, Magnolia obo a a, Be ula
pla yphylla and Be ula maximowicziana (S
UMIDA
&
K
OMIYAMA
1997). Simila ela ionships a
di e en spa ial le els may indica e a common eason o he decline. While he lea a ea / basal
a ea a io was linea and in e -indi idually cons an a he le el o b anches (Fig. 9), di e ences
be ween sun and shade boughs o oak and be ween he subdominan , in ec ed ee and he
dominan beech ee in he same s and occu ed a he le el o boughs (Fig. 10). These
di e ences may be explained by ca i a ion due o dying o appe aining b anches o he shade
main boughs o oak. Ca i a ion may also be he eason o he gene ally lowe lea a ea / basal
a ea a io o he wholly in ec ed beech Bu45.
The linea i y o all in es iga ed lea a ea s. basal a ea ela ionships on he bough and b anch
le el apa om ha o he shade boughs o oak s eng hens his explana ion. Ca i a ion is
expec ed o ha e less impac on he lea a ea / basal a ea a io o young b anches, because o
he ela i ely sho ime o hei exposi ion o s ess si ua ions. A linea ela ion in he lea a ea /
basal a ea a io can also esul , i ca i a ion a ec s all boughs o b anches wi h he same
p obabili y due o hei simila age, simila condi ions in he same ee c own, o simila i ali y
(same exposu e ega ding in ec ion as in Bu45). The age o ees, boughs, and b anches may,
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
40
hus, explain he gene al decline o lea a ea / basal a ea a ios ac oss spa ial scales. Di e en
species-speci ic mechanisms o a oid ca i a ion unde hei di e en li ing condi ions may be
esponsible o he high nume ical di e ences in he in es iga ed lea a ea / basal a ea a io
be ween species, which may especially be seen be ween he bigges and he e o e oldes ees
( o example o Fagus c ena a and Que cus spp. in Fig. 14 and Fig. 15).
2.3.3 Lea a angemen in whole ee c owns
2.3.3.1 3D- ep esen a ion o lea clumping
The a angemen o lea es in he canopy has a majo in luence on ligh clima e in he ee
c own and he ligh -dependen unc ion o all assimila ing issues. In mos ee species, lea
dis ibu ion is clumped along lea cloud suppo ing b anches, hough he e may also be some
single lea es close o he s em o o a main bough ha a e a away om o he lea es, and
he e o e, no pa o a lea cloud (as was ound in he in es iga ed Que cus pe aea c own). A
ull desc ip ion o he h ee-dimensional a angemen o lea clouds in he c own was achie ed
o beech Bu38 (139 lea clouds) and o oak G 13 (88 lea clouds) ia di ec measu emen o
he whole lea biomass, while he lea biomass o lea clouds o beech G 12 (66 lea clouds)
was calcula ed using he ela ionship ound on a sub-sample o i s b anches (see Fig. 9). The
esul s a e shown below in 3-D-illus a ions. The da a lis ing he exac co-o dina es o all lea
cloud en eloping polyhed ons a e long- e m s o ed and a ailable ia he BITÖK sample
collec ion.
500 1000 1500 2000 2500 3000 3500
200
400
600
800
1000
Oxydend um a bo eum
Li iodend on ulipi e a
Ca ya spp.
Be ula len a
Ace ub um
Que cus ub a
Que cus p inus
Que cus coccinea
Que cus alba
Que cus spp.
Fagus syl a ica
Fagus c ena a
Fig. 15:
In e -speci ic a ia ion o he a io be ween basal a ea and lea a ea o 261 ees o di e en
species.
cm
²
m²
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
41
3-D-g aphs in he ollowing a e cons uc ed wi h he so wa e Ma hema ica (Wol am esea ch,
Champaign, Illinois) using a ligh e lec ion model [Phong 1975] ha simula es he e lec ance o
su aces conside ing hei o ien a ion o ligh sou ces, he eby dis inguishing be ween specula
(low sca e -) and di use (high sca e -) ligh e lec ion. The esul ing 3-D-e ec can only be
Oak G 13
-
2.5 0 2.5 5 7.5
No h
H
m
L
5
10
15
20
25
Heigh
H
m
L
5
10
15
20
25
Heigh
H
m
L
Beech G 12
-4-202 4
No h HmL
5
10
15
20
25
Heigh HmL
5
10
15
20
25
Heigh HmL
Beech Bu38
-
4
-
2 0 2 4
No h
H
m
L
5
10
15
20
25
Heigh
H
m
L
5
10
15
20
25
Heigh
H
m
L
Lea a ea densi y
(m²/m³)
5 15
25
35 45 55 65
Fig. 16:
3-dimensional maps o ee c own s uc u es and lea a ea densi ies o lea cloud en eloping
polyhed ons in he canopies o beech Bu38, beech G 12 and oak G 13. Though beech Bu38 is smalle
han he “G oßebene”- ees, i is a dominan ee in i s s and “Buchenallee” (see also Fig. 3). The y-axis
o he g aphs ep esen s heigh abo e he loo (m). The o igin o he co-
o dina e sys em o oak G 13 is
he same as o beech G 12, so ha he s em base poin o oak G 13 is (-4,79 | 2,96 | 0,14 )
[Eas /No h/Heigh ], while he o he s em base poin s a e si ua ed in he o igin. This and he legend a e
also alid o Figu e 19 a and b, whe e ho izon al sec ions o he polyhed ons o 1m hickness can be
iewed om abo e. This and all ollowing ee c own igu es ely on he 3-D- ep esen a ion model
CRISTO (see chap e 4) ha was buil using he Ma hema ica p og amming language.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
48
Lea a ea calcula ions on he base o olume ic homogenei y con i m he non-mono one
dis ibu ion o e heigh laye s ha was shown o heigh ange homogenei y (Fig. 22).
The same maxima and minima a e appa en hough he lowe esolu ion smoo hes he da a so
much ha in o ma ion om he ine esolu ion da a is necessa y o in e p e he esul s. Fo
example, he heigh laye s 17.6m and 18.6m o beech 38 a e he e di icul o iew as minimum
laye s. The olume ic homogenei y assump ion ends o shi lea a ea minima and maxima o
lowe le els. This is a consequence o he olume dis ibu ion o e heigh ange o he lea
clouds, which a e usually wide in hei lowe , da ke ex en and smalle in he ligh e and uppe
po ion. Conside ing ha lea clouds usually g ow owa ds ligh e and highe egions
(de elopmen o new lea es) and away om he lowe and da ke pa s (die o o shaded pa s)
, bo h me hods seem o be jus i ied app oaches o examining s uc u e.
2.3.4.2 Lea a ea densi ies o heigh laye s
Ligh ha es o ee c owns is no only in luenced by he amoun o lea a ea a di e en
heigh s, bu also by he shadows cas on and by compe ing ees and on sel -shading
(L
EUSCHNER
2000). The e ec i e lea a ea densi ies o heigh laye s o single ee c owns
depend on lea a ea o he laye bu also on he ho izon al ex ension o he heigh laye , which is
usually no cons an . Heigh laye - ela ed lea a ea densi ies (LAD
L
) we e calcula ed on he
base o LA
L, dm
–da a, assuming ha he olume o heigh laye s may adequa ely be desc ibed
by mul iplying he laye heigh by he con ex hull a ea o p ojec ed polygon co ne poin s in ha
heigh laye . This assump ion equi es he heigh laye s no be oo small. Fo he sake o
14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5
10
20
30
40
50
60
70
Laye
lea
a ea
H
m²
L
uppe limi o heigh laye (m) uppe limi o heigh laye (m)
17.2 18.2 19.2 20.2 21.2 22.2 23.2 24.2 25.2 26.2
10
20
30
40
50
60
70
Laye
lea
a ea
H
m²
L
uppe limi o heigh laye (m)
Oak G 13
Beech G 12
13.6 14.6 15.6 16.6 17.6 18.6 19.6 20.6 21.6 22.6
10
20
30
40
50
60
70
Laye
lea
a ea
H
m²
L
Beech Bu38
Laye lea a ea (m²)
Fig. 22:
Lea a ea o 1m heigh laye s
calcula ed on he assump ion o olume ic
homogenei y o lea clouds. Axes we e
scaled o ep esen he same o dina e ange.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
49
simplici y, a heigh o 1m was chosen o all heigh laye s and lea a ea densi ies we e
calcula ed acco ding o
whe e V
L
deno es he laye olume. The LAD
L
/ heigh ela ionship was app oxima ed by a
polynomial unc ion o LAD
L
e sus ela i e heigh in he canopy ( anging om 0 o 1, see Fig.
23).
The esul s demons a e a pa ly di e en si ua ion in compa ison o Figs. 21 and 22. A g ea e
dis ibu ion o lea a ea densi y owa d he uppe pa o he c own occu s. Skewness o he
LAD
L
-dis ibu ion was posi i e in all cases (see Table 5), indica ing ha he ees p oduce some
single laye s ( hose in he uppe c own) wi h ex emely high lea a ea densi ies as compa ed o
o he laye s. Especially he beech ees G 12 and Bu38 had he highes lea a ea densi ies in
hei uppe mos c own laye , while oak G 13 had i s highes LAD
L
- alues 2,5m below he apex.
While oak G 13 had he g ea es amoun o lea a ea in a highe egion han he
neighbou ing beech G 12 (Fig. 21), and e en hough his was mo e han wice as much lea
a ea han ha o beech G 12 in he peak laye s, beech G 12 (and also beech Bu38) had a
highe maximum LAD
L
han oak G 13. Fu he mo e, e en hough beech G 12 was 0.7m sho e
LAD
L=
⁄
i
=
1
10
LA
L,dm
V
L
, (2)
13.6 14.6 15.6 16.6 17.6 18.6 19.6 20.6 21.6 22.6 uppe limi
H
m
L
0.5
1
1.5
2
2.5
3
Lea A ea Densi y
H
m²
ê
m³
L
14.5 15.5 16.5 17.518.5 19.520.5 21.5 22.5 23.5 24.5 25.5 uppe limi
@
m
D
0.5
1
1.5
2
2.5
3
Lea A ea Densi y @m²êm³D
17.2 18.2 19.2 20.2 21.2 22.2 23.2 24.2 25.2 26.2 uppe limi
H
m
L
0.5
1
1.5
2
2.5
3
Lea A ea Densi y
H
m²
ê
m³
L
Lea a ea densi y [m²/m³] Lea a ea densi y [m²/m³]
Lea a ea densi y [m²/m³]
uppe limi o heigh laye [m]
uppe limi o heigh laye [m]
uppe limi o heigh laye [m]
Fig. 23:
Lea a ea densi ies o 1m-heigh laye s o
he in es iga ed canopies. The olume calcula ion is
based on he con ex hull o he p ojec ed polygon
co ne poin s o each laye imes laye heigh (1m),
and he LAD calcula ion assumes equal dis ibu ion
o lea es o e he heigh ange o a lea cloud.
Polynomial app oxima ions on he base o x = mean
ela i e heigh in he canopy o beech Bu38, G 12
and oak G 13 we e ( espec i ely):
Oak G 13
Beech G 12
Beech Bu38
LAD
L
=
335.8
x
6
-
990.9
x
5
+
1119.2
x
4
-
615.2
x
3
+
174.7
x
2
-
22.8
x
+
1.3
LAD
L
=
1111.3
x
6
-
3245.9
x
5
+
3605.8
x
4
-
1897.2
x
3
+
477.5
x
2
-
48.2
x
+
1.6
LAD
L
=
211.9
x
6
-
544
x
5
+
495.9
x
4
-
176.9
x
3
+
11.4
x
2
+
5.2
x
-
0.1
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
50
han oak G 13, beech G 12 managed o p oduce i s maximum LAD
L
in a highe egion han he
maximum LAD
L
o oak G 13, which should be impo an in e ms o shading.
The lowe maximum LAD
L
o oak G 13 is no due o a gene ally highe olume o he whole ee
c own, because he sum o all laye olumes o he wo ees (=LAD
C own
) was nea ly he same
(see Table 5). Mo eo e , oak G 13 had a highe absolu e lea a ea densi y ela ed o he whole
c own olume (LAD
C own
, Table 5), so ha he highe maximum LAD
L
o beech G 12 only a ises
because o he much mo e posi i ely skewed dis ibu ion o LAD
L
- alues in compa ison o he
dis ibu ion o oak G 13 LAD
L
- alues , i.e., he high maximum LAD
L
- alue o beech G 12 can
unde hese ci cums ances only be achie ed due o many heigh laye s wi h low LAD
L
- alues.
The c own o oak G 13 on he o he hand expands o eno mously high laye olumes (40.1 -
58.8m³, compa e Table 5) in he 2
nd
o 6
h
laye below apex, which leads despi e hei high
amoun s o lea a ea o a he mode a e LAD
L
- alues o hese uppe laye s.
Table 5: canopy da a
Bu38 G 12 G 13
Lea a ea (m²)
240.7 236.6 328.3
Heigh ange (m)
13.13 - 22.6 14.0 - 25.5 16.92 - 26.2
C own olume (m³)
229.3 312.0 310.1
Range o laye olumes (1m-laye s, m³)
4.8 – 39.5 3.6 - 37.6 0.6 - 58.8
C own lea a ea densi y LAD
C own
(m²/m³)
1.05 0.76 1.06
Range o laye lea a ea densi ies LAD
L
(m²/m³)
0.11 - 2.37 0.07 - 2.38 0.20 - 2.03
Skewness* o LAD
L
–dis ibu ion
0.18 1.31 0.41
S anda d de ia ion o LAD
L
- alues
0.74 0.61 0.60
P ojec ed c own a ea (m²)
42.8 52.4 69.4
P ojec ed c own a ea (gap co ec ed, m²)
36 47.5 54.8
T ee lea a ea index TLAI (m²/m²)
5.6 4.5 4.7
T ee lea a ea index TLAI
g
(gap co ec ed, m²/m²)
6.7 5.0 6.0
*: Skewness calcula ion was based on maximum likelihood es ima es o s anda d de ia ions
2.3.4.3 E ec o gap co ec ion o lea a ea densi ies
Sepa a ing he canopy in o laye s o cons an dep h does no ela e in any way o a na u al
phenomenon and, he e o e, he choice o o he bounda ies which could signi ican ly in luence
he olume dependen de e mina ion o LAD
L
– alues could be conside ed. While ho izon al
bounda ies sp ead he oliage by sepa a ing lea es o lea clouds ha a e na u ally clumped,
e ical bounda ies can addi ionally conside he o m o he c oss-sec ion o a heigh laye in a
ine o coa se manne . Reasonable de ini ions o laye p ojec ed a eas a e he same as hose
o p ojec ed c own a eas and he con ex hull a ea ep esen s a de ini ion ha conside s he
o e all shape o he c oss-sec ion bu explici ly no ca i ies along he bo de o he c oss-sec ion.
Ano he easonable de ini ion would be o example o conside all ca i ies o a gi en size o o
conside only he bigges ca i y, which can ha e a s ong e ec on he heigh dependence o
LAD
L
– alues, when he oughness o he bo de o he c oss-sec ion o heigh -laye s a ies.
The po en ial magni ude o his e ec can be seen, when he calcula ed ee lea a ea indices o
he in es iga ion ees wi h o wi hou gap co ec ion a e unde s ood as lea a ea densi ies o a
single la ge laye wi h cons an heigh : Gap co ec ion led o an inc ease o TLAI in he ange o
10 - 28% (Table 5).
A ee and ca i y o ien ed laye de ini ion assuming olume ic homogenei y o lea clouds was
es ed o compa ison on he da a o beech G 12: The heigh o ho izon al bounda ies be ween
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
51
laye s was chosen by eye such ha bigge ca i ies along he bo de o he c oss-sec ion we e
no hidden by lea clouds abo e o below he ca i ies. The i egula o m o ho izon al c oss-
sec ions was app oxima ed by 8 o 12 sec o s o ci cles wi h di e en adii (see Figs. 112a,
112b). The assump ion o olume ic homogenei y o lea clouds again equi ed he use o he
p og am CRISTO (see chap e 4).
Using his app oach led o a sligh ly di e en LAD
L
s. heigh ela ionship (Fig. 24).
The lowes and he uppe mos laye we e no longe ex eme and hei LAD
L
- alues we e shi ed
owa ds alues close o he a e age. The highes LAD
L
now occu s in he second laye om
he op. This was again due o he assump ion o olume ic homogenei y ins ead o heigh
ange homogenei y. The lea a ea o lea cloud op segmen s in he uppe mos laye is
o e es ima ed and ha o lea cloud bo om segmen s in he lowes laye a e unde es ima ed,
when hei lea a ea is assumed o be equally dis ibu ed o e he heigh ange. Though his is
p incipally also ue o he o he laye s, he e ec appea s o be weake in he middle laye s:
The o e all ela ionship be ween he middle laye s ag ees well wi h ha ob ained om 1m-
heigh laye s, which accoun s o he ac ha he middle laye s con ain bo om and op
segmen s o lea clouds, so ha hei con ibu ions o ela i e o e - and unde es ima ion may
cancel each o he ou . The gene al end is s ill a mono onous and nea ly exponen ial inc ease
in LAD
L
owa ds he uppe mos laye s. I no undamen al changes in he opposi e di ec ion
would occu when oak G 13 would be laye ed in his manne , he laye wi h highes LAD
L
o
beech G 12 (mean heigh : 24.1m) would s ill be in a sligh ly highe egion han ha o oak G 13
(mean heigh : 23.7m), hough he beech is 0.7m sho e .
2.3.4.4 Volume gap ac ions
The meaning o laye lea a ea densi ies o ligh ansmission and abso p ion in a canopy is
s ongly dependen on clumping o lea es and discon inui y o he ee canopy (C
ESCATTI
1998).
The e o e he ques ion a ises, whe he he lea a ea densi y dis ibu ion om op o bo om o
he canopy is due o changes in lea a ea densi y o lea clouds o in he lea cloud densi y in
di e en laye s, i.e., he ac ion o hei olume wi h espec o he laye olumes (which can be
in e sely exp essed as olume gap ac ion). Volume o lea cloud segmen s as calcula ed wi h
he p og am CRISTO was summed o each laye and ela ed o he laye -speci ic con ex hull-
based laye olume V
L
o he calcula ion o laye gap ac ions as
0
0.5
1
1.5
2
2.5
15.1 16.1 17.2 18.4 19.3 20.2 21.2 22.6 22.9 23.8 24.4 25.5
uppe limi o heigh laye [m]
Lea a ea densi y [m²/m³] .
Fig. 24:
Lea a ea densi ies o i egula chosen
heigh laye s o beech G 12. Laye olume is
calcula ed as he sum o cylinde sec o olumes
wi h di e en adii and he LAD calcula ion is based
on he assump ion o olume ic homogenei y. The
polynomial app oxima ion on he base o x = mean
ela i e
heigh in he canopy was:
LAD
L
=
-
313.7
x
6
+
766.2
x
5
-
687.7
x
4
+
280
x
3
-
49.3
x
2
+
2.8
x
+
0.6
Beech G 12
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
52
whe e V
P i
deno es he olume o a polyhed on o polyhed on segmen and n he numbe o
polyhed ons and polyhed on segmen s in ha laye . The 1m-heigh laye lea a ea densi y was
es ima ed om he lea cloud lea a ea da a assuming olume ic homogenei y:
He e, V
C i
deno es he olume o he whole polyhed on, i. e., he lea clouds olume and LA
C i
is
he lea clouds lea a ea. Finally, a e age lea a ea densi y o polyhed ons and polyhed on
segmen s in he laye ( )was calcula ed acco ding o
Volume gap ac ions wi hin he c own laye s we e a he high (90%, 82% and 89% on a e age
o beech Bu38, beech G 12 and oak G 13), and anged om 82% o 98%, 58% o 96%, and
72% o 98% o he h ee ees, espec i ely. While he lowes gap ac ion o oak G 13 was in
LAD
P
`
Gap =1-
⁄
i
=
1
n
V
P
i
V
L
, (3)
LAD
L,m
=
„
i
=
1
n
V
Pi
VCi
¥
LA
Ci
V
L
(4)
LAD
P
`
=
„
i
=
1
n
V
Pi
V
Ci
¥
LA
C
i
⁄
i
=
1
n
V
P
i
. (5)
13.6 14.6 15.6 16.6 17.6 18.6 19.6 20.6 21.6 22.6
0.2
0.4
0.6
0.8
1
Laye gap ac ion
H
-
L
14.515.516.517.518.519.520.521.522.523.524.525.5
0.2
0.4
0.6
0.8
1
Laye gap ac ion
H
-
L
17.2 18.2 19.2 20.2 21.2 22.2 23.2 24.2 25.2 26.2
0.2
0.4
0.6
0.8
1
Laye gap ac ion
H
-
L
uppe limi o heigh laye (m)
uppe limi o heigh laye (m)
uppe limi o heigh laye (m)
Oak G 13
Beech G 12
Beech Bu38
Fig. 25:
Laye gap ac ions o 1m heigh
laye s, calcula ed on he assump ion o
olume ic homogenei y
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
53
i s uppe mos laye , he lowes gap ac ion o beech Bu38 and G 12 was 2.5m and 3.5m below
he apex (Fig.25).
In any case, he gene al end was a mo e o less con inuous dec ease in gap ac ions as one
mo ed owa ds he op laye . Gap ac ions explained 64%, 89%, and 89% o he a iabili y o
laye lea a ea densi ies (Bu38, G 12, and G 13 espec i ely), which we e signi ican
ela ionships a he 1%-le el. The eg ession on
was only signi ican o oak G 13 ( ² =
0.51), leading o he conclusion ha he inc ease o laye lea a ea densi ies o he beeches wi h
heigh was basically due o dec easing gap olumes; which is also alid o oak G 13, e en
hough inc easing lea a ea densi ies o lea clouds also occu ed.
2.3.5 Lea cloud o ien ed e alua ion o lea a angemen in he c own
Spa ial and quali a i e p ope ies o lea clouds we e in es iga ed because o hei po en ial
impo ance o up-scaling o pho osyn hesis and also because he a angemen o lea clouds
appea ed o be qui e egula (compa e Fig. 16). The g ow h o ee c owns is gene ally
unde s ood as dependen on a complex in e ac ion o species-speci ic ules and he esea ch
on his opic has been desc ibed in chap e 1. Bu hough i has epea edly been shown ha he
consequen applica ion o g ow h ules in simula ions o e se e al g ow h pe iods leads o
egula shaped, ypical c own o ms (K
URTH
&
S
LOBODA
1999,
DE
R
EFFYE ET AL
.
1997,
L
IST
&
K
ÜPPERS
1997,
S
IEVÄNEN ET AL
. 1997), a egula s uc u e o eal ee c own shapes in a ma u e
o es has no ye been desc ibed in de ail, while gene al concep s o ypical c own o ms exis
al eady o a long ime (H
ALLÉ ET AL
. 1978). The e o e, i becomes ques ionable, i ac al
simula ions o ee g ow h a e an adequa e me hod o hei desc ip ion (L
IST
&
K
ÜPPERS
1997).
A common a gumen o hese doub s is ha he in luence o ee g ow h pa e ns may become
less isible in ageing ees due o he g owing and accumula ing in luence o changing
en i onmen al condi ions du ing i s li e-span and he in luence o an inhomogeneous
en i onmen .
Regula i ies in canopy s uc u e may ha e a signi ican impac on up-scaling me hods since hey
sugges unde lying pa e ns in lows o mass and ene gy. Fo example, as he di ec ed
sepa a ion o elec ical cha ges ac oss he hylakoid memb ane o he chlo oplas by he spa ial
o ganisa ion o he elec on anspo chain causes a powe ul cha ge g adien (K
ARLSON
1999),
he spa ial o ganisa ion o ee c owns could in luence he dis ibu ion o pho osyn he ically
ac i e adia ion in he canopy ia ansmission and e lec ion. T ansmi ance and e lec ance o
PAR on ypical lea su aces a ies be ween 2 and 7%, and be ween 8 and 15%, espec i ely,
wi h an a e age alue o ca. 5% o ansmi ance and ca. 10% o e lec ance (J
ONES
1992).
Bo h p ocesses a e in i ually all canopy ligh models assumed o be andomly di ec ed,
knowing ha e lec ion is dependen on he angle be ween incoming adia ion and e lec ing
su ace, and he eby conside ing he lea es and o he c own elemen s o be andomly o ien ed.
E en hough 10% o he incoming adia ion is a small p opo ion, he esul ing i adiance a e
he i s e lec ion lies o en in he ange o ligh sa u a ion o pho osyn he ic ligh esponse
cu es o shade lea es (achie ed a 100 – 200 µmol/(m²*s) o beech, L
ICHTENTHALER ET AL
.
1981, S
CHULTE
1992), while he incoming global adia ion abo e he canopy is o en highe han
he sa u a ion alue o sun lea es (600 - 700 µmol/(m²*s) o beech).
I would be possible o ee c owns o op imise he use o adia ion o pho osyn hesis, i he
su plus o PAR in he uppe pa o he o es canopy could be passed o he lowe laye s by
LAD
P
`
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
54
di ec ed e lec ion. Addi ionally, shade lea es could be spa ially a anged such ha he amoun
o e lec ed and ansmi ed adia ion in he lowe laye s is op imally used.
The lea cloud o ien ed h ee-dimensional desc ip ion o he in es iga ed ees can no be used
o es he e lec ion o each lea , bu i can be used o check, whe he egula i ies exis ha
suppo he use o e lec ed and ansmi ed ligh in he lowe laye s.
Lea cloud p ope ies may be desc ibed wi h a g oup o pa ame e s ha desc ibe whe e he lea
cloud is si ua ed in ela ion o he s em, o he canopy base, o o he o es loo ; a second
g oup o pa ame e s ha desc ibe he in luence o o he c own elemen s on he en i onmen al
si ua ion o he lea cloud; a hi d g oup o quan i ies ha desc ibe he spa ial p ope ies (angles
and ex ensions) o he lea cloud, and, inally, a g oup o quali a i e p ope ies.
Loca ion p ope ies include he quan i ies:
H: ela i e heigh o he lea cloud cen e in he canopy (-),
H
abs
: absolu e heigh o he lea cloud cen e abo e he loo (m)
E: dis ance o he lea cloud cen e o he s em in eas di ec ion (m),
N: dis ance o he lea cloud cen e o he s em in no h di ec ion (m),
s emd: ho izon al dis ance o he lea cloud cen e o he s em (m),
AZ
s
: azimu h o he ho izon al ec o s em → lea cloud cen e, measu ed an i-clockwise om
he no h (°).
C own en i onmen al p ope ies a e:
CLA: sum o ee canopy lea a ea abo e he lea cloud (m²),
CVOL: ee canopy olume abo e he lea cloud (m³),
CLAD: a e age ee canopy lea a ea densi y abo e he lea cloud (m²/m³).
Lea cloud spa ial p ope ies a e:
AZ
P
: azimu h o he exposi ion o he lea cloud plane, ma hema ically de ined as azimu h o he
upwa ds di ec ed no mal ec o o he lea cloud plane, measu ed an i-clockwise om he
no h (°),
α
αα
α
h
: lea cloud angle; s eepes angle o he lea cloud plane owa ds a ho izon al plane
(°, posi i e and nega i e alues),
α
αα
α
AZ
: inclina ion o he main g ow h di ec ion o a lea cloud owa ds he ho izon. The main
g ow h di ec ion is he e de e mined as ha ec o in he lea cloud plane, ha goes h ough
he lea cloud cen e and comes om he s em. (°, posi i e and nega i e alues),
α
αα
α
s
: angle o he main g ow h di ec ion ec o owa ds he idealised su ace o he c own (°),
H
s
: heigh o he in e sec ion o main g ow h di ec ion ec o and idealised canopy su ace (m),
D
s
: de i a i e o he idealised canopy shape unc ion a he poin o in e sec ion wi h he main
g ow h di ec ion ec o (m/m),
a ea: e ically p ojec ed a ea o he lea cloud (m²),
olume: olume o he lea cloud (m³),
H ange: e ical ex ension o he lea cloud (m).
Quali a i e p ope ies include:
LAD: Lea a ea densi y o lea clouds (lea a ea pe lea cloud olume, m²/m³),
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
55
WAD: Wood a ea densi y o lea clouds (p ojec ed a ea o b anches and wigs pe lea cloud
olume, m²/m³)
CLA was calcula ed based on he cloud- ela ed heigh and lea a ea da a, summing up lea
a ea o all lea clouds whose cen e lies abo e a ce ain ela i e heigh . CVOL elies on he
olume calcula ions o heigh laye s (compa e Fig. 23), summing up all laye olumes abo e
he ela i e heigh o he lea cloud cen e and he heigh -p opo ional uppe pa o ha laye o
which he lea cloud cen e belongs. CLAD, in con as , is no ela ed o c own o m o ien ed
laye olumes, bu assumes a cons an olume o each laye abo e he lea cloud, hus
conside ing he ee c own as a cylinde . This was done o enable an es ima ion o he sel -
shading e ec o c own lea a ea densi ies on lea clouds on he basis o an applica ion o
Bee ’s law o heigh laye s (see below). The olume o hese heigh laye s was, he e o e
assumed o equal he maximum o heigh laye olumes o each ee. Volume ( olume) o lea
clouds has been es ima ed by calcula ion o hei en eloping polyhed on’s olume (see chap e
4.1.2.2).
The a iables α
αα
α
AZ
, α
αα
α
s
, H
s
, and D
s
we e in oduced o he in es iga ions on spa ial egula i ies in
he ee c own and equi e an app oxima e desc ip ion o he canopy shape. The discon inuous
eal c own shape may no be used o hei calcula ion, which e eals he idealising concep
behind he wo d “canopy shape”. The chosen concep o app oxima e he measu ed c own
ex ensions shall enable he conside a ion o de e minis ic ela ionships be ween p ope ies o
c own elemen s and he canopy shape and he e o e ies o desc ibe a ypical canopy shape
o he gi en ees in a o es en i onmen : I is assumed ha homogeneously changing
condi ions o he en i onmen do no undamen ally change he ypical canopy shape, and ha
he obse ed a ie y o canopy shapes om he same species mainly esul s om hei spa ially
inhomogeneous en i onmen s. Thus, he ypical canopy shape may no be ound in
inhomogeneous en i onmen s like a o es , and i may be di icul o econs uc i om he
ac ual spa ial si ua ion, because his si ua ion has changed du ing he li e-span o a ee. The
desc ibed ypical c own shape he e o e equalises he c own de elopmen in all ho izon al
di ec ions by aking he maximum ex ension o heigh laye s as he ypical ex ension in e e y
o he di ec ion. I is assumed ha he canopy would ha e de eloped o his maximum ex ension
in all ho izon al di ec ions, i no compe i ion e ec s due o he inhomogenei y o he o es
en i onmen would exis .
The canopy su ace was de ined o be a su ace o e olu ion a ound he s em on he basis o
5
h
o de polynomial unc ions ha we e app oxima ed o he maximum s em dis ances in each
1m-heigh laye . The lowes heigh laye o each ee was no conside ed in he app oxima ion
and he polynomial unc ion was cu a he bo om o he ee c own (see Fig. 26). The
app oxima ions show a simila c own shape o bo h beeches which is di e en om he canopy
su ace shape o he oak. This can de ini ely be shown by a compa ison o he de i a i es o
he h ee shape unc ions (Fig. 27). While he de i a i e o bo h beech c own shape unc ions
has wo maxima in he heigh ange o he ee canopies, he oak’s had only one, which is due
o a g ea heigh ange in he shape unc ion cu e, whe e he heigh laye s ha e nea ly
cons an and e y high maximum s em dis ances, while he laye s abo e and below his pa a e
much smalle , so ha he shape unc ion mono onously dec eases om he i e maximum
laye s owa ds bo h ends o he c own.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
56
Fig. 26
:
Polynomial app oxima ions o he maximum s em
dis ance in each laye ( i s ow). The canopy su ace was
assumed o be a su ace o e olu ion o hese unc ions
a ound he x-axis (second ow, all uni s in me e s). The
unc ions o he dependence o s em dis ance (Y) o heigh (X)
a e displayed below (Bu38, G 12, and G 13, espec i ely).
The angle be ween lea cloud plane and canopy su ace (
α
αα
α
s
)
was de e mined a he poin o in e sec ion o a s aigh line
h ough he lea cloud and he calcula ed canopy su ace ( igh
side, side iew). The s aigh line ep esen s he main g ow h
di ec ion o he lea cloud and goes h ough he cen al axis o
he s em and he lea cloud cen e and lies in he lea cloud
plane.
While
α
αα
α
h
is he s eepes inclina ion o he lea cloud plane,
α
αα
α
AZ
is he inclina ion o he lea cloud plane when measu ed in
di ec ion o i s s em ela i e azimu h o ien a ion
AZ
S
, which is
illus a ed in he g aph below ( iew om abo e)
14 16 18 20 22
heigh
H
m
L
1
2
3
4
5
6
7
8
me s ecna sid
H
m
L
beech Bu38
16 18 20 22 24 26
heigh
H
m
L
1
2
3
4
5
6
7
8
me s ecna sid
H
m
L
beech G 12
18 20 22 24 26 28
heigh
H
m
L
1
2
3
4
5
6
7
8
me s ecna sid
H
m
L
oak G 13
15
20
25
-5
-2.5
0
2.5
5-5
-2.5
0
2.5
5
15
20
25
-5
-2.5
0
2.5
5
15
20
25
-5
-2.5
0
2.5
5
-5
-2.5
0
2.5
5
15
20
25
-5
-2.5
0
2.5
5
15
20
25
-5
-2.5
0
2.5
5
-5
-2.5
0
2.5
5
15
20
25
-5
-2.5
0
2.5
5
Y
=
-
0.000827421
x
5
+
0.06824115
x
4
-
2.22255
x
3
+
35.64606
x
2
-
280.825
x
+
871.535
Y
=
-
0.000455346
x
5
+
0.04100925
x
4
-
1.45066
x
3
+
25.09886
x
2
-
211.399
x
+
694.228
Y
=
-
0.0000366738
x
5
+
0.00210313
x
4
-
0.0402233
x
3
+
0.27228
x
2
-
0.0546
x
+
0.039
Di ec ion o
inclina ion
calcula ions o
α
αα
α
s
and
α
αα
α
AZ
AZ
S
N
Di ec ion o s eepes
inclina ion o he lea
cloud plane (
α
αα
α
h
)
α
αα
α
AZ
α
αα
α
s
ho izon
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
57
An impo an consequence o he desc ibed canopy shapes is ha he maximum ex ension o
he canopy o oak G 13 lies in he uppe hal o he c own, while i is in he lowe hi d o bo h
beech canopies. Empi ical e idence o he ela i ely highe posi ion o he maximum ex ension
o oak canopies was ound in s and in es iga ions on all ees om he G oßebene and om he
S eink euz s and: While he heigh o maximum ex ension in sou h, eas , no h, and wes
di ec ion was on a e age 80% o he o al ee heigh o 48 oak ees, i was on a e age 67% o
he ee heigh o 58 beeches. Only ees highe han 15m we e conside ed in his compa ison
and he ange be ween i s and hi d qua ile was 76.7 - 84.9 % o oak ees and 57.2 - 75.6%
o beech ees. The same alue o all 80 beech ees highe han 15m om he Buchenallee
s and was 45% wi h an in e qua ile ange o 41% - 50.2%.
α
αα
α
s
was calcula ed by p olonging he main g ow h di ec ion o he lea cloud (a s aigh line in he
lea cloud plane ha goes h ough he s em and he lea cloud cen e) o he canopy su ace,
hus conside ing he azimu h o he lea cloud ela i e o he s em (AZ
s
) (Fig. 26). The angle was
calcula ed be ween he main g ow h di ec ion and he de i a i e D
s
o he polynomial unc ion a
he poin o in e sec ion o bo h lines in a wo-dimensional co-o dina e sys em in he plane o he
main g ow h di ec ion and he s em (x = H
abs
, y = s emd). The de i a ion o he pa ame e s is
desc ibed in he appendix.
2.3.5.1 P ope ies o he c own en i onmen o each lea cloud
T ee c own lea a ea abo e each lea cloud (CLA) e lec s he pa e n o lea a ea in di e en
heigh laye s (Fig. 21) om he iew poin o a lea cloud, hus, cumula ing he lea a ea abo e
i . Though big changes in lea a ea we e ound o 10cm heigh laye s, hese changes cause
16 18 20 22 24 26
heigh
H
m
L
-
4
-
3
-
2
-
1
0
1
d dme s
ê
d hgieh
Oak G 13
14 16 18 20 22 24
heigh
H
m
L
-
4
-
3
-
2
-
1
0
1
d dme s
ê
d hgieh
Beech G 12
14 16 18 20 22
heigh
H
m
L
-
4
-
3
-
2
-
1
0
1
d dme s
ê
d hgieh
Beech Bu38
Fig. 27:
De i a i es o he 5
h
o de polynom ha app oxima es he maximum ho izon al ex ensions o
1m-laye s o he h ee ees. While he de i a i e o he beech unc ions has wo maximums in hei
canopies’ heigh ange, only one maximum is o be ound in he heigh ange o oak G 13, which is a
consequence o he ou s anding posi ion o he 5 la ges laye s wi h nea ly cons an maximum s em
dis ance ela i e o he o he laye s.
0 0.2 0.4 0.6 0.8
ela i e heigh
H
-
L
50
100
150
200
250
300
350
ALC
H
²m
L
Oak G 13
0 0.2 0.4 0.6 0.8
ela i e heigh
H
-
L
50
100
150
200
250
300
350
ALC
H
²m
L
Beech G 12
0 0.2 0.4 0.6 0.8
ela i e heigh
H
-
L
50
100
150
200
250
300
350
ALC
H
²m
L
Beech Bu38
Fig. 28:
Cumula i e lea a ea o lea clouds in ela ion o ela i e heigh
H
. The cu ilinea
ela ionship was app oxima ed wi h one-pa ame ic unc ions o he o m:
CLA = T ee lea a ea – k *
H
². The coe icien k was 358.3, 302.6, and 358.4, espec i ely wi h ²-
alues 0.97, 0.98, and 0.96 o he ees Bu38, G 12, and G 13.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
64
The angle be ween main g ow h di ec ion o lea clouds and he idealised canopy su ace (α
αα
α
S
)
had a simila heigh dependence o bo h beech ees, while i was di e en om ha o oak
G 13 (Fig. 37).
The ange o achie able alues in his ela ionship is pa ly limi ed by he ee-speci ic canopy
shape unc ion ha was de i ed om measu ed da a o all ees using he same polynomial
unc ion. Fig. 38 shows ha he simila i y in he α
αα
α
S
s. heigh ela ionship o beech c owns was
no comple ely due o he simila canopy shape o bo h ees: The conside a ion o all α
αα
α
AZ
-
angles o beech Bu38 allows a much bigge ange o α
αα
α
S
- alues han was measu ed and his is
e en ue, when only he lowe a ia ion in α
αα
α
AZ
-angles om he bo om pa o he c own is
conside ed in he simula ion o α
αα
α
S
-angles o hei heigh ange.
The simila i y o main g ow h di ec ions o lea clouds om he wo beech ees may also be
obse ed wi hou ela ing hem o he idealised canopy shape: Fig. 39 shows he ec o ields o
he main g ow h di ec ions o lea clouds om bo h ees, i. e., he g aphs om Fig. 35 wo-
dimensionally scaled o a common heigh ange and supe imposed.
Lea clouds o bo h ees occupied nea ly he same space ela i e o apex and c own base,
which would no be he case when he ec o ield om oak G 13 would be supe imposed.
Thus, he simila c own shape wi h a den be ween 0.45 and 0.6 ela i e heigh is s ill isible.
Neighbou ing ec o s om bo h ees ollow o en he same di ec ion and he main pa e ns ha
ha e been desc ibed o beech Bu38 ec o s a e s ill alid. The al e na ion o heigh anges wi h
Fig. 39:
Main g ow h di ec ion o
lea clouds o beech G 12 (en i e,
da k, and longe a ows) and o
beech Bu38 (do ed, ligh ( ed),
and sho e a ows). The g aphs
om Fig. 35 we e wo-
dimensionally scaled o a common
heigh ange o bo h c owns.
0 0.1 0.2 0.3 0.4 0.5
s em dis ance
H
scaled
L
0
0.2
0.4
0.6
0.8
l
e
.
h
g
i
e
h
H
d
e
l
a
c
s
L
beech ees Bu38 and G 12
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
65
mo e upwa ds and mo e downwa ds inclined lea clouds in he lowe pa o he c own may s ill
be shown, when he absolu e heigh anges om beech Bu38 a e ecalcula ed o ela i e
heigh s (Fig. 40).
Assuming ha hese simila i ies e lec a species-speci ic end in ma u e beech c owns, he α
αα
α
S
s. heigh ela ionship o bo h ees was app oxima ed wi h a single cu e o bo h da a se s
(Fig. 41). The geome ical meaning o his cu e is ha lea clouds in he c own we e on
a e age anned-up owa ds he canopy su ace.
2.3.5.4 Azimu h angles
Though signi ican co ela ions we e no ound be ween he azimu h o ien a ion o he lea cloud
plane (
AZ
P
) and any o he ee inhe en quan i y, he compa ison be ween he neighbou ing
ees G 12 and G 13 e eals a signi ican simila i y in bo h dis ibu ions ( ²=0.41, p<0.01, Fig.
42). Thus, he
AZ
P
-dis ibu ion appea s no o be egula ly dis ibu ed, bu is possibly dependen
on en i onmen al ac o s ha a ec bo h ees.
A egula i y o
AZ
S
angles could only be ound in ela ion o he azimu h o he slope whe e he
ees we e s anding. While he la ges po ion o lea clouds o beech Bu38 was o ien ed
owa ds he Buchenallee slope azimu h, his was no ue o he G oßebene ees. No
signi ican co ela ions we e ound o he
AZ
S
equency dis ibu ions, which indica es i he ee
c own was de eloped symme ical in all di ec ions. The 30° angle classes o he
AZ
S
equency
dis ibu ions co espond o adial sec o s o he ee c own. While he beech ees had he
ela i ely mos lea clouds in he azimu h di ec ion o he slope o hei s and, oak G 13 had he
highes equency o lea clouds in ha angle class, ha was 30° close o sou h (Fig. 43).
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ela i e heigh
H
-
L
0
20
40
60
a
ZA
H
°
L
Beech ees Bu38 and G 12
Fig. 40:
A e age inclina ion o he main
g ow h di ec ion o lea clouds owa ds
he ho izon (
α
αα
α
AZ
) in laye s o beech ees.
Open iangles ep esen beech Bu38,
while he hombi s and o he
supe imposed ec o ield o bo h beech
ees (Fig. 39).
Fig. 41:
A unique ela ionship
has been d awn o he simila
ela ionships be ween
α
αα
α
S
and
ela i e heigh o bo h beech
ees (Bu38: illed iangles,
G 12: open squa es). The
app oxima ed ou h o de
polynomial unc ion was y =
1259.85 x
4
- 1778.46 x
3
+ 569.83
x
2
+ 96.89 x + 54.83.
0 0.2 0.4 0.6 0.8
ela i e heigh
H
-
L
25
50
75
100
125
150
175
a
s
H
°
L
Beech ees Bu38 and G 12
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
66
Uppe limi o
AZ
P
–class (°)
Uppe limi o
AZ
P
–class (°)
Uppe limi o
AZ
P
–class (°)
Fig. 42
:
F equency dis ibu ions o he
azimu h o ien a ion o lea cloud planes (
AZ
P
).
While he equency dis ibu ion o he beech
ees is comple ely di e en , he dis ibu ions
o he neighbou ing oak G 13 and beech G 12
appea o be simila ( ² = 0.41). The azimu h
o he slope o he s and is 157.5° o
Buchenallee and 225° o G oßebene.
30 60 90 120 150 180 210 240 270 300 330 360
0.025
0.05
0.075
0.1
0.125
0.15
p obabili y
BeechBu38
30 60 90 120 150 180 210 240 270 300 330 360
0.025
0.05
0.075
0.1
0.125
0.15
p obabili y
BeechG 12
30 60 90 120 150 180 210 240 270 300 330 360
0.025
0.05
0.075
0.1
0.125
0.15
p obabili y
OakG 13
Uppe limi o
AZ
S
-class (°)
Uppe limi o
AZ
S
-class (°) Uppe limi o
AZ
S
-class (°)
Fig. 43:
F equency dis ibu ions o
AZ
S
, he
lea cloud cen es’ azimu h o ien a ions
ela i e o he s em (0° = no h). The azimu h
o he slope o he s and is 157.5° o
Buchenallee and 225° o G oßebene. While
he beech ees had he ela i ely mos lea
clouds in he azimu h di ec ion o he slope o
hei s and, oak G 13 had he highes
equency o lea clouds in ha angle class,
ha is 30° close o sou h. No signi ican
co ela ions we e ound be ween he
AZ
S
equency dis ibu ion and ha o
AZ
P
.
30 60 90 120 150 180 210 240 270 300 330 360
0.05
0.1
0.15
0.2
p obabili y
BeechG 12
30 60 90 120 150 180 210 240 270 300 330 360
0.05
0.1
0.15
0.2
p obabili y
BeechBu38
30 60 90 120 150 180 210 240 270 300 330 360
0.05
0.1
0.15
0.2
p obabili y
OakG 13
el. equency el. equency
el. equency
el. equency
el. equency
el. equency
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
67
A compa ison o he a e age lea cloud azimu h angles (
AZ
P
) in 30°
AZ
S
-sec o s is shown in
Fig. 44. While he mean lea cloud azimu h (
AZ
P
) in mos sec o s o beech Bu38 was be ween
sou h-eas and sou h-wes (135°-225°), he lea clo uds in di ec ion o he slopes azimu h
(157.5°) a e o ien ed owa ds no h. The p e ailing a e age lea cloud azimu h o beech G 12
sec o s was be ween eas -sou h-eas and no h-no h-eas (247.5°-337.5°). No unique ange o
AZ
P
-angles was p e e ed in he sec o a e ages o oak G 13. These esul s a e only examples
o he azimu h o ien a ions o g ow h in hese ees, ha we e e alua ed in o de o assu e a
comple e ep esen a ion o he da a se . Fu he s udies on o he ees would be necessa y o
in es iga e i he ound endencies ha e a gene al meaning.
2.3.5.5 Spa ial ex ension o lea clouds
The quan i ies which desc ibe he spa ial ex ension o lea clouds a e pa ially dependen on
each o he , because p ojec ed a ea and heigh ange may be used o calcula e a olume
a ound he lea cloud plane wi h wo ho izon al bo de s abo e and below and e ical bo de s
along he lea cloud shape owa ds he side. The ela ionship be ween p ojec ed a ea imes
heigh ange (
a ea
*
H ange
) and calcula ed olume (
olume
) o he lea cloud en eloping
polyhed on is shown in Fig. 45. I was be e co ela ed o oak G 13 ( ²=0.9) han o beech
Bu38 ( ²=0.67) and beech G 12 ( ²=0.74). The slope o he linea equa ions was e y simila o
all ees (0.30, 0.30, and 0.33 o he ees Bu38, G 12, and G 13, espec i ely).
Fig. 44:
A e age azimu h o he lea cloud
planes in 30° sec o s o each ee c own.
While he mean lea cloud azimu h (
AZ
P
) in
mos sec o s o beech Bu38 was be ween
sou h-eas and sou h-wes (135°-225°), he
lea -
clouds in di ec ion o he slopes azimu h
(157.5°) a e o ien ed owa ds no h. The
p e ailing a e age lea cloud azimu h o
beech G 12 sec o s was be ween eas -
sou h-eas and no h-no h-eas (247.5°-
337.5°). No unique ange o
AZ
P
–angles
was p e e ed in he sec o s o oak G 13.
30 60 90 120 150 180 210 240 270 300 330 360
50
100
150
200
250
300
350
AZ
P
BeechBu38
30 60 90 120 150 180 210 240 270 300 330 360
50
100
150
200
250
300
350
AZ
P
BeechG 12
30 60 90 120 150 180 210 240 270 300 330 360
50
100
150
200
250
300
350
AZ
P
OakG 13
Uppe limi o
AZ
S
-class (°) Uppe limi o
AZ
S
-class (°)
Uppe limi o
AZ
S
-class (°)
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
68
0 0.5 1 1.5 2 2.5 3
a ea
*
h ange
H
m³
L
0
0.2
0.4
0.6
0.8
1
1.2
1.4
emulo
H
³m
L
Beech Bu38
0 1 2 3 4 5 6 7
a ea
*
h ange
H
m³
L
0
0.5
1
1.5
2
emulo
H
³m
L
Oak G 13
0 2 4 6 8 10
a ea
*
h ange
H
m³
L
0
1
2
3
4
emulo
H
³m
L
Beech G 12
Fig. 45:
The ela ionship be ween p ojec ed a ea imes heigh ange (
a ea
*
H ange
) and
calcula ed olume ( olume) o he lea cloud en eloping polyhed on was be e co ela ed o
oak G 13 ( ²=0.9) han o beech Bu38 ( ²=0.67) and beech G 12 ( ²=0.74). The slope o he
linea equa ions was 0.30, 0.30, and 0.33 o he ees Bu38, G 12, and G 13, espec i ely.
a ea * H ange (m³ ) a ea * H ange (m³ )
a ea * H ange (m³ )
0 0.2 0.4 0.6 0.8
ela i e heigh
H
-
L
0
0.5
1
1.5
2
2.5
3
hgieh egna
H
m
L
Beech Bu38
0.2 0.4 0.6 0.8
ela i e heigh
H
-
L
0.5
1
1.5
2
2.5
3
3.5
4
hgieh egna
H
m
L
Beech G 12
0.2 0.4 0.6 0.8
ela i e heigh
H
-
L
0.5
1
1.5
2
2.5
hgieh egna
H
m
L
Oak G 13
Fig. 46:
The heigh ex ension o he lea clouds (
H ange
) showed a signi ican (p<0.001) endency o
inc ease wi h ela i e heigh in he canopy. R²- alues we e highe o he beech ees (0.38 and 0.28,
espec i ely) han o oak G 13 (0.14).
30 60 90 120 150 180 210 240 270 300 330 360
2.5
5
7.5
10
12.5
15
p ojec ed
a ea
H
m²
L
OakG 13
30 60 90 120 150 180 210 240 270 300 330 360
5
10
15
20
25
p ojec ed
a ea
H
m²
L
BeechBu38
30 60 90 120 150 180 210 240 270 300 330 360
5
10
15
20
p ojec ed
a ea
H
m²
L
BeechG 12
Uppe limi o AZ
S
-class (°)
Uppe limi o AZ
S
-class (°) Uppe limi o AZ
S
-class (°)
p ojec ed a ea ( m² )
p ojec ed a ea ( m² ) p ojec ed a ea ( m² )
Fig. 47:
P ojec ed a ea o lea clouds (
a ea
)
summed o wel e di e en AZ
S
-angle
classes ( adial sec o s o he ee c own).
The dis ibu ion pa e n is simila o Fig. 43
and shows ha he beeches had he highes
amoun o lea cloud p ojec ed a ea in
di ec ion o he slope o hei s and (157.5°
and 225°) and ha hey p e e ed a unique
ange o angles o s eng hened
de elopmen , while a ea o oak G 13 lea
clouds was highes in ha angle class ha is
30° close o sou h han he slope o he
G oßebene s and (225°).
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
69
a ea
,
olume
, and
H ange
we e only weakly co ela ed o heigh o posi ion o he lea cloud.
The s onges ela ionship was ound be ween
H ange
and
H
(Fig. 46) wi h coe icien s o
de e mina ion below 0.4. R²- alues we e only in some cases highe han hose o Fig. 46, when
he ela ions a e based on he c own en i onmen al p ope ies
CLA
,
CVOL
, o
CLAD
. Fo
example he ela ionship be ween
H ange
and
CVOL
had an ² o 0.45 o beech Bu38 and he
ela ionship be ween
H ange
and
CLAD
sligh ly imp o ed he ²- alue o oak G 13 o 0.16.
Only mino changes o he pa e ns o equency dis ibu ions o
AZ
S
in Fig.43 we e de ec ed,
when olume (da a no shown) o p ojec ed a ea (
a ea
) o he lea clouds in each 30° angle
class o
AZ
S
a e conside ed. The posi ion o he lea cloud cen e ela i e o he s em was
decisi e o he classi ica ion o lea clouds. Figu e 47 shows ha he beeches had he la ges
amoun o lea cloud p ojec ed a ea in he di ec ion o he slope o hei s and (157.5° and 225°)
and ha hey p e e ed a unique ange o angles o s eng hened de elopmen , while
a ea
o
oak G 13 lea clouds was highes in ha angle class ha is 30° close o sou h han he slope o
he G oßebene s and (225°). In addi ion o his, oak G 13 shows s eng hened de elopmen in
h ee di e en
AZ
S
-angle anges (90-120°, 180-210°, and 300-390°) wh en compa ed o he
sec o s be ween hese anges.
2.3.5.6 Lea a ea densi ies o lea clouds
Lea a ea densi ies o lea clouds could be key pa ame e s o a lea cloud o ien ed 3D-ligh -
model o single ees and i was he e o e necessa y o in es iga e in some de ail i hey a e
andomly dis ibu ed in he canopy space o i hey depend on any o he quan i y, which would
acili a e he pa ame e isa ion o a lea cloud o ien ed ligh model.
Measu ed lea a ea densi ies we e pa ly in luenced by he measu emen me hod. Lea es o
e y small lea clouds we e o en a anged along one b anch axis o in one plane, so ha gaps
be ween wo b anches o be ween di e en lea -laye s did no occu . This inc eased hei
calcula ed lea a ea densi y. Addi ionally, e y small lea clouds o en had a mo e egula o m
ha i s mo e accu a ely in o a plane bo de ed polyhed on han hose o la ge lea clouds. Bo h
0.5 1 1.5 2 2.5 3 3.5 Volume
H
m³
L
10
20
30
40
50
60
Lea A ea Densi y
H
m²
ê
m³
L
BeechG 12
BeechBu38
Oak G 13
Fig. 48:
Lea a ea densi ies o all
ha es ed lea clouds. Di e en
esolu ions in he 3D-desc ip ion o
ee c owns esul om he de ined
minimum diame e o a lea cloud
suppo ing b anch, which was 2cm
in he Buchenallee s and and 3cm
in he G oßebene s and.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
70
e ec s led o some ex emely high lea a ea densi ies in e y small lea clouds o beech Bu38,
as can be seen in Fig. 48. The e o e, geode ic measu emen s on he G oßebene ees we e
pe o med wi hou conside ing e y small lea clouds as sepa a e uni s (see me hods). Then no
simila e ec s we e obse ed (compa e Fig. 48). Lea a ea densi ies we e in he ange o 1.63-
67.7 m²/m³ in beech Bu38 (139 lea clouds), 1.31-10.2 m²/m³ in beech G 12 (66 lea clouds) and
0.26-13.5m²/m³ in oak G 13 (88 lea clouds).
No clea ela ionship o lea a ea densi y could be demons a ed by eg ession analysis on each
o he in es iga ed lea cloud p ope ies (see abo e) o each ee. Howe e , when lea a ea
densi ies o lea clouds we e a e aged pe heigh laye , all ees showed a mo e o less clea
endency o inc ease lea a ea densi ies o lea clouds wi h heigh . (Fig. 49).
The a e age lea a ea densi ies o lea clouds in dis inc adial sec o s o he ees a e shown in
Fig. 50. A weak simila i y in he angula dis ibu ions o
LAD
has been ound be ween he
beeches in he di e en s ands ( ² = 0.22) and i u ned ou ha his was due o a ema kable
simila i y o he angula dis ibu ion in he no h hal o he c owns ( ² = 0.80, p<0.05), which was
also ound, when he angle classes we e la ge (45°: ²=0.93, p<0.05) o smalle (15°: ²=0.56,
p<0.01). Though no simila i y was ound o he oaks angula dis ibu ion o
LAD
, his migh be
chance and can no be in e p e ed as species-speci ic. Apa om his simila i y,
LAD
was
i egula ly dis ibu ed o e
AZ
S
-angle classes. A compa ison o he angula
LAD
-dis ibu ion o
he neighbou ing ees oakG 13 and beech G 12 (Fig. 51) shows ha neighbou hood e ec s
could ha e an in luence on
LAD
o oak lea clouds: The sec o s wi h high a e age
LAD
o lea
13.1 14.1 15.1 16.1 17.1 18.1 19.1 20.1 21.1 22.1
2.5
5
7.5
10
12.5
15
LAD
H
m²
ê
m³
L
BeechBu38
14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
1
2
3
4
5
LAD
H
m²
ê
m³
L
BeechG 12
16.7 17.7 18.7 19.7 20.7 21.7 22.7 23.7 24.7 25.7
2
4
6
8
10
12
LAD
H
m²
ê
m³
L
Oak G 13
A e age heigh o laye (m)
A e age heigh o laye (m) A e age heigh o laye (m)
Fig. 49:
A e age lea a ea densi y o lea
clouds in 1m-heigh laye s. The
classi ica ion is based on he posi ions o
he lea cloud cen es.
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
71
4.84m
7.82m
4.12m
30 60 90 120 150 180 210 240 270 300 330 360
5
10
15
20
LAD
H
m²
ê
m³
L
BeechBu38
30 60 90 120 150 180 210 240 270 300 330 360
1
2
3
4
5
6
LAD
H
m²
ê
m³
L
BeechG 12
30 60 90 120 150 180 210 240 270 300 330 360
2
4
6
8
10
12
LAD
H
m²
ê
m³
L
OakG 13
Fig. 50:
A e age lea a ea densi ies (
LAD
)
o lea clouds in adial sec o s o he ee
c own gi en by he azimu h o he lea
cloud cen e ela i e o he s em (AZ
S
).
Uppe limi o azimu h class
(°) Uppe limi o azimu h class (°)
Uppe limi o azimu h class (°)
300
330
36030
60
90
120
150 180 210 240
270
300
330
36030
60
90
120
150 180 210 240
270
Fig. 51:
A e age lea a ea densi ies
o lea clouds in adial sec o s o he
canopies o beech G 12 and oak
G 13. The c owns a e si ua ed in
hei s ems’ ela i e angula posi ion
o each o he . Angles and dis ances
owa ds he nea es neighbou ing
ees a e indica ed.
No h
A e age lea a ea densi y o lea clouds
(m²/m³)
126 10842
5.63m
7.62m
5.70m
3.40m
G 12
G 13
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
72
clouds we e mo e o less clea ly di ec ed owa ds he h ee closes ee s em posi ions o
neighbou ing ees. Beech G 12 did no show his coincidence.
Da a o he h ee ees we e sepa a ely used o a mul iple eg ession analysis o
LAD
on 8
quan i ies (
H, N, E,
α
αα
α
h
,
absolu e alue o
α
αα
α
h
, AZ
p,
AZ
s
, A ea
). The quan i ies we e chosen
because o hei expec ed po en ial o explain lea a ea densi y dis ibu ion inside ee c owns:
• Lea a ea densi ies a e likely o inc ease wi h heigh (
H
), because lea es canno su i e
wi hou ligh and he lowe pa s o he c own ge less ligh han he uppe pa s.
Ne e heless i is ques ionable i his e ec may be ound in lea a ea densi ies o lea
clouds, because he absolu e amoun o lea es in a heigh laye depends on lea a ea
densi y o lea clouds and as well on lea cloud densi y in he heigh laye . Though numbe
and lea a ea densi y o lea clouds we e low in he lowes laye s o c owns o oak and
beeches (Fig. 19b), no ob ious end in lea a ea densi ies o lea clouds was ound in
ela ion o heigh (da a no shown).
• A dependence o lea a ea densi y on dis ances o he s em in eas and no h di ec ion, lea
cloud inclina ion a he poin o a achmen , o azimu h o ien a ion ela i e o he s em (
E,
N,
α
α α
α
b
, AZ
p,
AZ
s
) could e lec a species-speci ic in e nal o ganisa ion scheme o he ee
c own. Fo example, i he lea less space in he cen al pa o he c own de elops ia pa ial
hinning o lea es o lea clouds o e ime, his should ha e a ema kable e ec on he
ela ionship be ween dis ances (
E,N
) and lea a ea densi y, o i lea clouds on he sou h
side o he canopy would ha e gene ally highe lea a ea densi ies when hey we e o ien ed
o he eas , his would a ec he ela ionship be ween
LAD
and he azimu h angles.
• Angle and p ojec ed a ea o he lea cloud plane (α
αα
α
p
, A ea
) may be co ela ed wi h lea a ea
densi y because hey ha e a majo in luence on ligh ha es ing o he lea cloud and, hus,
may be in luen ial i lea a ea densi ies pa ly depend on he ligh si ua ion.
Because eg ession analysis assumes no mal dis ibu ion o he dependen a iable (E
NGEL
1997), he p obabili y densi y unc ions o lea a ea densi y da a was analysed. A i s
loga i hmic ans o ma ion showed much be e ag eemen wi h he no mal dis ibu ion han he
o iginal dis ibu ion ( o example beech Bu38, see Fig. 52).
Fig. 52: Compa ison o he dis ibu ion o lea a ea densi ies o lea clouds o beech Bu38 (le side) wi h
he no mal dis ibu ion. The same da a a e loga i hmic ans o ma ion a e in be e ag eemen wi h he
no mal dis ibu ion. The o iginal da a we e s anda dised by shi ing hei mean alue o ze o and scaling
hei a iance o uni y.
This was con i med by an ²- alue o 0.97 o he ela ionship be ween p obabili y densi ies o
Log(
LAD
) and he co esponding alues o he no mal dis ibu ion. The o iginal da a we e
-
2 0 2 4 6 8
S anda dised LAD
0
0.2
0.4
0.6
0.8
y ilibabo p y isned
-
3
-
2
-
1 0 1 2 3 4
S anda dised Ln
H
LAD
L
0
0.1
0.2
0.3
0.4
0.5
y ilibabo p y isned
beech Bu38 beech Bu38
T ee c own s uc u es o ma u e Fagus syl a ica and Que cus pe aea ees
73
s anda dised o compa ison wi h he no mal dis ibu ion by shi ing hei mean alue o ze o and
scaling hei a iance o uni y. A sca e plo o bo h quan i ies (no mal p obabili y plo , see Fig.
53) e eals a cu ilinea ela ionship behind his ²- alue, indica ing ha he log-no mal
dis ibu ion is le skewed in he case o beech Bu38 (compa e Fig. 52).
Fig. 53: No mal p obabili y plo s o loga i hmic ans o med LAD da a o beech Bu38 agains
co esponding quan iles o he no mal dis ibu ion and he cubic oo loga i hmic ans o ma ion o LAD
agains co esponding quan iles o he no mal dis ibu ion. The cubic oo ans o ma ion made he
ela ionship mo e linea and imp o ed he eg ession om ²=0.97 o ²=0.993.
Thus, a second ans o ma ion aking he cubic oo o Log(
LAD
) was employed o make he
ela ionship mo e linea , esul ing in an ²- alue o 0.993 o he no mal dis ibu ion. The cubic
oo ans o ma ion was ound by he maximum-likelihood me hod acco ding o (B
OX
&
C
OX
1964), whe e he condi ional maximised log likelihood o a gi en powe ans o ma ion wi h
espec o he no mal dis ibu ion is calcula ed and i e a i ely e alua ed o a ange o exponen
alues. The same p ocedu e o he G oßebene ees led o he ans o ma ion Log
3/2
(
LAD
)
o bo h ees ( ²=0.986 o beech G 12 and ²=0.996 o oak G 13). Because he na u al
loga i hm o he lowes LAD- alue o beech G 12 was nega i e (-0.48), a cons an o 0.5 had o
be added o enable he Box-Cox ans o ma ion, which equi es posi i e alues.
Fig. 54: No mal p obabili y plo s o ans o med LAD da a o beech G 12 (le ) and oak G 13 ( igh )
agains co esponding quan iles o he no mal dis ibu ion.
Mul iple eg essions we e based on a linea combina ion o all quan i ies o he o m
whe e y
i
is he i
h
esponse,
pi
is he p
h
quan i y e alua ed a he i
h
case, and e
i
is he e o o
he i
h
case.
Es ima es o he coe icien s
β
ββ
β
i
a e calcula ed o minimise he esidual sum o
squa es.
y
i
= b
1
1
i
+ b
2
2
i
+
…
+ b
p
p
i
+
e
i
,
(8)
1 2 3 4 5 LogHLADL
-
3
-
2
-
1
1
2
3
co esponding quan ile
0.8 1.2 1.4 1.6
è!!!!!!!!!!!!!!!!!!!!
Log
H
LAD
L
3
-
3
-
2
-
1
1
2
3
co esponding quan ile
Log(LAD)
beech Bu38
beech Bu38
1 2 3 4 5 6 Log
3
ÅÅÅÅÅÅ
2
H
LAD
L
-
3
-
2
-
1
1
2
3
co esponding quan ile
1 2 3 4
H
Log
H
LAD
L
+
0.5
L
3
ÅÅÅÅÅÅ
2
-
3
-
2
-
1
1
2
3
co esponding quan ile
co esponding quan ile
beech G 12 oak G 13
Spa ial dis ibu ion o lea p ope ies in ee c owns
80
The esul s allowed he calcula ion o empe a u e no malised alues o ca boxyla ion capaci y
(
Vc
max
), elec on anspo capaci y (
J
max
) and day espi a ion (
R
d
) wi h he p og am RACCIA
(see below).
Addi ional es ima ions o
J
max
, he elec on anspo capaci y we e achie ed by chlo ophyll
luo escence measu emen s. They we e pe o med using he po able pulse-modula ion
luo ome e PAM-2000 (Heinz Walz GmbH, E el ich, Ge many), equipped wi h lea clip holde
2030-B, on some o he oak lea es be o e he gas-exchange measu emen on he same lea es.
These lea es we e da kened o a leas 30 minu es wi h aluminium oil o enable one
measu emen o minimum and maximum luo escence,
F
0
and
F
m
, wi h a sa u a ing ligh pulse
on da k adap ed lea es (S
CHREIBER ET AL
.
1994). Fluo escence o he illumina ed lea es (
F
m
’
)
was a e wa ds de e mined wi h sa u a ing ligh pulses o inc easing ligh in ensi ies up o 2500
µmol/(m²*s) o e en mo e, when he esul ing ligh esponse cu e o he elec on anspo a e
did no ye appea o sa u a e. A leas h ee epe i ions pe ligh le el we e done. Quan um yield
o he illumina ed lea es (
Y
) was calcula ed as
(S
CHREIBER ET AL
.
1994). The elec on anspo a e
J
was calcula ed acco ding o G
ENTY ET
AL
. (1989):
whe e
I
is inciden quan um lux densi y and he ac o 0.84 accoun s o abso p ance o lea es.
Elec on anspo capaci y
J
max
was ound as elec on anspo a e
J
a a quan um lux densi y
o 2000 µmol/(m²*s), which was de e mined by ex apola ion o he measu ed elec on anspo
a es a o he quan um lux densi ies on he base o equa ion (29), which was i ed o he
maximum measu ed alues pe ligh le el.
3.1.4 E alua ion o A/C
i
-cu es wi h RACCIA
The measu emen o
A/C
i
-cu es has been desc ibed as a cumbe some p ocedu e in he pas
(L
AISK
&
L
ORETO
1996), which is p obably due o he necessi y o long s abilisa ion imes o he
condi ions in he chambe a e changing he
C
a
- alue and o he use o la ge CO
2
-s o age and
mixing sys ems, ha made i necessa y o wo k in he labo a o y. This si ua ion has changed o
some ex en due o he de elopmen o small po able pho osyn hesis measu emen sys ems
wi h small CO
2
-mixing uni s, small cu e es, sho dis ances o gas-supply and IRGA-
measu emen s, and au oma ic immedia e calcula ions on he measu ed da a, which acili a e
he assessmen o s abili y o cu e e condi ions. The e o e much mo e da a can be measu ed
in he same ime and ha e o be e alua ed. The p og am RACCIA (
R
ou ine o
A/C
i
c
u e
e
a
lua ion) was de eloped o au oma e he ime-consuming de i a ion o species-speci ic key
pa ame e s o lea pho osyn hesis om hese measu emen s, as hey a e used in di e en
a ia ions o he Fa quha model o lea pho osyn hesis (F
ARQUHAR
&
VON
C
AEMMERER
1982).
Because his is ypically done by non-linea i s on a low numbe o da a poin s along he
A/C
i
cu e (H
ARLEY
&
T
ENHUNEN
1991), a plausibili y check is enabled by au oma ic g aphical
ep esen a ion o he da a and each i on he sc een du ing he au oma ic e alua ion p ocess.
RACCIA is based on he equa ions o he H
ARLEY
/T
ENHUNEN
pho osyn hesis model (H
ARLEY
&
T
ENHUNEN
1991), which links a modi ica ion o he biochemical Fa quha model (F
ARQUHAR
&
Y
=
I
F
m
-
F
m
'
M
ë
F
m
'
(20)
, (21)
J
=
0.5
*
0.84
*
Y
*
I
Spa ial dis ibu ion o lea p ope ies in ee c owns
81
VON
C
AEMMERER
1982) wi h he Ball/Be y model o s oma al conduc ance (B
ALL ET AL
.
1987),
and on he calcula ion o day espi a ion and CO
2
-compensa ion poin acco ding o B
ROOKS
and
F
ARQUHAR
(1985).
3.1.4.1 The H
ARLEY
/T
ENHUNEN
model o lea pho osyn hesis
The H
ARLEY
/T
ENHUNEN
model basically exp esses ne assimila ion a e (
A
) as he sum o
ca boxyla ion a e (
Vc
), oxygena ion a e (
Vo
), and day espi a ion (
R
d
), i. e., he a e o CO
2
-
e olu ion om p ocesses o he han pho o espi a ion ha con inues in he ligh :
(all quan i ies in µmol/(m²*s)). Pho o espi a ion losses a e exp essed dependen on
C
i
and he
pho ocompensa ion poin Γ
ΓΓ
Γ
*
(µmol/mol), ha
C
i
- alue, a which
A
would be 0, i no o he sou ce
o espi a ion han oxygena ion o ibulose-1,5-bisphospha e ca alysed by ubisco would occu .
I is assumed ha
Vc
is limi ed by he eloci y o h ee p ocesses, so ha equa ion (22) is
ans o med o he common o m o balance equa ion o mos pho osyn hesis models:
W
c
deno es he ca boxyla ion a e limi ed by ubisco ac i i y and
W
j
is he ca boxyla ion a e
limi ed by egene a ion o RuBP in he Cal in-cycle, which is ligh dependen . The phospha e
limi ed ca boxyla ion a e
W
P
is no included in mos pho osyn hesis models and was no
conside ed in he pa ame e de i a ion wi h RACCIA no in lea gas exchange calcula ions wi h
he H
ARLEY
/T
ENHUNEN
model.
The emaining wo exp essions o
W
c
-limi ed assimila ion a e (
A
) and
W
j
-limi ed assimila ion
a e (
A
j
) a e basically he same as in (F
ARQUHAR
&
VON
C
AEMMERER
1982):
He e
Vc
max
s ands o he enzyme-speci ic maximum a e o ca boxyla ion,
K
M,C
(µmol/mol) and
K
M,O
(mmol/mol) s and o he Michaelis-Men en cons an s o ubisco ( ibulose-1,5-bisphospha e
ca boxylase-oxygenase) o ca boxyla ion and oxygena ion o ibulose-1,5-bisphospha e, and
O
(209 mmol/mol ai a 101.3 kPa a mosphe ic p essu e) is he lea in e nal O
2
-concen a ion.
W
j
is gi en as
wi h
P
m
(µmol/(m²*s)), he CO
2
sa u a ed a e o pho osyn hesis a any gi en i adiance and
empe a u e.
On he assump ion ha 4 elec ons a e equi ed o he egene a ion o a single
RuBP in he Cal in cycle,
A
j
is exp essed as
A
V
=
Vc
max
C
i
-
G
*
K
M,C
H
1
+
O
ê
K
M,O
L
+
C
i
-
R
d
(24)
A=Vc-0.5 Vo-R
d
(22)
A=
i
k
1-
G
*
C
i
y
{
min
8
W
c
,W
j
,W
p
<
-R
d
(23)
W
j
=
P
m
1
+
2
G
*
ê
C
i
,
(25)
A
J
=
J
C
i
-
G
*
4
C
i
+
8
G
*
-
R
d
, (26)
Spa ial dis ibu ion o lea p ope ies in ee c owns
82
whe e
J
(µmol e
-
/(m²*s)) is he elec on anspo a e o e he hylakoid memb ane and equals
4
P
m
. Γ
ΓΓ
Γ
*
in he abo e equa ions is de ined as
wi h he dimensionless ubisco speci ici y ac o
τ
ττ
τ
. Tempe a u e dependence o his pa ame e
and also o
K
M,C
,
K
M,O
,
and
R
d
is exp essed in exponen ial equa ions, which we e con e ed in
he used e sion o he lea model o be based on he pa ame e alues a a empe a u e o
298.16K:
pa ame e
298
s ands o he empe a u e dependen pa ame e a a empe a u e (
T
) o 298.16K,
R
is he gas cons an , and
H
a
(J/mol) is he ac i a ion ene gy o he pa ame e .
P
m
and he eby
J
is he only ligh dependen quan i y:
(Smi h-equa ion). He e
I
(µmol/(m²*s)) is inciden quan um lux densi y,
P
ml
is
P
m
a ligh
sa u a ion, and
α
α α
α
(mol/mol) s ands o he ini ial slope o he cu e ela ing CO
2
-sa u a ed
pho osyn hesis o i adiance.
P
m
and
P
ml
in his equa ion may be eplaced by
J
and
J
max
(maximum elec on anspo a e), when
α
αα
α
is mul iplied by ou .
The empe a u e dependence o
P
ml
and
Vc
max
is desc ibed in a 4-pa ame ic he modynamic
equa ion (J
OHNSON ET AL
.
1942, S
HARPE
&
D
E
M
ICHELE
1977), which may be exp essed based
on he pa ame e alue a a empe a u e o 298.16K:
He e,
Vc
max, 298
s ands o he pa ame e alue a
T
= 298.16 K,
H
a
and
H
d
(J/mol) a e he
ene gies o ac i a ion and deac i a ion o
Vc
max
, and
S
(J/(K*mol)) s ands o a
Vc
max
-speci ic
en opy e m. The same equa ion wi h
P
ml
- o
J
max
-speci ic ene gies and en opy e m is applied
o
P
ml
o
J
max
.
A
in he abo e equa ion sys em is dependen on
C
i
, which is in u n dependen on
A
and
s oma al conduc ance
g
sw
:
C
a
(µmol/mol) s ands o he ex e nal CO
2
-concen a ion and 1.6 accoun s o he di e en
di usi i ies o wa e apou and CO
2
in ai . Addi ionally,
g
sw
is linea ly dependen on
A
and
C
a
as was i s desc ibed by B
ALL ET AL
.
(1987):
pa ame e
=
pa ame e 298
*
Exp
B
H
a
*
H
T
-
298.16
L
298.16
R
T
F
(28)
G
*
=
0.5
O
, (27)
P
m
=
a
I
$
1
+
a
2
I2
Pml2
(29)
Vc
max
=
Vc
max, 298
Exp
B
H
a
H
T
-
298.16
L
298.16RT
F
1
+
Exp
B
298.16
S
-
H
d
298.16R
F
1
+
Exp
B
ST
-
Hd
R
T
F
(30)
(31)
C
i
=
C
a
-
1.6A
ê
g
sw
(32)
g
sw
=
g
min
+
g
ac
A
h
s
C
s
Spa ial dis ibu ion o lea p ope ies in ee c owns
83
He e
g
min
(mol/(m²*s)) is he cons an cu icula conduc ance o wa e apou ,
h
s
(-) and
C
s
(µmol/(m²*s)) a e ela i e humidi y and CO
2
-concen a ion on he lea su ace and
g
ac
is an
empi ically ound ac o ha is de i ed om (B
ALL ET AL
.
1987). To calcula e
h
s
and
C
s
om
h
(ex e nal ela i e humidi y) and
C
a
, he bounda y laye conduc ance o wa e apou (
g
aw
,
mol/(m²*s)) is aken in o accoun (F
ALGE
1997):
The used e sion o he model sol es i e a i ely o
C
i
, he eby inding ha
C
i
- alue ha is
compa ible wi h ne assimila ion a e
A
(equa ion (23)) and s oma al conduc ance
g
sw
(equa ions (32), (33), and (34) combined), and whe e
A
and
g
sw
a e ela ed acco ding o
equa ion (31).
3.1.4.2 RACCIA ou ine o species-speci ic pa ame e isa ion
The species-speci ic pa ame e isa ion o he H
ARLEY
/T
ENHUNEN
model and o he Fa quha
models wi h RACCIA is ocused on he de e mina ion o h ee key pa ame e s ha a e no
ubisco-speci ic. Due o he - among highe plan s - simila s uc u e o he ubisco molecule and
i s highly conse ed ac i e si es (K
ELLOGG
&
J
ULIANO
1997), species-speci ic a ia ions in
ubisco kine ic pa ame e s (
K
M,C
,
K
M,O
,
τ
ττ
τ
, Γ
ΓΓ
Γ
*
) a e expec ed o be ela i ely small (B
ERNACCHI ET
AL
.
2001). In i o measu ed alues o
τ
ττ
τ
and Γ
ΓΓ
Γ
*
o many di e en species gene ally a y abou
±20% a ound a mean alue o 2560 (dimensionless) and 42 µmol/mol a 25°C o all species
(E
PRON ET AL
.
1995),
and a he big (±10%) in a-speci ic a ia ions we e ound unde he same
measu emen condi ions (P
ARRY ET AL
.
1987). Howe e , also single ou lying measu emen s
(-50% o τ
ττ
τ and +100% o Γ
ΓΓ
Γ
*
) exis o Fagus syl a ica and Cas anea sa i a (E
PRON ET AL
.
1995). The in i o de i a ion o
τ
ττ
τ
and Γ
ΓΓ
Γ
*
om Nico iana abacum and Spinacia ole acea (
VON
C
AEMMERER ET AL
. 1994) yielded
τ
ττ
τ
- alues o 2710 and 2975, which equals Γ
ΓΓ
Γ*- alues o 38.8
and 35.3 µmol/mol a 25°C, when oxygen concen a ion
O
is assumed o equal 210000
µmol/mol (equa ion 29). These measu emen s a e he only ones, whe e ca boxyla ion
dependen limi a ion o he assimila ion a e is assu ed by he use o ansgenic plan s wi h low
ubisco con en .
The e m
K
M,C
(1+210 /
K
M,O
) om he calcula ion o
A
V
(equa ion (24)) a ies o he low numbe
o measu ed species be ween 410 and 750, (M
AKINO ET AL
.
1988,
H
ARLEY
&
T
ENHUNEN
1991,
VON
C
AEMMERER ET AL
.
1994,
B
ERNACCHI ET AL
.
2001), hough
K
M,C
and
K
M,O
a e no expec ed o
a y among highe plan s (
VON
C
AEMMERER ET AL
. 1994). I has been a gued ha his a ia ion
migh be due o he in i o measu emen me hod. The wo newe measu emen s use
ansgenic Nico iana abacum plan s ha shall assu e he ubisco limi a ion o assimila ion o in
i o measu emen s and end up wi h 710 and 746 o he e m men ioned abo e (
VON
C
AEMMERER ET AL
. 1994, B
ERNACCHI ET AL
. 2001).
Rubisco-speci ic pa ame e s and hei empe a u e dependencies may, hus, be conside ed as
cons an among highe plan s, meaning ha species-speci ic a ia ions in assimila ion a es ha
a e no due o s oma al limi a ions p e ailingly esul om he quan i ies
P
ml
,
Vc
max
,
R
d
, and
α
αα
α
.
(33)
h
s
=
h
-
h
-
1
1
+
gaw
gsw
(34)
C
s
=
C
a
-
1.37
H
C
a
-
C
i
L
1.37
+
1.6
gaw
g
sw
Spa ial dis ibu ion o lea p ope ies in ee c owns
84
RACCIA and he appe aining pho osyn hesis measu emen s we e designa ed o es ima e he
quan i ies
P
ml
,
Vc
max
, and
R
d
ha a e c ucial o he calcula ion o lea gas-exchange, because
α
αα
α
is he mos conse a i e pa ame e ou o he ou and may app oxima ely be es ima ed o equal
0.06 mol CO
2
/mol pho ons among C
3
species unde mos condi ions (H
ARLEY
&
T
ENHUNEN
1991, E
HLERINGER
&
B
JÖRKMAN
1977).
While equa ions (24) and (26) a e a common pa o mos so-called Fa quha models, di e en
ypes o equa ions a e employed o desc ibe ligh dependence o elec on anspo a e
J
,
empe a u e dependencies, and e ec s o s oma al egula ion, i conside ed. The o iginal
Fa quha model (F
ARQUHAR
&
VON
C
AEMMERER
1982) o example employs a hype bolic
ela ionship ins ead o equa ion (29) o exp ess he sa u a ing ela ionship o elec on anspo
a e
J
on i adiance
I
:
The ac o 2.1 in his equa ion has o be changed unde ce ain condi ions.
J
max
s ands he e o
he elec on anspo capaci y, he maximum elec on anspo a e unde sa u a ing ligh
condi ions, and i is by de ini ion o
J
and
P
m
equal o 4
P
ml
. RACCIA can be used o de i e bo h
quan i ies, when
A/C
i
-measu emen s a e made a ligh sa u a ion, because i hen only uses he
common equa ions (24) and (26).
Published alues o
J
max
and
Vc
max
ange om 17 o 372 µmol/(m²*s) and om 6 o 194
µmol/(m²*s) (W
ULLSCHLEGER
1993), which has due o he mul iplica ion in equa ions (24) and
(26) an immense impac on calcula ed species-speci ic pho osyn hesis a es. The e ec o day
espi a ion (
R
d
) is o en smalle due o i s addi i e conside a ion and a he low absolu e alues:
Published es ima es o
R
d
a abou 25°C acco ding o he me hod o L
AISK
(1977) and B
ROOKS
&
F
ARQUHAR
(1985) lie p e ailingly in he ange om 0 o 0.8 µmol/(m²*s) (H
ÄUSLER ET AL
.
1996,
H
ÄUSLER ET AL
1999,
J
ACOB
&
L
AWLOR
1993,
H
ERPPICH ET AL
.
1998,
B
ROOKS
&
F
ARQUHAR
1985,
S
UMBERG
&
LAISK
1995,
LAISK
&
L
ORETO
1996,
A
TKIN ET AL
.
1997), bu also highe alues we e
measu ed (3.4 µmol/(m²*s) o Encelia a inosa, Z
HANG ET AL
.
1995), pa ly wi h ano he me hod
(1.1 µmol/(m²*s) o Pinus syl es is, W
ANG ET AL
.
1996).
RACCIA i s calcula es
R
d
as he nega i e assimila ion a e ha would be measu ed a
C
i
= Γ
ΓΓ
Γ
*
,
p olonging he linea ini ial slope o each
A/C
i
-cu e owa ds lowe alues (see Fig. 57, B
ROOKS
&
F
ARQUHAR
1985). The needed Γ
ΓΓ
Γ
*
- alue is calcula ed om he empe a u e dependence o Γ
ΓΓ
Γ
*
and
τ
ττ
τ
, which a e connec ed by equa ion (27). The used empe a u e dependence has been
ound by J
ORDAN
&
O
GREN
(1984) on spinach and was con i med by la e measu emen s on
spinach and whea (B
ROOKS
&
F
ARQUHAR
1985), F ench bean (G
HASHGHAIE
&
C
ORNIC
1994),
po a o (H
ÄUSLER ET AL
. 1999), and Eucalyp us pauci lo a (A
TKIN ET AL
.
2000), whe e i is
exp essed as a o mula:
Howe e , a di e en empe a u e dependence was ound o Epilobium hi su um a
empe a u es below 18°C (G
HASHGHAIE
&
C
ORNIC
1994). A Γ
ΓΓ
Γ
*
- alue o 38.8 µmol/mol a 25°C
and 210,000 µmol/mol oxygen concen a ion in he ai was de i ed om he measu emen s o
J
=
J
max
I
I
+
2.1
J
max
(35)
(36)
G
*
= G
*
25
+
1.88
H
T
-
298.16
L
+
0.036
H
T
-
298.16
L
2
Spa ial dis ibu ion o lea p ope ies in ee c owns
85
VON
C
AEMMERER ET AL
. (1994) and was applied conside ing equa ion (27) and co ec ing
O
o
ai p essu e o he measu emen .
The empe a u e dependen Michaelis-Men en cons an s o ubisco ca alysed oxygena ion and
ca boxyla ion,
K
M,O
and
K
M,C
, a e calcula ed acco ding o equa ion (28) based on he
measu emen s o
VON
C
AEMMERER ET AL
. (1994) and he speci ic
H
A
- alues o H
ARLEY
&
T
ENHUNEN
(1991), which a e simila o hose om B
ERNACCHI ET AL
. (2001).
The da a poin s below 350 µmol/mol CO
2
-concen a ion inside he lea in e cellula spaces (
C
i
)
a e hen used o a non-linea eg ession (based on he Le enbe g-Ma qua d me hod) o
equa ion (24) on each cu e, he eby assuming ha
Vc
max
is limi ing pho osyn hesis in ha pa
o he cu e, so ha
A
=
A
V
(Fig. 57).
Simila ly, equa ion (26) is i ed o he poin s abo e 350µmol/(m²*s), whe e
Vc
max
is no limi ing
and
J
max
is equal o
J
due o sa u a ing i adiance (2000µmol/(m²*s)) du ing he measu emen .
RACCIA hen e alua es g oups o
A/C
i
-cu es ha belong o he same lea (o o he same
g oup o lea es, i desi ed) and we e measu ed a di e en empe a u es. A non-linea
eg ession o equa ion (30) is pe o med on he calcula ed
Vc
max
alues o hese
A/C
i
-cu es
e sus empe a u e. An addi ional da a poin in he
Vc
max
e sus empe a u e diag am esul s
om comple e enzyme inac i a ion o ubisco, which was shown o occu a 60°C (G
EZELIUS
1975). A leas h ee addi ional
Vc
max
alues a di e en empe a u es a e necessa y, because
equa ion (30) is used o es ima e ou pa ame e s.
The same equa ion o
J
max
is i ed o he
J
max
alues o a leas h ee
A/Ci
-cu es a di e en
empe a u es again comple ed by a Ze o- alue, which was es ima ed om A
RMOND ET AL
.
(1978)
and
N
OLAN
&
S
MILLIE
(1976)
o occu
a 50°C. 4 da a poin s we e some imes no enough
o hese app oxima ions, especially when he measu ed alues we e close o each o he , so
ha a comple ely di e en shape o he cu e be e ul illed he equi emen s o he χ
2
me i
unc ion gi en by he sum o squa ed esiduals. In his case, da a poin s we e weigh ed and an
addi ional Ze o- alue a -30°C was added wi h 10% o he weigh o he measu emen -de i ed
da a o assu e ha he unc ional ela ionship s a s wi h low alues a 0°C ins ead o e y high
ones.
500 1000 1500 2000 2500
Ci
H
µmol
ê
H
m²
*
s
L
L
0
10
20
30
40
50
60
70
A
H
lomµ
ê
²m
*
s
L L
2
A
V
A
J
20 40 60 80 100
Ci
H
µmol
ê
H
m² *s
L
L
-1.5
-1
-0.5
0
0.5
1
1.5
2
A
H
l
o
m
µ
ê
H
²
m
*
s
L
L
Γ
*
R
d
Fig. 57:
De e mina ion o
Vc
max
and
J
max
wi h non-linea app oxima ions o equa ions (24) and (26)
(le g aph), and de e mina ion o
R
d
om he ini ial slope o he
A/C
i
-cu e.
Spa ial dis ibu ion o lea p ope ies in ee c owns
86
3.2 Resul s
3.2.1 Ligh and heigh dependence o lea p ope ies
3.2.1.1 Rela i e I adiance
Bee ’s law is he eason o expec an exponen ial dec ease o ela i e i adiance wi h dep h in
he canopy (M
ONSI
&
S
AEKI
1953). The dec ease o ela i e i adiance a he posi ion o sampled
lea es wi h e ical dis ance om he ee apex was close o exponen ial in he dominan beech
Bu38 ( ²=0.91) and no signi ican di e ences we e ound in he dec ease o ela i e i adiance
be ween i s 4 e ical lines o in es iga ion poin s. Rela i e i adiances om he subdominan
ee Bu45 we e much mo e sca e ed ( ² =0.44, Fig. 58).
An explana ion o he highe sca e in he da a o he subdominan ee Bu45 is ha i s ligh
clima e is much mo e dependen on neighbou ing ees han ha o beech Bu38. The e o e,
dep h in he canopy is o en highe han he e ical dis ance o he ee apex. This has been
conside ed by sepa a e app oxima ions on he ou e ical lines o in es iga ion poin s based
on a modi ica ion o he exponen ial i o beech Bu38, which allows o he co ec ion o e ical
dis ance (Fig. 59). The esul ing idealised heigh co ec ion (pa ame e b) was in he ange om
–0.68 m o 1.72 m. The heigh co ec ion imp o ed he coe icien o de e mina ion o da a o
beech Bu45 o 0.8.
2 4 6 8 10
heigh below apex
H
m
L
0.2
0.4
0.6
0.8
1
e i ale ecnaida I
Beech Bu38
Fig. 58:
Exponen ial dec ease o ela i e i adiance in he ee c owns wi h e ical dis ance o hei
apex. The app oxima ed lines we e y = Exp[-0.3764x] ( ² = 0.91) o beech Bu38 and
y = Exp[-0.4428x] ( ² = 0.44) o beech Bu45.
2 4 6 8 10 12
heigh below apex
H
m
L
0.2
0.4
0.6
0.8
1
e i ale ecnaida I
Beech Bu45
2 4 6 8 10 12 14
co ec ed heigh b. apex
H
m
L
0.2
0.4
0.6
0.8
1
e i ale ecnaida I
Beech Bu45, all lines
2 4 6 8 10 12
heigh below apex
H
m
L
0.2
0.4
0.6
0.8
1
e i ale ecnaida I
Beech Bu45, line 1
b = 1.72
² =
0.63
2 4 6 8 10 12
heigh below apex
H
m
L
0.2
0.4
0.6
0.8
1
e i ale ecnaida I
Beech Bu45, line 3
b = -0.68
² = 0.75
2 4 6 8 10 12
heigh below apex
H
m
L
0.2
0.4
0.6
0.8
1
e i ale ecnaida I
Beech Bu45, line 4
b = 0.41
² = 0.71
2 4 6 8 10 12
heigh below apex
H
m
L
0.2
0.4
0.6
0.8
1
e i ale ecnaida I
Beech Bu45, line 2
b = 1.25
² = 0.89
²=0.8
Fig. 59:
Sepa a e app oxima ions
o y = Exp[0.3764*(x+b)] o da a o
he ou lines o in es iga ion poin s.
The de i ed heigh co ec ion b is
indica ed in he g aphs. The g aph
below shows all in es iga ion poin s
a e
applica ion o he heigh
co ec ion.
Spa ial dis ibu ion o lea p ope ies in ee c owns
87
Fig. 60:
Lea angle dis ibu ions o 1m-heigh laye s o he ee c own o beech Bu45 in angle
classes o 10°.
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
11m-12m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
10m-11m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
9m-10m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
8m-9m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
7m-8m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
6m-7m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
5m- 6m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
4m- 5m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
3m- 4m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
2m- 3m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
1m- 2m below apex
0
0.1
0.2
0.3
0.4
0.5
10 20 30 40 50 60 70 80 90
0m-1m below apex
Spa ial dis ibu ion o lea p ope ies in ee c owns
88
3.2.1.2 Lea angles
Lea angles o he ho izon om bo h Buchenallee beech ees we e in he ange om 0° o 86°,
low inclina ions being much mo e abundan han s eep inclina ions. Da a o in es iga ion poin s
we e g ouped in 1m-heigh laye s o assu e ha a leas 30 lea angles a e e alua ed pe da a
poin . In a i s app oxima ion, lea angle dis ibu ions o heigh laye s did no appea o be
egula , despi e he ac ha e y s eep inclina ions abo e 70° did no occu in he lowe hal o
bo h c owns, bu we e ela i ely abundan in he uppe wo me es (compa e Fig. 60). A gene al
end owa ds highe a e age lea angles in egions o highe i adiance was obse ed (Fig. 61),
bu la ge a ia ions occu ed in his ela ionship.
Anyway i u ned ou ha hese lea angle dis ibu ions a e egula and belong o he same
amily o dis ibu ions: A mo e de ailed analysis o skewness and ku osis o he angle
dis ibu ions o bo h ees e ealed ha a close o linea ela ionship can be d awn be ween bo h
p ope ies. This has among o he hings he meaning ha lea angles in each c own egion we e
ne e no mal dis ibu ed, because skewness and ku osis o he no mal dis ibu ion a e 0 and
he poin (0,0) lies apa om he close o linea ela ionship. The non-no mal dis ibu ion o lea
angles is also appa en om Fig. 60. Ins ead, he ela ionship be ween skewness and ku osis
o he measu ed lea angle dis ibu ions lies close o ha ela ionship ha is ob ained o he
ellipsoidal dis ibu ion de i ed om an obla e sphe oid, which was p oposed o he desc ip ion
o lea angle dis ibu ions (C
AMPBELL
1989), he eby p o iding empi ical e idence o he
adequacy o his ype o dis ibu ion o he desc ip ion o lea angle dis ibu ions in beech
c owns (Fig. 60).
k
- alues o each ellipsoidal dis ibu ion, de i ed by non-linea app oxima ions o he ellipsoidal
dis ibu ion unc ion (in eg a ed o e 10° angle classes, a e age ² = 0.73), showed a s ong
dependence on absolu e e ical dis ance om he apex, which was simila o bo h beech ees
(Fig. 62). Howe e , only a weak dependence on ela i e i adiance was ound: While he heigh
dependence shows a clea linea inc ease o
k
- alues up o 6 o 7 m below apex and a linea
dec ease om his poin owa ds he bo om o bo h ee c owns, no linea dec ease can be
obse ed in he egion o lowe i adiances. This is mainly due o he s eep ligh g adien which
y = -0.0017x
6
+ 0.0193x
5
- 0.076x
4
+ 0.113x
3
+
1.3028x
2
- 0.1062x - 1.07
-1.5
-1
-0.5
0
0.5
1
1.5
-0.5 0 0.5 1 1.5
Skewness
Ku osis
beech Bu38
beech Bu45
a e age lea angles o heigh laye s
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8
ela i e i adiance
a e age lea angle (°)
beech Bu45 beech Bu38
Fig. 61:
Gene al inc ease o a e age lea angles o heigh laye s wi h ela i e i adiance (le ) and
ela ionship be ween ku osis and skewness o all lea angle dis ibu ions ( igh ). The cu e in he
igh g aph indica es he ela ionship be ween ku osis and skewness o ellipsoidal dis ibu ions wi h
a ying pa ame e k, which may also be exp essed as a 6
h
o de polynomial unc ion ( ² = 1). R² o
he eg ession be ween his line and he da a poin s was 0.83.
a e age lea angles o heigh laye s
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1
ela i e i adiance
a
e
a
g
e
l
e
a
a
n
g
l
e
(
°
)
beech Bu45 beech Bu38
Spa ial dis ibu ion o lea p ope ies in ee c owns
89
condenses he poin s ha belong o lea angle dis ibu ions o lowe laye s o a cloud o poin s in
he g aph.
The ela ionship be ween a e age lea angle o heigh laye s and he k- alue o he associa ed
ellipsoidal lea -angle dis ibu ion was sligh ly di e en o bo h ees as can be seen in Fig. 63.
0
1
2
3
4
5
0 5 10
e ical dis ance o apex (m)
k- alue
Beech Bu38 Beech Bu45
0
1
2
3
4
5
0
0.2
0.4
0.6
0.8
ela i e i adiance
k- alue
Beech Bu45
Beech Bu38
Fig. 62:
Dependence o he k- alue o he app oxima ed ellipsoidal dis ibu ion o lea angles on
e ical dis ance o he ee‘s apex (le ) and ela i e i adiance ( igh ). The endlines in he le
g aph we e d awn by hand and equal y = 0.24x +1.67 and y = -0.38x + 5.85 in he case o beech
Bu38.
0
1
2
3
4
5
0
0
.
2
0
.
4
0
.
6
0
.
8
1
e
l
a
i
e
i
a
d
i
a
n
c
e
k
-
a
l
u
e
B
e
e
c
h
B
u
4
5
B
e
e
c
h
B
u
3
8
y = -0.104x + 6.0716
R
2
= 0.6781
y = -0.0913x + 5.0359
R
2
= 0.7428
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
15 20 25 30 35 40
a e age lea angle (°)
k- alue
Beech Bu38 Beech Bu45
Fig. 63:
Rela ionship be ween k- alue
and a e age lea angle o lea angle
dis ibu ions o bo h beech ees.
Fig. 64:
A e age b anch angles o b anches and wigs closely abo e he lea a each
in es iga ion poin as dependen on heigh (m below apex) and ela i e i adiance. R² -
alues we e 0.68 and 0.64.
0.2 0.4 0.6 0.8
ela i e I adiance
10
20
30
40
50
hcna b elgna
H
°
L
beeches Bu38 and Bu45
y = 56.22 x
0.44
2 4 6 8 10 12
e ical dis ance oapex
H
m
L
0
10
20
30
40
50
hcna b elgna
H
°
L
Beeches Bu38 and Bu45
y= -3.67 x +46.34
Spa ial dis ibu ion o lea p ope ies in ee c owns
96
o lea es o he Buchenallee ees was he e o e dependen on ela i e i adiance ( ² = 0.87,
Fig. 75). The same was p incipally ue o ca bon concen a ions.
3.2.2 Pho osyn hesis measu emen s
3.2.2.1 Compa ison o PAM-2000 and RACCIA es ima es o J
max
J
max
es ima ions om luo escence and gas exchange measu emen s on he same lea should
lead o compa able esul s, when hey a e pe o med unde he same condi ions, hus
p incipally p o iding an oppo uni y o check accu acy o he measu emen s. Bu ield condi ions
we e a iable and hey could only pa ly be manipula ed: While he LICOR-6400 po able gas
exchange measu emen sys em can al e empe a u e in he measu emen chambe in he
ange o ambien empe a u e ± 7°C and maximum ligh in ensi y o he appe aining LED ligh
sou ce (LED 6400-02B) is 2000µmol/(m²*s), luo escence measu emen s wi h he PAM-2000
unde ield condi ions do no allow any adjus men o empe a u e, bu ligh in ensi y can be
a ied in a wide ange. Addi ionally, ime o day o he measu emen may play a ole o he
esul and di e ences could also occu be ween subsequen days a he same hou .
A compa ison be ween esul s o bo h me hods was enabled by measu ing a ligh esponse
cu e o
J
wi h he luo ome e PAM-2000 a a mo e o less cons an (± 2°C) empe a u e and a
empe a u e dependence cu e o
J
wi h he LICOR-6400 a he cons an maximum PPFD o
2000 µmol/(m²*s) on he same lea . The empe a u e a ia ion in he ligh esponse cu e is a
esul o he a ia ion in ambien condi ions and wa ming o he lea due o he ligh sou ce.
Assuming ha he maximum elec on anspo a e
J
max
is achie ed a 2000 µmol/(m²*s), he
e alua ion o
A/C
i
-cu es wi h RACCIA can p o ide a segmen o he empe a u e dependence
cu e o
J
max
, ep esen ing he maximum empe a u e ange ha can be ob ained wi h he
LICOR-6400 unde he ac ual ambien condi ions. The ex apola ion o his cu e o he
empe a u e o he PAM-2000 measu emen can be compa ed wi h he elec on anspo a e a
2000µmol/(m²*s) ha is de i ed om he ligh esponse cu e using a non-linea i o equa ion
(29) o in e pola ion.
Fig. 75:
A ea ela ed ni ogen con en o lea es e sus lea mass pe a ea (le ) and ela i e
i adiance ( igh ). Open squa es in he le g aph s and o lea es om 2 beeches in he
S eink euz s and, beech G 12, and 3 addi ional beeches in he G oßebene s and, all o he
symbols a e he same as in Fig. 73. Da a poin s o beeches Bu38 and Bu45 a e a e ages o a
leas 3 neighbou ing lea es, ² o hese da a only agains LMA was 0.97 and 0.99, espec i ely.
The ela ionships o ela i e i adiance we e y = 2.64x
0.383
( ² = 0.88) o beech Bu38, y = 2.48x
0.405
( ² = 0.9) o beech Bu45, and y = 2.54x
0.389
( ² =0.87) o bo h beech ees.
40 60 80 100 120
LMA
H
g
ê
m²
L
1
1.5
2
2.5
3
3.5
ael nego in
H
g
ê
²m
L
all ees
Beech lea es:
y = 0.025x + 0.025
² = 0.92
Oak lea es:
y = 0.025x + 0.124
² = 0.89
0.2 0.4 0.6 0.8 1
ela i e i adiance
1
1.5
2
2.5
ael nego in
H
g
ê
m
2
L
beeches Bu38 and Bu45
Spa ial dis ibu ion o lea p ope ies in ee c owns
97
Fi e lea es o oak G 13 we e selec ed in di e en ligh exposi ions and luo escence
measu emen s we e pe o med di ec ly a e gas-exchange measu emen s, excep in one case
(lea eb2_1, 20°C), whe e no gas-exchange measu emen s could be pe o med due o a
sudden ain e en (30.7.99). This lea was measu ed wice on wo subsequen days du ing he
same hou s o he day (11.00 h - 13.00 h), bu a di e en empe a u es. The esul s o
luo escence and gas-exchange measu emen s a e shown in Figs. 76 and 77.
The ligh esponse cu e o lea 3eb2_1 was di e en a bo h measu emen empe a u es in i s
ini ial slope, which was 0.25 in he 20°C and only 0.1 in he 28°C measu emen , while maximum
alues did no di e so much. The ligh esponse cu e a he highes empe a u e (lea 3eb2-2,
32°C) had also a a he low ini ial slope (0.12), while all o he es ima ions o he ini ial slope
we e in he ange om 0.22 o 0.3. I can he e o e no be excluded ha he wo lea es unde
he highes empe a u es su e ed s ess o some ex en , hough hey we e able o achie e high
Fig. 76:
Ligh esponse cu es o elec on anspo a e
J
o 5 lea es o oak G 13, de i ed om
luo escence measu emen s wi h he PAM-2000 luo ome e a 6 di e en empe a u es (so ed by
ni ogen con en ). The highes measu ed alue pe ligh le el was used o a non-linea app oxi-
ma ion o he ligh dependence unc ion o
J
om he H
ARLEY
/T
ENHUNEN
model (equa ion 29).
500 1000 1500 2000 2500
PPFD
H
µmol
ê
H
m²
*
s
L
L
50
100
150
200
250
J
H
lomµ
ê
H
²m
*
s
L
L
lea 3h4
-
1, 24°C
N = 2.71
g/m²
500 1000 1500 2000 2500
PPFD
H
µmol
ê
H
m²
*
s
L
L
50
100
150
200
250
J
H
lomµ
ê
H
²m
*
s
L
L
lea 3c4
-
2, 27°C
N = 2.41 g/m²
500 1000 1500 2000 2500
PPFD
H
µmol
ê
H
m²
*
s
L
L
50
100
150
200
250
J
H
lomµ
ê
H
²m
*
s
L
L
lea 3c4
-
3, 25°C
N = 1.82 g/m²
500 1000 1500 2000 2500
PPFD
H
µmol
ê
H
m²
*
s
L
L
50
100
150
200
250
J
H
lomµ
ê
H
²m
*
s
L
L
lea 3eb2
-
2,32°C
N = 1.7 g/m²
500 1000 1500 2000 2500
PPFD
H
µmol
ê
H
m²
*
s
L
L
50
100
150
200
250
J
H
lomµ
ê
H
²m
*
s
L
L
lea 3eb2
-
1,20°C
N = 1.52 g/m²
500 1000 1500 2000 2500
PPFD
H
µmol
ê
H
m²
*
s
L
L
50
100
150
200
250
J
H
lomµ
ê
H
²m
*
s
L
L
lea 3eb2
-
1,28°C
N = 1.52
g/m²
Spa ial dis ibu ion o lea p ope ies in ee c owns
98
maximum elec on anspo a es. Some luo escence measu emen s seem o indica e ha he
ligh dependence o
J
was no mono onously inc easing, bu achie ed a maximum alue below
2000 µmol/(m²*s). Bu his may also be a ibu ed o e ec s o he long measu emen pe iod
be o e measu ing he high PPFD alues and he e ec o he 1-2°C highe empe a u e a hese
PPFD alues due o lea wa ming by he lamp.
Shade lea es wi h lowe ni ogen con en pe a ea had gene ally lowe
J
max
alues han sun
lea es acco ding o bo h me hods.
A high co ela ion ( ²=0.93) was ound be ween he
J
max
es ima ions o bo h me hods (Fig. 78).
The PAM-2000 es ima ions we e gene ally sligh ly highe han hose de i ed wi h RACCIA om
gas-exchange measu emen s, and his si ua ion imp o ed a bi , when a e age alues ins ead o
5 10 15 20 25 30 35 40
Tempe a u e
H
°C
L
50
100
150
200
250
xamJ
H
lomµ
ê H
²m
*
s
L L
lea 3eb2-2
5 10 15 20 25 30 35 40
Tempe a u e
H
°C
L
50
100
150
200
250
xamJ
H
lomµ
ê H
²m *s
L L
lea 3eb2
-
1
5 10 15 20 25 30 35 40
Tempe a u e
H
°C
L
50
100
150
200
250
xamJ
H
lomµ
ê H
²m
*
s
L L
lea 3c4
-
3
5 10 15 20 25 30 35 40
Tempe a u e
H
°C
L
50
100
150
200
250
xamJ
H
lomµ
ê H
²m
*
s
L L
lea 3c4
-
2
5 10 15 20 25 30 35 40
Tempe a u e
H
°C
L
50
100
150
200
250
xamJ
H
lomµ
ê H
²m *s
L L
lea 3h4
-
1
Fig. 77:
Tempe a u e dependence
o
J
max
o he same lea es as in
Fig. 76, es ima ed wi h RACCIA
om
A/C
i
-cu es a h ee di e en
empe a u es and PPFD = 2000
µmol/(m²*s). Lea es a e so ed by
N-con en pe a ea.
N = 1.52 g/m²
N = 2.71 g/m² N = 2.41 g/m²
N = 1.82 g/m² N = 1.7 g/m²
R
2
= 0.9339
0
50
100
150
200
0 50 100 150 200
RACCIA es ima ion o Jmax (µmol/(m²*s))
PAM 2000 es ima ion o Jmax (µmol/(m²*s))
R
2
= 0.9212
0
50
100
150
200
0 50 100 150 200
RACCIA es ima ion o Jmax (µmol/(m²*s))
PAM 2000 es ima ion o Jmax (µmol/(m²*s))
Fig. 78:
Compa ison o
J
max
es ima ions om wo di e en me hods (RACCIA and PAM-2000). The
ci cles in he le g aph ep esen
J
max
esi ma ions wi h he PAM-2000 based on app oxima ions o
he maximum measu ed alues pe ligh -le el, while he c osses in he igh g aph ely on
app oxima ions o a e age alues.
Spa ial dis ibu ion o lea p ope ies in ee c owns
99
maximum alues we e used o he app oxima ion o equa ion (29) o he measu ed da a o he
ligh esponse cu e, hough co ela ion was somewha lowe hen ( ²=0.92).
3.2.2.2 Day espi a ion (R
d
)
All de e mined day espi a ion a es we e in he ange om 0 o 2.7 µmol/(m²*s) o lea es o
beech G 12 and om 0 o 2.7 µmol/(m²*s) o lea es o oak G 13.
R
d
o he same lea was
gene ally highe unde highe empe a u es and he g adual inc ease wi h empe a u e was
g ea e o sun lea es wi h high ni ogen con en pe a ea han o shade lea es o bo h species.
The e o e, empe a u e dependence o day espi a ion was in es iga ed o g oups o lea es
wi h simila ni ogen con en sepa a ely using equa ion (28). All ollowing app oxima ions o
equa ions (28) and (30) a e done o in e pola e be ween measu emen s a di e en
empe a u es. Fo his,
A/C
i
-da a o lea es we e so ed by ni ogen con en (see appendix) and
Fig. 79:
Tempe a u e dependence o day espi a ion
R
d
o oak G 13.
Each poin ep esen s he
R
d
es ima e o a single
A/C
i
-cu e.
A/C
i
-
cu es o h ee lea es wi h simila ni ogen con en pe a ea we e
pooled o each app oxima ion o aise he numbe o da a poin s pe
app oxima ion. Ni ogen con en is he a e age o e all da a poin s in
each g aph.
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
1.25 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
1.4 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
1.47 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
1.57 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
1.67 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
1.79 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
2. g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
2.19 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
2.32 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
2.37 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
2.55 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
2.77 g
ê
m²
5 10 15 20 25 30 35
Tempe a u e
H
°C
L
1
2
3
4
5
dR
H
lomµ
ê
H
²m
*
s
L
L
N
=
2.87 g
ê
m²
Spa ial dis ibu ion o lea p ope ies in ee c owns
100
g oups o consecu i e lea es in his ow we e combined in he e alua ion. G oups we e pa ly
o e lapping. Fig. 79 shows ha he g adual inc ease o
R
d
o oak lea es wi h empe a u e was
e y low o some shade lea es, while i was g ea e o mos o he sun lea es. Fo
compa ison: The occasionally de e mined gas-exchange a e o an oak lea wi h 2.33 g N/m² a
25°C, measu ed a e 6 minu es o da kness, was -1.85 µmol/(m²*s).
The low numbe o da a poin s and hei concen a ion on a na owe ange o empe a u es
was a p oblem o he app oxima ions wi h he exponen ial equa ion (28) o beech, because
ex emely high cu a u es (
H
a
in equa ion (28)) ga e he bes app oxima ion e en when he
beech da a we e spli ed in only wo g oups. Because his would ha e esul ed in un ealis ic o
a leas ne e measu ed
R
d
- alues o mo e han 10 µmol/(m²*s) a empe a u es abo e 30°C,
H
a
in he eg essions o beech (Fig. 80) and beech seedlings (Fig. 81) was no allowed o each
alues abo e 50 kJ/mol. This was also done conside ing ecen obse a ions ha espi a ion
con inuing in he ligh no necessa ily ollows an exponen ially inc easing unc ion, bu may also
dec ease abo e a maximum alue a 25 o 30°C (A
TKIN ET AL
.
2000).
Addi ional
A/C
i
-measu emen s ha e been sea ched o enla ge he da a basis o beech. M.
F
ORSTREUTER AND
J.
S
TRASSEMEYER
(Technische Uni e si ä Be lin)
me i o iously made
a ailable hei pa ly published
A/C
i
-measu emen s (M
EDLYN ET AL
. 1999) on beech seedlings a
di e en empe a u es o he e alua ion wi h RACCIA. The ni ogen con en pe a ea o hese
in es iga ed lea es a ied in a na owe ange han ha o he lea es o ma u e ees in
S eige wald o Fich elgebi ge (0.71 - 0.98 g/m² o hese in es iga ed lea es, 0.5 - 1.5 g/m² o
all measu ed seedling lea es, 0.6 - 2.6 g/m² o beech lea es om he Fich elgebi ge, and 1.0 -
3.4 g/m² o beech lea es om he S eige wald), which was due o less a ia ion in lea mass
pe a ea. Ni ogen con en pe a ea was on a e age lowe han ha o shade lea es om
ma u e ees in bo h s ands. A/Ci-cu es o seedlings we e sepa a ed in o h ee g oups (low,
middle, and high ni ogen) and we e analysed sepa a ely (Fig. 81).
H
a
in hese app oxima ions
was be ween 33.9 and 42 kJ/mol, while i eached he maximum allowed alue o 50kJ/mol in
he app oxima ions o beech G 12.
Respi a ion a es a 25°C (
Rd
298
) did no show a clea dependence on ni ogen con en , hough
lea es wi h simila ni ogen con en ended o ha e simila alues o
Rd
298
(Fig. 82). The esul s
Fig. 80:
Tempe a u e dependence o day
espi a ion
R
d
o beech G 12. All
R
d
- alues
we e spli ed in o wo non-o e lapping
g oups wi h low and high ni ogen con en s.
The app oxima ion wi h equa ion (28) was
pe o med wi h he condi ion ha
H
a
does
no exceed a h eshold alue o 50kJ/mol.
10 20 30 40
Tempe a u e
H
°C
L
0.5
1
1.5
2
2.5
3
3.5
4
d
R
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.23 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
0.5
1
1.5
2
2.5
3
3.5
4
d
R
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.41 g
ê
m²
Fig. 81:
App oxima ion
o equa ion (28) o
R
d
-
es ima ions om
A/C
i
-
cu es measu ed on
seedlings (
A
/
C
i
-
measu emen s o
Fo s eu e and
S assemeye (M
EDLYN
ET AL
.
1999))
10 20 30 40
Tempe a u e
H
°C
L
0.5
1
1.5
2
2.5
3
3.5
4
d
R
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N=0.73 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
0.5
1
1.5
2
2.5
3
3.5
4
d
R
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
0.84 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
0.5
1
1.5
2
2.5
3
3.5
4
d
R
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
0.97 g
ê
m²
Spa ial dis ibu ion o lea p ope ies in ee c owns
101
o oak G 13 show a sligh inc ease in espi a ion om he shade lea es wi h low ni ogen
con en owa ds a ni ogen con en o 1.7 g/m², sligh ly lowe espi a ion a es be ween 1.7 and
2.5 g/m² and a sudden inc ease owa ds he lea es wi h ni ogen con en s abo e 2.5 g/m². The
gene al end o e all lea es is an inc ease o espi a ion a es wi h ni ogen pe a ea.
3.2.2.3 Ca boxyla ion capaci y Vc
max
and elec on anspo capaci y J
max
Non-linea app oxima ions o equa ion (30) we e used o he desc ip ion o empe a u e
dependence o
Vc
max
and
J
max
o bo h species (Figs. 83 - 87). Because bo h quan i ies had
ob iously lowe alues o shade lea es han o sun lea es,
A/C
i
-da a we e g ouped in he
same manne as o he e alua ion o
R
d
e sus empe a u e (see 3.2.2.2) in o de o sepa a e
ni ogen classes.
Vc
max
o oak lea es was gene ally highe han
Vc
max
o lea es o beech G 12, eaching a
maximum alue o 158 µmol/(m²*s) a 33°C in he in es iga ed lea wi h he highes ni ogen
con en (3.1 g/m²), while he maximum de e mined alue o beech lea es was 63 µmol/(m²*s) a
24°C (N = 2.8 g/m²). This co esponds o he maximu m alues o
J
max
, which we e 231
µmol/(m²*s) ( 32°C, N = 2.3 g/m²) o oak G 13 and only 132 µmol/(m²*s) o beech G 12 (25°C,
N = 2.2 g/m²).
Vc
max
and
J
max
gene ally inc eased wi h ni ogen con en pe lea a ea, which was
also ue o seedlings (see below).
Addi ional
A/C
i
-cu es om beech seedlings (M
EDLYN ET AL
.
1999) we e in es iga ed and
showed o ha e much lowe
Vc
max
- and
J
max
- alues (Fig. 87), which may be a consequence o
hei low ni ogen con en s pe a ea. Maximum alues we e 47µmol/(m²*s) and 56 µmol/(m²*s)
a a empe a u e o 31°C and 30°C, espec i ely, me asu ed on a lea wi h a ni ogen con en o
0.96 g /m². Thus,
Vc
max
and
J
max
o beech seedlings appea o lie close o each o he han
hose o beech G 12.
Nea ly all
Vc
max
- alues o oak G 13, beech G 12, and beech seedlings we e ound o be on he
ascending pa o he app oxima ion cu e, while
J
max
- alues om he same
A/C
i
-cu es we e
mo e o en on he descending pa , indica ing a lowe empe a u e op imum o
J
max
han o
Vc
max
.
The ela ionship be ween bo h capaci ies was ound o be ela i ely cons an o a high numbe
o species (W
ULLSCHLEGER
1993,
L
EUNING
1997), wi h an a e age
J
max
/
Vc
max
a io be ween
2.16 and 2.68 a 20°C (depending on he used empe a u e unc ion). The abo e empe a u e
dependencies we e he e o e used o in e pola e o a empe a u e co ec ed alue o
Vc
max
and
J
max
a 20°C o each ni ogen class in o de o in es iga e he gene al ela ionship be ween
Fig. 82:
Va ia ion o day espi a ion
a 25°C wi h ni ogen pe lea a ea.
Tempe a u e in e pola ion was done
based on he esul s o Figs. 79-81.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.5 1 1.5 2 2.5 3 3.5
N (g/m²)
R
d
a 25°C (µmol/(m²*s))
oak G 13 beech G 12 beech seedlings
Spa ial dis ibu ion o lea p ope ies in ee c owns
102
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.25 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.4 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.47 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.57 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.67 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.79 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2. g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.19 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.32 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.37 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.55 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.77 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.87 g
ê
m²
Fig. 83:
Tempe a u e dependence o
Vc
max
o lea es o oak G 13.
Each da a poin ep esen s he
Vc
max
es ima ion o one
A/C
i
-cu e
a a ce ain empe a u e. Each app oxima ion uses da a o h ee
lea es wi h simila ni ogen con en pe a ea and is based on
equa ion (30). N-con en is gi en as he a e age o all da a poin s.
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.18 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.29 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.68 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.15 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.44 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.66 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.73 g
ê
m²
Fig. 84:
Same ype o
igu e as Fig. 83, bu
o lea es o beech
G 12. Da a o wo
lea es we e used pe
app oxima ion.
Spa ial dis ibu ion o lea p ope ies in ee c owns
103
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.25 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.4 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.47 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.57 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.67 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.79 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2. g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.19 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.32 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.37 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.55 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.77 g
ê
m²
5 10152025303540
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.87 g
ê
m²
Fig. 85:
Tempe a u e dependence o
J
max
o lea es o oak G 13.
Each da a poin ep esen s he
J
max
es ima ion o one
A/C
i
-cu e a
a ce ain empe a u e. Each app oxima ion uses da a o h ee
lea es wi h simila ni ogen con en pe a ea and is based on
equa ion (30). N-con en is gi en as he a e age o all da a poin s.
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.18 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.29 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
1.68 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.15 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.44 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N=2.66 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
2.73 g
ê
m²
Fig. 86:
Same ype
o igu e as Fig. 85,
bu o lea es o
beech G 12. Da a
o wo lea es we e
used pe
app oxima ion.
Spa ial dis ibu ion o lea p ope ies in ee c owns
104
bo h quan i ies. Those empe a u e dependence unc ions wi hou
Vc
max
o
J
max
alues below
21°C we e excluded om his analysis. Fig. 88 shows ha all da a lie ela i ely close o he
eg ession line, which ep esen s a gene al a io o 2.28 ( ² = 0.86) and lies in he ange o
p e iously ound a ios (L
EUNING
1997). Ne e heless,
J
max
/
Vc
max
a ios a ied: While he a io
o in es iga ed lea es o oak G 13 was nea ly he same as he mean esponse (2.24, ange:
1.97 - 2.79), lea es o beech seedlings had a lowe a e age
J
max
/
Vc
max
a io (1.58, ange: 1.51
-1.64) and lea es o beech G 12 a highe one (2.72, ange: 2.38 - 3.23). Thus, he high
coe icien o de e mina ion o he o e all ela ionship does no necessa ily mean ha
Vc
max
may be de i ed om
J
max
es ima ions, because species- o age-speci ic di e ences a e e iden .
3.2.2.4 Ni ogen dependence o J
max
and Vc
max
The inc ease o
J
max
and
Vc
max
wi h ni ogen con en o he lea es is ob ious om Figs. 83 - 86
and was in es iga ed on he base o he empe a u e co ec ed alue a 25°C o each ni ogen
class o lea es, which is one pa ame e o equa ion (30) (
J
max, 298
and
Vc
max, 298
) and was
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
0.73 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
0.84 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
50
100
150
200
250
x
a
m
J
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N=0.96 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
0.73 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
0.84 g
ê
m²
10 20 30 40
Tempe a u e
H
°C
L
20
40
60
80
100
120
140
x
a
m
c
V
H
l
o
m
µ
ê
H
²
m
*
s
L
L
N
=
0.96 g
ê
m²
Fig. 87:
Tempe a u e
dependence o
Vc
max
(uppe ow ) and
J
max
(below) o beech
seedlings as
de e mined wi h
RACCIA.
3
3
Fig. 88:
Ra io be ween
J
max
and
Vc
max
a 20°C
o in es iga ed
ni ogen classes o
lea es o beech G 12,
oak G 13, and beech
seedlings (M
EDLYN ET
AL
. 1999). The
in e pola ion o 20°C
was based on he
empe a u e esponse
cu es o Figs. 83-87,
excep hose wi hou
alues below 21°C.
The mean a io o all
da a was 2.28 ( ² =
0.86, long solid line)
y = 2.2824x
R
2
= 0.8603
y = 1.5814x
y = 2.2496x
y = 2.7202x
0
20
40
60
80
100
120
140
160
0 10 20 30 40 50 60 70
Vcmax a 20°C (µmol/ (m²*s))
Jmax a 20°C (µmol/(m²*s))
beech seedlings oak G 13
beech G 12
Spa ial dis ibu ion o lea p ope ies in ee c owns
105
measu ed o could be in e pola ed o all desc ibed ni ogen classes. Fig. 89 con i ms he s ic
endency o inc easing capaci ies wi h inc easing ni ogen con en , bu i also shows ha he
ela i e inc ease wi h inc easing ni ogen con en pe a ea became smalle and inally
disappea ed a highe ni ogen con en s o lea es in he uppe sun c own. Abo e a ni ogen
h eshold o a ound 2.2 g/m², addi ional ni ogen pe a ea did no aise pho osyn hesis
capaci ies o lea es o beech G 12. While
Vc
max
o oak G 13 was ni ogen sa u a ed a a
ni ogen con en o 2.3 g/m²,
J
max
o oak G 13 s ill inc eased wi h inc easing ni ogen pe a ea
up o 2.9 g/m², bu he slope o he
J
max
s. ni ogen ela ionship was al eady dec easing a his
ni ogen con en . The non-linea app oxima ion o a bi a ily chosen unc ions o he ype y = a
x
b
/ (x
b
+ c) ep esen s he da a e y well ( ² ≥ 0.96) and may be ex apola ed o a sa u a ing
ni ogen con en abo e 4.5 g/m² in his case.
6 addi ional A/Ci-cu es om lea es o ma u e Fagus c ena a (Blume) ees (S
AITO
&
K
AKUBARI
1999), measu ed a 21°C, we e e alua ed wi h RACCIA and he ni ogen dependence o hei
Fig. 89:
Va ia ion o
J
max
and
Vc
max
a 25°C o lea es o oak G 13 (open s a s) and bee ch G 12 ( illed
squa es) wi h ni ogen con en pe a ea. Each da a poin ep esen s he empe a u e in e pola ed
alue om ni ogen classes o lea es as in Figs. 83 - 86. The obse ed sa u a ion a highe ni ogen
con en s was desc ibed wi h an app oxima ion unc ion o he ype y = a x
b
/ (x
b
+ c). Coe icien s a,
b, and c we e 120.3, 5.94, and 3.02 (
J
max
, ² = 0.99) and 53.9, 5.85, and 3.68 (
Vc
max
, ² = 0.99) o
beech G 12. Coe icien s o oak G 13 we e 221.1, 3.07, and 4.44 (
J
max
, ² = 0.99) and 93.7, 4.93,
and 5.9 (
Vc
max
, ² = 0.96), espec i ely.
0.5 1 1.5 2 2.5 3
N
H
g
ê
m²
L
20
40
60
80
100
xamcV
H
lomµ
ê
H
²m
*
s
L
L
0.5 1 1.5 2 2.5 3 3.5
N
H
g
ê
m²
L
50
100
150
200
250
xamJ
H
lomµ
ê
H
²m
*
s
L
L
0
5
10
15
20
25
30
35
40
45
0 0.5 1 1.5 2 2.5 3
N (g/m²)
Vcmax a 21°C (µmol/(m²*s))
beech G 12 beech seedlings Fagus c ena a
0
20
40
60
80
100
120
0
0.5
1
1.5
2
2.5
3
N (g/m²)
Jmax a 21°C (µmol/(m²*s))
beech G 12
beech seedlings
Fagus c ena a
Fig. 90:
Compa ison o
Vc
max
(le ) and
J
max
( igh ) a 21°C o beech G 12 wi h da a om beech
seedlings and om ma u e Fagus c ena a ees.
Spa ial dis ibu ion o lea p ope ies in ee c owns
112
ex eme shade lea es was lowes (9.8) and inc eased linea ly wi h inc easing ni ogen con en
up o a maximum alue o 16.3 a 2.4g/m². Abo e his alue,
g
ac
o oak G 13 lea es ended o
dec ease.
3.2.3 Ni ogen dependen model o lea pho osyn hesis o beech
3.2.3.1 Model desc ip ion
Ni ogen pe lea a ea co ela ed wi h hose lea p ope ies o oak G 13 and beech G 12 ha a e
mos impo an o he de e mina ion o pho osyn hesis a es and i has been shown o be
dependen on ela i e i adiance in ee c owns o beech. I is he e o e well sui able o up-
scaling along ligh g adien s in ee c owns. The ni ogen dependen model o lea
pho osyn hesis ex ends he model o H
ARLEY
and T
ENHUNEN
(1991) as desc ibed abo e in
o de o conside he ound ni ogen dependen a ia ion in pho osyn hesis capaci ies o lea es
in ee
c owns o beech. Thus, i combines he abo e indings on ni ogen dependence o
J
max
,
Vc
max
,
and
R
d
in he calcula ion o pho osyn hesis a es o single lea es.
The N-dependen pa ame e isa ion o equa ion (30) o
J
max
and
Vc
max
is done acco ding o he
equa ions displayed in Figs. 89, 92, 95, and 96. Thus, a es a 25°C a e dependen on ni ogen,
H
a
is dependen on he a e a 25°C and
S
and
H
d
depend on
H
a
acco ding o he ollowing
equa ions:
J
max
-speci ic:
J
max,298
=
120.3
N
5.94
N
5.94
+
3.02
(37)
H
a
=4.1659 J
max,298
0.5224
(38)
0.01 0.02
A* H
ê
Ca
H
mol
ê
H
m²*s
L
L
0.05
0.1
0.15
0.2
ecna cudnoC
H
lom
ê
H
²m *s
L
L
N=1.18 g
ê
m²
0.01 0.02
A
*
H
ê
Ca
H
mol
ê
H
m²
*
s
L
L
0.05
0.1
0.15
0.2
ecna cudnoC
H
lom
ê
H
²m
*
s
L
L
N
=
1.29 g
ê
m²
0.01 0.02
A
*
H
ê
Ca
H
mol
ê
H
m²
*
s
L
L
0.05
0.1
0.15
0.2
ecna cudnoC
H
lom
ê
H
²m
*
s
L
L
N
=
1.68 g
ê
m²
0.01 0.02
A
*
H
ê
Ca
H
mol
ê
H
m²
*
s
L
L
0.05
0.1
0.15
0.2
ecna cudnoC
H
lom
ê
H
²m
*
s
L
L
N
=
2.15 g
ê
m²
0.01 0.02
A
*
H
ê
Ca
H
mol
ê
H
m²
*
s
L
L
0.05
0.1
0.15
0.2
ecna cudnoC
H
lom
ê
H
²m
*
s
L
L
N
=
2.44 g
ê
m²
0.01 0.02
A
*
H
ê
Ca
H
mol
ê
H
m²
*
s
L
L
0.05
0.1
0.15
0.2
ecna cudnoC
H
lom
ê
H
²m
*
s
L
L
N
=
2.66 g
ê
m²
Fig.100:
Same ype
o igu e as Fig. 98,
bu o ni ogen
classes o lea es o
beech G 12.
0.01 0.02 0.03
A
*
H
ê
Ca
H
mol
ê
H
m²
*
s
L
L
0.1
0.2
0.3
ecna cudnoC
H
lom
ê
H
²m
*
s
L
L
N
=
2.73 g
ê
m²
S
H
d
+
7.8
=
0.004563H
a
+
2.925
(39)
Spa ial dis ibu ion o lea p ope ies in ee c owns
113
Vc
max
-speci ic:
H
d
in equa ions (39) and (42) is assumed o ollow he ela ionship
R
d
was also desc ibed as ni ogen dependen . While
H
a
om equa ion (28) o
R
d
was held
cons an a 70 kJ/mol, a linea inc ease o
R
d,298
wi h ni ogen pe lea a ea (
N
) was assumed,
ha was de i ed om he wo da a poin s o beech G 12 in Fig. 82:
(compa e Fig. 80).
While
g
min
was held cons an equalling 0,
g ac
was a ied acco ding o a quad a ic i o he
beech da a in Fig. 100 (R² = 0.9):
3.2.3.2 Pa ame e isa ion
Nea ly all pa ame e s ha a e no ubisco-speci ic cons an s we e eplaced by a ni ogen
dependen unc ion, so ha he numbe o pa ame e s o he calcula ion o pho osyn hesis and
anspi a ion o single lea es was educed om 18 o 8, as can be seen in able 7.
ubisco-speci ic cons an s (
K
M,C
,
K
M,O
, τ
ττ
τ ) and he
K
M,C
- and
K
M,O
- speci ic
H
a
- alues o
equa ion (28) we e aken om he in i o measu emen s o
VON
C
AEMMERER ET AL
. (1994). The
τ
τ τ
τ
-speci ic
H
a
- alue was aken om H
ARLEY
&
T
ENHUNEN
(1991), which p oduced Γ
ΓΓ
Γ
*
- alues e y
close o hose om equa ion (36), when equa ions (27) and (28) we e applied in he model (Fig.
101). This o mula ion was p e e ed, because i includes he dependence o Γ
ΓΓ
Γ
*
on oxygen
concen a ion o he a mosphe e.
α
αα
α
was se cons an o 0.06 mol CO
2
/mol pho ons.
g
ac
=
5.0071
N
2
-
22.704N
+
31.884
(45)
(44)
R
d,298
=
0.874N
-
0.269
Vc
max,298
=
53.9
N
5.85
N
5.85
+
3.68
(40)
H
a=
7.9856
Vc
max,298
0.5314
(41)
S
Hd+7.8 =0.003381Ha+2.89
(42)
H
d
=
0.311S
-
0.8521
. (43)
270 280 290 300 310
Tempe a u e
H
K
L
0
10
20
30
40
50
60
70
G
*
H
lomµ
ê
lom
L
Fig. 101:
Simila esul o al e na i e
o mula ions o he empe a u e
dependence o
Γ
ΓΓ
Γ
*
. While he en i e line
ep esen s equa ion (36)
(A
TKIN ET AL
.
2000), he do ed line is he esul o
equa ions (27) and (28) o an
a mosphe ic oxygen concen a ion o
209 mmol/mol, using pa ame e s
τ
τ τ
τ
om
VON
C
AEMMERER ET AL
. (1997) and
H
a
om Ha ley & Tenhunen (1991).
Spa ial dis ibu ion o lea p ope ies in ee c owns
114
Table 7:
Pa ame e s o he lea models
H
ARLEY
/T
ENHUNEN
model
Ni ogen dependen
model
Nume ical alue in he ni ogen
dependen model
K
M,O
K
M,O
248 mmol/mol
K
M,O
-speci ic
H
a
K
M,O
-speci ic
H
a
35000 J/mol
K
M,C
K
M,C
404 µmol/mol
K
M,C
-speci ic
H
a
K
M,C
-speci ic
H
a
63500 J/mol
τ
ττ
τ
τ
ττ
τ
2710
Rubisco-
speci ic
cons an s
τ
ττ
τ
-speci ic
H
a
τ
ττ
τ
-speci ic
H
a
-28990 J/mol
α
αα
α
α
αα
α
0.06 mol CO
2
/mol pho ons
P
ml,298
H
a
S
Ligh -use
pa ame e s
H
d
Vc
max,298
H
a
S
Ca boxyla ion
pa ame e s
H
d
R
d,298
Respi a ion
pa ame e s
H
a
g
ac
Conduc ance
pa ame e s
g
min
Ni ogen
N
a iable
3.2.3.3 Valida ion Measu emen s
While A/Ci-measu emen s ook place be ween 27
h
o July and 6
h
o Augus 1998, alida ion
measu emen s a ambien CO
2
-concen a ions we e pe o med on 7
h
and 8
h
o Augus 1998,
which we e wo o he d ies and wa mes days o ha yea in he S eige wald (Fig. 102).
Pho osyn hesis was measu ed wo o ou imes du ing he day o a ound 20 minu es on each
lea , al e na ing be ween di e en lea es o bo h ees, whe eby single poin s o he daily cou se
5
10
15
20
25
30
35
1/5/98 1/6/98
2/7/98
2/8/98
2/9/98
da e
empe a u e (°C)
0
2
4
6
8
10
12
14
16
18
VPD (hPa)
Daily mean empe a u e Daily mean VPD
8/8/98
7/8/98
Fig. 102:
Time cou se
o VPD and
empe a u e
o summe
1998. 7
h
and
8
h
o Augus
we e wo o
he d ies
days o his
yea .
Spa ial dis ibu ion o lea p ope ies in ee c owns
115
0
200
400
600
800
1000
1200
1400
1600
1800
2000
6:00
10:00
14:00
18:00
22:00
2:00 6:00
10:00
14:00
18:00
da e
PPFD (µmol/(m²*s))
0
5
10
15
20
25
30
35
40
empe a u e and VPD (°C, hPa)
hou ly mean PPFD hou ly mean ai empe a u e hou ly mean VPD
A
C
D
D
C
B
B
A
A
A
Fig. 103:
Cou se o clima e a iables du ing he measu emen pe iod, measu ed i e me es
abo e he loo on a nea by clea -cu . Ve ical lines indica e he a e age poin o ime o each
measu emen . The le e s abo e each line indica e he name o he lea .
10
15
20
25
30
35
40
06:00
12:00
18:00
00:00
06:00
12:00
18:00
ime
ai empe a u e (°C)
Ai empe a u e 5m abo e he loo Ai empe a u e in he canopy
0
10
20
30
40
50
60
70
06:00
12:00
18:00
00:00
06:00
12:00
18:00
ime
VPD (hPa)
VPD 5m abo e he loo VPD in he canopy
Fig. 104:
Cou se o ai empe a u e and VPD du ing 7
h
and 8
h
o Augus 1998. The measu ed
alues in he canopy we e eco ded in a heigh o 19 m abo e he loo on he sou h side o
beech G 12 and oak G 13, while he alues 5m abo e he loo we e measu ed abo e a clea -
cu .
ime
Spa ial dis ibu ion o lea p ope ies in ee c owns
116
o pho osyn hesis could be de e mined o each lea . The objec i e o measu e lea es wi h
di e en ni ogen con en and ligh exposi ion in he c owns o bo h species was only pa ly
eached, because lea es o oak G 13 we e e en in he mo ning hou s no esponding o ligh
and s oma a o mos measu ed oak lea es emained a low conduc ances du ing he whole day.
Less o he measu ed lea es o beech G 12 seemed o be a ec ed by d ough , and hei
ni ogen con en u ned ou o ange om 1.8 o 2.3 g/m². All beech lea es we e measu ed in
he same heigh abo e he loo (19m), wo lea es wi h 1.83 and 1.85 g N/m² ep esen a
posi ion shaded by o he lea es and close o he s em (lea es B and C), while lea es A and D
we e ully sun-exposed and had ni ogen con en s o 1.96 g/m² and 2.28 g/m².
Day ime o hese measu emen s and clima e condi ions a e depic ed in Fig. 103. PPFD, ai
empe a u e, and VPD we e measu ed i e me es abo e he loo on a nea by clea -cu .
Though hey di e om he condi ions a he posi ions o he lea es, hey may gi e insigh in o
he ela i e changes o clima e condi ions o e he wo days. The de ia ion om hese
condi ions a he posi ion o a lea in he canopy may be de i ed om he alida ion
measu emen s in he canopy (Fig. 104). Ai empe a u e was on a e age 4.2°C highe han 5m
abo e he loo and a maximum empe a u e di e ence o 9°C was eached in he a e noon.
VPD was on a e age 12.3 hPa highe wi h a maximum di e ence o 25 hPa. This may pa ly be
a ibu ed o he ac ha he clea -cu is su ounded by o es , which cas s a shadow in he ea ly
mo ning and in he la e e ening on he measu emen s a ion and may be he sou ce o coole
and mo e humid ai ha is exchanged e en a low wind eloci ies. On he o he hand i may
e lec he inc eased empe a u e o sun-exposed lea es and b anches ha a e sun-exposed
and poo ly cooled by wind and anspi a ion, hus wa ming up he su ounding ai . Be ween
12:00 and 16:00 MET, he a e age measu ed di e ence be ween empe a u e o lea es and ai
empe a u e was 1.1°C wi h a maximum alue o 3.1°C , measu ed a 13:51 MET on 8
h
o
Augus a a sun-exposed oak lea .
Inc easing i adiances we e unde hese ci cums ances gene ally accompanied by d ama ic
changes in VPD, which is p obably he eason o an unusual ligh esponse ha was obse ed
when he pho osyn hesis a es o all lea es a e iewed agains PPFD (Fig. 105). The
pho osyn hesis a es o beech lea es a abo e 1000µmol/(m²*s) PPFD we e all lowe han he
a e o lea A a 660µmol/(m²*s).
0
0.5
1
1.5
2
2.5
3
3.5
4
0 300 600 900 1200 1500
PPFD (µmol/(m²*s))
A (µmol/(m²*s))
lea A lea B lea C lea D
T = 39°C
VPD = 56.6 hPa
T = 33.2°C
VPD = 36.7 hPa
T = 36.2°C
VPD = 47.5 hPa
T = 35°C
VPD = 42.2 hPa
T = 29.1°C
VPD = 25.9 hPa
Fig. 105:
Ligh dependence o
assimila ion a es o ou
di e en lea es in he c own
o beech G 12. A e age lea
empe a u e and VPD a he
lea ’s posi ion du ing he
measu emen a e gi en o
he measu emen s unde high
PPFD. Ni ogen con en s o
he lea es we e A: 1.96 g/m²,
B: 1.83 g/m², C: 1.85 g/m²,
and D: 2.28 g/m²
Spa ial dis ibu ion o lea p ope ies in ee c owns
117
3.2.3.4 Model alida ion
The compa ison be ween modelled and measu ed alues o assimila ion (
A
) and s oma al
conduc ance (
g
sw
) e ealed a gene al o e es ima ion by he model: The di e ence be ween
modelled and measu ed alues was on a e age 0.52 µmol/(m²*s) and 1.89 mmol/(m²*s),
espec i ely, which co esponds o 34% and 9% o he mean o measu ed alues (mean
absolu e e o , M
AYER
&
B
UTLER
1993). The high pe cen age o
A
is a consequence o he
ela i ely low pho osyn hesis a es ha we e measu ed du ing he alida ion measu emen s, bu
i also e lec s he pa ly big de ia ions om he 1:1 line in Fig. 106. The ag eemen be ween
measu ed and modelled alues may adequa ely be desc ibed by he oo mean squa e e o
( , J
ANSSEN
&
H
EUBERGER
1995), which was 1.1 µmol/(m²*s) o
A
and 6.8 mmol/(m²*s)
o
g
sw
.
This o e es ima ion was al eady expec ed om hei unusual ligh esponse (Fig. 105), which
mus be seen wi h espec o he unusually d y condi ions o he lea es on he measu emen
days. The s onges obse ed impac o he low ela i e humidi y on lea pho osyn hesis was
ha oak lea es had pe manen ly low conduc ances, hus educing assimila ion o alues below
1µmol/(m²*s). Though only some beech lea es wi h ex emely low conduc ances we e obse ed
(da a no shown), he ques ion a ises, i hei s oma al eac ion o d ough has been assessed
as accu a ely as necessa y.
I has been shown ha s oma al ape u e o se e al species including beech is gene ally no
uni o m bu pa chy dis ibu ed o e he lea es (K
ÜPPERS ET AL
.
1999,
E
CKSTEIN
1997). The
phenomenon o s oma al pa chiness may lead o an o e es ima ion o pho osyn hesis a es,
when - like in he used model - only he a e age esponse o he s oma a is conside ed
(C
HEESEMAN
1991). This o e es ima ion is expec ed o be mos se e e in he e oba ic lea es,
whe e la e al gas di usion is es ic ed, which causes di e en
C
i
- alues in di e en pa s o he
lea (
VON
W
ILLERT ET AL
.
1995). In lea es o medi e anean plan s, bu also o Que cus pe aea,
Picea abies, and Abies alba, selec i e s oma al closu e is known o be a esponse o low ai
humidi y and may cause mo e o less big pa s o he lea o be excluded om pho osyn he ic
ac i i y, while o he pa s emain physiologically ac i e (E
PRON
&
D
REYER
1993,
B
EYSCHLAG ET
AL
.
1992,
B
EYSCHLAG ET AL
.
1994). S oma al pa chiness has also been shown o be ligh
induced (K
ÜPPERS ET AL
.
1999) and has been discussed as a mechanism o a oid
pho oinhibi ion (B
EYSCHLAG
&
E
CKSTEIN
1997).
$
1
n
⁄
ε
εε
ε
2
Fig. 106:
Modelled e sus measu ed alues o assimila ion a e
A
(le ) and s oma al conduc ance
o wa e apou
g
sw
( igh ). The line ep esen s he a io 1 be ween modelled and measu ed da a.
-1
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7
A
measu ed (µmol/(m²*s))
A
modelled (µmol/(m²*s))
lea A lea B
0
10
20
30
40
50
60
0 10 20 30
40
50
60
g
sw
measu ed (mmol/(m²*s))
g
sw
modelled (mmol/(m²*s))
lea C lea D
Spa ial dis ibu ion o lea p ope ies in ee c owns
118
Since Fagus syl a ica lea es ha e a sep a e lea ana omy due o skle enchyma ic issues
(“Skle enchymscheide”) a ound he lea eins, which causes he lea o be he e oba ic (
VON
W
ILLERT ET AL
.
1995), i seems o be plausible, ha he measu ed assimila ion a es and
conduc ances may be in luenced by s oma al pa chiness.
A simple es was pe o med o e alua e he e ec o inac i a ed lea pa s on he model
calcula ions: I was assumed ha he shaded lea es inside he c own (B and C) s ill beha e as
he model expec s, while he sun-exposed lea es (lea es A and D) a e pa ly inac i a ed. 30%
o hei lea a ea is assumed o be comple ely inac i a ed, while he es o he lea is
physiologically ac i e and beha es as he model expec s. Unde hese ci cums ances,
Vc
max
,
J
max
, and
R
d
ha e o be educed o 70% (B
EYSCHLAG
&
E
CKSTEIN
1997), while he a e age
sensi i i y o he s oma a o humidi y, assimila ion, and CO
2
(
g
ac
) emains unchanged.
The e ec o hese changes on he compa ison be ween model esul s and measu emen s is
shown in Fig. 107. The p e iously epo ed o e es ima ion o assimila ion (
A
) and conduc ance
(
g
sw
) disappea ed: The a e age di e ence be ween modelled and measu ed alues was 0.17
µmol/(m²*s) o
A
and -1.1 mmol/(m²*s) o
g
sw
, which is an o e es ima ion o 11% o he mean
o measu ed assimila ion a es and an unde es ima ion o 5% o he mean o measu ed
s oma al conduc ances. The oo mean squa e o e o s imp o ed o 0.48 µmol/(m²*s) and 4.9
mmol/(m²*s), when he inac i a ion o pa s o he sun-exposed lea es was conside ed his way.
This imp o emen in modelled assimila ion a es was a consequence o lowe ed assimila ion
a es (due o dec eased
Vc
max
and
J
max
) as well as o one inc eased assimila ion a e o lea A,
which is a ibu ed o he dec ease in
R
d
.
3.3 Summa y and discussion
The in es iga ions o ela i e i adiance abo e lea es along e ical lines con i m he gene al
alidi y o Bee ’s law in he in es iga ed beech c owns, hough de ia ions om a s ic ly
exponen ial dec ease we e also ound. These de ia ions we e mainly ound on he smalle ee,
whose ligh clima e is s ongly in luenced by he di e en heigh o neighbou ing ees and hey
may pa ly be a ibu ed o he e ec s o gaps be ween lea clouds. Addi ional de ia ions occu
in he lowes hi d o bo h c owns, whe e ela i e i adiances a e no as low as an exponen ial
app oxima ion would sugges .
The sca e in he ela ionship be ween ela i e i adiance and dis ance o apex allows one o
-1
0
1
2
3
4
5
6
7
01234567
A
measu ed (µmol/(m²*s))
A
modelled (µmol/(m²*s))
lea A lea B
0
10
20
30
40
50
60
0 10 20 30
40
50
60
g
sw
measu ed (mmol/(m²*s))
g
sw
modelled (mmol/(m²*s))
lea C lea D
Fig. 107:
Modelled e sus measu ed alues o
A
(le ) and
g
sw
( igh ) unde he condi ion ha he
pho osyn he ically ac i e lea a ea o he wo sun-exposed lea es is educed o 70%. The line
ep esen s he a io 1 be ween modelled and measu ed da a.
Spa ial dis ibu ion o lea p ope ies in ee c owns
119
dis inguish be ween de e minis ic and adap i e lea p ope ies: While heigh below apex may
no be expe ienced by a lea , i adiance is he mos impo an d i e o i s physiological ac i i y.
Hence, s ongly ligh dependen quan i ies appea o be a consequence o he en i onmen al
condi ions, while heigh dependen quan i ies may simply be de e mined by egula i ies o
g ow h.
In his sense, lea angle dis ibu ions in he canopies o beech ees we e ound o be
de e minis ic: The lea angle dis ibu ion o each heigh le el was an ellipsoidal dis ibu ion and
he single pa ame e k o hese dis ibu ions was linea ly dependen on heigh , while i did no
show a clea ela ionship o ela i e i adiance. Tha he linea dependence changes i s di ec ion
in he lowe hi d o he ee c owns may no be he esul o changing i adiance, because only
e y small di e ences in ela i e i adiance occu in his pa o he c own.
The heo y o PPFD ex inc ion in homogeneous canopies wi h ellipsoidal lea angle dis ibu ion
(C
AMPBELL
&
N
ORMAN
1989) would expec a unc ional ela ionship ha allows he calcula ion o
a cons an ex inc ion coe icien o Bee ’s law om an assumed cons an pa ame e o he
ellipsoidal dis ibu ion and he zeni h angle, bu he assump ion is no con i med by his
in es iga ion. The e ical g adien in pa ame e k o he ellipsoidal lea angle dis ibu ions mus
be conside ed in such calcula ions wi h he consequence o de ia ions om a s ic ly
exponen ial dec ease o i adiance wi h heigh . Thus, he de ia ions om Bee ’s law in beech
Bu45 and beech Bu38 a e pa ly a consequence o he de e minis ic change in lea angle
dis ibu ions.
Compa able esul s ha e been ound o a ma u e ee c own o Que cus obu (K
ULL ET AL
.
1999) and we e in e p e ed as ligh dependen . The low numbe o six da a poin s in his da a
se allows o d aw an exponen ial ela ionship on canopy ligh ansmi ance wi h ² = 0.89, bu
he e-e alua ion o hese da a shows, ha also a linea ela ionship o heigh exis s ( ² = 0.85,
da a no shown).
A de e minis ic and adap i e change o lea p ope ies was ound in he b anch angles o hei
abo e neighbou hood. This may be unde s ood on he assump ion o au onomous g ow h o
b anches owa ds a be e ligh si ua ion, which would esul in mo e ho izon al g ow h owa ds
he su ace o he canopy in he lowe pa and inc easing b anch angles wi h inc easing heigh ,
as was ound in he measu emen s. Since his adap i e g ow h o m was p obably mo e
success ul in e olu ion han o he s i may ha e become pa o a de e minis ic g ow h scheme
and may he e o e no be classi ied as adap i e o de e minis ic.
Wid h o lea space is a mo e impo an quan i y o ligh ansmission h ough he canopy han
wid h o lea blade. Simila ly o he pa ame e k o lea angle dis ibu ions i ollowed a quasi-
linea end and inc eased up o 7m below apex bu hen he di ec ion o he quasi-linea
ela ionship changed owa ds dec easing wid hs. This e ec con ibu es o he “be e han by
Bee ’s law expec ed” ela i e i adiances in he lowe hi d o he canopies since i inc eases he
ansmission h ough he lowes lea laye s. The much mo e sca e ed ela ionship be ween
wid h o lea blade and heigh indica es he ela i e i ele ance o his quan i y o ligh
abso p ion and ansmission.
Heigh o lea space was su p isingly no simply a consequence o lea bending by wid h
educ ion, bu had oge he wi h wid h o lea space a meaning o he ela ionship be ween ligh
in e cep ion and chemical composi ion o he lea , as may be de i ed om Fig. 74. Though i is
no easy o ind easons o his highly signi ican ela ionship, i shows ha lea bending is mo e
impo an o he in e cep ion o adia ion han could be expec ed. The simila ela ionship in Fig.
Spa ial dis ibu ion o lea p ope ies in ee c owns
120
73 desc ibes a ela ionship be ween lea space dimensions and ni ogen and ca bon
concen a ion o he lea biomass and may be in e p e ed in e ms o s uc u al equi emen s o
achie e a gi en lea o m.
Lea mass pe a ea was p ima ily ligh dependen and no as s ic ly heigh dependen , which
sugges s an adap a ion o en i onmen al condi ions. S and-speci ic di e ences a e ob ious
om Figs. 68 and 69, whe eas species-speci ic di e ences be ween oak G 13 and beech G 12
we e no de ec ed. Because nu ien and deposi ion si ua ion o bo h s ands we e simila , o he
g ow h condi ions like leng h o ege a ion pe iod, a e age humidi y, o a e age empe a u e
come in o ques ion as easons o s and-speci ic di e ences.
Though s and-speci ic di e ences exis , i is p obably no chance ha he maximum lea mass
pe a ea measu ed on beech G 12 was he highes alue when compa ed wi h published alues
om he las 110 yea s. The es ima ed a e age lea mass pe a ea o all h ee in es iga ed
beech ees was mo e han double ha o ma u e ees om 1945! The same was also ound o
oak G 13 when compa ed wi h da a om 1947. Fig. 108 shows ha he da a om he s udies
men ioned in able 5 desc ibe a mo e o less con inuous inc ease o maximum LMA- alues
du ing he las decades. Thus, he ex emely high maximum LMA- alue om beech G 12 is no
in e p e ed as a special quali y o he s and bu as pa o a gene al end owa ds inc easing
lea mass pe a ea in beech lea es in Eu ope du ing he las 110 yea s. A po en ial eason o
his end is he pa allel change in he en i onmen al si ua ion due o CO
2
-inc ease and ni ogen
deposi ions. Howe e , (P
ETERSON ET AL
. 1999) desc ibe only weak e ec s o high CO
2
on LMA
o lea es o beech seedlings, while o he seedlings we e mo e suscep ible o CO
2
-induced
inc eases o LMA.
The s ong ela ionship be ween ela i e i adiance and lea mass pe a ea ( ² = 0.88, Fig. 68)
was e en alid o he a ia ion o LMA in lea clouds. I co esponds o he simila ela ionship
be ween ela i e i adiance and ni ogen pe lea a ea (Fig. 75) and bo h oge he p o ide a
solid basis o up-scaling pu poses, since he a ia ion in mos pho osyn hesis pa ame e s has
been ound o be ni ogen dependen .
The measu ed lea ni ogen con en s we e pa ly e y high. While he ‘no mal ange’ o ni ogen
concen a ions pe d y weigh o lea es in adul o es s ands is 1.8 o 2.91% o d y weigh
(Que cus pe aea,
VAN DEN
B
URG
1990) and 1.8 o 2.78% o d y weigh (Fagus syl a ica,
VAN
DEN
B
URG
1990), a ange om 2.2 o 3.1% has been ound in beech lea es om he uppe hi d
o he c owns along a Eu opean ansec (B
AUER ET AL
.
1997). Thus, oak G 13 had lea es wi h
ex emely high ni ogen concen a ions, while beech G 12 had no mal o high concen a ions
Fig. 108:
Inc ease o maximum
and es ima ed a e age alues o
lea mass pe a ea o ma u e
beech ees du ing he las 30-110
yea s as de i ed om published
alues.
A e age alues o he newe
s udies since 1970 we e es ima ed
as he mean o minimum and
maximum alues, which was a
10% o e es ima ion in he case o
beech ees om he own ha es .
The ange o means om olde
whole ee ha es s is indica ed as
e o ba s.
0
20
40
60
80
100
120
140
1875 1900 1925 1950 1975 2000
in es iga ion yea
LMA (g/m²)
a e age LMA maximum LMA
Spa ial dis ibu ion o lea p ope ies in ee c owns
121
and he Buchenallee beeches had lea es wi h absolu ely no mal ni ogen concen a ions pe
d y weigh . These concen a ions combined wi h he ound high LMA- alues esul in he
p esen ed high lea ni ogen con en s pe a ea o he G oßebene ees. A di ec e ec o
ni ogen deposi ions on hese alues could no be ound due o he simila amoun o ni ogen
deposi ions in Buchenallee and G oßebene, al hough he C/N a io o he humus laye was
sligh ly highe in he Buchenallee s and.
The dependence o ca bon concen a ions on ela i e i adiance may be in e p e ed as a
consequence o inc easing lea mass pe a ea wi h ela i e i adiance, which leads in addi ion o
he cons uc ion o addi ional issue o inc eased equi emen s o mechanical s abili y o he
lea , hus equi ing mo e s uc u al ca bon. The p oduc ion o mo e excess ca bohyd a es o
s o age unde highe i adiance may no be he cause due o he low ca bon con en o
ca bohyd a es (N
IINEMETS
&
K
ULL
1998).
Ex emely high LMA- alues and ni ogen concen a ions co espond o ela i ely high
Vc
max
and
J
max
alues ha we e de i ed o oak and beech, when compa ed wi h p e iously published
da a: While mean alues o an o e iew o empe a e ha dwoods we e 47µmol/(m²*s) ±33(SD)
o
Vc
max
and 104 µmol/(m²*s) ±64(SD) o
J
max
(W
ULLSCHLEGER
1993), oak G 13 eached a
25°C maximum alues ha we e 100% and 81% highe .
Vc
max,298
and
J
max,298
o beech G 12
we e 21% and 15% highe han he mean alues o empe a e ha dwoods. The epo ed alues
o Fagus syl a ica seedlings a 20°C om T
AYLOR
&
D
OBSON
(1989) we e much lowe (11
µmol/(m²*s) and 35µmol/(m²*s)). Values o di e en Que cus species (Q. alba, Q. ub a, Q.
s ella a) om his o e iew we e also lowe and a ied be ween 18 and 51 µmol/(m²*s) (
Vc
max
)
and 29 and 127µmol/(m²*s) (
J
max
). Only D
REYER ET AL
. (2001) epo simila alues o hose
ound in his s udy om an expe imen wi h N- e ilised seedlings, ha we e 8% and 18% lowe
o Que cus pe aea and 16% and 7% highe o Fagus syl a ica han he alues measu ed on
he G oßebene ees and, hus, con i m his s udy.
The good ag eemen be ween he ni ogen dependence o
Vc
max
and
J
max
o bo h species wi h a
sa u a ing cu e (Fig. 89) may be in e p e ed as ni ogen sa u a ion o pho osyn hesis. Though a
ni ogen dependence o
Vc
max
and
J
max
o o he maximum pho osyn hesis a e
A
max
has also
been obse ed by o he in es iga o s (H
ARLEY ET AL
.
1992, N
IINEMETS
&
T
ENHUNEN
1997,
P
ORTÉ
&
L
OUSTEAU
1998,
L
E
R
OUX ET AL
.
1999,
M
EDLYN ET AL
.
1999,
K
AZDA ET AL
.
2000,
and
K
AKUBARI
2000
(pe sonal communica ion)), a sa u a ion has no ye been obse ed. This may ha e
se e al easons:
Fi s , ni ogen pe lea a ea in he men ioned s udies was o en in a lowe ange han ha o he
G oßebene ees (0.3 - 2.4 g/m², 0.4 - 1.1 g/m², 1.3 - 2.4 g/m², 0.9 - 3.0 g/m², 0.5 - 1.7 g/m², 1.3
- 2.8 g/m², and 0.5 - 2.5 g/m² in he o de o s udies men ioned), while oak G 13 eached 1.3 -
2.8 g/m² and beech G 12 eached 1.3 - 2.7 g/m². Thus, an e ec ha appea ed abo e 2.3 g/m²
may ha dly be ecognised in some o hese s udies.
Secondly, di e ences be ween ma u e ees and seedlings o annual plan s, ha we e used in
some s udies (H
ARLEY ET AL
.
1992,
M
EDLYN ET AL
.
1999) migh exis .
And hi dly, all s udies wi h maximum ni ogen con en s abo e 2.4 g/m² we e in e p e ed as
linea ela ionship, hough mo e o less clea endencies owa ds sa u a ion may be obse ed,
when he da a a e e-e alua ed. This is especially alid o he s udy wi h he highes ni ogen
con en s on Juglans egia (L
E
R
OUX ET AL
.
1999), whe e maximum
Vc
max
and
J
max
a e achie ed
a 2.4 g/m², while 3 mo e da a poin s up o 3 g/m² show lowe o e en high a es. The
A
max
-
da a o K
AZDA ET AL
. (2000) o Que cus obu (1.4 - 2.8 g/m²) a e pa ly sca e ed, bu nea ly
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
128
4.1.3 Pa ame e isa ion o STANDFLUX-SECTORS
4.1.3.1 Segmen a ion o lea cloud en eloping polyhed ons
Bounda ies o heigh laye s, sec o s, and sec ions as well as sec ion heigh anges ha e been
chosen in o de o cons uc compa men s wi h as homogeneous condi ions as possible,
he eby explici ly ep esen ing la ge gaps and inhomogenei y o he c own. This is bes
achie ed, when he esul ing compa men s a e ei he emp y o densely illed wi h lea es. As
less in e sec ions as necessa y we e equi ed on he o he hand o educe he numbe o
compa men s ha ha e o be pa ame e ised and calcula ed in he ligh -model.
Heigh laye bounda ies o beech G 12 ha e been chosen in an a e age e ical dis ance o
a ound 1m wi h de ia ions due o canopy gaps. Figs. 113 a and b show he chosen sec o
bounda ies in each heigh laye : 4-6 e ical in e sec ion planes cu he polyhed ons in each
laye in o 3 - 12 illed sec o s. The sec o bounda ies we e chosen such ha gaps in he c own
may well be ep esen ed by addi ional cylinde shaped bounda ies.
The 94 esul ing sec o s we e cu in o 410 sec ions using he op ical ep esen a ion o beech
G 12 in CRISTO (Fig. 114).
4.1.3.2 Segmen a ion o c own app oxima ing polyhed ons in he s and G oßebene
The con ex shape and g adien s o lea a ea densi y o lea angles in he c own could be
ep esen ed by di ision o he homogeneous ee c own app oxima ing polyhed ons in o eigh
45°-sec o s in he main azimu h di ec ions and ou heigh laye s pe sec o . The heigh laye
bounda ies o opposi e sec o s a e he same due o he segmen a ion scheme (Fig. 115):
20
20.1 20.220.320.4
20
20.2
20.4
20.6
24.5
24.6
24.7
20
20.1 20.220.320.4
19.6
19.8
20
20
20.2
20.4
20.6
24.6
24.8
25
19.6
19.8
20
1
5
4
3
2
Fig. 1
12:
The in e sec ion o a conca e polyhed on
wi h a e ical plane p oduces wo incomple e
polyhed ons (le side, he incomple e polyhed on
which was on he le side o he in e sec ion plane is
displayed below and has been u ned a ound). The
in e sec ion a ea is conca e. The Delaunay
iangula ion is based on he con ex hull o he
in e sec ion poin s and he e o e has o be co ec ed
by emo ing he indica ed iangle (below).
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
129
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
0 - 1.05m
4.1 - 5.25m
1.75 - 2.55m
2.95 - 4.1m
1.05 - 1.75m
2.55 - 2.95m
Fig. 113a:
Segmen a ion o heigh laye s o beech G 12 in o sec o s o he ligh -model
STANDFLUX-SECTORS. The heigh ange o each laye is gi en in m below apex.
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
130
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
-
5 0 5
Eas
H
m
L
-
5
0
5
No h
H
m
L
-
5
0
5
No h
H
m
L
5.25 - 6.15m
10.35 - 11.5m7.05 - 8.35m
9.35 - 10.35m
6.15 - 7.05m
8.35 - 9.35m
Fig. 113b:
Segmen a ion o heigh laye s o beech G 12 in o sec o s o he ligh -model
STANDFLUX-SECTORS. The heigh ange o each laye is gi en in m below apex.
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
131
Heigh bounda ies o opposi e sec o s (eas /wes , sou h/no h, no h-eas /sou h-wes , no h-
wes /sou h-eas ) we e d awn in he middle be ween neighbou s in heigh o 4 poin s: 2
measu ed ou e mos bo de poin s, c own-base and apex. The ho izon al ex ension o 45°-
sec o s was gi en by he maximum ex ension o a linea app oxima ion o he c own o m (Fig.
115). This kind o segmen a ion esul s in cylinde s, when ee c owns a e symme ical o he
s em and may ep esen bigge ca i ies along he shape o he canopy.
-
5 0 5
-
5
0
5
-
5
0
5
1 2 3 4 5 6
-
1
-
0.5
0.5
1
1 2 3 4 5 6
23
23.2
23.4
23.6
SSE-Sec o
Radius (m)
Heigh (m)
Radius (m)
Sec o wid h (m)
No h (m)
Eas (m)
1.75 - 2.55m
below apex
Fig. 114:
Di ision o he Sou h-Sou h-Eas -sec o o he hi d heigh laye o beech G 12 in o 7
sec ions, isually suppo ed by an op ical ep esen a ion ou ine in CRISTO. The SSE-sec o is
shown om abo e wi h cylinde -shaped sec ion bounda ies ( igh side, abo e) and om he wes
side, whe e he cylinde shaped sec ion bounda ies occu as e ical lines ( igh side, below). The
sec ion bounda ies we e chosen in a way ha allows o d aw he heigh bounda ies close o he
bo de o lea clouds, he eby enabling he ep esen a ion o la ge gaps.
Eas
Apex
C own base
Wes
Fig. 115:
Segmen a ion o ee c owns o he
G oßebene ees ( e ical c oss-sec ion h ough he
s em in wes -eas di ec ion). The do ed line ep esen s
he c oss-sec ion o a ee c own app oxima ing
polyhed on wi h i s co ne s a he wes e n and eas e n
bo de poin s o he c own as explained abo e. The
o iginal c own o m ( hickes line) o mos ees was
mo e con ex han he o m o he polyhed on, which is
conside ed in he segmen a ion.
Heigh bounda ies we e se in he middle be ween he
heigh s o measu ed poin s. The ho izon al ex ensions
o 45°-sec o s (g ey ields) a e gi en by he maxim um
ex ension o he c own app oxima ing polyhed on in
each speci ic laye and di ec ion.
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
132
4.1.3.3 Pa ame e de e mina ion o single compa men s
Each compa men o beech G 12 was au oma ically pa ame e ised based on lea a ea and
olume sha e o included lea cloud en eloping polyhed ons assuming olume ic homogenei y
o lea a ea densi y in he lea clouds.
The ela ionship be ween p ojec ed wood a ea and lea a ea o lea clouds om Fig. 56 was
employed o calcula e wood a ea densi y o each compa men . The s em was conside ed as a
cylinde wi h i s diame e in 1.35m heigh , ha eaches he middle heigh o he c own (19.75m
abo e he loo , 5.75m below apex) and builds he cen al compa men o he simula ed ee.
A e age lea angles o each compa men we e calcula ed based on he a e age heigh o he
compa men below apex using he ela ionships ound o beech Bu38 (Figs. 61 and 62), which
we e ecalcula ed o
in he uppe pa o he c own ( ange o 0 - 6.75m below apex) and o
in he lowe pa o he c own.
B anch angles in each compa men we e calcula ed using he linea ela ionship om Fig. 64.
T ansmissi i y and e lec ance we e assumed o equal 10% and 6%, using he alues o F
ALGE
(1997).
The lea a ea densi ies o ee sec o s om he su ounding s and we e de i ed om he heigh
dependence o lea a ea densi y as displayed in Fig. 24. All o he pa ame e s o he
su ounding ee c owns we e de i ed in he same manne as hose o beech G 12, because
speci ic da a o Que cus pe aea ees we e no a ailable. F om o me s udies i was expec ed
ha lea and b anch angles o neighbou ing ees play a mino ole o he ligh calcula ion and
ha he main impac o he di e en ee species is a esul o hei canopy o m.
4.1.4 Valida ion o STANDFLUX-SECTORS
4.1.4.1 Ligh and LMA simula ions
All ligh calcula ions a e based on PPFD measu emen s wi h a Li-Co quan um senso abo e a
clea -cu 1300m sou h-eas o he in es iga ed s and be ween 19.6.1998 and 2.7.1998
(measu emen s o M.
S
CHMIDT
). The ma ix poin s we e placed in a 10cm g id sp ead o e he
olume o a e ical p ojec ion o 6 lea cloud en eloping polyhed ons ha ep esen lea clouds
whose sap low was measu ed by M.
S
CHMIDT
(D
EPARTMENT OF PLANT ECOLOGY
,
UNPUBLISHED
) -
see Fig. 116. The olume o a e ical p ojec ion wi h he same heigh ex ension as he lea
cloud en eloping polyhed on was chosen because he segmen a ion in STANDFLUX-
SECTORS allows only e ical bo de s. Di ec and di use i adia ion we e calcula ed hou ly
(336 hou s) o each o 125058 ma ix poin s - 5460 poin s in he olume o lea cloud E and
33670 poin s in he olume o lea cloud B, o example. The maximum in eg a ed alue o e
336 hou s o di use plus di ec i adiance o all ma ix poin s om a lea cloud was exp essed
ela i e o he measu ed i adiance abo e he clea -cu as maximum ela i e i adiance o each
lea cloud. Assuming ha he si e o maximum ela i e i adiance in he olume o a lea cloud is
angle
= -
2.63
H
heigh belowapex
L
+
36.86
(51)
angle
=
4.162
H
heigh belowapex
L
-
8.92
(52)
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
133
he loca ion o i s lea es wi h maximum LMA, maximum LMA was calcula ed om maximum
ela i e i adiance based on he ela ionships in Fig. 75 adjus ed o beech G 12 (see below).
The in eg a ed a e age o all ma ix poin s in he uppe mos 10cm-laye o each lea cloud
p ojec ion was calcula ed as an es ima ion o he lea cloud’s ligh clima e and exp essed as
a e age ela i e i adiance abo e he lea cloud. Whole lea mass di ided by whole lea a ea o
each lea cloud (lea cloud LMA) was assumed o ollow he same ligh dependence as ha o
single lea es and was calcula ed based on he equa ions in Fig. 75 and an adjus men o beech
G 12 (see below).
4.1.5 Valida ion da a
Lea clouds A,C,D,E, and F we e ha es ed on 10
h
- 12
h
o Augus 1998 de e mining minimum
and maximum LMA o each o hei 1m b anch segmen s wi h 5 lea es om he p oximal pa
and 5 lea es om he dis al pa o he segmen . Each o hese lea clouds consis ed o 11-20
-
4
-
2
0
24 No h
H
m
L
15
20
25
Heigh
H
m
L
15
20
25
Heigh
H
m
L
-
4
-
2 0 2 4
Eas
H
m
L
-
4
-
2
0
2
4
No h
H
m
L
-
4
-
2
0
2
4
No h
H
m
L
-
4
-
2
0
2
4Eas
H
m
L
-
4
-
2
0
2
4No h
H
m
L
22
23
24
25
Heigh
H
m
L
22
23
24
25
Heigh
H
m
L
-
5
-
2.5 0 2.5 5
Eas
H
m
L
-
4
-
2
0
2
4
No h
H
m
L
-
4
-
2
0
2
4
No h
H
m
L
Fig. 116:
Sap low has been measu ed on 3 shade lea clouds (A, B, C) and 3 sun lea clouds (D,
E, F) o beech G 12 using he he mal dissipa ion me hod (G
RANIER
1985, 1987, measu emen s
o M. S
CHMIDT
, D
EP
.
OF
P
LANT
E
COLOGY
). The measu ed a e age anspi a ion a es o he 6 lea
clouds du ing 19.6.98 - 2.7.98 a e indica ed by in ensi y o hei colou . The le igu es show a
iew om abo e he ee (abo e) and om abo e he shade c own in heigh 20.25m (below). One
hidden sun-lea cloud may only be seen om wes side abo e ( igh abo e), while all o he lea
clouds a e isible om he wes side o he ee ( igh side, below). Lea cloud F was inse ed as
one o he wo las b anches di ec ly below he apex lea cloud ha is isible be ween he le e s
E and F.
20 30 40 50
T anspi a ion (
mol/(
m²*d))
A
FED
C
B
FED
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
134
1m b anch segmen s. Lea d y mass o he o en-d ied samples was sepa a ely di ided by he
a e age LMA o each segmen o calcula e he lea cloud’s lea a ea. Maximum LMA o he lea
clouds was he maximum LMA ha was measu ed on any lea sample om he lea cloud.
Lea cloud B los all i s lea es du ing he ege a ion pe iod 1998 by i sel and i s lea a ea du ing
he measu emen pe iod could only be es ima ed by eye o equal 2.25m². I s lea d y mass was
calcula ed based on allome ic ela ionships o 144.1 g. Maximum LMA o his lea cloud was no
de e mined.
4.2 Resul s
4.2.1 S and S uc u e
4.2.1.1 C own leng h and posi ion o oak and beech ees in he S eige wald s ands
Oak and beech ees in he s ands G oßebene and S eink euz had di e en c own leng hs wi h
espec o hei s ems’ basal a ea (Fig. 117): While c own leng h o beech ees in bo h s ands
inc eased wi h basal a ea o alues be ween 15 and 20m (G oßebene) o e en 30m
(S eink euz), oak ees had much sho e c owns (leng h a ound 10m) in bo h s ands.
In con as o his, mean heigh s (a e age o heigh s o apex and c own base) o he same
c owns we e highe o oaks han o beech ees in he same basal a ea class (Fig. 117, igh ).
The e o e, oaks in bo h s ands occupy spaces in he abo e pa o he s and and a e
unde ep esen ed in he lowe pa s (compa e Figs. A1 and A2 in he appendix), which is
con i med by he obse a ion o a high p opo ion o dead b anches in he lowe pa o oak
canopies (compa e chap e 1). Beech c owns on he o he hand o en p oduced lea es a he
close o he loo , some imes e en when he ees we e la ge and old.
0
5
10
15
20
25
30
35
0 1000 2000 3000 4000
basal a ea
(cm²)
c own leng h (m)
Oak S eink euz Beech S eink euz
Oak G oßebene Beech G oßebene
0
5
10
15
20
25
30
35
0 1000 2000
3000
4000
basal a ea
(cm²)
mean heigh (m)
Oak S eink euz
Beech S eink euz
Oak G oßebene
Beech G oßebene
Fig. 117:
Leng h o beech and oak canopies om he wo mixed s ands in he S eige wald (le )
and mean heigh (a e age o apex and c own base) o hese canopies ( igh ). The log-log-
ans o med da a we e app oxima ed wi h linea unc ions o show he gene al end o bo h
species. The i s a e indica ed in he e- ans o med da a by a (G oßebene) and hin
(S eink euz) lines.
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
135
4.2.2 LMA-calcula ions
4.2.2.1 Valida ion o he ligh model wi h he LMA/i adiance ela ionship
The ela ionship be ween ela i e i adiance and LMA om he Buchenallee lea es leads o an
unde es ima ion o 14.3g/m² (mean absolu e e o ), when combined wi h he maximum ela i e
i adiance simula ions o STANDFLUX-SECTORS o calcula e maximum LMA- alues o lea
clouds (Fig. 118). This unde es ima ion equals 13.5% o he mean o measu ed alues and is
mainly due o he ela i ely high maximum LMA- alues o he h ee sun lea clouds (D, E, F).
The oo mean squa e e o o his compa ison was 17.5 g/m².
The main eason o his unde es ima ion is he di e ence be ween maximum LMA- alues o
beech G 12 (128 g/m²) and he beech ees om he Buchenallee s and (110 g/m²). The e o e,
he equa ion o he app oxima ion line om he Buchenallee p oduces LMA- alues close o
110g/m² (104.6) a ela i e i adiance 1, which canno be adequa e o he G oßebene beech.
This indi idual o s and-speci ic di e ence may be conside ed by adjus ing he equa ion o he
LMA s. ela i e i adiance (
Q
el
) ela ionship o
he eby assuming he gene al shape o he cu e o be conse ed. Making his adjus men
leads o a smalle o e es ima ion (6.1g/m², = 5.9% o mean o measu ed alues) wi h a oo
mean squa e e o o 10.3 g/m², indica ing ha he co ec ed o mula leads o ele an
imp o emen s. Thus, equa ion (55) should be p e e ed due o i s adjus men o beech G 12
LMA da a.
4.2.2.2 Es ima ion o lea cloud LMA
An addi ional indica ion o he alidi y o LMA calcula ion based on STANDFLUX-SECTORS
and equa ion (55) was gained om he es ima ion o lea cloud LMA (Fig. 119). When lea cloud
Fig. 118: The dependence o LMA on
ela i e
i adiance has been measu ed on lea es o
beeches
Bu38 and Bu45 (le side, iangles) and he app oxima ion line equals y = 104.6
(( ela i e(
ela i e
i adiance)
0.377
, ² = 0.87. The measu ed maximum LMA o i e lea clouds in ela ion o maximum
simula ed ela i e i adiance abo e each lea cloud ( illed squa es) is compa ed o alida ion o
STANDFLUX-SECTORS. The maximum LMA o lea cloud B (open squa e) was no measu ed
and may be es ima ed o equal app oxima ely ha o lea cloud C.
When STANDFLUX-SECTORS and he adjus ed equa ion (eq. 53) a e used o model
maximum LMA o each o he 5 lea clouds, modelled s. measu ed maximum LMA a e compa ed
wi h an ² o 0.87 ( igh side), a mean absolu e e o o -6.1 g/m² (-5.9% o mean o measu ed
alues), and a oo mean squa e e o o 10.3 g/m².
0.2 0.4 0.6 0.8 1
ela i e i adiance
40
60
80
100
120
AML
H
g
ê
m
2
L
A C B EDF
y = 1.04x
R
2
= 0.87
0
30
60
90
120
150
0 30 60 90 120 150
maximum LMA measu ed (g/m²)
maximum LMA modelled (g/m²)
( ela i e
, (53)
LMA
=
128Q
el
0.377
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
136
LMA was es ima ed om a e aged ela i e i adiance abo e i , he eby ea ing he whole lea
cloud as a la ge lea , he mean absolu e e o was +1.5 g/m² (2% o mean o measu ed alues)
and he oo mean squa e e o equalled 10.28 g/m². Thus, lea cloud LMA could be modelled
wi h a simila accu acy as ha o single lea es using he same ela ionship. The e ec o he
used LMA s. ela i e i adiance ela ionship has been shown o be a he big when applied o
single lea da a and so is i s e ec in he lea cloud LMA calcula ion: Using he o iginal LMA s.
ela i e i adiance ela ionship om he Buchenallee ees (Fig. 75) u ns he sligh
o e es ima ion in o a s onge unde es ima ion (-9.9g/m² mean absolu e e o ) and inc eases
he oo mean squa e e o o 13.1 g/m². Bo h model compa isons (maximum LMA and lea
cloud LMA) show ha he ela i e i adiance simula ion wi h STANDFLUX-SECTORS may
p o ide a easonable basis o LMA calcula ions.
4.2.3 Compa ison o clima e and anspi a ion da a
4.2.3.1 Daily cou ses
Absolu e alues o clima e a iables abo e a clea -cu nea he BITÖK in es iga ion si e
S eink euz we e measu ed by G.
L
ISCHEID
, Uni e si y o Bay eu h and a e shown in Fig. 120.
The days du ing he wo weeks om 19.6. -2.7.1998 we e mos ly cloudy, hough no e y ainy:
Only he days 21.6., 22.6., and 25.6. had pe manen ly clea , sunny condi ions. These days we e
also he wa mes days, so ha he i s week was gene ally wa me han he second week. Main
ain e en s occu ed du ing he e ening o nigh hou s o 21.6., 26.6., and 27.6., while smalle
ain e en s ook place on 19.6., 23.6., 26.6., and 1.7.1998. The daily cou ses o VPD, PPFD,
and empe a u e we e mo e o less pa allel on he h ee clea sunny days, on 24.6., and du ing
A C B E D F
Fig. 119:
The LMA o lea clouds is gi en as hei whole lea mass di ided by hei lea a ea and
equals he a e age LMA o hei lea es. Lea cloud LMA has been se in ela ion o he a e age o
simula ed ela i e i adiance alues in all ma ix poin s di ec ly abo e he lea cloud (le side, illed
squa es). Equa ion (55) is plo ed in he same g aph o compa ison. E o ba s ep esen he ange
o LMA alues occu ing in each lea cloud apa om lea cloud B, whe e his was no measu ed.
Modelled lea cloud LMA on he base o a e aged simula ed ela i e i adiance and he co ec ed
LMA s. ela i e i adiance ela ionship is well co ela ed o he measu ed lea cloud LMA alues
( igh side, ²=0.87). The model sligh ly o e es ima es lea cloud LMA alues by 1.5 g/m² (mean
absolu e e o ), equalling 2% o he mean o measu ed alues. The oo mean squa e e o was
10.28g/m².
0 0.2 0.4 0.6 0.8 1
ela i e i adiance
0
20
40
60
80
100
120
ael duolc AML
H
g
ê
m
2
L
y = 0.99x
R
2
= 0.87
0
30
60
90
120
0 30 60 90 120
lea cloud LMA measu ed (g/m²)
lea cloud LMA modelled (g/m²)
(53)
Applica ion o a 3D-ligh model o he 3D- ep esen a ion o beech G 12 and i s s and
137
26.6. - 29.6.. Opposi e endencies in he cou ses o VPD and PPFD we e due o empe a u e
and we e obse ed on 19.6., 24.6., 30.6., and 2.7..
Some obse a ions may be summa ised abou he cou se o anspi a ion a es o sun and
shade lea clouds du ing he in es iga ion pe iod:
• The daily cou se o anspi a ion a es o sun lea clouds was gene ally smoo he han ha
o shade lea clouds: while sun lea clouds D, E, and F had wide and ound daily peaks o
anspi a ion (Fig. 122), he peaks in he cou se o anspi a ion a es om shade lea clouds
A, B, and C we e mo e poin ed (Fig. 121).
• When a con inuous inc ease in i adiance was gi en, anspi a ion a es o lea cloud D and
he o he sun lea clouds s eeply inc eased ea ly in he mo ning and hen app oached o a
maximum alue a noon. Discon inui ies in he i adiance inc ease wi h pa allel
discon inui ies o he usual VPD inc ease in he mo ning - p obably due o dew all o smalle
ain e en s - caused a dec ease in anspi a ion a es e en i i adiances jus s ayed
cons an , which may be obse ed on 19.6., 22.6., and 26.6. on all sun and shade lea
clouds.
• The shade lea clouds o en did no ye s a o anspi e on hese days, when such a
discon inui y occu ed, which may indica e ha a c i ical ligh o VPD le el was no ye
eached be o e ha ime. Thei la e s a is one eason o he mo e p onounced peaks in
anspi a ion.
• Ano he eason was ha he cou se o PPFD abo e hese lea clouds consis s also o
poin ed peaks, he eby inducing high i adiances o a sho ime.
Fig. 120:
Synopsis o clima e a iables du ing he in es iga ion pe iod 19.6.1998 - 2.7.1998. While
empe a u e and VPD a e scaled on he le y-axis, PPFD (in mmol/(m²*s)
!
) and p ecipi a ion a e
scaled on he igh side. All measu emen s we e pe o med a he BITÖK in es iga ion si e
S eink euz, 5m abo e a clea -cu app oxima ely 1300m in dis ance o he G oßebene s and by
G.
L
ISCHEID
, Uni e si y o Bay eu h.
0
5
10
15
20
25
30
19/06/98
21/06/98
23/06/98
25/06/98
27/06/98
29/06/98
01/07/98
03/07/98
Da e
empe a u e (°C) | VPD(hPa)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
PPFD (mmol/(m²*s)) | p ecipi a ion (mm)
empe a u e (°C) VPD (kPa)
p ecipi a ion (mm)
PPFD (mmol/(m²*s))
In eg a ing discussion
144
A e y high coe icien o de e mina ion ( ²=0.98) was ound be ween lea mass and he sum o
anspi ed wa e o each lea cloud du ing he in es iga ion pe iod (Fig. 126). Fu he
in es iga ions a e necessa y o analyse, i his use ul ela ionship is also alid o o he
condi ions o e en o he ees and species. Fu he conclusions may be de i ed wi h his model
combina ion and his da a base since addi ional sap low measu emen s on b anches and s em
o oak G 13, as well as on s ems o o he ees in he s and we e no ye e alua ed.
5 In eg a ing discussion
5.1 Cha ac e is ics o oak and beech in he s and G oßebene
Many cha ac e is ics o oak and beech in he G oßebene s and ha e been collec ed on di e en
le els o o ganisa ion and i seems wo hwhile o compa e hese p ope ies species-o ien ed o
e alua e i hey d aw a easonable pic u e o ecological specializa ion o he species in hei
s and, hough gene al conclusions can no be d awn due o he low numbe o in es iga ed
ees. Table 9 summa ises he clea es di e ences be ween he species ound in his s udy.
Cha ac e is ics Fagus syl a ica Que cus pe aea
Na u al eg ow h in he mixed
s ands
Yes (Fig. 3) No (Fig. 3)
Heigh posi ion o c owns in
he s and
All heigh posi ions (Fig. 117) Uppe mos 8-12m o he s and
(Figs. 19b, 117 )
C own leng h Long (Fig. 117) Sho (Fig. 117)
P opo ion o dead b anches
and boughs in he lowe c own
Low (Figs. 7, 10) High (Figs. 7, 10)
G ow h pa e n o b anches Mo e de e minis ic (Figs. 9, 33, 34, 46)
Less de e minis ic (Figs. 9, 33, 34, 46)
C own cons uc ion Fan-shaped opening owa ds he
su ace
(Figs. 16, 35, 37,40,41)
Mo e i egula (Figs. 16, 35, 37)
C own shape Con ex bo de s, g ea es diame e in
he lowe pa , long and pea -shaped
(Figs. 18, 26)
Conca e bo de s, g ea es diame e in he
uppe pa , sho and s awbe y-shaped
(Figs. 18, 26)
Di ec ions o s eng hened
de elopmen
One main di ec ion, no owa ds a
neighbou ing ee (Figs. 43, 47, 51)
Se e al di ec ions owa ds neighbou ing
ees (Figs. 43, 47, 51)
To al lea a ea densi y Lowe (Table 5) Highe (Table 5)
Lea a ea densi ies in he
c own
Highes lea a ea densi y in he
uppe mos me e o he c own,
con inuously low densi ies in he lowe
hal (Fig. 23)
Highes lea a ea densi y 2-3m below he
apex, dec easing owa ds he apex and
he bo om (Fig. 23)
Sel -shading Less se e e (Figs. 31, 32) S onge (Figs. 31, 32)
Lea pho osyn hesis capaci ies
Low (Figs. 83-86, 89) High (Figs. 83-86, 89)
S oma al sensi i i y (
g ac
) High in shade lea es, low in sun
lea es (Fig. 98)
High in medium sun lea es, lowe in
uppe mos sun lea es, low in shade
lea es (Fig. 98)
In eg a ing discussion
145
Oak c owns in he s ands G oßebene and S eink euz occupy only he mos sun-exposed
posi ions in he s and, bu a e no able o each his posi ion by na u al eg ow h in he dense
s and. This is in acco dance wi h he o es managemen p ac ice o sa e oaks om compe i ion
o neighbou ing beeches by elling hese beech ees. Once in he op o he canopy, he
s a egy o oak seems o be he occupa ion o high olumes in he uppe egion, p oducing a
high o e all lea a ea densi y and he eby shading compe ing species below ha egion - and
i sel . The s onge sel -shading o oak may be one eason o i s sho c own wi h se e al dead
boughs in he lowe pa . This may also be seen as a specializa ion o oak in he use o only
high ligh posi ions.
The occupa ion o high olumes in he uppe pa o he canopy is isible in he oak’s c own
shape. I is open o specula ion i he conca e (= ugged) and app oxima ely s awbe y-shaped
c own o m is a consequence o a gene al mul i-di ec ional de elopmen o oaks owa ds
compe ing ees. Such a g ow h eac ion o he spa ial si ua ion would equi e lexibili y in he
g ow h pa e n o b anches, which is appa en ly be e achie ed in oak han in beech. The
in es men in o high pho osyn hesis capaci ies makes sense o a ee in a high-ligh
en i onmen . Tha s oma al sensi i i y (
g ac
) is high in medium sun lea es indica es ha oak
allowed high anspi a ion especially o hese lea es, e en when hei CO
2
use e iciency
(assimila ion pe CO
2
-concen a ion) and ela i e humidi y we e no e y high. The isk o high
wa e losses in sun lea es is mo e easonable when lea es ha e high pho osyn hesis
capaci ies and may p o ide he esou ces o expansi e g ow h in he egion o hese lea es.
The lowe anspi a ion suppo o shade lea es p obably causes hem o die ea lie and again
indica es he consequen adap a ion o oak o high ligh en i onmen s.
Beech on he o he hand was gene ally mo e ca e ully a oiding high wa e losses due o low
coe icien s o s oma al sensi i i y. Only he lowes shade lea es we e allowed o ha e high
conduc ances when CO
2
use e iciency and ela i e humidi y we e no e y high. This seems
no as haza dous as allowing i o sun lea es, because ela i e humidi y in he lowes pa o he
c own is usually highe han in he uppe pa . Bu i includes he possibili y o useless
anspi a ion due o he lowe chance o su icien ly high assimila ion gains o shade lea es.
While beech, hus, seems o ha e suppo ed shade lea es in allowing hem high anspi a ion
a es, oak mainly suppo ed medium sun lea es in hei wa e consump ion.
The wa e suppo o he lowes shade lea es may help hem o achie e a posi i e CO
2
-
balance and his could be one ac o ha allows beech o main ain high amoun s o shade lea
biomass and o de elop ex ensi e shade c owns. The gene ally spa ing equipmen o beech
lea es conce ning pho osyn hesis capaci ies may addi ionally be ad an ageous in main aining
he high numbe o shade lea es. Ano he ac o o he su i al o shade lea es may be ound
in he an-shaped o ma ion o beech lea clouds owa ds he canopy su ace which p obably
imp o es he ligh si ua ion o shade lea es. The mo e de e minis ic g ow h o b anches o a
beech ee, i s unidi ec ional de elopmen , and he conse ed con ex c own p ojec ion may
indica e ha a p e- o med in e nal o ganisa ion scheme could be ele an o he CO
2
-balance
o shade lea es. A s eng hened de elopmen owa ds se e al di ec ions in o de o compe e
wi h ho izon al neighbou s would ha dly be possible, i a p e- o med pa e n is o be conse ed,
while a gene al d i owa ds he mos p omising gap in he su ounding s and seems o be
possible, especially since he an-shaped o ma ion o lea clouds appea s o be gap-o ien ed
anyway. A gene ally and mainly in he shade c own lowe lea a ea densi y also imp o es he
condi ions o shade lea es due o less sel -shading.
In eg a ing discussion
146
All hese ac o s oge he wi h he a he low lea pho osyn hesis capaci ies o beech may be
seen as adap a ions o shade condi ions ha a e necessa y o a ee wi h a la ge shade c own.
The heigh dis ibu ion o lea a ea densi ies in beech shows ha i may on he o he hand also
be e y compe i i e wi h ega d o he mos sunny posi ions in he s and. I s ela i e success in
a mixed s and o oak and beech may, hus, be explained wi h wo complemen a y, de ensi e
and agg essi e s a egies: A ligh -o ien ed o ganisa ion o he shade c own can make he whole
ee ela i ely insensible o shading by a neighbou ing ee, which is suppo ed by a g ow h
pa e n o he sun c own ha a oids sel -shading by occupying only small olumes. This could
allow i o su i e in he shade o o he ees o yea s and e en p o ide he esou ces o he
g ow h o he sun c own. The concen a ion o highes amoun s o lea a ea in he uppe mos
laye o he sun c own on he o he hand can assu e high shading e iciency o his pa o he
c own, because shadow cas o his laye is ele an o he bigges possible pa o he
su ounding s and canopy. This may on he long un imp o e he condi ions o he whole ee
by e ec i ely educing g ow h a es o compe i o s (L
EUSCHNER
2001). The double s a egy o
beech may also be exp essed in i s c own shape ha is mo e clea ly sepa a ed in sun c own
and shade c own han ha o he oak.
Thus, he cha ac e is ics ound on single ees o bo h species i in o a easonable desc ip ion
o hei ecological specializa ion, hough hey can no p o e he gene al alidi y o his concep .
5.2 Applica ion o Bee ’s law
The desc ip ion o ligh p o iles in he s and wi h Bee ’s law was in a i s app oxima ion
applicable o he beech c owns in he Buchenallee s and (Figs. 58, 59). Howe e , wo
assump ions o Bee ’s law ha e been shown o be iola ed in hese c owns:
• The lea angle dis ibu ion was no cons an h oughou he canopies o beeches Bu45 and
Bu38 (Figs. 62, 63). The equency o s eep inclina ions ha allow mo e ligh o pene a e a
lea laye dec eased om he apex o a dep h o a ound 6 m (Bu38) o 7 m (Bu45) in he
c own, whe e ho izon al inclina ions we e mos abundan . The equency o s eep
inclina ions inc eased again om he e owa ds deepe pa s o he c own. The ex inc ion
coe icien o Bee ’s law was, he e o e, a iable along a e ical g adien h ough he c own.
• Lea a ea densi y o c own laye s was no cons an and exhibi ed he gene al pa e n o 2-3
“peak”-laye s wi h highe lea a ea densi y ha we e sepa a ed by laye s wi h lowe lea a ea
densi y (Figs. 21-23). The peak-laye s o lea a ea densi y o beech Bu38 we e in a heigh o
3 m and 6 m below apex. The a ia ion o lea a ea densi y has o be included in he
calcula ion o ligh p o iles acco ding o Bee ’s law.
The signi icance o he laye 6 - 7 m below apex o bo h c owns o he ligh p o ile is
inc eased h ough he obse ed end in wid h o lea space and in angles o lea cloud
planes:
While wid h o lea blade did no show a clea dependence on i adiance o heigh below
apex, he e ec i e wid h o lea space was wides in his laye and dec eased om he e
owa ds bo h ends o he c own (Fig. 66). This end inc eases he e ec i e lea a ea densi y
(based on p ojec ed lea a ea ins ead o lea a ea) o he laye 6 - 7 m below apex ela i e o
he o he laye s.
The angles o lea clouds we e nea ly ho izon al in he laye 6 - 7m below apex and became
nega i e below ha laye , while hey we e posi i e abo e (Figs. 33 and 35). Thus, ligh
ex inc ion on a lea cloud basis is maximum in his laye .
In eg a ing discussion
147
The consequence o he lea angle a iabili y o ligh p o iles would be a s onge ligh g adien
han calcula ed wi h Bee ’s law (using cons an coe icien s) in he uppe 6 - 7 m o he c own
and a less s ong dec ease in ligh in ensi y below ha heigh . Lea a ea densi y a iabili y
would s eng hen his e ec in he uppe 3 m o he c own o beech Bu38 and in he lowes pa
below 7 m below apex, while i would damp he dec ease o ligh in ensi y in he c own pa
be ween 3 m and 7 m below apex.
Thus, a s onge ligh g adien is o be expec ed in he uppe 3 m o he beech c own Bu38 and
a weake ligh g adien in he lowes pa below 7 m below he apex. This expec a ion is
con i med in a compa ison wi h he measu ed ela i e i adiance in beech Bu38 (Fig. 58).
Rela i e i adiance in he uppe 3 m dec eased s onge han an exponen ial i based on he
assump ion o cons an coe icien s in Bee ’s law, hough his app oxima ion is o ma hema ical
easons s onge o ien ed on he ela i e high i adiance alues han on he low i adiance
alues. This i is no able o ep oduce he “ oo high” ela i e i adiance alues in he c own pa
below 6 m below he apex, indica ing ha no exponen ial unc ion may adequa ely exp ess bo h
pa s. The high coe icien o de e mina ion does no eally conside he de ia ion in he lowe
c own pa , which is big in ela i e uni s bu small in absolu e uni s. This migh be he eason o
i o be o e looked in compa able in es iga ions. A “ oo high” ela i e i adiance in he lowes
c own pa was also obse ed on he da a o beech Bu45 (Figs. 58, 59).
The “ oo high” ela i e i adiance alues in he lowes c own pa o hese bo h ees may be
in e p e ed as ano he adap a ion o beech ees o he low ligh en i onmen ha hey p oduce
hemsel es o hei shade c own. The ligh dis ibu ion inside he c owns becomes mo e
homogeneous h ough he desc ibed a ia ion in angles and densi y o oliage elemen s, which
lowe ed ela i e i adiance in he abo e c own pa and inc eased i in he lowe shade c own.
5.3 Lea mass pe a ea (LMA)
The epo ed LMA- alues o sun lea es o beech om di e en o igins (Table 5, Fig. 108) show
an inc easing long- e m end since 1968, while i seemingly was lowes a ound 1943. Since he
posi ion o he in es iga ed lea es is no men ioned in he s udy o B
URGER
(1945), he appa en
ela i e dec ease o a e age LMA be ween 1891 and 1943 could also be due o he di e en
exposi ion and ligh si ua ion o he in es iga ed lea es (compa e Figs. 68 and 69), hough ees
ha e been elled in he ex ensi e s udies o B
URGER
and a di e en ia ion be ween sun and
shade lea es was gene ally made. This could lead - apa om di e en s and condi ions - o an
a i icial LMA-dec ease, because his in es iga ion is he only da a poin be ween 1891 and
1968.
Bu e en he newe li e a u e since 1970 shows an inc easing long- e m end. The lowes LMA-
alues (40 - 60 g/m²) o sun lea es in his pe iod we e measu ed 1968 om a owe in 26m
heigh on he ou e mos lea es o he sun c own o beech “B68” in he IBP s and Solling
(in e na ional biological p og am,
S
CHULZE
1970). Though di e ences be ween s ands like
al i ude, exposi ion, deposi ions, a e age empe a u e, o o he di e ences may be in luen ial,
hese di e ences would no necessa ily lead o he compiled gene al inc ease o LMA o sun
lea es. S and-speci ic di e ences a e no ele an in he case o beech B68 in he Solling
p ojec , whose sun lea es in 26m we e in es iga ed again in he pe iod 1986 - 1988 and hen
had LMA- alues o 80 o 110 g/m² (S
CHULTE
1992).
Since he inc ease in LMA- alues o beech B68 (Solling) goes along wi h he gene al end
ound on da a om a ious o igin, i becomes likely ha his di e ence shows a ealis ic
In eg a ing discussion
148
s uc u al change in his c own ha occu ed appa en ly also on o he beech ees in Eu ope.
The newes compa ed alues ( hose o his s udy) we e also he highes LMA- alues. This could
mean ha LMA o sun lea es o beech ees is s ill inc easing and easons as well as
consequences o his end need o be assessed, hough addi ional LMA-da a ha e o be
e alua ed o assu e he alidi y o he LMA- end.
A mosphe ic CO
2
, clima e change, o ni ogen deposi ions come in o ques ion as po en ial
causes o physiological changes ha lead o an inc ease o LMA o sun lea es o beech. While
e ec s o clima e change a e unlikely o be de ec able in clima e da a be ween 1968 and 1987,
ni ogen deposi ion o o es s was inc easing be ween 1968 and 1991 and dec easing in he
la es yea s since 1991 (Le el II - p og am, BML 1997). Yea ly a e ages o a mosphe ic CO
2
concen a ion as measu ed a Mauna Loa (Hawaii) con inuously and s ill exponen ially
inc eased om he yea s 1968 (323 µmol/mol) o 1987 (349 µmol/mol) and 1999 (368 µmol/mol)
(K
EELING
&
W
HORF
2000), which was he s onges inc ease o his quan i y since 1800 when i
s a ed o inc ease om a s able p e-indus ial alue o 270 ppm (S
ALISBURY
&
R
OSS
1992). The
ime cou se o CO
2
-concen a ions co esponds bes wi h ha o he compiled LMA-inc ease,
since he LMA- end does no show a dec ease.
A consequence o he LMA-inc ease in sun lea es o beech ees could be a highe sink
s eng h o sun c owns o beech o CO
2
du ing he ege a ion pe iod, since mo e assimila es
a e needed o build up hicke lea es. This poin needs u he in es iga ion due o a possible
opposi e end in he allome ic ela ionship be ween lea a ea and basal a ea o ees, which
was lowe in all ha es ed ees han in he eg essions based on o me in es iga ions (Fig. 14),
so ha ees e en ually jus o ganise he same lea mass o a smalle a ea. Lowe lea a ea o
beech ees and o he o es species is also epo ed om public o es y s udies in Ge many
(HMU 2000). The combina ion o bo h ends could po en ially lead o a highe wa e use
e iciency due o educed anspi a ion a es (as a consequence o educed lea a ea) and
inc eased ligh a ailabili y in he shade c own.
Though he deposi ion a es a e dec easing since 1991, i can no be excluded ha he LMA-
inc ease is due o high ni ogen deposi ion, because ni ogen up ake by he ees migh s ill be
high. The obse ed ni ogen sa u a ion o pho osyn hesis capaci ies o lea es o oak and beech
indica es ha he in es iga ed sun lea es con ained mo e ni ogen han hey need o
pho osyn hesis (Fig. 89).
5.4 Implica ions o gas-exchange modelling
I has been shown ha homogenei y is no gi en on he le el o ee c owns and, he e o e, on
he le el o s ands. Thus, he assump ion o homogeneous condi ions in smalle o bigge
compa men s (big lea es, laye s, o 3D-compa men s) is gene ally iola ed o some ex en ,
hough many e ec s o small scale inhomogenei y a e p obably neu alized on la ge scales.
The la e seemed also o be alid o he dec ease o ela i e i adiance wi h dep h in he
canopy, since he gene al shape o he unc ion o Bee ’s law was in a i s app oxima ion
con i med by ish-eye pho os in beech canopies (Figs. 58, 59) and he ound de ia ions we e
small in absolu e uni s. Ne e heless hese small de ia ions need conside a ion e en in la ge
scale models since gas-exchange models a e e y sensi i e o changes in ligh p o iles and he
de ia ions a e likely o ep esen a gene al phenomenon.
An indica ion o he ele ance o hese de ia ions is gi en by he applica ion o laye -o ien ed
gas-exchange models in ne ecosys em exchange (NEE) calcula ions o beech s ands: Such
In eg a ing discussion
149
models o en use a ia ions o Bee ’s law o desc ibe he ligh g adien in s and canopies and
hen ypically conside he lea es in he lowe hal o beech canopies as CO
2
-sou ces on each
day o he ege a ion pe iod due o ligh in ensi ies below he ligh compensa ion poin o hese
lea es (own simula ions wi h he laye model GASFLUX (S
ALA
&
T
ENHUNEN
1996), da a no
shown). This is a consequence o he use o an exponen ial unc ion ha ine i ably app oaches
ze o in he lowe pa o he c own when i is i ed o ep esen he highe ligh alues in he
uppe canopy. I is no impossible bu unlikely ha beech ees can a o d his was e o
esou ces.
The ound de ia ions om Bee ’s law a e likely o ep esen gene al p ope ies o beech canopy
s uc u e ha ha e an equalizing e ec on he ligh p o ile, he eby inducing a s eepe g adien
in he uppe canopy and a much lowe g adien in he lowe pa o he c own. Thus, he heigh
dependen lea angle dis ibu ions and na u ally laye ed lea a ea densi y dis ibu ions (see 5.2.)
should be conside ed in laye ed gas-exchange models.
Mos gas-exchange models do no conside he lea es as ben and, he e o e, p obably
conside abou 20% oo much lea a ea in he c owns a leas o beech, since p ojec ed lea
a ea is he ele an quan i y o ligh ansmission and abso p ion. Since bending has been
ound o be heigh dependen (Fig. 66), he a ea educ ion may easily be included in gas-
exchange models.
Mo e complex e alua ions would be necessa y o in es iga e he e ec o lea cloud inclina ions
and hei o ien a ion owa ds he canopy su ace, which p obably imp o es he use o e lec ed
and ansmi ed adia ion in he shade c owns o beech due o a an-shaped o ma ion owa ds
he canopy su ace. Such an e ec would again imp o e he ligh si ua ion o shade lea es. This
could a ec gas-exchange calcula ions especially when lea es a e we and hei e lec ance
may each alues abo e 50% (dependen on he angle o inciden ligh , G
ATES
1980). No all
models o gas-exchange conside he changes in ansmission and e lec ance occu ing on we
lea es.
A ine-scale 3D- ep esen a ion o o es s ands migh be he mos accu a e way o ep esen
inhomogenei y o s ands and o e alua e small-scale e ec s, bu i is no sui able o an
applica ion o la ge a eas. This si ua ion may change o some ex en due o up-scaling
ela ionships like hose o he ni ogen dependen lea gas exchange model, which may use he
s uc u e dependen ligh clima e o lea es o he de i a ion o ni ogen pe lea a ea ( ² ≥ 0.87,
Fig. 75) and he eby yields a comple ely pa ame e ised lea gas-exchange model ha is alid o
his spa ial si ua ion. Thus, an in eg a ed and e y de ailed model o s and gas-exchange esul s
om he combina ion o he ni ogen dependen lea gas exchange model wi h STANDFLUX-
SECTORS o any o he 3D ligh model and es ima ions o soil and wood espi a ion (F
LECK ET
AL
.
2001).
Such an in eg a ed 3D model may be alida ed on many di e en scales using ligh
measu emen s, LMA-dis ibu ions, lea ni ogen con en s, pho osyn hesis measu emen s on
lea es and b anches, sap low measu emen s on b anches and s ems, o e en eddy
measu emen s, when ex ensi e s uc u e in o ma ion has been ga he ed and soil espi a ion
has been es ima ed. I hus may imp o e he eliabili y o s and gas exchange models in a way
ha allows up-scaling om sap low measu emen s on ees o s and gas-exchange along
canopy s uc u es and could he eby be use ul o p o ide eliable es ima ions o gas-exchange
o s ands, whe e eddy measu emen s can no be pe o med ( o example s ands in
In eg a ing discussion
150
moun ainous egions). Reliable es ima ions o gas-exchange in hese egions could be use ul o
alida e egional NEE calcula ions.
The da a se om he G oßebene s and combines sap low measu emen s on s ems o beech
G 12, oak G 13, o he ee s ems, and on b anches om oak G 13 wi h a de ailed s uc u e
desc ip ion ha allows u he es ing o an in eg a ed model. Au oma ed me hods o s uc u e
measu emen a e unde de elopmen (K
OCH
&
R
EIDELSTÜRZ
1998,
L
EFSKY ET AL
.
2000,
T
ANAKA
ET AL
.
1998) and migh soon p o ide he necessa y s uc u e in o ma ion o la ge scale
applica ions o a eliable in eg a ed 3D model.
Summa y
151
6 Summa y
The gas exchange o mixed o es s ands is - due o hei high p opo ion wi hin he o es ed
a ea - an impo an quan i y o he es ima ion o CO
2
- and wa e balances on la ge scales, bu
di icul o e i y. This hesis assumes ha a undamen ally new si ua ion in e ms o heo y o
cogni ion has eme ged in his ield o esea ch due o he apid de elopmen o compu e -based
da a p ocessing in ecen yea s, since i allows o he i s ime he explici conside a ion o
spa ial he e ogenei y in p ocess-o ien ed models. This p o ides he oppo uni y o alida e
models ac oss spa ial scales, he eby imp o ing he eliabili y o o es s and gas-exchange
calcula ions. The bo le-neck o his kind o e alua ion is no da a-p ocessing o simula ion, bu
a he he co-o dina ed eco ding o all in o ma ion ele an o he mul iple e i ica ion o a
p ocess-o ien ed model o mixed s and gas-exchange.
The con ibu ion o his in es iga ion lies in he comp ehensi e ep esen a ion and compa a i e
ine-scale analysis o he spa ially explici desc ip ion o ees in a 120 yea old mixed s and o
oak and beech in he S eige wald. The 3-dimensional s uc u e desc ip ion is associa ed wi h
he measu ed a iabili y o pho osyn hesis pa ame e s and alida ion da a on di e en spa ial
scales. These da a a e discussed oge he wi h da a om compa ed s ands. Sub ou ines o an
in eg a ing up-scaling model we e imp o ed and e i ied wi h measu emen s.
The canopy s uc u es o wo beech ees and one oak we e simula ed in an op ically
con ollable way based on b anch-o ien ed ha es s, b anch-o ien ed geode ic measu emen s
(Figs. 4, 5), and allome ic ela ionships (Figs. 9, 14). The newly de eloped p og am CRISTO
o spa ial analysis is based on he ep esen a ion o b anches and hei appending lea biomass
(lea clouds) as polyhed ons and enables he calcula ion o heigh p o iles o lea a ea densi y in
laye s o 1m heigh (Fig. 23). A endency o build single laye s wi h e y high lea a ea densi ies
was de ec able. The canopies consis ed o 2-3 na u al laye s o lea es, which con as ed wi h
he op ical imp ession o he ees (Figs. 20, 21). The p opo ion o gaps be ween lea clouds
was highe han 80% in mos laye s o all h ee ees (Fig. 25).
Measu ed species-speci ic di e ences be ween he c own shapes o 186 oak and beech ees
we e also ound in he cha ac e is ic canopy shapes o he h ee in es iga ed ees ha we e
de i ed om maximum ho izon al ex ensions o laye s o 1m heigh (Fig. 26). S onge sel -
shading o he oak ee was a consequence o i s di e en canopy shape (Figs. 30 - 32).
Lea clouds o bo h beech ees showed s iking simila i ies in hei main g ow h di ec ions (Figs.
35, 37, 39 - 41), which a ec ed ligh pene a ion in o he canopy by he a ia ion o lea cloud
angles owa ds he ho izon (Fig. 33) and hei o ien a ion owa ds he canopy su ace (Fig. 41).
The lea a ea densi y o lea clouds was la gely independen o any o 8 in es iga ed c own
s uc u e pa ame e s (Fig. 55).
The ligh p o iles o beech c owns we e measu ed using ish-eye-pho os and we e shown o
di e om Bee ’s law (Fig. 58) in a way ha may be explained by he a ia ion o lea a ea
densi y and ex inc ion coe icien , he la e o which was due o he a iabili y o lea angles. A
heigh dependen a ia ion o lea angle equency dis ibu ions o beech was ound ha could
be desc ibed by single-pa ame ic ellipsoidal dis ibu ion unc ions (Figs. 60, 62).
While he ela ionship be ween heigh o ligh and he wid h o lea blades was sca e ed, he
p ojec ed wid h o he beech lea es (which conside s lea bending) was shown o be heigh and
ligh dependen (Fig. 66). Clea ligh dependencies we e also es ablished o lea mass pe a ea
Summa y
152
(LMA, Fig. 69), lea ca bon concen a ion (Fig. 71), and a ea- ela ed lea ni ogen con en (Fig.
75).
Occasionally e y high LMA- alues and a ea- ela ed ni ogen con en s ha e been measu ed.
LMA- alues om he S eige wald we e he highes when compa ed o li e a u e da a om 110
yea s and i in o a gene al endency o inc easing LMA- alues o sun lea es o beech.
The p og am RACCIA has been de eloped o he au oma ed de i a ion o pho osyn hesis
capaci ies (
J
max
, Vc
max
) om
A/C
i
-cu es ha we e measu ed on oak and beech in he
S eige wald. The p og am is based on he H
ARLEY
/T
ENHUNEN
(1991) - model and was e i ied
using chlo ophyll luo escence measu emen s (Fig. 78).
J
max
and
Vc
max
we e shown o inc ease
wi h ni ogen pe lea a ea up o a ce ain ni ogen le el, whe e lea pho osyn hesis becomes
appa en ly ni ogen sa u a ed (Fig. 89). Ni ogen sa u a ion o pho osyn hesis capaci ies and
measu ed empe a u e dependencies we e conside ed in he de elopmen o a ni ogen
dependen model o lea pho osyn hesis (Fig. 97) ha educes he numbe o necessa y
pa ame e s by mo e han 50% (Table 7). The model alida ion was based on measu ed daily
cou ses and p o ided e idence o he po en ial e ec s o s oma al pa chiness (Figs. 106, 107).
The applica ion o he highly esol ing 3D ligh model STANDFLUX-SECTORS o he geome ic
ep esen a ion o a beech ee and i s su ounding s and in he S eige wald was enabled by he
de elopmen o a segmen a ion and pa ame e isa ion ou ine in he amewo k o CRISTO (Fig.
112 - 114). A beech c own was segmen ed in o 410 pa ame e ised homogeneous
compa men s. The ligh model was e i ied using he ligh dependence o LMA (Fig. 118, 119).
A s onge ligh sensi i i y o anspi a ion was de i ed o shade lea clouds o beech and was
a ibu ed o he highe sensi i i y o s oma a o shade lea es o CO
2
use e iciency and ela i e
humidi y (
g ac
) (Fig. 98, 125).
To als o anspi a ion o e 14 days o he in es iga ed b anches we e well co ela ed o he
calcula ed quan um sum abo e he lea clouds and o hei lea biomass (Fig. 126).
The esul s p o ide a easonable pic u e o he ecological specializa ion o oak and beech in a
mixed s and: While beech has a s a egy o cope wi h a shady en i onmen ha keeps a high
amoun o shade lea biomass ali e and educes he ee’s suscep ibili y o shadow cas om
compe ing ees, oak secu es a once achie ed posi ion in he uppe canopy by expansi e
g ow h o he uppe c own laye s and is la gely specialized in he mo e e icien pho osyn hesis
o sun lea es.
Implica ions o gas-exchange models a e de i ed om hei high sensi i i y o he used ligh
p o ile. The use o exponen ial unc ions o he calcula ion o ligh p o iles may lead o s ong
unde es ima ions o CO
2
-up ake when he heigh dependence o lea angle dis ibu ions and he
mul i-laye ed canopy s uc u e a e no adequa ely conside ed in he equa ion. Ligh abso bing
lea a ea is o e es ima ed in mos gas-exchange models by a ound 20%, because lea bending
is mos ly no conside ed. The high e lec ance o we lea es should be conside ed due o he
po en ially highe i adiance in shade c owns unde hese condi ions.
The model sub ou ines p esen ed in his hesis may be combined o an in eg a ed 3D model
ha may imp o e eliabili y o gas-exchange models, when u he alida ion on di e en scales
is pe o med. This is possible on addi ional da a om he G oßebene s and. The in eg a ed
model migh be e y use ul in combina ion wi h au oma ed s uc u e measu emen s in u u e
alida ion o NEE calcula ions in moun ainous egions, whe e eddy measu emen s a e mo e
unce ain.
Zusammen assung
153
7 Zusammen assung
De Gaswechsel on Waldmischbes änden is au g und ih es hohen Flächenan eils eine
bedeu ende, abe nu schwe zu e i izie ende G öße in übe egionalen Be echnungen on
CO
2
- und Wasse aus ausch. Die o liegende A bei geh da on aus, dass du ch die asche
En wicklung de compu e ges ü z en Da en e a bei ung de le z en Jah e eine neue
e kenn nis heo e ische Si ua ion in diesem Fo schungsgebie einge e en is , die e s mals die
explizi e Be ücksich igung äumliche He e ogeni ä in p ozesso ien ie en Modellen e möglich .
Hie du ch we den skalenübe g ei ende Validie ungsmöglichkei en e ö ne , die
Gaswechselbe echnungen au Bes andesebene e lässliche machen können. Engpässe
bes ehen du ch diese En wicklung wenige in de Da en e a bei ung und Simula ion als in de
koo dinie en E assung alle ele an en In o ma ionen, die zu meh achen Ve i izie ung eines
p ozesso ien ie en Modells des Mischbes andsgaswechsels no wendig sind.
De Bei ag diese A bei bes eh in de um assenden Da s ellung und e gleichenden
einskaligen Analyse de äumlich explizi en Besch eibung on Bäumen eines 120-jäh igen
Eichen-Buchen-Mischbes ands im S eige wald. Die zu Simula ionszwecken e we ba e 3-
dimensionale S uk u besch eibung is mi de gemessenen äumlichen Va iabili ä on
Pho osyn hesepa ame e n und mi Validie ungsda en au e schiedenen äumlichen Ebenen
e knüp . Diese Da en we den zusammen mi Ve gleichsbes änden disku ie . Sub ou inen
eines skalenübe g ei enden Modells wu den wei e en wickel und anhand on Messda en
übe p ü .
De K onenau bau on zwei Buchen und eine Eiche wu de au de Basis as bezogene E n en,
as bezogene geodä ische Messungen (Abb. 4, 5) und allome ische Beziehungen (Abb. 9,
14) op isch e i izie ba simulie . Die äumliche Analyse mi dem da ü en wickel en P og amm
CRISTO be uh au de Rep äsen a ion on Äs en mi ih e anhängenden Bla masse
(Bla wolken) als Polyede und e möglich du ch Ze legung de K onen in 1m-Schich en die
Be echnung on Höhenp o ilen de Bla lächendich e (Abb. 23). Hie an wa eine Tendenz zu
Bildung einzelne seh dich e Schich en e kennba . De K onenau bau e wies sich en gegen
dem äuße en Anschein als na ü liche weise meh schich ig hinsich lich de Ve eilung on
Bla lächen (Abb. 20, 21). De An eil bla eie Räume auße halb de Bla wolken lag in den
meis en Höhenschich en alle d ei Bäume übe 80% (Abb. 25).
Gemessene a spezi ische Un e schiede in de K onen o m on 186 Buchen und Eichen
spiegeln sich in den cha ak e is ischen K onen o men de d ei Un e suchungsbäume wide , die
aus de maximalen ho izon alen Ausdehnung on Höhenschich en abgelei e wu den (Abb. 26).
Als Konsequenz de un e schiedlichen K onen o m wu de eine höhe e Selbs bescha ung de
Eichenk one im Ve gleich zu den Buchen e mi el (Abb. 30-32).
Bla wolken in beiden Buchenk onen wiesen au ällige Übe eins immungen hinsich lich ih e
Wuchs ich ung au (Abb. 35, 37, 39 - 41), die sich au g und des höhenabhängigen
Bla wolkenwinkels (Abb. 33) und de S ellung zu K onenobe läche (Abb. 41) au die
Lich e eilung in de K one auswi ken. Die Bla lächendich e on Bla wolken wa wei gehend
unabhängig on 8 un e such en S uk u pa ame e n (Abb. 55).
Die mi els Fish-eye-Fo og a ie e s ell en Lich p o ile on Buchenk onen zeig en Abweichungen
om Lambe -Bee ’schen Gese z (Abb. 58), die sich aus de on Bla s ellungswinkeln
e u sach en Va iabili ä des Ex ink ionskoe izien en und de inhomogenen
Bla lächendich en e eilung e klä en lassen. Es konn e eine höhenabhängige Va ia ion de
