Senso s 2013, 13, 12698-12743; doi:10.3390/s130912698
senso s
ISSN 1424-8220
www.mdpi.com/jou nal/senso s
A icle
C op Biome ic Maps: The Key o P edic ion
F ancisco Ro i a-Más * and Ve ónica Sáiz-Rubio
Ag icul u al Robo ics Labo a o y, Uni e sidad Poli écnica de Valencia, Camino de Ve a s/n 3F,
Valencia 46022, Spain; E-Mail: [email p o ec ed]
* Au ho o whom co espondence should be add essed; E-Mail: o i a@dm a.up .es;
Tel.: +34-963-877-291; Fax: +34-963-877-299.
Recei ed: 24 June 2013; in e ised o m: 6 Sep embe 2013 / Accep ed: 17 Sep embe 2013 /
Published: 23 Sep embe 2013
Abs ac : The sus ainabili y o ag icul u al p oduc ion in he wen y- i s cen u y, bo h in
indus ialized and de eloping coun ies, bene i s om he in eg a ion o a m managemen
wi h in o ma ion echnology such ha indi idual plan s, ows, o sub ields may be
endowed wi h a singula “iden i y.” This app oach app oxima es he na u e o ag icul u al
p ocesses o he enginee ing o indus ial p ocesses. In o de o cope wi h he as a iabili y
o na u e and he unce ain ies o ag icul u al p oduc ion, he concep o c op biome ics is
de ined as he scien i ic analysis o ag icul u al obse a ions con ined o spaces o educed
dimensions and known posi ion wi h he pu pose o building p edic ion models. This a icle
de elops he idea o c op biome ics by se ing i s p inciples, discussing he selec ion and
quan iza ion o biome ic ai s, and analyzing he ma hema ical ela ionships among measu ed
and p edic ed ai s. C op biome ic maps we e applied o he case o a wine-p oduc ion
ineya d, in which ege a ion amoun , ela i e al i ude in he ield, soil compac ion, be y size,
g ape yield, juice pH, and g ape suga con en we e selec ed as biome ic ai s. The enological
po en ial o g apes was assessed wi h a quali y-index map de ined as a combina ion o
i a able acidi y, suga con en , and mus pH. P edic ion models o yield and quali y we e
de eloped o high and low esolu ion maps, showing he g ea po en ial o c op biome ic
maps as a s a egic ool o ineya d g owe s as well as o c op manage s in gene al, due
o he wide e sa ili y o he me hodology p oposed.
Keywo ds: p ecision a ming; global posi ioning; yield p edic ion; c op moni o ing;
ineya d managemen ; p ecision i icul u e; ag icul u al obo ics; in o ma ion echnology
OPEN ACCESS
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1. In oduc ion
S uc u al c ises and widesp ead p oblems ha e his o ically been c ea i e d i e s o echnology and
inno a i e solu ions, some o hem epheme al bu e y o en induce s o philosophical ans o ma ions
and e en e olu iona y ou comes. In 2006, millions o beehi es wo ldwide emp ied ou as honeybees
mys e iously disappea ed, pu ing a isk nea ly 100 c ops ha equi e pollina ion [1]. The e may be no
easy emedy o he colony collapse diso de ; many suspec s so a bu no con ic ions ye , and solu ions
may equi e aking be e ca e o he en i onmen and making long- e m changes o ag icul u al
p ac ices. This kind o s uc u al changes in some hing as old as ag icul u e will likely equi e
he ad en o new echnology in pa allel wi h op imized da a-based decision-making. Clima e change,
popula ion g ow h, and inc easingly sca ce esou ces a e pu ing ag icul u e unde p essu e [2]. Nume ous
No h Ame ican special y c ops ( ui s, ege ables, ee nu s, d ied ui s, be ies, and nu se y c ops),
ep esen ing i y pe cen o he o al alue o US c op p oduc ion, a e acing g owing p essu es ha
h ea en hei long- e m iabili y [3]. Un o una ely, he implemen a ion o echnologies based on p ecision
ag icul u e in p ac ical a ming has slowed in ecen yea s on global scale compa ed o he mid- and
la e- 1990s [4]. In ac , un il he la e-1970s signi ican sums o money we e in es ed in mechaniza ion,
obo ics, and au oma ion esea ch and de elopmen in he US, bu since ha ime, ede al suppo o
imp o e a m p oduc ion h ough enhanced machine sys em has g ea ly declined, and he e o e he
esea ch in as uc u e o ag icul u al au oma ion has de e io a ed signi ican ly o e he pas qua e
cen u y [3]. The easons o his decay may es in he di icul y o quan i y bene i s [5], he complexi y o
managing la ge amoun s o da a, and he in icacies o using ad anced echnology de eloped by academic
o esea ch ins i u ions and hi ing he ma ke in an incomple e o m [4].
In 2007, he US Depa men o Ag icul u e (USDA), he Na ional Science Founda ion (NSF), and
he Na ional Ae onau ics and Space Adminis a ion (NASA), join ly sponso ed a wo kshop o ind he
undamen al esea ch and echnology needs o special y c ops indus ies. P ecision ag icul u e
applica ions o yield mapping, yield and nu ien p edic ion, da a managemen , decision suppo
sys ems, and diagnos ic ools un high among he key needs iden i ied [3]. As a ma e o ac , cu en
a me s a e uelling a g owing ma ke o imaging sys ems whe e pho onics is being used o gauge
plan s ess [2], and op ics manu ac u e s con i m he mo e om desc ip i e echniques owa ds
quan i a i e imaging, as machine ision acili a es objec i e measu emen s [6]. E en some hing as
uncon en ional as space wea he o ecas o sa elli e-based applica ions may soon become common as
p ecision ag icul u e p ac i ione s ecoun how hey depend on eliable access o high-accu acy global
posi ioning [7]. Moni o ing and mapping c ops is, a e all, like plane a y explo a ions whe e u h ul
pe cep ion and accu a e posi ioning mus be e icien ly synch onized, some hing ha NASA’s
Cu iosi y o e achie es wi h no ewe han 17 came as onboa d.
Mapping o moni o ing and decision-making necessa ily in ol es sensing, measu ing, p ocessing,
and eal- ime posi ioning. C op inspec ion is la gely done manually, bu humans ha e a h eshold
beyond which hey canno see, and ce ain disease condi ions a e impossible o de ec [2]. The mal
imaging, o example, has been success ully used o moni o ee canopy in ci us, p o iding a eco d
o he empo al a ia ion o ege a ion ha allowed he de ec ion o he ui s, and he e o e an
es ima ion o yield, al hough he lack o geog aphical e e ences p e en ed he gene al assemblage o
maps [8]. Gauging c op yield mon hs be o e he ha es is no easy, hanks o a hos o elemen s ha
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can impac g ow h and o en a e ou o a a me ’s hands [2]. A eliable and low-cos me hod o
gene a ing yield maps o ci us has been by localizing hand-ha es ed con aine s o o anges wi h a
GPS eco de , acknowledging yield a ia ions wi hin a ci us block, and allowing su ace in e pola ion
o yield da a. This s aigh o wa d echnique is applicable o o he c ops wi h li le o no modi ica ion,
al hough i does no map he yield o indi idual ees as desi ed by many g owe s [9]. In addi ion o
yield, he e a e many o he pa ame e s o moni o be o e ha es ing. Field-based, high- h oughpu
pheno yping seeks o implemen in o ma ion echnologies o cha ac e ize he g ow h esponse o
gene ically di e se plan popula ions in he ield, which p ac ically hinges on he a ailabili y o a
p oximal sensing sys em [10]. In ac , al hough emo e sensing pionee ed many applica ions o
p ecision a ming —especially ela ed o hype spec al ision–, esolu ion, g owe con ollabili y, and
he need o high upda e a es p ac ically unbalance he scale in a o o p oximal sensing. Ci us
g o es, o ins ance, a e ae ially pho og aphed in Flo ida a leas once e e y wo yea s o axa ion
pu poses [9], which ob iously is insu icien o moni o c op pa ame e s along he season. Being
Flo ida ci us one o he mos echnology-d i en c ops in he Wo ld, o he egions will ce ainly ha e a
much lowe upda e a e, and hus emo e sensing canno o e he deg ee o lexibili y equi ed by mos
o medium and small g owe s in a global scale. Ye , sa elli e image y may esul help ul o alida e
g ound da a, as he weed mapping sys em de eloped o measu e weed in ensi y and dis ibu ion in a
co on ield [11]. G ound measu emen s we e ca ied ou wi h he Weedseeke senso module in
combina ion wi h a GPS, and la e compa ed o emo ely sensed image y in o de o p edic c op
canopy co e age, which e en ually was mos closely co ela ed wi h he No malized Di e ence
Vege a ion Index (NDVI) plus weed in ensi y a a coe icien o a ia ion 0.2 ≤ R2 ≤ 0.53. The majo i y
o he es ima ions, measu emen s, and p edic ions made be o e ha es ing a e o ien ed o enhance
mechanized o obo ized ha es ing, whe e expe sys ems somehow y o emula e and subs i u e he
skills o picke s. The Eu opean Commission- unded DASH p ojec has de eloped a wo king p o o ype
o an aspa agus-picking obo , cu en ly being eadied o ma ke , and imaging sys ems a e being
in oduced in Eu ope o so g apes acco ding o he quali y o he wine hey will p oduce [2]. Once
so ed, he g apes may be collec ed by an au onomous machine such as he Japanese mul ipu pose
obo capable o ha es ing, be y hinning, sp aying, and bagging o he g ape bunches [12].
The main objec i e o he esea ch epo ed in his a icle is he es ablishmen o a amewo k o
ake he ich ideas and concep s behind p ecision ag icul u e and in o ma ion echnology o he eali y
o o cha ds, p oposing a p ocedu e o handling la ge amoun s o da a gene a ed by ad anced sys ems
bu a ge ed o use s wi h no high- ech educa ion. A s ep-by-s ep applica ion o his me hodology o
such a high- alue c op as wine-making ineya ds illus a es he key s ages o he me hod and
demons a es he eal po en ial o c op biome ic maps.
2. Concep ual Founda ion o C op Biome ics (CB)
The economic and social eali y ound in indus ialized coun ies, whe e p oduc ion cos s in
ag icul u e keep g owing while p oduce main ain e e -dec easing p izes, bene i s om he e icien
applica ion o in o ma ion echnologies (IT) o ag icul u al p oduc ion, in such a way ha speci ic
in o ma ion a plan , ow, o subplo scale can be a ained. This idea app oxima es he na u e
o ag icul u al p ocesses o he mechanics o indus ial p ocesses in wha could be pe cei ed as a
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na u aliza ion o con ol sys em. Howe e , ag icul u al p oduc ion p ocesses a e u he challenged by
an eno mous a iabili y and he unce ain ies o wo king ou doo s in uncon olled en i onmen s. The
scien i ic and sys ema ic s udy o ag icul u al p ocesses is ins umen al o inc ease he quali y o
p oduc s, enhance managemen e iciency, and de elop p edic ion models. P edic ion, in pa icula , is
c ucial o he igh managemen o many c ops. Wi h he pu pose o se ing he g ound o p edic ion
in ag icul u al p oduc ion, he e m c op biome ics is de ined as he scien i ic analysis o ield
obse a ions con ined o spaces o educed dimensions and known ime-in a ian posi ion. The
p ac ical ealiza ion o his idea in ol es deciding which physiological –o biome ic– iden i ie s mus
be selec ed o each applica ion, he op imal size o each indi idual space holding he magni ude o a
biome ic ai , he way o quan ize ai s and p edic ed pa ame e s ela ed o yield and quali y, he
ma hema ical o s a is ical ela ionship among ai s and p edic ions, and he scope o p edic i e
models based upon he biome y o speci ic c ops.
The idea o c op biome ics is no a away om he concep o human biome ics, om which i
ge s he inspi a ion. Fo he human case, i can be de ined as he au oma ed ecogni ion o people ia
dis inc i e ana omical and beha io al ai s [13]. Ne e heless, al hough bo h e ms ocus on biological
ai s, and he e o e bo h need o make decisions on he basis o impe ec measu es, he ope a ional
philosophy is ema kably dis inc . The mos signi ican di e ences a e he ollowing: i s , he pu pose o
c op biome ics is p edic ing he ou comes o ag icul u al p ocesses, assuming ha hese models make
p edic ions acco ding o impe ec measu emen s; secondly, unlike human biome ic ai s, c op ai s a e
no unique, a he , i will be he opposi e as many plan s o he same ield will sha e simila o iden ical
ege a i e igo , p oduc ion yield, o quali y indices; hi dly, plan biome ic ai s change wi h ime o e
he season, which is jus he opposi e o he immu abili y o , say, inge p in s; ou hly, senso s o c op
biome ics a e no always low cos ; and inally, he holis ic concep o c op biome ics includes ac o s ha
a ec he plan bu a e no a pa o i , as wa e a ailabili y, sun adia ion, o soil esis ance ound by he
oo s, ye all can be enclosed in he same wo king si e and be s a is ically ela ed.
The p ac ical implemen a ion o he concep o c op biome ics equi es making impo an
echnical decisions:
1. The selec ion o speci ic c op biome ic ai s (CB- ai s) depending on each pa icula
applica ion, c op, o manage ial need. A abula o ma o he app op ia eness o po en ial
ai s may be help ul a his s age o he p ocess. The de ini e se o ai s will always emain
opened o new addi ions o he emo al o poo pe o mance ai s. Table 1 p o ides an
example o po en ial CB- ai s o ineya ds.
2. The es ablishmen o a p o ocol o he measu emen o ai s, speci ying he p ocedu e, he
senso s, and he ime and equency o he es ima ions. Such issues as he sensi i i y o he
measu emen s in ela ion o he size o he cells mus be add essed along he p ocess.
3. The design o he g id, de e mining mesh esolu ion and cell size.
4. The me hod o analyzing he ai s, e i ying hei s a is ical signi icance and es ablishing
co ela ions among ai s o p opose p edic ion models wi h a known le el o unce ain y.
The ineya d case enounced in Table 1 will be u he de eloped o alida e he idea o c op
biome ics. I ea u es a i-le el di ision o ai s gi en by soil le el, plan le el, and p oduce le el
ai s. Figu e 1 schema ically shows he mul i-le el compa ibili y o maps ha is necessa y o es ablish
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p edic ion models. Table 1 lis s some o he c op ai s o in e es o he ineya d applica ion.
Howe e , no all o hem ended up being help ul, and by con as , u u e ai s no conside ed he e will
p obably play a key ole in he de ini ion o u u e models. Al e na i e pa ame e s such as soil
conduc i i y, ni ogen con en in lea , sun adia ion, lea empe a u e, canopy densi y, phenolic s a us
o g apes, o e en lase -based ca bon dioxide abso bed and emi ed by oliage in he pho osyn hesis [14]
migh be ins umen al o he e icien managemen o he ineya d o he u u e.
Table 1. Selec ion o c op biome ic ai s o wine p oduc ion ineya ds.
Vigo Al i ude Soil Res. Yield Acidi y Suga Be y Size pH
Cos Medium Low Medium High High High High High
Au oma ion High High Low Low Low Low Low Low
Reliabili y Medium High Low High High High High High
Speed High High Medium Low Low Low Low Low
Co ela ion High High Low High High Low Low High
In e es High Low Low High High High Low High
A ea samp. High High Low H-L Low Low Low Low
Figu e 1. T i-le el di ision o ai s o ineya d managemen .
3. Selec ion o CB-T ai s
The goal behind he idea o c op biome ics is o p o ide an IT-based managemen ool o mode n
ag icul u e based on wo co e p inciples: he cons uc ion o compa ible use - iendly c op maps, and
he ep esen a ion o key in o ma ion o he g owe h ough CB- ai s. As a esul , in o de o build

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use ul maps, CB- ai s mus be ca e ully chosen acco ding o pa icula ield needs. Howe e , in
addi ion o hei in e es o he g owe , he e exis o he impo an ac o s ha need o be aken in o
accoun oo, as he lis o p ope ies conside ed in Table 1. The ideal si ua ion occu s when a ai is
essen ial o he g owe , i can be measu ed au oma ically, quickly, a low cos , and is well co ela ed
wi h he pa ame e s being p edic ed, usually yield and quali y. Fo he pa icula case o wine g apes,
he quali y o he u u e wine is e en mo e in e es ing han he quali y o g apes a ha es ing ime, and
consequen ly, he p edic i e na u e behind he concep o c op biome ics esul s in a s a egic ool o
wine make s. Un o una ely, he majo i y o CB- ai s do no comply wi h hese ideal p ope ies, bu
his should no be a cause o ejec ion; a he , any CB- ai ha adds alue o he solu ion mus be
conside ed, e en i he senso s cu en ly a ailable a e o e p ized o di icul o au oma e. Fo hcoming
esea ch will e en ually pallia e hese incon eniences and by he ime una o dable senso s become
accessible, he al eady exis ing amewo k o p ocess hei da a will esul in highe accu acy o he
models and smoo he in eg a ion o he senso s. This could be he case, o example, o he
assessmen o soil compac ion and he measu emen o g ape juice acidi y in Table 1; hus a , bo h
ai s a e manually sampled, bu u u e scou ing obo s may be capable o conduc ing sampling
missions au onomously, inc easing he amoun o da a while educing ime and cos . Whene e his
becomes a ailable, he elabo a ion o hese pa icula maps will be as e and be e , bu he p ocedu e
o in eg a e da a in he p edic i e models will be exac ly he same ollowed wi h he
manually-gene a ed maps, as all maps –new and old– a e designed o be compa ible among hem and
wi h he es o he maps included in he model. As a ma e o ac , he de elopmen o au oma ed
measu ing sys ems is in con inuous expansion, wi h new solu ions o soil sampling and phenolic
ma u i y eaching eal ime pe o mance.
As shown in Table 1, p ope ies o di e en na u e mus be con on ed o candida e CB- ai s be o e
choosing he se o ai s associa ed o a gi en applica ion, as wha is in e es ing o a c op may no be
app op ia e o o he s. Vege a i e igo , o example, is known o in luence g ape yield and wine
quali y, bu i will p obably esul in a poo indica o o p edic yield in an o ange g o e. As a esul ,
each pa icula applica ion equi es a cus omized CB- ai s able. In he cons uc ion p ocess o a
ai -p ope y c oss able, he ollowing poin s should be conside ed:
1. Cos induced by he ai , including he p ize o pu chasing he senso plus he expendi u es
in ol ed in he measu ing p ocess.
2. The mo e au oma ed a measu emen is, he lowe eliabili y i ends o ha e.
3. The in e es o a me s in acking ce ain ai s, as i a ies wi h applica ions and may di e o
he same c op cul i a ed in di e se loca ions.
4. The s eng h o co ela ion among CB- ai s es ablishes he alidi y o p edic i e models, and
ypically equi es he suppo o s a is ics. In ha espec , eliabili y in he measu emen s mus be
assu ed be o e applying s a is ical me hods o analysis. E en so, s a is ical p ocedu es a e no
in ended o eplace subjec -ma e judgmen s based on heo e ical knowledge and ield expe ience.
4. Measu emen and Posi ioning o CB- ai s: Map Cons uc ion
The me hodology o p ocess and handle biome ic in o ma ion is as impo an , o e en mo e, han
he ac ual acquisi ion o da a. Some senso s can p o ide a p ecise measu emen in less han a second
Senso s 2013, 13 12704
bu he a ea pe sample is la ge. O he imes, ins ead o a sampling p obe, c op in o ma ion is ga he ed
om digi al images. Yield moni o s a e designed o es ima e ins an aneous yield on- he-go. How can
all his in o ma ion be e icien ly combined in a s anda d map? Two p inciples accoun o he
managemen o c op biome ic in o ma ion wi h compa ible maps:
1. The selec ion o a con enien coo dina e sys em wi h unc ional axes gua an ees epea abili y
du ing a season and compa ibili y o e he yea s. In addi ion o his, Euclidean geome y acili a es
he measu emen o dis ances and he calcula ion o a eas, especially i compa ed o sphe ical
(geode ic) coo dina es. All hese condi ions a e me by he Local Tangen Plane (LTP) coo dina e
sys em, as i uses he Ca esian axes no h, eas , and al i ude, and allows he selec ion o a local
o igin chosen by he use , and se o all he c op maps associa ed o he ield analyzed.
2. The homogeniza ion o da a h ough egula g ids o use -selec ed esolu ion, ega dless o he
na u e o he senso implemen ed, i s sampling a e, o he a ea co e ed pe measu emen .
Gi en ha he o igin o coo dina es in each ield can be ixed by he p oduce , and he size o
he g id’s cell is kep cons an h ough ime, he esul ing c op maps can be easily s anda dized
o each gi en ield, esul ing in a g id o ma o de e mined esolu ion. This p ocedu e leads o
impo an implica ions, as biome ic in o ma ion and u u e p edic ions o a ield should be
eely exchanged o e ime and space. Local o igins and in ui i e coo dina es help a me s and
ield manage s ela e map cells wi h he ac ual e ain. E en i he esolu ion o he g id is
changed by modi ying he cell size, c op maps can s ill be compa ed zone by zone, and
he e o e compa ibili y is always g an ed. Cells wi hou in o ma ion do no c ea e any p oblem
because he global posi ioning o cells allows he comple ion o maps in subsequen passes and
da a co ela ion only occu s among cells s o ing biome ic da a.
The ul illmen o hese wo p inciples allows he compa ison and co ela ion o compa ible
maps ca ying biome ic in o ma ion. Howe e , se e al sub le ies need o be u he discussed be o e
assembling he se o c op maps ha cha ac e ize a ield. To begin wi h, he ela ionship be ween cell
size and he na u e o he CB- ai s should be in es iga ed in de ail. Gene ally speaking, he e will be
many ai s bu only one cell size will be adop ed o all he maps. Ob iously, he measu ing echnique
o each ai se s he smalles size unde which addi ional subdi isions a e meaningless. Fo example, i
soil is sampled e e y 5 m along a ow sepa a ed om i s neighbo ing ows by 6 m, squa e cells o 3 m
size will esul in many emp y cells, bu expanding he cell size o 6 m, 10 m , o 15 m will lead o
al e na i e maps ep esen ing equi alen biome ic in o ma ion a di e en esolu ion. When se e al
measu emen s all inside he same cell, he magni ude o he ai s is a e aged o p o ide he mean
alue o he ai co esponding o ha cell. Na u ally, he bigge he cell he less accu acy will ha e
he model, as speci ic c op in o ma ion is los h ough he a e aging p ocess. Some applica ions,
howe e , may equi e labeling he cells wi h he op alues a he han he a e ages. In any case, map
a iabili y will inc ease as cell size diminishes. As a esul , he biome ic pa ame e s ep esen ed in a
map possess ce ain sensi i i y o he ac ual size o he cells (map esolu ion), mainly gi en by he
equilib ium be ween sampling a e and sampling spa ial ange. The e o e, he igh ade-o mus be
es ablished in such a way ha he in o ma ion ca ied by each pa icula cell is meaning ul by i sel
and in ela ion wi h he es o he c op map.
Senso s 2013, 13 12705
This sec ion p o ides he amewo k o build c op biome ic maps in gene al e ms, bu he speci ic
equa ions and de ailed algo i hms o assemble hem all ou side he scope o his pape . The ollowing
e e ences may help o apply hese ideas o pa icula cases. The ans o ma ion om geode ic
coo dina es o he local angen plane is explained s ep-by-s ep in ([15], Chap e 3, pp. 68–71). The
cons uc ion o egula g ids wi h global e e ences gi en in he LTP coo dina e sys em is desc ibed
in [16]. The implemen a ion o condi ioning il e s o enhance he obus ness o GPS da a can be checked
in [17], and inally, he es ima ion o spa ial a ia ion o ine ege a ion wi h machine ision has been
epo ed in [18]. Sec ion 6 applies his me hodology o he pa icula case o ineya ds, p esen ing mo e
insigh s and p ac ical solu ions on he p oposed philosophy.
5. Ma hema ical Analysis o CB-T ai s
In he me hodology p oposed, he wo king uni is he cell o a CB map, and consequen ly
e e y hing happens a cell le el. This implies ha he e will be a se Z o n biome ic ai s
Z = {T1, T2, …, Tn} ep esen ing di e se c op- ela ed p ope ies, and a se o cells o ming a map
whe e he elemen s o Z a e ep esen ed, so ha he o al numbe o maps ela ed o a ield will be g ea e
o equal han n. As a esul , CB maps may be co ela ed a cell le el–i.e., cell by cell o equi alen
posi ions– and checked o s a is ical signi icance among ai s in such a way ha p edic ion models may
be enounced o a ce ain subse o Z. P edic ed ai s mus be e en ually e alua ed acco ding o hei
p oximi y o he ac ual measu emen s de e mined by he “g ound- u h” e i ica ion conduc ed in he ield
unde s udy. Again, his e alua ion mus ake place a cell le el. E e y CB map will ha e a ho izon al
esolu ion o h cells and a e ical esolu ion o cells, summing up a o al o h

cells. Map cells can be
iden i ied using he s anda d ma ix no a ion Tk (i, j) whe e i = {1, 2, …, }, j = {1, 2, …, h}, and
k = {1, 2, …, n}.
The p edic i e models in e ed om co ela ing a selec ed numbe o ai s will always be s a is ical
models a he han ma hema ical models, as hey canno ep esen p ecise ela ionships ee o e o
bu app oxima e ela ions deduced om da a p one o expe imen al e o s. The s a is ical analysis o
CB- ai s p oceeds acco ding o he ollowing ac ua ion p o ocol.
5.1. S a is ical Na u e o Selec ed CB-T ai s
Be o e making any a emp o es ablishing s a is ical co ela ions among di e en ai s, i is
impo an o analyze he s a is ical na u e o he selec ed ai s. In pa icula , i hey ep esen s ochas ic
(o andom) a iables and how hey beha e in e ms o basic s a is ics. These p ope ies a e key
o explain a iabili y wi hin he ield, he ounda ional concep behind p ecision ag icul u e. A andom
a iable usually akes on a se o possible alues, each wi h an associa ed p obabili y, which
concep ually may ep esen he subjec i e andomness (c op a iabili y) esul ing om incomple e
knowledge on he biological p ocesses behind c op p oduc ion. F om ha s andpoin , c op ai s can be
conside ed andom a iables, e en hough hei alues a e no in insically andom, because
measu emen e o s end o ollow a andom dis ibu ion. In ac , no mally dis ibu ed e o s a e
assumed o eg ession models, F- es s, and ANOVA [19]; he e o e, he assump ion o no mali y
should be checked o he se o ai s p oposed in he s udy o a ield, and i da a beha es app oxima ely
no mal, he se o con en ional s a is ical ools can be used o gene a e p edic i e models. The no mal
Senso s 2013, 13 12706
quan ile-quan ile plo p o ides a di ec e alua ion o he assump ion o no mali y, whe e app oxima e
linea i y indica es no mally dis ibu ed e o s.
Once he assump ion o no mali y has been e i ied, in e ences on means and s anda d de ia ions
may be p ope ly in e p e ed. A his poin , especial a en ion mus be paid o he appea ance o ou lie s,
i.e., ex eme alues wi h espec o o he obse a ions made unde he same condi ions. When senso s
and o he elec onic de ices a e se o ga he da a o long pe iods o ime unde ough en i onmen al
condi ions, noise is p one o appea , and p edic i e models based on eg ession may esul ex emely
a ec ed by uncon olled ou lie s. The e o e, p o isions should be made o deal wi h un ealis ic da a
be o e composing he CB maps. In gene al, wo app oaches can be ollowed wi h ega ds o ou lie s:
iden i ica ion, de e mining wha obse a ions a e ou lie s o hei emo al; and accommoda ion,
mi iga ing hei e ec s wi hin he map. I he p esence o ou lie s becomes an ope a i e p oblem, he
echnique o s uden ized dele ed esiduals can be used o ou lie -de ec ion s a is ics.
5.2. Cohe ence be ween Equi alen o Rela ed Biome ic T ai s
As elec onic and in o ma ion echnologies apidly e ol e, mo e and new measu emen echniques
o c op ai s will become a ailable. Unde hese ci cums ances, i will no be uncommon o end up
collec ing di e en maps o he same o closely ela ed ai s, as he al e na i e ege a ion co e age
es ima ed in Sec ion 6 om digi al images aken wi h wo di e en ields o iew. As se e al CB maps
model he beha io o a unique ai , he in o ma ion epo ed, while di e en , mus be equi alen . This
ac mus be e i ied by es ablishing co ela ion models among equi alen quan i ica ions o he same
ai . In ac , p edic i e models will mos ly need he pa icipa ion o only one ype o measu emen pe
signi ican ai , and hus he bes co ela ed pa ame e s should be iden i ied be o e de e mining he
de ini i e p edic o a iables o he model.
5.3. Enuncia ion o CB P edic ion Models
A CB p edic ion model is he eg ession-based es ima ion o a quan i a i e a iable ela ed o
p oduce yield o quali y gi en as a unc ion o one o se e al p edic o c op ai s, es ablishing a
s a is ical co ela ion among ai s wi h a solid ounda ion o dealing wi h obse a ional da a.
Howe e , when analyzing da a in which mos o he a iables a e no con olled, ex eme ca e mus be
aken o ensu e ha p ope in e ences a e d awn when s a is ically signi ican esul s a e ob ained [19].
Con ounding is especially impo an as he e ec o ai s may no be uniquely asc ibed o he subse
o ai s conside ed as p edic o a iables. Since he e olu ion o ai s in he ield uns mos ly
uncon olled, con ounding is likely o occu , and modes y should always be p esen in he claims made
abou p edic i e models.
The eg ession models deduced o making CB p edic ions a e ma hema ically based on
leas -squa es es ima es, and ini ially may be linea , mul i a ia e, o polynomial. Fo leas -squa es
p edic ions o he simples linea ype, he slope is ela ed o he Pea son’s p oduc -momen co ela ion
coe icien in such a way ha bo h a e equal when he s anda d de ia ion o bo h a iables (p edic o
and p edic ed) is he same [19]. In such case he absolu e alue o he slope necessa ily has o be less
o equal o one because | | ≤ 1. As a esul , slope alues unde 1 canno be in e p e ed as a lowe
esponse because his e ec is expec ed i he a iabili y o in ol ed a iables is simila . Consequen ly,
Senso s 2013, 13 12713
Figu e 8. CB map o ela i e ine igo es ima ed wi h a 12 mm lens: V-12 (%).
Figu e 9. CB map o g ape yield (kg o g apes/16 m2).
Figu e 10. CB map o suga con en in mus (º Baumé).

Senso s 2013, 13 12714
Figu e 11. CB map o mus pH.
Figu e 12. CB map o mus acidi y (g/L).
Figu e 13. CB map o 10-be y weigh (g).
Senso s 2013, 13 12715
Figu e 14. CB map o be y a e age diame e (mm).
Figu e 15. CB map o a e age be y densi y (g/cm3).
6.2. S a is ical Na u e o Selec ed CB-T ai s
Be o e conduc ing in e ences on means and s anda d de ia ions o he 12 biome ic ai s
conside ed in he ineya d s udy, and mapped in Figu es 4–15, he assump ion o no mali y mus be
e i ied. To do so, he no mal quan ile-quan ile plo s o e an excellen ool o quan i y he s a is ical
alidi y o he conclusions la e d awn om co ela ion and eg ession analyses. Figu e 16 depic s he
quan ile plo s o he soil esis ance o oo g ow h, ei he a e age (a) o maximum (b). Simila ly,
Figu e 17 e alua es he no mal beha io o he ela i e igo , ei he es ima ed wi h an 8 mm lens (a)
o h ough he 12 mm lens (b). Figu e 18a depic s he quan ile plo o ield ele a ion, and he beha io
o yield is examined in Figu e 18b. The acidi y o he mus is checked in Figu e 19, di ec ly in g/L (a)
and also h ough he pH (b). The pa e n ollowed by he dis ibu ion o suga con en wi hin he ield
is shown in Figu e 20a. The s a is ical na u e o be y physical pa ame e s was s udied by analyzing
Senso s 2013, 13 12716
he no mali y o he dis ibu ion o weigh (Figu e 20b), a e age diame e (Figu e 21a), and be y
densi y (Figu e 21b). Table 2 summa izes he main s a is ical a iables o he 12 ai s ini ially
conside ed in he Cabe ne -Sau ignon ineya d o Figu e 2. The able shows ha he e a e no
signi ican ou lie s in he da a, and he s ochas ici y o ai s is excellen excep o he e ain ele a ion
(Figu e 18a), which ob iously canno ollow a andom pa e n as i ac ually ep esen s he p o ile o
he e ain whe e he ines a e plan ed. This ac mus be aken in o accoun i he ele a ion ai
con ibu es o p edic i e models.
Figu e 16. No mal quan ile-quan ile plo s o soil esis ance (MPa): (a) A e age alues;
(b) Maximum alues.
(a)
(b)
Senso s 2013, 13 12717
Figu e 17. No mal quan ile-quan ile plo s o ela i e igo o ines (%): (a) V-8;
(b) V-12.
(a)
(b)
Senso s 2013, 13 12718
Figu e 18. No mal quan ile-quan ile plo s: (a) Te ain ela i e ele a ion (cm); (b) G ape
yield (kg/16 m2).
(a)
(b)

Senso s 2013, 13 12719
Figu e 19. No mal quan ile-quan ile plo s o mus acidi y: (a) To al acidi y (g/L); (b) pH.
(a)
(b)
Senso s 2013, 13 12720
Figu e 20. No mal quan ile-quan ile plo s: (a) Suga con en in mus (º Baumé);
(b) 10-be y weigh (g).
(a)
(b)
Senso s 2013, 13 12721
Figu e 21. No mal quan ile-quan ile plo s: (a) Be y a e age diame e (mm); (b) Be y
densi y (g/cm3).
(a)
(b)
6.3. Cohe ence be ween Equi alen o Rela ed Biome ic T ai s
In he au oma ic assessmen o ine igo , and om a physical s andpoin , he pe cep ion o ines
wi h a 12 mm lens (V-12) necessa ily ills he image be e han i s equi alen image aken wi h he 8 mm
lens (V-8), as he o me p o ides a close look ha a oids pe iphe al dis ac ions such as soil, ellis
ames, o ehicle pa s. Howe e , he goal o igo maps is he acknowledgemen o he spa ial a ia ion
Senso s 2013, 13 12722
o ege a ion, and a p io i, bo h es ima ions (8 mm and 12 mm lenses) should lead o simila
conclusions wi h independence o he measu ing scale used. A close look a hei a iances (Table 2)
yields 219%2 o he 8-mm assessmen and 276%2 o he 12-mm es ima ion, which a e di e se enough
no o conside he eg ession allacy issue explained in Sec ion 5.3.
Table 2. In e ence s a is ics o ineya d biome ic ai s.
C op Pa ame e T acked n Max Min A e age Median S . De . No mali y
A e age soil esis ance (MPa) 218 5 1.6 2.74 2.63 0.68 S ong
Maximum soil esis ance (MPa) 218 8.5 2.3 4.8 4.5 1.4 S ong
Ele a ion (cm) 273 321 1 85.3 31 97.3 Weak
Vine igo wi h 8 mm lens (%) 274 69 1 39.5 41 14.8 S ong
Vine igo wi h 12 mm lens (%) 276 88 13 47.6 43 16.6 S ong
G ape yield (Kg/16 m2) 219 8.4 0.7 4.1 4 1.84 Ve y s ong
Suga con en in juice
(º Baumé) 219 15.1 10.1 13.1 13.2 0.62 S ong
To al acidi y (g/L) 219 13 2.8 7.5 7.1 1.8 Ve y s ong
Mus pH 219 4.3 2.8 3.3 3.3 0.2 Ve y s ong
Weigh o 10 be ies (g) 219 13.4 4.8 9.4 9.5 1.61 Ve y s ong
Diame e o be ies (mm) 219 12.9 8.9 11 11.1 0.74 Ve y s ong
Be y densi y (g/cm3) 219 1.9 0.9 1.36 1.3 0.17 S ong
Figu e 22. Co ela ion be ween al e na i e ege a ion indices V-8 and V-12.
I bo h a iables p o ide equi alen in o ma ion on ege a ion a iabili y, he e mus be a
con e sion equa ion ha ansla es any gi en le el o olia co e age o ei he V-8 o V-12; in o he
wo ds, he e should be a signi ican co ela ion be ween bo h a iables when a eg ession i be ween
hem is ob ained. Due o he high a iabili y ound in he ield wi h biome ic ai s, he esis an
coe icien o de e mina ion gi en in Equa ion 2 esul s help ul o selec he bes i be ween V-8 and
V-12. Figu e 22 depic s he sca e plo o V-12 s. V-8 supe posed wi h he linea , quad a ic, and
cubic i s speci ied in Table 3.
Senso s 2013, 13 12729
6.5. P edic ion Models o G ape Quali y and Enological Po en ial: Quali y Po en ial Index (QPI)
Unlike yield, which is a ai easy o measu e, he e is no such ai called g ape quali y. Ye quali y is a
key ac o , i no he mos de e minan nowadays o winemake s, because a educ ion on yield can be
coun e weigh ed by an excellen quali y, bu i ne e wo ks he o he way a ound, as a d op in quali y
a ec s he epu a ion o he b and and may ha e nega i e consequences o many yea s ega dless o yield.
The key ques ion is how o de ine he e m quali y wi h ega ds o g apes, and consequen ly o p ospec i e
wine. As a ma e o ac , i seems mo e easonable o speak o po en ial quali y, as he de eloped models
y o p edic he quali y o he u u e wine based upon da a eco ded in he ield om plan s and g apes in
g owing s ages anging om é aison o ha es ing ime. Roge Pellenc, he F ench manu ac u e o g ape
ha es e s, s a es [22] ha he base cha ac e is ics o he ine a e essen ially he quan i y o g apes
ha es ed, he suga o he g apes, hei acidi y, and he heal h s a us o he plan , which is unde s ood as
he g ow h o ine shoo s du ing he ege a i e pe iod.
Be o e de ining an index o quali y po en ial as a unc ion o he ai s and measu emen s a ailable
om he CB maps de eloped, i is necessa y o ind ou wha i icul u is s and winemake s conside i o be
he ideal balance o g apes a he ime o ha es ing, ha is, de e mining he pe ec ipeness o ob aining
he bes possible wine. The equen upda e and acking o ce ain maps may lead o associa e ce ain
as es wi h ce ain changes in measu ed ac o s. Acco ding o Cox [23], he ac o s o be measu ed a e
deg ees B ix, i a able acidi y in g/100 mL (TA), and pH, wi h a ge eadings o pe ec ed g apes o 22
B ix, 0.75 acid, and a pH abou 3.4. B ix deg ees p o ide he pe cen age o suga in he g ape juice,
whe eas acids gi e c ispness, b igh ness, and hi s -quenching quali ies o wines, being essen ial
componen s o he balance in a ine wine. On he o he hand, pH is ela ed o TA bu di e s om i and
may o may no be co ela ed wi h he amoun o a a ic acid o g ape juice. The ideal alue o pH is 3.4
o ed wine, bu i may be highe e en when TA is wi hin he op imum ange.
The a io o B ix o TA is a be e indica o o ipeness and quali y han swee ness o a ness alone.
Resea che s a he Uni e si y o Cali o nia a Da is [23] ha e ound ha wines a e p ope ly balanced
when B ix:TA is be ween 30 and 35, and p e e ably 30. An e en mo e accu a e measu e o quali y
se s he op imal si ua ion when B ix imes pH2 app oaches 260 o ed wines o 200 o whi e wines.
The lis o ai s measu ed om he g apes and ep esen ed in he c op maps o Figu es 10–12 allow
o he implemen a ion o hese quali y indica o s in he ques o a gene al quali y index ha can ake
pa in p edic i e models wi hin he scope o c op biome ics. In pa icula , le X6 be he suga con en
measu ed in deg ees Baumé (Figu e 10), X7 he o al acidi y in g/L (Figu e 11), and X8 he mus pH
(Figu e 12), he suga con en in deg ees B ix (X9) and he i a able acidi y in g/100 mL (X10) can be
easily calcula ed wi h Equa ions 4 and 5:

1.8·

 (4)

 0.1·

 (5)
Taking he nomencla u e used o he CB ai s measu ed in he ineya d o he ecommenda ions
gi en abo e by Cox and he Uni e si y o Cali o nia [23], he exp essions gi en in Equa ions (6) and
(7) mus hold o he op imum quali y o Cabe ne -Sau ignon g apes:

Senso s 2013, 13 12730


30·

 1 (6)

·



260 1 (7)
The mul iplica ion o Equa ions (6) and (7) leads o he exp ession o Equa ion (8), ha pe mi s he
e alua ion o quali y om he p edic o ai s es ima ed in he ield and mapped in Figu es 10–12.


30·

·

·



260 󰇛

·

󰇜
7800·

 1 (8)
The exp ession deduced in Equa ion (8) is he basis o measu ing he quali y po en ial in a new CB
map. Howe e , pi o ing a ound 1 as he ideal quali y is no con enien because alues will g ow
une enly acco ding o whe he hey a e abo e o below 1. In o de o ci cum en his issue and
es ablish a mo e symme ical dis ibu ion a ound ze o (maximum quali y), he Quali y Po en ial Index
(QPI) was de ined by aking common loga i hms o Equa ion (8), as shown in Equa ion (9):
log 󰇛

·

󰇜
7800·

 2·log󰇛

·

󰇜log
󰇛7800·

󰇜 (9)
The applica ion o he na u al loga i hm o Equa ion (8) would ha e expanded he scale, bu wi h
he use o common loga i hms in base 10, he wo king scale o quali y po en ial is p ac ically limi ed
o he in e al [−1,1], which acili a es he use and in e p e a ion o QPI maps, he CB map e sion o
g ape quali y. Gi en ha o al acidi y was mapped in g/L in Figu e 11, and ep esen ed by X7, he inal
exp ession o QPI should use X7 a he han X10, which can be easily pe o med by in oducing
Equa ion (5) in o Equa ion (9). The inal exp ession o he QPI is gi en in Equa ion (10), whe e X8 is
he mus pH, X7 is o al acidi y in g/L, and X9 is he suga con en in deg ees B ix. The bes quali y will
be ob ained o QPI alues a ound ze o (log10), mo ing u he away as quali y dec eases; so,
o he op imal si ua ion ecommended by Cox o X7 = 7.5 g/L, X8 = 3.4, and X9 = 22, he QPI is 0.019,
which in p ac ical e ms can be conside ed as 0:
 2 · log󰇛

·

󰇜log
󰇛780·

󰇜 (9)
The QPI map esul an om applying Equa ions (4) and (9) o he CB maps o Figu es 10–12 is
plo ed below in Figu e 25. In e ence s a is ics o a o al numbe o 219 cells lead o a maximum QPI
o 0.796 and a minimum o −0.416, bo h in he ange [−1,1] as no mally expec ed. The a e age is
0.031 and he median 0.051, wi h a s anda d de ia ion o 0.1698.
The QPI alues assigned o he cells o ming he ineya d ows highligh he op imum quali y o
magni udes a ound ze o, ep esen ed in he map by ed cells. As alues mo e u he away om ze o,
ei he posi i e o nega i e, he quali y o g apes de e mined a ha es ing ime dec eases. The
maximum alue o QPI in he map is abou 0.8, so, o con enience, a alue o 1 was assigned o cells
wi hou in o ma ion in o de o ease he in e p e a ion o he QPI map. All he a iables (p edic o
ai s X7, X8, and X9) used in he de ini ion o QPI (Equa ion (9)) a e no mally dis ibu ed acco ding o
Figu es 19 and 20a, bu due o he ac ha his de ini ion in ol es he p oduc o a iables and he use
o loga i hms, he no mali y assump ion o QPI mus be ca e ully checked. Fo una ely, he
quan ile-quan ile plo o Figu e 26 p o es ha QPI beha es as a no mal dis ibu ion wi h an excellen
Senso s 2013, 13 12731
ma ch o s anda d no mal quan iles. Once he QPI has been de ined as he sys ema ic p ocedu e o
quan i y quali y po en ial o he u u e wine, exp essed as a combina ion o objec i e measu emen s
a ailable om CB maps, he nex s age consis s o p edic ing QPI om c op ai s a ailable be o e o
a ha es ing ime. As occu ed o he p edic ion o yield, mul iple models need o be e alua ed, each
one ea u ing di e se ai s, in o de o selec he mos app op ia e model o es ima e spa ial a ia ions
o g ape quali y in he ield. The p e ious expe ience wi h yield p edic i e models and some
p elimina y en a i e ials sugges no o conside igo V-12 (X2), soil p ope ies (X4 and X5), and
ele a ion (X3) due o hei poo con ibu ion o he p edic ion o g ape p oduc ion.
Figu e 25. CB map o he Quali y Po en ial Index QPI.
Figu e 26. No mal quan ile-quan ile plo o he Quali y Po en ial Index QPI.
Table 9 summa izes he s a is ical e alua ion o he 13 models p oposed o p edic quali y in QPI
o ma , whe e X1 is igo V-8 (%), Xy is he ac ual yield (kg/16 m2), X11 is he weigh o 10 andom be ies
(g), X12 is he a e age diame e o he be ies (mm), and X13 is he a e age be y densi y (g/cm3).
Acco ding o Table 9, he goodness o he 13 i s p oposed o quali y p edic ions is, gene ally
speaking, weake han o yield p edic ions; ye in e es ing conclusions can be wi hd awn om hei
analysis. The s a is ical examina ion o he models clea ly indica es ha he quali y o g apes,
unde s ood as he op imal balance be ween acidi y and suga con en a ha es ing ime, is independen
Senso s 2013, 13 12732
o he size, weigh , and densi y o he be ies. Fu he mo e, based on hese esul s, i does no depend
on he yield bu can be co ela ed o ine igo in such a way ha op imal quali y occu s wi h a
mode a e ege a i e de elopmen o he ines, as shown in Figu e 27a. In ac , excessi e olia g ow h
has a nega i e in luence, nume ically se by he QPI, on g ape quali y, some hing ha was al eady
known in b oad e ms by i icul u is s and g owe s, bu ha can be ma hema ically de e mined h ough
his me hod. The main conclusion o he QPI p edic ion model is ha be y quali y mos ly depends on
he ela i e igo o he plan s, and e en hough he a iabili y in he ield is e y high, an imp o ed
assessmen o ine olia g ow h will su ely lead o mo e p ecise p edic ions o quali y be o e
ha es ing. The mul i a ia e analysis summa ized in Table 9 consis en ly ejec s all he a iables
(p edic o ai s) di e en om X1 as in luencing he quali y po en ial index QPI. In coincidence wi h
he yield p edic o model selec ed (15Y), he spa ial a iabili y o ege a ion g ow h is, by a , he
mos in luen ial pa ame e o ack in he managemen o ineya ds, especially when i is pe o med on
a s ong echnological basis.
Table 9. Summa y able o QPI p edic ion models.
Model R2 
 F-S a -S a Non-Signi .
1Q 0.8460.006·0.057·0.122·
0.216· 0.002· 0.32 0.23 18.13 Cons an ;
; ;
;

2Q 0.4070.006·0.096·0.002· 0.31 0.17 29.31 ;

3Q ..·0.31 0.24 85.33
4Q 0.3310.221· 0.05 0.17 9.34
5Q 0.1460.028· 0.09 0.01 18.7
6Q 0.3720.036· 0.11 0.16 24.02
7Q 0.4340.037· 0.02 0.06 4.54
8Q 0.3380.008·0.015·4.2·10 ·· 0.31 0.29 28.64 ;
·
9Q 0.2860.007·0.002· 0.31 0.29 42.52 
10Q 0.25610.0044·0.00003·
0.31 0.32 42.78 ;


11Q 0.54510.1444·ln 0.24 0.12 60.06
12Q 0.2562·
. 0.27 0.01 25.61
13Q 0.01010.5248
 0.06 0 * 12.83 Cons an
* Nega i e alue.
The s a is ical indica o s o Table 9 poin o he conclusion ha he bes way o p edic ing quali y is
om he ela i e igo V-8 es ima ed wi h X1, al hough his ela ionship can be linea o nonlinea .
Figu e 27a shows ha he e is no much di e ence be ween he linea , quad a ic, and loga i hmic i s.
Howe e , in addi ion o he highes F-s a and coe icien o de e mina ion, he linea model is always
easie o use o i s simplici y, and he e o e Model 3Q will be he selec ed choice. The esiduals o he
da a a e applying Model 3Q beha e qui e close o a no mal dis ibu ion, as plo ed in Figu e 27b.
This model yields a QPI o 0.289 o no ege a ion (X1 = 0%), which indica es low quali y; bu also
p oduces a QPI o -0.41 o ull co e age (X1 = 100%), which ep esen s e y poo quali y. Model 3Q
allows, oo, he calcula ion o he ela i e ege a ion X1 ha leads o he maximum quali y QPI = 0.
Senso s 2013, 13 12733
This alue co esponds o 41%, olia co e age ha can be aken o he V-8 map o Figu e 7 o
disco e ha hese cells co espond o he wes side o he ield, wi h highe ele a ion, less ege a ion,
less yield, and less wa e con en in he soil.
Figu e 27. (a) P edic ion models o QPI as a unc ion o V-8 ela i e igo ; (b) Residuals
o p edic i e Model 3Q (linea i ).
(a)
(b)
6.6. Impac o C op Biome ic Maps Resolu ion on P edic i e Models
One o he ad an ages ha make global g ids and CB maps powe ul is he capabili y o adjus he
esolu ion o he maps o he needs o he use . Howe e , he in a iance o p edic ion models o
di e se esolu ions canno be aken o g an ed unless he e is a p oo o he model’s alidi y o
al e na i e sizes o he cells. As a esul , i is impo an o de e mine o wha ex en p edic i e models
change when esolu ion a ies. To do so, he de aul cells o 4 m × 4 m we e doubled in bo h
dimensions o inc ease he wo king a ea ou old and become squa e cells o dimension 8 m × 8 m.
Figu e 28 shows he ela i e ege a i e igo V-8 (%) wi h he new esolu ion, and Figu e 29
ep esen s he low esolu ion e sion o he yield map. As he wo king a ea has augmen ed ou imes,
Senso s 2013, 13 12734
se e al ield measu emen s coincide in each cell o be a e aged, and as a esul he e a e no gaps
indica ing cells wi hou ield da a as occu ed in Figu es 7 and 9, which ep esen he same da a a
highe esolu ion. Table 10 speci ies he same 19 yield p edic ion models o mula ed in Table 5 bu
adap ed o he new esolu ion, whe e he meaning o he a iables Xi is he same de ined o Table 5
bu ela i e o he low esolu ion maps. No e ha in spi e o inc easing he wo king a ea ou old, yield
measu emen s a e kep in kg pe 16 m2 o ease he compa ison be ween maps o di e en cell size.
Figu e 28. Low esolu ion CB map o ela i e ine igo es ima ed wi h an 8 mm lens:
V-8 (%).
Figu e 29. Low esolu ion CB map o g ape yield (kg o g apes/16 m2).
The immedia e appa en ac o downg ading CB map esolu ion has been a signi ican inc ease o
he 
, as e idenced by Table 10. The signi ican educ ion in he amoun o da a has esul ed in he
educ ion o a iabili y, which in u ns has led o a sligh ly be e i wi h ele a ion X3. Ye , he
co ela ion o yield wi h ela i e igo X1 is equally good, and aking in o accoun he signi icance o
ai s (p edic o a iables) in he eal ield, he bes al e na i e seems o model yield p edic ions om
ege a ion (X1). Addi ionally, he assump ion o no mali y canno be assumed o X3 and he e a e
collinea i y issues be ween X1 and X3 (p o ed by -s a in Models Y3§, Y6§, and Y18§). As a esul , a
i ing equa ion wi h X1 as p edic o has o be ound and compa ed o Model 15Y. As occu ed wi h

Senso s 2013, 13 12735
high esolu ion maps and Figu e 24a, Figu e 30a shows iny di e ences be ween he i e models
applied; ye , he bes pe o mance belongs o he powe unc ion o Model 15Y§, as i possesses he
highes F-s a and is cohe en wi h na u e o X1 = 0. No ice, howe e , ha he magni udes o he
pa ame e s in he equa ion ha e changed wi h espec o Model 15Y. The new model p edic s a yield
o 5.6 kg/16 m2 o ull co e age X1 = 100, which is sligh ly lowe han he 6.3 kg ound o high
esolu ion maps. The esiduals o applying Model 15Y§, plo ed in Figu e 30b, also ollow a no mal
dis ibu ion shape. In addi ion o al e na i e i s, Figu e 30a p o ides a g aphical compa ison be ween
he powe unc ions o Models 15Y and 15Y§. Bo h unc ions ace close pa hs, wi h la ge
disc epancies below X1 = 30%.
Table 10. Summa y able o yield p edic ion models adap ed o low esolu ion maps.
Low Resolu ion Model R2 
 F-S a T-S a Non-Signi .
1Y§ 8.4040.028·0.012·0.007·
1.227·1.328·0.53 0.60 12.9  ; 
2Y§ 6.3920.007·0.009·0.641· 0.37 0.66 11.4 ;

3Y§ 4.1450.019·0.009·0.33 0.55 15.0 
4Y§ 4.3170.045·0.68·0.28 0.49 11.7 
5Y§ 4.5460.039·0.755·0.002·· 0.28 0.48 7.6 Cons an ;  ; X4 ;

6Y§ 4.1430.019·0.009·5.46·10
·· 0.33 0.54 9.8  ; ;
†
7Y§ 0.9170.066·0.026·2.55·10
·· 0.26 0.62 6.9 All
8Y§ 1.880.059· 0.24 0.55 19.4
9Y§ 5.0930.011·0.32 0.54 28.9†
10Y§ 2.7860.033·0.08 0.5 5.6
11Y§ 1.14570.1060·0.0006·
 0.25 0.56 10.1 Cons an ; 

12Y§ 5.31890.0206·3.53·10·
0.34 0.59 15.2 

13Y§ 1.79930.0048·0.0033·
3.91
·10·
 0.27 0.67 7.2
14Y§ 0.13931.152·ln0.21 0.41 16 Cons an
15Y§ .·
. 0.3 0.5 26.3 Cons an
16Y§ 4.45384.0956
 0.10 0.17 7
17Y§ 4.1191.111·0.32 0.54 28.9†
18Y§ 3.3740.019·0.878·5.31·10
·· 0.33 0.54 9.8 ; ;
·†
19Y§ 3.3740.019·0.879·0.33 0.55 15 †
† Possible collinea i y.
Senso s 2013, 13 12736
The possible a ia ions o he p edic i e model o QPI (3Q in Table 9) when map esolu ion is
lowe ed om 35 × 12 cells o 17 × 5 cells we e s udied ollowing he same p ocedu e ou lined o he
p edic ion o yield. Figu e 31 shows he low esolu ion map o he quali y po en ial index QPI, and
Table 11 lis s he 13 new models o p edic ing QPI ha esul om inc easing he cell size o 8 m × 8 m.
The meaning o he p edic o a iables ea u ed in he models coincides wi h ha o Table 9.
Figu e 30. (a) P edic ion models o low esolu ion CB maps o yield as a unc ion o V-8
ela i e igo ; (b) Residuals o p edic i e Model 15Y§ (powe unc ion, Table 10).
(a)
(b)
As happened wi h yield p edic ion, esul s do no change signi ican ly wi h he modi ica ion o he
map esolu ion. Again, he e is an imp o emen o R2 and 
 induced by he educ ion o he da ase ,
bu he linea model 3Q§ s ill ep esen s he bes i and highes F-s a . In he same ashion, yield and
be y densi y a e always ejec ed om he models by he s a is ics gi en in Table 11. Figu e 32a
con i ms ha he new linea i (Model 3Q§) is in eali y e y close o he high- esolu ion i
Senso s 2013, 13 12737
(Model 3Q) and no oo a om he quad a ic i (Model 10Q§). O e all, he p incipal conclusions
emain and he op imum quali y (QPI  [−0.1,0.1]) occu s wi h a medium igo index X1 be ween 30%
and 60%, dec easing in (QPI) quali y o ege a ion indices abo e 60%. Acco ding o linea Model
3Q§, he bes quali y (QPI = 0) is ound o ela i e ege a ion X1 = 43%, which is e y close o he
high- esolu ion alue o 41%. The dis ibu ion o esiduals depic ed in Figu e 32b easonably
ep oduces a no mal dis ibu ion p o ile.
Figu e 31. Low esolu ion CB map o he Quali y Po en ial Index QPI.
Table 11. Summa y able o QPI p edic ion models adap ed o low esolu ion maps.
Low Resolu ion Model R2 
 F-S a T-S a Non-Signi .
1Q§ 1.960.005·0.123·0.249·
0.437·0.001· 0.48 0.44 11.4 Cons an ; ;
;

2Q§ 0.4030.006·0.105· 0.002· 0.42 0.39 15.3 ;

3Q§ ..·0.41 0.39 45.9
4Q§ 0.410.292· 0.05 0.02 3.6 Cons an ; 
5Q§ 0.1330.027· 0.11 0* 8.2
6Q§ 0.4730.049· 0.26 0.13 23.3
7Q§ 0.9160.081· 0.14 0 * 11
8Q§ 0.3380.008·0.024·10 ·· 0.42 0.41 15.3 ; ·
9Q§ 0.2690.006·0.002· 0.41 0.40 22.6 
10Q§ 0.1970.0016·0.000062·
0.42 0.51 24 ; 

11Q§ 0.41440.1112·ln0.29 0.13 26.5
12Q§ 0.0888·
. 0.12 0.2 6.1 Cons an
13Q§ 4.7·10 0.3864
 0.13 0.1 9.6 Cons an
* Nega i e alue.
Senso s 2013, 13 12738
Figu e 32. (a) P edic ion models o low esolu ion CB maps o QPI as a unc ion o V-8
ela i e igo ; (b) Residuals o p edic i e Model 3Q§ (linea i , Table 11).
(a)
(b)
6.7. G owe s Expec ancy based on C op Biome ic Models
The s anda d language o c op biome ics consis s o maps, hus all p edic ions o mula ed wi hin
his amewo k ha e o be deli e ed in such o ma o p oduce s o sha e, use, and make s a egic
decisions. As a esul , he ma hema ical body de eloped hi he o mus be in eg a ed in compa ible
maps. Based on he esul s ound and a ailable ield da a on ineya d biome ics, and inspi ed in
MIMO con ol sys ems, a Con ol Biosys em may be de ined such ha he inpu o he sys em is he
ela i e ege a i e igo es ima ed wi h he 8 mm lens (X1) be ween é aison and ha es ing, and he
ou pu comp ises he p edic ion maps o yield and quali y s anda dized by QPI. This biosys em can be
applied o ei he high o low esolu ion maps as schema ized in Figu e 33.