The variation of apparent crown size and canopy heterogeneity across lowland Amazonian ...

13 Pages·2009·1.41 MB·English

GlobalEcologyandBiogeography,(GlobalEcol.Biogeogr.)(2010)19,72–84
The variation of apparent crown size
RESEARCH
PAPER and canopy heterogeneity across
lowland Amazonian forests
geb_49372..84
NicolasBarbier1,3*,PierreCouteron2,ChristopheProisy2,YadvinderMalhi3
andJean-PhilippeGastellu-Etchegorry4
1FNRS-FWA,LaboratoiredeComplexitéet ABSTRACT
DynamiquedesSystèmesTropicaux,Université
Aim Thesizestructureofaforestcanopyisanimportantdescriptoroftheforest
LibredeBruxelles,50Av.FDRoosevelt,CP
environmentthatmayyieldinformationonforestbiomassandecology.However,
169,B-1050Bruxelles,Belgium,2IRD-UMR
itsvariabilityatregionalscalesispoorlydescribedorunderstoodbecauseofthestill
BotaniqueetBioinformatiquedel’Architecture
prohibitivecostofveryhigh-resolutionimageryaswellasthelackofanappropri-
desPlantes(AMAP),BoulevarddelaLironde,
atemethodology.Wehereemployanovelapproachtodescribeandmapthecanopy
TAA-51/PS2,34398MontpellierCedex05,
France,3EnvironmentalChangeInstitute, structureoftropicalforests.
SchoolofGeographyandtheEnvironment,
Location Amazonia.
UniversityofOxford,OxfordOX13QY,UK,
4Centred’EtudesSpatialesdelaBiosphère Methods WeapplyFouriertransformtexturalordination(FOTO)techniquesto
(CESBIO).UniversitédeToulouse,UPS, subsamplesofveryhigh-resolutionsatelliteimageryfreelyavailablethroughvirtual
CNRS,CNES,IRD,18Av.Ed.Belin,31401 globe software (e.g. Google Earth®) to determine two key structural variables:
Toulouse,France apparentmeancrownsizeandheterogeneityincrownsize.Asimilarapproachis
usedwithartificialforestcanopyimagesgeneratedbythelightinteractionmodel
(discrete anisotropic radiative transfer, DART) using three-dimensional stand
models.Theeffectsofsunandviewinganglesareexploredonbothmodelandreal
data.
Results Itisshownthatinthecaseof canopiesdominatedbyamodalsizeclass
ourapproachcanpredictmeancanopysizetoanaccuracyof5%.InAmazonia,we
couldevidenceaclearmacrostructure,despiteconsiderablelocalvariability.Appar-
ent crown size indeed consistently increases from about 14m in wet north-west
Amazonia to more than 17m for areas of intermediate dry season length (1–3
months)insouthandeastAmazonia,beforedecreasingagaintowardstheecotone
withtheCerradosavannabiome.Thisgeneraltrendreflectstheknownvariationof
other forest physiognomic properties (height) reported for South America and
Africa.Someregionsshowsignificantlygreatercanopyheterogeneity,afeaturethat
mayberelatedtosubstratum,perturbationrateand/orforestturnoverrate.
Mainconclusions Ourresultsdemonstratethefeasibilityandinterestof large-
*Correspondence:NicolasBarbier,FNRS-FWA,
scaleassessmentofrainforestcanopystructure.
LaboratoiredeComplexitéetDynamiquedes
SystèmesTropicaux,UniversitéLibrede
Keywords
Bruxelles,50Av.FDRoosevelt,CP169,
Forest structure, Fourier transform textural ordination, rain forest, remote
B-1050Bruxelles,Belgium.
E-mail:[email protected] sensing,SouthAmerica.
2005).Inparticular,theinternationaldecisiontoreducecarbon
INTRODUCTION
emissions linked not only to deforestation but also to forest
Tropicalforestsareamajorcomponentofthecarboncycle,and degradation(reducingemissionsfromdeforestationanddegra-
importanteffortsarebeingmadetoquantifytheirspatialand dation (REDD), United Nations Framework Convention on
temporal dynamics in a context of rapidly changing environ- ClimateChangeconference,Bali,December2007)hasnecessi-
mental and human pressures (Malhi & Phillips,2005;Wright, tated the development of reliable operational methods to
DOI:10.1111/j.1466-8238.2009.00493.x
72 ©2009BlackwellPublishingLtdwww.blackwellpublishing.com/geb
Amazonforestcanopyproperties
monitor forest structure at regional to continental scales thesefreelyavailableimagesdoprovidesufficientinformation
(Defriesetal.,2007).Thisrecentrenewedimpetushasledtoa toderivetexturalproperties.
surgeofinterestinmappingthestructureandbiomassoftropi- Inthispaperwepresentanovelapplicationoffreelyavailable
calforestregions. GoogleEarth®datatomapcanopystructureandheterogeneity
Oneapproachtoobtainingsuchinformationisthroughspa- across the Amazonian forest biome. The analysis is based on
tially extensive field inventories. Whilst providing important Fouriertransformtexturalordination(FOTO),whichproduces
information on forest structure (typically diameter distribu- an ordination of the canopies in function of the length scale
tions)andallometry,theseapproachescanbelimitedbytheir (spatialfrequency)distributionanddominance.Inotherwords,
spatial coverage and the difficulty of accessing many remote canopies are sorted as a function of the presence of one or
tropical forest regions.Useful complementary information on severalmodalapparentcrownsizes.Inthiscontributionweshall
canopy and crown structure can be obtained from remote thus refer to the value of the dominant apparent crown size
sensing approaches. Airborne remote sensing data (e.g. Lidar (ACS)aswellastoitsdegreeofdominance(homogeneity).Our
(Véga & St-Onge, 2008) and canopy video stereography) are aimsareto:
potentially very powerful but are expensive to acquire and 1. Evaluatethevariationinapparentcrownsizeinforestcano-
present challenging data management issues. Satellite remote piesacrosstheregion.
sensing (whether optical or radar band L) provides useful 2. Evaluate the variation in homogeneity in forest canopies
insightsintostructureandphenologybutisusuallylimitedby acrosstheregion.
low spatial resolution. These data are generally used without 3. Assess the impacts of sun-angle and systematic biases in
referencetotexture,onapixel-wisebasis(butseeWeishampel imageacquisitionondeterminationofthesecanopyparameters,
etal., 2001; Saatchi etal., 2007). Moreover, these signals have usingbothartificialcanopiesobtainedusingalightinteraction
beenshowntosaturateforintermediatebiomass(c.250tha-1 model(discreteanisotropicradiativetransfer,DART;Gastellu-
Mouginetal.,1999;Foody,2003)orleafareaindex(LAI)values Etchegorry etal., 1996) and an analysis of real forest canopy
(Hueteetal.,2002),preventingtheirapplicationintheinvesti- data.
gation of structure change in natural pluri-strata forests for 4. Interpret these findings in the context of what is known
which biomass can frequently reach 500 t ha-1. Attempts to aboutAmazonianforestecologyandgeomorphology.
produce non-saturating vegetation indices (e.g. an enhanced
vegetation index) with MODIS data exist, but the results
METHODS
obtained,forinstanceconcerningthetemporalvariationofthe
indices,remaindifficulttointerpret(Hueteetal.,2006;Myneni
Samplingandimagery
etal.,2007;Saleskaetal.,2007).
Veryhigh-resolution(VHR)data,i.e.of approximately1-m ThestudyregioncorrespondstotheextentofAmazonforests
resolution,arenowbecomingwidelyavailablefromcommercial sensu lato, i.e. the continuous stretch of forest covering the
satellites (Ikonos, QuickBird, Spot5). However, exploiting the AmazonandOrinocowatershedsandtheGuyanaShield(Eva
thematicinformationconveyedbytheseimagesrequirestaking etal.,2004).Weconcentrateonlowlandterrafirmeforests,using
their geometrical/textural characteristics into account more forestcovermasksderivedfromthemapsofSaatchietal.(2007)
than the individual pixel values. Very encouraging attempts andEvaetal.(2004).Wethereforeincludeddenseforests,open
havebeenpublishedrecentlytocharacterizethetexturalprop- forests,bambooforests,liana/dryforestsandseasonalforestsas
ertiesofVHRcanopyimages,onthebasisofspatialautocorre- a single entity, but excluded both seasonally flooded and
lation methods such as variography (Bruniquel-Pinel & montaneforeststypes.
Gastellu-Etchegorry, 1998), lacunarity analysis (Frazer etal., Twohundredsampleareas(1km2)wereidentifiedinGoogle
2005; Malhi & Roman-Cuesta, 2008) and two-dimensional Earth®, within homogeneous, apparently undisturbed, closed
power spectral analysis (Fourier transform) (Couteron etal., canopy lowland terra firme forests on relatively flat ground,
2005;Proisyetal.,2007).Asthedimensionalityoftheresulting where VHR DigitalGlobe QuickBird images were available.
multiscale indices is inherently high, multivariate ordination Theseimagesconsistoftruecolourcompositesoftheblue(450–
methods(e.g.principalcomponentsanalysis,PCA)arerequired 520nm), green (520–600nm) and red (630–690nm) bands,
tocharacterizeandcompareforesttexturalpropertiesoverlarge sharpened to 0.6-m resolution using the panchromatic band.
areas and many images (Couteron etal., 2005; Frazer etal., Theimagesareorthorectified.Wecouldnotfindinformationon
2005). Attempts have also been made to detect and map possibleradiometriccorrections.Imageextractswereexported
individual tree crowns, either manually or automatically, but fromtheGoogleEarthPro®interfaceatthenominalresolution
validation proved to be challenging (Asner etal.,2002; Palace of theQuickBirdimagery(0.6–0.7m).Forcomparabilitywith
etal.,2008). model simulations (see below), images were then resampled
Another limitation to the use of VHR data has been the (averagingaggregation)to2-mpixelresolutionandconverted
expense involved in acquiring targeted data from commercial togreyscalelevels.
providers.However,manyoftheseimagesarenowfreelyavail- Metadata for the QuickBird imagery used in this study are
ablefromproviderssuchasGoogleEarth®,albeitinaformthat listedinTableS1inSupportingInformation.Figure6(laterin
prevents detailed analysis of pixel-by-pixel data. Nonetheless, theresultssection)presentsthespatialvariationandfrequency
GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd 73
N.Barbieretal.
distributions of the acquisition parameters.Sun vertical angle (Couteronetal.,2006)forrepetitivepatternsortextures,suchas
(q)variedbetween44.4°and73.5°(0°towardshorizon),view thoseformedbyforestcanopies.Aswewerenotinterestedhere
s
zenith angle (q) between 1° and 21° and relative sun–sensor in anisotropic properties of the images, periodograms were
v
angle(j )between0.0°(backscattering,i.e.thesunislocated simplified through the computation of the radial spectra
s–v
behindthesensor)and178.2°(forwardscattering). (r-spectrum) that is the average of the frequency information
acrossazimuthaldirectionsofspace.Frequenciesareexpressed
incycleshm-1,thatisthenumberof repetitionsovera100m
TheFOTOmethod
distance.
TheuseoftheFOTOmethodtocharacterizethespatialstruc- Thesizeof samplingunitwindows(i.e.imageextracts)was
tureofvegetationinVHRimageryhasbeenpresentedelsewhere chosen to include several repetitions of the largest pattern of
(Couteron,2002;Couteronetal.,2005,2006;Proisyetal.,2007). interest.In the present case,average tree crown diameters are
Inbrief (Fig.1),verticalaerialcanopyimagesof adequatesize notexpectedtoexceed30m,andwindowsizewasthereforeset
(seebelow)wereeitherextractedfromsatelliteimageryorpro- to150m(atleastfiverepetitions).Substantialvariations(bya
videdbyDARTsimulations,andsubjectedtoatwo-dimensional factorofthreeormore)ofthewindowsizehave,however,been
Fourier transform [via the fast Fourier transform algorithm; showntoprovideequivalentresultsintermsoftexturegradients
implemented in Matlab® (MathWorks, Inc.)], and to subse- (Couteronetal.,2006;Proisyetal.,2007).
quent computation of the two-dimensional periodogram or A table was constructed (Fig.1) containing the r-spectra of
powerspectrum,i.e.thesquaredamplitudeoftheFouriertrans- allanalysedunitwindows.Inthistablecolumnscorrespondto
form.Thelatterexpressestheapportioningof theimagevari- the set of Fourier harmonic spatial frequencies and rows to
ance (or power) into frequency bins along the two Cartesian individual windows. The table was centred and standardized
axes,orequivalently,fordifferentspatialfrequenciesandorien- across lines (i.e. column-wise subtraction of the mean and
tationsinpolaraxes.Thischaracterizationofimagesintermsof division by the standard deviation) and an ordination per-
spatial frequencies constitutes a very efficient way to quantify formed (PCA) to identify the main gradients of variation
pattern scale and intensity, especially but not exclusively between windows on the basis of their spatial (frequency)
attributes. In order to attenuate the variability resulting from
varying acquisition parameters of the QuickBird scenes, a
variant (Fig.1) of this ordination method was used,in which
unit windows were separated into pre-defined bins of similar
acquisition parameters. Standardization was then performed
separately for each bin,and the resulting standardized spectra
werereunitedagaininasingletableforordination(hencethe
name partitioned standardization). The objective of this
approach was to minimize the variability component due
toinstrumentaldiscrepancies.Thisisefficientonlyifthecom-
plete observable canopy texture gradient is present in each of
the instrumental bins.
Figure1 FlowchartillustratinghowFouriertransformtextural Figure2 Principalcomponentsanalysis(PCA)ofsatellite
ordination(FOTO)analysisisappliedinthispaperonboth imagerydata(QuickBird).Plotofeigenvalues.Inset:correlation
real-world(QuickBird)andsimulated(discreteanisotropic oftheoriginalvariables,i.e.thefrequenciesoftheFourier
radiativetransfer,DART)imageswitheither‘global’or r-spectra,expressedincycleshm-1,withthePCAaxes.Some
‘partitioned’standardizationofr-spectra. intermediatevaluesarenotlabelledforclarity.
74 GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd
Amazonforestcanopyproperties
Simulatingreflectanceimagesofforestcanopy asymptotic equation given by the authors. Indeed, the latter
couldnotbeusedforrealisticextrapolationsabovethemaximal
Asetofartificiallygeneratedforestcanopysceneswassimulated
values studied by the authors, that is a DBH of c. 1.6m
usingDART(v.2.0.4,CESBIO)inorder:to(1)verifytherela- max
(asymptotic H = 45m). In our simulations, mean crown
tionship between the textural ordination and controlled mor- max
diametersofthedominantstratumrangedbetween5and25m.
phologicalparameters–inparticularcrowndiameters,and(2)
Acquisitionparameters(viewingzenithangle,sunverticalangle
quantify the impact of varying acquisition parameters on the
and sun-sensor horizontal angle) were also made to vary
resultsoftheFOTOanalysis.Adetaileddescriptionofthemodel
independently from each other and from the morphological
hasbeenpresentedelsewhere(Gastellu-Etchegorryetal.,1996;
parameters(Table1),withinasimilarrangeofvariationasthat
Bruniquel-Pinel&Gastellu-Etchegorry,1998),andwewilllimit
observedinthesetofactual(QuickBird)images(TableS1and
ourselvestoaquickoverview.ADARTsceneismodelledasa
Fig.6).Atotalof330sceneswerethusmodelled.
three-dimensionalarrayofvolumetriccells(orvoxels),eachof
which presents specific optical properties (transmittance and
phasefunctions)dependingonthecelltype(soil,water,trunk,
RESULTS
leaves,etc.).Certainvoxels(e.g.leaves)aremodelledasturbid
media with volume interaction properties and others (trunks,
Ordinationresultsandcrownsizeinversion
soil)assolidmediawithsurfaceproperties.Structuralcharac-
teristicswithinthecell(e.g.LAIorleafangledistribution)influ- Theordinationofthe7200(200areas¥36unitwindows/area)
ence the cell’s optical properties. Radiation transport (i.e. the satelliteviewsofAmazoniancanopiessynthesizedmosttextural
scattering of rays from each cell) is simulated iteratively in a information along the two first PCA axes. The first axis
discretenumberofdirections.Interactionwiththeatmosphere accountedfor47.6%ofthevariationinimagespatialstructure
or soil topographic features can possibly be added, as well as (Fig.2),while the second axis only contributed 8.7%.As with
wavelength-specificbehaviours.However,inthepresentstudy, previous applications of the FOTO methods to tropical forest
we kept to a monospectral (visible) domain on a flat terrain canopies(Couteronetal.,2005;Proisyetal.,2007),thecorrela-
withoutatmosphericeffects.DARTscenesweremodelledusing tioncircle(Fig.2,inset)showedatypicalclockwisedistribution
the same extent and resolution as the satellite unit windows ofthefrequencies(expressedincycleshm-1,i.e.thenumberof
(150mand2m,respectively). repetitionsof thetemplateperiodicpatternona100-mrefer-
Trees were modelled using an ellipsoidal approximation of encedistance).Inotherwords,thegradientalongPCA1ranges
the crowns,with trunks randomly located within a given dis- from windows characterized by small frequencies (2–3 cycles
tance (l, location radius; Table1) from the nodes of a square hm-1, thus a wavelength between 50 and 30m) up to those
mesh(internodedistancer).Onlytwostratawereincluded,with characterizedbylargefrequencies(8–10cycleshm-1,wavelength
distinct normal distributions (i.e. distinct mean and standard between12.5and10m),whilenegativePCA2valuesreflectthe
deviations)ofthemorphologicalparameters.Table1showsthe relative prominence of intermediate frequencies around 5
ranges of values for the morphological parameters used to cycles/hm(wavelengthofabout20m),thereforeallowingafiner
modelthedominantstratum,aswellastheallometricrelation- characterizationof medium-scaletextures.Hencetheposition
shipslinkingtheseparameters.Theserelationshipswerederived along the PCA1 axis indicates the mean length scale of image
from a set of 54 Bolivian moist-forest species (Poorter etal., spatialstructure,whereasradialdistancefromthePCAorigin
2006), although we took a simpler, linear relation between indicatesrelativedominancebyasinglelengthscale,i.e.homo-
diameteratbreastheight(DBH)andheight(H),insteadofthe geneityoftheimagespatialstructure.Aselectionofcharacter-
Table1 ParametervaluesandallometryrulesusedtogenerateartificialstandsandtoruntheDARTlightinteractionmodel.
Parameter
symbol Definition Rangeorallometryrule Std.dev. Unit
r Meshsize 5–25(10levels) d/4(onlocation) m
l radiusoftreepositionsaroundnodes r/2
d Crowndiameter(ellipsoidhorizontalaxes) r d/4 m
A Crownarea(intermediateparameter) 0.25pd2 m2
H Totalheight(intermediateparameter) exp[(lnA+1.853)/1.888] m
h Crownheight exp(-1.169+1.098lnH) h/4 m
c c
h Trunkheightbelowcrown H–h h/4 m
t c t
DBH Trunkdiameterbelowcrown H/42 DBH/4 m
q Sunverticalangle 45–75(threelevels) Degreesfromhorizon
s
q Sensorzenithangle 0–24(threelevels) Degreesfromzenith
v
j Differencebetweensunandsensorazimuthangles 0–180(threetofourlevels) Degrees
s–v
GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd 75
N.Barbieretal.
Theadjective‘apparent’aimshereatunderliningthepossibility
that a dominant scale in ‘complex’ real-world canopies, as
opposedtoourDARTscenes,mightinsomecasescorrespondto
a modal size of crown clumps rather than individual tree
crowns.
Influenceofinterscenevariationofacquisition
parameters
The very high correlation obtained for DART scenes between
texturalordinationresultsandcrowndiametersintheabsence
of any correction for varying acquisition angles (see previous
section) suggests that the influence of acquisition parameters
couldalsobesmallforoursetof real-worldimages.However,
thegeographicalvariationofthesunverticalacquisitionangle,
q, presents a strongly organized spatial pattern (Fig.6a), in
s
Figure3 Principalcomponents(PCA)plotofQuickBird whichrelativelylowsunverticalanglesaremoreabundantinthe
(satellite)unit-windowswithdiscreteanisotropicradiative southerntipofthestudyarea.Thisisbecausemostcloud-free
transfer(DART)(simulated)windowsaddedassupplementary imageacquisitionsoccurinthedryseason.InsouthernAmazo-
individuals.Eachpointcorrespondstoasingle150-msideunit nia this corresponds to the period May–September, when the
window,characterizedbyitsFourierr-spectrum.Only sun (and hence the tropical convection zones) is above the
homogeneous(marginal)texturesareproducedbytheDART
NorthernHemisphereandsunanglesarehencelow.Innorthern
model,i.e.texturesdominatedbyasinglespatialfrequency.
Amazonia(neartheequator)thecorrelationbetweensunangle
QuickBird(Q1–Q10)andDART(D1–D8)unitwindows
andcloud-freeconditionsislessstrong.Thevariationofq and
characterizingthegradientofhomogeneouscanopiesaswellas v
j doesnotshowanyclearspatialpatternoverthestudyarea
typicalheterogeneouscanopies,asshowninFig.4andinFigsS1 s–v
(Fig.6b,c).
&S2,arelocalizedinthePCAplane.
Therefore, it was necessary to investigate, and if necessary
mitigate,potentialbiasduetothenon-randomgeographicdis-
istic windows (provided in the Supporting Information) tributionofthesunverticalacquisitionangle.Afirstqualitative
illustrates the overall gradient of observed canopy textures indicationofthelimitedimportanceofbiasisthatthepatternof
(FigsS1&S2)andof theirr-spectra(Fig.S3).Thepositionof geographicalvariationofq isquitedifferentfromtheonefound
s
thesewindowsinthePCAispresentedinFig.3. forcanopytexture,asitisshiftedtowardsthesouthanddoesnot
Tohelpinterprettherelationshipbetweentheresultsoftex- presentthesamefeaturestowardstheGuianaShield.However,
turalordinationandforestmorphologicalparameters,theposi- linearregressionofPCA1valueswithq gaveasignificantresult
s
tionofDART-simulatedimagesintheordinationisalsoshown (P<0.001)(Fig.7a).Nosignificantinfluenceofthetwoother
(Fig.3).Althoughmodelledstandstructureswereverysimple, angles could be evidenced (figures not shown). Performing a
forest canopy mock-ups are visually realistic (Fig.4) and the partitionedstandardizationpriortoordination,i.e.standardiz-
limitsofthetwocloudscloselymatchinthePCAplane(Fig.4), ing r-spectra within bins of homogeneous acquisition angles,
although DART stands only occupy the cloud’s margins. The allowed us to factor out unwanted influences of acquisition
latter result confirms that points located away from the PCA conditionsonthequantificationofthecanopytexturalgradient.
origin correspond to more homogeneous canopies,which are Partitioned standardization of QuickBird unit windows in as
dominatedbyasinglespatialscale. fewasthreelevelsof q indeedallowedtheremovalof allsig-
s
Quadratic regressions between the two first PCA axes and nificant trends (Fig.7b) due to this factor. Results presented
mean crown size (d) of the DART unit windows showed the hereafterarethusproducedusingPCAvaluescomputedusing
potentialofthemethodforretrievingcrownsizevaluesinreal- thelatterpartitioningapproach.
world stands.R2 values reached 0.96 for the following model: Wealsocheckedforpossibleinteractionsbetweenacquisition
d=16.553+0.904PCA1-0.019PCA12+0.619PCA2-0.018 anglesandthecrownsize–texturerelationshipusingthesimu-
PCA22.Thisresultwasobtainedwithoutanycorrectionlinked latedimages.Forinstance,extendedshadowsduetolowersolar
tothevariationoftheacquisitionparameters(aswillbeimple- anglescouldhaveamoreimportanteffectonthecharacteriza-
mentedbelow).Figure5presentstherelationbetweeninverted tion of forests made of larger trees. Using a linear model, we
mean crown sizes (on the basis of the quadratic model) and first checked for the homogeneity of slopes between crown
mean crown sizes (d) used for DART modelling. A simpler diameter and PCA1, with the different levels (experimentally
linear fit with PC1 scored an R2 of 0.88: d = 15.206 + 0.871 defined,Table1)ofacquisitionanglestakenasadiscretefactor.
PCA1. Thisallowedustodiscardtheexistenceofanysignificantinter-
Boththesemodels(quadraticandlinear)wereusedinsub- actionbetweenthecrownsize–texturerelationshipandacqui-
sequentanalysestoinferACSinreal-world(QuickBird)images. sition angles. However, the ANCOVA indicated a significant
76 GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd
Amazonforestcanopyproperties
D1 D2 D3 D4
D5 D6 D7 D8
Figure4 Discreteanisotropicradiativetransfer(DART)simulatedunitwindowscharacterizingthegradientofmeancrownsize.These
modelledcanopyimagesareproducedusingtheDARTlighttransfermodelonthree-dimensionalartificialstandscorrespondingtothe
parameterrangesummarizedinTable1.SeeFig.3forlocalizationofthesewindowsinthefirstprincipalcomponentsanalysisplan.
windows.Hereagain,thepartitionedstandardizationprocedure
allowed efficient minimization of the influence of acquisition
angles.
MappingapparentcrownsizeinAmazonia
We have shown above that PCA coordinates could be used to
infer mean crown sizes, or in the case of real, potentially
complexcanopies,ACS.Wefirstusedthesimplelinearmodel
based on PCA1 values (see above), to derive the apparent
crown size of the 7200 QuickBird unit windows. These ACSs
were then averaged for each sample area,to provide a sample
of 200pointswithmeanACSvalues.ThesymbolsinFig.8(a)
showthespatialdistributionof thesemeanACSvaluesacross
Amazonian terra firme forests. In the same figure, the colour
Figure5 Matchbetweenpredicted(inverted)apparentcrown scale represents a kriged interpolation (ordinary kriging,
size(ACS),obtainedusingaquadraticmodelinvolvingPCA1and spherical model;Cressie,1993) of ACS for terra firme forests.
PCA2,andthe‘actual’meancrowndiameter(d)ofthediscrete
Hatched and cross-hatched areas represent zones where the
anisotropicradiativetransfer(DART)simulatedscenes.The1:1
kriging standard error is above 1.95m and 2m, respectively.
lineisalsorepresented.Ther2ofthelinearfitisof0.95and
Interpolation error is higher in areas where sampling is rela-
exactlymatchesthe1:1line.
tively sparse, such as French Guyana, southern Colombia or
north-eastern Brazil.
FigureS4 shows a second ACS map, resulting from a more
(P<0.05)effectforq andj ,andaverysignificanteffectfor restrictive approach based on the quadratic inversion model
v s–v
q (P<10-5)onPCA1values.Nosignificantinteractionbetween involvingPCA1andPCA2,butwithinferencelimitedonlyto
s
thedifferentanglescouldbeevidenced.Therefore,acquisition the most homogeneous unit windows. For this map we took
properties, and in particular sun vertical angle, did have a onlythesubsetofunitwindowslocatedbeyondthe75%quan-
small influence on the textural ordination of DART unit tile of the distance to the centre of the PCA.These are image
GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd 77
N.Barbieretal.
Figure6 Distributionofacquisition
anglesoftheQuickBirdsetofimages
withmapsofparametervaluesoverthe
studyarea(left)andhistogramsof
absolutefrequencies(numberof
images).(a)Sunverticalangle,q.
s
(b)Sun–sensorazimuthangle,j .
s–v
(c)Viewzenithangle,q.Symbols
v
representlocationsofsampledsatellite
(QuickBird)images.Symbolsizeis
proportionaltothestandardizedvalueof
eachparameter.Squaresrepresent
negativestandardizedvalues,circles
representpositiveones.Geographical
coordinates;datum,WGS84.
types where the relationship between image length, scale and overallpatternofvariationincanopytextureprovedrobustwith
crown size has been validated by our modelling with DART regard to alternative interpolation procedures (i.e. different
above.ThegaininconfidenceinlocalACSvaluesisbalancedby krigingmodelsorinversedistanceweighting)ortothefaculta-
anincreaseinkrigingstandarderror(above3m)inducedbya tivecorrectionofacquisitionparameters.
reducedsample(n=145).
A similar large-scale pattern of the variation in ACS across
MappingcanopyhomogeneityinAmazonia
Amazonianterrafirmeforestswaspresentinbothmaps(Figs8a
& S4).ACSs tend to be highest (>16m) in a broad east–west Another interesting textural characteristic of the canopy is its
band stretching 5–10° S of the equator, and also fairly high degreeofhomogeneity(i.e.singlescaledominance).Wethere-
(>15m)inthecontiguousregioninnorth-easternAmazonia. foreinvestigatedthespatialdistributionof scale-specific(peak
Smallcrownsizes(<14m)dominateinnorth-westernAmazo- dominated)versusmultiscalecanopies(flatspectrum)inAma-
nia(althoughimagedensityislowerbecauseofcloudiercondi- zonianterrafirmeforest.Theindexusedwasthestandardized
tions)andalsoattheverysouthernfringe.Hencebroadlythere distancetothePCAorigin(onlyfortheangulardirectionsinthe
is a directional gradient inACS,with the lowest values in the PCAforwhichthedistancecorrespondedtosinglepeakdomi-
north-westandhighervaluestothesouth,south-eastandeast, nance,i.e.PCA2values(cid:2)0).Theresultingpattern(Fig.8b)is
although there is substantial local variability inACS probably different from the ACS pattern presented above. There is no
related to local landscape and hydrological conditions. The clearoverallregionaltrendincanopyhomogeneity,butdistinct
78 GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd
Amazonforestcanopyproperties
thereforehavemuchinfluenceontheresultof theanalysis,as
long as the spatial arrangement of relative greyscale values is
conserved.Thisisofcourseanimportantpre-requisiteforthe
use of virtual globe imagery, or for tropical applications in
general, for which the user does not have access to base (i.e.
multispectral and atmospheric) data to perform radiometric
corrections. However, variations in other scene acquisition
parameters, namely sun and sensor vertical angles and sun–
sensorazimuthalangle,hadthepotentialtoaltertheobserved
sizeandproportionofthetreeshadows,andthereforethevery
spatialarrangementweaimtocharacterize.Forinstance,forthe
case of VHR images of Amazon rain forests,Asner & Warner
(2003)discussedthevariationoftheshadowfractioninasetof
29 Ikonos® images taken in the LBA dataset.Using their data
(Table2 of Asner &Warner,2003),we found that the relative
sun–sensor azimuth angle explained a significant part (R2 =
0.25,P<0.001)ofthemeanshadowfraction.However,wecould
showbothonthebasisofrealworlddataandthroughtheDART
modelling of structurally and radiometrically realistic stands,
that the FOTO method is only marginally dependent on sun-
viewing geometry, and that an appropriate, simple correction
Figure7 LinearregressionsbetweenthePCA1,i.e.themain
(partitioned standardization) can completely remove this
texturalgradientintheimagedataset,andsunverticalanglefor
satellite(QuickBird)images(n=200,r2=0.07).Eachpoint dependence.
correspondstotheaveragePCA1valuesforonesamplingzone
(i.e.36unitwindowsextractedfromagivenQuickBirdimage).
(a)Afteraglobal,non-partitionedstandardization(r2=0.06).(b)
Explainingspatialvariationincrownsizeand
Afterapartitionedstandardizationwiththreebinsofsunvertical
angle(r2<10-4). heterogeneity
AnyspatialtrendinACSislikelytobeinfluencedbytherainfall
regimeandlocallandscapetopography,hydrology,soiltypeand
regions dominated by more heterogeneous canopies (square perhapsotherbiogeographicalquirks.Oneusefulmetricofthe
symbols,brownishinterpolatedvalues)dostandout.Theseare rainfall regime is the number of months with rainfall below
in: (1) north-west Amazonia (ranging from Ecuador through 100mm(i.e.dryseasonlength,orDSL;Sombroek,2001),which
northernPeru,southernColombiaandnorth-westernBrazil), isplottedinFig.9(a).Itcanbeseenthatthebroadbandoflarger
(2)northernBoliviainsouth-westernAmazonia,and(3)north- ACSscorrespondstoaregionwithasignificantbutmoderate
eastern Amazonia, ranging from the Amazon River to the dry season (1–3 months), with a maximum ACS (c. 17m on
Guyanas.Zonesdominatedbyhomogeneouscanopiesareless average) at a DSL of 2 months. Regions with no dry season
distinct,butthereisanindicationofsuchazoneattheeastern correspondtosmallcrownsizes,asdoregionswithalongdry
fringe of Amazonia, and also perhaps in central-northern season(>5months),whereelementsofsavanna(Cerrado)veg-
Amazonia. etation may begin to appear. Hence maximum ACS shows a
unimodalrelationshipwithDSL,butwithinthisbroadenvelope
therecanbesubstantiallocalvariabilityinACS.Theecological
DISCUSSION
reasonfortherelationshipbetweenACSandDSLisnotclear:
moderateseasonaldroughtandaclear,sunnydryseasonmay
TheapplicabilityoftheFOTOmethod
competitivelyfavourastratumoflarger-canopy,deeper-rooted
InthispaperwehaveshownthepotentialoftheFOTOmethod trees,butstrongerseasonaldroughtmaycausehydrauliclimi-
toconsistentlyprovidenon-saturating,large-scaleestimatesof tations and a restriction in crown size. This very consistent
canopystructuralpropertiesobservedinVHRimagery,particu- pattern of variation has already been reported through field
larlyimagerynowfreelyavailableonvirtualglobesoftware. observationsofotherstructuralparameters,suchasmaximum
AnimportantadvantageofFOTOasperformedhereliesinits tree height,and indeed the whole forest physiognomy (Ellen-
relativeindependencefromtheabsolutevalueofbothmeanand berg,1975;Longman&Jenik,1987;Richards,1995).According
varianceoftheimages,sincethemean-centredimagesarechar- tothesameauthors,themosthumidCentralAfricanforestsalso
acterizedintermsoftheproportionoftheirvariance(however showadecreaseintreeheight,biomassanddiameters.ForAma-
largeitis)explainedbythespatialfrequencybins(Diggle,1989; zonia,Saatchietal.(2009)alsoreportthatthenorth-west(most
Mugglestone&Renshaw,1998).Variationsincontrastandlumi- humid) region presents a distinctively lower fraction of large
nosity,orpoorradiometricalignmentsbetweenimages,donot trees.
GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd 79
N.Barbieretal.
Figure8 Mapsofcanopytexturevariationinlowlandterrafirmeforests(pointwiseandinterpolatedvalues).(a)Apparentcrownsize
(inm)estimatedusingalinearfunction(modelinversion)ofthefirstcomponentoftheprincipalcomponentsanalysis(PCA;n=200).
Symbolsrepresentthelocationofsampledsatellite(QuickBird)images.Symbolsizeisproportionaltothedeviationfromthemean.
Squaresrepresentvaluesbelowthemean,circlesrepresentvaluesabovethemean.Hatchedzonesindicateakrigingstandarderrorabove
1.95m;cross-hatchedzonesindicateakrigingstandarderrorabove2m.(b)QuantilesofthedistancetoPCAorigin,quantifyingthe
degreeofhomogeneityofthecanopy(highervaluesaredominatedbyasinglescale).Symbolsrepresentlocationsofsampledsatellite
(QuickBird)images(n=200).Symbolsize/shapeindicatesthedistancetoPCAorigin(inquantilesofthedistributioninthecorresponding
angularsector).Hatchedzonesindicateakrigingstandarderrorabove20%.Inboth(a)and(b),PCAisrunusingapartitioned
standardization(threebinsofsunverticalangle)ofther-spectra.Interpolationusesordinarykriging(sphericalmodel).Geographical
coordinates;datum,WGS84.
Soilsandlandformmightbeexpectedtoexplainsomeofthe hilly landscapes in the south-west (dominated by acrisols and
regional variability in ACS (Fig.9b,c). However, the band of cambisols),withlittleapparenttrendinmeanACS.Theregion
large ACS ranges over regions of crystalline shield in the east ofsmallACSinthenorth-westcontainsareasofpoorlydrained,
(dominated by well-drained ferralsols and nitisols), through low-elevation, plinthosol-dominated Amazonian peneplain;
low,poorly drainedAmazonian peneplain in the centre-south hence high rainfall and poor drainage and soil structure may
(dominatedbyplinthosols),throughtoslightlymorefertileand interacttofavoursmallcrownsizesinthisregion.Hypotheses
80 GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd
Amazonforestcanopyproperties
Figure9 Mapsofpotentialenvironmentaldrivers.(a)Dryseasonlength,inmonthsbelow100mmrainfall(sourceTRMM;Wolffetal.,
2005).(b)Landtypes(sourceFAOetal.,1998).(c)Dominantsoilclasses(sourceFAOetal.,1998).Pointsrepresentlocationsofsampled
satellite(QuickBird)images.
GlobalEcologyandBiogeography,19,72–84,©2009BlackwellPublishingLtd 81