a new approach to modeling tree rainfall interception

7/30/2019 A New Approach to Modeling Tree Rainfall Interception

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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. D23, PAGES 29,173-29,188,DECEMBER 16, 2000

A new approach o modeling ree rainfall interceptionQingfu XiaoHydrologyrogram, epartmentf Land,Air andWaterResources,niversityf California, avisE. Gregory McPhersonUSDA ForestService, acificSouthwest, estern enter or UrbanForestResearchndEducation, avis,CalifomiaSusan L. Ustin and Mark E. GrismerHydrology rogram, epartmentf Land,Air andWaterResources,niversity f California, avisAbstract. A three-dimensionalhysically ased tochastic odelwasdevelopedodescribe anopy ainfall nterception rocessest desired patialand emporalresolutions. uchmodeldevelopments importanto understandheseprocessesecauseforest anopynterception ayexceed 9% of annual recipitationn old growth rees.The modeldescribeshe nterceptionrocessroma single eaf, to a branch egment, ndthenup to the ndividual ree evel. It takes nto accountainfall,meteorology,ndcanopy rchitectureactors s explicitvariables.Leaf and stemsurface oughness,architecture,ndgeometric hape ontrolboth eaf dripandstemflow.Model predictionswereevaluated singactual nterception atacollected or two matureopengrown rees,a 9-year-oldbroadleafdeciduous ear ree (Pyruscalleryana Bradford"or Callery pear)and an 8-year-oldbroadleaf vergreen ak tree (Quercus uberor cork oak). Whensimulating 8 rainfall events or the oak ree and 16 rainfall events or the pear ree, hemodelover estimatednterceptionossby 4.5% and 3.0%, respectively,while stemflowwasunderestimated y 0.8% and 3.3%, and hroughfallwasunderestimated y 3.7% forthe oak ree andoverestimated y 0.3% for the pear ree. A modelsensitivity nalysisindicateshat canopy urface torage apacity ad he greatestnfluenceon interception,and nterceptionossesweresensitiveo leaf andstemsurface rea ndices.Amongrainfall actors,nterceptionosseselative o gross recipitation eremostsensitiveorainfallamount.Rainfall ncident nglehada significant ffecton totalprecipitationinterceptinghe projected urface rea. Stemflowwas sensitiveo stemsegment nd eafzenithangledistributions. nhanced nderstandingf interceptionossdynamics houldlead o improvedurban orestecosystemmanagement.1. Introduction IL = S + Ket, ()

Natural forests'canopy nterceptionanges rom 15% to 40%of annualprecipitationn coniferstands nd from 10% to 20% inhardwood tands Zinke, 1967], while it may exceed59% for oldgrowth forests [Baldwin, 1938]. Canopy interception iscontrolled by widely variable meteorologicaland canopyarchitecture factors [Crockford and Richardson, 1990].Empirical, physically based, and stochasticmodels have beenused to study the role of different factors that influenceinterception. Empirical and statistical models are first-orderapproximations hat use linear formulas to determine rainfallinterception,stemflow (ST), and throughfall TH) as constantproportions f grossprecipitationP) [Horton, 1919; Kittredge,1948;Helvey nd Pattic, 1965;Zinke,1967]. For example,Horton's [ 1919] model is:

Copyfight000by heAmericaneophysicalnion.Paper umber 000JD900343.0148-0227/00/2000JD900343509.00

while Kittredge 1948] usedST = b P- a , (2)

andHelveyand Pattic [ 1965] usedTH = b2 P- a2, (3)

where L is total nterceptionoss,S is canopy torageapacity,is the ratio of evaporation urface o projectedarea, e isevaporationate, is time, anda, b, a2, andb2 are site-specificempirical i.e., regression) arameters btained rom long-termrainfall nterceptionmeasurements. his type of model ails forsmall ainfalldepthshat do not fill the surface torage apacity.The empirically derived coefficients do not account for theinfluenceof the magnitudeof the rainfall event (i.e., rainfallintensity ndduration) ndcanopy rchitecturen nterception.The first physically ased nterceptionmodels Rutteret al.,1971, 1975; Rutter and Morton, 1977] relied on water balancecalculations or canopy surfacewater storage. This model29,173


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29,174 XIAO ET AL.' MODEL FOR TREE RAINFALL INTERCEPTIONconsideredcanopy surface storage as a function of grossprecipitationallingon the canopy urface, rip from he canopy,andevaporationrom hecanopy urface ndcanbe written

simulateshe meannumber f raindropsn') retained n thecanopyurfacelementnd hemean umberf raindropsm')striking he canopysurface lement hroughdCdt - (1 fg -fs) P- Doexp b (C- S))- e, (4)

whereC is canopy ater torage,g is a gap ractionhatcontrolsthe precipitationcontributing o free throughfall,s is theprecipitationractioncontributingo stemflow, ndp and e areprecipitationndevaporationates, espectively.heexponentialterm of equation 4) represents anopysurfacedrip rateswhereDo and b are empiricaldrainageparameters nd S is the canopystorage apacity. his modelhas beenwidely used n wildlandforests Eltahir and Bras, 1993], especiallyn tropical ain forests[Jetten,1996], and hasbeenmodified or urbanwaterand energybalance studies Grimmond and Oke, 1991; Xiao et al., 1998].Massman [1983] incorporated rainfall rate into the dripcomponent f the modelusingCd= O0 d0 )T, (5)

wherep is rainfhll ate,d is drip rate rom crown eaves ndstemsurfhces, rip parameter o s an empirical rainage onstant, ndthe drainageparameter o s determinedor eachevent.Neithermodel representedby equation (4) and (5) considers anopyarchitecture ffectson interceptionosses.Gash 1979] modified he Ruttermodelby describingainfallas a series of events such that the time lag betweenevents ssufficient o dry the canopy urface.Gash 1979] urtherassumedthat rainfall and evaporation atesare constant uring he stormand that there is only one rain event per day. For M rainfhllevents that are insufficient to saturate the canopy surfacecompletely, nd N events hat are large enough o completelysaturatehe canopy urface,Gash'smodelcanbe writtenN+M , NZ [gj= l-fgfs) +''Z(Pj-P')j=l j=l

Mfgj=l

M+N-JEt,,o,k=Jt fsZ ej, (6)j=l

p,_ RSn(l- E ),E R(1-fg -fs)where E and R are mean evaporationand rainfall rates, St istrunk storagecapacity,and J is the numberof eventsabove hecritical rainfall (St/fs). Several applications f this model tointerception osses n natural forests Pearce and Rowe, 1981;Gash et al., 1995; Llorens, 1997] yielded satisfacto agreementbetween predicted and field measurements. However, in thewest United States, winter cyclonic precipitationcan occurseveral times through the day and the shoff time intealsbetween events allow only a small action of canopy surfacestorage o be removed hroughevaporation.A stochasticmodeldeveloped y Ca[der [1986, 1996] used hePoissondistribution to model wetting and ding of the canopysurface. Hall [1992] incoorated condensation o improvemodel peffoance for high-intensity tos. Raindropsize wasintroduced to simulate canopy surface wetting. The model

n =J ( 1 exp(-B)) + exp (-B) (i - J ') i=1

PB-

i i

(7)

where ' s hemaximumumberfraindropshat an e etainedon the canopysurfaceelement,M is the largest ntegernumberthats esshan',Vps hemeanolumef he aindrop,nd ' sthe numberof surface lements er unit groundarea.More recently, Liu [1997] presenteda combinedphysical-empiricalmodel hat estimatesainfall nterceptionossusing

R (8)

where DRY0 is initial canopydryness efore ainfall, DRY is acanopy rynessndex,and T is rainfallduration.Throughfall ndstemflow are estimated rom linear relationshipswith rainfall.However, he rainfall ncidentangleand canopy rchitecture erenot considered.It is difficult to apply event-basedpproacheso simulate hedynamicprocess f rainfall interception ecause f the largespatialand emporal ariation n processes. or example, vent-basedmodelsdo not considerhe gradual low of wateralong reestems,yet models hat incorporate uch actorscan enhanceourunderstandingf how interception rocessesmpactstorm unoff.An ideal nterceptionmodel or tree rainfall nterception hould

consider both meteorologicaland tree architectural actors hatinfluence he interception rocess. The results rom the modelsimulations, n addition o providingaccurate stimationof treeinterception, houldbe capableof distinguishinghe influenceoftree factors e.g., species, rchitecture, imension, hape, nd eafand stem surfhce roughness), ainfall factors (e.g., intensity,magnitude,and duration),and meteorologicalactors e.g., windspeed,wind direction, olar adiation, ndair temperature) n treeinterception rocesses.Nearly 80% of the United States population lives inmetropolitan reasand, on average, ree canopies rom about75billion treescover 33% of this land area [Johnson,1998; Dwyeret al., 1998]. The impact of urban orestson runoff and possibleflood control is of growing interestas part of efforts to protectwater quality within urban watersheds. ree planting s one ofseveral best managementpractices BMPs) demonstrated t aresidential etrofit in Los Angeles Condon and Moriarty, 1999].The site has been converted into a "miniwatershed" that retainsrunoff on site and stores roof runoff for summer landscapeirrigation. Policymakers re consideringmplementing his typeof decentralized pproach o urban watershedmanagement, utlack quantitative ata on the effectiveness f differentBMPs. Forinstance, one need is a better understanding f how differentspeciesof trees and their spatial configuration mpact runofftiming and volume at the scale of an individual tree anddevelopmentarcel.Becausemanyurban reesare opengrownand relatively isolated from each other, interceptiondata fromnatural forest standsmay not be directly transferable o urbantrees.Anotherneed s for data to scaleup from the development


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XIAO ET AL.: MODEL FOR TREE RAINFALL INTERCEPTION 29,175

site to the urban watershed. Understanding and accuratelyestimating ainfhll nterception rocessest the single-treeevel skey to understandingainfall interceptionn the urban orest,Existing rainfall interceptionmodelshave limitations o theirapplication for estimating single-tree interception in urbanenvironments.The primary constraint s insufficient attention otree crown shape and structure.For example, actual rainfallinterceptiondepends ess on crown projectionarea as seen romabove han on "effectivecrown projectionarea" as seen rom theangle of incoming rainfall. Effective crown projection area isinfluenced by tree shape. For example, Italian cypress(Cupressus sempervirens "stricta") is a columnar tree. Itseffectivecrown projectionarea s leastwhen the rainfall incidentat zenithangle s at 0,but ncreasesuicklyas he ncident enithangle ncreaseso the maximumat 90 In contrast, rofusioncrabapple Malus ioribunda "profusion") s umbrella-shaped.tseffectivecrownprojectionarea s largestwhen he zenith angle s0 and decreasess the incident enithangle ncreases. xistingrainfall interceptionmodelsdo not incorporateree crown shapeor effectivecrownprojection rea.Rainfall nterception rocesseslsodependon tree structure rarchitecture.For example, stemflow s greater or specieswithsmoothbark and vertically oriented branches han for specieswith roughbark surfaces nd horizontallyorientedbranches.In this paperwe present physicallybased, hree-dimensional,stochasticree rainfall interceptionmodel. The model describesthe interceptionprocesses t the individual tree level based onprocesses ccurringon eachsingle eaf and branchsegment.Themodel accounts or rainfall, meteorological, nd tree architecturefactorsas explicit variablesderived rom meteorological nd treemeasurement data. Results from the model simulations arecomparedwith actual field measurements sing two tree specieswith very different crown structures: deciduous ear tree (Pyruscalleryana 'Bradford') and an evergreen cork oak (Quercussuber). The size and form of these trees were similar to thatobserved or other trees of the samespeciesand age. Examplesof the model'sperformanceor 16 rainfall eventson a deciduouspear tree and 18 rainfall eventson an evergreenoak tree areprovided. Because he fbcus s on the individual ree rather hanthe forest canopy, henceforth, he term "crown interception" sused.

Both Th and D account or throughfall; ummingTh.,D, and STyieldsnet precipitation.C andE account or interception/), andE accounts or interceptionoss (IL). Differentiating quation(10) with respect o time yieldsdCdt -p -fg p- st-d -e (11)

where st is stemflow rate.While equation (11) describes the water balance andinterceptionprocesses t a single-tree evel, more information sneeded o understandheseprocesses ithin the canopy. Forexample, a few secondsmay be all that is required or waterdrippingoff the crown surface o reach he ground,but stemflowmay take severalminutes o flow from branches o the bottom ofthe tree. Drips from leaf surfacesmay fall directly o ground,orbe reintercepted y stems nder he leaves,suggestinghatpathsfor throughfall nd stemflow e consideredeparately.To model the spatial possibilitiesof water flow on the treesurface, the tree crown is divided into n vertical layers.Precipitation over each layer is either interceptedby crownsurfaces r directlypasseshroughcrowngaps o the groundas

free throughfall. Two "reservoirs"n each ayer nclude he leafand stemsurface torage see Figure 1). Leaf surface toragesfilled by raindrop nterception nddrips rom upper ayers, nd semptiedby evaporation nd dripping. Stem surfacestorage salso filled by raindrop nterception nd drips from the upperlayers,as well as the water low along he stemsurface rom theupper ayer. The reservoirs emptied y evaporation, ater lowdown to the next layer along the stem surface,and drip off thestem surface. Stemflow gradually moves from tree branches othe bottom of the bole. The rainfall interceptionprocessoccurssimultaneously n each layer, and the rainfall interceptionmodelflowchart s shown n Figure 2. Considering ainfall interceptionprocesses f a single layer of the tree crown, the change nstorage s given bydC115+dsld,,,pe- digdisd,dow,, 12)t

dCsdt - .p + dis+ dsu+ Stup es - dsg dsl Stdowndsdow

2. Model Derivation, Parameterization, andApplication2.1. Tree Rainfall Interception Model

Assuming hat there s no water absorption t the tree surface,precipitation (P) falling on crown surfaces s interceptedbycrown leaf surfacesor stem surfaces,or directly passed hroughthe eaf and stemgapsas free throughfall Th); that s,

e= fg r+j5 r+ fs e, (9)whereg,?5, nd are he ractionsf precipitationecomingreethroughfall, leaf surface storage, and stem surface storage,respectively. These fractionsvary with rainfall incident angleand seasonal changes of tree characteristics.Change in treesurfacewater storage C) is the differencebetweenprecipitation(P) and free throughfall Th), crown drip (D), stemflow ST), andevaporationrom the tree.surfaceE). Symbols sedhereafter relisted in the notation section.

AC- P -(Th + ST + D + E). (10)

where the subscripts, s, and g represent he leaf surface,stemsurthce,and ground surface. The sequenceof the subscriptsindicates he flow direction. For example,dxlhere indicates hestem drip from upper layer stem surfaces o the leaf surfaceofthis layer. The subscripts up" and "down" indicate he upperand lower layers.Grossprecipitationalling on crownsurfacess intercepted yleaf surfacesOSP),and thus may becomepart of leaf surfacestorage,and by stem surfaces fsP), n which case t goes o stemsurface water storage. The remaining precipitation directlypasseshrougheafgaps s ree hroughfallfgP).For each segmentof the stem at layer i, water storage sincreased y intercepted ainfall, stemflow rom an upper ayer,and interceptedwater dripping rom upper ayers. Water storageis decreasedby evaporationand water flowing down the stemsurfaceor dripping off the stem surface.Whether water flows tothe next lower layer or drips dependson the stem segment'szenith angle. We assume hat each segment s straightbut thatinclinationvarieswith zenith angle. The zenith angle 8) of thesestem egmentss normallyistributedsN(u, o2) where is themean and cy is the standard deviation. Consider a section of astemsegment's urface n the principal low direction. The planeis inclined at a zenith angle O alignmentwith the stemsegment).


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29,176 XIAO ET AL.: MODEL FOR TREE RAINFALL INTERCEPTION

P E

TH ST

lip El fsP E

Dis:>Ds

Dig ST

fP

Th

flP Dsl DnupE fsP Ds STup sup s fgP

I I

Dg Dllaown Dis STaown sg Dsl DsaownTh

a bFigure 1. Rainfall nterceptionmodel. (a) Rainfall nterception rocessest single-treeevel. (b) rainfall nterception t one sliceof the tree crown.The crownhasa coneshapewith angle p.P is the symbol or precipitation, for evaporation, for crownwaterstorage, H for throughfall, T for stemflow, ndD for thedrip,and hesubscripts,s, andg indicateshe eaf,stem, ndgroundsurface.

Assume he flow is uniformat each ime stepAt, that s, the depthand velocitydistributionso not changewith distance long heplane. Apply he momentumquationo a flow elementhat sboundedy theair-waternterface. heelement asunitwidthnormal o the engthplane, engthAL, anddepth Y-y) from hewater surface. Y is the water depthon the stemsurface bovedetention torage. he pressures hydrostaticcross nysectionnormal o the inclinedplanebecause niform low is assumedover time At. In addition, he water depth s constant, nd theshear stress on the water surface at the water-air interface isassumedo be negligible. hereforehe momentumquation anbe written

Wsin (90 0)- rAL= 0.Consequently,

Pw g (Y - y)ALcos(O)= rAL,r = iow g (Y- y) cos(O), (13)

where ow s the density f rainwater, is shear tress, is theacceleration ue to gravity, and W is the weight of the flowelement.The flow velocity (v) varieswith water depthon thestem surface. Becauseof the slow flow rate along crown stemsurfaces,#dv/dy is substituted or r such that the velocitydistributionwith the "no-slip"boundary onditions givenby

wherep is dynamic iscosity. So the discharge er unit widthand the average elocityareYI Pwgy3os(O)._._g3 os(O),= vdy= 3v0

v= y2cos(O),3v(15)

where v is kinematicviscosity.For each ayer, there are resteratemsegments.Each of theresterntemsegmentss divided nto two groups:one group orsegmentsith nclinationenith nglesess han90wherewaterflows down to the next segmentsQaown);nd a second roup,with segments hose nclination enith anglesare equal o orgreater han 90 .fromwhich water drips (Qar). Then thedischarge rom these stem surfaces an be mathematicallypresented s

2QctowniCIRirob0) dO, (16)0

Qdripi' CIRirob0) dO2

dvyy= og r y)cos(O), (14) where CIRi is the circumference f the stemsurface,a functionofthe stemsurface reaand segmentength. The stemsurface rea


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XIAO ET AL.: MODEL FOR TREE RAINFALL INTERCEPTION 29,177

Model initializationand parameterization

Readmeteorological ata

Rainfall characterization

Mass balance

I Outnut

Figure 2. Tree rainfall interceptionmodel lowchart.

or wind gusts. In this case, eaf surfacewater storage s quicklyreleasedand water free-falls off the leaf surface. Assuming heleaves are randomly located in the crown surface andsymmetricallydistributedabout the azimuth and zenith angle[ Vethoer 1984], leaf inclinationdistribution an be described ya two-parameter beta distribution [Goel and Strebel, 1984].Consider one leaf in layer i; this leaf is presented n spacecharacterizedby zenith angle and azimuth angle rp. Here, theazimuth angle is measured relative to the dominant winddirection. Ignoring he wind effect and applyinga massbalancefor the water on this eaf surfacegivesAC= P + Dsl+ Dllup - Dl,D = Dig+ Dis+ Dlldown.

(17)

Here, Dt is water dripping from leaf surfaces. Because he leavesare locatedat the crown surface,Dttup nd Dttdo,,can beeliminated rom equation 17), and taking a finite difference ormyields

dC pcos(afl+ cos((p)dslin(fl) dlgdis(18)- ) - - -where a is the rainfall incidentangle zenith angle).During a very short ime period At, the massof the water drip(top)rom ainfall p) falling o the eafsurfacesmp= Alea.cos(afl+ -)cos((p)pwAt, (19)

whereAteafs theone-sideeaf surface rea. For each aindroptis assumed hat the raindrop passes ll of its kinetic energy o theleaf. From conservation f momentum, he raindrop orce thatstrikes he leaf surface F) isFdt=d(mpV), (20)

d(mpv) A(mpv)dt At

21) = Vt+ 1)= PAlearos(a,+ )cos((P)PwV

and zenith angle distributionsare discussedn more detail insection2.2. Thus the total water transportedo the next layer isQdo,,i,nd hewater hatdrips s Qdripi. do,niddswater o thenext ayer's tem urface ater torage.Qdripirips o thegroundsurfacedsgi) r the layers elow. Thereare few leavesocatedunderneath these stems because it is assumed that all the leavesgrow in the surface ayer of the crown. Thus reinterception fstemdrip by leaves s ignored.An additional ayer s added or modelingstemflowalong hetree bole. The total throughfallcontributed rom stem surfacedrip s the sumof stemsurface rip rom all layers, or example,

dsg-dsgi=1

Thusstemflows Qdo,,from hebole ayer.While at the single-treeevel, he tree crown nterceptionfrainfall is not like a bucket [Massman,1980; Whelan andAnderson., 996];eachsingle eaf behavesike a tippingbucketwith residualstorage saturation torage) eft in the bucket.Water is stored on the leaf surface until it exceeds the maximumstoragecapacity. Several actors rigger water drip off leafsurfaces,ncluding dditionalainfall,waterdrippingromabove,

where vt and v,. are the raindrop terminal velocity and windspeed. The total force applied o the leaf surface s the sumof theweight of storedwater and the force causedby raindropshittingthe leaf surface. This force will determine f the leaf will tip ornot. Defininga leaf rigidity factor (Frigid) s the force ofmaximum water storageFrigid= Aleaf maxOw , (21)

where Smax s the leaf maximum water storage and g isgravitational cceleration.When the total forceactingon the leafsurfaceFtef) sa result f both hewater tored nd he aindrophitting the leaf is greater han the rigidity factor, he leaf will tip.Once the leaf tips, the water storage n the leaf surface s reducedto no more than the saturation torage.Flea./'Alea./' Pwg + F. (22)

WhenFteaf> ,gia,hisgivesDs = Y + pdt- Sinin (23)

whereY is the waterdepthon the eafsurface t thebeginning f


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29,178 XIAO ET AL.: MODEL FOR TREE RAINFALL INTERCEPTIONthis time step. Stains the saturation torage hat is the minimumamount of water required to saturate he leaf surface. Surfaceroughness,he finely spaced exture rregularitiesLoper, 1987],is an important actordeterminingeaf saturation torage.Maximum leaf surface water storage for individual leaveschangeswith the zenith angleof the leaf. When the zenithangleapproaches ero, the leaf surfacestoragecapacity eaches heminimum Stain), nd when he zenithangleapproaches0, theleaf surface water storagecapacityreachesa maximum (Sma-).AssumihghatSma-andmi nlyvarywith eafsurfaceoughnessand leaf geometric shape, then maximum leaf surface waterstorage s

Ymaxfl) = (Smax Smin) in(fl) + Smi (24)Not al l of the water drippingoff leaf surfacesDr) from layerfalls to the ground urface nd contributeso throughfalldtg).Some drips are reintercepted y the stem surfaceat differentlayers underneath hese leaves (dtx). The magnitudeof thisreinterceptiondependson the projectedeffective stem surfacearea of the layer. Here, effectivestem surface s definedas thecross-sectional rea along the stem. Projecting his area onto a

horizontalplaneyields he projected ffectivestemsurface rea.The reinterceptionn layerj from this ayer s calculated ydtsjdl 5')2ESPAj, (25)

where i and s are hecrown adiiof layer and ayer, ESPAjsthe effective crown projectionarea (defined as the stemsurfaceareawithin the tree drip line) of layerj. The remainder f dt willbe reintercepted y stemsbelow layer until layer n, or when tfinally drips o the groundsurface.Although limited evapotranspiration ccurred during therainfall events considered in our measurements, after rainfallceases, vaporation f the wetted ree surface an occurat thepotential ate. However, ranspirations restricted ue to watercoverage f the treesurfaces.When ocusing n tree nterceptionprocesses, ranspirationcan be ignored because his wateroriginated rom the soil. Open grown reeshave imited heatstoragewithin he crown,and he crown's bility o changewindspeedand direction s also minimal. In the sameenvironment,precipitationntercepted y vegetation vaporates t a greater atethan transpiration Murphy, 1970; Murphy and Knoerr, 1975].Meteorologicaldata from the field can be directly used forestimatinghe potential vaporationEp). Whencrownsurfacewater storage s below the saturation torage,evaporationromthe crown surface s proportional o surfacewater storage Rutteret al., 1971; Massman, 1983; Jetten, 1996]:

CE = fmaxEp -- C < S, (26)SE = fmax p C>_S, (27)

wheremas the raction f maximumeafsurface etting. p sestimatedbasedon the Penman ormula [Penman, 1948' Xiao etal., 1998]:A AEp -- Qne+A+

RnQne = el ,LeE,4= c2fe (e2-ea),

EA,(28)

whereA is the slopeof saturated atervaporpressureersus irtemperature, ' s the psychometriconstant,Qne nd Rn are netradiationndifferentnits,Asdryingowerf he ir, Le slatent heat of vaporization f water, e and e are saturationvaporpressure nd vaporpressure t air temperature,nd c; andc2 are unit constantssed o convert he units.The term is thewind unction escribedy PruittandDoorenbos1977a, ] asf = au+ buU(z) (29)

where andb areconstantsndU(z) s windspeedmeasuredtheight aboveground urface.This wind unctionwas ocallycalibratednd s currentlysedorestimatingp n theCaliforniaIrrigation Management nformationSystem CIMIS) network[Pruitt et al., 1987;Snyderet al., 1989].2.2. Model Parameterization

Thereare six boundariesn the problemdomain X+, Y+, andZ+ directions).The flux of rainfallandevaporationeterminehetop boundaryZ+) condition.Throughfalle.g., crowndrip andTable 1. Tree Architecture and Simulation Time Variables

Variable Definition Units aH

DBHLAI

SAI

CPA

SPA

ECPAESPA

Alear

tepTotal

Tree Architecturetreeheightmeasuredrom ground urface mcrownheightmeasured bove he first branch mtreebole height maverage crown diameter which is measured n mthe crownprincipalaxesdirectionswhen hecrown s projectedo the horizontal lanediameter at breast height is the bole diameter mmeasured t 1.3 m from groundsurfaceleaf area index, which is the ratio of the total

one-side leaf surface area to the crownprojection area. The maximum LAI ismeasured when the tree is in full-leaf. Theminimum LAI is measured after most leavesfall

stem surface area index is the ratio of the totalstemsurface rea o the crownprojection reagap fi'action s the ratio of the total gap areainside the silhouette to the tree silhouettearea. Projecting he crown o the plane hat snormal to the rainfall incident angle, theoutline of the crown boundary s the treesilhouette. The area inside these boundariesis the silhouette areacrown rojectionrea also alled ormal rown m2projectionarea (NCPA)), defined as the areasurrounded y the crowndrip linestem projection rea, definedas the stem m2segment cross-section rea along the stemsegment urrounded y the drip line.effective rownprojectionrea,defined s the m2CPA "seen" y rainfalleffective temprojectionrea,defined s the m2SPA "seen"by rainfallaverage eaf size, definedas one-side eaf cmsurface area

stemsegment enithangle degleaf zenithangle degleaf azimuth ngle degtotal number of layers nto which the crown sdividedSimulation Time Variables

time increment length or time step of the ssimulationtotal simulation time s

a: Unitsused n the model nputdata ile.


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XIAO ET AL.' MODEL FOR TREE RAINFALL INTERCEPTION 29,179free throughfall) and stemflow ates control the bottom boundary(Z-) condition. All water fluxesgiven n equation 12) are in thevertical direction; thus we assume that there is no water fluxacross hese our boundaries f X+ (e.g., Y-Z plane) and Y+ (e.g.,X-Z plane). The initial treesurfacewetnesss knownor specifiedbefore rainfall begins.The model required hree setsof input data. The first setdescribes ree crown architecture: ree height, crown height,crown diameter,diameterat breastheight (DBH), leaf surfacearea ndex LAI), stemsurface rea ndex SAI), gap raction, eafsize,zenithangleof the stemand eaf, and surfacewaterstoragecapacity f the leaf and stem Table 1). The second et ncludedtime (Julianday, hour-minute),ainfall ate (mm h'l), airtemperatureC), elativeumidity%),wind peedms'l),winddirectionC) ndnet adiationW m'2).The hirdnput ata etwas user-defined nd included he numberof tree crown layers,tll 3IIILLIIO. LI.JI[ tlllJ 3t,.}J, O. lLl tlJ LULO. 3IIIIUIOLIUII tJJJJ;.Crown shape parameters affect both effective rainfallinterceptionarea and maximum surfacewater storageof thecrown. Tree crownshape asbeenmodeledwith basicgeometricsolidssuchas spheroid, llipsoid,parabaloid, one,and cylinder[McPherson t al., 1985;Sattleret al., 1987]. Tree crownprofileareas calculated using equations for geometric shapes werecorrelated to actual crown profile areas measured fromphotographs McPherson and Rowntree, 1988]. Previously,astudyof canopyarchitecturen a walnut orchard Martens andUstin, 1991; Ustin et al., 1991 found that the distributionofleaves and stem surface area was related to crown diameter atdifferent ree heightsand that stemzenith angleswere normallydistributed. Stem surface area decreased from the bole to branchtips n Douglas ir [ Webb nd Ungs,1993].The followingassumptionsnderlieparameterizationf crownarchitectureXiao, 1998]: (1) The tree crown s multi-layeredand has a perfectgeometric hape; (2) Stem surface rea isrelated o the average rowndiameter nd s uniformlydistributedacrossazimuth angles for each layer; and (3) Leaves areuniformly ocatedat the outsideof the crown volumeand allleaves have the same surface area, surface roughness andgeometric hape.The effectivecrownprojection rea ECPA) differs rom thenormalcrownprojection rea, akenas the areawithin the tree'sdrip line. The ECPA is the area"seen" y rainfall,so it is theareanormal o the anglea of incident ainfall; that s, assumingthe tree alignment s in the Z+ direction, he incident ainfallECPA is

ECPA(a) ECPAxyos(a), (3O)where CPA,,ys theeffectiverown rojectionrea rojectedn

theX-Y plane. ECPA,,ys crowngeometrichape ependentndFigure3 illustrates ow ECPA varies or a cone-shapedrown.The tree crowngap raction,or percentageransmission,s theratio of gaparea nside he tree silhouetteo the silhouetteea. Itis used to describe the fraction of incident solar radiation that istransmitted through the canopy [McPherson, 1984]. Gapfractions reported in the literature for different tree 4eci.[Schiler, 1979; Hammond et al., 1981; McPherson, 1984] weremeasured t varyingelevationanglesor on the ground. However,in rainfall interceptionstudies, he gap fraction of the crowndetermines ree throughfalland dependson the rainfall incidentangle. Therefore t is necessaryo considerhow gap fractionschange with different rainfall incident angles. Gap fractionsmeasured t different ncidentangleson two treeswere usedhere.The gap fractionsweremeasured ith zenithangles arying rom0 o 90at 5 ntervals Xiao, 1998].q'e median raindrop size formodeled as a power function of rainfall intensity Laws andParsons, 1943; Torres et al., 1994; Uijlenhoet and Stricker,1999]. The median-volumeiameter, e (mm),of the rainfalldropssrelatedorainfallate, (mm 1)by Laws ndParsons,1943]

Dp= 1.238p'182. (31)Rainfallerminalelocity,I (m s l) canbedeterminedrombasic luid mechanics.Assuminghat a raindrop s releasedromrest, t will accelerate ntil it reacheshe terminalvelocity Chowet al., 1988]

14gDpPw1)]-e0.1 m,vt 3Col a (32)wherePa s the densityof the air. Ca s the dimensionlessragcoefficient. Mason [ 1957] definedC,/values or raindropsizesgreater han 0.1 mm. For raindrop sizes less than 0.1 mmdiameter,Cd is specified y usingStokes' aw, that is Cct=24/RewhereRe is the Reynoldsnumber.The velocityof water drops alling on the stemsurfacesromupper ayer dripping s ignoredbecause cross he shortdistancesno greater than the crown height, stem segmentshave muchgreater igidity than eaves.The azimuth angle of rainfall drops is associatedwith winddirection. The incident angle (zenith angle) of rainfall isdetermined from the relationship between rainfall terminalvelocity (vt) and horizontalwind speed vw)at half of the crownheight,given by

z y

a. b. c.Figure3. Effective rown rojectionrea n anX-Y plane or a cone-shapedrown.The reewas ocatedn theX-Y-Z space ndthenprojected nto heX-Y planeasshownn theshadow.Here, x s rainfall ncident ngle.


8/16


Figure . Fieldainfallnterceptioneasurementnstallationor heoak nd earrees.

arctan'"' (33)v tHere v,. is estimated from wind speed measurementson site[Jetten, 1996].3. Field Experiments and Model Analysis3.1. Field Methods

The rainthll interceptionexperimentswere conductedat theDepartment of Environmental Horticulture field site, in thesoutheastcorner of the University of California, Davis campus(longitude2146'32", and atitude8032'09N). Onaverage,90% of the average annual precipitationof 446 mm + 36 mmoccurs between November and April at the study site. Nosnowthll occurred n the study area. Rainfall intensity rangesfrom to i 13mmh and sheaviesturing inter torms, hichdeliver most of the annual precipitation. Interceptiondata werecollected rom a 9-year-old broadleafdeciduouspear tree (Pyru$calleryana "Bradford" or Ca!!ery pear) and an 8-year-oldbroadleafevergreenoak tree (Qtterctts itbet or cork oak). Thepear tree and the oak tree were open grown and separated yabout63 m. The micrometeorologicaltationwas 20 m from theoak tree site and 70 m away from the pear tree site. Rainfallinterceptiondata were collectedduring the winter of 1996-1997for the pear tree and during he winter of 1997-1998 tbr the oaktree.

A catchment was constructed below each tree to collectincident precipitation. The catchment onsisted f two panelswith sloping sides angle dependent n the tree size and shape)linked togetherby a plasticrain gutter. The tree was located nthe geometric center of the catchment. The catchmentconstruction eight was near the bottomof the crown, so that itdid not influence urbulence,or vertical mixing of water vapor.The rain gutter guided water into the throughfall storagecontainer. Using a massbalance, hroughfallwas determined sthe difference between the water collected in the throughfallcontainer and catchment surface detention storage, and theprecipitation hlling outsideof the crown drip line. Stemflowwasdirectly collected rom the tree bole using a channel abricated

from a 2.54 cm diametersoft Tygon tubing that was split andspiraledaround he tree bole. Gaps between he tubing and treebole were sealed with clear 100% silicone sealant. A watercontainerwas used or storingstemflow. Grossprecipitationwascollectedwith a 15.2 cm diameterglass/hnnel set at the upwindcorner of the catchment inked to a grossprecipitationcontainer.The water evel change nside he containers asmonitored singa pressure gauge (Honeywell, Inc.) and a CRi0 datalogger(Campbell Scientific, Inc.). A standardmicrometeorologicalstation was established over turf grass for measuring airtemperature, elative humidity, wind speed,wind direction,andnet radiation. Catchment etention torage nd water ravel timefrom the catchment o the water storagecontainerwere directlymeasuredn the field [Xiao et al., 2000]. Figure4 shows he fieldmeasurement setup.Tree dimensionstree height, crown height,crown diameter,DBH or diameter at breastheight, and crown shape)and treearchitecture ata (leaf surfacearea, stemsurface rea,crowngap

Table 2. Architecture of the Oak Tree and Pear TreeVariable Oak Pear

Tee TreeTree height,m 5.6 8.5Crown height,m 4.8 6.8Crown diameter, in 3.2 4.8DBH, cln 12.5 22.0LAI, Max. 4.0 ...LAI, Min. 4.0 0.0SAI 1.7 1.7Averageeafsize, m 2.4 ...Gap fi'action leaf on) 0.3Gapractionleafff) 0.4 )'.Leaf zenithangledistribution, eg ininilnuln) 0.0 ...Leaf zenithangledistribution, eg maxilnuln) 160.0 ...Leaf zenith angledistribution,deg (mean) 65.0Stemenithngleistribution,egminilnum) .0 )'.)Stemzenithangledistribution, eg inaxilnum) 120.0 120.0Stemzenithangledistribution, eg mean) 60.0 50.6Leaf surfacewater storage,mm (inaximum) 0.7 ...Leaf surfacewater storage, mn (saturation) 0.3Stemurfaceatertorageapacity,m 0.8 )'.Numberof layera n crown 20 20a: Parameters re not used or wintmime rainfall interception


9/16

XIAO ET AL.: MODEL FOR TREE RAINFALL INTERCEPTION 29,181fraction, eaf and stem segmentangle) were directly measuredafter the experimentended. A dry weight - leaf surfaceareamethod was used to estimate the total leaf surface area fromsampled eaves. The stem surfacearea was directly measuredfrom eachstemsegment.The leaf and stemsegmentnclinationangleswere estimated singa photographicmethod Xiao, 1998].The gap ractionwas estimated s the ratio of the gaparea nsidethe crown silhouettearea to the crown silhouettearea using animage analysis echnique Xiao et al., 2000]. These measureddata or the pear and oak treesare listed n Table 2.3.2. Interception Model Calibration and Sensitivity

The model equation 12) was explicitly solvedusing he finitedifferencemethodwhere numerical nstabilityerrorsare reducedby limiting the maximum ime step o I min. The error function[Press et al., 1992] was used to estimate the cumulativeprobability distributionof equation 16). The model crown wasdivided nto 20 vertical ayers.Two meteorologicaldata sets and tree architecturaldata setswere used o calibrate he model. Only surfacestoragewas notdirectly measured in the field but was adjusted via modelcalibration such that differences between the simulated and fieldmeasurement results were less than 10%. We assumed the treesurfacewas initially dry when starting simulations. Rainfallhyetographs sed to drive the model calibration or the oak andpear trees are shown n Figures5a and 5b. Figures 5c and 5dshow he calibration esults or both the oak tree (Figure 5c) andthe pear ree (Figure 5d). For the oak tree the grossprecipitationwas 8.75 mm for this event as recorded at themicrometeorologicaltation,but 8.76 mm grossprecipitation ellon the crown. Similarly, for the pear tree thesevalueswere 6.05mm and 5.93 mm, respectively. The difference in grossprecipitation hat fell on the tree surface s due to wind effectsduring the event. Wind changed he raindrop pathway fromvertical, thereby changing the effective crown projection area.When we comparedmodel results o field observations,he mean

absolute percent error [Mayer and Butler, 1993] for allinterception rocesses as ess han 5% for the oak tree, and essthan4% for the pear ree. Thesedifferences eemed cceptableconsideringhe measured ifferencesn gross recipitationndthatdrycanopy urface asassumedhen tartingimulations.A sensitivity analysis was conducted to determine theparameters aving he greatest ffectson interception rocesses.This analysiswasperformed singdataonly from the evergreenoak tree because he pear tree was dormantand leaflessat thetime of measurement. n the sensitivity nalysis he followingparameterswere changed by + 50% to assess heir effect oninterception:ainfall ateandduration,wind speed, AI, SAI, gapfraction, stem and leaf zenith angle distributions, nd stemandleaf surface torage apacities.Results using the index below of the detailed sensitivityanalyses re listed n Table 3a for meteorologicalarametersndTable 3b for treearchitecture arameters.

sensitivity_indexPRc PRb, PRbPar Par

Parx 100. (34)

PRc s the predicted esultbasedon the adjusted arameter alue(Parc),and PRb s the predicted aluebasedon the parameter asevalue (Parb).Not surprisingly, nterceptionprocesseswere sensitive torainfall rate, but less so to its duration. At a given rainfallduration,decreasing ainfall intensityby 50% caused nterceptionloss o increase rom 32% to 57% for the oak tree, or a sensitivityindex of 22.7%. Decreasing ainfall intensity educed he amountof rainwater added to the tree crown. This increased theproportionof rainwater used for wetting the crown surface,amain component f interceptionoss rom rainfall. Increasingherainfall rate by 50% causedhe interceptionoss o decreaserom

18161412,lO8

6420

a. Precipitationoak) .... _: 976

3 a-21

, [ , , i , i , [ , 00 30 60 90 120 150 180

Time (min.)

1614

',128

' 6420

10 c. 79 6.-. 8 'E 7 []Observation 5_ 6 --u5 []simulation3'T- 4 0:2E 30 ..... 0

P TH ST I

b. Precipitationpear) 7

E3'21

, , , , , 00 15 30 45 60 75 go

Time (min,)

[] ObservationB simulation

P TH ST

Figure 5. Calibration f the modelparametersor rainfall nterceptionrocessesn oak and pear rees. (a) Rainfall started t0000:00,January , 1998,and t lasted bout hours.Thesedatawereused or thesimulation n theoak ree. (b) Rainfallstartedat 0052:00,February , 1997,and t lasted bout80 min. Thesedatawereused or the simulation n thepear ree. (c) The fieldobservationesults nd hesimulationesults recomparedor thecalibration n heoak ree. (d) The field observationesults ndthe simulation esultsare comparedor the calibrationon the pear tree. P indicates umulative recipitation, H indicatesthroughfall,ST indicates temflow, nd indicatesnterceptionoss.


10/16


Table 3a. SensitivityAnalysesResults or Meteorological arametersInput

Precipitation WindSpeedRate Duration

OutputGross Net Precipitation InterceptionPrecipitation,temflow, Freehroughfall,anopyrip, Total Loss,

mm (%) iron %) mm (%) mm (%) mm (%) mm (%)0.5 I I 4.4(99.1) 0.0(200.0) 1.6(99.0) 0.4(160.8) 1.9(135.5) 2.5(22.7)1.5 I I 13.1 (98.4) 2.0 (219.1) 4.6 (98.4) 3.6 (174.2) 10.2 (142.2) 2.9 (5.0)2 0.5 I 8.7 (1.6) 0.9 (6.4) 3.0 (2.0) 1.9 (1.0) 5.9 (2.7) 2.8 (0.7)0.5 2 I 8.8 (0.9) 1.0 (3.2) 3.1 (0.7) 2.0 (1.5) 6.0 (1.5) 2.8 (0.7)I I 0.5 8.5 (6.8) 0.9 (17.0) 3.0 (7.2) 1.8 (10.3) 5.7 (9.7) 2.8 (1.4)I I 1.5 9.3 (12.3) 1.1 (31.9) 3.3 (11.7) 2.1 (20.6) 6.5 (18.2) 2.8 (0.7)I I I 8.8 (...) 0.9 (...) 3.1 (...) 1.9 (...) 6.0 (...) 2.8 (...)a: Here I in the input parametersndicates unit, 0.5 means educe50%, 1.5 means ncrease 0%, and 2 means ncrease100%from the original value. All of the canopyparameters re n 1 unit of originalvalue.b: Outputvalues representedn totalamountn millimetersand n sensitivityn percentage)alculated ased n equation34).

32% to 22%, or a sensitivityof 5.0%. Using a constant ainfalldepth, we tested the sensitivityof interception rocessesorainfall duration. Rainfall ateswereadjustedo keep he rainfalldepth constant or stormsof different durations. nterceptionprocesses ere not as sensitive o changesn rainfall durationascompared o changesn the rainfall rate.Interception processeswere sensitive o changes n windspeed. An increase n wind speed of 50% caused grossprecipitation n the canopysurface o increase y more han6%.The sensitivity of precipitation on the tree surface,stemflow,canopydrip, net precipitation, nd interceptionoss o increasedwind speed by 50% were 12.3%, 31.9%, 20.6%, 18.2%, and0.7%, respectively.The influenceof interceptionosswas small

comparedwith other processcomponents; owever, ncreasedwind speed hangedhe distribution f the components.Of all tree fhctors, nterceptionosswas mostsensitiveo thesurface reaand surfacewater storage apacity. Changing temsurfaceby 50% causeda 50% sensitivity o interceptionoss.Increasing temsurfacewaterstorage apacity y 50% caused n8.0% increase n interception oss. Decreasing A! by 50%caused 6.8% decreasen interceptionosswhere he sensitivityis 44.7%. Increasingeaf surfacewaterstorage apacity y 50%caused 6.8% increasen interception.The sensitivity f interceptionoss o a 50% increasen gapfraction was only 12.1%. However, the distribution andproportion of throughfall and stemflow changed. The

Table 3b. SensitivityAnalysesResults or Tree Architecture arametersInput

Tree Structure SurfaceStorage GrossGap ZenithAngle Capacity Precipitation, Stemflow,Fraction LAI S A1Leaf Stem Leaf Stem nm mm (%)

OutputNet PrecipitationFree CanopyDrip, Total,Throughfall,mm (%) mm (%) mm (%)

InterceptionLoSS,mm (%)0.5 I I I I I I 8.8 1.2 (61.7) 1.5 (102.9) 3.2 (126.8) 5.9 (2.0) 2.9 (4.3)

1.5 I I 1 I I I 8.8 0.7(57.4) 4.6 (102.3) 0.8(118.6) 6.1 (5.4) 2.7(12.1)I 0.5 I 1 I 1 I 8.8 1.1 (23.4) 3.1 (0.0) 2.5 (52.6) 6.6 (20.8) 2.2 (44.7)I 1.5 I I I I I 8.8 0.8 (21.3) 3.1 (0.0) 1.5 (44.3) 5.4 (17.8) 3.3 (36.9)I I 0.5 I I I I 8.8 1.2 (61.7) 3.1 (0.0) 2.4 (43.3) 6.7 (23.5) 2.1 (50.4)1 I 1.5 I I I I 8.8 0.6 (72.3) 3.1 (0.0) 1.6 (38.1) 5.2 (23.9) 3.5 (49.6)I I I 0.5 I I I 8.8 2.1 (248.9) 3.1 (0.0) 1.4 (53.6) 6.6 (21.5) 2.2 (46.1)I I I 1.5 1 I I 8.8 1.0 (4.3) 3.1 (0.0) 2.1 (19.6) 6.2 (7.1) 2.6 (15.6)1 I I I 0.5 1 I 8.8 2.1 (244.7) 3.1 (0.0) 1.4 (57.7) 6.5 (19.8) 2.2 (42.6)I I I I 1.5 I I 8.8 1.0 (4.3) 3.1 (0.0) 2.1 (19.6) 6.2 (7.1) 2.6 (15.6)I 1 I I I 0.5 I 8.8 1.0(10.6) 3.1 (0.0) 2.2(22.7) 6.2(8.7) 2.6(19.1)1 I I 1 1 1.5 I 8.8 0.8 (23.4) 3.1 (0.0) 1.4 (52.6) 5.3 (20.8) 3.4 (43.3)I I I I I 1 0.5 8.8 1.4 (91.5) 3.1 (0.0) 2.2 (22.7) 6.6 (21.8) 2.2 (46.1)I I I I I 1 1.5 8.8 0.5 (89.4) 3.1 (0.0) 1.7 (21.6) 5.3 (21.5) 3.5 (44.7)I I I 1 I I I 8.8 0.9 (...) 3.1 (...) 1.9 (...) 5.95 (...) 2.8 (...)a: Here I in the nputparametersndicates unit, 0.5 means educe 0%, and 1.5 meansncrease 0% from he originalvalue.All meteorologicalparameters re n I unit of original value.b: Outputvalues representedn totalamountn millimete (and n sensitivityn percentage)alculated ased n equation34).


11/16

XIAO ET AL.' MODEL FOR TREE RAINFALL INTERCEPTION 29,183sensitivities f canopydrip and stemflow o a 50% decreasengap ractionwere 126.8%and61.7%, espectively. temflowwas also sensitiveo changesn stern/leafenithangle,asdecreasingtemsegmentenithangles y 50% caused 13.6%increasen the amount f stemflow. his sensitivityollowsbecause he zenith angle controls he stemflowrate anddetermineshe water low fromonestemsegmento the nextsegmentr drip o ground urface.he sensitivityf stemflowochange n leaf zenith anglewas 248.9% for a 50% decreasenleafzenith ngle. Increasinghe eafzenith ngle aused orewater o flow from he eaf o stem urfaces,herebyncreasingstemflow.4. Results and Discussion

We applied the model to 16 rainfall events or the broadleafdeciduous ree (pear) and 18 rainfall events or the broadleafevergreen ree (oak) with meteorologicaland tree architecture

parametersdetermined rom field measurements.A minimum 4hour period of no precipitation as used o differentiate nerainfallevent rom the next. The amount f precipitationinterceptedy the tree surface, temflow,hroughfall,ndinterceptionossesreexpressedn depth nitswith espectonormalcrownprojection rea.Figure 6 showsa comparison f field measurementsersussimulated stimates f rainfall, throughfall, temflow, ndinterceptionoss or both he oak Figures a- 6d) andpear(Figures e- 6h) trees. Therewas elatively oodagreementbetween easuredndestimatedalues, s R2 valuesangedfrom 0.84 to 0.99. The difference n measuredand estimatedprecipitationtrikinghe reecrownwas elatively mall orboththeoakandpear reesFigure a and6e).Throughfallasonlyslightlyunderestimatedor the oak tree (Figure 6b), butoverestimatedor the pear ree Figure f), as ndicated y theslightly egative ndpositiventerceptsf theregressionines.Stemflow asunderestimatedor both he oak Figure c) and

0 4 8 12 16 0 2 4 6 8 10Field Measurement mm) Field Measurement mm)

lO .hroughfallOaktl_o o i 41=4 =2i 0.986x0.152 }2 [ R = .984

0 2 4 6 8 10 12Field Measurement mm)

y =0.965x0.058R2 = 0.987 'I I I I4 6 8

Field Measurement (mm)

c. StemFI ;i

o" Y= 1._ 16x-.138 R =0.952 ---: ; i i i i0 1 2 3


,--

g. StemFlow (Pear)

0 .

I t0 1 2


Oio y = 0.754x + 0.483R2 = 0.8381 2

Field Measurement (ram)I I I I

o 1 2Field Measurement (mm)

Figure. Field easurementnd umericalimulationesultsf ainfall,hroughfall,temflow,ndnterceptionossn hea-d)oak nd e-h) earrees.he olidine neach lot s hebestitregressionine.


12/16


110%105%100%

95%

90%0 10 20 30 40 50 60 70 80 go

Rainfall ncidentangle (degree)Figure 7. Effective crown projectionarea (ECPA) varies withincident ainfall angle. The verticalaxis presentshe normalizedECPA value, which is the ratio of ECPA to the normal crownprojection area. The minimum ECPA existed when incidentrainfall anglewas 20.0 for the oak tree. The pear ree'sECPAreaches minimumvalueat 21.0 ncident ainfallangle.

pear trees Figure6g). Interceptionosseswereoverestimatednsimulation or both the oak and pear trees Figures6d and 6h).We consider heseprocesses nd differencesndividually n thetb!lowingparagraphs.Use of the ECPA to standardize he input precipitationdetermineshe amountof precipitation vailable or interceptionby the crownsurface. othwind speed nd ainfall atedeterminethe incidentangle of rainfall as well as the ECPA. Thus themodel simulationof precipitation hat fell over the effectivecrown surfacewas different rom the amountof precipitationhatfell over the normal crown projectionsurface.For example,onJanuary3, 1998 (between 2059 and 2318), 6.2 mm of grossprecipitation as ecorded t themicrometeorologicaltation, utthe model simulation for the oak tree indicated that 6.6 mm ofgrossprecipitation ell on the tree crown when referencedonormal crown projectionarea. This 0.4 mm increase6.5%) ingrossprecipitation n the tree surfacewascaused y the wind'schanging he raindroppathway rom vertical, hereby ncreasingthe ECPA relative to the normalcrownprojectionarea. Figure7showshow rainfall ncidence ngleaffected he ECPA for the oakand pear trees. When rainfall incidentangle s greater hanzeroand less han 32 for the oak tree and ess han36 for the peartree, the ECPA was less than the normal crown projectionarea.The ECPA quickly increasedwhen rainfall incidentangle waslarger han21o or theoak reeand22 or thepear ree. For he18 rainfall eventsused n the rainfall interception imulationorthe oak tree, the meteorological station recorded totalprecipitation f 91.2 mm, but themodelsimulationndicated 1.0mm of rainfall onto the oak tree crown. For the 16 rainfall eventson the pear tree, 54.7 mm of precipitationwas recorded t themeteorologicaltation, nd54.0 mm waspredicted y themodel.

The simulatedaverage nterceptionosseswere 3-4% greaterthan measured values. For the 16 rainfall events measured on thepear tree, the predicted interception was 26.6% of grossprecipitation, while the field-measured value was 23.6%.Similarly, of the 18 rainfall eventson the oak tree, the averagesimulated nterception oss (25.0% of grossprecipitation)was4.5% higher than the field-measured alue (20.5% of grossprecipitation).The modelpredicted ear tree 7.1% stemflowonaverage s comparedo 10.4% n the field. Throughfallor thepear tree was nearly the same as that measured 66.3% versus.66.0%). Free throughfallaccountedor 95.7% and drip frombranch or stem surfacesonly accounted or 4.3% of totalthroughfall. In contrast, or the oak tree, throughfallandstemflow values were 3.7% and 0.8% lower than observedvalues, espectively.Free throughfall ccountedor 62.0% of thetotal throughfall or the oak tree, while the remainderwas crowndrip. Evaporation as only 0.8% of grossprecipitationor theoak tree and 1.1% for the pear tree. Simulation ccuracywasevaluated using mean prediction error, its standarddeviation(STD), androot-mean-squarerror RMSE), and hese esults resummarizedn Table 4. Prediction ccuracy assimilar or bothtrees.

Consideringmodel predictions or individualrain events,weillustrate n Figure8 interception rocessesor the pearandoaktreesduringone rainfall event. For the leafless ear ree (Figure8a), not surprisingly,ree hroughfallwas he maincomponentftotal throughfall.Water ntercepted y stemsurfaces f the peartree flowed down the trunk and becamestemflow.Canopydripwassignificantor the evergreen ak ree. Rainfall nterceptedythe oak reebegan o drip off leaf surfaces ftersaturationFigure8b). Drip from canopy surfacescontinuedafter the rainfallstopped. Figures9a and 9b show the rainfall hyetograph ndfield-measurednd simulatedhroughfall or the oak (Figure9a)and pear trees Figure 9b). Free throughfallwas the principalcomponentof total throughfall, and its temporal variationfollowed the rainfall pattern. The smoother urve or the fielddata and the shift in time between field-observed and simulateddatawere caused y the travel ime delay approximately .5 minand 0.5 min for the pear tree and oak tree, respectively)orthroughfall moving from the catchment o the measurementdevices.

Initial surface wetness conditions explain some of thedifferences between measured and simulated results. While themodel assumed hat leaf and stem surfaces'water storagewaszero, n reality the canopysurface id not entirelydry in the fourhour nterval ue to low evaporationates. Hence or eventsStarting soon after a 4 hour interval, antecedentmoistureincreased temflow nd hroughfall elative o values redicted ythe model. The wetness of the crown surface at the start ofrainfall affected the temporal pattern of the interceptionprocesses.For example,simulated temflowbegins5 and 10 minearlier for the oak tree if we assume an initial crown wetness of50% and95% comparedo a drycrown Figure10).Data used for the simulation are from field measurements.The crown shapeof the oak tree was similar to a cone,but the

Table 4. Simulation ccuracyOak

Total Prediction ErrorMeasurement Prediction Mean STD RMSE

PearTotal Prediction Error

Measurement Prediction Mean STD RMSEPrecipitation 91.2 91.0 0.1 0.1 0.1Throughfall 60.8 57.3 0.0 0.2 0.2Stemflow 11.7 10.9 0.1 0.1 0.2Interceptionoss 18.7 22.8 -0.1 0.1 0.2

54.7 54.0 0.0 0.2 0.236.1 35.8 0.2 0.3 0.45.7 3.8 0.0 0.2 0.212.9 14.4 -0.2 0.2 0.3

a: Units n millimeters.STD denotes tandard eviation, ndRMSE denotesoot-mean-squarerror.


13/16

XIAO ET AL.' MODEL FOR TREE RAINFALL INTERCEPTION 29,185

_5

E 4E'-3

10

0

10-

8 -

oo

RainfallFree Throughfall

At.m surface water storage

Stem dp .i i I i i60 90 120 150 180

Time (min.)b.

Rainfall

Free hroughfall Canopytorage ....., Stemlow,i i i i i i i i

30 60 g0 120 150 180 210 240Time (min.)

Stem flow

Figure8. Rainfall nterceptionrocesses.a) Rainfall nterceptionn thepear reestarted t 0000:00,January , 1998,and tlasted bout hours. b) Rainfall nterceptionn heoak reestarted t 0052:00,February , 1997,and t lasted bout 0 min.

8

4

2

0

a. Oak treethroughfall_field

0 30 0 90 120 150 180 210Time (min.)

b. Pear treethroughfall_fieldthroughfall_simulation

0 30 60 90 120 150 180 210 240 270 300 330Time (min.)

Figure9. Rainfall nterceptionrocesses.a) Rainfallon theoak reestarted t 1556,January , 1998,and asted bout hoursandsimulatedhroughfall tarted t the same ime.Field-observedhroughfall tarted min later.This delay s mainlycaused ydetention torage ndwater ravel imeon themeasurementevices. b) Rainfallon thepear reestarted t 130,January 2, 1997,and t lasted bout14 hourswithout break onger han4 hours.We present .5 hoursof data o showprocessest high emporalresolution.Simulatedhroughfall asobservedo startat the same imeasrainfall,but the ield-observedhroughfall tarted 0min after ainfallstarted, gain,showinghe detention torage ndwater ravel imedelay.


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29,186 XIAO ET AL.' MODEL FOR TREE RAINFALL INTERCEPTION0.090.08

_. o.o70.060.050.040.030.020.01

/

/

95 apaci .... "'"' Dysurace,,, -- ,,,.-...::: ,10 15 20 25 30 35 40 45 50 55 60

Time (min.)Figure 10. Influence of previouscanopysurfacewetnessoninterception rocesses.

bottomsectionof the pear ree crownwasmore ike an ellipsoid.In the model we assumedhat the crownshapeof both reeswas acone. One source of estimation error may be caused bydifferencesn crown shape.Although this model can enhanceunderstanding f rainfallinterception rocessest different emporal cales,meteorologicalconditions, and tree architectures, t has several imitations.1. The modelwasdevelopedor rainfall nterception f opengrown rees n urbansettings. t cannot e directlyusedin rural forestswhere reesare influencedby nearby rees.2. A data set for describing ree architectures neededasmodel nput. Obtaining hesedata equiresntensiveield

measurements.3. Wind blowing on the leaves and stemscan break theequilibrium and causewater to drip from the leaf andstem surfaces. In most situations the wind does not result

in tipping of a leaf, but changeshe zenithangle, herebyreducing he water storage f the leaf. The wind canexertforce on the leaf itself and/or on the layer of water on theleaf. This model accounted for wind effects onevaporation,ut not on reducing urface aterstorage.Relations etweenwind speed nd eafzenithanglehavenot beenestablished,nddetermininghese elationswasbeyond he scope f thisstudy.4. Snowand og interception re not included n the model.

5. ConclusionsA numerical model for predicting rainfall interceptionprocessesn open grown urban reeswas developed nd testedusing ield measurementsor cyclonic-typetorms n pear andoak trees. Comparisonof results rom the field measurements

and simulationsndicated hat the model correctlypredictedrainfall interception or both types of trees. From the modelsensitivityanalysis,crown rainfall interception oss was mostsensitive o rainfall depth and crown surfacestorage apacity,followed by leaf area index and stem surfacearea index. Stemand eaf zenithangles re the most mportantactorsnfluencingstemflow. Wetness of the crown surface at the onset of rainfallalsoaffects nterception rocesses.This model providesa new tool for scientists nd managersinterestedn betterunderstandingainfall interception f singletrees n urbansettings. urrently, tatistical odels rovide ong-term average data for interceptioncomponents e.g., grossprecipitation, throughfall, stemflow, canopy storage, andinterceptionoss),but they do not reveal he dynamic rocesseswithin stormevents. his model's igh emporalesolution anbe

used o investigate ow interceptionnfluences atershedime ofconcentration,n important arametern urban lood control.Unlike otherphysically ased ainfall nterception odels,hemodel presented n this paper more fully considers reearchitecture nd meteorologicalactors. The model's highresolution nd accuracy an be useful or evaluatingmpacts finterception n runoff volumeduring essextreme vents.Smallstorms, or which urban forest nterceptions greatest, reresponsibleor most annualpollutantwashoff Chang et al.,1990]. Becausehe model ncorporatesarametershat describeimportant ifferencesn treearchitecturemong pecies,t canbeused o identify specieshat will intercept he most ainfall orregions f thecountrywith differentainfallpatterns.The diverse peciesmix andheterogeneoustructure f urbanforests reate uniquechallengeo hydrologistsndcommunityforesters. Models hat accurately imulatenterception,unoff,and other hydrologiccomponents t the site scale are neededbecause tormwatermanagementontrols reshifting rompointsourceso dispersed, on point sources. his modelprovidesnew method for understandingand estimating rainfallinterceptionor suchurban rees.

NotationRainfallc rainfall ncidentangle zenithangle) deg].p precipitationate mmh-I].P grossprecipitation mm].v, rainfallerminalelocityms-I].De medianaindrop iametermm].Treefg gap raction.f stemsurface nterception oefficient.fi leaf surface nterception oefficient.fma maximum ractionof leaf surfacewetting.C surfacewater storage mm].S surfacewater storage apacity mm].ClimateTair air temperature,measuredat 1.5 m above ground surface[oc].RH relativehumidity.Ws wind peedms-].Wa wind direction reference o north) [deg].U(z) wind peedtheight above roundurfacems'].R,net radiationW m-2].Water flowTH throughfall mm].ST stemflow mm].Th free throughfall mm].E evaporation mm].d drip ate mm -].q stemflowate mm '].IL interceptionoss mm].e evaporationate mm ']].D crowndrip [mm].Sma maximumsurfacewater storage mm].Smin minimumsurfacewater storage ram].St trunk storage apacity mm].Do empiricaldrainage arameters.b empiricaldrainage arameters.E mean vaporationate mm -].


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XIAO ET AL.' MODEL FOR TREE RAINFALL INTERCEPTION 29,187

meanainfallate mms-l].drainage arameters,eterminedrom eacheventstemflowate mms'].Miscellaneousg gravityccelerationonstantms'2].p water ensitykgm-3].T time Is].r sheartressN m'2]./ dynamiciscosityN sm-2].

Acknowledgments.e thankWilliam . MassmantheRockyMountaintationf USDAForest ervice)ndGui-Ling angtheSchoolfEngineeringf heMassachusettsnstitutefTechnology)ortheir elpfulommentsnd uggestionsor mprovinghismanuscript.This esearchassupportedn partby funds rovidedy thePacificSouthwestesearchtation, orestService, .S. DepartmentfAgriculture.ReferencesBaldwin,J. I., Interception f snowfallby forests, or. Notes6 (mimeo),N.H. For. and Recreat.Dep., Concord,1938.Calder, . R., A stochastic odelof rainfall merception,. Hydrol.,89,65-71, 1986.Calder, I. R., Rainfall imerceptionand drop size - Developmentandcalibration of the two-layer stochastic merception model, TreePhysiol., 16, 727-732, 1996.Chang,G., J. Parrish, nd C. Souer,The first flushof runoffand ts effecton control structure design, report, 33 pp., Environ. Resour.Manage. Div. Dep. of Environ.and Conserv.Serv.,City of Austin,Austin,Tex., 1990. 36 pp.Chow, V. T., D. R. Maidment, and L. W. Mays, Applied Hydrology,McGraw-Hill, New York, 1988.Condon, P., and S. Moriarty (Eds.), Second Nature: Adapting LALandscapeor Sustainable iving,TreePeople, everlyHills, Calif.,

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(Received anuary , 2000; revisedMay 8, 2000;acceptedMay 24, 2000.)

a new approach to modeling tree rainfall interception

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