Click Here Full Article A simple surface conductance model

A simple surface conductance model to estimate

regional evaporation using MODIS leaf area

index and the Penman-Monteith equation

Ray Leuning,1 Y. Q. Zhang,2 Amelie Rajaud,1 Helen Cleugh,1 and Kevin Tu3

Received 1 October 2007; revised 19 May 2008; accepted 30 July 2008; published 25 October 2008.

[1] We introduce a simple biophysical model for surface conductance, Gs, for use withremotely sensed leaf area index (Lai) data and the Penman-Monteith (PM) equation tocalculate daily average evaporation, E, at kilometer spatial resolution. The model for Gs

has six parameters that represent canopy physiological processes and soil evaporation: gsx,maximum stomatal conductance; Q50 and D50, the values of solar radiation andatmospheric humidity deficit when the stomatal conductance is half its maximum; kQ andkA, extinction coefficients for visible radiation and available energy; and f, the ratio of soilevaporation to the equilibrium rate corresponding to the energy absorbed at the soilsurface. Model parameters were estimated using 2–3 years of data from 15 flux stationsites covering a wide range of climate and vegetation types globally. The PM estimates ofE are best when all six parameters in the Gs model are optimized at each site, but there isno significant reduction in model performance when Q50, D50, kQ, and kA are heldconstant across sites and gsx and f are optimized (linear regression of modeled mean dailyevaporation versus measurements: slope = 0.83, intercept = 0.22 mm/d, R2 = 0.80, andN = 10623). The average systematic root-mean-square error in daytime meanevaporation was 0.27 mm/d (range 0.09–0.50 mm/d) for the 15 sites. The averageunsystematic component was 0.48 mm/d (range 0.28–0.71 mm/d). The new model forGs with two parameters yields better estimates of E than an earlier, simple modelGs = cL Lai,where cL is an optimized parameter. Our study confirms that the PM equation providesreliable estimates of evaporation rates from land surfaces at daily time scales andkilometer space scales when remotely sensed leaf area indices are incorporated into asimple biophysical model for surface conductance. Developing remote sensing techniquesto measure the temporal and spatial variation in f is expected to enhance the utility of themodel proposed in this paper.

Citation: Leuning, R., Y. Q. Zhang, A. Rajaud, H. Cleugh, and K. Tu (2008), A simple surface conductance model to estimate

regional evaporation using MODIS leaf area index and the Penman-Monteith equation, Water Resour. Res., 44, W10419,

doi:10.1029/2007WR006562.

1. Introduction

[2] Accurate estimates of evaporation are required toreduce uncertainties in constructing weekly to monthly waterbalances at catchment and regional scales. Accurate esti-mates of water yield (runoff) is needed by water resourcemanagers responsible for urban and rural water supplies andknowledge of soil water availability is required for applica-tions such as agricultural production. Improved estimates ofevaporation from soils and transpiration from vegetation(combined symbol E) can constrain both of these importantquantities because E is the largest term in the terrestrial waterbalance after precipitation. Evaporation is also of interest to

meteorological agencies because energy partitioning at theEarth’s surface affects weather and climate. A major problemis that these diverse applications typically require knowledgeof distribution of E across catchments and regions at dailytime scales, whereas measurements are mostly made at apoint, such as at a flux tower or a stream flow gauging stationfrom which the spatial distribution of E must be inferred. Akey research question is therefore how to spatialize infor-mation from points to areas; combining in situ and remotelysensed observations offer part of the solution to this chal-lenge [Cleugh et al., 2007; Zhang et al., 2008].[3] Remotely sensed data from satellites provides tempo-

rally and spatially continuous information on biophysicalproperties of the land surfaces such as land surface temper-ature [Wan et al., 2002], leaf area index [Myneni et al.,2002], vegetation indices [Huete et al., 2002] and vegeta-tion type [Los et al., 2000]. Given the challenges and needsdescribed above, there has been considerable effort by thescientific community to use such remotely sensed data toestimate spatially and temporally distributed evaporation.

1CSIRO Marine and Atmospheric Research, Canberra, ACT, Australia.2CSIRO Land and Water, Canberra, ACT, Australia.3Department of Integrative Biology and Center for Stable Isotope

Biogeochemistry, University of California, Berkeley, California, USA.

Copyright 2008 by the American Geophysical Union.0043-1397/08/2007WR006562$09.00

W10419

WATER RESOURCES RESEARCH, VOL. 44, W10419, doi:10.1029/2007WR006562, 2008ClickHere

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FullArticle

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http://dx.doi.org/10.1029/2007WR006562

Several classes of evaporation models use remotely sensedradiative surface temperature to estimate E, such as SEBAL[Bastiaanssen et al., 1998a, 1998b], SEBS [Su, 2002, 2005],NTDI [McVicar and Jupp, 2002], the resistance surfaceenergy balance (RSEB) [Kalma and Jupp, 1990], the trianglemethod [Nemani and Running, 1989; Nishida et al., 2003;Gillies and Carlson, 1995], and the dual-source modeldeveloped by Norman et al. [1995] and Kustas and Norman[1999].[4] Cleugh et al. [2007] found that multiseasonal time

series of E estimated using MODIS measurements of theradiative surface temperature and the resistance surfaceenergy budget approach compared poorly to eddy fluxmeasurements of evaporation for two Australian ecosys-tems. Instead, they obtained satisfactory results when E wasestimated using the Penman-Monteith (PM) equation[Monteith, 1964; Thom, 1975] with a simple model forsurface conductance to evaporation given by Gs = cL Lai +Gs,min where Lai is the leaf area index obtained fromMODIS remote sensing and cL is a constant and Gs,min isthe surface conductance controlling soil evaporation. Theythen used the PM algorithm to produce an evaporationclimatology for Australia at 1 km resolution. Mu et al.[2007] also used the PM equation to estimate E, but foundthat the simple surface conductance model of Cleugh et al.[2007] was inadequate when tested against evaporationmeasurements from 19 AmeriFlux sites. Mu et al. [2007]revised the model for Gs by introducing scaling functionsthat range between 0 and 1 to account for the response ofstomata to humidity deficit of the air, Da, and air temper-ature, Ta. They also introduced a separate term for evapo-ration from the soil surface, a term that was acknowledgedby Cleugh et al. [2007], but which they incorporated via thecoefficient cL. The revised Gs algorithm of Mu et al. [2007]resulted in good agreement between predictions of E by thePM equation and the AmeriFlux measurements. They thenused the revised algorithm to predict the global distributionof mean annual E at a spatial resolution of 0.05�.[5] The results of Cleugh et al. [2007] and Mu et al.

[2007] show that the PM equation is a biophysically soundand robust framework for estimating daily E at regional toglobal scales using remotely sensed data. This paper buildson the original proposition of Cleugh et al. [2007] and theimportant developments ofMu et al. [2007] by introducing anew, simple biophysical algorithm for Gs based on ourunderstanding of leaf- and canopy-level plant physiology,radiation absorption by plant canopies and evaporation fromthe underlying soil surface. The formulation for Gs modifiesthat of Kelliher et al. [1995] (hereinafter referred to as K95),by including the influence of Da on stomatal conductanceand by introducing a soil evaporation algorithm that issimpler than that proposed by Mu et al. [2007] and whichhas the potential to be estimated using remote sensing.Performance of the new algorithm for Gs is then tested onseveral years of evaporation measurements at each of 15 fluxstation sites covering a wide range in climate and vegetationglobally, including deciduous and evergreen forests, a corncrop, a wetland, grassland and two woody savannas. In acompanion paper, Zhang et al. [2008] use mean annual Eestimated from runoff measured at the gauged catchmentsand leaf area indices obtained from MODIS remote sensingto estimate parameters of the Gs model developed in this

paper. They then used the calibrated model and the PMequation to provide spatially resolved estimates of E acrossthe Murray Darling Basin in SE Australia.[6] The following section describes the surface conduc-

tance model, followed by a brief description of the datasources and methods used to control the quality of the data.We then examine the performance of the model as wereduce from six to two the number of parameters to beestimated for each vegetation type. Model performance isassessed against measurements at the individual flux sta-tions and across all vegetation types.

2. Theory

2.1. Surface Conductance

[7] Since its derivation by Monteith [1964], the Penman-Monteith (PM) equation has been used extensively in theliterature to describe the biophysics of evaporation, E, fromland surfaces. The equation states that the flux of latent heatassociated with E is given by

lE ¼eAþ rcp=g

� �DaGa

eþ 1þ Ga=Gs

; ð1Þ

where l is the latent heat of evaporation, e = s/g, in whichg is the psychrometric constant and s = de*/dT is the slopeof the curve relating saturation water vapor pressure totemperature, A is the available energy absorbed by thesurface (net absorbed radiation, Rn minus soil heat flux, G),r is the density of air, cp is the specific heat of air at constantpressure, Da = e* (Ta) � ea is the water vapor pressuredeficit of the air (humidity deficit), in which e* (Ta) is thesaturation water vapor pressure at air temperature and ea isthe actual water vapor pressure, Ga is the aerodynamicconductance and Gs is the surface conductance accountingfor evaporation from the soil and transpiration by thevegetation. In this paper we assume that the quantities A,Da and Ga are either known or are estimated usingmeasured meteorological fields of incoming solar radiation,temperature, humidity and wind speed [Cleugh et al., 2007].The main challenge in practical application of equation (1)is thus to determine Gs.[8] Total evaporation is the sum of transpiration from the

plant canopy, Ec, and evaporation from the soil, Es:

E ¼ Ec þ Es: ð2Þ

Using separate versions of the PM equation for E and Ec,and the assumption that evaporation from the soil occurs atsome fraction, f, of the equilibrium rate at the soil surface,eAs/(1 + e), we can write

eAþ rcp=g� �

DaGa

eþ 1þ Ga=Gs

¼eAc þ rcp=g

� �DaGa

eþ 1þ Ga=Gc

þ f eAs

eþ 1: ð3Þ

Note that we distinguish between surface conductance, Gs,and the canopy conductance Gc, and that we partition thetotal available energy A into that absorbed by the canopy,Ac, and by the soil, As. For the purposes of this study, f is aparameter to be estimated from the data, although in reality fwill vary with moisture content of the soil near to thesurface. Discussion of potential remote sensing techniques

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W10419 LEUNING ET AL.: MODIS-LAI-BASED EVAPORATION MODEL W10419

for estimating the temporal and spatial variation of f isdeferred until later.[9] The fraction of the total available energy absorbed by

the canopy and by the soil are given respectively by Ac/A =1 � t and As/A = t, where t = exp (�kALai), kA is anextinction coefficient for available energy and Lai is leafarea index. Note that this ignores the soil heat flux, G,because G ! 0 when we later use daily average meteoro-logical variables.[10] With these definitions, equation (3) can be written as

eþ Ga=Gi

eþ 1þ Ga=Gs

¼ e 1� tð Þ þ Ga=Gi

eþ 1þ Ga=Gc

þ f eteþ 1

; ð4Þ

where Gi is the ‘‘climatological’’ conductance defined byMonteith [1964] as

Gi ¼A

rcp=g� �

Da

: ð5Þ

An expression for Gs in terms of Gc, t, f, Gi and Ga isobtained by rearranging equation (4):

Gs ¼ Gc

1þ tGa

eþ 1ð ÞGc

f � eþ 1ð Þ 1� fð ÞGc

Ga

� �þ Ga

eGi

1� t f � eþ 1ð Þ 1� fð ÞGc

Ga

� �þ Ga

eGi

2664

3775: ð6Þ

Several useful limits can be derived from this equation.When f = 1, evaporation at the soil surface occurs at theequilibrium rate and equation (6) reduces to

Gs ¼ Gc

1þ tGa

eþ 1ð ÞGc

þ Ga

eGi

1� t þ Ga

eGi

2664

3775; ð7Þ

which is the same as equation (10) derived by K95 in theirsurvey of maximum surface conductances of various landcover types.[11] When the soil surface is completely dry, f = 0 and

then

Gs ¼ Gc

1� t þ Ga

eGi

1þ teþ 1ð ÞGc

Ga

þ Ga

eGi

2664

3775: ð8Þ

Note that Gs 6¼ Gc because Gc depends on radiationabsorbed by the plant canopy, whereas Gs is a function ofradiation absorbed by both canopy and soil.[12] If all radiation is absorbed by the canopy, t = 0, and

thus

GS ¼ Gc

1þ Ga

eGi

1þ Ga

eGi

2664

3775 ¼ Gc: ð9Þ

Figure 1. Response of Gs/gsx to (a) Da, (b) A, (c) D50, (d) Q50, (e) gsx, and (f) f. Except when varied,parameter values are gsx = 0.008 m/s, Q50 = 30 W/m2, Ga = 0.033 m/s, kQ = kA = 0.6, Da = D50 = 1.0 kPa,f = 0.5, and A = 500 W/m2. Photosynthetically active radiation, Qh, is assumed to correlate withA according to Qh = 0.8A in all plots.

W10419 LEUNING ET AL.: MODIS-LAI-BASED EVAPORATION MODEL

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W10419

Finally, when t = 1, Gc = 0 because there is no canopy, andthen from equation (4) we obtain

Gs ¼efGa

eþ 1ð Þ e 1� fð Þ þ Ga=Gi½ : ð10Þ

In this case Ga and Gi appropriate to bare soil should beused, rather than those relevant to plant canopies.

2.2. Canopy Conductance and Evaporative Fraction

[13] Gs is dependent on the as yet unspecified Gc in eachof equations (6)–(9). K95 developed an expression forcanopy conductance in terms of maximum stomatal con-ductance of leaves at the top of the canopy, gsx, Lai and anhyperbolic response to absorbed shortwave radiation. Theyshowed that

Gc ¼gsx

kQln

Qh þ Q50

Qh exp �kQL� �

þ Q50

" #; ð11Þ

where Qh is the flux density of visible radiation at the top ofthe canopy (approximately half of incoming solar radiation),kQ is the extinction coefficient for shortwave radiation andQ50 is the visible radiation flux when stomatal conductanceis half its maximum value. A similar expression was derivedby Saugier and Katerji [1991] and Dolman et al. [1991].Here we modify this expression to include the response ofstomatal conductance to humidity deficit as developed byLeuning [1995] to give

Gc ¼gsx

kQln

Qh þ Q50

Qh exp �kQL� �

þ Q50

" #1

1þ Da=D50

� �; ð12Þ

where D50 is the humidity deficit at which stomatalconductance is half its maximum value. This formula wasused by Isaac et al. [2004] and Wang et al. [2004], andfound to be an improvement over that of K95. Substitutionof equation (12) into (6) shows that model for Gs containsthe six parameters gsx, Q50, D50 kQ, kA and f.

Figure 2. Contour plots of the evaporative fraction, fE = lE/A, as a function of absorbedphotosynthetically active radiation, Qh, and leaf area index (Lai 100) for (a) Da = 0.5 kPa, (b) Da =1.0 kPa, (c)Da = 1.5 kPa, and (d)Da = 2.0 kPa. Fixed parameter values are gsx = 0.008 m/s,Q50 = 30W/m2,Ga = 0.033 m/s, kQ = kA = 0.6, D50 = 1.0 kPa, and f = 0.5.

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Table

1.DetailsofFluxnet

Sites

Usedto

EvaluatePerform

ance

oftheSurfaceConductance

Model

inEstim

atingLandSurfaceEvaporation

SiteID

aSiteNam

eCode

IGBPClass

DominantSpecies

Country

Latitudeand

Longitude

Elevation

(m)

Canopy

Height

(m)

Tem

perature

(�C)

Annual

Precipitation

(mm)

References

Minim

um

Average

Maxim

um

830

Bondville

crp

Croplands

Corn/soybean

USA

40�0

0 21.9600 N

,88�170 30.7200 W

300

3�16.9

34.0

11.7

644.6

MeyersandHollinger

[2004]

777

Griffin

enf

Needleleaf

forest

Picea

sitkensis,

Pseudotsuga

menziesii,Betula

pendula

UK

56�360 23.5900 N

,3�470 48.5500 W

340

9�5.5

22.8

7.2

1169.0

Falgeet

al.[2002]

392

Hainich

dbf

Deciduous

broadleaf

forest

Fagussylvatica,

Acer,Fraxinus

Germany

51�4

0 45.3600 N

,10�270 7.200 E

430

33

�13.2

30.8

8.0

853.9

Knohlet

al.[2003]

476

Hesse

dbf

Deciduous

broadleaf

forest

Fagussylvatica,

Quercuspetraea

France

48�400 27.1800 N

,7�3

0 52.6200 E

300

13

�14.0

32.6

10.5

1154.5

Granieret

al.[2000]

890

Howland

mf

Mixed

forest

Red

spruce,

Eastern

hem

lock

USA

45�120 14.6500 N

,68�440 2500 W

60

19.5

�23.6

33.7

7.2

645.1

Hollinger

etal.[1999]

814

Kendall

grass

Grassland

C4grasses

USA

31�440 11.5000 N

,109�560 30.7700 W

1531

0.5

�17.6

38.1

13.1

356

–

235

Mer

Bleue

wet

Wetland

Sphagnum

mosses

Canada

45�240 33.8400 N

,75�310 1200 W

70

–�30.7

36.2

6.8

725.0

Admiralet

al.[2006]

1071

Mize

bare

Slash

pine

clearcut

Pinuselliottii

USA

29�450 53.2800 N

,82�140 41.3400 W

50

5�9.6

37.6

20.0

898.3

GholzandClark

[2002]

968

Morgan

Munroe

dbf

Deciduous

broadleaf

forest

Acersaccharum

USA

39�190 23.3400 N

,86�240 47.3000 W

275

27

�15.7

34.8

13.0

1121.4

Ehmanet

al.[2002],

Oliphantet

al.[2004]

997

NiwotRidge

enf

Evergreen

needleleaf

forest

Abieslasiocarpa,

Picea

engelmannii,

Pinuscontorta

USA

40�010 58.3600 N

,105�320 47.0500 W

3050

11.5

�31.5

26.6

1.1

562.9

Turnipseed

etal.[2002]

85

Santarem

Km83

ebf

Evergreen

broadleaf

forest

Cleared

forest

Brazil

3�1

0 4.90500 S,

54�580 17.16600 W

–19.9

36.9

26.0

1598.5

Goulden

etal.[2004],

Milleret

al.[2004]

259

SSA-O

ldBlack

Spruce

enf

Evergreen

needleleaf

forest

Picea

mariana

Canada

53�59013.8100 N

,105�7

04.0400 W

629

1–21

�39.8

35.2

�2.2

376.3

Griffiset

al.[2003],

MahrtandVickers

[2002]

1078

Tonzi

wsa

Woody

savanna

Quercusdouglasii

plusC3winter

grasses

USA

38�250 53.7600 N

,120�570 57.5400 W

117

10.1

�2.6

42.9

16.0

532.7

Baldocchiet

al.[2004]

43

Tumbarumba

ebf

Evergreen

broadleaf

Eucalyptus

delagatensis

Australia

35�390 20.600 S,

148�9

0 7.500 E

1200

40

�4.7

28.9

9.2

1011.2

Leuninget

al.[2005]

45

Virginia

Park

wsa

Woody

savanna

Eucalyptuscreba,

Eucalyptus,

drepanophyllaplus

C4grasses

insummer

Australia

19�530 0000 S,

146�330 1400 E

200

5–8

4.0

38.9

21.8

402.9

Leuninget

al.[2005]

aFulldetailsoneach

site

canbefoundat

theORNLDAACbysubstitutingthesite

identification(ID)number

forxxxat

http://www.fluxnet.ornl.gov/fluxnet/sitepage.cfm?SITEID

=xxx.


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[14] Predictions of the ratio Gs/gsx, using equations (6)and (12), are shown as a function of Lai in Figure 1 fortypical values of the meteorological parameters Da and A,the physiological parameters D50, Q50 and gsx and the soilevaporation parameter f. We note first that values of Gs/gsxare lower than in the work by K95 for all the sensitivityanalyses in Figure 1 because the extra term 1/(1 + Da/D50)in equation (11) reduces Gc compared to correspondingvalues of K95. As a result, increasing Da from 0.5 to2.0 kPa causes Gs/gsx to decrease by >50% at all Lai(Figure 1a), in contrast to the model of K95 that has no suchdependence. Compared to the work by K95, the revisedmodel also shows a greater dependence of Gs/gsx on A athigh Lai (Figure 1b) because here we maintain a realisticcorrelation between Qh and A using Qh = 0.8A (R. Leuning,unpublished data, 2008), whereas K95 held Qh fixed whenAwas varied. Increasing values of the physiological param-eter D50 causes Gs/gsx to increase, while increasing Q50

causes it to decrease at all Lai (Figures 1c and 1d). Incontrast, the influence of varying gsx and f on Gs/gsx is onlysignificant when Lai < 3 (Figures 1e and 1f). Soil evapora-tion is assumed to occur at the equilibrium rate in the K95model (equivalent to f = 1) and this causes a minimum inGs/gsx around Lai � 1, whereas this minimum is absent orless pronounced in the new model, where f 1. Low ratesof evaporation from sparse canopies correspond to lowvalues of f and hence Gs.[15] Contour plots of the evaporative fraction, fE = lE/A, as

predicted by the evaporation model, are shown in Figure 2 asa function of Qh and Lai 100 for values of Da = 0.5, 1.0,1.5, and 2.0 kPa. Increasing Da for any combination ofQh and Lai results in an increase in evaporative fraction;for example, fE is predicted to increase from 0.75 to 1.45 forQh = 300 W m�2 and Lai = 3 as Da increases from 0.5 to2.0 kPa. The contour spacing decreases with increasing Da,indicating increasing sensitivity of fE to variations in hu-midity deficit and leaf area index at higher humidity deficits.Sensitivity of fE to Lai is greatest at low values of Qh andvice versa.

[16] We next describe the data sources for evaporationfluxes, meteorology and Lai used to estimate model param-eters and to evaluate model performance.

3. Methods

3.1. Sites, Fluxes, and Meteorological Data

[17] Table 1 provides details of the 15 Fluxnet sites usedto evaluate performance of the surface conductance modelin estimating land surface evaporation. References describ-ing each site are also listed. The sites are located acrossseveral continents and include savannas, grasslands, a corncrop, mixed deciduous forests, evergreen needleleaf andbroadleaf forests, a wetland and cleared forest land. Lat-itudes of the sites vary from 54�N to 35�S, while climaticregions range from subarctic, cool temperate, warm tem-perate to tropical. Maritime and continental climates are alsorepresented. Minimum temperatures at the continental SSAOld Black Spruce site reach �39.8�C while maximumtemperatures exceeded 35�C at many sites. Annual precip-itation across sites ranged from 376 to 1599 mm.[18] A plot of mean annual precipitation versus mean

annual temperature (Figure 3a) shows that the sites chosenfor analysis cover much of the observed range in globalclimate. The sites ranged from the boreal SSA-Old BlackSpruce site with mean annual temperature of �1.2�C andprecipitation of 376 mm to the tropical Santarem Km83 sitewith 1600 mm rainfall and mean annual temperatures of26.1�C. High mean temperatures of 22.3�C are also ob-served at Virginia Park, which is a seasonally wet/drysavanna but with an annual rainfall of only 403 mm thatoccurs during the summer wet season.[19] For the analysis, time series of latent heat flux, wind

speed, minimum and maximum air temperature, watervapor pressure, solar radiation, air pressure, net radiationand soil heat flux for the selected sites were obtained fromthe Oak Ridge National Laboratory, Distributed ActiveArchive Center (ORNL-DAAC, http://www.fluxnet.ornl.gov/MODIS/modis.html).[20] Latent heat flux data were eliminated from the

analysis when measured values were consistently at zero

Figure 3. (a) Mean annual temperature and precipitation at each of the 15 flux station sites used in thedata analysis. (b) Mean Lai at each flux station versus mean annual precipitation.

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or when jjAj�jH + lEjj > 250 W m�2, where H and lE arethe measured sensible and latent heat fluxes. Values outsidethis broad range arise either because of instrumentationproblems or because the site is subject to considerableadvection. Wilson et al. [2002] found that H + lE < A atmany eddy flux sites globally. This is also the case for mostof the15 flux sites used in this study, as seen in thescatterplots in Figure 4 of daily average H + lE versusdaily average A. The exceptions are Bondville, NiwotRidge, Tumbarumba and Virginia Park, for which linearregression slopes are close to unity, with the worst casesbeing Hess and Kendall where the slopes are 0.70. Wehave assumed that A = H + lE to ensure internal consis-tency in the analysis used to estimate the model parametersfor each site. Using the measured A and lE to estimate theparameters in the model for Gs would be incorrect since thisassumes the lack of energy closure is due to errors in Halone. An alternative is to assume that the mean Bowenratio (H/lE) is correct so that we can divide both H and lEby the slopes of the respective regression plots shown inFigure 4. A comparison of results for the two approachesare discussed later for the Hess and Kendall sites.[21] Aerodynamic conductance was calculated using

Ga ¼k2um

ln zm � dð Þ=zom½ ln zm � dð Þ=zov½ ; ð13Þ

where zm is the height of wind speed and humiditymeasurements, d zero plane displacement height, zom andzov are the roughness lengths governing transfer ofmomentum and water vapor, k von Karman’s constant(0.41), and uz is wind speed at height zm [Monteith andUnsworth, 1990]. The quantities d, z0m and z0v wereestimated using d = 2h/3, z0m = 0.123h and z0v = 0.1z0m,where h is canopy height [Allen et al., 1998]. Atmosphericstability modifies the values of Ga calculated usingequation (13) by up to ±25% but we have neglectedstability effects because evaporation from dry canopies isrelatively insensitive to errors in Ga. Similar argumentsapply to uncertainties in the ratio z0v/z0m. The sensitivity ofE to Ga is particularly weak at the daily time steps used inthis study and this fact is exploited in the companion paperby Zhang et al. [2008], who assign constant values of Ga =0.033, 0.0125 and 0.010 m/s for forests, shrubs, grasslandand crops, respectively, because of the lack of routinelyavailable, quality wind speed data at 1-km resolution.[22] Meteorological variables measured at each flux sta-

tion have been used in this paper rather than large-scalemeteorology that would likely be used in any operationalapplication of the algorithms developed in this paper. This isnot a significant weakness since both Cleugh et al. [2007]and Mu et al. [2007] showed that there is very littledegradation in the performance of the PM equation when

Figure 4. Scatterplots of measured daily average H + lE versus daily average Rn � G (=A) for each ofthe 15 flux sites used in this analysis. Slopes and R2 values are shown for linear regressions forcedthrough the origin.


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W10419

meteorological data at 0.05� (latitude and longitude) scalesare substituted for locally measured inputs.

3.2. Leaf Area Index

[23] The Lai data needed to compute Gc, and hence Gs,were extracted for a 7 7 km2 area centered on each fluxtower from the 8-day standard MOD15A2 collection 5product [Myneni et al., 2002] from the ORNL-DAAC.These data were derived from MODIS, the ModerateResolution Imaging Spectrometer mounted on the polar-orbiting Terra satellite, which has a daily overpass at around1030 local time. The MOD15A2 product contains four datalayers: the fraction of photosynthetically absorbed radiation,fPAR and Lai, plus their respective quality control layers. Thequality assessment (QA) flags in the database were used tocheck the quality of the MODIS-Lai data. At each grid, allpoor quality Lai data were deleted and replaced by interpo-lated values obtained from a piecewise cubic, hermiteinterpolating polynomial [Zhang et al., 2006]. Then, all ofthe quality-controlled Lai data for each pixel were smoothedby the Savitzky-Golay filtering method that is widely usedfor filtering MODIS-Lai [Fang et al., 2008] and otherremote sensing data.[Jonsson and Eklundh, 2004; Ruffinet al., 2008; Tsai and Philpot, 1998]. The MODIS Laiprovides reasonable estimates for most Australian vegeta-tion types except for the open forest and woodlands ineastern Australia [Hill et al., 2006].[24] Figure 3b shows there is essentially no correlation

between annual precipitation, P, and annual mean Lai for the15 selected sites. Lai ranged from 3.6 for an evergreen broad

leaf forest with P = 1600 mm to Lai = 0.7 for a savanna with400 mm of rainfall.

4. Results

4.1. Parameter Estimation

[25] The generalized pattern search algorithm inMATLAB1 (The MathWorks, Inc.) was used to optimizefor each site the parameters gsx, Q50, D50, kQ, kA and f in themodel for Gs (equations (12) and (6)). This was done byminimizing the cost function F

F ¼

XNj¼1

Emeas;j � ERS;j

� �2XNj¼1

Emeas;j � Emeas

� �2 ; ð14Þ

where Emeas,j and ERS,j are the jth measured and simulateddaily average evaporation rates, Emeas is the arithmetic meanof the measurements and N is the number of samples. ERS,j

was calculated by substituting the modeled Gs intoequation (1), in conjunction with the required meteorolo-gical variables as measured at each flux station.[26] Optimized values for the six parameters in the

surface conductance model are listed for the 15 sites inTable 2, with the last row listing the ranges allowed for eachparameter in the optimization calculations. Figure 5a showsvalues of gsx extracted from Table 2 in rank order for the

Figure 5. Values of gsx and f extracted from Tables 2 and 3 in rank order for the various biomes for (aand b) the six-parameter model and (c and d) the two-parameter model (gsx and f). Biome codes are givenin Table 1.

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Table 2. Site Name, Biome Code, and Optimized Values for All Six Parameters of the Surface Conductance Model for the 15 Flux

Stations Used in the Analysisa

Site Name Codegsx(m/s) f

Q50

(W/m2)D50

(kPa) kQ kA ab

(mm/d) R2Emeas

(mm/d)Percent ErrorSystematic

Percent ErrorUnsystematic

Tonzi wsa 0.0030 0.05 20.0 0.70 0.30 0.80 0.52 0.51 0.52 1.09 37.9 40.3Hesse dec 0.0067 0.06 50.0 0.70 0.30 0.80 0.87 0.16 0.87 1.10 14.7 36.4Virginia Park wsa 0.0063 0.09 20.0 0.70 0.30 0.80 0.36 0.80 0.48 1.20 40.3 23.0Howland dec 0.0038 0.16 50.0 0.74 0.62 0.80 0.76 0.37 0.81 1.23 22.5 34.0Morgan dec 0.0036 0.21 30.6 0.70 0.30 0.80 0.71 0.29 0.73 1.22 33.6 49.2SSA_OBS con 0.0020 0.51 20.0 0.70 0.74 0.50 0.86 0.07 0.82 0.74 13.1 37.0Kendall gra 0.0048 0.53 20.0 0.70 0.30 0.50 0.88 0.13 0.84 1.68 8.1 25.1Hainich dec 0.0046 0.76 20.0 0.70 1.00 0.60 0.91 0.05 0.86 1.13 7.9 27.9Bondville cer 0.0053 0.80 20.0 0.70 0.30 0.50 0.88 0.12 0.81 2.18 8.6 25.4Mize con 0.0039 0.92 48.8 0.70 0.30 0.50 0.78 0.51 0.80 2.37 10.9 20.0Tumbarumba ebf 0.0047 1.00 38.1 0.70 0.68 0.50 0.92 0.09 0.84 2.11 6.2 24.2Santerem Km83 ebf 0.0076 1.00 20.9 0.70 1.00 0.50 0.71 0.87 0.74 3.06 7.9 11.6Griffin con 0.0085 1.00 20.0 0.70 1.00 0.50 0.84 0.00 0.69 1.61 18.9 41.1Niwot Ridge con 0.0027 1.00 20.0 0.70 0.30 0.50 0.60 0.56 0.43 1.79 24.2 38.9Mer Bleue wet 0.0028 1.00 20.0 0.70 0.30 0.50 0.86 0.13 0.79 1.50 13.5 35.2Parameter ranges – 0.002–0.015 0.05–1.00 20–50 0.7–1.5 0.3–1.0 0.5–0.8 – – 0.73 1.60 17.9 31.3

aAlso shown are the slope, a, and intercept, b, of the linear regression ERS6 = aEmeas + b, the R2 value, mean annual Emeas, and the percentage systematicand unsystematic root-mean-square error in average evaporation. Allowable parameter ranges used in the optimization are shown in the last row, as well asaverages for Emeas and the percentage errors across all sites. The flux sites have been sorted according to increasing f value.

Figure 6. Time series of (top) 8-day averages for Emeas, ERS6, and Eeq and (middle) precipitation (cm/d)and Lai and (bottom) scatterplots of ERS6 versus Emeas for the Hesse, Tumbarumba, and Bondville sites.


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various biomes. Maximum stomatal conductance rangedbetween 0.0020 and 0.0085 m/s, which is below themaximum of 0.012 m/s reported by K95 for variousvegetation types, but is similar to the range reported byIsaac et al. [2004] for water stressed to well-watered cropsand pastures. The soil evaporation parameter f reduces soilevaporation below the equilibrium rate when water avail-ability limits evaporation. While this is a rather crudeparameterization, the optimized values of f were reasonable,ranging from a low of <0.1 for the rather dry savannas atVirginia Park and Tonzi, to a maximum of 1.0 for the wettertemperate evergreen forests, the tropical broadleaf forestand the permanent wetland (Figure 5b and Table 2).[27] The light response of stomata is represented by the

parameter Q50 in the model and optimum values for Q50

given in Table 2 tended to fall near the upper and lowerbounds of the allowable range of 20–50 W/m2. There wasalmost no variation in D50, the parameter that accounts forstomatal sensitivity to water vapor deficit, with all valuesexcept one at the lower bound of 0.7 kPa. When the lowerallowable bound for D50 was decreased to 0.5 kPa, therewas a corresponding proportional increase in the optimizedvalues for gsx (data not shown), as may be expected from

inspection of the model for Gc (equation (12)). These resultssuggest that Q50 and D50 are not constrained particularlywell by the data, and this is in accordance with Figure 1 thatshows Gs/gsx is relatively insensitive to these parameters inthe range of leaf area indices available in our data set. Therewas considerable variation in the optimum values of kQacross the various biomes, ranging across the allowablelimits of 0.3 to 1.0, and similar variability between allow-able limits was obtained in the value of kA, the extinctioncoefficient for available energy. Later we examine modelperformance when the parameters Q50, D50 kQ and kA areheld constant across biomes.

4.2. Model Performance: Gs Model With SixParameters

[28] Figures 6 and 7 present for six of the 15 sites the timeseries of Emeas, ERS6 and Eeq (8-day averages are shown forclarity), daily precipitation and daily Lai interpolated fromeach 8-day MODIS compositing period. Scatterplots ofdaily average Emeasversus ERS6 are also shown, whereERS6 was calculated using equation (1) with average daytimemeteorological data. Gs was calculated using equations (12)and (6) with interpolated Lai and the six optimized parameter

Figure 7. Time series of 8-day averages for (top) Emeas, ERS6, and Eeq and (middle) precipitation (cm/d)and Lai and (bottom) scatterplots of ERS6 versus Emeas at the SSA Old Black Spruce site and two savannasites, Virginia Park and Tonzi.

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values for each corresponding site given in Table 2. The lastsubscript onERS6 denotes that six parameters were used in thecalculation. Equilibrium evaporation was calculated using

lEeq ¼eA

eþ 1; ð15Þ

where A is the available energy absorbed by both vegetationand the soil. The objective of Figures 6 and 7 is to see howmuch of the observed variability in evaporation rates iscaptured by ERS6 and by the simpler Eeq.[29] Figure 6 shows that at the relatively moist sites of

Hesse, Tumbarumba and Bondville, Emeas is closely ap-proximated by Eeq for much of the annual cycle. For suchsites Gs is relatively large compared to Ga and the PMmodel reduces to the equilibrium rate. The strong variationin Emeas is largely driven by the seasonal variation inavailable energy at Tumbarumba, an evergreen forest wherethere is little seasonal variation in Lai. The influence of Lai,and hence Gs, on evaporation rates is not so clear at theHesse deciduous forest and the corn crop at Bondvillewhere seasonal Lai varies in parallel with available energy.While the equilibrium model may be sufficient at these sitesfor some purposes, Eeq overestimates Emeas at both Hesseand Tumbarumba in the summer, indicating some limitationto evaporation through the influence of atmospheric humid-ity deficit on canopy conductance. In contrast, Figure 7shows there are large differences between Emeas and Eeq atmost times at the SSA-OBS and Tonzi sites, while atVirginia Park Emeas < Eeq at all times. For such sites it isessential to have accurate knowledge of A, D, Ga and Gs tocalculate evaporation rates using the PM equation. Errors inthe magnitude and seasonal variation of remotely sensed Laiat such sparsely vegetated sites also contribute to uncertain-ties in ERS6. When Gs was calculated using the optimizedparameter values given in Table 2 there was good agreementbetween Emeas and ERS6 at all times of the year at SSA-OBSand ERS6 provided a significant improvement over Eeq atVirginia Park and at Tonzi, especially in the dry season(Figure 7). There was also an improvement in modeledevaporation during summer at Hesse and Tumbarumbawhen Emeas < Eeq (Figure 6), but there was little advantagein using ERS6 instead of Eeq for the corn crop at Bondville.[30] Scatterplots of daily mean ERS6 versus Emeas in

Figures 6 and 7 confirm the strong correlation betweenmeasured and modeled E. The slopes of the linear regres-sion analyses are close to unity, and intercepts are close tozero, for all except the two savanna sites. The modelunderestimates the springtime peak in Emeas and overesti-mates summertime evaporation at Tonzi, while at VirginiaPark the model underestimated evaporation in the summerwet season in 2002 and overestimated it in the late dryseason of 2004. The discrepancies may arise because wehave modeled soil evaporation using the single parameter f,held fixed for each site, whereas it will be expected to varyduring wetting/drying cycles as shown by Baldocchi et al.[2004] at the Tonzi savanna site. Errors in MOD15A2 leafarea indices will also contribute to a mismatch betweenmodel and measurements. Huemmrich et al. [2005] foundthat Lai from MODIS was systematically high by 0.25 unitsfor sparse vegetation. Differing degrees of accuracy havebeen also found in several field validation studies of

MOD15A2 leaf area indices [Abuelgasim et al., 2006;Cohen et al., 2006; Pisek and Chen, 2007] and such studiesare stimulating the development of improved algorithms forestimating Lai [Yang et al., 2006].[31] Statistical details of model performance for all sites

presented in Table 2 show that the slopes of the linearregressions of ERS6 versus Emeas range from 0.36 at VirginiaPark to 0.92 at Tumbarumba, while the intercepts rangefrom 0.00 mm/d at Griffin to 0.87 mm/d at the tropicalSanterem 83Km site. On average, the model explained 73%of the variance in Emeas across all sites, ranging from a lowof 43% at Niwot Ridge to 87% at Hesse.[32] Willmott [1981] concluded that R2 values obtained

from plotting model predictions, Pi, against observations,Oi, are insufficient to evaluate model performance. Herecommended that the total mean square error,

e2MSE;t ¼ 1=Nð ÞXNi¼1

Pi � Oið Þ2; ð16Þ

be partitioned into systematic and unsystematic componentsgiven by

e2MSE;s ¼ 1=Nð ÞXNi¼1

Pi � Oi

� �2and e2MSE;u ¼ 1=Nð Þ

XNi¼1

Pi � Pi

� �2;

ð17Þ

where Pi = aOi + b, in which a and b are coefficientsobtained from linear regression of Pi (dependent variable)versus Oi (independent variable). Note that eMSE,t

2 = eMSE,s2 +

eMSE,u2 . The systematic component, eMSE,s

2 , results from the

deviation of Pi from the 1:1 line of a perfect model, since Pi�Oi = (a � 1) Oi + b, whereas the unsystematic component,eMSE,u2 , results from scatter of Pi about Pi. In the followingwe present root-mean-square errors (eRMSE), the squareroots of the quantities in equation (17).[33] Table 2 shows that the systematic component of the

error in E is greater than or similar in magnitude to theunsystematic component only at Tonzi and at Virginia Parkbecause at these sites the variation in modeled evaporationis significantly less than is observed in the data (Figure 7).The percentage systematic error, 100eRMSE,s/Emeas, is >30%for the two savanna sites and for Morgan, 24.2% at NiwotRidge, and an average of 13.8% for the other 11 sites. Thereis a significant inverse relationship between f and thesystematic component of the error but not in the unsystem-atic component, 100eRMSE,u/Emeas, which has an average of31.3%.[34] The scatterplot in Figure 8a shows daily average

ERS,6 versus Emeas for all sites combined and linear regres-sion yields a slope of 0.85, intercept of 0.21 mm/d and R2 =0.82, N = 10630. The results show that good estimates ofdaily average evaporation are obtained when the PMequation is used with the model for Gs when all sixparameters are optimized at each site and with MODISLai data.

4.3. Comparison With Cleugh et al. [2007]

[35] Cleugh et al. [2007] obtained good agreementbetween measured evaporation rates at two Australian sites,Tumbarumba and at Virginia Park, when they used thesimple linear model Gs = cLLai + Gs,min in the PM equation,


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where cL is an empirical coefficient and Gs,min is the surfaceconductance controlling soil evaporation (set to zero in theiranalysis).The current data set was used to optimize cL foreach site before calculating daily average evaporation rates,EcL, using the PM equation. Values of cL ranged from0.0005 to 0.0037 (Table 4), compared to values of 0.0019 atTumbarumba and 0.0025 at Virginia Park reported byCleugh et al. [2007]. Figure 8b shows that daily averageevaporation rates calculated using the simple linear modelfor Gs captures much of the variation in the measuredevaporation, but the larger scatter (R2 = 0.61) indicates thatthe results obtained using EcL are less satisfactory than ERS6.Both models are clearly superior to using Eeq to estimateactual evaporation (Figure 8c), since Eeq is generally greaterthan the measurements, often by a factor of two or more, the

intercept of the regression is significantly greater than zeroand the scatter in Eeq is unacceptably large (R2 = 0.57).

4.4. Reducing the Number of Free Parametersin the Gs Model

[36] The general utility of the Gs model for estimatingevaporation will be greatly enhanced if we can reduce thenumber of parameters to be estimated without substantiallydegrading model performance. To examine this possibilitywe explore two different approaches. The first is to takeadvantage of the observation, made earlier when discussingFigure 1, that Gs is relatively insensitive to Q50, D50 kQ andkA, and hence the optimization for gsx and f was repeatedwhile holding the other parameters constant. The resultanttwo-parameter model for Gs is then used to calculate

Figure 8. Predicted daily average daily evaporation rates (mm/d) plotted against average dailymeasured evaporation rates. Predictions use (a) the six-parameter model for Gs; (b) Gs = cL Lai, [Cleugh etal., 2007]; (c) equilibrium evaporation, Eeq; (d) the two-parameter model for Gs; and (e) the one-parameter model with gsx assigned from K95.

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evaporation rates, defined as ERS2. The fixed values chosenfor parameters Q50 = 30 W m�2 and D50 = 0.7 kPa wereguided by the results in Table 2. In principle, the extinctioncoefficient for visible radiation, kQ is expected to differ fromthat for available energy, kA, which accounts for the transferof the sum of visible, near infrared and net thermalradiation. This is because reflection and transmissioncoefficients of leaves are considerably lower in the visiblewaveband than in the near infrared while in the thermalwaveband the leaves have very high emissivity and lowtransmissivity. However, Gs is insensitive to values of theextinction coefficients, and a constant kQ = kA = 0.6 wasused in the subsequent analysis.[37] Table 3 and Figures 5c and 5d show that optimizing

just two parameters caused only minor changes in the valuesand relative ranking of gsx and f compared to those shown inTable 2 and Figures 5a and 5b for the six-parameter model.This provides further evidence that modeled evaporationrates are relatively insensitive to Q50, D50 kQ and kA.

Comparison of Tables 2 and 3 and Figures 8a and 8d showsthat the two-parameter model for Gs performs almost as wellas the six-parameter model in describing the variation indaily average evaporation rates across all sites. The linearregression of ERS2 versus Emeas has a slope of 0.83,intercept = 0.22 mm/d and R2 = 0.80. The nonzero interceptis largely due to the systematic bias of the model at the twosavanna sites, Tonzi and Virginia Park. The model performsleast well for the three sites with values of f 0.09,indicating the importance of soil evaporation at these sitesand the desirability of finding a means to estimate thetemporal and spatial variation of f using remote sensingrather than treating f as a fixed parameter. The averagesystematic root-mean-square error in daily mean E across all15 sites was 0.31 mm/d (19.3% of 1.60 mm/d), with a rangeof 0.05–0.50 mm/d. Compared to the six-parameter model,the two-parameter model resulted in a <2% increase in themean systematic and unsystematic components of modelerror when averaged across all sites.

Table 3. Site Name, Biome Code, and Optimized Values of gsx and f of the Two-Parameter Surface Conductance Model for the 15 Flux

Stations Used in the Analysisa

Site Name Code

Two-Parameter Optimization

gsx(m/s) f a

b(mm/d) R2

Emeas

(mm/d)Percent ErrorSystematic

Percent ErrorUnsystematic

Tonzi wsa 0.0037 0.05 0.48 0.54 0.47 1.09 41.0 40.9Hesse dec 0.0063 0.13 0.84 0.22 0.87 1.10 17.8 36.0Virginia Park wsa 0.0069 0.09 0.34 0.82 0.45 1.20 41.3 23.1Howland dec 0.0029 0.25 0.73 0.42 0.81 1.23 25.5 32.4Morgan dec 0.0050 0.05 0.67 0.33 0.69 1.22 38.1 50.5SSA_OBS con 0.0022 0.55 0.86 0.07 0.81 0.74 13.6 37.9Kendall gra 0.0060 0.50 0.88 0.12 0.83 1.68 8.4 26.2Hainich dec 0.0040 0.84 0.91 0.04 0.86 1.13 8.1 28.5Bondville cer 0.0069 0.79 0.87 0.12 0.79 2.18 9.4 26.6Mize con 0.0044 0.70 0.75 0.59 0.77 2.37 12.6 20.5Tumbarumba ebf 0.0042 1.00 0.90 0.13 0.83 2.11 7.1 24.5Santerem Km83 ebf 0.0066 1.00 0.74 0.73 0.65 3.06 7.4 14.8Griffin con 0.0086 1.00 0.82 0.02 0.67 1.61 20.7 41.7Niwot Ridge con 0.0038 1.00 0.59 0.55 0.41 1.79 24.9 39.6Mer Bleue wet 0.0043 1.00 0.85 0.15 0.76 1.50 14.4 37.6Average 0.0051 0.71 1.60 19.3 32.1

aAlso presented are the slope, a, and intercept, b, of the linear regression ERS2 = aEmeas + b, the R2 value, mean annual Emeas, and the percentagesystematic and unsystematic root-mean-square error in average evaporation. Fixed parameter values are kQ = kA = 0.6, Q50 = 30 W/m2, and D50 = 0.7 kPa.

Table 4. Values of gsxa

Site Name Superclass Vegetation Type Two-Parameter gsx (m/s) K95 gsx (m/s) cL

Bondville cer Cereal/crop 0.0069 0.0110 0.0024Griffin con Conifer 0.0086 0.0057 0.0037Mize con Conifer 0.0044 0.0080 0.0009Niwot Ridge con Conifer 0.0038 0.0057 0.0013SSA_OBS con Conifer 0.0022 0.0057 0.0005Hainich dec Deciduous forest 0.0040 0.0046 0.0010Hesse dec Deciduous forest 0.0063 0.0046 0.0016Howland dec Deciduous forest 0.0029 0.0046 0.0005Morgan dec Deciduous forest 0.0050 0.0046 0.0011Santerem Km83 ebf Evergreen broadleaf forest 0.0066 0.0053 0.0010Tumbarumba ebf Evergreen broadleaf forest 0.0042 0.0053 0.0010Kendall gra Grassland 0.0060 0.0080 0.0016Mer Bleue wet Wetland 0.0043 0.0042 0.0009Tonzi wsa Woody savanna 0.0037 0.0040 0.0007Virginia Park wsa Woody savanna 0.0069 0.0040 0.0018

aValues are (1) for the two-parameter optimization, (2) after assignment of gsx to the ‘‘superclasses’’ of vegetation defined by K95, and (3) for thecoefficient cL in the model Gs = cL Lai. The sites have been sorted according to the vegetation ‘‘superclasses’’ of K95.


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[38] The second approach to simplify implementation ofour modeling approach at large spatial scales is to usecommon values of gsx for broad vegetation classes. For thiswe use the set of gsx values for several ‘‘superclasses’’ ofvegetation listed in Table 1 of K95 in their analysis ofevaporation measurements from 33 field studies reported inthe literature. Each site in the current study was assigned toan appropriate superclass and the corresponding gsx valuesfrom K95 were used to reoptimize for the soil evaporationparameter f. Table 4 compares the gsx values obtained usingthe two-parameter optimization and those from K95.Evaporation rates, ERS1, calculated using the PM equationand Gs with the new parameter values are compared tomeasurements in Figure 8e. The linear regression has aslope of 0.86, intercept of 0.29 mm/d and R2 = 0.68. Thissingle-parameter approach results in a larger scatter ofpredicted versus measured evaporation rates and hence itprovides less satisfactory results than the two parametermodel. It is clear that best results are obtained when bothparameters gsx and f are used to estimate evaporation withthe model proposed in this paper (Figure 8d).

5. Discussion

[39] There is good agreement between evaporation ratesmeasured at 15 globally distributed flux stations and thosecalculated using the PM equation and the simple biophys-ical model for surface conductance developed in this paper.This is testament to the strengths of the PM equation as amodel framework and the value of parameterizing thesurface conductance using fundamental understanding ofthe influence of meteorology and plant physiology onevaporation from plant and soil surfaces. As discussed byCleugh et al. [2007] and references contained therein, this isbecause (1) evaporation rates estimated using the PMequation are inherently constrained by the surface energybalance, (2) much of the seasonal variation in evaporation isdriven by variation in available energy, and (3) the PMequation is not highly sensitive to errors in Gs except whenthe canopy is wet [Thom, 1975]. This study has confirmedthe results of Cleugh et al. [2007] and Mu et al. [2007] thatusing the PM equation with a simple model for surfaceconductance and remotely sensed leaf area indices is a veryuseful approach for spatializing evaporation across regionsat daily to weekly timescales.[40] The advance of this study is that we have developed

a simple, but biophysically sound model for estimating Gs,thus overcoming what has often been a significantimpediment to the practical implementation adoption ofthe PM equation for modeling actual evaporation. We haveestimated values of the physiological parameter gsx and thesoil evaporation parameter f at each site using multiple yearsof data from 15 flux stations located in a wide range ofecosystems. Specifying two parameters, gsx and f, for eachsite provides the best trade-off between minimizing thenumber of model parameters and maximizing the explainedvariance in evaporation when using the PM equation withour surface conductance model (Figure 8d).[41] Parameters of the surface conductance model have

been estimated in this study as the sum of the measuredvalues of H and lE to calculate A, rather than using themeasured value of A. At most of the sites used in this study,daily average eddy flux measurements of H + lE were less

than the available energy measured using radiation instru-ments (Figure 4) and this may lead to errors and/oruncertainties in the derived parameter values. In analternative analysis, we assumed that the mean Bowen ratio(H/lE) is correct, thereby allowing both H and lE to bedivided by the slopes of the respective regression plotsshown in Figure 4. For most sites where H + lE � 0.75A,the revised analysis caused insignificant changes to theoptimized values for either the six- or two-parameter models(data not shown). This was not the case for the Hess andKendall sites where H + lE 0.70A. For Hess, the revisedanalysis caused gsx to increase from 0.0063 to 0.0097 m/sand for Kendall the increase was from 0.0060 to 0.088 m/s.For both sites the root-mean-square error in ERS2 increasefrom 0.45 to 0.89 mm/d, but the corresponding increase ineRMS,t was quite small at the other sites. Given the increasein eRMS,t caused by assuming a constant Bowen ratio, anduncertainties in knowing whether errors in energy closureare due to radiation measurements or in the eddy fluxes, theresults in this paper are based on using A = H + lE.[42] Calculation of evaporation rates using the PM equa-

tion and our model for surface conductance requires knowl-edge of solar radiation, net radiation, air temperature,humidity deficit and wind speed. Downwelling solar radi-ation and maximum and minimum temperature data areroutinely available at 0.05� spatial resolution and Cleugh etal. [2007] showed that there was little degradation inperformance of the evaporation model when local meteor-ological forcing data were replaced with large-scalemeteorological fields. Albedo is also required to calculatethe radiation terms in the model but a spatially distributedclimatology rather than monthly varying value is adequatefor our purposes. Cleugh et al. [2007] used relatively simplealgorithms that are widely used in the literature to calculatenet all-wave radiation and available energy from the solarradiation and temperature data. Soil heat flux cannot becalculate in this way but this is not critical at time scalesdaily or longer when its average tends to zero. Airtemperature and humidity are also needed to calculatewater vapor pressure deficit, Da, but Cleugh et al. [2007],Hashimoto et al. [2008], and others show that these can beestimated from remotely sensed land surface temperature.As noted above, wind speed is not needed since thecalculation of evaporation from dry surfaces is insensitive toaerodynamic conductance. As shown by Mu et al. [2007],practical implementation of the PM model at regional toglobal scales is possible because the necessary input dataare readily available.[43] Flux station data were used to estimate model

parameters for MODIS pixels surrounding the flux stationsand a significant problem exists in assigning parametervalues for other MODIS pixels when the goal is to estimateevaporation at larger spatial scales. The usual approach tothis ‘‘scaling-up’’ problem is to assign parameters to eachpixel according to classifications such as plant functionaltype or land cover class. Examples include using look-uptables to estimate gross primary production from MODISradiances [Running et al., 2000] and in assigning parametersfor global climate models [Bonan et al., 2002; Sitch et al.,2003; Krinner et al., 2005]. This is the logic behind the useof vegetation ‘‘superclasses’’ in Figure 8e, but it comes atthe cost of a reduction in model performance compared to

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when parameter values are known locally. Zhang et al.[2008] adopted an alternative approach to estimate gsx and fat catchment scale using 5-year average evaporation ratesestimated from the water balances of gauged catchments.The parameters for the surface conductance model werethen used with the PM equation, meteorological data andMODIS Lai to estimate evaporation from nearby ungaugedcatchments.[44] The soil evaporation factor f has been considered a

parameter in this study whereas in reality it is a variable thatdepends on the moisture status of the soil near the surface.Synthetic aperture radar (SAR) has the potential to providethis information [Moran et al., 2004] through the correlationbetween variations in microwave emissivity from theground surface and changes in the moisture content of thetop few centimeters of soil. Water in vegetation also affectsthe microwave signal, but this is not of major concern inestimating f, because this parameter is only important incalculating the surface conductance for sparse canopies(Lai < 3, Figure 1f), when the signal from the soil isstrongest. An aircraft-mounted polarimetric scanning radio-meter operating in the C and L wavebands was used byVivoni et al. [2008] to measure soil moisture contents at thefiner resolution of 800 m. Such measurements are of limiteduse for routine estimates of soil moisture at regional tocontinental scales because of the finite flying time andlimited spatial coverage of an aircraft. In contrast, theAdvanced Microwave Scanning radiometer AMSR-E on theEOS Aqua and Terra satellites is used to measures soilmoisture content of the top few centimeters of soil at aspatial resolution of approximately 50 km [Njoku et al.,2003]. While this is considerably larger than the MODISspatial resolution of 1 km, the AMSR-E data may still be ofuse when the spatial correlation in soil moisture is greaterthan 50 km. Further work is needed to explore these andalternative remote sensing techniques to estimate thevariation in the soil evaporation factor f and to see whetherthis improves the performance of the model proposed in thispaper.

6. Conclusions

[45] Excellent agreement was obtained between measuredmean daily evaporation rates and those calculated usingthe PM equation, MODIS Lai and a simple, biophysicalmodel for surface conductance, Gs, given by equations (6)and (12). The model for Gs accounts for responses of plantcanopies to photosynthetically active radiation and humiditydeficit, the amount of radiation absorbed in the visible andthermal wavebands (dependent on Lai) and the fraction ofradiation absorbed by the soil surface that is partitioned intosoil evaporation. Performance of the evaporation model isbest when all six parameters in Gs are optimized at each site,but there is no significant degradation in model performancewhen four parameters (Q50, D50 kQ and kA) are held constantacross vegetation classes while gsx and f are optimized foreach site. Assigning values of gsx according to broadvegetation classes to estimate Gs gave somewhat inferiorresults to the two-parameter model. To calculate evaporationrates for land surfaces at weekly time scales and kilometerspace scales it is clear that both parameters gsx and f areneeded to estimate evaporation accurately with the modelproposed in this paper. Developing remote-sensing techni-

ques to measure the temporal and spatial variation in f willconsiderably enhance the utility of the model proposed inthis paper.

[46] Acknowledgments. We gratefully acknowledge the followingprincipal investigators and their teams for providing the evaporation andmeteorological data used in this analysis: Dennis D. Baldocchi (Tonzi),Hans Peter Schmid (Morgan Munroe), David Y. Hollinger (Howland),Russell Scott (Kendall), T. A. (Andy) Black (SSA-Old Black Spruce),Andre Granier (Hesse), Nina Buchmann (Hainich), Nigel Routlet (MerBleue), Russ K.Monson (Niwot Ridge), Henry L. Gholz and Timothy A.Martin (Mize), Humberto R. da Rocha and Mike L. Goulden (SantaremKm83), Tilden P. Meyers (Bondville), and John B. Moncrieff (Griffin). Wethank staff and funding agencies of the ORNL-DAAC for providing anindispensable resource to the scientific community. This work was partiallyfunded through the CSIRO Water for a Healthy Country Flagship and theAustralian Climate Change Science Program, supported by the AustralianGreenhouse Office.

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��H. Cleugh, R. Leuning, and A. Rajaud, CSIRO Marine and Atmospheric

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Y. Q. Zhang, CSIRO Land and Water, P. O. Box 1666, Canberra, ACT2601, Australia.


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