A simple surface conductance model to estimate regional evaporation using MODIS leaf area index and the Penman-Monteith equation



This article is corrected by:

  1. Errata: Correction to “A simple surface conductance model to estimate regional evaporation using MODIS leaf area index and the Penman-Monteith equation” Volume 45, Issue 1, Article first published online: 24 January 2009


[1] We introduce a simple biophysical model for surface conductance, Gs, for use with remotely sensed leaf area index (Lai) data and the Penman-Monteith (PM) equation to calculate 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 and atmospheric humidity deficit when the stomatal conductance is half its maximum; kQ and kA, extinction coefficients for visible radiation and available energy; and f, the ratio of soil evaporation to the equilibrium rate corresponding to the energy absorbed at the soil surface. Model parameters were estimated using 2–3 years of data from 15 flux station sites covering a wide range of climate and vegetation types globally. The PM estimates of E are best when all six parameters in the Gs model are optimized at each site, but there is no significant reduction in model performance when Q50, D50, kQ, and kA are held constant across sites and gsx and f are optimized (linear regression of modeled mean daily evaporation versus measurements: slope = 0.83, intercept = 0.22 mm/d, R2 = 0.80, and N = 10623). The average systematic root-mean-square error in daytime mean evaporation was 0.27 mm/d (range 0.09–0.50 mm/d) for the 15 sites. The average unsystematic component was 0.48 mm/d (range 0.28–0.71 mm/d). The new model for Gs with two parameters yields better estimates of E than an earlier, simple model Gs = cLLai, where cL is an optimized parameter. Our study confirms that the PM equation provides reliable estimates of evaporation rates from land surfaces at daily time scales and kilometer space scales when remotely sensed leaf area indices are incorporated into a simple biophysical model for surface conductance. Developing remote sensing techniques to measure the temporal and spatial variation in f is expected to enhance the utility of the model proposed in this paper.

1. Introduction

[2] Accurate estimates of evaporation are required to reduce uncertainties in constructing weekly to monthly water balances at catchment and regional scales. Accurate estimates of water yield (runoff) is needed by water resource managers responsible for urban and rural water supplies and knowledge of soil water availability is required for applications such as agricultural production. Improved estimates of evaporation from soils and transpiration from vegetation (combined symbol E) can constrain both of these important quantities because E is the largest term in the terrestrial water balance after precipitation. Evaporation is also of interest to meteorological agencies because energy partitioning at the Earth's surface affects weather and climate. A major problem is that these diverse applications typically require knowledge of distribution of E across catchments and regions at daily time scales, whereas measurements are mostly made at a point, such as at a flux tower or a stream flow gauging station from which the spatial distribution of E must be inferred. A key research question is therefore how to spatialize information from points to areas; combining in situ and remotely sensed observations offer part of the solution to this challenge [Cleugh et al., 2007; Zhang et al., 2008].

[3] Remotely sensed data from satellites provides temporally and spatially continuous information on biophysical properties of the land surfaces such as land surface temperature [Wan et al., 2002], leaf area index [Myneni et al., 2002], vegetation indices [Huete et al., 2002] and vegetation type [Los et al., 2000]. Given the challenges and needs described above, there has been considerable effort by the scientific community to use such remotely sensed data to estimate spatially and temporally distributed evaporation. Several classes of evaporation models use remotely sensed radiative surface temperature to estimate E, such as SEBAL [Bastiaanssen et al., 1998a, 1998b], SEBS [Su, 2002, 2005], NTDI [McVicar and Jupp, 2002], the resistance surface energy balance (RSEB) [Kalma and Jupp, 1990], the triangle method [Nemani and Running, 1989; Nishida et al., 2003; Gillies and Carlson, 1995], and the dual-source model developed 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 the radiative surface temperature and the resistance surface energy budget approach compared poorly to eddy flux measurements of evaporation for two Australian ecosystems. Instead, they obtained satisfactory results when E was estimated using the Penman-Monteith (PM) equation [Monteith, 1964; Thom, 1975] with a simple model for surface conductance to evaporation given by Gs = cLLai + Gs,min where Lai is the leaf area index obtained from MODIS remote sensing and cL is a constant and Gs,min is the surface conductance controlling soil evaporation. They then used the PM algorithm to produce an evaporation climatology for Australia at 1 km resolution. Mu et al. [2007] also used the PM equation to estimate E, but found that the simple surface conductance model of Cleugh et al. [2007] was inadequate when tested against evaporation measurements from 19 AmeriFlux sites. Mu et al. [2007] revised the model for Gs by introducing scaling functions that range between 0 and 1 to account for the response of stomata to humidity deficit of the air, Da, and air temperature, Ta. They also introduced a separate term for evaporation from the soil surface, a term that was acknowledged by Cleugh et al. [2007], but which they incorporated via the coefficient cL. The revised Gs algorithm of Mu et al. [2007] resulted in good agreement between predictions of E by the PM equation and the AmeriFlux measurements. They then used the revised algorithm to predict the global distribution of 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 sound and robust framework for estimating daily E at regional to global scales using remotely sensed data. This paper builds on the original proposition of Cleugh et al. [2007] and the important developments of Mu et al. [2007] by introducing a new, simple biophysical algorithm for Gs based on our understanding of leaf- and canopy-level plant physiology, radiation absorption by plant canopies and evaporation from the underlying soil surface. The formulation for Gs modifies that of Kelliher et al. [1995] (hereinafter referred to as K95), by including the influence of Da on stomatal conductance and by introducing a soil evaporation algorithm that is simpler than that proposed by Mu et al. [2007] and which has the potential to be estimated using remote sensing. Performance of the new algorithm for Gs is then tested on several years of evaporation measurements at each of 15 flux station sites covering a wide range in climate and vegetation globally, including deciduous and evergreen forests, a corn crop, a wetland, grassland and two woody savannas. In a companion paper, Zhang et al. [2008] use mean annual E estimated from runoff measured at the gauged catchments and leaf area indices obtained from MODIS remote sensing to estimate parameters of the Gs model developed in this paper. They then used the calibrated model and the PM equation to provide spatially resolved estimates of E across the Murray Darling Basin in SE Australia.

[6] The following section describes the surface conductance model, followed by a brief description of the data sources and methods used to control the quality of the data. We then examine the performance of the model as we reduce from six to two the number of parameters to be estimated for each vegetation type. Model performance is assessed against measurements at the individual flux stations 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 the literature to describe the biophysics of evaporation, E, from land surfaces. The equation states that the flux of latent heat associated with E is given by

equation image

where λ is the latent heat of evaporation, ɛ = s/γ, in which γ is the psychrometric constant and s = de*/dT is the slope of the curve relating saturation water vapor pressure to temperature, A is the available energy absorbed by the surface (net absorbed radiation, Rn minus soil heat flux, G), ρ is the density of air, cp is the specific heat of air at constant pressure, Da = e* (Ta) − ea is the water vapor pressure deficit of the air (humidity deficit), in which e* (Ta) is the saturation water vapor pressure at air temperature and ea is the actual water vapor pressure, Ga is the aerodynamic conductance and Gs is the surface conductance accounting for evaporation from the soil and transpiration by the vegetation. In this paper we assume that the quantities A, Da and Ga are either known or are estimated using measured 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:

equation image

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

equation image

Note that we distinguish between surface conductance, Gs, and the canopy conductance Gc, and that we partition the total available energy A into that absorbed by the canopy, Ac, and by the soil, As. For the purposes of this study, f is a parameter to be estimated from the data, although in reality f will vary with moisture content of the soil near to the surface. Discussion of potential remote sensing techniques for estimating the temporal and spatial variation of f is deferred 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 − τ and As/A = τ, where τ = exp (−kALai), kA is an extinction coefficient for available energy and Lai is leaf area index. Note that this ignores the soil heat flux, G, because G → 0 when we later use daily average meteorological variables.

[10] With these definitions, equation (3) can be written as

equation image

where Gi is the “climatological” conductance defined by Monteith [1964] as

equation image

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

equation image

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

equation image

which is the same as equation (10) derived by K95 in their survey of maximum surface conductances of various land cover types.

[11] When the soil surface is completely dry, f = 0 and then

equation image

Note that GsGc because Gc depends on radiation absorbed by the plant canopy, whereas Gs is a function of radiation absorbed by both canopy and soil.

[12] If all radiation is absorbed by the canopy, τ = 0, and thus

equation image

Finally, when τ = 1, Gc = 0 because there is no canopy, and then from equation (4) we obtain

equation image

In this case Ga and Gi appropriate to bare soil should be used, 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 each of equations (6)(9). K95 developed an expression for canopy conductance in terms of maximum stomatal conductance of leaves at the top of the canopy, gsx, Lai and an hyperbolic response to absorbed shortwave radiation. They showed that

equation image

where Qh is the flux density of visible radiation at the top of the canopy (approximately half of incoming solar radiation), kQ is the extinction coefficient for shortwave radiation and Q50 is the visible radiation flux when stomatal conductance is half its maximum value. A similar expression was derived by Saugier and Katerji [1991] and Dolman et al. [1991]. Here we modify this expression to include the response of stomatal conductance to humidity deficit as developed by Leuning [1995] to give

equation image

where D50 is the humidity deficit at which stomatal conductance is half its maximum value. This formula was used by Isaac et al. [2004] and Wang et al. [2004], and found to be an improvement over that of K95. Substitution of equation (12) into (6) shows that model for Gs contains the six parameters gsx, Q50, D50kQ, kA and f.

[14] Predictions of the ratio Gs/gsx, using equations (6) and (12), are shown as a function of Lai in Figure 1 for typical values of the meteorological parameters Da and A, the physiological parameters D50, Q50 and gsx and the soil evaporation parameter f. We note first that values of Gs/gsx are lower than in the work by K95 for all the sensitivity analyses in Figure 1 because the extra term 1/(1 + Da/D50) in equation (11) reduces Gc compared to corresponding values of K95. As a result, increasing Da from 0.5 to 2.0 kPa causes Gs/gsx to decrease by >50% at all Lai (Figure 1a), in contrast to the model of K95 that has no such dependence. Compared to the work by K95, the revised model also shows a greater dependence of Gs/gsx on A at high Lai (Figure 1b) because here we maintain a realistic correlation between Qh and A using Qh = 0.8A (R. Leuning, unpublished data, 2008), whereas K95 held Qh fixed when A was varied. Increasing values of the physiological parameter D50 causes Gs/gsx to increase, while increasing Q50 causes it to decrease at all Lai (Figures 1c and 1d). In contrast, the influence of varying gsx and f on Gs/gsx is only significant when Lai < 3 (Figures 1e and 1f). Soil evaporation is assumed to occur at the equilibrium rate in the K95 model (equivalent to f = 1) and this causes a minimum in Gs/gsx around Lai ≈ 1, whereas this minimum is absent or less pronounced in the new model, where f ≤ 1. Low rates of evaporation from sparse canopies correspond to low values of f and hence Gs.

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 with A according to Qh = 0.8A in all plots.

[15] Contour plots of the evaporative fraction, fE = λE/A, as predicted by the evaporation model, are shown in Figure 2 as a 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 of Qh and Lai results in an increase in evaporative fraction; for example, fE is predicted to increase from 0.75 to 1.45 for Qh = 300 W m−2 and Lai = 3 as Da increases from 0.5 to 2.0kPa. The contour spacing decreases with increasing Da, indicating increasing sensitivity of fE to variations in humidity deficit and leaf area index at higher humidity deficits. Sensitivity of fE to Lai is greatest at low values of Qh and vice versa.

Figure 2.

Contour plots of the evaporative fraction, fE = λE/A, as a function of absorbed photosynthetically 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 = 30 W/m2, Ga = 0.033 m/s, kQ = kA = 0.6, D50 = 1.0 kPa, and f = 0.5.

[16] We next describe the data sources for evaporation fluxes, meteorology and Lai used to estimate model parameters and to evaluate model performance.

3. Methods

3.1. Sites, Fluxes, and Meteorological Data

[17] Table 1 provides details of the 15 Fluxnet sites used to evaluate performance of the surface conductance model in estimating land surface evaporation. References describing each site are also listed. The sites are located across several continents and include savannas, grasslands, a corn crop, mixed deciduous forests, evergreen needleleaf and broadleaf forests, a wetland and cleared forest land. Latitudes of the sites vary from 54°N to 35°S, while climatic regions range from subarctic, cool temperate, warm temperate to tropical. Maritime and continental climates are also represented. Minimum temperatures at the continental SSA Old Black Spruce site reach −39.8°C while maximum temperatures exceeded 35°C at many sites. Annual precipitation across sites ranged from 376 to 1599 mm.

Table 1. Details of Fluxnet Sites Used to Evaluate Performance of the Surface Conductance Model in Estimating Land Surface Evaporation
Site IDaSite NameCodeIGBP ClassDominant SpeciesCountryLatitude and LongitudeElevation (m)Canopy Height (m)Temperature (°C)Annual Precipitation (mm)References
830BondvillecrpCroplandsCorn/soybeanUSA40°0′21.96″N, 88°17′30.72″W3003−16.934.011.7644.6Meyers and Hollinger [2004]
777GriffinenfNeedleleaf forestPicea sitkensis, Pseudotsuga menziesii, Betula pendulaUK56°36′23.59″N, 3°47′48.55″W3409−5.522.87.21169.0Falge et al. [2002]
392HainichdbfDeciduous broadleaf forestFagus sylvatica, Acer, FraxinusGermany51°4′45.36″N, 10°27′7.2″E43033− et al. [2003]
476HessedbfDeciduous broadleaf forestFagus sylvatica, Quercus petraeaFrance48°40′27.18″N, 7°3′52.62″E30013−14.032.610.51154.5Granier et al. [2000]
890HowlandmfMixed forestRed spruce, Eastern hemlockUSA45°12′14.65″N, 68°44′25″W6019.5−23.633.77.2645.1Hollinger et al. [1999]
814KendallgrassGrasslandC4 grassesUSA31°44′11.50″N, 109°56′30.77″W15310.5−17.638.113.1356
235Mer BleuewetWetlandSphagnum mossesCanada45°24′33.84″N, 75°31′12″W70−30.736.26.8725.0Admiral et al. [2006]
1071MizebareSlash pine clearcutPinus elliottiiUSA29°45′53.28″N, 82°14′41.34″W505−9.637.620.0898.3Gholz and Clark [2002]
968Morgan MunroedbfDeciduous broadleaf forestAcer saccharumUSA39°19′23.34″N, 86°24′47.30″W27527−15.734.813.01121.4Ehman et al. [2002], Oliphant et al. [2004]
997Niwot RidgeenfEvergreen needleleaf forestAbies lasiocarpa, Picea engelmannii, Pinus contortaUSA40°01′58.36″N, 105°32′47.05″W305011.5−31.526.61.1562.9Turnipseed et al. [2002]
85Santarem Km83ebfEvergreen broadleaf forestCleared forestBrazil3°1′4.905″S, 54°58′17.166″W 19.936.926.01598.5Goulden et al. [2004], Miller et al. [2004]
259SSA-Old Black SpruceenfEvergreen needleleaf forestPicea marianaCanada53°59′ 13.81″N, 105°7′ 4.04″W6291–21−39.835.2−2.2376.3Griffis et al. [2003], Mahrt and Vickers [2002]
1078TonziwsaWoody savannaQuercus douglasii plus C3 winter grassesUSA38°25′53.76″N, 120°57′57.54″W11710.1−2.642.916.0532.7Baldocchi et al. [2004]
43TumbarumbaebfEvergreen broadleafEucalyptus delagatensisAustralia35°39′20.6″S, 148°9′7.5″E120040−4.728.99.21011.2Leuning et al. [2005]
45Virginia ParkwsaWoody savannaEucalyptus creba, Eucalyptus, drepanophylla plus C4 grasses in summerAustralia19°53′00″S, 146°33′14″E2005–84.038.921.8402.9Leuning et al. [2005]

[18] A plot of mean annual precipitation versus mean annual temperature (Figure 3a) shows that the sites chosen for analysis cover much of the observed range in global climate. The sites ranged from the boreal SSA-Old Black Spruce site with mean annual temperature of −1.2°C and precipitation of 376 mm to the tropical Santarem Km83 site with 1600 mm rainfall and mean annual temperatures of 26.1°C. High mean temperatures of 22.3°C are also observed at Virginia Park, which is a seasonally wet/dry savanna but with an annual rainfall of only 403 mm that occurs during the summer wet season.

Figure 3.

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

[19] For the analysis, time series of latent heat flux, wind speed, minimum and maximum air temperature, water vapor pressure, solar radiation, air pressure, net radiation and soil heat flux for the selected sites were obtained from the Oak Ridge National Laboratory, Distributed Active Archive 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 or when ∣∣A∣−∣H + λE∣∣ > 250 W m−2, where H and λE are the measured sensible and latent heat fluxes. Values outside this broad range arise either because of instrumentation problems or because the site is subject to considerable advection. Wilson et al. [2002] found that H + λE < A at many eddy flux sites globally. This is also the case for most of the15 flux sites used in this study, as seen in the scatterplots in Figure 4 of daily average H + λE versus daily average A. The exceptions are Bondville, Niwot Ridge, Tumbarumba and Virginia Park, for which linear regression slopes are close to unity, with the worst cases being Hess and Kendall where the slopes are ≤0.70. We have assumed that A = H + λE to ensure internal consistency in the analysis used to estimate the model parameters for each site. Using the measured A and λE to estimate the parameters in the model for Gs would be incorrect since this assumes the lack of energy closure is due to errors in H alone. An alternative is to assume that the mean Bowen ratio (H/λE) is correct so that we can divide both H and λE by the slopes of the respective regression plots shown in Figure 4. A comparison of results for the two approaches are discussed later for the Hess and Kendall sites.

Figure 4.

Scatterplots of measured daily average H + λE versus daily average RnG (=A) for each of the 15 flux sites used in this analysis. Slopes and R2 values are shown for linear regressions forced through the origin.

[21] Aerodynamic conductance was calculated using

equation image

where zm is the height of wind speed and humidity measurements, d zero plane displacement height, zom and zov are the roughness lengths governing transfer of momentum and water vapor, k von Karman's constant (0.41), and uz is wind speed at height zm [Monteith and Unsworth, 1990]. The quantities d, z0m and z0v were estimated using d = 2h/3, z0m = 0.123h and z0v = 0.1z0m, where h is canopy height [Allen et al., 1998]. Atmospheric stability modifies the values of Ga calculated using equation (13) by up to ±25% but we have neglected stability effects because evaporation from dry canopies is relatively insensitive to errors in Ga. Similar arguments apply to uncertainties in the ratio z0v/z0m. The sensitivity of E to Ga is particularly weak at the daily time steps used in this study and this fact is exploited in the companion paper by Zhang et al. [2008], who assign constant values of Ga = 0.033, 0.0125 and 0.010 m/s for forests, shrubs, grassland and crops, respectively, because of the lack of routinely available, quality wind speed data at 1-km resolution.

[22] Meteorological variables measured at each flux station have been used in this paper rather than large-scale meteorology that would likely be used in any operational application of the algorithms developed in this paper. This is not a significant weakness since both Cleugh et al. [2007] and Mu et al. [2007] showed that there is very little degradation in the performance of the PM equation when meteorological data at 0.05° (latitude and longitude) scales are 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 flux tower from the 8-day standard MOD15A2 collection 5 product [Myneni et al., 2002] from the ORNL-DAAC. These data were derived from MODIS, the Moderate Resolution Imaging Spectrometer mounted on the polar-orbiting Terra satellite, which has a daily overpass at around 1030 local time. The MOD15A2 product contains four data layers: the fraction of photosynthetically absorbed radiation, fPAR and Lai, plus their respective quality control layers. The quality assessment (QA) flags in the database were used to check the quality of the MODIS-Lai data. At each grid, all poor quality Lai data were deleted and replaced by interpolated values obtained from a piecewise cubic, hermite interpolating polynomial [Zhang et al., 2006]. Then, all of the quality-controlled Lai data for each pixel were smoothed by the Savitzky-Golay filtering method that is widely used for filtering MODIS-Lai [Fang et al., 2008] and other remote sensing data.[Jonsson and Eklundh, 2004; Ruffin et al., 2008; Tsai and Philpot, 1998]. The MODIS Lai provides reasonable estimates for most Australian vegetation types except for the open forest and woodlands in eastern Australia [Hill et al., 2006].

[24] Figure 3b shows there is essentially no correlation between annual precipitation, P, and annual mean Lai for the 15 selected sites. Lai ranged from 3.6 for an evergreen broad leaf forest with P = 1600 mm to Lai = 0.7 for a savanna with 400 mm of rainfall.

4. Results

4.1. Parameter Estimation

[25] The generalized pattern search algorithm in MATLAB® (The MathWorks, Inc.) was used to optimize for each site the parameters gsx, Q50, D50, kQ, kA and f in the model for Gs (equations (12) and (6)). This was done by minimizing the cost function F

equation image

where Emeas,j and ERS,j are the jth measured and simulated daily average evaporation rates, equation imagemeas is the arithmetic mean of the measurements and N is the number of samples. ERS,j was calculated by substituting the modeled Gs into equation (1), in conjunction with the required meteorological 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 in Table 2, with the last row listing the ranges allowed for each parameter in the optimization calculations. Figure 5a shows values of gsx extracted from Table 2 in rank order for the various biomes. Maximum stomatal conductance ranged between 0.0020 and 0.0085 m/s, which is below the maximum of 0.012 m/s reported by K95 for various vegetation types, but is similar to the range reported by Isaac et al. [2004] for water stressed to well-watered crops and pastures. The soil evaporation parameter f reduces soil evaporation below the equilibrium rate when water availability limits evaporation. While this is a rather crude parameterization, the optimized values of f were reasonable, ranging from a low of <0.1 for the rather dry savannas at Virginia Park and Tonzi, to a maximum of 1.0 for the wetter temperate evergreen forests, the tropical broadleaf forest and the permanent wetland (Figure 5b and Table 2).

Figure 5.

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

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 NameCodegsx (m/s)fQ50 (W/m2)D50 (kPa)kQkAab (mm/d)R2Emeas (mm/d)Percent Error SystematicPercent Error Unsystematic
  • a

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

Virginia Parkwsa0.00630.0920.00.700.300.800.360.800.481.2040.323.0
Santerem Km83ebf0.00761.0020.90.701.000.500.710.870.743.067.911.6
Niwot Ridgecon0.00271.0020.00.700.300.500.600.560.431.7924.238.9
Mer Bleuewet0.00281.0020.00.700.300.500.860.130.791.5013.535.2
Parameter ranges0.002–0.0150.05–1.0020–500.7–1.50.3–1.00.5–0.80.731.6017.931.3

[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 lower bounds of the allowable range of 20–50 W/m2. There was almost no variation in D50, the parameter that accounts for stomatal sensitivity to water vapor deficit, with all values except one at the lower bound of 0.7 kPa. When the lower allowable bound for D50 was decreased to 0.5 kPa, there was a corresponding proportional increase in the optimized values for gsx (data not shown), as may be expected from inspection of the model for Gc (equation (12)). These results suggest that Q50 and D50 are not constrained particularly well by the data, and this is in accordance with Figure 1 that shows Gs/gsx is relatively insensitive to these parameters in the range of leaf area indices available in our data set. There was considerable variation in the optimum values of kQ across the various biomes, ranging across the allowable limits of 0.3 to 1.0, and similar variability between allowable limits was obtained in the value of kA, the extinction coefficient for available energy. Later we examine model performance when the parameters Q50, D50kQ and kA are held constant across biomes.

4.2. Model Performance: Gs Model With Six Parameters

[28] Figures 6 and 7present for six of the 15 sites the time series of Emeas, ERS6 and Eeq (8-day averages are shown for clarity), daily precipitation and daily Lai interpolated from each 8-day MODIS compositing period. Scatterplots of daily average Emeasversus ERS6 are also shown, where ERS6 was calculated using equation (1) with average daytime meteorological data. Gs was calculated using equations (12) and (6) with interpolated Lai and the six optimized parameter values for each corresponding site given in Table 2. The last subscript on ERS6 denotes that six parameters were used in the calculation. Equilibrium evaporation was calculated using

equation image

where A is the available energy absorbed by both vegetation and the soil. The objective of Figures 6 and 7 is to see how much of the observed variability in evaporation rates is captured by ERS6 and by the simpler Eeq.

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.

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 savanna sites, Virginia Park and Tonzi.

[29] Figure 6 shows that at the relatively moist sites of Hesse, Tumbarumba and Bondville, Emeas is closely approximated by Eeq for much of the annual cycle. For such sites Gs is relatively large compared to Ga and the PM model reduces to the equilibrium rate. The strong variation in Emeas is largely driven by the seasonal variation in available energy at Tumbarumba, an evergreen forest where there is little seasonal variation in Lai. The influence of Lai, and hence Gs, on evaporation rates is not so clear at the Hesse deciduous forest and the corn crop at Bondville where seasonal Lai varies in parallel with available energy. While the equilibrium model may be sufficient at these sites for some purposes, Eeq overestimates Emeas at both Hesse and Tumbarumba in the summer, indicating some limitation to evaporation through the influence of atmospheric humidity deficit on canopy conductance. In contrast, Figure 7 shows there are large differences between Emeas and Eeq at most times at the SSA-OBS and Tonzi sites, while at Virginia Park Emeas < Eeq at all times. For such sites it is essential to have accurate knowledge of A, D, Ga and Gs to calculate evaporation rates using the PM equation. Errors in the magnitude and seasonal variation of remotely sensed Lai at such sparsely vegetated sites also contribute to uncertainties in ERS6. When Gs was calculated using the optimized parameter values given in Table 2 there was good agreement between Emeas and ERS6 at all times of the year at SSA-OBS and ERS6 provided a significant improvement over Eeq at Virginia Park and at Tonzi, especially in the dry season (Figure 7). There was also an improvement in modeled evaporation during summer at Hesse and Tumbarumba when Emeas < Eeq (Figure 6), but there was little advantage in 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 between measured and modeled E. The slopes of the linear regression analyses are close to unity, and intercepts are close to zero, for all except the two savanna sites. The model underestimates the springtime peak in Emeas and overestimates summertime evaporation at Tonzi, while at Virginia Park the model underestimated evaporation in the summer wet season in 2002 and overestimated it in the late dry season of 2004. The discrepancies may arise because we have modeled soil evaporation using the single parameter f, held fixed for each site, whereas it will be expected to vary during wetting/drying cycles as shown by Baldocchi et al. [2004] at the Tonzi savanna site. Errors in MOD15A2 leaf area indices will also contribute to a mismatch between model and measurements. Huemmrich et al. [2005] found that Lai from MODIS was systematically high by 0.25 units for sparse vegetation. Differing degrees of accuracy have been 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 studies are stimulating the development of improved algorithms for estimating Lai [Yang et al., 2006].

[31] Statistical details of model performance for all sites presented in Table 2 show that the slopes of the linear regressions of ERS6 versus Emeas range from 0.36 at Virginia Park to 0.92 at Tumbarumba, while the intercepts range from 0.00 mm/d at Griffin to 0.87 mm/d at the tropical Santerem 83Km site. On average, the model explained 73% of the variance in Emeas across all sites, ranging from a low of 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. He recommended that the total mean square error,

equation image

be partitioned into systematic and unsystematic components given by

equation image

where equation imagei = aOi + b, in which a and b are coefficients obtained from linear regression of Pi (dependent variable) versus Oi (independent variable). Note that ɛMSE,t2 = ɛMSE,s2 + ɛMSE,u2. The systematic component, ɛMSE,s2, results from the deviation of equation imagei from the 1:1 line of a perfect model, since equation imageiOi = (a − 1) Oi + b, whereas the unsystematic component, ɛMSE,u2, results from scatter of Pi about equation imagei. In the following we present root-mean-square errors (ɛRMSE), the square roots 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 the unsystematic component only at Tonzi and at Virginia Park because at these sites the variation in modeled evaporation is significantly less than is observed in the data (Figure 7). The percentage systematic error, 100ɛRMSE,s/Emeas, is >30% for the two savanna sites and for Morgan, 24.2% at Niwot Ridge, and an average of 13.8% for the other 11 sites. There is a significant inverse relationship between f and the systematic component of the error but not in the unsystematic component, 100ɛRMSE,u/Emeas, which has an average of 31.3%.

[34] The scatterplot in Figure 8a shows daily average ERS,6 versus Emeas for all sites combined and linear regression yields a slope of 0.85, intercept of 0.21 mm/d and R2 = 0.82, N = 10630. The results show that good estimates of daily average evaporation are obtained when the PM equation is used with the model for Gs when all six parameters are optimized at each site and with MODIS Lai data.

Figure 8.

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

4.3. Comparison With Cleugh et al. [2007]

[35] Cleugh et al. [2007] obtained good agreement between measured evaporation rates at two Australian sites, Tumbarumba and at Virginia Park, when they used the simple linear model Gs = cLLai + Gs,min in the PM equation, where cL is an empirical coefficient and Gs,min is the surface conductance controlling soil evaporation (set to zero in their analysis).The current data set was used to optimize cL for each site before calculating daily average evaporation rates, EcL, using the PM equation. Values of cL ranged from 0.0005 to 0.0037 (Table 4), compared to values of 0.0019 at Tumbarumba and 0.0025 at Virginia Park reported by Cleugh et al. [2007]. Figure 8b shows that daily average evaporation rates calculated using the simple linear model for Gs captures much of the variation in the measured evaporation, but the larger scatter (R2 = 0.61) indicates that the results obtained using EcL are less satisfactory than ERS6. Both models are clearly superior to using Eeq to estimate actual evaporation (Figure 8c), since Eeq is generally greater than the measurements, often by a factor of two or more, the intercept of the regression is significantly greater than zero and the scatter in Eeq is unacceptably large (R2 = 0.57).

4.4. Reducing the Number of Free Parameters in the Gs Model

[36] The general utility of the Gs model for estimating evaporation will be greatly enhanced if we can reduce the number of parameters to be estimated without substantially degrading model performance. To examine this possibility we explore two different approaches. The first is to take advantage of the observation, made earlier when discussing Figure 1, that Gs is relatively insensitive to Q50, D50kQ and kA, and hence the optimization for gsx and f was repeated while holding the other parameters constant. The resultant two-parameter model for Gs is then used to calculate evaporation rates, defined as ERS2. The fixed values chosen for parameters Q50 = 30 W m−2 and D50 = 0.7 kPa were guided by the results in Table 2. In principle, the extinction coefficient for visible radiation, kQ is expected to differ from that for available energy, kA, which accounts for the transfer of the sum of visible, near infrared and net thermal radiation. This is because reflection and transmission coefficients of leaves are considerably lower in the visible waveband than in the near infrared while in the thermal waveband the leaves have very high emissivity and low transmissivity. However, Gs is insensitive to values of the extinction coefficients, and a constant kQ = kA = 0.6 was used in the subsequent analysis.

[37] Table 3 and Figures 5c and 5d show that optimizing just two parameters caused only minor changes in the values and relative ranking of gsx and f compared to those shown in Table 2 and Figures 5a and 5b for the six-parameter model. This provides further evidence that modeled evaporation rates are relatively insensitive to Q50, D50kQ and kA. Comparison of Tables 2 and 3 and Figures 8a and 8d shows that the two-parameter model for Gs performs almost as well as the six-parameter model in describing the variation in daily average evaporation rates across all sites. The linear regression of ERS2 versus Emeas has a slope of 0.83, intercept = 0.22 mm/d and R2 = 0.80. The nonzero intercept is largely due to the systematic bias of the model at the two savanna sites, Tonzi and Virginia Park. The model performs least well for the three sites with values of f ≤ 0.09, indicating the importance of soil evaporation at these sites and the desirability of finding a means to estimate the temporal and spatial variation of f using remote sensing rather than treating f as a fixed parameter. The average systematic root-mean-square error in daily mean E across all 15 sites was 0.31 mm/d (19.3% of 1.60 mm/d), with a range of 0.05–0.50 mm/d. Compared to the six-parameter model, the two-parameter model resulted in a <2% increase in the mean systematic and unsystematic components of model error 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 NameCodeTwo-Parameter Optimization
gsx (m/s)fab (mm/d)R2Emeas (mm/d)Percent Error SystematicPercent Error Unsystematic
  • a

    Also presented are the slope, a, and intercept, b, of the linear regression ERS2 = aEmeas + b, the R2 value, mean annual Emeas, and the percentage systematic 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.

Virginia Parkwsa0.00690.090.340.820.451.2041.323.1
Santerem Km83ebf0.00661.000.740.730.653.067.414.8
Niwot Ridgecon0.00381.000.590.550.411.7924.939.6
Mer Bleuewet0.00431.000.850.150.761.5014.437.6
Average 0.0051   0.711.6019.332.1

[38] The second approach to simplify implementation of our modeling approach at large spatial scales is to use common values of gsx for broad vegetation classes. For this we use the set of gsx values for several “superclasses” of vegetation listed in Table 1 of K95 in their analysis of evaporation measurements from 33 field studies reported in the literature. Each site in the current study was assigned to an appropriate superclass and the corresponding gsx values from K95 were used to reoptimize for the soil evaporation parameter f. Table 4 compares the gsx values obtained using the two-parameter optimization and those from K95. Evaporation rates, ERS1, calculated using the PM equation and Gs with the new parameter values are compared to measurements in Figure 8e. The linear regression has a slope of 0.86, intercept of 0.29 mm/d and R2 = 0.68. This single-parameter approach results in a larger scatter of predicted versus measured evaporation rates and hence it provides less satisfactory results than the two parameter model. It is clear that best results are obtained when both parameters gsx and f are used to estimate evaporation with the model proposed in this paper (Figure 8d).

Table 4. Values of gsxa
Site NameSuperclassVegetation TypeTwo-Parameter gsx (m/s)K95gsx (m/s)cL
  • a

    Values are (1) for the two-parameter optimization, (2) after assignment of gsx to the “superclasses” of vegetation defined by K95, and (3) for the coefficient cL in the model Gs = cLLai. The sites have been sorted according to the vegetation “superclasses” of K95.

Niwot RidgeconConifer0.00380.00570.0013
HainichdecDeciduous forest0.00400.00460.0010
HessedecDeciduous forest0.00630.00460.0016
HowlanddecDeciduous forest0.00290.00460.0005
MorgandecDeciduous forest0.00500.00460.0011
Santerem Km83ebfEvergreen broadleaf forest0.00660.00530.0010
TumbarumbaebfEvergreen broadleaf forest0.00420.00530.0010
Mer BleuewetWetland0.00430.00420.0009
TonziwsaWoody savanna0.00370.00400.0007
Virginia ParkwsaWoody savanna0.00690.00400.0018

5. Discussion

[39] There is good agreement between evaporation rates measured at 15 globally distributed flux stations and those calculated using the PM equation and the simple biophysical model for surface conductance developed in this paper. This is testament to the strengths of the PM equation as a model framework and the value of parameterizing the surface conductance using fundamental understanding of the influence of meteorology and plant physiology on evaporation from plant and soil surfaces. As discussed by Cleugh et al. [2007] and references contained therein, this is because (1) evaporation rates estimated using the PM equation are inherently constrained by the surface energy balance, (2) much of the seasonal variation in evaporation is driven by variation in available energy, and (3) the PM equation is not highly sensitive to errors in Gs except when the canopy is wet [Thom, 1975]. This study has confirmed the results of Cleugh et al. [2007] and Mu et al. [2007] that using the PM equation with a simple model for surface conductance and remotely sensed leaf area indices is a very useful approach for spatializing evaporation across regions at 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 significant impediment to the practical implementation adoption of the PM equation for modeling actual evaporation. We have estimated values of the physiological parameter gsx and the soil evaporation parameter f at each site using multiple years of data from 15 flux stations located in a wide range of ecosystems. Specifying two parameters, gsx and f, for each site provides the best trade-off between minimizing the number of model parameters and maximizing the explained variance in evaporation when using the PM equation with our surface conductance model (Figure 8d).

[41] Parameters of the surface conductance model have been estimated in this study as the sum of the measured values of H and λE to calculate A, rather than using the measured value of A. At most of the sites used in this study, daily average eddy flux measurements of H + λE were less than the available energy measured using radiation instruments (Figure 4) and this may lead to errors and/or uncertainties in the derived parameter values. In an alternative analysis, we assumed that the mean Bowen ratio (H/λE) is correct, thereby allowing both H and λE to be divided by the slopes of the respective regression plots shown in Figure 4. For most sites where H + λE ≥ 0.75A, the revised analysis caused insignificant changes to the optimized values for either the six- or two-parameter models (data not shown). This was not the case for the Hess and Kendall sites where H + λE ≤ 0.70A. For Hess, the revised analysis caused gsx to increase from 0.0063 to 0.0097 m/s and for Kendall the increase was from 0.0060 to 0.088 m/s. For both sites the root-mean-square error in ERS2 increase from 0.45 to 0.89 mm/d, but the corresponding increase in ɛRMS,t was quite small at the other sites. Given the increase in ɛRMS,t caused by assuming a constant Bowen ratio, and uncertainties in knowing whether errors in energy closure are due to radiation measurements or in the eddy fluxes, the results in this paper are based on using A = H + λE.

[42] Calculation of evaporation rates using the PM equation and our model for surface conductance requires knowledge of solar radiation, net radiation, air temperature, humidity deficit and wind speed. Downwelling solar radiation and maximum and minimum temperature data are routinely available at 0.05° spatial resolution and Cleugh et al. [2007] showed that there was little degradation in performance of the evaporation model when local meteorological forcing data were replaced with large-scale meteorological fields. Albedo is also required to calculate the radiation terms in the model but a spatially distributed climatology rather than monthly varying value is adequate for our purposes. Cleugh et al. [2007] used relatively simple algorithms that are widely used in the literature to calculate net all-wave radiation and available energy from the solar radiation and temperature data. Soil heat flux cannot be calculate in this way but this is not critical at time scales daily or longer when its average tends to zero. Air temperature and humidity are also needed to calculate water vapor pressure deficit, Da, but Cleugh et al. [2007], Hashimoto et al. [2008], and others show that these can be estimated from remotely sensed land surface temperature. As noted above, wind speed is not needed since the calculation of evaporation from dry surfaces is insensitive to aerodynamic conductance. As shown by Mu et al. [2007], practical implementation of the PM model at regional to global scales is possible because the necessary input data are readily available.

[43] Flux station data were used to estimate model parameters for MODIS pixels surrounding the flux stations and a significant problem exists in assigning parameter values for other MODIS pixels when the goal is to estimate evaporation at larger spatial scales. The usual approach to this “scaling-up” problem is to assign parameters to each pixel according to classifications such as plant functional type or land cover class. Examples include using look-up tables to estimate gross primary production from MODIS radiances [Running et al., 2000] and in assigning parameters for global climate models [Bonan et al., 2002; Sitch et al., 2003; Krinner et al., 2005]. This is the logic behind the use of vegetation “superclasses” in Figure 8e, but it comes at the cost of a reduction in model performance compared to when parameter values are known locally. Zhang et al. [2008] adopted an alternative approach to estimate gsx and f at catchment scale using 5-year average evaporation rates estimated from the water balances of gauged catchments. The parameters for the surface conductance model were then used with the PM equation, meteorological data and MODIS Lai to estimate evaporation from nearby ungauged catchments.

[44] The soil evaporation factor f has been considered a parameter in this study whereas in reality it is a variable that depends on the moisture status of the soil near the surface. Synthetic aperture radar (SAR) has the potential to provide this information [Moran et al., 2004] through the correlation between variations in microwave emissivity from the ground surface and changes in the moisture content of the top few centimeters of soil. Water in vegetation also affects the microwave signal, but this is not of major concern in estimating f, because this parameter is only important in calculating the surface conductance for sparse canopies (Lai < 3, Figure 1f), when the signal from the soil is strongest. An aircraft-mounted polarimetric scanning radiometer operating in the C and L wavebands was used by Vivoni et al. [2008] to measure soil moisture contents at the finer resolution of 800 m. Such measurements are of limited use for routine estimates of soil moisture at regional to continental scales because of the finite flying time and limited spatial coverage of an aircraft. In contrast, the Advanced Microwave Scanning radiometer AMSR-E on the EOS Aqua and Terra satellites is used to measures soil moisture content of the top few centimeters of soil at a spatial resolution of approximately 50 km [Njoku et al., 2003]. While this is considerably larger than the MODIS spatial resolution of 1 km, the AMSR-E data may still be of use when the spatial correlation in soil moisture is greater than 50 km. Further work is needed to explore these and alternative remote sensing techniques to estimate the variation in the soil evaporation factor f and to see whether this improves the performance of the model proposed in this paper.

6. Conclusions

[45] Excellent agreement was obtained between measured mean daily evaporation rates and those calculated using the PM equation, MODIS Lai and a simple, biophysical model for surface conductance, Gs, given by equations (6) and (12). The model for Gs accounts for responses of plant canopies to photosynthetically active radiation and humidity deficit, the amount of radiation absorbed in the visible and thermal wavebands (dependent on Lai) and the fraction of radiation absorbed by the soil surface that is partitioned into soil evaporation. Performance of the evaporation model is best when all six parameters in Gs are optimized at each site, but there is no significant degradation in model performance when four parameters (Q50, D50kQ and kA) are held constant across vegetation classes while gsx and f are optimized for each site. Assigning values of gsx according to broad vegetation classes to estimate Gs gave somewhat inferior results to the two-parameter model. To calculate evaporation rates for land surfaces at weekly time scales and kilometer space scales it is clear that both parameters gsx and f are needed to estimate evaporation accurately with the model proposed in this paper. Developing remote-sensing techniques to measure the temporal and spatial variation in f will considerably enhance the utility of the model proposed in this paper.


[46] We gratefully acknowledge the following principal investigators and their teams for providing the evaporation and meteorological 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 (Mer Bleue), Russ K.Monson (Niwot Ridge), Henry L. Gholz and Timothy A. Martin (Mize), Humberto R. da Rocha and Mike L. Goulden (Santarem Km83), Tilden P. Meyers (Bondville), and John B. Moncrieff (Griffin). We thank staff and funding agencies of the ORNL-DAAC for providing an indispensable resource to the scientific community. This work was partially funded through the CSIRO Water for a Healthy Country Flagship and the Australian Climate Change Science Program, supported by the Australian Greenhouse Office.