Comparison of terrestrial evapotranspiration estimates using the mass transfer and Penman-Monteith equations in land surface models


  • Jing Chen,

    1. State key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Nature Resources Research, Chinese Academy of Sciences, Beijing, China
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  • Baozhang Chen,

    Corresponding author
    1. State key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Nature Resources Research, Chinese Academy of Sciences, Beijing, China
    • Corresponding author: B. Chen, State key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Nature Resources Research, Chinese Academy of Sciences, Beijing, China. (

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  • T. Andrew Black,

    1. Faculty of Land and Food Systems, University of British Columbia, Vancouver, British Columbia, Canada
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  • John L. Innes,

    1. Department of Forest Resources Management, University of British Columbia, Vancouver, British Columbia, Canada
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  • Guangyu Wang,

    1. Department of Forest Resources Management, University of British Columbia, Vancouver, British Columbia, Canada
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  • Gerard Kiely,

    1. Civil and Environmental Engineering Department, Environmental Research Institute, University College Cork, Cork, Ireland
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  • Takashi Hirano,

    1. Division of Environmental Resources, Research Faculty of Agriculture, Hokkaido University, Sapporo, Japan
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  • Georg Wohlfahrt

    1. Institute of Ecology, University of Innsbruck, Innsbruck, Austria
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[1] The mass transfer (MT) equation and the Penman-Monteith (PM) equation are two common approaches used in various land surface models for simulating evapotranspiration (ET). Yet assessments are rarely conducted to determine how well these structurally differing equations simulate ET across various biomes and climatic environments with different canopy upscaling strategies. We evaluated the capacity of models to estimate ET using the MT equation with the one-leaf strategy in the Community Land Model version 4 and the PM equation in the Dynamic Land Model using the one-leaf and two-leaf upscaling approaches for 22 selected eddy covariance flux towers representing 10 typical plant functional types. Overall, across half-hourly, daily, monthly, and seasonal scales, the MT equation performed less robust than the PM equation in forests. The former had 8–15% higher root-mean-square error and 1–4% lower index of agreement and a large uncertainty in warm and wet seasons for several sites. It leaves a doubt about its application of estimating ET across regional to global scales. Considering the net radiation available on the surface of leaf/soil and adopting the two-leaf approach made the PM equation closer to the EC measurements on average but still could not capture the variation during the cold season. We suggest that further improvements in simulation of ET require seasonal variation of some key parameters and quantification of spatial heterogeneity.

1 Introduction

[2] Evapotranspiration (ET), which includes transpiration and evaporation from the soil-plant system, is a major component of the terrestrial water cycle and energy balance (i.e., latent heat flux, LE) [Katul et al., 2012]. This process returns ~ 60% of annual land precipitation to the atmosphere [Jung et al., 2010; Oki and Kanae, 2006], which affects and then is affected by local climate. One of the extensive adoptions for evaluating and predicting ET is the land surface models (LSMs) [Jaksa et al., 2013; Vinukollu et al., 2012]. Not only because LSMs have a mechanism-based structure and applicability to a wide range of space and time scales [Chen and Coops, 2009] but also it can be coupled to a global circulation model for estimating the effects of climate change and accounting for possible feedback [Cox et al., 2000; Gent et al., 2011; Subin et al., 2011]. Therefore, estimating ET and quantifying the process accurately in LSMs are critical to evaluating the potential impacts on the terrestrial water balance and climate change [Bonan, 2008; Cao et al., 2010].

[3] ET is estimated by meteorological data in models. The mass transfer (MT) equation is one of the classical methods to estimate terrestrial water vapor flux, based on the proportional relationship between vapor flux and vapor pressure difference [Singh and Xu, 1997; Verstraeten et al., 2008]. Based on the combination of mass and heat transfer equations, and the energy balance equation, many expressions have been derived, such as the Penman-Monteith (PM) equation [Monteith, 1965] and the Shuttleworth-Wallace equation [Shuttleworth and Wallace, 1985]. Much effort has been made to compare performances of different approaches to ET estimation that is systematically independent from the land surface modeling systems [Fisher et al., 2005; Nazeer, 2010; Sentelhas et al., 2010; Stannard, 1993; Tabari et al., 2011; Vinukollu et al., 2011]. These studies paid considerable attention to selecting an ET equation which has a simple structure and an acceptable result, since some driven data are incomplete or unavailable [Fisher et al., 2005; Nazeer, 2010; Sentelhas et al., 2010; Tabari et al., 2011]. It has been shown that the uncertainties in ET estimation mainly stemmed from the differences of model structures [Fisher et al., 2005; Tabari et al., 2011].

[4] LSMs calculate the total water vapor flux with three parts: transpiration from the canopy, evaporation from the intercepted water by canopy, and evaporation from soil surface, in which the soil evaporation integrates with the soil moistures [Chen et al., 2007a; Lawrence et al., 2007]. Many LSMs adopt the MT equation to computer ET, such as the Community Land Surface Model (CLM) [Oleson et al., 2010], ecosys [Grant et al., 2012], and Cross-Chain Loran Atmospheric Sounding System [Verseghy et al., 1993]. CLM is the land surface model component of the Community Earth System Model (CESM, developed by the National Center for Atmospheric Research (NCAR). The model uses an improved MT equation for determining transpiration and evaporation with the one-leaf upscaling strategy [Oleson et al., 2010]. Recent assessments of CLM version 4 indicated that the model can capture the spatial distribution and the interannual variability of ET well compared with observations-based estimates at a global scale [Shi et al., 2013]. The ET estimation has a better performance with improved model structure or/and parameters of plant canopy [Bonan et al., 2011]. Bonan et al. [2012] also reported that the modeled latent heat flux decreased in the tropics after replacing the two-leaf photosynthesis simulation method with a multilayer upscaling strategy. The PM equation is another option adopted by LSMs [Chen et al., 2007a; Alton, 2011]. One of them is the remote-sensing-based Ecosystem-Atmosphere Simulation Scheme (EASS) [Chen et al., 2007a]. EASS adopts the PM equation for modeling ET components and follows the sunlit-shaded leaf stratification strategy in both canopy-level photosynthesis and energy flux estimations. This canopy strategy enhanced the realism and accuracy in the simulation of net radiation and energy component fluxes of about 10% compared with the one-leaf strategy [Chen et al., 2007a]. In a further development, the EASS was coupled with the atmospheric global environmental multiscale model (GEM), and the EASS-GEM was reasonably successful in capturing both the spatial and temporal variation in energy fluxes [Chen et al., 2007b]. However, most of these results did not address the impact of the ET equation itself on the ET simulation or could not be used to improve the accuracy of estimation based on the functional structures.

[5] More than functional structures, less attention has been given to the model's suitability of water vapor flux for multiple biome types across different time scales and over relatively long time periods. Previous studies have only evaluated the ET (or LE) estimation performance of LSMs for individual sites [Chen et al., 2007a; Grant et al., 2005; Wang et al., 2011] or for a limited number of vegetation functional types [Hou et al., 2012; Stöckli et al., 2008], although lots of model-data comparison for many sites have been conducted in evaluating carbon dynamics models [Keenan et al., 2012; Schaefer et al., 2012; Schwalm et al., 2010; Sprintsin et al., 2012]. Another fact is that few existing performances of ET estimation operate across a number of time scales (diurnal to interannual). This would leave a debate about the success of ET simulation yearly. The issues mentioned above need to be clarified and resolved in order to reduce uncertainties in ET estimates at regional or global scales.

[6] In this study, we sought to address and to compare the performances of the MT equation in CLM and the PM equation in the Dynamic Land Model (DLM) using measurements of water vapor fluxes with the eddy covariance (EC) technique at typical sites for major biomes. DLM is an updated version of EASS. The selected EC towers represent 10 plant functional types across six biomes in three main climate zones. We tested the equations' ability at a series of time scales, including half-hourly, daily, monthly, and seasonal time scales, and then conducted a sensitivity test, so as to find the uncertainties in performance of these two equations for their potentials at regional or global scales. By using existing data set and uncertainty quantification, this research proves a solid foundation for evaluating equations to estimate water vapor flux in LSMs across multiple plant functional types and across a range of time scales.

2 Methods and Materials

2.1 FLUXNET Data

[7] We used the FLUXNET database ( to calibrate the DLM and validate the water vapor flux estimates for both LSMs. The data set contains annual files of half-hourly flux and meteorological data at more than 400 EC stations across Europe (CarboEurope), America (AmeriFlux and Fluxnet-Canada), Asia (AisaFlux and ChinaFLUX), etc. We selected the EC towers according to a criterion in order to reduce the error derived from the observations by doing the following steps: (1) the site provides three or more years of continuous driver and validation data as a part of publicly accessible standardized level 4 or 3 database; (2) a “site-year” is accepted for analysis if more than 90% of the half hours in a year contained nonmissing values for each of the meteorological data (downwelling solar radiation, precipitation, wind speed, air temperature, and relative humidity) and the energy fluxes (net radiation (Rn), ground heat flux (G), latent heat flux (LE), and sensible heat flux (H)); and (3) energy balance closure is evaluated for each site-year according to the ratio of the dependent flux variables (H + LE) against the independently derived available energy (RnG) for each half hour [Wilson et al., 2002]. The values of the half-hourly energy balance closure ratio (H + LE)/(RnG) deviated from the ideal closure (the value of 1) since random error exists [Wilson et al., 2002], so we recorded the number of the ratio within 0.6–1.4 in the daytime and then accepted a “site-year” when the accumulated number exceeded 60% of the total numbers of the half hour during the daytime of the growing season. Finally, 256 site-years were selected, representing eight biome types across three main climatic environments (i.e., plant functional types (PFTs)) [Oleson et al., 2010] at 67 EC sites. We used half of the sites for calibrating the model and used the others for the validation. Before that, energy fluxes were corrected for lack of energy balance closure by partitioning the available energy flux into LE and H according to the measured Bowen ratio [Twine et al., 2000; Ingwersen et al., 2011].

[8] In this study, the representative simulations of 22 EC towers (Table 1) were selected covering major six biomes across three climate zones: 8 sites in boreal regions, 12 sites in temperate regions, and 2 sites in tropical regions. The JP-Tom site in the temperate zone was categorized as a boreal forest ecosystem because of the absence of the temperate needleleaf deciduous forest in the PFTs we used [Oleson et al., 2010]. For the same reason, five sites that have mediterranean style climates were characterized as in temperate zones.

Table 1. The Descriptions of Study Sites
           Soil Texture 
NumberSite IDaLatitudeLongitudeElevationBiome TypebClimate ZoneSite-YearPercipitationGrowing Season LengthLAImaxSand (%)Clay (%)References
  1. aThe site ID was taken from FLUXNET.
  2. bBiome types: needleleaf evergreen forest (NEF), needleleaf deciduous forest (NDF), broadleaf evergreen forest (BEF), broadleaf deciduous forest (BDF), broadleaf deciduous shrub (BDS), grassland (GRA).
  3. cThe JP-Tom site was categorized as a boreal forest ecosystem for the absence of the temperate needleleaf deciduous forest in the PFTs [Oleson et al., 2010].
  4. dData for growing season calculation are not available.
  5. eData were extracted from a global LAI map based on 10 day synthesis VEGETATION images at 1 km spatial resolution [Chen et al., 2005b, 2012; Deng et al., 2006].
  6. fData acquired from North American Carbon Program.
  7. gData obtained from
1CA-Ca149.867−125.334313NEFTemperate200614562537.381.43.7fChen et al. [2011a]; Krishnan et al. [2009]

Grünwald and Bernhofer [2007]


Blyth et al. [2010]


Hollinger et al. [2004]


Li et al. [2007]

6CA-Ojp53.916−104.692518NEFBoreal20084181472.032.927.7fBergeron et al. [2007]; Kljun et al. [2006]

Hill et al. [2011]


Tanja et al. [2003]


Hirata et al. [2007]


Hirano et al. [2007]


Kamo et al. [2002]; Hirata et al. [2008]


Rambal et al. [2003]


Garbulksy et al. [2008]; Reichstein et al. [2007]


Valentini et al. [1996]


Gu et al. [2006]

16CA-Oas53.629−106.198580BDFBoreal20032611092.646.020.8fBarr et al. [2006]; Krishnan et al. [2006]

Pilegaard et al. [2003]

18CA-Mer45.409−75.51965BDSTemperate200612031741.263.115.9fLafleur et al. [2003]; Roulet et al. [2007]

Oechel et al. [2000]

20CA-NS655.917−98.964271BDSBoreal2002267473.0e3.481.1gGoulden et al. [2006]; McMillan et al. [2008]

Wohlfahrt et al. [2008]

22IE-Dri51.987−8.752187GRATemperate200413412165.2e15.050.0Montaldo et al. [2007]; Peichl et al. [2011]

2.2 Model Description

[9] We estimated water vapor flux using the MT equation and the PM equation in two land surface models, respectively. One is CLM4 [Bonan et al., 2011; Lawrence et al., 2011; Oleson et al., 2010] in CESM version 1.0.3. We revised the modules on two-stream radiative transfer, leaf photosynthesis, and canopy scaling according to Bonan et al. [2011]. The other model is DLM, which is an updated version of EASS by Chen et al. [2007a] including an improved coupled nitrogen-carbon dynamics module and a vegetation dynamic model with a state-of-art phenology module. DLM has been coupled to CESM 1.0.3 by replacing the original photosynthesis and energy flux modules with EASS-based formulations and optimizing the parameters. These two LSMs adopt identical calculation approaches in their biogeophysical modules except for ET estimation, including the flux-gradient approach in modeling sensible heat flux, the stomatal resistance model by Ball et al. [1987], and the photosynthesis model by Farquhar et al. [1980] and Collatz et al. [1991]. In both of LSMs, leaf photosynthesis is linked to transpiration through the Ball-Woodrow-Berry stomatal model. In addition, both models use the two-leaf upscaling strategy in simulating canopy photosynthesis, but this strategy is only adapted by DLM to model energy flux.

[10] We employed the published parameters for CLM, e.g., the leaf maximum carboxylation rate at 25°C constrained by leaf nitrogen [Bonan et al., 2011] and the slope of conductance-to-photosynthesis relationship [Oleson et al., 2010] in Table 2, and optimized some PFTs-dependent parameters about biochemistry and biophysics for DLM (Table 2) because of its updating. Adopting the parameter optimization algorithm by Chen et al. [2011a], we first identified the sensitive parameters to photosynthesis and energy fluxes by analyzing the response of parameters by random sampling of parameters within their possible ranges. Then we applied the ensemble Kalman filter data model synthesis approach, which encompasses both model parameter optimization and data assimilation, to optimize these parameters by minimizing the difference between observations and predications [Mo et al., 2008]. Based on a 102 site-years analysis, we combined the parameters for each PFT to perform a process-based analysis at the global scale. The key PFTs-dependent parameters in ET estimates are shown in Table 2 for both LSMs.

Table 2. Plant Functional Types-Dependent Parameters Used in CLM and DLM for ET Estimationa
Biome TypeClimate ZoneCLMDLM
(µmol m−2 s−1)(µmol m−2 s−1)
  1. aThe terms Vcmax25·f(N), m, and Ω are the leaf maximum carboxylation rate at 25°C constrained by leaf nitrogen, the slope of conductance-to-photosynthesis relationship, and the foliage clumping index, respectively.
  2. bParameters obtained from Tang et al. [2007].

[11] We considered that the effects of using the MT and PM equations in land surface modeling systems could be assessed by comparing the estimates using CLM and DLM, respectively. Three simulations were performed to determine the biases arising for the ET estimation: MT, a control simulation with the MT equation and the one-leaf strategy in water vapor flux estimation by CLM4, which is revised according to Bonan et al. [2011] based on the public release code in CESM1.0.3; PM2L, a simulation with the PM equation and a two-leaf strategy in carbon and energy fluxes simulation (default DLM); and PM1L, a simulation in which the two-leaf strategy has been replaced by a one-leaf strategy in ET estimation and kept the other module unanimous with the default DLM. The design of PM1L is aimed at distinguishing the effects of the two canopy upscaling strategies on ET estimation. We only utilized the biogeophysical module for each of the simulation so that the estimates were unaffected by biases in biogeochemistry (e.g., carbon-nitrogen coupling) [Bonan et al., 2011; Lawrence et al., 2011].

2.2.1 Evapotranspiration

  • 1.Mass transfer equation

In CLM, the water vapor flux is determined by vegetation and ground specific humidity differences simultaneously in the case of a vegetated surface and is the sum of the water vapor transfer from the canopy to the canopy air for the vegetation (inline image) and from the ground to the canopy air for the ground (inline image) [Oleson et al., 2010]:

display math(1)

[13] The water vapor flux from vegetation is determined by water vapor flux from wetted leaf and stem area (inline image) and transpiration from the dry leaf surface (inline image) [Oleson et al., 2010]

display math(2)
display math(3)

where inline image is the potential evaporation from wet foliage per unit wetted area, f′′ and inline image are fractions of potential evaporation from leaf and through transpiration (see below), respectively, Wcant is the water stored on the canopy at each time step, rb is the leaf boundary layer resistance, qs is the canopy specific humidity (in kg kg−1) affected by a combination of heat conductance and specific humidity of air, leaf, and ground, and inline image is the saturation specific humidity at the vegetation temperature (Tveg) [Flatau et al., 1992; Oleson et al., 2010]. Similarly, the expression for the actual specific humidity at the ground surface (qgrnd) can be substituted to obtain the water vapor flux from the ground beneath the canopy (inline image) [Lawrence et al., 2011; Oleson et al., 2010]:

display math(4)

where βsoi is an empirical function of soil water, inline image is the aerodynamic resistance to water vapor transfer between the ground and the canopy air, and rlitter is a resistance of the plant litter layer. The value of qgrnd is assumed to be proportional to the saturation specific humidity at the ground surface temperature, and the proportion is a weighted combination of the soil water matric potential of the top soil layer and the fraction of ground covered by snow. See Oleson et al. [2010] for more details.

  • 2.Penman-Monteith equation

In DLM, canopy-scale ET can be expressed as [Chen et al., 2007a] follows:

display math(5)

where TC is the transpiration from the canopy, EC is the water vapor from the canopy including evaporation of rain and sublimation of snow, and ES is the combination of evaporation and sublimation from the soil surface.

[15] Each ET component was calculated using the PM equation expressed in a general form as given below [Chen et al., 2005a; Chen et al., 2007a; Govind et al., 2009]:

display math(6)

where ETi is the amount of water evaporated from the surface of the leaf or soil (layer i = 1 or 2) or transported from the leaf over the period δt, inline image is the net radiation available on the surface of layer i, which is calculated from the shortwave and longwave radiation absorbed by the surface, ρatm is the density of moist air, cp is the specific heat of air at a constant pressure, inline image is the saturated water vapor pressure in Pa, which is calculated from an eighth-order polynomial function of the temperature of each layer [Flatau et al., 1992], inline image is the actual water vapor pressure, λv is the latent heat of vaporization of water, Δ is the slope of the saturated vapor pressure-temperature curve, γ is the psychrometric constant, inline image is the sunlit/shaded stomatal or soil resistance to vapor transport, and inline image is the aerodynamic resistance to vapor transport for layer i. Details can be found in the supplemental material and Chen et al. [2007a].

2.2.2 Canopy Upscaling

  1. [16] Two-leaf strategy

The DLM calculates canopy evaporation (EC) for sunlit and shaded parts separately by adopting the sunlit and shaded leaf area indices (LAIsun and LAIsha). The leaf stratification strategy for EC is [Chen et al., 2007a]

display math(7)
display math(8)
display math(9)

where G(θ) is the foliage projection coefficient taken as 0.5 assuming a spherical leaf angle distribution and μ is the cosine of the solar zenith angle. The clumping index (Ω) characterizes the leaf spatial distribution pattern in terms of the degree of its deviation from the random case. This approach is also applied to modeling transpiration (TC).

  • 2.One-leaf strategy

Analogous to equations (8) and (9), CLM separates the canopy into two parts (LAIsun and LAIsha) in photosynthesis and further in stomatal resistance estimations[Oleson et al., 2010] but adopts the foliage projection area as a function of the departure of leaf angles from a random distribution and ignores the impact of the clumping index. To combine the effects from both sunlit and shaded leaves in the ET estimation, CLM uses a fraction of potential evaporation through transpiration (inline image)[Oleson et al., 2010]in the following:

display math(10)

where fdry is the fraction of leaves that are dry and depends on canopy water storage, LAI, and stem area index. inline image and inline image are the sunlit and shaded stomatal resistances, respectively, both obtained using the Ball-Woodrow-Berry conductance model [Oleson et al., 2010].

[18] In the one-leaf strategy of the PM equation (PM1L), we replaced the value of fdry with 1.0 and removed rb in equation (10) to gain the one-leaf stomatal resistance from inline image and inline image. The water vapor flux was scaled up to the canopy level with an exponential equation from that of an unshaded leaf [Alton et al., 2007; Mercado et al., 2007; Sprintsin et al., 2012], which is analogous to the calculation of half-hourly canopy evaporation and transpiration in the two-leaf strategy (equations (7) and (8)). The one-leaf strategy in the EC estimation follows

display math(11)
display math(12)

where Ec0 is the evaporation from an unshaded leaf and fscale is a multiplicative factor, in which the canopy photosynthetically active radiation (PAR) extinction coefficient k is taken to be 0.5. The same approach is also used for TC estimate.

2.3 Model Simulations

[19] Off-line single point simulations with a 30 min time step were performed using observed meteorological data and land surface data. The half-hourly meteorological data were measured at the EC towers, including downwelling solar radiation (in W m−2), precipitation (in mm), wind speed (in m s−1), air temperature (in K), and relative humidity (in %). Missing half-hourly values of these key model inputs due to periods of instrument failure were gap filled by linear interpolation of gaps less than 2 h. Larger gaps were filled by applying a simple interpolation technique of mean diurnal variation [Falge et al., 2001; Moffat et al., 2007].

[20] For each site, the soil texture (i.e., percentages of sand and clay) were obtained from the site's information or published articles (Table 1). We adopted soil property data sets (i.e., soil color and organic matter content at each soil depth) provided by CESM1.0.3 as a source of land surface data for the year 2000 [Lawrence et al., 2011; Stöckli et al., 2008]. Soil state variables (e.g., soil temperature and moisture) of each site for the off-line simulations were initialized by spinning up for 200 years with repeat years 1982–2001 atmospheric forcing data set from the National Centers for Environmental Prediction reanalysis data set [Qian et al., 2006] provided by NCAR.

[21] Monthly LAI values for each site were extracted from a global LAI map based on 10 day synthesis VEGETATION images at 1 km spatial resolution in 2003, which has been corrected based on a global clumping index map produced from the multiangle observation of POLDER 1, 2, and 3 sensors [Chen et al., 2005b, 2012; Deng et al., 2006]. We corrected the monthly LAI for each site according to the LAImax value (Table 1) supplied by the biological information for each site. Although the years for which available supplementary land surface data are available do not always correspond to the years being modeled, we assumed that the data are adequate for our water vapor flux modeling.

2.4 Model Performance

[22] We quantified model performance using statistical analysis based on half-hourly LE for each model-data pair. Model-data mismatch was evaluated using bias, root-mean-square error (RMSE) [Willmott, 1982; Willmott and Matsuura, 2005; Willmott et al., 1985], normalized mean absolute error (NMAE) [Marlin, 2004], as well as index of agreement (IA) [Vörösmarty et al., 1996; Willmott, 1982]. The skills were calculated by the following:

display math(13)
display math(14)
display math(15)


display math(16)

where Pi and Oi denote predicated and observed values, respectively; Ō is the mean of the observed data.

[23] A final characterization of model performance uses the Taylor diagram [Taylor, 2001], in which a single point indicate the linear correlation coefficient (R) and the ratio of the standard deviations between the prognosis and the observation (σnorm = σp/σo), along with the root-mean-square difference of the two patterns on a two-dimensional plot. An ideal model would have a standard deviation ratio of 1.0 and a correlation coefficient of 1.0, i.e., the reference point on the x axis. Taylor skill (S) is a single value summary of a Taylor diagram where unity indicates perfect agreement with observations. More generally, each point for any arbitrary data group [Schwalm et al., 2010; Taylor, 2001] can be scored as follows:

display math(17)

3 Results

3.1 Estimates of Important Variables

[24] Key variables used to simulate water vapor flux are derived from the outputs of other modules in both LSMs, as the stomatal resistance is based on the Ball-Woodrow-Berry stomatal model (equation S25 in the supporting information) in equations (6) and (10), the leaf and soil temperatures (equations S26–S29) used to calculating saturation specific humidity in the equations (3) and (4) and saturation vapor pressure in the equation (6), and the soil moisture distribution (equation S30) in simulating soil moisture dynamics to limit soil evaporation (βsoi in equation (4) and inline image in equation (6)). We drew a comparison between these modeled and measured variables to clarify a potential module structure effect on the accuracy of ET estimation. Examples were presented for CA-Ca1 and CA-Ojp (Figure 1). These two needleleaf evergreen forests in temperate and boreal regions, respectively, provided complete observations, including the tree foliage temperature, in all sites we selected. We only show one preventative year at each site since the behavior is comparable from year to year in simulation.

Figure 1.

Simulated (color lines) and observed (dark lines and symbols) vegetation and soil temperatures and soil moistures for two site-years (CA-Ca1 (2006) in the left-hand side and CA-Ojp (2008) in the right-hand side). (a,b) Daily gross primary production (GPP); (c,d) annually averaged diurnal composites of simulated vegetation temperature (lines), observed tree foliage temperature (filled circles), and observed air temperature above the canopy (open circles); (e,f) daily averaged soil temperature in the surface layer (10 cm depth); and (g,h) daily averaged soil moisture in surface layer (10 cm depth, lines) and daily cumulative precipitation (bars).

[25] In the Ball-Woodrow-Berry stomatal model (equation S25), the stomatal resistance is calculated based on the photosynthetic rate, which derived from Farquhar photosynthesis mode in both LSMs. As shown in Figures 1a and 1b, the daily gross primary productions (GPP) simulated by CLM and DLM were comparable to the observations in both sites, excepting that both LSMs underestimated the values at CA-Ojp from August to October in 2008. Annual averaged diurnal variations of modeled vegetation temperatures of these two sites were higher than air temperature at midday (Figures 1c and 1d). The errors of DLM-PM1L and DLM-PM2L estimations were usually less than 1°C, but CLM errors far exceeded 2°C. Moreover, all models did not capture the elevated temperature of tree foliage in the afternoon. DLM-PM1L and DLM-PM2L adopted the same approach as that used in CLM to estimate soil temperature (equation S29). As shown in Figures 1e and 1f, modeled daily averaged soil temperatures (10 cm depth) agreed well with observations during the warm days for both sites. The models explained 70–96% and 80–83% of the variance at CA-Cal and CA-Ojp, respectively, from April to October (n = 214 for each site in each model). However, the soil temperatures were underestimated during the cold months especially in CA-Ojp. The average biases of this site were −2.7°C, −5.9°C, and −5.0°C for MT, PM1L, and PM2L (n = 151 for each model), respectively. We compared daily averaged soil moisture contents at a soil depth of 10 cm and precipitation at CA-Cal and CA-Ojp (Figures 1g and 1h). The simulated soil moisture contents in the surface layer agreed well with the measurements, excepting that CLM underestimated soil moisture content in the middle of the year 2008 at CA-Ojp. Peak values of simulated and observed soil moisture values were associated with high daily accumulated precipitation, which indicate that changes in soil water content in response to rainfall events and drying were reasonably captured by the three models. Similar results were also observed in other sites. These comparisons suggest that with the same methods in modeling GPP, soil temperature, and soil moistures, there are no obvious discrepancy in these key variables used to simulate water vapor flux in all three models. The differences existed in leaf temperature estimates, which are calculated during the iterated process in modeling canopy energy fluxes in three simulation scenarios.

3.2 Model-Data Agreement on Half-Hourly and Daily Time Scales

[26] Comparisons between modeled and observed LE in Figure 2 and Table 3 provided an overview of performances among models on half-hourly and daily time scales. Overall, the three models had a similar R range within the same time scale, but PM2L performed better than MT and PM1L with σnorm closer to 1, smaller RMSE and NMAE, and greater IA.

Figure 2.

Performance of the three models for the 22 selected tower sites (number 1–22). Statistics in the Taylor diagram are derived from simulated and observed LE fluxes of site-year: (a) half-hourly and (b) daily averaged. Color regimes: blue for MT, green for PM1L, and red for PM2L. An ideal model would have a standard deviation ratio (σnorm) of 1.0 and a correlation coefficient of 1.0 (REF, the reference point).

Table 3. Comparison of Model Performance in Estimating Latent Heat Flux (LE) at Half-Hourly and Daily Time Scalesa
NumberSite ID (W m−2)   (W m−2)   (W m−2)  
  1. aBold numbers show the best of the three models for each diagnostic and site.

[27] Half-hourly LE was well quantified by the three models for the 22 tower sites. As shown in Figure 2a, model fittings to the observed data ranged in R values of 0.55–0.93, 0.59–0.93 and 0.61–0.94 for MT, PM1L and PM2L, and in σnorm of 0.54–1.54, 0.54–1.03, and 0.68–1.11, respectively. Note that although these models had similar R values, values of σnorm in PM2L were close to unity, i.e., the reference point (REF on the x axis). Figure 2 shows a smaller estimation error of PM2L compared with MT and PM1L. Overall agreements across the selected 22 sites were better using the PM equation than using the MT equation, with NMAE and IA values being close to zero and 1.0, respectively, for PM2L on average.

[28] By averaging half-hourly LE into a daily time scale, the performance of the PM equation was more robust than the MT equation (Figure 3). The R2 of daily LE were larger for the PM equation (PM1L and PM2L) compared to the MT equation at most forest sites (Figures 3a–3g), varying from 0.25–0.74 (MT) to 0.34–0.73 (PM1L) and 0.32–0.80 (PM2L), except for two broadleaf evergreen forests located in the temperate climate zone (FR-Pue and IT-Cpz, Figure 3e). The LE values of this PFT were overestimated by the MT equation as indicated by a slope >1. The simulation biases using the two equations for shrubs (Figures 3h and 3i) and grasslands (Figure 3j) were similar. A further improvement in both correlation and variability was achieved using the two-leaf strategy with the PM equation. The averaged slope of daily LE for various plant functional types increased from 0.64 (±0.16) (±standard deviation, PM1L) to 0.75 (±0.16) (PM2L), and the corresponding R2 ranged from 0.61 (±0.16) to 0.65 (±0.17) (Figure 3). These suggest that the PM equation with a two-leaf upscaling strategy performed better than the MT equation.

Figure 3.

Comparison of the observed daily averaged latent heat flux (LE) simulated by MT (open symbols, blue lines), PM1L (gray symbols, green lines), and PM2L (dark symbols, red lines) across the selected 22 sites for different plant functional types: (a, b) needleleaf evergreen forests in temperate and boreal zones; (c) needleleaf deciduous forest in boreal zone; (d, e) broadleaf evergreen forests in tropical and temperate zones; (f, g) broadleaf deciduous forests in temperate and boreal zones; (h, i) broadleaf deciduous shrubs in temperate and boreal zones; and (j) grasslands.

3.3 Model-Data Agreement at Monthly and Seasonal Time Scales

[29] To explore the equations' responses to varying weather conditions during different seasons, we compared the simulated monthly and seasonal LE variations among the models for 20 sites in temperate and boreal zones (Table 4). Two tropical sites (ID-Pag and TH-Sak) were excluded, as ET shows hardly any seasonality under these climate conditions. The LE differences were not significant (p > 0.05) by one-way analysis of variance among three models during the same season but were significant during the different seasons for each model. For the four seasons, all three models underestimated LE in winter and spring seasons (negative bias), and three estimates were variable in summer and fall with both positive and negative biases. Removing biases of opposite sign, R values were close to 1.0 with large RMSE during the growing season for individual models. Moreover, model skill (Figure 4) and regression analysis (Table 4) show that PM2L performed well for summer (R = 0.81(±0.11)) and fall (R = 0.72 (±0.12)) across the 20 sites, while MT was better than PM2L for winter (R = 0.44 (±0.22)) and spring (R = 0.72 (±0.17)). Overall, all three models performed well in summer and less well during the other seasons, indicating that it may be challenging to capture ET dynamics during the cold season.

Table 4. Bias, Correlation Coefficient (R), and Root-Mean-Square Error (RMSE) of Half-hourly Latent Heat Flux (LE) With Respect to Individual Months and Seasons in Temperate and Boreal Sites
Months/Seasons(W m−2) (W m−2)(W m−2) (W m−2)(W m−2) (W m−2)
  1. aValues in parentheses are ±1 standard deviation.
  2. bWinter is given by December, January, and February with divided 1 year into four seasons.
All year−3.1(±47.6)0.77(±0.10)43.66(±19.62)−6.8(±44.1)0.75(±0.10)41.60(±16.80)−2.2(±43.6)0.78(±0.10)40.72(±16.17)
Figure 4.

Boxplots of Taylor skill (S) for half-hourly LE by models and seasons across the selected 20 sites in temperate and boreal regions. Panels show interquartile range (box), mean (square), median (solid line), range (whiskers), and outliers (cross). Colors indicate models: blue for MT, green for PM1L, and red for PM2L. Models and seasons sorted by the median Taylor skill.

[30] Figure 5 compared simulations and observations of monthly composite diurnal variations. Examples are presented for each plant functional types. Overall modeled LE captured the observed diurnal variation within or near the margins of ±1 standard deviation range of the mean observations for most site-years, except for the US-MOz site (Figure 5f), in which underestimation by all the three models occurred during the winter and early spring. The MT equation performance was variable in seasonal simulation, especially in summer (from June to August). For instance, for some boreal forest sites (FI-Hyy and DK-Sor), it underestimated LE by 30% on average (Figures 5c and 5g), while it overestimated LE by 91% on average for a tropical climate site (TH-Sak, Figure 5d) and two sites in mediterranean climate zones (FR-Pue and US-MOz, Figures 5e and 5f). LE modeled by the PM equations (PM1L and PM2L) was quite consistent with measurements without obvious bias for all the EC sites during the warm seasons. Linear regression analyses of the diurnal composites for these site-years showed that the values of R2 were 0.57–0.95 and 0.60–0.96 for PM1L and PM2L, respectively, and the corresponding RMSE were 10.7–54.3 W m−2 and 6.9–50.6 W m−2. Systematic biases as a result of using PM1L were found for most of the 10 sites with the one-leaf strategy generally underestimating LE around midday in the warm seasons (Figure 5).

Figure 5.

Monthly averaged diurnal composites of observed latent heat flux (dark lines) and simulated by MT (blue lines), PM1L (green lines), and PM2L (red lines) at sites representing each plant functional type: (a, b) needleleaf evergreen forests in temperate and boreal zones; (c) needleleaf deciduous forest in boreal zone; (d, e) broadleaf evergreen forests in tropical and temperate zones; (f, g) broadleaf deciduous forests in temperate and boreal zones; (h, i) broadleaf deciduous shrubs in temperate and boreal zones; and (j) grasslands. The gray bars indicate ±1 standard deviation of the averaged observations.

3.4 Dominant Factors in ET Estimation Approaches

[31] To explore the further reasons that induced the differences among the ET estimations mentioned above, we conducted a set of sensitivity tests and assessed them as errors. Table 5 shows that the ET estimations varied within 12% of their base values when the parameters in each of these models increased or decreased by 20%.

Table 5. Sensitivity of Site-Averaged Evapotranspiration (ET, mm H2O yr−1) to Errors in the Major Input Parameters of Leaf Area Index (LAI), Foliage Clumping Index (Ω), Slope of Conductance-to-Photosynthesis Relationship (m) for Stomatal Conductance, Maximum Rate of Carboxylation (Vcmax) for Photosynthesis, Albedo (α), and Friction Velocity (u*) for Aerodynamic Resistance of Canopy
  1. aThe base values are calculated based on observed latent heat flux (LE) from eddy covariance tower measurements: ET = LE/λ. We assume a latent heat of vaporization (λ) of 2.501 × 106 J kg−1 [Oleson et al., 2010].
  2. bValues in parentheses are standard deviations.
  3. cThe percentage in brackets is the difference relative to the base value.
1.2 × LAI447.8(±333.3)373.6(±215.8)451.9(±280.8)10.8(2.5%)c19.5(5.5%)16.3(3.7%)−4.1(−0.9%)−78.3(−17.3%)
0.8 × LAI422.8(±316.4)336.3(±193.4)420.3(±267.3)−14.1(−3.2%)−17.8(−5.0%)−15.4(−3.5%)2.6(0.6%)−84.0(−20.0%)
1.2 × Ω354.8(±205.2)436.0(±276.6)0.7(0.2%)0.4(0.1%)−81.2(−18.6%)
0.8 × Ω353.5(±201.4)432.8(±268.5)−0.6(−0.2%)−2.8(−0.6%)−79.3(−18.3%)
1.2 × m479.6(±360.2)376.9(±218.7)468.4(±301.7)42.7(9.8%)22.7(6.4%)32.8(7.5%)11.2(2.4%)−91.5(−19.5%)
0.8 × m386.1(±277.3)330.2(±182.9)388.6(±235.0)−50.9(−11.6%)−23.9(−6.7%)−47.0(−10.8%)−2.5(−0.6%)−58.4(−15.0%)
1.2 × Vcmax438.2(±328.4)369.7(±211.4)456.0(±273.0)1.3(0.3%)15.6(4.4%)20.3(4.7%)−17.7(−3.9%)−86.3(−18.9%)
0.8 × Vcmax411.7(±306.8)334.5(±190.2)422.3(±260.2)−25.3(−5.8%)−19.7(−5.6%)−13.3(−3.1%)−10.7(−2.5%)−87.9(−20.8%)
1.2 × α432.6(±322.8)344.9(±198.6)422.6(±267.4)−4.3(−1.0%)−9.2(−2.6%)−13.0(−3.0%)10.0(2.4%)−77.7(−18.4%)
0.8 × α439.1(±327.0)362.9(±206.5)449.0(±280.3)2.2(0.5%)8.8(2.5%)13.3(3.1%)−9.8(−2.2%)−86.1(−19.2%)
1.2 × u*446.1(±319.6)358.3(±206.2)442.3(±262.3)9.1(2.1%)4.2(1.2%)6.7(1.5%)3.8(0.8%)−84.0(−19.0%)
0.8 × u*424.0(±315.0)348.9(±197.5)426.1(±264.0)−13.0(−3.0%)−5.2(−1.5%)−9.5(−2.2%)−2.1(−0.5%)−77.2(−18.1%)

[32] The relative differences change by 6% to 12% with the slope of conductance-to-photosynthesis relationship (m, equation S25) was found for all of the three models. This PFTs-dependent factor is a constant and affects stomatal conductance in canopy transpiration and evaporation simulations (equations (2) and (6)) by adopting the Ball-Woodrow-Berry conductance model in both of the two land surface models [Chen et al., 2007a; Oleson et al., 2010]. LAI is another sensitive factor in ET estimation. Increasing or decreasing it by 20% altered ET by ~5% on average (Table 5), with the increase mainly in canopy transpiration (data not shown). In general, modifying other parameters in the land surface models, such as maximum rate of carboxylation (Vcmax, equation S19) for net photosynthesis and then for gs, albedo (α, equations S8–S11), and friction velocity (u*, equation S2) for aerodynamic resistance of canopy, caused ET to change in the same direction for the three models. Moreover, our test (Table 5) shows that there was little sensitivity of ET to variation in the clumping index (Ω). It is noteworthy that an increase or decrease of albedo by 20% changed the relative differences between the base values and three models by −3.0 to 3.1% (Table 5), even though the albedo was considered in the MT equation indirectly by effecting inline image and inline image in equation (10). Given the direct beam albedo and diffuse albedo in MT, radiative transfer within vegetative canopies was calculated from the two-stream approximation [Sellers, 1985]. As a part of the solutions, the photosynthetically active radiation absorbed by the vegetation was used to estimate the light-limited rate of carboxylation by the Farquhar's photosynthesis model and then the stomatal resistances of the sunlit and shaded leaves (inline image and inline image) by the Ball-Woodrow-Berry conductance model. The values of inline image and inline image were used in equation (10) to estimate ET based on the MT equation [Oleson et al., 2010].

[33] Furthermore, we quantified the simulated differences in annual ET for each modeling test by normalizing the PM2L results. As shown in Table 5, all of the 10 cases, including the increase and decrease of input variables or parameters by 20%, changed in the same direction for PM1L with a relative error of around −18%, but for MT, relative errors were quite variable with a relative span from −3.9% to 2.4%. These results suggest that changes in parameters or input variables within 20% of their initial values can reduce the difference between the results of using the MT and PM equations but not for that between the one-leaf and two-leaf upscaling strategies both using the PM equation.

4 Discussion

4.1 Effects of Model Structure on ET Estimates

[34] The differences of ET estimate between these two LSMs were not indirectly caused by their uncertainties, because the same methods were adopted in each model to computer key variables for ET calculation, and the comparisons did not show systematic errors for model ET-sensitive variables (Figures 1a, 1b, and 1e–1h), though CLM overestimated the canopy temperature during the daytime and underestimated the value at nighttime (Figures 1c and 1d) for each site-year. We also found that for some sites, e.g., CA-Ca1 (Figure 5a), the monthly averaged diurnal composites of LE modeled by the MT equation were close to the observations (Figure 5) or even better than that by the PM equation. One possible reason for this is that the errors stemmed from the biases in simulated leaf temperature would be compensated by parameters adjustment during the energy fluxes calculation. As described by Bonan et al. [2011] and Chen et al. [2010a], a revision of model parameters could reduce the errors caused by model structure and the improved carbon and energy fluxes estimation. A second possible cause is the structure of iterated process in modeling canopy energy fluxes. Based on these analyses, we believe that the errors in ET estimated by MT, PM1L, and PM2L are not mainly caused by the biases in the simulated ET-sensitive variables in CLM and DLM.

[35] There are two structural differences among the MT, PM1L, and PM2L models: (i) which upscaling strategy from leaf to canopy is adopted (i.e., one-leaf or two-leaf strategy) and (ii) whether the model separately calculate the net radiation at the interface between canopy and soil (inline image in equitation 6). It is obvious that the variance in half-hourly and daily ET explained by the two-leaf strategy is better than that by the one-leaf strategy using the same PM equation (Figures 2, 3, and 5 and Tables 3 and 4). This is because the latter ignores a large contribution of diffuse PAR to the shaded leaves, which is more efficiently absorbed by the canopy for photosynthesis than direct PAR [Dai et al., 2004; Sprintsin et al., 2012]. Underestimation was also found in water vapor flux simulation by the MT equation with one-leaf strategy in CLM, but only for several PFTs (Figures 3a, 3c, and 3g). The other structural difference is the inline image. This variable is adopted by the PM equation (equation (6)) but not employed by the MT equation (equations (3) and (4)), which could explain the sensitivity difference of albedo between the two ET equations in Table 5. Using an improved model base on the PM equation to simulate soil evaporation and plant transpiration in a crop field, Gao et al. [2013] also found that the model was extremely sensitive to the radiation captured by crop. In the ET process, solar radiation proves the energy to change the state of the molecules of water on leaf/soil surface from liquid to vapor and control ET combined with the ambient temperate [Allen et al., 1998]. In general, increasing radiation loading on the leaf surface results in an increase in transpiration [Phyo and Chung, 2013], partly due to an increase in stomatal conductance [Hetherington and Woodward, 2003], and the difference between the rate of transpiration and the rate of production of water vapor inside the leaf by absorbed radiation controls the water potential of the epidermis in the leaf [Pieruschka et al., 2010]. Therefore, ignoring the impacts of solar radiation captured by leaf/soil will lead to errors in the estimates of water vapor fluxes. However, this could not be an important cause leading to the different performances between these two equations (MT and PM) in the two LSMs, because we did not find a systematic model bias in all the site-years simulations.

4.2 Seasonal Uncertainties in Model Performance

[36] The simulated ET with the MT equation has larger biases than with the PM equation (larger RMSE and σnorm, Table 3 and Figure 2), especially for FI-Hyy, JP-Tom, FR-Pue and IT-Cpz. Table 6 shows that the daytime ET estimations by the MT equation during warm and wet seasons were almost equivalent to that during the whole year in IT-Cpz or even higher in FR-Pue, but the modeled values were 29% and 14% lower than the measurements in FI-Hyy and JP-Tom from May to October, respectively. A further exploration for the MT equation revealed that more water was lost as a result of canopy transpiration for these sites, which was ~10% high in warm and wet seasons compared with that in whole year around. It is similar to PM1L and PM2L, but the contribution of transpiration was ~6% high (Table 6). This result is consistent with our analysis results shown in Table 4. These ET estimation errors using the MT equation in CLM are expected to be stemmed from biases in calculations of transpiration, stomatal conductance, and photosynthesis (Table 5). The water vapor flux contributed from transpiration was relatively low during other seasons for all three models (Table 6).

Table 6. Total Evaportranspiration (ET, mm H2O yr−1) and Relative Contribution of Transpiration From Vegetation (TC/ET) During the Daytime for the Whole Year and Seasons
Number and Site IDYear/SeasonsObserved ETETTC/ETETTC/ETETTC/ET
  1. aThe warm and wet seasons involve summer and fall (from May to October). Two months are advanced for IT-Cpz because of its mediterranean climate.
  2. bThe value represents the water vapor flux with default parameters as shown in Table 5.
  3. cThe value in brackets is the difference relative to the observed ET.
8 FI-HyyWhole year course264.6b189.9(−0.28)c0.68212.0(−0.20)0.70268.5(0.01)0.71
 Warm and wet seasonsa239.1170.3(−0.29)0.74202.9(−0.15)0.72255.8(0.07)0.74
 Other seasons25.519.6(−0.23)0.159.1(−0.64)0.1812.7(−0.50)0.20
9 JP-TomWhole year course330.3291.0(−0.12)0.40317.8(−0.04)0.57359.4(0.09)0.54
 Warm and wet seasons259.8222.5(−0.14)0.52277.4(0.07)0.64285.5(0.10)0.65
 Other seasons70.568.5(−0.03)0.0140.4(−0.43)0.0773.9(0.05)0.09
12 FR-PueWhole year course399.0621.7(0.56)0.61398.9(0.00)0.48408.0(0.02)0.52
 Warm and wet seasons271.9473.9(0.74)0.70269.4(−0.01)0.54279.2(0.03)0.58
 Other seasons127.1147.8(0.16)0.34129.5(0.02)0.36128.8(0.01)0.39
13 IT-CpzWhole year course317.5510.3(0.61)0.75271.3(−0.15)0.60357.4(0.13)0.64
 Warm and wet seasons218.2302.6(0.63)0.85185.2(−0.15)0.66247.2(0.13)0.71
 Other seasons99.3207.7(1.09)0.5786.1(−0.13)0.44110.2(0.11)0.46

[37] Many studies reported that the stomatal conductance and photosynthesis are changed with seasons or phenology. Zhang et al. [2009] estimated that the slope between net assimilation rate (An) and stomatal conductance (gs) for four broadleaf species significantly increased in the dry season compared with the wet season (Figure 4), indicating increased photosynthetic water-use efficiency. Gratani et al. [2000] also reported that the daily gs/An change of a forest in the Mediterranean Basin could be described by a linear equation with negative slope over time (Figure 2), which was very close to 80 mol µmol−1 as the leaves expanded (February) but less than a half at midyear. Using a top-down approach based on a double-source canopy model and eddy flux measurements, Ono et al. [2013] estimated the canopy-scale relationship between gross photosynthesis adjusted for environmental variables and gs for a paddy rice canopy throughout the growing season. They found that m appeared to vary seasonally with the ontogenic changes. Similarly, many studies have found that m could be higher in growth or young stages, e.g., in temperate deciduous broadleaf trees [Kosugi et al., 2003], tropical rainforest [Kosugi et al., 2012], boreal forest [Stokes et al., 2010], and grassland [Wolf et al., 2006], since there is a more rapid increase in gs compared with the An during periods of leaf expansion [England and Attiwill, 2011; Ono et al., 2013]. However, two sensitive parameters m and Vcmax are empirical variables in the LSMs, which could not well capture temporal changes in gs and An. Unrobustly, seasonal performance in ET simulation was also reported by Schwalm et al. [2010] by comparing monthly CO2 exchange from 44 EC towers using 22 terrestrial biosphere models. It means that even these key parameters have been optimized well, the discrepancies between modeled seasonal photosynthesis and ET and observations could not be removed if the seasonal or phenology impacts are not reasonably considered by the models. Many efforts have been made to quantify the seasonal variations of some key parameters in gs and An in calculation. In the parameterization in CLM4 for each ecoregion based on 3125 inventory plots measured during 2001 to 2006 in Oregon forests, Hudiburg et al. [2013] modeled monthly GPP that fell within the observed range of uncertainty for the majority of the year but still could not capture the seasonal response of Vcmax to temperature, precipitation, and day length. Moreover, the seasonal variation of Vcmax at the ecosystem scale was not sufficiently explained by upscaling with LAI [Groenendijk et al., 2011]. By changing the parameter m in the stomatal conductance calculation equation, Zhu et al. [2011] tested the observed responses of m to simulated net assimilation and transpiration rates. Their results suggest that more efforts are needed to adjust the values of some key parameters varying seasonally, such as m in land surface models in order to extend its application to regional or global scales. Bonan et al. [2011] and Chen et al. [2010a] pointed out that the uncertainties in land surface model estimations due to errors in input parameters would be the same as those from different structures. Our results agree with it, and we consider that the errors in modeling water vapor flux induced by the key parameters would be larger than those from the structures of ET equation.

[38] More than the model structures and variables, the uncertainties in seasonal ET estimates are also contributed from the EC data, which have gaps especially in the cold season. Even we have corrected energy fluxes according to the measured Bowen ratio (section 2.1). Following the linear regression slope from the ordinary least squares (OLSs) relationship between the half-hourly values of LE + H against RnG and energy balance ratio (EBR), i.e., Σ(LE + H)/Σ(RnG), described by Wilson et al. [2002], we evaluated the energy balance closure of measurements over each season for 20 temperate and boreal sites. The results showed that the R2 values of OLSs increased from winter to summer months, with an average of about 0.67 in January and February and 0.87 in July and August. The mean EBR is lower in winter (0.79) than in summer (0.84). It was associated with biophysical characteristics, where the sampling error is generally greater in open canopies or at topographically complex sites [Misson et al., 2007; Scott et al., 2004; Scott, 2010; Stoy et al., 2013; Sun et al., 2010]. Regarding the uncertainty resulting from spatial heterogeneity, an approach to deal with this issue is to couple a LSM with a footprint model, such as SAFE-f (Simple Analytical Footprint model on Eulerian coordinates for flux), in which the model considers the effects from land surface heterogeneity around the EC tower [Chen et al., 2009]. This method has been applied to assessing carbon budget estimation by combining EC flux and remote sensing at landscape to regional scales and to characterize the spatial representativeness of EC measurements [Chen et al., 2010b, 2011b]. However, its applications in land surface modeling are few. The combination of these two methods and the data-model fusion approach [Chen et al., 2010b; Hu et al., 2009; Kattge et al., 2009] would effectively increase the accuracy in upscaled regional flux estimation.

5 Conclusions

[39] By comparing the two commonly used equations for estimating terrestrial ET in land surface models across 10 PFTs across half-hourly, daily, monthly, and seasonal scales, our multisite study illustrated that the ET estimated by the MT equation in CLM has large uncertainties in warm and wet seasons, especially in deciduous forests. The errors mainly stemmed from ill parameterization in the stomatal conductance module. It raises a doubt on the accuracy of simulated temporal and spatial distribution of ET distribution by CLM even though the modeled global sum of water vapor flux was reasonable [Bonan et al., 2011; Shi et al., 2013]. Except for underestimation during cold season, the ET estimation by the PM equation is robust and much better with two-leaf strategy than with one-leaf strategy. This may attribute to its structure considering net radiation on both the surfaces of leaf and soil and the different contributions of diffused PAR to the shaded leaves compared to direct PAR to the sunlit leaves. This ET equations comparison study suggested the LSM community that the PM equation with a two-leaf canopy upscaling strategy is a better choice in ET simulation. One of future work directions is a need to improve seasonal or phenology variations of key parameters in stomatal conductance calculation to reduce the uncertainties in simulated ET in LSMs. Another thing worthy to do is to extend the calibration of the PM equation in DLM for cropland to expand its application to large heterogeneous of regions.


[40] This research was supported by a research grant (No. 2010CB950902 and 2010CB950904) under the Global Change Program of the Chinese Ministry of Science and Technology, a research grant (2012ZD010) of Key Project for the Strategic Science Plan in IGSNRR, CAS, a research grant funded by the China Postdoctoral Science Foundation (O7Z76032Z1), the research grants (41071059 and 41271116) funded by the National Science Foundation of China, a Research Plan of LREIS (O88RA900KA), CAS, and “One Hundred Talents” program funded by the Chinese Academy of Sciences. We acknowledge the agencies that supported the operations at the flux towers used here, which are part of FLUXNET. We thank Mingliang Che for porting CESM, Xianming Dou for gap-filling meteorological data and two anonymous reviewers who provide useful comments that led to the improvement of this paper.