2.1 FLUXNET Data
 We used the FLUXNET database (http://fluxnet.ornl.gov/) 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 (Rn − G) for each half hour [Wilson et al., 2002]. The values of the half-hourly energy balance closure ratio (H + LE)/(Rn − G) 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].
 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
|1||CA-Ca1||49.867||−125.334||313||NEF||Temperate||2006||1456||253||7.3||81.4||3.7f||Chen et al. [2011a]; Krishnan et al. |
Grünwald and Bernhofer 
Blyth et al. 
Hollinger et al. 
Li et al. 
|6||CA-Ojp||53.916||−104.692||518||NEF||Boreal||2008||418||147||2.0||32.9||27.7f||Bergeron et al. ; Kljun et al. |
Hill et al. 
Tanja et al. 
Hirata et al. 
Hirano et al. 
Kamo et al. ; Hirata et al. 
Rambal et al. 
Garbulksy et al. ; Reichstein et al. 
Valentini et al. 
Gu et al. 
|16||CA-Oas||53.629||−106.198||580||BDF||Boreal||2003||261||109||2.6||46.0||20.8f||Barr et al. ; Krishnan et al. |
Pilegaard et al. 
|18||CA-Mer||45.409||−75.519||65||BDS||Temperate||2006||1203||174||1.2||63.1||15.9f||Lafleur et al. ; Roulet et al. |
Oechel et al. 
|20||CA-NS6||55.917||−98.964||271||BDS||Boreal||2002||267||47||3.0e||3.4||81.1g||Goulden et al. ; McMillan et al. |
Wohlfahrt et al. 
|22||IE-Dri||51.987||−8.752||187||GRA||Temperate||2004||1341||216||5.2e||15.0||50.0||Montaldo et al. ; Peichl et al. |
2.2 Model Description
 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. . 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. , and the photosynthesis model by Farquhar et al.  and Collatz et al. . 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.
 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
 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.  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].
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 () and from the ground to the canopy air for the ground () [Oleson et al., 2010]:
 The water vapor flux from vegetation is determined by water vapor flux from wetted leaf and stem area () and transpiration from the dry leaf surface () [Oleson et al., 2010]
where is the potential evaporation from wet foliage per unit wetted area, f′′ and are fractions of potential evaporation from leaf and through transpiration (see below), respectively, Wcan/Δt 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 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 () [Lawrence et al., 2011; Oleson et al., 2010]:
where βsoi is an empirical function of soil water, 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.  for more details.
- 2.Penman-Monteith equation
In DLM, canopy-scale ET can be expressed as [Chen et al., 2007a] follows:
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.
 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]:
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, 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, 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], 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, is the sunlit/shaded stomatal or soil resistance to vapor transport, and 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
 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]
(7) (8) (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).
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 ()[Oleson et al., 2010]in the following:
where fdry is the fraction of leaves that are dry and depends on canopy water storage, LAI, and stem area index. and are the sunlit and shaded stomatal resistances, respectively, both obtained using the Ball-Woodrow-Berry conductance model [Oleson et al., 2010].
 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 and . 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
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
 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].
 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.
 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
 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:
(13) (14) (15)
where Pi and Oi denote predicated and observed values, respectively; Ō is the mean of the observed data.
 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: