Several studies have attempted to quantify sublimation using field observations or model simulations for different regions of the world (Mott et al., 2018). Previous studies have suggested that snow sublimation during winter periods varies between 0.1% and 90% of the total snowfall depending on geographical locations, meteorological conditions, and model complexity (Groot Zwaaftink et al., 2013;MacDonald et al., 2010;Strasser et al., 2008). Sublimation was estimated at 0.36 mm d -1 in continental Sweden (Bengtsson, 1980) and 1-2 mm d -1 in the eastern Canadian Rocky Mountains (Golding, 1978). A total of 15% of snowfall was found to be lost through sublimation in the alpine regions (Hood et al., 1999;Kattelmann & Elder, 1991;Marks et al., 1992), whereas this fraction was 20% in the Atlas Mountains (Boudhar et al., 2016). Higher rates of sublimation were observed along the edge of the Eurasian cryosphere in Mongolia at the beginning and end of the snow-covered periods, especially under strong wind conditions (Zhang et al., 2008). Sublimation could reach 70% of the annual snowfall at wind-exposed locations in a mountainous region of southeastern Germany (Strasser et al., 2008). The progress in monitoring and modeling sublimation was hampered by difficulties in field observations of latent heat fluxes over snow surfaces, especially over complex terrain (Prueger et al., 1998). The total water vapor flux (ET) or associated latent heat flux (λET, with the latent heat of sublimation/evaporation λ) under partly snow-covered and heterogeneously vegetated terrain consists of soil evaporation, snow sublimation, and vegetation transpiration. Since latent heat fluxes during wintertime are relatively small compared with the other seasons, common ET models mainly focus on the snow-free seasons. Snow ET is commonly estimated using bulk transfer models, which relate water vapor fluxes to the corresponding scalar-gradients with wind speed and surface-roughness-dependent transfer coefficients. The major difficulties of the bulk transfer models are mainly caused by the need for two-level atmospheric humidity data, which are often not available over complex terrain in remote areas. Parameterization of the transfer coefficients under stable atmospheric conditions, which often prevail over snow surfaces, is challenging. Fitzpatrick et al. (2017) assessed the performance of the bulk transfer models of turbulent heat fluxes over a mid-latitude glacier during one melting season. They showed good agreement between the observed and estimated heat fluxes, but found that this approach was sensitive to atmospheric conditions and roughness lengths. Schlögl et al. (2017) showed that the stability corrections used in the bulk transfer models need to be improved for large temperature gradients and wind speed. Radic et al. (2017) also found that the bulk transfer model overestimates the turbulent heat fluxes. Therefore, alternative ET models for snow-covered surfaces are desirable.

A new model, referred to hereafter as MEP-E snow model based on the theory of maximum entropy production (MEP; Wang et al., 2014), has been developed for simulating latent heat (water vapor) fluxes over snow and ice surfaces. The MEP theory as a selection criterion for non-equilibrium systems has been applied successfully in many fields (e.g., Dewar et al., 2006;Franklin et al., 2012;Lorenz et al., 2001;Malkus, 2003;Ozawa et al., 2001;Paltridge, 1978). The MEP principle applied to non-equilibrium thermodynamic systems offers an alternative approach to finding a solution by selecting the most likely partition of net radiation into evapotranspiration (ET) and heat flux among all possibilities allowed by the conservation of energy (Wang & Bras, 2011;Wang et al., 2014). Compared with other approaches, the MEP-E snow model predicts latent heat fluxes (sublimation) without using wind speed, surface roughness, and aerodynamic resistances in bulk flux formulae. One major advantage of the MEP-E snow model is that it requires only two input variables: net radiation and snow surface temperature, where the water vapor right above the snow (water/ice) surface is often assumed to be saturated. The thermal inertia of turbulent latent and sensible heat fluxes (not shown here), characterizing the boundary layer turbulent transport of water vapor and heat, are parameterized by implicitly taking into account the effect of wind speed, roughness, and aerodynamic resistance (Wang et al., 2010). More importantly, the MEP-E snow model always satisfies the conservation of energy. More details about the MEP-E snow model are given in Wang et al. (2014). The MEP-E snow model has been validated (Wang et al., 2014) at a full snow cover site during the period of snow accumulation. More tests are desirable to evaluate its performance under more general conditions of snow-vegetation cover. Note that the MEP models of soil evaporation (MEP-E v ) and canopy transpiration (MEP-T r ; Wang & Bras, 2011) have been extensively validated over homogeneous terrain (e.g., Shanafield et al., 2015;Wang et al., 2017). Hajji et al. (2018) recently generalized MEP models (MEP-E v and MEP-T r ) to estimate ET over heterogeneous surfaces with variable vegetation cover and water stress using a vegetation coefficient for improving the simulations of soil evaporation and canopy transpiration. Their analysis confirmed the effectiveness of the MEP model under conditions of zero to moderate water stress by introducing a soil-moisture-dependent water stress function.

To our knowledge, the physical process of ET over partially vegetated surfaces in the presence of seasonal snow cover is not fully understood. Moreover, the performance of the MEP model for estimating latent heat flux under the conditions when (soil) evaporation, transpiration, and sublimation may coexist has not been evaluated. It is well understood that snow accumulation and melting, as well as plant phenological cycles, play essential roles in water vapor transfer into the atmosphere (Wang et al., 2013). Both the energy and moisture regimes during the transition periods between the cold (snow) and warm (snowfree) seasons drive the water vapor transfer. The objective of this study is to develop a framework for the simulation of total water vapor flux over the lifecycle of a snowpack, including snow accumulation and snowmelt in the early growing seasons, and to evaluate its performance under various geographical and climatic conditions.

The paper is organized as follows: Section 2 briefly describes the MEP-ET model (Wang & Bras, 2011;Wang et al., 2014), highlighting its formulae for the cases of soil, canopy, and snow surfaces. Section 3 presents the hypotheses for two scenarios of snow conditions characterizing the transition from the cold to the warm season. Section 4 describes the study sites and input data. Section 5 presents the findings.

The MEP model provides a unique method of partitioning net radiation, R n , into surface heat fluxes (latent ET, sensible H and ground/snow heat flux Q) for various types of land covers (Wang & Bras, 2011; Wang et al., 2014). The MEP formulation of ET, H, and Q for soil, canopy, and snow surface is expressed as follows:

with the following surface energy balance equations:

where R n and R ns are the net radiation and net solar radiation, respectively, I s is the thermal inertia of the soil/snow material, and I 0 is the apparent thermal inertia of the air (see Equation 3 of Wang & Bras, 2011).

is the inverse of the Bowen ratio:

where σ is a dimensionless parameter as a function of surface temperature (T s (K)) and surface-specific humidity (q s (kg kg -1 )). In Equation 3, c p is the specific heat of the air at constant pressure (J kg -1 K -1 ), R v is the gas constant of water vapor (J kg -1 K -1 ), λ is the latent heat of vaporization of liquid water or sublimation of solid water (J kg -1 ),  is the ratio of the eddy diffusivities for water vapor and heat (taken as one here), and  s is the water stress factor representing the relative plant water availability defined in Hajji et al. (2018). Since the natural landscape is often covered with bare soil, canopy, and snow with time-varying proportions, the MEP formulae for the three types of land covers need to be used simultaneously.

The total ET consists of soil evaporation, canopy transpiration, and snow sublimation. Each component of ET varies with the biological and environmental conditions. For the case of coniferous forests located in the cold regions considered in this study, most plants are in dormancy and do not contribute to ET during the winter, while transpiration dominates during the summer when energy and water are abundant. Figure 1 illustrates snow and vegetation cover change during the winter-spring-summer transition period. According to previous observational studies of coniferous canopies, snow is the main local source of atmospheric water vapor during winter (Harding & Pomeroy, 1996;Nakai et al., 1999). The total surface water vapor flux into the atmosphere is expressed as

where  (0 or 1) is an indicator of snow sublimation (see Section 3.2), E snow , E v , and T r the MEP modeled snow sublimation, soil evaporation, and transpiration, respectively, f snow the fractional snow cover, and f veg the fractional canopy cover. In this study, f veg is parameterized following Wittich and Hansing (1995) as

where NDVI is the Normalized Difference Vegetation Index, and NDVI max and NDVI min are its values for dense vegetation and bare soil, respectively. The fractional snow cover may be parameterized as a nonlinear function of snow depth (Liston, 2004;Niu & Yang, 2007). During the snowmelt period, this parameterization tends to overestimate the snow fraction (Niu & Yang, 2007;Su et al., 2008). Therefore, a modified parameterization of snow fraction based on snow depth and snow density (Niu & Yang, 2007) is used in this study as

where d s is the snow depth (m), T snow the snow surface temperature, z 0 ( = 0.01 m) the surface roughness,    s,old and    s,new old and fresh snow density, and m an empirical coefficient. Niu and Yang (2007) test- ed Equation 6 using long-term (1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996) ground-based snow depth data from North America (Brown et al., 2003) and satellite-derived monthly f snow , with a focus on larger river basins. Using the same database, Su et al. (2008) m = 2.23. Note that during the snow accumulation period (T snow <0), f snow is assumed to be 1, since ET during this period is dominated by sublimation.

Variations of snowpack and vegetation cover strongly affect canopy transpiration (Betts, 2011), especially during the early growing season. Increasing net radiation due to declining albedo results in rising canopy temperature, which in turn leads to higher atmospheric evaporation demand in favor of canopy transpiration (Kelly & Goulden 2016;Liu et al., 2016;Monson et al., 2005;Wieser & Tausz, 2007;Winchell et al., 2016).

Numerous studies focusing on cold forested regions have shown that canopy transpiration and photosynthesis rates during transition from the dormant to active vegetation periods are strongly dependent on the temperature (Mellander et al., 2006;Monson et al., 2005). Cold-temperature-induced inhibitory effects on photosynthesis and transpiration in forest ecosystems have been well documented (Bergh & Linder, 1999;Liu et al., 2016;Mellander et al., 2006). For instance, Mellander et al. (2006) showed that low soil temperature during the spring-early summer reduced transpiration of Scots pines in Sweden using a coupled heat and mass transfer model for the soil-plant-atmosphere system (COUP model). Later, Mellander et al. (2008) suggested that air and soil temperatures must be considered when estimating the rate of gas exchange (transpiration and photosynthesis) of boreal environments. Repo et al. (2008) showed that frozen soils effectively blocked the water uptake and trunk sap flow (transpiration) of Scots pine saplings. Below ground water transfer is often limited by low soil water (liquid) content due to freezing. Low soil temperature reduces the soil and plant hydraulic conductance and water uptake (e.g., Kramer & Boyer, 1995). In early spring, low soil and air temperature reduce the water uptake, and hence transpiration and photosynthesis (Kozlowski et al., 1991). Mellander et al. (2004) and Wang et al. (2018) found that soil temperature below 8°C, which is common in spring in the northern boreal biome, restricts transpiration as a result of low stomatal conductance and, likely, lower root permeability. Bergh and Linder (1999) found that sap flow (transpiration) was greatly reduced when the ground was covered with snow and soil temperature was close to freezing point.

Considering the aforementioned phenomena, the MEP model needs to be configured for the beginning of the growing season. A recent study (Hajji et al., 2018) proposed an empirical coefficient in the MEP-T r model to account for soil water availability for transpiration during dry spells. To account for the effect of cold temperatures on transpiration, the following empirical function m(Tmin) is proposed in the MEP-T r model: (2007). Following Hajji et al. (2018),  in Equation 3is reformulated as

where all the variables are defined as in Equation 3.

HAJJI ET AL.

10.1029/2020JD033049

The isothermal (or ripe) condition (uniform 0°C snow temperature) is observed during snowmelt (e.g., DeWalle & Rango, 2008). Theoretically, the net radiative energy at the snow surface can be used for both melting and sublimation depending on, among other factors, the atmospheric vapor demand. During the snowmelt season in spring, net radiation is considered to be the main source of energy for melting. Numerous studies have attempted to quantify sublimation during snowmelt. For instance, Harding (1986) and Kuusisto (1986) have found that sublimation represents a small fraction of the snowpack energy budget during melting. Martinelli (1960) reported that sublimation accounted for only 2% of the snowpack ablation (sublimation + melt) in the Rocky Mountains. Likewise, van den Broeke et al. ( 2008), who investigated several sites in western Greenland, have found that sublimation during snowmelt was rather small (<10 W m -foot_0 ). Spring latent heat fluxes over snow surfaces are also reported to be limited (Lee, 2004;Link & Marks, 1999). Some studies have reported non-negligible sublimation during snowmelt. Beaty (1975) found that sublimation was responsible for 60% of the spring ablation in the White Mountains of California. Jackson and Prowse (2009) reported that sublimation was continuous during the melting phase with rates of about 0.4 mm d -1 in southern British Columbia. Stiegler et al. (2016) demonstrated that water loss through sublimation reached 8.6 mm during the entire spring snowmelt (17 days) at a wet and exposed site in northeastern Greenland. Schulz and de Jong (2004) showed that strong solar radiation and high air temperatures over semiarid regions supported high sublimation rates for long periods, provided that the snowpack remained cold and snowmelt did not dominate snow ablation. In the Mediterranean mountains, sublimation was reported at 20% of the total snowpack ablation (Jepsen et al., 2012). Zhou et al. (2012) studied sublimation in different stages of snow cover (the cumulative, stable, and melting stages) and found that the average daily sublimation during the melting stage was greater than that during the cumulative and stable stages. Overall, all these past studies suggest that the sublimation rates during snowmelt may vary depending on the geographical and meteorological conditions.

In this study, the total ET, including sublimation, over a seasonal snowpack is simulated using the MEP model according to Equations 1-8. As mentioned above, β is introduced to control the occurrence of sublimation during snowmelt periods (see Equation 4): sublimation is turned on when β = 1 and it is turned off when β = 0. The sensitivity of the MEP-ET model to β is evaluated by comparing the modeled water vapor fluxes with the field observations.

The performance of the MEP-ET model was evaluated using the following metrics: the Kling-Gupta efficiency (KGE; Gupta et al., 2009), the mean bias (MB) index, and the root mean square error (RMSE) as follows:

dicated by KGE values approaching 1, while values less than 0 indicate a model performance inferior to the mean observation ( obs ET ) at all-time steps. RMSE provides a measure of differences between the observed and simulated ET.

Eddy covariance (EC) observations over snow-covered forests have become increasingly available (e.g., Arck & Scherer, 2002;Marks et al., 2008;Molotch et al., 2007;Nakai et al., 1999;Parviainen & Pomeroy, 2000;Pomeroy & Granger, 1997) and are now commonly used in snow studies (Gryning et al., 2001;Harding & Pomeroy, 1996;Molotch et al., 2007;Nakai et al., 1999;Pomeroy & Essery, 1999;Reba et al., 2012;Sexstone et al., 2016;Turnipseed et al., 2002Turnipseed et al., , 2003)). In this analysis, FLUXNET (http://fluxnet.ornl.gov/) data were used to evaluate the MEP model for simulating ET over the snowpack's lifecycle. FLUXNET provides half-hourly EC fluxes and meteorological variables needed for our analyses. Eleven sites in Canada, Finland, Russia, Italy, Switzerland, and China (Figure 2) are selected in this study, one per country except for Canada, due to data availability. Six Canadian boreal forest sites were chosen across three provinces (Saskatchewan, Quebec, and Ontario).

The selected Fluxnet sites are from different biomes (Table 1): grassland (GRA) such as CN-Du2, IT-Tor and Ru-Tks sites, cropland (CRO), as FI-jok site and mixed (MF), and evergreen needleleaf (ENF) forests with diverse climatic conditions. For example, the Russian site (Ru-Tks) is characterized by a cold subarctic climate (Dfd) with annual mean temperature lower than -12°C and 235 snow cover days. The Chinese site (CN-Du2) has a monsoon humid continental climate (Dwb) with cold and dry winter. The climate of Canadian sites varies from semiarid subarctic in Saskatchewan (annual precipitation less than 400 mm and annual temperature close to 0°C) to humid subarctic in Quebec (annual precipitation greater than 900 mm and lower annual temperature; Table 1. Logistic difficulties of field experiments due to snow deposition on sensors and limited site accessibility during winter are responsible for data gaps. The test periods are carefully selected with minimum missing data for the analysis.

To assess the performance of the MEP-ET model for the lifecycle of the snowpack, three critical periods were selected (Figure 3): (1) a winter accumulation period with a growing snowpack when the snow temperature is below the freezing point (0°C); (2) a spring snowmelt period with an isothermal snowpack and above freezing air temperatures and elevated soil moisture caused by melting snow; and (3) a spring-summer veg-HAJJI ET AL. etation awakening period when snowmelt ends and the growing season begins. Note that the early stage of snow accumulation period when f snow varies from 0 to one is excluded in this study.

The CA-OJP and CA-Qcu sites have different seasonal cycles as shown in Figure 3. During the accumulation period, surface albedo reaches its maximum, then decreases as the snowpack melts to reach its annual minimum when snow vanishes. During the accumulation period, surface albedo is 0.9 at the CA-Qcu cleared forest site, 0.2 at the CA-OJP dense forest site, and 0.6 and 0.15, respectively, during snowmelt. At the cleared forest site, the ground may be completely covered with snow, while trees partially mask the snowpack below the canopy at the dense forested site. For the latter case, surface albedo is much lower as a result of the darker surface. The variability in snowpack depth for 2009 and 2010 at CA-Qcu is shown in Figure 3. The 2009 snowpack was deeper than in 2010; snowmelt also began and finished later than in 2010. A longer lasting snowpack increases albedo, leading to cooler near-surface temperatures. CA-OJP and CA-Qcu are not windy sites, where the mean winter wind speed was relatively low at 2.6 and 3.7 m s -1 at CA-OJP and CA-Qcu, respectively. Therefore, no major snow redistribution by wind is expected. Soil specific humidity (kg kg -1 ) Computed from closest to the surface air temperature and relative humidity measurements Leaf specific humidity (kg kg -1 ) Computed from air temperature and relative humidity measurements closest to the canopy top

Input Data Required to Run the MEP-ET Model and its Components radiation (R n ) data are needed for the MEP-E snow model. When snow temperature data were not available at the CA-Qcu and CA-Qfo sites, air temperatures at 1.6 and 1.5 m were used as a surrogate. The sensitivity of using air temperature as a surrogate for snow temperature in the simulation of sublimation by the MEP-E snow model was analyzed using field observations at the four sites where both snow and air temperature data are available. Note that the air temperature used in the MEP-E snow model was measured close to the ground (Table 1).

The MEP-T r and MEP-E v models require near-leaf/soil surface temperature and humidity data. Since they were often not available, observations closest to the canopy/soil surface were used instead. For example, since the canopy height at the CA-OJP site is 14 m, the leaf surface temperature and humidity were assumed equal to the air temperature and humidity averaged from two measurement heights (10 and 16 m). Soil temperatures measured at a 2-cm depth are used as the surrogate for soil surface temperature (T ss ). Soil-surface-specific humidity (q ss ) was taken as the air-specific humidity near the soil surface calculated from 2 m T ss and relative humidity (RH) measurements using the well-known Clausius-Clapeyron equation. Net radiation, soil moisture, and snow depth were directly measured at the study sites.

In addition to the above data, snow and vegetation fractional covers f snow, f veg in Equation 4 are required to estimate the total ET, especially once the melting process starts. However, with the exception of Canadian sites, f snow, f veg data are not available for the other sites (CH-Dav, Ru-Tks, IT-Tor, FI-jok, and CN-Du2) where the MEP model can only be evaluated for snow accumulation periods.

Figures 4 and 5 compare hourly MEP-ET water vapor fluxes with observations at the study sites during the snow accumulation period only (i.e., as long as the snow is not ripe). The statistical metrics describing the performance of the MEP-ET model are presented in Table 3. The results of the statistical metrics of some sites (CA-SJ3, CA-Qcu, IT-Tor, and Ru-Tks) are not presented due to low data quality.

Overall, MEP-ET fluxes are in close agreement with observations. KGE values vary from 0.50 to 0.76 MB and from 0.83 to 1.24 MB. The agreement tends to be less close at night times when sublimation is underestimated HAJJI ET AL. at some sites (e.g., CA-Qcu, IT-Tor, and Ru-Tks). This is arguably due to the measurement errors of EC fluxes under stable nocturnal conditions (Marks et al., 2008). Therefore, the nighttime data are excluded in the calculation of the metrics (Table 3, Figure 11). The observed and estimated daily mean sublimation rates at the CA-OJP site from February 15 to March 12, 2006 (26 days) are 0.17 , respectively. For the same period, much higher values have been obtained at the closer humid forest site CA-Gro, at 0.14 (max. 0.26 mm d -1 ) for the observed sublimation rate and 0.17 (max. 0.23 mm d -1 ). At cold and dry sites, such as Ru-Tks, the MEP-ET model accurately simulates the diminishing sublimation rates. Obviously, cold temperature limits sublimation during the winter months.

Low sublimation rates during wintertime should not be considered negligible because of its importance in determining the water and energy balance over cold regions (Liston & sturm, 2004;Svoma, 2016). For example, in the Gurbantunggut Desert, low winter precipitation results in the sublimation of 24% of the snowfall (Svoma, 2016). At dryer grassland sites, such as CN-Du2, the observed and estimated daily mean sublimation rates are 0.18 (max. 0.47) mm d -1 and 0.20 (max. 0.60) mm d -1 , respectively, for two winter months (January and February 2006). The observed and estimated sublimation rates at open sites (dry or humid) are always lower than those at closed forest sites, which contrasts with previous studies (Marks & Dozier, 1992;Jackson & Prowse, 2009) showing that ground sublimation from open sites is generally higher than for closed forested sites. In general, sublimation rates increase with the forest opening size, wind speed (increasing surface layer turbulence), and temperature (Bernier & Swanson, 1993;Schmidt et al., 1998). Equation 4) overestimates water vapor fluxes assuming that sublimation continues during snowmelt in the early growing season. Figure 7 compares the simulated versus observed hourly MEP-ET water vapor fluxes assuming sublimation during the snowmelt period (β = 1 in Equation 4) for spring 2006 at the CA-OJP site.

When the snow depth starts declining on day 75, the model predicts significant sublimation (>50 W m -2 ), which is inconsistent with the observations. Note also that transpiration starts when there is still ∼40 cm of snow on the ground, again leading to an overestimation of latent heat fluxes in the final stage of the snowmelt period, as well as in the early growing season.

HAJJI ET AL. 4) and no constraint on the beginning of growing season (Equation 3 is used instead of Equation 8) at the CA-OJP site.

Figure 3b shows that the atmospheric vapor pressure tends to be lower than that right above the snow surface during the snow accumulation period, which makes sublimation possible. Sharply increasing atmospheric vapor pressures tend to suppress sublimation at the beginning of the snowmelt period. For snow sublimation to take place, the saturation-specific humidity above the snow surface needs to exceed the air-specific humidity above. Hence, the sublimation rates should decrease with snowmelt. This finding is consistent with earlier studies (Herrero & Polo, 2016;Ohta et al., 1993;Suzuki et al., 1999). A recent study of latent heat flux at the snow surface of the Sierra Nevadas in Spain showed that sublimation decreases sharply when snowmelt occurs (Herrero & Polo, 2016). They reported that sublimation accounted for about 50% of wintertime ablation (February), but only for about 12% in April and 4% in May.

Figures 8 and9 show the MEP-ET water vapor flux with sublimation (β = 1 in Equation 4) and without sublimation (β = 0 during snowmelt period) compared with the observed latent heat flux at the four study sites. It is evident that the MEP-ET modeled latent heat flux with no sublimation agrees closely with the observed ET. The agreement is closer when the snow depth is higher as shown at the CA-Qfo and CA-Gro sites (Figure 8). This is due to the fact that the soil surface is less exposed when the snow depth is high. At these study sites, very short episodes of snowfall may occur during snowmelt. For example, snowfall was observed on the day of year 93-94-103-104 of year 2008 at the CA-Gro site, 96-104 of year 2006, and 96 of year 2007 at the CA-Qfo site. For these days, MEP-ET with sublimation (β = 1 in Equation 4) is consistent with the observed ET since sublimation occurs over fresh snow with sub-freezing snow temperatures. If the snow temperature measurements are sufficiently accurate, the MEP-ET model can simulate sublimation during snowfall when the snow surface temperature is below the freezing point. Figure 8 indicates that the MEP-ET modeled ET is always in close agreement with the observations as long as the snow surface temperature data are accurate. The above analysis provides strong evidence for supporting the hypothesis that sublimation diminishes during snowmelt.

The MEP-ET model is capable of capturing the behavior of vegetation when it awakens and starts to transpire. Figures 6 and7 show that the original MEP-ET overestimates water vapor flux not only during 4) versus the MEP-ET with no sublimation (β = 0 in Equation 4) compared with observed water vapor flux during snowmelt at the CA-Gro and CA-Qfo sites.

snowmelt (as discussed in the previous section) but also in the early stage of the growing season. The MEP-ET model, with the two proposed revisions, can consistently simulate the total ET for the case of persistent snow cover (Figures 4 and5) during the snowmelt and early spring dormant periods (Figure 6) under temperature stress conditions. Figure 12 presents a seasonal analysis of the original versus revised MEP-ET (boxplot) at the four study sites. The revised MEP-ET model, taking into account of sublimation and vegetation awakening, improves the ET estimation, especially for the snowmelt and canopy awakening months (March-May).

The partitioning of available energy in the MEP model is directly represented by the Bowen ratio (H/LE) according to Equation 3. Figure 13a, illustrating the estimated versus observed Bowen ratios over a 5-month period (January to May), clearly shows close agreement between the MEP and observed Bowen ratios. High Bowen ratios (>15) occurred in winter at some sites with cold temperatures and low latent heat fluxes. It has been reported that the Bowen ratio is expected to be much higher than one with substantial fluctuations when the air temperatures fall below 14°C (Andreas, 1989). Lower Bowen ratios, but still higher than those at the CA-Qcu site, are common at open sites with low air and surface temperatures and high albedos.

Differences between the estimated and observed Bowen ratios (Figure 13a) are more evident at some sites (CA-SJ3 and CA-Qcu) during the transition periods (April-May). This is in part caused by higher data uncertainties for the transition period, which lead to uncertainty in the Bowen ratio as a function of ( 2 / s s q T ) according to the MEP model. Close correspondence between the observed and estimated Bowen ratios and between the Bowen ratios and air temperature and wind speed (Figures 13b and13c) further confirm the performance of the revised MEP model. The MEP Bowen ratios tend to decrease with the air temperature. The highest Bowen ratios occurred at sub-freezing temperatures, consistent with previous studies. As winter progresses, latent heat fluxes increase with temperature and net radiation, leading to lower, but still greater than 1, Bowen ratios. As explained previously, canopy heating due to increasing sensible heat flux accelerates melting, while sublimation diminishes it. At the beginning of the growing season, the above-freezing temperature allows transpiration, but low (air) temperature limits the transpiration rate leading to a high Bowen ratio. This behavioral change in the Bowen ratio is well captured by the revised MEP model. It should be emphasized that the MEP model is able to reproduce the observed relationship between the Bowen ratio and wind speed, even though the wind speed is not an input parameter to the MEP model (Figure 13c). HAJJI ET AL.

This study tested and analyzed, for the first time, the capability of the MEP model for estimating water vapor fluxes over land surfaces with variable snow and vegetation cover during the winter-spring-summer transitions. The MEP-ET model performs well under these three critical periods characterizing the lifecycle of snowpacks: winter accumulation with growing snowpack, spring melting with isothermal snowpack, and spring-summer vegetation awakening when the growing season begins. During snow accumulation, the total water vapor loss is well captured by the MEP-ET model, at multiple sites and in consecutive years. A major finding of this study is that sublimation diminishes during snowmelt. The good performance of the MEP-ET model for seasonal snowpack results from parameterizing the effects of temperature stress on canopy transpiration and diminishing sublimation during snowmelt for heterogeneous land surfaces.