A snowpack has a profound effect on the hydrology and surface energy
conditions of an area through its effects on surface albedo and roughness and
its insulating properties. The modeling of a snowpack, soil water dynamics,
and the coupling of the snowpack and underlying soil layer has been widely
reported. However, the coupled liquid–vapor–air flow mechanisms considering
the snowpack effect have not been investigated in detail. In this study, we
incorporated the snowpack effect (Utah energy balance snowpack model, UEB) into a
common modeling framework (Simultaneous Transfer of Energy, Mass, and
Momentum in Unsaturated Soils with Freeze-Thaw, STEMMUS-FT), i.e.,
STEMMUS-UEB. It considers soil water and energy transfer physics with three
complexity levels (basic coupled, advanced coupled water and
heat transfer, and finally explicit consideration of airflow, termed
BCD, ACD, and ACD-air, respectively). We then utilized in situ observations
and numerical experiments to investigate the effect of snowpack on soil
moisture and heat transfer with the abovementioned model complexities.
Results indicated that the proposed model with snowpack can reproduce the
abrupt increase of surface albedo after precipitation events while this was
not the case for the model without snowpack. The BCD model tended to
overestimate the land surface latent heat flux (
In cold regions, the snowpack has a profound effect on hydrology and surface energy through its change of surface albedo, roughness, and insulating properties (Boone and Etchevers, 2001; Zhang, 2005). In contrast to rainfall, the melted snowfall enters the soil with a significant lag in time, and a large and sudden outflow or runoff may be produced because of the snowmelt effect. The heat-insulating property of snow cover also provides a buffer layer to reduce the magnitude of the underlying subsurface temperature variations and thus markedly affects the thickness of the active layer in cold regions. The effect of snow cover on the subsurface soils has been studied and reviewed (e.g., Zhang, 2005; Hrbáček et al., 2016). For instance, snow cover can act as an insulator between atmosphere and soil with its low thermal conductivity (Zhang, 2005; Hrbáček et al., 2016). The snowmelt functions as the energy sink via the absorption of heat due to phase change (Zhang, 2005). Yi et al. (2015) investigated the seasonal snow cover effect on the soil freezing and thawing process and its related carbon implications. Such studies mainly focus on the thermal effect of snowpack on the frozen soils. However, the effect of snowpack on the soil water and vapor transfer process is rarely reported (Hagedorn et al., 2007; Iwata et al., 2010; Domine et al., 2019).
Brief overview of current soil–snow modeling efforts.
Continued.
The abbreviations used in the table are as follows: HT_cond, heat conduction; Advc, advection; LH_phas, latent heat due to phase change; HT_Convect, convective heat due to liquid; SHP, soil physical process; Albedo_SNW_1A, snow albedo 1A, a function of snow age; Albedo_SNW_1B, snow albedo 1B, empirical function considering dry and wet states; Albedo_SNW_1C, snow albedo 1C, a function of extinction coefficient, grain size, and solar zenith angle; Albedo_SNW_2, snow albedo 2, a two-stream radiative transfer solution considering snow aging, solar zenith angle, optical parameters, and impurity; Albedo_SNW_3A, snow albedo 3A, prognostic snow albedo considering aging effect; Albedo_SNW_3B, snow albedo 3B, prognostic snow albedo considering aging effect and vegetation type dependent; Albedo_SNW_3C, snow albedo 3C, prognostic snow albedo considering aging and optical diameter; Albedo_SNW_3D, snow albedo 3D, prognostic snow albedo considering age and microstructure; Albedo_SNW_3E, snow albedo 3E, prognostic snow albedo considering aging effect and dry and wet states; Albedo_SNW_3F, snow albedo 3F, prognostic snow albedo considering aging effect and solar zenith angle; Albedo_SNW_4, snow albedo 4, diagnostic snow albedo considering snow aging, sleet and snowfall fraction, grain diameter, cloud fraction, and solar elevation effect; Density_SNW_1, snow density 1 relying on in situ measurements; Density_SNW_2A, snow density 2A, a function of air temperature; Density_SNW_2B, snow density 2B, a function of extinction coefficient and grain-size; Density_SNW_2C, snow density 2C, a function of old (densification), newly fallen (air temperature) snow pack density, and snow depth; Density_SNW_3, snow density 3, diagnostic density considering wet-bulb temperature; Density_SNW_4A, snow density 4A, prognostic density considering temperature, wind effect, snow compaction, and water and ice states; Density_SNW_4B, snow density 4B, prognostic density considering overburden and thermal metamorphisms; Density_SNW_4C, snow density 4C, prognostic snow density considering snow compaction and settling; Density_SNW_4D, snow density 4D, prognostic snow density considering snow compaction and wind-induced densification; Density_SNW_4E, snow density 4E, prognostic snow density considering snow compaction, settling, and vapor transfer; Density_SNW_4F, snow density 4F, prognostic density, a function of wind speed and air temperature; Density_SNW_4G, Snow density 4G, prognostic density, a function of stress state and microstructure; Density_SNW_4H, Snow density 4H, prognostic density considering snow temperature.
A great amount of effort has been made to better reproduce the snowpack characteristic and its effects in models. Initially, snowpack dynamics were expressed as a simple function of temperature. Nevertheless, these empirical relations have limited applications in complex climate conditions (Pimentel et al., 2015). Many physically based models for the mass and energy balance in the snowpack have been developed for their coupling with hydrological models or atmospheric models. Boone and Etchevers (2001) divided these snow models into three main categories: (i) simple force-restore schemes with the snow modeled as the composite snow–soil layer (Pitman et al., 1991; Douville et al., 1995; Yang et al., 1997) or a single explicit snow layer (Verseghy, 1991; Tarboton and Luce, 1996; Slater et al., 1998; Sud and Mocko, 1999; Dutra et al., 2010); (ii) detailed internal snow process schemes with multiple snow layers of fine vertical resolution (Jordan, 1991; Lehning et al., 1999; Vionnet et al., 2012; Leroux and Pomeroy, 2017); and (iii) intermediate-complexity schemes with physics from the detailed schemes but with a limited number of layers, which are intended for coupling with atmospheric models (e.g., Sun et al., 1999; Boone and Etchevers, 2001). The intercomparison results of the abovementioned snow models at an alpine site indicated that all three types of schemes are capable of representing the basic features of the snow cover over the 2-year period but behaved differently on shorter timescales. Furthermore, the Snow Model Intercomparison Project (SnowMIP) at two mountainous alpine sites revealed that the albedo parameterization was the major factor influencing the simulation of net shortwave radiation. Though this parameterization is independent of model complexity (Etchevers et al., 2004) it directly affects the snow simulation. SnowMIP2 evaluated 33 snowpack models across a wide range of hydrometeorological and forest canopy conditions. It identified the shortcomings of different snow models and highlighted the necessity of studying the separate contribution of individual components to the mass and energy balance of snowpack (Rutter et al., 2009). With the majority of research focused on the intercomparison of the snowpack models with various physical complexities, little attention has been paid to the treatment of the underlying soil physical processes (see the brief overview of current soil–snow modeling efforts in Table 1).
In current soil–snow modeling research, soil water and heat transfer are usually not fully coupled, and moreover the vapor flow and airflow are absent (Koren et al., 1999; Niu et al., 2011; Swenson et al., 2012). This may lead to the unrealistic interpretation of the underlying soil physical processes and the snowpack energy budgets (Su et al., 2013; Wang et al., 2017). Researchers have emphasized the need to consider the coupled soil water and heat transfer mechanisms (Scanlon and Milly, 1994; Bittelli et al., 2008; Zeng et al., 2009a, b; Yu et al., 2018a). As a consequence, dedicated efforts have been made to implement it in the recent updated models (e.g., Painter et al., 2016; Wang et al., 2017; Cuntz and Haverd, 2018). On the other hand, the role of the airflow has been reported as being important in many relevant studies, including retarding soil water infiltration (Touma and Vauclin, 1986; Prunty and Bell, 2007), enhancing surface evaporation after precipitation (Zeng et al., 2011a, b), enlarging the temperature difference between the upper and lower part of a permafrost talus slope (Wicky and Hauck, 2017), interacting with soil ice and vapor components, and enhancing the vapor transfer in frozen soils (Yu et al., 2018a, 2020c). However, to our knowledge, few soil–snow models have taken into account the soil–dry air transfer processes and moreover the multi-parameterization of the soil physical processes (from the basic coupled to the advanced coupled water and heat transfer processes and then to the explicit consideration of airflow), resulting in the lack of understanding on how and to what extent the complex soil physics affect the model interpretation of the snowpack effects.
In this paper, one of the widely used snowpack models (Utah energy balance snowpack model, UEB, Tarboton and Luce, 1996) was incorporated into a common soil modeling framework (Simultaneous Transfer of Energy, Mass and Momentum in Unsaturated Soils with Freeze-Thaw, STEMMUS-FT, Zeng et al., 2011a, b; Zeng and Su, 2013; Yu et al., 2018a). The new model is named STEMMUS-UEB and is configured with various levels of model complexity in terms of mass and energy transport physics. We utilized in situ observations and numerical experiments with STEMMUS-UEB to investigate the effect of snowpack on the underlying soil mass and energy transfer with different complexities of soil models. The description of the coupled soil–snow modeling framework STEMMUS-UEB and the model setup for this study are presented in Sect. 2. Section 3 verifies the proposed model and identifies the effect of snowpack on soil liquid–vapor fluxes. The uncertainties and limitations of this study and the applicability of the proposed model are discussed in Sect. 4.
This section first presents the coupling procedure of STEMMUS-FT and UEB model, followed by the detailed description of the two models and their successful applications. Then the used model configurations and two tested experimental sites in the Tibetan Plateau were elaborated. The Maqu case is for investigating the effect of snowpack on the underlying soil hydrothermal regimes. The Yakou case is for demonstrating the validity of the developed STEMMUS-UEB model in reproducing the snowpack dynamics (results were presented in Appendix B). In addition, the relationship between the snow cover properties and albedo was presented in Appendix B4, which confirmed the validity of using the albedo to identify the presence of snowpack and its lasting time.
The coupled process between the snowpack model (UEB) and the soil water
model (STEMMUS-FT) was illustrated in Fig. 1. The sequential coupling is
employed to couple the soil model with the current snowpack model. The role
of the snowpack is explicitly considered by altering the water and heat flow
of the underlying soil. The snowpack model takes the atmospheric forcing as
the input (precipitation, air temperature, wind speed and direction,
relative humidity, shortwave and longwave radiation) and solves the snowpack
energy and mass balance (Eqs. A8 and A9; subroutines: ALBEDO, PARTSNOW,
PREDICORR), which provides the melt water flux and heat flux as the surface
boundary conditions for the soil model STEMMUS-FT (subroutines:
h_sub and Enrgy_sub for the advanced coupled models and Diff_Moisture_Heat for the basic coupled model). The
soil–snow coupling variables are the snowmelt water flux
The overview of the coupled STEMMUS-FT and UEB model framework and
model structure. SFCC is soil freezing characteristic curve,
Main subroutines in STEMMUS-UEB.
Continued.
Note that
—
The detailed physically based two-phase flow soil model (STEMMUS) was first developed to investigate the underlying physics of soil water, vapor, and dry air transfer mechanisms and their interaction with the atmosphere (Zeng et al., 2011a, b; Zeng and Su, 2013). It is achieved by simultaneously solving the balance equations of soil mass, energy, and dry air in a fully coupled way. The mediation effect of vegetation on such interactions was recently incorporated via the root water uptake sub-module (Yu et al., 2016) and by coupling with the detailed soil and vegetation biogeochemical process (Wang et al., 2021; Yu et al., 2020a). It facilitates our understanding of the hydrothermal dynamics of respective components in the frozen soil medium (i.e., soil liquid water, water vapor, dry air, and ice) by implementing the freeze–thaw process (hereafter STEMMUS-FT, for applications in cold regions, Yu et al., 2018a, 2020c).
The frozen soil physics considered in STEMMUS-FT includes three parts: (i) the ice blocking effect on soil hydraulic conductivities (see Sect. S2.2.2 in the Supplement), (ii) the inclusion of ice effect in the calculation of soil thermal capacity and conductivity (see Sect. S2.2.8), and (iii) the exchange of latent heat flux during phase change periods. With the aid of Clausius–Clapeyron relation, which characterizes the phase transition between liquid and solid phase in the thermal equilibrium system, the soil water characteristic curve (e.g., van Genuchten, 1980) is then extended to consider the freezing temperature dependence, i.e., soil freezing characteristic curve (Hansson et al., 2004; Dall'Amico et al., 2011). The fraction of soil liquid–solid water at a given temperature was then calculated prognostically with the soil freezing characteristic curve. Soil hydraulic parameters were further used in the Mualem (1976) model to compute the soil hydraulic conductivity. The ice effect is considered by reducing the soil saturated hydraulic conductivity as a function of ice content (Yu et al., 2018a).
In response to minimize the potential model-comparison uncertainties from various model structures and to figure out which process matters, three levels of complexity of mass and heat transfer physics are made available in the current STEMMUS-FT modeling framework (Yu et al., 2020c). First, the 1D Richards equation and heat conduction were deployed in STEMMUS-FT to describe the isothermal water flow and heat flow (termed BCD). The BCD model considers the interaction of soil water and heat transfer implicitly via the parameterization of heat capacity, thermal conductivity, and the water phase change effect. The water flow is fully affected by soil temperature regimes in the advanced coupled water and heat transfer model (termed ACD model). The movement of water vapor, as the primary linkage between soil water and heat flow, is explicitly characterized. STEMMUS-FT further enables the simulation of temporal dynamics of three water phases (liquid, vapor, and ice), together with the soil dry air component (termed ACD-air model). The governing equations of liquid water flow, vapor flow, airflow, and heat flow were listed in Appendix A1 (see the more detailed model description in Zeng et al., 2011a, b; Zeng and Su, 2013; Yu et al., 2018a, 2020c).
The Utah energy balance snowpack model (UEB; Tarboton and Luce, 1996) is a
single-layer physically based snow accumulation and melt model. Two
precipitation types, i.e., rainfall and snowfall, are discriminated by their
dependence on air temperature. The snowpack is characterized using two
primary state variables, snow water equivalent (SWE), and the internal energy
UEB is recognized as one simple yet physically based snowmelt model. It captures the snow process well (e.g., diurnal variation of meltwater outflow rate, snow accumulation, and ablation; see the general overview of UEB model development and applications in Table S6.3). It requires little effort in parameter calibration and can be easily transferable and applicable to various locations (e.g., Gardiner et al., 1998; Schulz and de Jong, 2004; Watson et al., 2006; Sultana et al., 2014; Pimentel et al., 2015; Gichamo and Tarboton, 2019), especially for data-scarce regions like the Tibetan Plateau. We thus selected the original parsimonious UEB (Tarboton and Luce, 1996) as the snow module to be coupled with the soil module (STEMMUS-FT).
On the basis of the aforementioned STEMMUS-UEB coupling framework, the various complexities of vadose zone physics were further implemented as three alternative model versions. First, the soil ice effect on soil hydraulic and thermal properties and the heat flow due to the water phase change were taken into account, while the water and heat transfer is not coupled in STEMMUS-FT and is termed the BCD model. Second, the STEMMUS-FT with the fully coupled water and heat transfer physics (i.e., water vapor flow and thermal effect on water flow) was applied and termed the ACD model. Lastly, on top of the ACD model, the air pressure was independently considered as a state variable (therefore, the airflow) and termed the ACD-air model. With the abovementioned model versions (STEMMUS-FT_Snow), taking into account the no-snow scenarios (STEMMUS-FT_No-Snow), Table 3 lists the configurations of all six designed numerical experiments. The model parameters used for all simulations for the tested experimental site are listed in Table S6.2.
Numerical experiments with various mass and energy transfer schemes with and without explicit consideration of snow cover (Eqs. A1–A7 are listed in Appendix A1; Eqs. (A8)–(A9) are listed in Appendix A2).
Maqu station, equipped with a catchment-scale soil moisture and soil
temperature (SMST) monitoring network and micro-meteorological observing
system, is situated on the northeastern edge of the Tibetan Plateau (Su et
al., 2011; Dente et al., 2012; Zeng et al., 2016). According to the updated
Köppen–Geiger climate classification system, it can be characterized as
a cold climate with dry winter and warm summer. The annual mean
precipitation is about 620 mm, and the annual average potential evaporation is about
1353.4 mm. Precipitation in Maqu is uneven over the year, with most of the
precipitation events occurring from May to October and little
precipitation or snowfall during the wintertime. The average annual air
temperature is 1.2
The Maqu SMST monitoring network spans an area of approximately 40 km
Yakou super snow station (
The integrated hydrometeorological, snow cover, and frozen ground data were published and available from the Cold and Arid Regions Science Data Center at Lanzhou (Che et al., 2019; Li et al., 2019; Li, 2019). The meteorological data (air temperature, wind speed, precipitation, downward shortwave and longwave radiation, and relative humidity) were recorded by the automatic meteorological station (AMS). In situ measurements of snow cover properties (snow depth and snow water equivalent) were obtained using the state-of-the-art instruments (SR50A and GammaMONitor, Campbell Scientific, USA). Soil moisture profiled at 4, 10, 20, 40, 80, 120, and 160 cm soil depth was measured using ECH2O-5 probes (METER Group, Inc., USA). In addition to the seven soil depths, the surface soil temperature (0 cm) was also recorded using the Avalon AV-10T sensors (Avalon Scientific, Inc., USA). The eddy covariance system was equipped at the Yakou site for measuring land surface turbulent fluxes. The dataset from 1 September to 31 December 2016 was used to validate the model performance in mimicking the dynamics of snow water equivalent, soil hydrothermal regimes, and land surface evaporation. The calibrated soil hydraulic and snow cover properties were listed in the Supplement in Table S6.2.
The time series of surface albedo, calculated as the ratio of upwelling shortwave radiation to the downwelling shortwave radiation and estimated using BCD, ACD, and ACD-air models, is shown in Fig. 2 together with precipitation. As the snowpack has a higher albedo than the underlying surface (e.g., soil, vegetation) compared to the observations, models without snow module presented a relatively flat variation of daily average surface albedo and lacked the response to the winter precipitation events (Fig. 2, Table 4). With the snow module, STEMMUS-UEB models can mostly capture the abrupt increase of surface albedo after winter precipitation events. The mismatches in terms of the magnitude or absence of increased albedo after precipitation events indicated that the model tended to underestimate the albedo dynamics. The shallow snowfall events might be not well captured by the model (see Sect. 4.1). Three model versions (BCD-Snow, ACD-Snow, and ACD-air-Snow) produced similar fluctuations regarding the presence of snow cover with slight differences in terms of the magnitude of albedo.
Time series of observed and model simulated daily average albedo
using
Comparative statistics values of various model versions for snow
albedo,
Note that BIAS
The observed spatial and temporal dynamics of soil temperature from five
soil layers were used to verify the performance of different models (Fig. 3).
The initial soil temperature state can be characterized as the warm bottom
and cool surface soil layers (based on in situ observations). The freezing
front (indicated by the zero-degree isothermal line, ZDIL) developed
downwards rapidly until the 70th day after 1 December 2015, when it reached
its maximum depth. Following this, the freezing front stabilized as an offset effect
of latent heat release (termed the zero-curtain effect). Such influence can be
sustained until all the available water to that layer is frozen, at which
point the latent heat effect is negligible compared to the heat conduction.
At shallower layers, the atmospheric forcing dominates the fluctuation of
thermal states. The isothermal lines (e.g.,
The spatial and temporal dynamics of observed
The spatial and temporal dynamics of observed
Figure 4 shows the spatial and temporal dynamics of observed and simulated
soil water content in the liquid phase (SWCL). The SWCL of active layers
depends to a large extent on the soil freezing and thawing status. Soil is
relatively wet at soil layers of 10–60 cm for the starting period. Its
temporal development was disrupted by the presence of soil ice and tended to
increase wetness during the thawing period. A relatively dry zone (
Figure 5 shows the comparison of time series of observed and model-simulated
surface cumulative latent heat flux using three models with and without
consideration of the snow module. Considerable overestimation of latent heat
flux was produced by the BCD-Snow model: 121.79 % more than was observed.
Such overestimations were largely reduced by ACD and ACD-air models. There
is a slight underestimation of cumulative latent heat flux in the ACD-Snow and
ACD-air-Snow models, with values of
Time series of observed and model simulated surface cumulative
latent heat flux (
To further elaborate the effect of snowpack on
Diurnal dynamics of the observed and simulated latent heat flux during the
rapid freezing period with the occurrence of precipitation events, from
10th to 14th days after 1 December 2015, are shown as Fig. 6a, b,
and c. Compared to the observations, the diurnal variations of latent heat
flux were captured by the proposed model with various levels of
complexities. Performance of BCD, ACD, and ACD-air models in simulating
Observed and model simulated latent heat flux using
The overestimation of
During the thawing period, the diurnal variations of
Observed and model simulated latent heat flux using
For the ACD model, the difference in latent heat flux between snow and
no-snow simulations was noticeable 2 d after precipitation. The larger
values of
During the freezing period, the soil water vapor rather than the liquid water flux dominated the surface mass transfer process. Missing the description of the vapor diffusion process hindered the BCD models ability to realistically depict the decomposition of surface mass transfer dynamics (Fig. 8a and b).
Model-simulated latent heat flux and surface soil (0.1 cm) thermal
and isothermal liquid water and vapor fluxes (
There is a visible diurnal variation of thermal vapor flux
During the thawing period, a certain amount of upward liquid water flux was
produced by the BCD model, supplying the water to the topsoil and evaporate
into the atmosphere (Fig. 9a and b). Compared to the isothermal liquid flux
Model-simulated latent heat flux and surface soil (0.1 cm) thermal
and isothermal liquid water and vapor fluxes (
For the ACD model, the diurnal variation of thermal vapor flux
Compared to the ACD-No-Snow simulations, the upward thermal vapor flux
After a winter precipitation event, land surface albedo increases considerably (Fig. 2), indicating the presence of the snowpack. However, such snowfall events were episodic with small magnitudes (similar to those in Li et al., 2017), which means that they are difficult to capture well. Such difficulties can be partially attributed to the inherent uncertainties in precipitation measurements (both the precipitation amount and types). Due to the spatial variability of precipitation, the accurate observation of winter precipitation has proven to be a challenge, especially during windy winters (Barrere et al., 2017; Pan et al., 2017). It is necessary to have more snowpack-relevant measurements (e.g., the high-resolution measurements of the spatiotemporal field of wind speed, precipitation, and snowpack variations) to understand the dynamics of snowpack and its effect on energy and water fluxes. Furthermore, the temporal resolution of precipitation measurements adopted in this study is relatively coarse (3 h). In the current precipitation partition parameterization, the amount of snowfall was determined as a function of precipitation and air temperature thresholds. Given the coarse temporal resolution of precipitation measurements, the model may produce a time shift of snowfall events or even the misidentification of snowfall. The simple relation between the air temperature and precipitation types may be not suitable for this region because air temperature is not the best indicator of precipitation types, as argued by Ding et al. (2014). Other factors, i.e., relative humidity, surface elevation, and wet-bulb temperature, are also very relevant and should be taken into account for the discrimination of precipitation types. The other uncertainty lies in the representation of the snow process. For example, the wind blow effect and canopy snow interception, which have been recognized as important to the accurate simulation of snowpack dynamics (Mahat and Tarboton, 2014), are not taken into account in detail. Last but not least, the interpretation of surface albedo dynamics needs to be adapted to the specific site, especially regarding the shallow snow situations (Ueno et al., 2007, 2012; Ding et al., 2017; Wang et al., 2017). The albedo of the underlying surface should also be properly accommodated to this Tibetan meadow system. Regardless of the aforementioned uncertainties, our proposed model was capable of capturing the surface albedo variations with precipitation (Fig. 2) and can be seen as acceptable for analyzing snow cover effects in such a harsh environment.
In contrast to precipitation water from rainfall, precipitation water from snowfall enters the soil considerably lagged in time due to the water storage by snow cover (You et al., 2019). With the snow module, precipitation was partitioned into rainfall and snowfall. Part of the snowfall evaporated into the atmosphere as sublimation, and the other part, together with the rainfall, infiltrated into the underlying soil. It resulted in the delay of incoming water to the soil with a lower amount compared to that without consideration of the snow module. This amount of incoming water increased the evaporation after precipitation (Figs. 6 and 7). The other source for the enhanced evaporation flux after precipitation is snow sublimation, which is absent from the model without the snow module. Sublimation occurs readily under certain weather conditions (e.g., with freezing temperatures, enough energy). It can be more active in regions with low relative humidity, low air pressure, and dry winds. Such an amount of sublimation has been reported as being important from the perspective of climate and hydrology (e.g., Strasser et al., 2008; Jambon-Puillet et al., 2018), especially in high-altitude regions with low air pressure. During the freezing period, the evaporation enhancement can be also sourced from the sublimation of surface ice. The amount of the ice sublimation appeared to decrease during the freezing period in the presence of a transient snowpack (e.g., Fig. 8c vs. Fig. 8d). This is consistent with the results of Hagedorn et al. (2007), who investigated the effect of snow cover on the mass balance of ground ice with an artificially continuous annual snow cover. According to their results, the snow cover enhanced the vapor transfer into the soil and thus reduced the long-term ice sublimation. The relative contribution of increased surface soil moisture, snow sublimation, and surface ice sublimation to the enhanced evaporation is dependent on the pre-precipitation soil moisture and temperature states, air temperature, and the time and magnitude of precipitation events. Under the conditions of the low pre-precipitation SWCL with a freezing soil temperature (e.g., Fig. 8e, 11th vs. 12th day after 1 December), the precipitation falls on the surface as snowfall and rainfall (most freezes as ice). The sublimation from surface ice can contribute to most of the total mass transfer (e.g., Fig. 8e, 11th day after 1 December). If the soil temperature rises above the freezing temperature, there will be no sublimation of surface ice, in terms of contributing to the enhanced evaporation (e.g., Fig. 9e, 102nd day after 1 December).
The model with different complexities of soil mass and energy transfer physics behaves differently in response to the winter precipitation events. During the freezing period, there is no significant difference in soil moisture simulated using the BCD models with and without the snow module. The precipitation water freezes at the soil surface, which cannot be transferred downwards with the BCD model physics. The sublimation, from either the snow or the surface ice, contributes to the precipitation-enhanced evaporation for the BCD model. As with vapor flow, the surface ice increases the soil moisture at lower layers via the downward isothermal vapor flux (Fig. 8). The surface ice sublimation and increased moisture-induced soil evaporation enhancement can be identified from the ACD model simulation. The role of airflow was negligible for the mass transfer during the freezing period.
When it comes to the thawing period, the BCD model produced a certain amount of liquid water flow, contributing considerably to the mass transfer. The obvious fluctuation of SWCL was noticed due to the thawing water and precipitation event. The main source for the increased evaporation was interpreted as isothermal liquid water flow, while for the ACD model the situation becomes more complex. Thawing surface ice and snowmelt water may coexist at the soil surface, resulting in different soil moisture response to precipitation events. The ice sublimation, snow sublimation, and increased soil moisture contribute to the evaporation enhancement after precipitation. When considering airflow, dry air interacts with soil ice and liquid and vapor water in soil pores (Yu et al., 2018a) and alters the soil moisture state. It thus considerably changes the relative contribution of each component to the mass transfer (Fig. 9).
With the aim to investigate the hydrothermal effect of the snowpack on the
underlying soil system, we developed the integrated process-based
soil–snow–atmosphere model, STEMMUS-UEB v1.0.0, which is based on the easily
transferable and physically based description of the snowpack process and
the detailed interpretation of the soil physical process with various
complexities. From STEMMUS-UEB simulations, snowpack affects not only the
soil surface conditions (surface ice and SWCL) and energy-related states
(albedo, latent heat flux) but also the transfer patterns of subsurface soil
liquid and vapor flow. STEMMUS-FT model can mostly capture the abrupt increase
of surface albedo after winter precipitation events with consideration of
the snow module. There is a significant overestimation of cumulative surface
latent heat flux by the BCD model. The ACD and ACD-air models produce a slight
underestimation of cumulative
Three mechanisms, surface ice sublimation, snow sublimation, and increased soil moisture, can contribute to enhanced latent heat flux after winter precipitation events. The relative role of each mechanism in the total mass transfer can be affected by the time and magnitude of precipitation and pre-precipitation soil moisture and temperature states (see Sect. 4.3). The simple BCD model cannot provide a realistic partitioning of mass transfer. The ACD model, which takes into consideration vapor diffusion and thermal effect on water flow and snowpack, can produce a reasonable analysis of the relative contributions of different water flux components. When considering airflow, the relative contribution of each component to the mass transfer was substantially altered during the thawing period. Further work will take into account the thermal interactive effects between snowpack and the underlying soil, which explicitly considers the convective and conductive heat fluxes and the solar radiation attenuation due to the snowpack. Such work will inevitably enhance our confidence in interpreting the underlying mechanisms and physically elaborating on the role of snowpack in cold regions.
The Richard equation, which describes the water flow under gravity and
capillary forces in isothermal conditions, is solved for variably saturated
soils.
The heat conservation equation, considering the latent heat due to water
phase change, can be expressed as follows:
For the coupled water and heat transfer physics, the liquid water flow is
non-isothermal and affected by soil temperature regimes. The movement of
water vapor, as the linkage between soil water and heat flow, is explicitly
characterized. With modifications made by Milly (1982), the extended version
of Richards (1931) equation with consideration of the liquid and vapor flow
is written as follows:
On the basis of the work of De Vries (1958) and Hansson et al. (2004), the heat
transport function in frozen soils, considering the fully coupled water and
heat transport physics, can be expressed as follows:
In STEMMUS-FT, the temporal dynamics of three phases of water (liquid, vapor
and ice), together with the soil dry air component are explicitly presented
and simultaneously solved by spatially discretizing the corresponding
governing equations of liquid water flow, vapor flow, and airflow.
STEMMUS-FT takes into account different heat transfer mechanisms, including
heat conduction (
The increase or decrease of snow water equivalence with time equals the
difference of income and outgoing water flux:
The energy balance of snowpack can be expressed as follows:
Equations (8) and (9) form a coupled set of first-order, nonlinear ordinary differential equations. The Euler predictor–corrector approach was employed in the UEB model to solve the initial value problems of these equations (Tarboton and Luce, 1996).
Instead of the constant bare soil albedo in the original UEB model, the bare
soil albedo is expressed as a decreasing linear function of soil moisture in
STEMMUS-UEB.
The calculation of vegetation albedo is developed to capture the essential
features of a two-stream approximation model using an asymptotic equation. It
approaches the underlying surface albedo
The bulk snow-free surface albedo, averaged between bare-ground albedo and
vegetation albedo, is written as follows:
According to Dickinson et al. (1993), snow albedo can be expressed as a
function of snow surface age and solar illumination angle. The snow surface
age, which is dependent on snow surface temperature and snowfall, is updated
with each time step in UEB. Visible and near-infrared bands are separately
treated when calculating reflectance and are further averaged as the
albedo with modifications of illumination angle and snow age. The
reflectance in the visible and near-infrared bands can be written as follows:
where
The reflectance of radiation with illumination angle (measured relative to
the surface normal) is computed as follows:
When the snowpack is shallow (depth
STEMMUS-UEB can reproduce the dynamics of snow water equivalent (Fig. B1). The discrepancies mainly happened under conditions with lower snow water equivalent. These intermittent shallow snowpack processes are difficult to capture well due to the drifting snow effect and temporal and complex ground heat conditions, and they require both high-quality observations and advanced snowpack models.
Compared to the observations, surface evaporation was underestimated by the model with no snow module during the snowfall periods (Fig. B2). Models with snow module, however, produced a generally good agreement but with overestimations and underestimations, which corresponds to the mismatches in the snow water equivalent results. When the snow water equivalent is overestimated, snowpack sublimation and surface evaporation were overestimated.
Compared to the model without the snow module, the model with the snow module produced a better correlation with the measured daily surface evaporation (Fig. B3). Surface evaporation was underestimated by the model without the snow module and slightly overestimated by the model with snow module.
Models both with and without the snow module can reproduce the soil moisture dynamics in terms of their response to precipitation events (Fig. B4). Soil moisture was underestimated by the model without the snow module due to the lower amount of incoming water flux. Such underestimation was damped as the soil depth increases. Models with the snow module gain more incoming water (snowmelt water), and thus the underestimation of soil moisture was alleviated.
The dynamics of soil temperature were reproduced well by models both with and without the snow module (Fig. B5). There is no significant difference between soil temperature simulations of models with and without the snow module.
There is a good correlation between the snow depth and surface albedo (Fig. B6). Figure B7 shows that surface albedo variations correspond well to the dynamics of the snow cover properties. This demonstrated that surface albedo is a reliable indicator to identify the presence of the snowpack and its influencing periods. Three example periods were selected to illustrate the validity of using the indirect method (albedo variation and ancillary meteorological data, i.e., air temperature, and precipitation) to define the presence and lasting time of the snowpack. Results indicated that the snowpack duration was successfully characterized using the indirect method (results were shown in Table S6.4 in the Supplement).
Time series of the observed and estimated snow water equivalent using the developed STEMMUS-UEB model.
Intercomparison of the observed and estimated surface evaporation using the model with and without the snow module.
Measured and estimated daily surface evaporation using the model
with and without snow module (
Observed and estimated soil moisture at various soil layers using the model with and without the snow module.
Observed and estimated soil temperature at various soil layers using the model with and without the snow module.
Scatterplot of snow depth and albedo (Yakou station, 2014–2017).
Time series of the snow depth, snow water equivalent (SWE), and albedo (Yakou station).
Notation.
Continued.
Continued.
The coupled soil–snow model (STEMMUS-UEB v1.0.0) with three levels of
complexity of soil water and heat transfer physics was developed based on
the STEMMUS-FT (Simultaneous Transfer of Energy, Momentum and Mass in
Unsaturated Soils with Freeze and Thaw) and UEB (Utah energy balance) models.
The original STEMMUS source code is available from the GitHub website via
The supplement related to this article is available online at:
ZS, YZ, and LY designed and conceptualized this study. YZ and ZS provided the original version of STEMMUS model code and supervised the further modeling development. LY developed the STEMMUS-UEB model coupling framework with contributions from YZ. LY and YZ prepared the original draft of the paper. LY, YZ, and ZS all contributed to the reviewing and editing of the final paper.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors thank the editors and referees very much for their constructive comments and suggestions for improving the manuscript.
This research has been supported by the National Natural Science Foundation of China (grant no. 41971033) and the Fundamental Research Funds for the Central Universities (CHD; grant no. 300102298307).
This paper was edited by Heiko Goelzer and reviewed by three anonymous referees.