Subgrid snow cover is one of the key parameters in global land models since snow cover has large impacts on the surface energy and moisture budgets, and hence the surface temperature. In this study, the Subgrid Snow Distribution (SSNOWD) snow cover parameterization was incorporated into the Minimal Advanced Treatments of Surface Interaction and Runoff (MATSIRO) land surface model. SSNOWD assumes that the subgrid snow water equivalent (SWE) distribution follows a lognormal distribution function, and its parameters are physically derived from geoclimatic information. Two 29-yr global offline simulations, with and without SSNOWD, were performed while forced with the Japanese 25-yr Reanalysis (JRA-25) dataset combined with an observed precipitation dataset. The simulated spatial patterns of mean monthly snow cover fraction were compared with satellite-based Moderate Resolution Imaging Spectroradiometer (MODIS) observations. The snow cover fraction was improved by the inclusion of SSNOWD, particularly for the accumulation season and/or regions with relatively small amounts of snowfall; snow cover fraction was typically underestimated in the simulation without SSNOWD. In the Northern Hemisphere, the daily snow-covered area was validated using Interactive Multisensor Snow and Ice Mapping System (IMS) snow analysis datasets. In the simulation with SSNOWD, snow-covered area largely agreed with the IMS snow analysis and the seasonal cycle in the Northern Hemisphere was improved. This was because SSNOWD formulates the snow cover fraction differently for the accumulation season and ablation season, and represents the hysteresis of the snow cover fraction between different seasons. The effects of including SSNOWD on hydrological properties and snow mass were also examined.
Seasonal snow cover is a key variable in the global climate system. For example, snow albedo feedback is important for climate change in heavily populated Northern Hemisphere extratropical landmasses, and its strength in the Coupled Model Intercomparison Project phase 3 and 5 (CMIP3 and CMIP5) models exhibits a large spread (Hall and Qu 2006; Qu and Hall 2014). Seasonal snow cover also plays an important role in the hydrological cycle. In Arctic rivers, changes in the amounts and timing of discharge (i.e., freshwater to the Arctic Ocean) have been documented (e.g., Peterson et al. 2002), and snow cover is one of the key processes regulating seasonal streamflow fluctuations (Tan et al. 2011). Runoff from mountain snow packs contributes to seasonal streamflow in conjunction with glaciers (Immerzeel et al. 2010). Considering the roles snow plays in Earth system processes, realistic representation of snow in climate and hydrological models is crucial for atmosphere–land interaction studies, quantifying hydrological changes at high latitudes, and water resource assessment with models. However, snow modeling schemes still contain considerable uncertainties, as highlighted by recent studies that examined CMIP5 snow cover outputs and found some discrepancies between the observations and models (Derksen and Brown 2012; Brutel-Vuilmet et al. 2013).
In the discussions that follow, the subgrid snow cover fraction is defined as the ratio of the snow-covered area in a grid cell to the total area of that grid cell. Large-scale land surface models usually diagnose the snow cover fraction because the presence or absence of snow cover has a large effect on the amount of energy absorbed by land. Some models use the snow cover fraction to weight the snow-covered and snow-free albedos linearly, and apply the average albedo to a single snow-covered energy balance computation. Other models calculate the surface fluxes for the snow-covered and snow-free areas, and use the snow cover fraction to linearly weight the surface fluxes. Liston (2004) showed that the latter procedure was appropriate because the energy balances over snow-covered and snow-free areas were not identical. The snow cover fraction has been treated relatively simply in global and regional models so far. It has been diagnosed as a simple function of snow depth (Dutra et al. 2010; Best et al. 2011), snow water equivalent (SWE; Takata et al. 2003), snow depth and roughness length (Yang et al. 1997; Best et al. 2011), and SWE and subgrid orography (Roesch et al. 2001). The detail review of snow cover parameterization in GCMs can be found in previous studies (Roesch et al. 2001; Essery 2008). These studies assumed that the relationship between snow cover fraction and snow depth or SWE did not vary with the season.
Several studies have assessed subgrid snow cover fraction parameterizations in land surface models (e.g., Roesch and Roeckner 2006; Niu and Yang 2007). For example, Niu and Yang (2007) analyzed the observed snow cover, snow depth, and SWE over North America, and presented an empirical representation between snow cover fraction and snow depth for their North American study domain. They showed hysteresis in the snow cover fraction with season, and suggested a relationship that accounted for the variation in the snow cover fraction with snow depth. They used the variation in snow density and a melting factor that determined the curves in the melting season and was adjustable depending on the scale. Liston (2004) developed the global Subgrid Snow Distribution (SSNOWD) model and showed that premelt snow depth distributions were largely responsible for the mosaic of snow-covered and snow-free area that evolves as the snow melts. SSNOWD has the potential to improve the representation of the snow cover fraction in global models, including regions without sufficient observations. It may also allow simulations for different climate conditions from those at present because it considers the physical processes that result in patchy, subgrid-scale snow cover.
In the present study, we tried to improve the representation of the snow cover fraction in the Minimal Advanced Treatments of Surface Interaction and Runoff (MATSIRO; Takata et al. 2003) land surface model. As part of other studies, MATSIRO has been coupled with a general circulation model: the Model for Interdisciplinary Research on Climate version 5 (MIROC5; Watanabe et al. 2010). We incorporated SSNOWD into MATSIRO because SSNOWD has the abovementioned advantages and the formulation of MATSIRO matches SSNOWD; surface energy balances are calculated separately on snow-covered and snow-free portions of a grid cell, and grid average snowfall and snowmelt are available for SSNOWD. By incorporating SSNOWD, we expected to be able to represent the realistic relationship between SWE and the snow cover fraction. This relationship varies according to the region and season. Improvements in the surface water and energy budgets are also expected as a result of improved modeling of the snow cover fraction. Liston (2004) developed SSNOWD, incorporated it into a regional climate model, and evaluated the effects of the snow cover fraction on the surface fluxes and 2-m air temperatures in North America. However, long-term global simulations and validations using observations have not been performed. The aims of this paper are 1) to present the global coupling of SSNOWD with MATSIRO, 2) to validate the simulations in standalone mode using multiple satellite-based observation products, and 3) to evaluate the effects of the snow cover fraction on hydrological properties and characteristics.
In the following sections, we present two model runs: MATSIRO with the standard settings of MIROC5 (referred to as MAT5), and MATSIRO with SSNOWD. In section 2, the MATSIRO and SSNOWD models are described. Section 3 describes the forcing and boundary data, parameters, and experimental design. Section 4 describes the results and validations. Discussion of improvement in a parameterization for snow cover fraction and future directions is presented in section 5. A summary and conclusions are provided in section 6.
2. Model description
a. Snow scheme of MATSIRO
The MATSIRO land surface model was originally developed for climate studies at global and regional scales. It has also been used as a macroscale hydrological model in standalone mode (e.g., Hirabayashi et al. 2005). The latest version of MATSIRO consists of six soil layers (14 m in total), up to three snow layers, and a single canopy layer. It predicts the temperature and water amount in the canopy, soil, and snow. To account for multiple land uses within one grid cell, a tile scheme is adopted. All diagnostic and prognostic variables, including snow, are calculated in each tile and averaged over the grid cell weighted by its areal fraction. The surface fluxes are calculated in the snow-covered and snow-free portions of each tile and averaged with weighting by the snow cover fraction, following the method of Liston (2004). The relationship between the SWE and snow cover fraction is shown in Fig. 1. The equations of the MATSIRO snow scheme are described in the appendix.
b. SSNOWD model
To simulate the snow cover fraction in an advanced way, we incorporated SSNOWD into MATSIRO. SSNOWD was developed to be used in the studies of the land–atmosphere interaction and feedbacks in regional and global weather, climate, and hydrological models. SSNOWD uses a lognormal distribution function for the subgrid SWE distribution, which was developed based on previous studies that analyzed observed snow depths (e.g., Faria et al. 2000). The model details are described in what follows, and the equations are described in the appendix. In SSNOWD, snow depth and SWE are used interchangeably, with the assumption that the bulk density, which is a constant in our land surface model, is known and can be used to convert from one to the other.
SSNOWD formulates the snow cover fraction for accumulation and ablation seasons separately. The accumulation season starts when the net solid water input to the surface (i.e., the sum of snowfall, freezing of rainfall, and refreezing of snowmelt minus the sum of snowmelt and sublimation from snow) is positive for a given time step. Then, when any net snowmelt occurs (i.e., the net solid water input to the surface is negative), it switches to the melting season. If new snow accumulation occurs in the melting season, there are two options. The first option is to assume that the new snow falls over the entire grid cell and that the accumulated snowfall is equal to the new snow plus the cell-average snow depth at the previous time step. The second option is to assume that the new snow decreases the accumulated melt depth. For this study, we chose the second option, following Liston (2004), except for the special case of grid cells with perennial snowpack. Usually, if the new snow was greater than the accumulated snowmelt, the melting season was switched to the accumulation season. SSNOWD was originally developed for parameterizing the seasonal snow cover fraction, and the melting season ended when the snowpack disappeared. To apply SSNOWD to global simulations, we needed to set the timing of when the melting season changed to the accumulation season for perennial snow. In the special case of grid cells with perennial snow, we assume that this change occurred on the first day after 1 August for the Northern Hemisphere and 1 February for the Southern Hemisphere that meets the following conditions: snowfall occurred and the net solid water input for the perennial snowpack was positive in the same time step. On that day, we took the first option and the melting season was reset to the accumulation season. The detailed equations of SSNOW can be found in the appendix.
The coefficient of variation (CV) of the lognormal distribution was determined for the nine global categories by investigating the published literature based on a binary method, as follows. The nine categories are 1: ephemeral snow; 2: midlatitude nonmountainous forest; 3: high-latitude nonmountainous forest; 4: high-latitude mountainous forest; 5: arctic tundra; 6: midlatitude prairie; 7: midlatitude mountainous forest; 8: high-latitude mountains; and 9: midlatitude treeless mountains. The air temperature, topographic variability, and wind speed were considered, which affect the solid precipitation amounts, solid orographic precipitation patterns, and snow redistribution by wind, respectively. Land cover data were used as a surrogate for the wind speed. Here, the CV categories were determined using the same method as in Liston (2004) but with datasets at the same horizontal resolution as the simulations (i.e., 1° × 1°). The CV category map is shown in Fig. 2. It also shows the air temperature, topographic variability, and wind speed for each category. The CV values were the same as the original SSNOWD: 0.06, 0.09, 0.12, 0.17, 0.40, 0.50, 0.60, 0.70, and 0.85 for CV categories 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. Because SSNOWD was developed to realistically represent the snow cover fraction of seasonal snow cover, we used the original root function, Eq. (A2), for grid cells with continental ice (mainly in Greenland) and excluded them from the following analysis.
Figure 1 shows the temporal variation of the relationship between the snow cover fraction and SWE for MAT5 and SSNOWD. In MAT5, the relationship between the snow cover fraction and SWE is described by Eq. (A2) and is the same for both accumulation and ablation seasons. In SSNOWD, the snow cover fraction in the accumulation season is unity, whereas it follows Eq. (A8) in the ablation season. During the ablation season, this relationship is determined by premelt SWE (i.e., accumulated snowfall) and CV. Figure 1a is for 200-mm premelt SWE and different CV values: 0.06, 0.40, and 0.85. Figure 1b is for CV value of 0.40 and different premelt SWE: 50, 100, 200, and 500 mm. In these figures, SSNOWD with CV value 0.40 (category 5) and premelt SWE of 200 mm is almost the same as MAT5 during the ablation season.
3. Data and experiments
a. Global offline experiments
We used atmospheric variables (i.e., rainfall, snowfall, air temperature, specific humidity, wind speed, cloud cover, surface pressure, shortwave radiation, and longwave radiation) from Kim et al. (2009); these data are a hybridization of the Japanese 25-Year Reanalysis (JRA-25) atmospheric reanalysis data (Onogi et al. 2007) and an observation-based precipitation dataset. They corrected the JRA-25 monthly precipitation using the observation-based Global Precipitation Climatology Centre (GPCC) dataset. The 6-hourly variation of precipitation and the ratio of snowfall and rainfall are as in JRA-25. Therefore, this dataset is suitable for comparing hydrological simulation outputs with snow observations. The horizontal resolution is 1° × 1°. The temporal resolution is 6 hourly over the period from 1979 through 2007. The deposition of dust and black carbon, which is used to calculate the reduction in snow albedo, uses the climatology from MIROC5 historical runs (Watanabe et al. 2010).
We conducted two global simulations on land for the 29 years from 1 January 1979 to 31 December 2007, with a 1-h time step, forced by the atmospheric variables. The horizontal resolution was 1° × 1°. The first simulation used the standard MATSIRO settings for the MIROC5 simulation (hereafter referred to as MAT5). The second simulation used SSNOWD as the MATSIRO snow cover fraction parameterization, with the other settings the same as in MAT5 (hereafter referred to as SSNOWD). The land use and soil type boundary datasets were from the Global Soil Wetness Project 2 (GSWP2; Dirmeyer et al. 2006). Although MIROC5 can use a tile scheme, to allow easy interpretation of the results we did not turn this feature on. As stated before, the region where the land use was continental ice was excluded from the analysis. As part of our model integrations, we followed the GSWP2 offline simulation procedure.
b. Validation data
We used two snow cover observational datasets and one snow water equivalent dataset for model validation: the Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover fraction (Hall et al. 2006), the Interactive Multisensor Snow and Ice Mapping System (IMS) snow cover analysis (National Ice Center 2008), and the European Space Agency’s (ESA’s) Global Snow Monitoring for Climate Research (GlobSnow) snow water equivalent (Takala et al. 2011).
The MODIS Aqua and Terra snow cover monthly level-3 (L3) global 0.05° climate modeling grid (CMG) dataset (MOD10CM and MYD10CM; Hall et al. 2006) was used for validation of the monthly climatology of the snow cover fraction. The accuracy of MODIS snow products was assessed by Hall and Riggs (2007), who concluded that the daily MODIS snow maps have an overall accuracy of approximately 93%, with lower accuracy found in forested areas and complex terrain, and when snow is thin and ephemeral. We first averaged the Aqua and Terra data and interpolated them to the 1° model simulation grid. Then, we calculated the monthly means for the period 2001–07.
The Northern Hemisphere daily snow cover area was compared with the IMS daily Northern Hemisphere snow and ice analysis available at 24-km resolution (National Ice Center 2008). The IMS snow and ice analysis is a binary snow cover dataset created from multiple observations and is suitable for comparing the daily snow cover area across a hemisphere. A similar evaluation was made by Dutra et al. (2010). These data were interpolated onto the 1° model grid, masked with the same land–sea mask as the simulations, multiplied by the grid area, and summed over the target regions.
Northern Hemisphere monthly snow water equivalent values were compared with the GlobSnow snow water equivalent dataset (Takala et al. 2011). GlobSnow assimilates synoptic weather station snow depth data with satellite passive microwave radiometer data. Takala et al. (2011) showed that GlobSnow has an improved accuracy level when compared with uncertainty statistics calculated for a typical standalone brightness temperature channel difference algorithm, and has been used recently as part of other model validation studies (Hancock et al. 2014). For our analysis, the original 25-km Equal-Area Scalable Earth Grid (EASE-Grid) data were interpolated onto the 1° simulation grid and averaged for monthly climatologies from 1979 through 2007.
The MODIS daily snow cover product was also available for our analyses. However, this dataset includes missing values during the polar night and cloudy days/areas, and thus can include snow cover fraction values with low confidence levels that are not suitable for calculation of daily snow cover area. Therefore, we used the most appropriate dataset available depending on the validation objectives.
4. Results and discussion
a. Validation of the monthly global snow cover fraction
Figure 3 compares the simulated snow cover fraction with the MODIS snow cover fraction products for November, February, and May. The simulated snow cover fraction was averaged for the same period as the MODIS data (from 2001 through 2007).
In November, the MODIS monthly snow cover fraction showed a latitudinal gradient in the Northern Hemisphere. The MAT5 simulation underestimated the snow cover fraction for almost all high-latitude regions. Because of MAT5’s monotonically increasing function and constant threshold across the globe, the distribution of the snow cover fraction reflects the distribution of snow mass. The threshold value for a snow cover fraction of 1 (120 kg m−2) appears to be too large in the accumulation seasons. The SSNOWD simulation improved these underestimations and showed a latitudinal gradient in the Northern Hemisphere. However, there were some regions where the snow cover fraction was overestimated (e.g., around the border between China and Russia). This is because SSNOWD assumes that the snow cover fraction is unity when new snowfall occurs. This assumption is true if the grid size is as small as the horizontal scale of the clouds and associated precipitation forcing and the topographic variation is small. For 1° resolution, this assumption causes an overestimation of the snow cover fraction.
In February, the MAT5 simulation was closer to the observations but still underestimated the snow cover fraction in regions with relatively small amounts of snowfall in the Northern Hemisphere (e.g., eastern Siberia). These underestimates were also improved in SSNOWD. The SSNOWD assumption that the snow cover fraction in the accumulation season was unity slightly overestimated the snow cover fraction in some regions. However, the overall representation was much better than the MAT5 formulation.
In May, the differences among MODIS, MAT5, and SSNOWD were smaller than in the accumulation season in the Northern Hemisphere. Both MAT5 and SSNOWD overestimated the snow cover fraction along the snow line. One possible reason for this is the formulation of the snow scheme. MATSIRO uses constant (in space and time) snow density and snow thermal conductivity. This approach is an oversimplification of the natural system and should be improved in the future. Another possible reason is that, in general, the physical consistency is broken in offline experiments. In reality, as the snow melts and snow-free ground is exposed, the energy available for snowmelt becomes larger than the snowmelt because snow-free ground with low albedo absorbs more energy than the snow-covered area. Thus, in a system where these feedbacks are included, this results in higher air temperatures with more available energy for snowmelt (Liston 1999). However, in this standalone offline simulation, we assume that feedbacks are effectively included in the driving data and are not modified by the inclusion of new snow cover parameterization. Therefore, the snowmelt energy did not increase as the snow cover fraction decreased.
b. Northern Hemisphere snow cover area
The Northern Hemisphere snow cover area is compared with the IMS daily Northern Hemisphere snow and ice analysis in Fig. 4. The snow cover area from the IMS snow analysis shows the seasonal cycle, with increasing snow cover area in the fall and decreasing area in spring. Moreover, the snow cover area in winter showed short-term variations, with the maximums appearing in either December or January.
The snow cover areas for MAT5 and SSNOWD simulations were converted from snow cover fractions in the same way as IMS (see section 3b) for the Northern Hemisphere and for each CV category. As was the case for the snow cover fraction distribution, the MAT5 simulation underestimated the snow cover area, especially during the accumulation season. It could not represent the observed short cycle of the snow cover area within the seasons. After SSNOWD was incorporated, the daily Northern Hemisphere snow cover area was well represented in terms of interannual variations and short cycles within the seasons.
Figure 5 shows the observed versus simulated snow cover area for the Northern Hemisphere and the regions for each CV category. Category 1 is for ephemeral snow and was excluded from this figure. For all categories, the MAT5 simulation underestimated the snow cover area. The extent of underestimation differs depending on the season; the underestimation is larger in accumulation season than in melting season. By incorporating SSNOWD, the underestimations were improved. In the category 4, 5, and 8 regions, some underestimation by SSNOWD was produced during the melt season.
c. Relationship between snow depth and snow cover fraction over North America
Niu and Yang (2007) analyzed the observed snow depth and snow cover fraction over North American river basins (Mackenzie, Yukon, Churchill, Fraser, St. Lawrence, Columbia, Colorado, and Mississippi), as mentioned in section 1. The horizontal resolution of their analysis was 1° × 1°. The analysis period was from 1979 through 1996, and the monthly snow cover fraction and snow depth were used. Figure 2 of Niu and Yang (2007) shows a scatterplot of the snow depth and snow cover fraction. The plots in the accumulation season (i.e., October and November) were scattered around the function that reached a snow cover fraction of unity with a relatively shallow snow depth (about 10 cm), and the variation was small. The plots during the melting season (i.e., April and May) reached unity with a deeper snow depth (about 30 cm) than in the accumulation season and the variability was also larger.
Here, we compare our MAT5 and SSNOWD results against the analysis of Niu and Yang (2007). These validations were crucial for expanding the approach used in this study to simulations of SWE in regions with insufficient observations, as stated in the introduction. If we illustrate the relationships between the snow cover fraction and snow depth as the y and x axes, as done by Niu and Yang (2007), we expect that, for the MAT5 simulation, most plots can be predicted from Eq. (A2). For the SSNOWD simulations, the relationship can be predicted from Fig. 1: the snow cover fraction in the accumulation season of October and November becomes unity regardless of the SWE, and the snow cover fraction in the melting season of April and May is variable depending on the CV values, accumulated snowfall, and accumulated snowmelts. As stated in section 2, MATSIRO adopts a constant snow density of 300 kg m−3, and the snow depth increases in proportion with SWE.
The results are shown in Fig. 6. Each point represents a grid cell in the major basins in North America, and the shape and color of the symbols show the CV categories. The black line is the observation fitted curve in Fig. 2 of Niu and Yang (2007). In MAT5, the relationships between snow depth and the snow cover fraction fell around the root function [Eq. (A2)], with a small variation with season. The variability was smaller than in the analysis of Niu and Yang (2007). The relatively large variability was explained by the large snow depth variability in the ablation season. In the SSNOWD results, there were many plots with a snow cover fraction of unity in November, as expected. However, there were some plots with a smaller snow cover fraction in regions with high surface air temperatures (symbols with yellow and red). This was because there were many events in which snowfall and snowmelt occurred within a short time in relatively warm regions. In February and May, the gradient of the function decreased with the season. Hysteresis was observed between the accumulation and ablation seasons. If we changed the MATSIRO constant snow density (300 kg m−3) to vary in space and time, the resulting plotted distributions would move right in the accumulation season and left in the ablation season and be closer to the observation-fitted curve of Niu and Yang (2007). When comparing the results against those of Niu and Yang (2007), it is clear that SSNOWD is better than MAT5.
d. The effects of the snow cover fraction on hydrologic properties
Table 1 shows the annual water budget and the SWE in February averaged for 29 years for the major Arctic river basins. There were only small differences between the MAT5 and SSNOWD schemes. One possible reason for this is that the effect of the snow cover fraction was underestimated because the land surface model was forced by meteorological data. If a simulation were conducted with an atmospheric model, the available energy would increase as the snow cover decreased. However, some effects of the snow cover fraction on the SWE can be seen in the grid cells with perennial snowpack.
e. Northern Hemisphere snow water equivalent
Figure 7 shows Northern Hemisphere SWE from GlobSnow (Takala et al. 2011), and two simulations for November, February, and May from 1979 to 2007. In November, The MAT5 simulation overestimates SWE in western Siberia, Europe, and northern Canada, and underestimates SWE in Alaska and eastern Siberia. This may be because of the precipitation dataset bias. SSNOWD has similar tendencies, with slightly smaller values because snow cover fraction in the SSNOWD simulation was generally larger than MAT5 in the accumulation season, and larger snow cover fraction enhances the snowmelt.
In February, the maximum SWE is found in the Yenisey River basin and both simulations reproduce this geographical distribution. However, the same bias as in November is found in both simulations; SWE is overestimated in Europe and is underestimated in eastern Siberia.
In May, SWE was overestimated in almost all of the snow-covered regions. This may be because of other physical parameterizations related to snow in MATSIRO. The SSNOWD simulation has smaller SWE, except in eastern Siberia.
Because this is an “offline” simulation, further investigation using an AGCM is required to fully evaluate the effects of incorporating SSNOWD on snow mass/depth.
In this section, we discuss the general issue of improving snow cover fraction parameterizations and our direction for future work in this regard. In this study, we have shown that the more physically realistic parameterization yields improved results. As shown by Liston (1999), the premelt SWE distribution (largely controlled by snowfall) and snow cover fraction evolution during melt are tightly coupled to the atmospheric forcing and associated surface energy budget and melt rates. Therefore, accurate reproduction of the snow cover evolution requires accurate and reliable input surface meteorological data. This tight coupling between the premelt SWE distribution, snow cover fraction evolution, and atmospheric forcing (i.e., melt rates and snowfall) presents a unique and potentially valuable opportunity: because snow cover fraction is relatively easy to measure using remote sensing, accurate meteorological forcing and the associated melt rates allow reconstructing of the premelt SWE (Liston 1999). A study focusing on these three snow evolution features and the associated interrelationships could be used to increase the credibility of any global or regional atmospheric modeling system used to simulate snow evolution. Clearly the potential use of snow fraction datasets for analyzing model representations of snow evolution and surface meteorological forcing in an integrated manner has not been completely realized for mid- and high-latitude regions where snow is an important feature of the landscape and climate system. This is not a completely straightforward challenge; for example, in this study we could not eliminate the possibility that the SSNOWD parameterization worked well even with the possibility of poor input surface meteorological data. However, snow cover fraction is one of the more easily obtainable measurements to make with the current Earth observing satellite network (with some exceptions, such as forested areas), and it represents a readily available dataset for analyzing Earth system models, particularly variables such as melt rates and snowfall fluxes. By way of example, these interrelationships are readily available to take use as part of data assimilation programs (e.g., analyzing the input meteorological forcing data, or something else, by constraining the snow cover fraction evolution). We believe the work presented herein is a first step toward such a data assimilation study that takes advantage of high-quality snow cover fraction and other snow datasets to improve the simulation of both snow and atmospheric processes and interactions.
For the case of an atmosphere–land coupled model experiment (or “online” experiment), improvements in snow cover fraction should have even larger practical merit. As already presented, the surface radiation flux is significantly influenced by the snow cover and the positive feedback from the snow cover fraction (less snow cover results in higher air temperature and enhances the snow cover reduction). This suggests that an accurate and realistic representation of snow cover fraction and its interactions with the atmosphere above would play a role in influencing medium-range to seasonal predictability. Therefore, the types of experiments outlined above are necessary and desirable as a next step in the development of an optimal subgrid snow cover parameterization or submodel.
Finally, in the development of improved Earth system models, the snow-related contribution presented herein is a small part of the whole system, but it may well play a nonnegligible role for the reasons discussed above. Currently many land surface models use relatively simple parameterizations of snow cover fraction, like the original MATSIRO. In reality, by thoroughly tuning the simpler parameterizations one would always be able to produce reasonable results for the snow cover fraction evolution. However, land surface models that account for subgrid snow cover variability in unrealistically simple ways will also likely misrepresent other critical features of the more general snow evolution. For example, misrepresenting the hysteresis relationship between SWE and snow cover fraction may cause significant errors in the snow accumulation and/or melting seasons associated with the changing climate. Thus, representing subgrid snow processes is expected to be critical to the success in the next generation of Earth system models.
6. Summary and conclusions
We examined the impacts of improving the parameterization of snow cover fraction within the context of a global land surface hydrology model. The parameterization of the snow cover fraction in the original MATSIRO land surface model over simplified the natural system, leading to a poor representation of snow cover. Therefore, we changed it to SSNOWD, which assumes that the subgrid SWE distribution follows a lognormal distribution function, thus improving the modeled fit with observed snow-depth distribution datasets and accounting for the physical processes that produce subgrid SWE and snow cover fraction variability.
We conducted offline simulations with and without SSNOWD, when forced by meteorological data consisting of merged JRA-25 reanalysis and observed precipitation datasets. The simulation period spanned 29 years, from 1979 through 2007, at a global 1° × 1° resolution covering all land grid cells. The large-scale distributions of monthly snow cover fraction simulated with SSNOWD were more accurate than those without SSNOWD, especially in the accumulation season and in areas with relatively small snowfall amounts. Validation of the daily snow cover area in the Northern Hemisphere showed that simulations with SSNOWD improved the timing of the peak snow cover area and the absolute error. This was because SSNOWD formulates the snow cover fraction differently in the accumulation and ablation seasons.
However, the SSNOWD assumption that the snow cover fraction is unity in the accumulation season sometimes led to overestimates of the snow cover fraction. Future model development should be directed toward incorporating more physically based snow property representations (i.e., variable density and thermal conductivity if constant values are used, or revised surface albedo) and validation of SSNOWD for in situ observations of snow and/or water equivalent depth.
We thank H. Kim for providing the meteorological datasets. MODIS and IMS were provided by the National Snow and Ice Data Center. This work was supported by the GRENE Arctic Climate Change Research Project, Program for Risk Information on Climate Change, and JSPS/Grant-in-Aid for Scientific Research (S) 23226012.
a. Snow scheme in MATSIRO
The SWE is calculated as
where Sn is the snow water equivalent, P*sn is the snowfall that goes through or drops from the canopy layer, Es(sn) is the snow sublimation, Msn is snowmelt, and FR is the refreezing of rainfall and snowmelt.
The snow cover fraction Asn is defined as
with the threshold value Snmax = 120 kg m−2 determining when the whole grid cell is covered with snow. The number of snow layers is determined by the SWE, with a maximum of three.
Snow temperature Tsn is predicted using the thermal conductivity equation. When the Tsn is higher than the melting point temperature after the thermal conductivity equation is solved, Tsn is set to 0°C and the residual thermal convergence is used for snowmelt.
The snow albedo αb is calculated as
where αb,new is the albedo of newly fallen snow for band b, αb,old is the albedo of old snow, and Ag is an aging factor from Yang et al. (1997). This factor evolves with time, as a function of snow temperature and the densities of dust and black carbon. We consider the three bands of wavelength, visible (vis), near infrared (nir), and infrared (ifr), and used 0.9, 0.7, 0.01, 0.4, 0.2, and 0.1 for αvis,new, αnir,new, αifr,new, αvis,old, αnir,old, and αifr,old, respectively.
In the accumulation season, snowfall occurred uniformly and the snow cover fraction was assumed to be equal unity. During snowmelt, under the assumption of uniform melt depth Dm, the sum of snow-free and snow-covered fraction equals unity:
where D is the snow water equivalent depth and f(D) is the probability distribution function (PDF) of snow water equivalent depth within the grid cell. The snow depth distribution within each grid cell was assumed to follow a lognormal distribution:
Here CV is the coefficient of variation and μ is the accumulated snowfall.
The snow cover fraction Asn(Dm) is represented as
Then, the grid-averaged SWE is represented as
To incorporate SSNOWD into MATSIRO consistently, we slightly modified the computational flow that diagnosed the snow cover fraction. In the original SSNOWD model, the accumulated melt depth Dm and the accumulated snowfall μ are predicted in the host atmospheric or hydrological models by summing the snow accumulation and the snowmelt rates simulated by the host model. However, this produces some differences between the SWE calculated from MATSIRO and SSNOWD, because the original SSNOWD does not account for the amount of snow that completely melts during the time step. Therefore, we first calculated Dm from Eq. (A9) and Sn using Newton–Raphson methods. Then, we calculated the snow cover fraction using Eq. (A8) and Dm. This modification was introduced to avoid physical inconsistency between the two models.