Abstract

Numerical simulations of two snowfall events over the Black Hills of South Dakota are made to demonstrate the use and potential of a coupled atmospheric and land surface model. The Coupled Atmospheric–Hydrologic Model System was used to simulate a moderate topographic snowfall event of 10–11 April 1999 and a blizzard event of 18–23 April 2000. These two cases were chosen to provide a contrast of snowfall amounts, locations, and storm dynamics. The model configuration utilized a nested grid with an outer grid of 16-km spacing driven by numerical forecast model data and an inner grid of 4 km centered over the Black Hills region. Simulations for the first case were made with the atmospheric model, the Advanced Regional Prediction System (ARPS) alone, and with ARPS coupled with the National Center for Atmospheric Research Land Surface Model (LSM). Results indicated that the main features of the precipitation pattern were captured by ARPS alone. However, precipitation amounts were greatly overpredicted. ARPS coupled with LSM produced a very similar precipitation pattern, but with precipitation amounts much closer to those observed. The coupled model also permits simulation of the resulting snow cover and snowmelt. Simulated percentage snow melting occurred somewhat more rapidly than that of the observed. Snow–rain discrimination may be taken from the precipitation type falling out of the atmospheric model based on the microphysical parameterization, or by the use of a surface temperature criteria, as used in most large-scale models. The resulting snow accumulation patterns and amounts were nearly identical. The coupled model configuration was used to simulate the second case. In this case the simulated precipitation and snow depth maximum over the eastern Black Hills were biased to the east and north by about 24 km. The resulting spatial correlation of the simulated snowfall and observations was only 0.37. If this bias is removed, the shifted pattern over the Black Hills region has a correlation of 0.68. Snow-melting patterns for 21 and 22 April appeared reasonable, given the spatial bias in the snowfall simulation.

Introduction

Although many long-term simulations of snow accumulation and ablation have been made using stand-alone land surface models or surface models coupled with general circulation models (GCMs; Schlosser et al. 2000; Forster et al. 1996), less research has focused on short-term event simulations. Because of the shortage of snow accumulation observations, validation of simulations has sometimes been limited to only a single station (Schlosser et al. 2000). Accurate event simulations of snow-related processes are the basis for successful long-term simulation because snow accumulation is the balance of a series of intermittent snowfall events and subsequent snow-melting processes. Event simulations of cold-season processes permit 1) the use of intensive observational data from field experiments for validation, 2) spatial analysis approaches to examine and validate simulations, and 3) the use of more physically realistic precipitation schemes to simulate snowfall in atmospheric models.

In GCMs, microphysical information is generally inadequate to distinguish types of precipitation (rain or snow). Precipitation is identified as snow or rain based on the local surface air temperature at a given station. The temperature criteria typically range from 0° to 2.2°C and vary among different models. Potential problems created by this approach have been highlighted by Lackman et al. (2002), especially for freezing-rain conditions. The alternative to this method is the inclusion of full microphysics rather than precipitation parameterization. This method is not possible in current climate models because of coarse resolution (Molinari and Dudek 1992). For event simulations over limited areas, mesoscale atmospheric models, coupled with a land surface model to calculate snow accumulation/ablation, can be run on a resolution of a few kilometers. At this resolution, the inclusion of ice microphysics in the atmospheric model allows for a more direct prediction of snowfall or rainfall. This is to say, the mesoscale atmospheric model provides the simulated snowfall and rainfall amounts directly rather than just as total precipitation for the snow module in land surface models. Therefore, it is not necessary for land surface models to determine if the precipitation is in the form of snow or rain.

In addition to the complexities of snow-related processes themselves, terrain-induced effects on snowfall and snowmelt make simulations of snow events more difficult. Climatological observations indicate that terrain features, such as the Black Hills of South Dakota and Wyoming, can exert important effects on snow processes (Bunkers et al. 1996; Farley et al. 2000). One of the primary effects is orographic lifting, which causes atmospheric waves to form both upwind and downwind. Airflow often splits around the obstacle and converges on the lee side, leading to precipitation enhancement. The topography also provides an elevated heat and moisture source enhancing atmospheric instability (Banta 1990; Kuo and Orville 1973). In addition to the spatial heterogeneity of snowfall caused by the terrain, the rate of snow melting is also modulated by hilly terrain because the key factors in the snow-melting process, such as surface air temperature and radiation balance at the surface, are sensitive to terrain effects (Dozier 1980). Subsequent surface hydrological processes (e.g., overland flow), that are induced by the meltwater are also strongly influenced by terrain (Stieglitz et al. 1997).

Successful simulation of snowfall amount, distribution, and evolution using atmospheric models is important to subsequent modeling of snowmelt with snow submodels in land surface schemes. In this paper, a coupled model system, consisting of an atmospheric model and a land surface model, is used to simulate two Black Hills snowfall cases of different severity.

Model description and model setup

South Dakota School of Mines and Technology has developed the Coupled Atmospheric–Hydrologic Model System (CAHMS) to simulate the interactions of atmospheric precipitation processes, surface hydrological processes (including overland flow and channel flow), and ground water processes in complex terrain (e.g., the Black Hills) (Capehart et al. 2000). The Advanced Regional Prediction System (ARPS) (Xue et al. 2000, 2001) is the atmospheric component of this model system. The original land surface model in the ARPS is replaced by the National Center for Atmospheric Research (NCAR) Land Surface Model (LSM; Bonan 1996). A surface hydrological model based on the CASC2D model of Julian et al. (1995) was developed (Zheng 2001) to couple to LSM. The ground water model component of the coupled model system is MODFLOW (McDonald and Harbaugh 1988). This paper will focus on ARPS–LSM interactions in simulations of snowfall and snowmelt for two snowstorms over the Black Hills.

ARPS is a detailed mesoscale model developed by the Center for Analyses and Prediction of Storms at the University of Oklahoma (Xue et al. 2000, 2001). The dynamic model is based on the fully compressible equations of motion and permits interactive nesting of multiple grids of differing resolution. Precipitation processes are simulated using an explicit bulk-water microphysical parameterization and/or an implicit convective parameterization scheme (Kain and Fritsch 1990, 1993).

The microphysics scheme employed in the model is a modified form of the ice microphysics scheme developed by Lin et al. (1983), who extended the concepts originally proposed for liquid processes by Kessler (1969). Six classes of water substance are treated—water vapor, cloud water, rainwater, cloud ice, snow, and graupel/hail. These various water forms interact with each other through parameterizations of the physical processes of condensation/evaporation, collision/coalescence and collision/aggregation, accretion, freezing, melting, and deposition/sublimation. Cloud water and cloud ice are assumed to have zero terminal velocity. Rain, snow, and graupel/hail are assumed to follow inverse exponential size distributions and possess appreciable terminal velocities. Implementation of the ice scheme follows Tao and Simpson (1993) and includes the ice water saturation adjustment procedure of Tao et al. (1989). Rain, snow, and graupel/hail reaching the surface are added to the precipitation.

Land surface processes in the ARPS model, as used in the study (version 4.5.0), are treated by a simple force–restore, surface energy balance parameterization, which is based on the work of Noilhan and Planton (1989) and Pleim and Xiu (1995). In this version of ARPS, snow is included as a land surface type, but snow depth and snow cover processes are not included. Snowfall does not change the land surface type. Snow on the surface is recognized only on initialization and is treated as an “on–off” state variable, which alters the surface soil albedo and thermal properties, evaporative flux, and surface temperature calculations.

To better represent snow processes that occur during a simulation, the native land surface parameterization in ARPS has been replaced by the LSM (Bonan 1996) scheme. LSM is a spatially distributed, one-dimensional, vertical model of energy, momentum, water, and CO2 exchanges. The ARPS model provides data of the atmospheric forcing, such as the simulated precipitation rate, radiation, and the air temperature and moisture and wind at the lowest layer of the atmospheric model. LSM, in turn, provides predicted fluxes of heat, moisture, and momentum to the ARPS model.

A simple one-layer snow module is built into the NCAR LSM (Bonan 1996). Precipitation in the atmosphere is intercepted by the canopy and throughfall is identified as snow or rain and added to the snowpack based on the surface air temperature in LSM. However, in the coupled version of the model, ARPS provides a downward snowfall via its ice microphysics scheme, which precludes the need for this temperature criterion. Once on the ground, snow accumulation is determined by a simple mass balance of gains from the flux of snow at the ground surface and surface dew, and losses from snowmelt and sublimation. The snow layer and topmost surface layer are integrated as one single layer in calculating surface properties and the surface energy budget. The mass of snow, divided by a constant bulk snow density of 250 kg m−3, determines snow depth on the ground. Once the snowpack is ablated by a given process, the resulting water is either infiltrated, converted to “runoff,” or otherwise removed from the potential of rejoining the snowpack. Snow gravitational compaction with depth, the interaction of sublimated vapor, melted water and snow, and other factors are not taken into account in this model.

For both the ARPS and LSM land surface conditions, the land surface is characterized by using a combination of static land cover descriptors and more temporally dynamic values of surface temperature and moisture. Data for land cover is derived from the 1-km Global Land Cover Characterization dataset (Loveland et al. 2000) and is modified to accommodate the land classes for the LSM and ARPS resident land categories. Soil textures are extracted from the Pennsylvania State University CONUS-SOIL database, a 1-km national-scale product derived from the U.S. Department of Agriculture Natural Resources Conservation Service STATSGO soils database (Miller and White 1998). Values of soil moisture and soil temperature and surface temperature are extracted from the Global Energy and Water Cycle Experiment (GEWEX) Continental-Scale International Project (GCIP) and the National Centers for Environmental Prediction Eta Data Analysis System (EDAS) archived at NCAR. Terrain is derived from 1-km-resolution U.S. Geological Survey (USGS) Digital Elevation Model data.

For the present study, two grids were used to nest down to the region of interest over the Black Hills. The outermost, coarse grid spacing of 16 km, with dimensions 73 × 73 × 35 grid points (grid 1), covers the state of South Dakota and parts of bordering states. Nested within this grid was a higher-resolution, 4-km grid, with dimensions of 91 × 91 × 35 (Fig. 1) covering the entire Black Hills region (grid 2). Figure 1 displays the grid-2 domain and also shows the locations of observing stations discussed in the text. For grid 1, the implicit Kain and Fritsch (1990) cumulus parameterization scheme and the explicit microphysical parameterization scheme of Tao and Simpson (1993) are used together. Only the explicit precipitation parameterization scheme is adopted in grid 2 [as suggested by Molinari and Dudek (1992)]. The coupling of ARPS and LSM also occurs on the grid-2 domain. EDAS 40-km-resolution gridded atmospheric analyses archived at the National Center for Atmospheric Research provides initial fields for grids 1 and 2, and also gives lateral boundary conditions for grid 1 (updated every 3 h). Grid 1 provides lateral boundary conditions for grid 2 (updated every hour).

Fig. 1.

Topography in the domain of grid 2. Thin lines are the contours of topography, beginning at 1000 m, with an interval of 200 m. Dashed lines denote state boundaries. The positions and names of several stations are also shown.

Fig. 1.

Topography in the domain of grid 2. Thin lines are the contours of topography, beginning at 1000 m, with an interval of 200 m. Dashed lines denote state boundaries. The positions and names of several stations are also shown.

Brief summary of two snow events

Two snow events that occurred in the Black Hills were selected for this study, one with moderate snowfall and the other with heavy snowfall. These cases provide two contrasting cases of snowfall amount, location, and forcing over the Black Hills. The results should be indicative of model performance over a range of snowfall conditions for moderate orography.

Case 1: 10–11 April 1999 snow event

During the period from 5 April to 5 May 1999, the Upper Missouri River Basin Pilot Project (UMRBPP; Smith and Farwell 1997) made intensive observations of precipitation events occurring in the Black Hills. On 10 and 11 April 1999, moderate snowfall occurred in the Black Hills and surrounding regions. The observed daily precipitation [snow water equivalent (SWE)] in the model domain of grid 2 is depicted in Fig. 2. Two precipitation maxima were situated in the Black Hills region, one located in the northern part, near Sundance, Wyoming, with a daily precipitation of 36.3 mm, and another in the southern Hills, near Ardmore, South Dakota (also 36.3 mm). There were generally larger precipitation amounts in the northern Black Hills and along their western slopes. The very high variability is in part real, and in part indicative of the difficulty of making representative snow precipitation measurements in complex terrain.

Fig. 2.

Daily precipitation (snow water equivalent plus rain) for 10 Apr 1999 in the grid-2 domain (thick solid line). Contours are drawn in 10-mm increments. Thin lines are topographic contours. The Black Hills are located at the middle of the domain. The dotted lines are state boundaries.

Fig. 2.

Daily precipitation (snow water equivalent plus rain) for 10 Apr 1999 in the grid-2 domain (thick solid line). Contours are drawn in 10-mm increments. Thin lines are topographic contours. The Black Hills are located at the middle of the domain. The dotted lines are state boundaries.

Most of the precipitation fell as rain over the southern Black Hills (the observed snowfall depth at Ardmore was only 2.5 cm). At the northern edge and inside the Black Hills, the main precipitation form was snow. For example, Lead, South Dakota (in the northern hills), had a daily precipitation of 25.9 mm and a snowfall depth of 27.2 cm (the ratio of snow to liquid is greater than 10:1). The daily precipitation for the Gillette 6 SE site in Wyoming (at the northern edge of the Black Hills) was 14.2 mm and the snowfall was 12.7 cm (snow-to-liquid ratio about 9:1).

The synoptic situation that led to the moderate snowfall event began as an extratropical cyclone crossing the central United States (Fig. 3). As the cyclone progressed across the Black Hills region, a cold front extended southeastward from Montana across several Midwest states. As this cold front moved across the Black Hills, the front was slowed by the terrain and interacted with the orography, causing moderate snowfall along the western slopes of the Black Hills.

Fig. 3.

Surface analysis for 1200 UTC 10 Apr 1999 depicts the synoptic situation during the moderate snowfall event. Star indicates area of study.

Fig. 3.

Surface analysis for 1200 UTC 10 Apr 1999 depicts the synoptic situation during the moderate snowfall event. Star indicates area of study.

Case 2: 18–23 April 2000 severe snowstorm event

On 18 April 2000, a powerful spring storm hit western South Dakota. Total precipitation from the storm, shown in Fig. 4a, exhibits a belt of high precipitation amounts extending from northwest Nebraska, south of the Black Hills toward the northeast, and into the South Dakota plains east of the Black Hills. A secondary maximum is observed over the eastern Black Hills. Snowfall depths, shown in Fig. 4b, ranged from 10–30 cm on the plains to 30–60 cm in the foothills, and 60–90 cm in the Black Hills. Strong north to northeast winds of 13–20 m s−1, with gusts to 31 m s−1, occurred for nearly 18 h, creating drifts of 0.9–2.4 m. Lighter snow and winds were observed east of the Black Hills. The snow was preceded in many areas by heavy rainfall of as much as 5–10 cm. Some areas also reported intermittent sleet throughout the day. Thus, as in the first snow case, the form of precipitation for this event was not uniform in the grid-2 domain. To the east and the south of the Black Hills regions, much of the precipitation was rainfall.

Fig. 4.

Observations in the grid-2 model domain for the Apr 2000 storm: (a) precipitation (including rain and SWE) and (b) snow depth (cm) of total snowfall. The thick lines are SWE contour with the interval equal to 20 mm. The thin lines are topography contour. The Black Hills is located at the middle of the figure. The dotted lines are state boundaries.

Fig. 4.

Observations in the grid-2 model domain for the Apr 2000 storm: (a) precipitation (including rain and SWE) and (b) snow depth (cm) of total snowfall. The thick lines are SWE contour with the interval equal to 20 mm. The thin lines are topography contour. The Black Hills is located at the middle of the figure. The dotted lines are state boundaries.

This snow event occurred when a strong surface extratropical cyclone (center pressure of 992 hPa) passed through the Black Hills region (Fig. 5). The cold front, extending southwestward from eastern Nebraska to western Texas, occluded at the vicinity of the surface low. At 500 hPa, a cold cutoff low lay above the surface cyclone (not shown) and provided upper-level support.

Fig. 5.

Surface analysis for 1200 UTC 19 Apr 2000 depicts the synoptic situation during the heavy snowfall event. Star indicates area of study.

Fig. 5.

Surface analysis for 1200 UTC 19 Apr 2000 depicts the synoptic situation during the heavy snowfall event. Star indicates area of study.

The snowfall amounts, locations, and storm dynamics and interactions with the topography provide a contrast to the much weaker UMRBPP storm of case 1. The greater snow depths also provide an opportunity for simulation of snowmelt.

Results and discussion

In a predictive hydrological model system, the ability of atmospheric models to provide accurate prediction of precipitation for input to the surface hydrological model is crucial to subsequent successful simulation of hydrological phenomena such as the timing and intensity of peak streamflow. The whole process of snowfall and snow melting can take several days.

Discussion of the simulations of snowfall and snowmelt for the above two cases and comparisons with observations of snowfall and snow on the ground are made in the following sections.

Case 1: Numerical simulation of 10–11 April 1999 snowfall event

A numerical simulation, using ARPS alone, was made beginning at 0000 UTC 10 April 1999. The simulated 24-h total precipitation (rain plus SWE) is shown for the 4-km grid in Fig. 6. The heaviest simulated snowfall occurs on the western slope of the Black Hills, aligned north-northwest–south-southeast. This is consistent with the observations (Fig. 2), though greatly smoothed. The simulation also replicates the positions of the observed snowfall maxima. At the southern edge of the Black Hills, the simulation reproduces the heavy precipitation with a maximum of 66.7 mm, located near Ardmore (but nearly twice the 36.3 mm as observed). At the northern edge of the Black Hills, the simulation has another heavy precipitation center with a maximum of about 57.4 mm, located near Sundance (36.3 mm observed). In general, the isohyets of simulated precipitation shown in Fig. 6 are much larger (as much as a factor of 2 for heavier snowfall in the Black Hills) than the observed amounts shown in Fig. 2, except near the southwestern and east-central edges of the domain. Comparison between Fig. 6 and Fig. 2 and the specific values for Ardmore and Sundance indicate that this simulation predicts the general features of the precipitation pattern but overestimates the amounts throughout the Black Hills.

Fig. 6.

Simulated precipitation (including rain and SWE) of 10–11 Apr using stand-alone ARPS. The thick lines denote precipitation field with the interval of 10 mm.

Fig. 6.

Simulated precipitation (including rain and SWE) of 10–11 Apr using stand-alone ARPS. The thick lines denote precipitation field with the interval of 10 mm.

The effect of land surface processes on the simulated precipitation

In the ARPS model, the effects of snow accumulation are not calculated, although a simple two-layer “force–restore” land surface model is present in ARPS to describe the surface energy balance and to solve for soil surface skin temperature (Xue et al. 2001). In the ARPS–LSM coupled model, this surface parameterization is replaced by the LSM. The LSM provides a much more complete parameterization of land processes, including modification of surface properties by snowfall. The sensitivity of the results to the different land surface process models is now examined.

Figure 7 depicts the simulated daily precipitation in the 4-km grid using the coupled model of ARPS–LSM with the snow/rain determination based on the actual form of precipitation simulated by the microphysics scheme, starting at 0000 UTC 10 April 1999. In comparison with the default version of ARPS, the area distribution of the precipitation is essentially unchanged although precipitation amounts are different. In comparison with the observed amounts shown in Fig. 2, the predicted precipitation from the coupled model shown in Fig. 7 is closer than that for ARPS alone (Fig. 6). The outer 20- and 10-mm, and even the 30-mm contour along the western Black Hills are nearly the same. The heavy precipitation areas are greatly reduced for the ARPS–LSM run, especially in the southern Black Hills where the 60-mm contours in the ARPS-only run are replaced by only 35-mm contours in the ARPS–LSM run. The observations in this area do not exceed 37 mm. For the coupled model, the major precipitation region over the northern Black Hills has a precipitation maximum of 48.8 mm. A 38.2-mm maximum is simulated over the southern Black Hills. These values are much closer to the observed precipitation maxima of 36.6 mm than are those of the ARPS-only run. Therefore, the incorporation of the LSM improved the simulation of precipitation. Furthermore, greater improvement occurs at the southern edge of the Black Hills. The precipitation difference between the two simulations is 28.5 mm, that is, a 93% reduction in the error at this point for the run using LSM. In the southern Black Hills area, the precipitation is primarily rainfall.

Fig. 7.

Simulated precipitation (SWE) between 10 and 11 Apr (thick line) using ARPS coupled with LSM. Ice microphysics scheme is adopted for identifying the phase of precipitation on the ground. The contours are 10, 20, 30, 35, and 40 mm.

Fig. 7.

Simulated precipitation (SWE) between 10 and 11 Apr (thick line) using ARPS coupled with LSM. Ice microphysics scheme is adopted for identifying the phase of precipitation on the ground. The contours are 10, 20, 30, 35, and 40 mm.

Considering that the precipitation type is not uniform in this case, the simulated snow precipitation amount (snow water equivalent) is also provided in Fig. 8 in order to check if this simulation has the ability to distinguish between rain and snow in the precipitation area. It can be seen that in the southeastern Black Hills, there is much less snowfall, although there is a simulated precipitation maximum (Fig. 7). This means that the majority of the precipitation in the southeastern Black Hills is rain, not snow, which agrees with the precipitation observations. For the middle and northern portions of the Black Hills, the main precipitation type is snow. Some of this snow may also melt on contact, or melt before the time of observation. A direct comparison of simulated and observed snow depths are made below. Overall, this simulation successfully reproduces key features of the observed event.

Fig. 8.

Same as Fig. 7, but for precipitation in the form of snow only (SWE) (thick line). The interval of contours is 10 mm.

Fig. 8.

Same as Fig. 7, but for precipitation in the form of snow only (SWE) (thick line). The interval of contours is 10 mm.

Comparison of simulated and observed snow depth and snow melting

The coupled ARPS–LSM model at 4-km resolution was used to simulate the snow-melting processes in this case, starting at 0000 UTC on 10 April. Snow accumulation is the balance of the gains from snowfall and surface dew and losses from snowmelt and sublimation. Among them, snowfall is the dominant positive term and snowmelt is the dominant negative term.

The available observations about snow accumulation are snowfall and snow depth at the ground. The model simulations provide SWE. Thus, it is necessary to convert the simulated SWE amounts to equivalent depths to compare with observed snow accumulation and snow melting if the snow density is known. Actually, the snow depth at the ground is calculated by LSM through the simulated snow accumulation divided by a fixed snow density of 250 kg m−3. This snow density corresponds to a 4:1 ratio of snow to water. The value is obviously not applicable to this case because the observed ratio of snow to liquid is not constant. In this case, a comparison of daily snowfall depths to precipitation amounts (assuming that all of the precipitation is snow) reveals that the calculated values range from 2.5 to 10.5 (Table 1). This assumption certainly does not apply for the Wind Cave station, where much of the precipitation fell as rain; therefore this ratio is not calculated for Wind Cave. The lowest calculated snow-to-liquid ratio, that is, 2.53:1, is questionable because this low value is usually found in snowpack rather than in new-fallen snow and so some of the precipitation at this station also was probably rain.

Table 1.

The snow-to-liquid ratios on 11 Apr 1999 based on the observed precipitation (SWE) and observed snowfall depth (cm)

The snow-to-liquid ratios on 11 Apr 1999 based on the observed precipitation (SWE) and observed snowfall depth (cm)
The snow-to-liquid ratios on 11 Apr 1999 based on the observed precipitation (SWE) and observed snowfall depth (cm)

The accuracy of simulated snow depth on the ground (snow accumulation) is not only dependent on the accurate simulation of snowmelt but also depends on the accuracy of the simulation of the snowfall. To reduce the effects of inaccuracies in the snowfall simulation on the estimated snowmelt, the snowmelt percentage, that is, the snowmelt amount divided by snowfall, is calculated. Snowdrifts and snow melting before the observation time can also cause errors in the snowfall depth observations and, thus, in the snow density estimation. However, such estimates are undoubtedly better than the fixed, high-density value used in LSM. Thus, the calculated snow depth at the ground in LSM was discarded and recalculated based on the observed snow-to-liquid ratio.

One of the problems involved in evaluating the snowmelt simulation is that, unlike precipitation, fewer stations have observations of snowfall and only a small number report snow on the ground (see Table 2). As a result, comparison with observation is done only for individual stations.

Table 2.

Number of reporting stations in the 4-km model domain.*

Number of reporting stations in the 4-km model domain.*
Number of reporting stations in the 4-km model domain.*

The cooperative observers measure snow on the ground only once per day (and often only report snow depth to the nearest inch, 2.54 cm). Because of differences in observation time of daily precipitation from station to station, comparisons of observed and modeled precipitation amounts are difficult. The observation time of precipitation ranges from 1200 UTC of the current day to 0700 UTC of the next day. Table 3 shows the comparison between the simulated and observed snow on the ground. Observation times are also given for each station. Data for the present day (10 April, LST) and the next day (11 April, LST), separated by commas, are listed for some stations. The reason for giving the next day of observed snowfall/snow on the ground data is to account for these differences in observation periods. The period used for the simulated daily precipitation is 0000 UTC 10 April to 0000 UTC 11 April. For some stations, data for the previous day (in parentheses) are given because there is snow on the ground during the previous day (9 April, LST). This snow makes a contribution to the snow on the ground the next day (but of course not to accumulation).

Table 3.

Comparison of the simulated snow accumulation and snow melting (cm) with the observation on 11 Apr 1999 (T indicates “trace”)

Comparison of the simulated snow accumulation and snow melting (cm) with the observation on 11 Apr 1999 (T indicates “trace”)
Comparison of the simulated snow accumulation and snow melting (cm) with the observation on 11 Apr 1999 (T indicates “trace”)

Using the first-day values for snowfall/snow depth (minus the residual snow on the ground for two stations) for evaluation of the simulation of snowfall, we obtain an rms error of 3.5 cm and a mean percentage error of 27%. We also note that the largest errors occur for Wyoming stations near the grid boundaries, not over the Black Hills region of interest.

The comparisons of snowmelt percentages given in the table may be summarized in terms of error relative to the observed percentage melting. The rms error is 56%, and the median error is less than 33%. Again, the worst errors occurred in Wyoming and not in the Black Hills. The model overestimates the melting. Only two stations indicated less melting than simulated, and they were relatively small errors. This is consistent with results of Yang et al. (1999), who also found that LSM tends to overestimate surface heating in snow conditions.

There are some problems involved in the point-to-point comparison. The observation at each individual station may be affected by local features (e.g., subgrid topographical effects) that the numerical simulation cannot resolve. That is to say, the numerically simulated value at each grid represents the average in that grid. Costigan et al. (2000) discuss some of the problems involved in point-to-point comparison of model-simulated and observed precipitation, noting that it “assumes that the model would predict precipitation at the station location when it is only predicting it for a grid cell, which may have a terrain elevation quite different from the observation station.”

The effect of different snow identification schemes on the simulation of snowfall and snowmelt

In most large-scale models, the precipitation is identified as snowfall or rain based on the surface air temperature Tatm. In LSM, if Tatm is less than 2.2°C, the precipitation is snow; otherwise, the precipitation is rain. However, in the ARPS–LSM coupled model, the ice microphysics parameterization scheme in the ARPS atmospheric model provides the simulated snowfall (not just total precipitation) directly to LSM for snow accumulation and snowmelt calculations. Figure 9a shows the simulated daily snow accumulation by the simple snow-identification scheme of LSM. In LSM, snow accumulation is mainly the difference between the simulated snowfall amount and the simulated snowmelt amount. The contribution to snow accumulation from surface dew and the loss from sublimation are insignificant in this case. From this figure, there are two major snow accumulation areas in the Black Hills. One is located at the northern edge of the mountains. The maximum of this snow accumulation area is 29.3 mm, which is situated at Sundance where the simulated snowfall (SWE) is 47.9 mm. Therefore, the snowmelt amount by 0000 UTC 11 April at this location is about 18.6 mm. The other maximum is 26.3 mm, occurring in the west-central Black Hills; the simulated maximum snowfall in this area reaches 42.7 mm, giving a snowmelt of 16.4 mm.

Fig. 9.

Simulated snow accumulation by 0000 UTC 11 Apr using the (a) surface temperature criteria and (b) microphysical scheme. The contour interval is 5 mm.

Fig. 9.

Simulated snow accumulation by 0000 UTC 11 Apr using the (a) surface temperature criteria and (b) microphysical scheme. The contour interval is 5 mm.

The corresponding plot for snowfall determined directly from the microphysical scheme is shown in Fig. 9b. This figure is remarkably similar to Fig. 9a. The differences are minor, with the microphysical scheme showing a slightly larger coverage, including the area between the northern section of the Black Hills near Sundance, Wyoming, and the main body of the Black Hills. The very small differences suggest that obtaining the snowfall directly from the microphysical scheme does as well as the temperature criteria without the artificiality and arbitrariness of the prescribed temperature criteria.

Simulations of the 10–11 April 1999 Black Hills snow case indicated that the coupled model could successfully simulate a moderate topographically influenced snow event. Simulations with the basic ARPS model with the native simple surface parameterization simulated the basic pattern of precipitation, but had significant errors in the precipitation amounts. With the more complete land surface treatment included in the LSM scheme, the coupled model produced a much more accurate simulation of the snowfall. The results suggest that the best model choices are to use the coupled model of ARPS with the LSM surface scheme and use the ice microphysics prediction of snow and rain to determine the precipitation type.

Case 2: Numerical simulation of the 18–23 April 2000 snowfall event

Based on the above results, the simulation of the April 2000 case employs the coupled ARPS–LSM framework with snow/rain determination based on the microphysical parameterization of the atmospheric model (ARPS). Unlike the above-moderate snow case, the periods of snowfall and snowmelt are much longer in this case. Therefore, a 5-day simulation was made for modeling snowfall and snowmelt. The simulation of this case begins at 1200 UTC 18 April and ends at 1200 UTC 23 April.

Comparison of simulated precipitation and observed precipitation

In addition to the problems noted earlier in section 4a another problem related to observing times is that the precipitation at neighboring stations (with similar periods of precipitation occurrence) can be assigned to different dates because of differences in observing times. This makes spatial analysis of the observations difficult. One method to avoid the problems associated with differing observation times is to compare storm totals of both observed and simulated precipitation. The distribution of the storm total observed precipitation for the 18–21 April storm was shown in Fig. 4a. There is a heavy precipitation belt, ranging from 75 to 125 mm from the middle and southern Black Hills (in the middle of the figure), extending south of the Black Hills. There is much less precipitation north and west of the Black Hills, about 50 mm. Comparing the simulated total precipitation, shown in Fig. 10, with the above observations, it can be seen that this simulation of precipitation reproduces the observed features with heavy precipitation ranging from 75 to 100 mm east and south of the Black Hills. The simulated heavy precipitation area at the eastern side of the Black Hills is situated about 24 km too far to the north and east, as is the area of much lighter precipitation along the western slopes of the Black Hills. This is less than 1 grid spacing of the large-scale model, which provides the large-scale context for these simulations. The model also replicates the observed heavy precipitation near the middle of the east edge of the model domain, having 80-mm precipitation as compared with observed values of 80–100 mm. However, precipitation in the southeastern part of the domain, in Nebraska, is much less than observed.

Fig. 10.

Simulated total precipitation for the Apr 2000 storm.

Fig. 10.

Simulated total precipitation for the Apr 2000 storm.

Comparison of simulated snowfall with the observed snowfall depth

The heaviest observed snowfall occurred in the southeastern Black Hills, near Custer, South Dakota, with a maximum snow depth of 88.9 cm (Fig. 4b). To the south of the Black Hills and around the middle of the eastern boundary of the model domain, only moderate or light snow fell. However, these two areas received heavy precipitation (Fig. 4a); thus, rain accounts for most of the observed precipitation. The western side of the Black Hills only had light snowfall.

Figure 11 is the simulated snowfall (SWE) for this case, determined by the difference in the total precipitation (liquid equivalent) and total rainfall. The snow/liquid ratios at several representative stations are calculated in Table 4. The average snow-to-liquid ratio is about 9.2:1, near the widely used 10:1 ratio. At the eastern side of the Black Hills, there is a simulated severe snowfall belt with a maximum of 63.5 mm in SWE, which converts to 58.4 cm in snow depth using this average value. The observed maximum snow depth of this area is about 63.5–76.2 cm. The difference in magnitude of the observed and the simulated snow depth is due to underprediction by the model or the use of the average snow/liquid ratio. If the largest value of the snow/liquid ratio in this area from Table 4, 13;rc1, is used, the simulated maximum snow depth would be 82.6 cm.

Fig. 11.

Same as Fig. 10, but for the simulated total snowfall (liquid amount) in the model domain grid 2. The interval of contours is 20 mm.

Fig. 11.

Same as Fig. 10, but for the simulated total snowfall (liquid amount) in the model domain grid 2. The interval of contours is 20 mm.

Table 4.

The snowfall (cm), SWE (cm), and ratio of snow to liquid for several stations

The snowfall (cm), SWE (cm), and ratio of snow to liquid for several stations
The snowfall (cm), SWE (cm), and ratio of snow to liquid for several stations

A spatial correlation analysis comparing the gridded observed and simulated snow depth gave a correlation, r, of 0.37. However, as noted, the simulated precipitation occurred too far northeast. If this spatial bias is accounted for by moving the precipitation in the Black Hills region 24 km west and south, then the correlation is r = 0.69. To the south of the Black Hills, and at the middle of the eastern boundary of the model domain, there are moderate/light snowfalls, although both the simulated and observed precipitation are heavy in these areas. In the southeast the simulations underestimate both precipitation and snowfall. This means that the simulation distinguishes different precipitation types (rain or snow).

Comparison of simulated and observed snowmelt

While the above comparisons of the simulated precipitation or snow depth with observations were used to check the accuracy of the atmospheric model, snowmelt comparisons are used to verify the ability of LSM (especially the snow component) and the coupling of the ARPS and LSM to simulate snowmelt processes.

Typically, few stations make observations of snow depth on the ground. Fortunately, in this case, in the most severe snowfall area, that is, in the Black Hills, there is a sufficient density of snowmelt observations available to reveal the spatial pattern of snowmelt. Therefore, figures for the simulated and observed snowmelt are plotted for comparison.

Figures 12a and 12b show the simulated and observed, respectively, snowmelt amounts (cm) on 21 April. The simulated snowmelt depth is based on snow densities for the stations with snowmelt observation data and has the same period as the observation data. As pointed out when comparing the simulated and observed snowfall, the simulated maximum snowfall area in the Black Hills region is situated northeastward as compared with the observed heavy snowfall area in this region. This spatial difference between the simulated and observed snowfall is also seen in the simulated and observed snowmelt field. Except for this spatial shift, the simulated snowmelt pattern in the Black Hills is consistent with the observed snowmelt. The greatest observed snowmelt on 22 April reached 25.4 cm in depth, while the simulation gives the maximum of 20.3 cm. The simulated and observed snowmelt amount for 22 April is shown in Fig. 13. On this day, the primary simulated snow-melting area occurs near the middle of the Black Hills with a maximum of 17.8 cm, which agrees with the observations (15.2 cm). For both days the snowmelt amounts in the southeastern part of the domain are much smaller than observed. This occurs as a result of the lower precipitation amounts in the simulations and some early melting on 20 April.

Fig. 12.

(a) Simulated and (b) observed snowmelt depth (cm) on 21 Apr. The interval is 5 cm.

Fig. 12.

(a) Simulated and (b) observed snowmelt depth (cm) on 21 Apr. The interval is 5 cm.

Fig. 13.

(a) Simulated and (b) observed snowmelt depth (cm) on 22 Apr. The interval is 5 cm

Fig. 13.

(a) Simulated and (b) observed snowmelt depth (cm) on 22 Apr. The interval is 5 cm

Conclusions

This research has made an evaluation of the performance of the coupled atmospheric model (ARPS) and land surface (LSM) modeling system developed by the South Dakota School of Mines and Technology in two event simulations of snowfall/snow ablation of contrasting severity. The results for the moderate case reveal that:

  1. The coupling of ARPS and LSM produces better predictions of precipitation than does ARPS alone.

  2. Determination of precipitation type using the ice microphysics parameterization scheme gave comparable results when compared with precipitation type, as determined by a surface air temperature criteria, without the artificiality and arbitrariness of the prescribed temperature criteria.

Although a simple snowmelting module is used in LSM to simulate snowmelt processes, simulations of both events of different severity indicated that this simple snow model can effectively melt the simulated snowfall.

The simulations captured general features of both the moderate snowfall event over the central-northern Black Hills and the heavy blizzard event over the eastern Black Hills. However, hydrologic responses are sensitive to details of the precipitation field, especially over complex terrain. Spatial biases of only fractions of the operational forecast model analysis (EDAS) grid as in the second case here can have severe consequences for directly coupled hyrologic simulations (Yu et al. 2002; Wang 2002). Thus, further development is needed for reliable direct coupled model forecasts, including hydrologic response.

Fig. 4.

(Continued)

Fig. 4.

(Continued)

Fig. 9.

(Continued)

Fig. 9.

(Continued)

Fig. 12.

(Continued)

Fig. 12.

(Continued)

Fig. 13.

(Continued)

Fig. 13.

(Continued)

Acknowledgments

This research was supported under NSF-EPSCoR Grants OSR-9252894, NSF-EPSCoR Cooperative Agreement EPS-9720642, the South Dakota Future Fund, NOAA Award NA 96GP0321, and NASA Grant NAG 8-1447. Observations were taken from the UMRBPP archive maintained by the Joint Office for Science Support of the University Corporation for Atmospheric Research. The atmospheric simulations were made using the Advanced Regional Prediction System (ARPS) developed at the Center for Analysis and Prediction of Storms, University of Oklahoma. We gratefully acknowledge the assistance of Ms. Connie Crandall in preparing the manuscript.

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Footnotes

Corresponding author address: Dr. Mark R. Hjelmfelt, IAS, SDSM&T, 501 E. St. Joseph Street, Rapid City, SD 57701-3995. mark.hjelmfelt@sdsmt.edu