Abstract

The National Operational Hydrologic Remote Sensing Center (NOHRSC) Snow Model (NSM) is an energy- and mass-balance model used by the National Oceanic and Atmospheric Administration’s National Weather Service for moderate-resolution spatially distributed snow analysis and data assimilation over the United States. The NSM was evaluated in a one-dimensional mode using meteorological and snowpit observations from five sites in Colorado collected during 2002–03. Four parameters estimated by the NSM [snow water equivalent (SWE), snow depth, average snowpack temperature, and snow surface temperature] were compared with snowpit observations and with estimates from another snow energy and mass-balance model, SNTHERM. Root-mean-squared differences (RMSDs) between snowpit SWE observations (January–June) at all sites and estimates from the NSM were about 11% (RMSD = 0.073 m) of the average maximum observed SWE from all sites of 0.694 m. SNTHERM exhibited only a slightly better agreement (RMSD = 0.066 m). During the winter and early spring period before snowpacks became isothermal at 273.15 K, both NSM and SNTHERM simulated significantly cooler average snowpack temperatures than observed (RMSD = 3 and 2 K, respectively). During this snow accumulation period estimates of SWE by both models were very similar. Differences in modeled SWE were traced to short periods (5–21 days) during isothermal conditions in early spring when the two models diverged. These events caused SWE differences that persisted throughout the ablation period and resulted in a range in melt-out times of 0.2–7.2 days between depth observations and modeled estimates. The divergence in SWE resulted from differences in snowmelt fluxes estimated by the two models, which are suggested to result from 1) liquid water fractions within a snowpack being estimated by the NSM using an internal energy method and by SNTHERM using a semiempirical temperature-based approach, and 2) SNTHERM, but not the NSM, accounting for the small liquid water fraction that coexists in equilibrium with snow when the snowpack surface is dry (<273.15 K).

1. Introduction

Snow is an important component of the global water and energy cycles, and in many regions is vital to both health and commerce. Annual maximum snow cover, including supraglacial snow, can exceed 4.3 × 106 km2 (∼55% of land area) in the conterminous United States, 15.5 × 106 km2 (∼74%) in North America (Frei et al. 1999), and 52.5 × 106 km2 (∼35%) globally (NSIDC 2005). Numerical models that accurately simulate snowpack energy and mass-balance processes are required for water, weather, and climate analysis and prediction. They are used to estimate and understand freshwater stored in snowpacks; the timing, rate and magnitude of snowmelt; and exchanges of energy and mass between the snowpack and the atmosphere. Information derived from these models often has significant socioeconomic consequences.

The National Operational Hydrologic Remote Sensing Center (NOHRSC) Snow Model (NSM) was developed as part of the National Oceanic and Atmospheric Administration’s National Weather Service. The purpose of this model is to support operational, near-real-time, spatially distributed modeling and analyses of snow energy and mass-balance processes at moderate resolution (1 km) over continental scales (Carroll et al. 2001). It is used operationally in a multisensor data fusion framework to assimilate available snow observations from ground, airborne, and satellite sensors. In several respects the NSM is a hybrid of two earlier snow models: 1) SNTHERM.89 (Jordan 1991), and 2) the Utah Energy Balance Model (UEB; Tarboton and Luce 1996). Table 1 illustrates that both models have been extensively evaluated in a wide range of hydroclimatological conditions in terrestrial and marine environments. The NSM exploits the strengths of these models, notably the physical algorithms used by SNTHERM to solve all soil–snow–atmosphere mass and energy fluxes, other than the solution of snow surface temperature, which follows conventions of the UEB model. Euler predictor–corrector methods that reduce uncertainty between time steps of mass and energy state variables, as used by the UEB model, are also exploited by the NSM. The NSM incorporates these strengths within a contemporary land surface modeling framework for efficient processing over large regions. In terms of its basic physics and algorithmic approach, the NSM is similar and comparable to the snow model components of many contemporary land surface models.

Table 1.

Use of SNTHERM and UEB models in existing literature.

Use of SNTHERM and UEB models in existing literature.
Use of SNTHERM and UEB models in existing literature.

In this paper we evaluate the fundamental capability of the NSM physics by comparing snow water equivalent (SWE), snow depth, and snow temperature, simulated in a one-dimensional mode at five sites in Colorado, with independent in situ observations from the National Aeronautics and Space Administration (NASA) Cold Land Processes Field Experiment (CLPX, Elder et al. 2008b). Here we are interested in the ability of the physical formulations and algorithms in the NSM to accurately simulate the evolution of these key snowpack properties, given accurately observed meteorological forcings at points. The operational version of the NSM (used by the NOHRSC for the 2004–06 snow seasons) is a one-dimensional (vertical) model run over 1 km × 1 km grid cells that are spatially uncoupled from each other (where advection of mass from one cell to another is not considered). This operational version of the NSM was forced with observed meteorological data at each of the five sites (air temperature, relative humidity, wind speed, incoming and outgoing shortwave radiation, and incoming longwave radiation and precipitation) and was evaluated with intensive in situ snow observations at each site.

2. Background

a. NSM

The NSM is a five-layer land surface model focused on the mass and energy balance of seasonal snow cover. It accounts for vertical mass fluxes to and from the snowpack by snowfall, rainfall, sublimation from both the snow surface and from wind-transported snow, and snow meltwater outflux. The NSM also accounts for snowpack energy fluxes from radiation, turbulent and conductive transfer, advection from snow meltwater and precipitation, and heat exchange between the snowpack and top soil layer.

For a given set of atmospheric forcings, the NSM solves the snow surface energy balance equation for snow surface temperature based on the numerical scheme of the UEB snow model (Tarboton and Luce 1996). Using this solution of snow surface temperature (considered as the skin temperature of the thin, top, snow layer), the NSM then estimates mass and energy exchange between snow and the atmosphere based on the physical algorithms of SNTHERM.89 (Jordan 1991) and the Prairie Blowing Snow Model (Pomeroy et al. 1993). The Euler predictor–corrector numeric scheme (Gerald 1978) is used in the NSM, as it is in the UEB model, to improve the representation and reliability of simulated snow surface temperatures between each hourly time step. As a consequence of changes in the top snowpack layer, state variables in lower layers are subsequently updated by calculating energy and mass fluxes between the layers. Compaction of all snow layers is calculated.

The NSM represents the snowpack with a maximum of three layers of variable thickness. The soil is represented by two layers of constant thickness. The top snowpack layer is constrained between 0.02 and 0.05 m and the second (lower) layer is constrained between 0.02 and 0.15 m. The thickness of the third (basal) layer is unconstrained beyond a minimum of 0.02 m. Snow layers are combined if they become thinner than the minimum because of loss of mass, or are subdivided if they became thicker than the maximum because of mass gain. These layer ranges are designed to capture the dynamic temperature gradients near the snow surface that respond more rapidly to changing meteorological conditions.

b. SNTHERM.89

SNTHERM.89 (hereafter referred to as SNTHERM) is a well-known snowpack model with widely demonstrated capability to accurately simulate snowpack accumulation, ablation, and the vertical structure of snowpack properties (Table 1). As noted above, the NSM uses significant components of SNTHERM’s physical algorithms, but key differences remain between the model formulations. In this study, SNTHERM is used as a standard for comparison to the NSM and to help diagnose NSM behavior.

The solution of snow surface temperature using the snow surface energy balance equation is handled almost identically in both SNTHERM and the NSM. The major differences between the models are in the layer structure, the temporal resolution of each forward estimate, and the representation of snowpack thermal conditions.

First, SNTHERM allows an unlimited number of layers to represent the vertical structure and thermal characteristics of the snowpack, whereas the NSM limits the number of snow layers to three. SNTHERM can therefore potentially resolve more detail in the snowpack profile, and a larger number of thinner layers can allow more accurate solution of vertical fluxes through the snowpack. Second, SNTHERM makes forward estimates by subdividing hourly meteorological inputs into smaller time steps, ranging between several seconds and several minutes, until convergence criteria for mass and energy fluxes in each layer have been satisfied. Long-term accuracy is maintained by ensuring the accuracy of each smaller time step. In contrast, the NSM holds the hourly time step constant and uses a predictor–corrector scheme to maintain the accuracy of each hourly time step. Third, SNTHERM uses the temperature and liquid water content of each layer to estimate the thermal conditions of the snowpack, whereas the NSM directly updates internal energy as a state variable to represent the thermal conditions. Also, the NSM ignores liquid water content in snow when the snow temperature is less than 273.15 K, whereas SNTHERM accounts for the small fraction of liquid water that coexists in equilibrium with snow at temperatures less than 273.15 K.

3. Methods

a. Study sites

CLPX was conducted in northwestern Colorado in the winter of 2002/03 to develop a more complete understanding of fluxes, storage, and transformations of water and energy in cold land areas (Cline et al. 2003). Extensive hydrometeorological and snowpack measurements were made at five sites (Elder et al. 2008b) covering a variety of vegetative and topographic conditions (Table 2).

Table 2.

Location and characteristics of CLPX meteorological sites.

Location and characteristics of CLPX meteorological sites.
Location and characteristics of CLPX meteorological sites.

b. Data collection

1) Meteorological data

At or near each CLPX site, the necessary forcing data were measured (Elder et al. 2008a) to evaluate the energy and mass balance of the snowpack (Table 3). For this study, the occurrence and amount of hourly precipitation was determined from snow depth observations using an acoustic sensor. The density of new snow and amount of rain precipitation were determined from precipitation observations, collected as daily totals close (0.1–1.36 km) to each CLPX site (Table 4). Forcing data at the CLPX sites were collected between the time of the first snow pit at each site, between 17–19 December 2002, and snowmelt-out in May or June 2003. All variables, except for snow depth, were recorded at 30-s intervals and averaged to 10-min values. Snow depth was recorded as a single sample value at the start of each 10-min period. Data were recorded on Campbell CR10X dataloggers using manufacturer-supplied calibration sensitivities for each instrument where appropriate.

Table 3.

Specifications of instrumentation at CLPX meteorological sites.

Specifications of instrumentation at CLPX meteorological sites.
Specifications of instrumentation at CLPX meteorological sites.
Table 4.

Location and specifications of precipitation gauges.

Location and specifications of precipitation gauges.
Location and specifications of precipitation gauges.

2) Snowpit data

Snowpit measurements were made at CLPX meteorological sites as close as possible to the footprint of the acoustic depth sounder without disturbing the depth measurements. Elder et al. (2008b) described the snowpit measurement protocol for density and temperature profiles that were made at each site at approximately monthly intervals (Table 5). Briefly, density and temperature were measured at 10-cm intervals between the snow surface and the snow–ground interface. Two 1000-ml-density samples were taken from each consecutive 10-cm interval to calculate an average snowpack density. Point measurements of snow temperature were made at the snow surface and then at the boundaries of each 10-cm interval.

Table 5.

Date of snowpits.

Date of snowpits.
Date of snowpits.

3) Quality control and data manipulation

CLPX meteorological measurements were quality controlled to a level 1 standard (Williams et al. 1999) where data at a 10-min frequency were calibrated, outliers were removed, and supporting metadata were supplied. These level 1 standard data are publicly available (Elder and Goodbody 2005). In addition, estimates of radiometric snow surface temperature were made from measured outgoing longwave radiation (↑LW) using the Stefan–Boltzmann relationship and an assumed snow surface emissivity of 0.99.

Small gaps of missing data (less than 12 h) were linearly interpolated to provide a continuous time series of each variable where appropriate. Hourly averages were then created for each variable except precipitation. Precipitation was measured at a daily resolution. The daily total precipitation was arbitrarily subdivided into four equal volumes of 6-h intervals to avoid representing a 24-h total as a 1-h event in the models.

Differences between acoustic and snowpit depth measurements were minor at all sites other than Walton Creek. At this site logistical considerations meant that the snowpit was located farther away (∼10 m) from the sounder footprint than at other sites, which were directly adjacent to the footprint of the acoustic sounder. Consequently, localized topographic influences at Walton Creek caused variability in snow depth that resulted in an offset of 0.29 m at the time of model initialization in December and varied between 0.45 and 0.27 m at the subsequent four snowpits. A constant offset of 0.29 m was applied throughout the season to all nonzero acoustic depth observations at this site, despite subsequent snowpit measurements suggesting errors of up to 0.16 m may exist. However, a difference of only 0.02 m between the depth of the snowpit at the start of melt-out in May and the corrected acoustic depth suggests that this error will have a minimal impact on estimation of the final melt-out date.

c. Modeling

Hourly NSM and SNTHERM model runs were initialized using December snowpit measurements at each site. The observed pit layer structure was reformulated to satisfy the input layer format requirements of each model. This resulted in slight differences between initial SWE, temperature, and density for each model (Table 6). The initial NSM and SNTHERM temperature and density profiles approximate the observed pit profile (Fig. 1). As SNTHERM allows for an unlimited number of snowpack layers, the initialization profile replicates the in situ pit profiles of temperature and density, whereas the NSM is limited to three temperature and density nodes (for a maximum of three snowpack layers). All other parameters in SNTHERM initialization files (see, e.g., Fig. 2) were constant apart from average barometric pressure and the number of nodes (or snowpack layers), which were site-specific. After initialization, both the NSM and SNTHERM used the same meteorological input data to model snowpack mass and energy conditions.

Table 6.

Summary of model initialization data.

Summary of model initialization data.
Summary of model initialization data.
Fig. 1.

NSM and SNTHERM snowpack temperature and density initialization profiles at each CLPX site.

Fig. 1.

NSM and SNTHERM snowpack temperature and density initialization profiles at each CLPX site.

Fig. 2.

Sample SNTHERM initialization file.

Fig. 2.

Sample SNTHERM initialization file.

d. Analytical techniques

The physical performance of the NSM was assessed by comparison to snowpit and meteorological observations, and to SNTHERM. The comparison of the NSM with snowpit observations was evaluated using the root-mean-squared differences (RMSDs) by site and the collective RMSD from all sites grouped together. For comparison of the NSM with hourly meteorological observations and hourly SNTHERM estimates, pairs of modeled and observed values (NSM or SNTHERM paired with meteorological observations) were randomly selected from the entire time series to prevent statistical error due to serial autocorrelation. Subsamples totaling 10% of each hourly time series were randomly selected at each site. Model performance was then evaluated using the RMSD between subsampled paired variables at each site and the RMSD from all sites grouped together. Correlations from differences between paired subsamples grouped together from all sites, using the square of the Pearson product moment correlation coefficient, and comparison between means and variances of observed and modeled estimates at individual sites using appropriate Z tests and F tests were also evaluated.

4. Results

a. SWE and depth

Seven-month records of hourly modeled SWE and depth estimates from the NSM and SNTHERM at five CLPX sites were compared to observed SWE (Fig. 3) and observed depth (Fig. 4). Differences between modeled estimates and pit observations were summarized by site, by month, and as a seasonal summary of all sites over all months for SWE (Table 7) and for depth (Table 8). Of the five sites, snowpits at St. Louis Creek and nearby Fraser Headquarters (HQ) had the smallest seasonal maximum SWE (0.24 and 0.32 m) and depth (0.89 and 1.08 m), and Buffalo Pass had the largest (1.41-m SWE and 3.12-m depth). In most cases the maximum snowpit SWE did not occur at the same time as maximum depth.

Fig. 3.

Hourly modeled SWE estimates and snowpit SWE observations at five CLPX meteorological sites between December and July 2002–03.

Fig. 3.

Hourly modeled SWE estimates and snowpit SWE observations at five CLPX meteorological sites between December and July 2002–03.

Fig. 4.

Hourly modeled snow depth estimates, hourly acoustic snow depth observations, and snowpit depth observations at five CLPX meteorological sites between December and July 2002–03.

Fig. 4.

Hourly modeled snow depth estimates, hourly acoustic snow depth observations, and snowpit depth observations at five CLPX meteorological sites between December and July 2002–03.

Table 7.

Observed SWE at snowpits, observed − modeled percentage difference, and aggregate RMSD of observed − modeled by month and by site (in italics).

Observed SWE at snowpits, observed − modeled percentage difference, and aggregate RMSD of observed − modeled by month and by site (in italics).
Observed SWE at snowpits, observed − modeled percentage difference, and aggregate RMSD of observed − modeled by month and by site (in italics).
Table 8.

Observed depth at snowpits, observed − modeled percentage difference, and aggregate RMSD of observed − modeled by month and by site (in italics).

Observed depth at snowpits, observed − modeled percentage difference, and aggregate RMSD of observed − modeled by month and by site (in italics).
Observed depth at snowpits, observed − modeled percentage difference, and aggregate RMSD of observed − modeled by month and by site (in italics).

During the early snowpack accumulation period (January–March) both the NSM and SNTHERM consistently overpredicted SWE snowpit measurements and, with the exception of Fool Creek, consistently overestimated depth. During snowpack ablation in May, however, NSM and SNTHERM SWE and depth estimates were less consistent. SWE was underestimated by both models at Fool Creek, Fraser HQ, and Walton Creek. At Buffalo Pass SNTHERM underestimated SWE and depth values while NSM overestimated both. At St. Louis Creek both models overestimated SWE, but depth was overestimated by NSM and underestimated by SNTHERM.

When observed and estimated differences were grouped by month, the NSM consistently produces greater differences in depth and SWE relative to SNTHERM, except for SWE estimates during snowpack ablation in May. Differences between observed and estimated depth and SWE from both models were seasonally highest in January, for all but NSM estimates of SWE. Differences then decline in February, rise again in March (when NSM estimates of SWE were seasonally highest), and subsequently drop during snowpack ablation. When differences were grouped by site, in comparison to SNTHERM, the NSM estimates greater differences in depth at all sites other than Fool Creek; however, differences between observed and estimated SWE from SNTHERM were greater than the NSM at Buffalo Pass and Walton Creek.

The NSM had a greater RMSD than SNTHERM for SWE and depth (a difference between modeled estimates of 0.007 and 0.1 m, respectively) when SWE and depth were grouped separately over all sites and dates (N = 20). These differences were small in relation to the RMSD of SWE for the NSM (0.073 m) and SNTHERM (0.066 m), but relatively large compared to the RMSD of depth for the NSM (0.32 m) and SNTHERM (0.22 m).

A more complete analysis of temporal differences in snow depth is enabled by using hourly depth measurements from acoustic sounders. Random subsamples (10% of the total time series at each site) increased the sample sizes from N = 20 to between N = 348 and N = 434 depending on the site, and to N = 1930 for all sites combined (Table 9). These data reveal a slightly greater range of RMSD by site between modeled and acoustic depth observations (0.09–0.51 m) than between modeled and snowpit depth observations (0.11–0.44 m). Consequently, the RMSD grouped over all sites over all months, between acoustic depth observations and the NSM (0.35 m) and SNTHERM (0.31 m), was also only slightly greater (0.03 m greater for the NSM and 0.09 m greater for SNTHERM) than when compared with grouped depth observations from pits. The NSM (p = 0.05, R2 = 0.96) and SNTHERM (p = 0.05, R2 = 0.92) show a high correlation with acoustic depth measurements. The significance of differences between the means of observed acoustic depths and both the NSM and SNTHERM modeled estimates was found using Z tests at critical values of Z (0.05) = 1.96. For all sites grouped together and at each individual site other than SNTHERM at Fool Creek, the means were found to be significantly different.

Table 9.

RMSD between observed variables and both the NSM and SNTHERM at individual sites and the aggregate of all sites. Correlation between the aggregate observed variables and both the NSM and SNTHERM at all sites.

RMSD between observed variables and both the NSM and SNTHERM at individual sites and the aggregate of all sites. Correlation between the aggregate observed variables and both the NSM and SNTHERM at all sites.
RMSD between observed variables and both the NSM and SNTHERM at individual sites and the aggregate of all sites. Correlation between the aggregate observed variables and both the NSM and SNTHERM at all sites.

Because of limitations of acoustic depth sensor accuracy, melt-out was considered to occur when sensor observations dropped below 0.02 m. For consistency, melt-out of modeled snowpacks was also considered to occur when the depth dropped below 0.02 m. Differences of 0.2–7.2 days between observed and modeled melt-out existed over all sites (Table 10). Both models melted out earlier than observations at all sites other than at St. Louis Creek (NSM lags observations) and Fraser HQ (SNTHERM lags observations). When the differences in melt-out times over all sites were averaged the NSM had a smaller average difference (2.58 days) than SNTHERM (3.14 days).

Table 10.

Observed and modeled snowpack melt-out.

Observed and modeled snowpack melt-out.
Observed and modeled snowpack melt-out.

b. Average snowpack temperature

Average snowpack temperature observations from thermocouples, snowpits, and modeled estimates from the NSM and SNTHERM show a distinct seasonal pattern, primarily reflecting synoptically driven midwinter weather events and an increase in temperatures to become isothermal at 273.15 K in spring (Fig. 5). Thermocouple observations and estimates from SNTHERM also show strong diurnal variability. Evaluation of observed and modeled snowpack temperatures was restricted to the “cold” period at each site after the December snowpit (used for model initialization) and before the snowpack became isothermal around 273.15 K, or “warm,” during melt-out (marked by arrows with dates in Fig. 5).

Fig. 5.

Hourly modeled average snowpack temperature estimates, hourly average thermocouple observations, and average snowpit temperatures at five CLPX meteorological sites between December and July 2002–03.

Fig. 5.

Hourly modeled average snowpack temperature estimates, hourly average thermocouple observations, and average snowpit temperatures at five CLPX meteorological sites between December and July 2002–03.

Snowpit and thermocouple observations of average snowpack temperature show only very small differences of 1 K or less when compared either by site or by date (Table 11). Comparison of pit observations with modeled estimates by either site or date indicates larger differences. The RMSD in average snowpack temperature is greatest for the NSM, ranging from 2 to 5 K, whereas the RMSD of SNTHERM ranges between 1 and 3 K.

Table 11.

Observed average snowpit temperature, snowpit-thermocouple, and snowpit-modeled differences; and aggregate RMSE of comparisons by month and by site (in italics). All temperatures are presented to the nearest whole kelvin.

Observed average snowpit temperature, snowpit-thermocouple, and snowpit-modeled differences; and aggregate RMSE of comparisons by month and by site (in italics). All temperatures are presented to the nearest whole kelvin.
Observed average snowpit temperature, snowpit-thermocouple, and snowpit-modeled differences; and aggregate RMSE of comparisons by month and by site (in italics). All temperatures are presented to the nearest whole kelvin.

Hourly thermocouple observations of snowpack temperature compared with modeled estimates indicate RMSD were largest at St. Louis Creek and smallest at Walton Creek (Table 9). Observations grouped together from all sites shows the NSM has a higher RMSD (3 K) and lower correlation (p = 0.05, R2 = 0.24) than SNTHERM (RMSD = 2 K; p = 0.05, R2 = 0.45). Further comparison of hourly thermocouple observations with both the NSM and SNTHERM estimates indicated that their means were significantly different [critical values of Z (0.05) = 1.96] from each other at all five sites. Comparison of variances using F tests, at critical values of F(0.05) = 0.138, showed significant differences in variances at all sites other than comparison of thermocouples with both the NSM and SNTHERM at Walton Creek.

At all five sites, whenever a sustained period of increasing average snowpack temperature occurs between mid-January and the beginning of March, the NSM temperatures lag SNTHERM temperatures in both the timing and magnitude of the increase. In March this time lag is particularly evident at all sites when the snowpack temperature increases toward 273.15 K.

c. Snow surface temperature

Snow surface temperatures were observed directly in snowpits, indirectly by IR thermocouples and ↑LW, and were inferred from air temperature and thermocouples above and below the snow surface. Comparison of differences between snowpit and other measurements was limited to cold snowpacks when snow surface temperatures were less than 272.15 K. Over all sites and all months, ↑LW had the smallest differences with surface temperatures observed in snowpits (RMSD = 2 K), and the IR thermocouple, the NSM, and SNTHERM all had the largest differences (RMSD = 4 K) (Table 12).

Table 12.

Observed snowpit surface temperatures; differences between snowpit surface temperatures, modeled estimates, and other temperatures; and aggregate RMSE of comparisons by month and by site (in italics). For calculation of RMSD only snowpit surface temperatures from cold snowpacks (<270 K) were used.

Observed snowpit surface temperatures; differences between snowpit surface temperatures, modeled estimates, and other temperatures; and aggregate RMSE of comparisons by month and by site (in italics). For calculation of RMSD only snowpit surface temperatures from cold snowpacks (<270 K) were used.
Observed snowpit surface temperatures; differences between snowpit surface temperatures, modeled estimates, and other temperatures; and aggregate RMSE of comparisons by month and by site (in italics). For calculation of RMSD only snowpit surface temperatures from cold snowpacks (<270 K) were used.

5. Discussion

Throughout the observation period at all five sites, differences between SWE estimates from the NSM and snowpit observations were approximately 11% (RMSD = 0.073 m) of the average observed maximum SWE from all sites of 0.694 m. SNTHERM, a well-established snow model, only exhibited slightly smaller differences (RMSD = 0.066 m) than the NSM in comparison to snowpit observations.

Before further discussion of the comparison of the models to observations, it is important to consider the certain, but largely unknown, error and uncertainty associated with the snow observations. Variations between observers, weather and snow conditions, and other factors influence the observation error, but to unknown degrees. One source of observation uncertainty that can at least be approximated is the effect of common small-scale variations in snow depth, density, and other properties. Although depth measurements in snowpits were made to the nearest 0.01 m, a range of depths often existed along exposed pit walls that could vary over a magnitude of tens of centimeters depending on the roughness of the snowpack surface and the underlying topography. Similarly, although acoustic depth sounder measurements were calibrated by the manufacturer to an accuracy of ±0.01–0.02 m (depending on the measurement height), they incorporated differences in depths due to variation in snow surface topography across a field of view of up to 1.54 m at 4 m between the sensor and the ground. Grouped density measurements (N = 461) from all snowpits revealed a 3.6% average difference between replicate density samples within vertical profiles. Considering a range of 1–3-m snow depth and 100–300 kg m−3 snow density, depth and density observation uncertainties of 10 cm and 4%, respectively, can result in SWE uncertainties of ±4%–10% if the uncertainties are compounding. Because this is similar in magnitude to the RMSD between the models and the observations, we consider the overall differences between the models and observations to be small. The following discussion recognizes this and focuses on particular situations where differences have greater significance.

a. SWE divergence

Before snowpacks warmed to an isothermal state near 273.15 K, differences between snowpit observations and each modeled estimate were very similar. Shortly after this time, near peak seasonal accumulation, periods of divergence lasting 5–21 days occurred where differences developed between observed SWE and estimates from the NSM and SNTHERM. Following these periods, the observations and models again tracked each other well but the differences persisted throughout ablation, creating a range in melt-out times of 0.2–7.2 days between depth observations and modeled estimates. To understand the situations when observed and modeled SWE diverged, the energy and mass fluxes to and from the snowpack were evaluated further for these periods.

Blowing snow and condensation were ruled out as potential mass-flux contributors to SWE divergence. When warm snowpacks exhibited periods of surface melt, initiation speeds for wind transport of snow under wet snow conditions (7 m s−1 for wet snow; Li and Pomeroy 1997) were only briefly exceeded at one site (Walton Creek) for a total of 3 h. Any mass loss during these 3 h was considered negligible and was not considered in overall mass-flux calculations. No condensation was estimated by either model at any time during periods of SWE divergence, or indicated by any of the observed meteorological conditions.

Evaluation of the remaining mass fluxes to and from the snowpack (Table 13) showed that during periods of divergence, differences in modeled estimates of SWE were predominantly the result of differences in modeled estimates of meltwater. Mass losses due to sublimation were small relative to meltwater, ranging between 0.4% and 16.0% of mass loss at all sites for both models other than for estimates by the NSM at Buffalo Pass where sublimation accounted for the total mass loss. The difference between total estimates of sublimation by the NSM and SNTHERM were very small (≤0.001 m); however, differences between estimates of meltwater were larger (≥0.029 m) over the same periods of SWE divergence at each site.

Table 13.

Mass budget and energy flux estimates during periods of divergence in modeled estimates of SWE. All mass values (other than density) are rounded to 3 decimal places. Positive energy fluxes into the snowpack, negative energy fluxes from the snowpack. Italics signify the total energy flux in units of (MJ).

Mass budget and energy flux estimates during periods of divergence in modeled estimates of SWE. All mass values (other than density) are rounded to 3 decimal places. Positive energy fluxes into the snowpack, negative energy fluxes from the snowpack. Italics signify the total energy flux in units of (MJ).
Mass budget and energy flux estimates during periods of divergence in modeled estimates of SWE. All mass values (other than density) are rounded to 3 decimal places. Positive energy fluxes into the snowpack, negative energy fluxes from the snowpack. Italics signify the total energy flux in units of (MJ).

The relationship between energy balance and mass balance in each model is predominantly, but not always, a direct relationship. Table 13 shows that at all sites other than Walton Creek, when the NSM estimated greater total energy fluxes into the snowpack than SNTHERM, meltwater values produced by the NSM were also greater than SNTHERM, and vice versa. At Walton Creek, however, despite the NSM estimating greater total energy fluxes into the snowpack, SNTHERM estimated greater meltwater fluxes from the snowpack. Consequently, larger estimates of energy inputs by one model do not necessarily create larger estimates of meltwater fluxes from the same model because of different methods used by the NSM and SNTHERM to represent thermal conditions of the snowpack.

b. Modeled meltwater fluxes

The methods used by the NSM and SNTHERM to calculate thermal conditions and liquid water content in each layer of the snowpack are important, as they control the dominant mass flux (meltwater), which creates SWE divergence that persists throughout ablation to create differences in melt-out times. Both models calculated irreducible water saturation (water withheld in the snowpack by capillary forces) in the same manner, both initiated water flow when the mass of liquid water exceeds a snow liquid holding capacity of 0.04, and both used Darcian flow of water through unsaturated snow (Colbeck 1972) to estimate meltwater flow from each layer in the snowpack once the volume of the liquid water fraction of each layer was estimated. However, differences between the models exist in the manner in which the liquid water fraction is calculated. The NSM calculated the liquid water fraction of the mass of a melt layer (Lf) after Tarboton and Luce (1996):

 
formula

where U is the internal snowpack energy (kJ), ρw is the water density (1000 kg m−3), hf is the latent heat of fusion (333.5 kJ kg−1), and Vwater is the volume of snow water equivalent (m3). In contrast, SNTHERM estimated the liquid water fraction solely from the temperature of each layer in the snowpack using a semiempirical function after Guryanov (1985):

 
formula

where af is an arbitrary parameter (100) in the range 100–1000 (Jordan 1991: Jordan et al. 1999) and Tsnow is the snow temperature (K).

When snow surface temperatures were at 273.15 K (wet), the internal energy of the NSM surface layer was calculated from components of the energy fluxes listed in Table 13 (advected heat fluxes from precipitation were included in the calculation of internal energy, but were omitted from Table 13 as both models were forced by the same precipitation). Energy from the NSM surface layer was then translated within the snowpack to lower layers (a maximum of two lower layers exist in the NSM) by convection of latent heat flux through meltwater infiltration and conduction of sensible heat. The resulting internal energy in each lower layer was used to calculate the respective liquid water fractions. However, when snow surface temperatures were less than 273.15 K (dry), the NSM ignored any liquid water content in the snowpack.

When snow surface temperatures were at 273.15 K (wet), SNTHERM calculated the liquid water fraction of each layer (unlimited number of layers) solely as a function of snow temperature. When snow surface temperatures were less than 273.15 K (dry), SNTHERM accounted for the small fraction of liquid water (1% of the water equivalent of each layer) that coexists in equilibrium with snow when the surface temperature is between 273.05 and 273.15 K.

It is suggested that potential causes of divergence of modeled SWE estimates at each site are a function of 1) the difference between using internal energy and a semiempirical temperature-based approach to calculate liquid water fractions within the snowpack and 2) the amount of time during divergent periods that snow surface temperatures were estimated to be 273.15 K (wet).

c. Overall mass and energy balance summary

Overall, at all five sites, when the snowpack was cold the NSM provided comparable estimates of SWE to SNTHERM. Similarly, when the snowpack was warm neither model clearly provided better estimates of SWE than the other.

Compared to snowpit SWE observations during ablation (after periods of modeled SWE divergence), the NSM provided more accurate estimates of SWE than SNTHERM at Buffalo Pass and Walton Creek (deeper snowpacks within sparse forest), but less accurate estimates of SWE at Fool Creek, Fraser HQ, and St. Louis Creek (shallower snowpacks within denser forest). The less accurate NSM SWE estimates resulted from larger energy fluxes to the snowpack by the NSM in comparison to SNTHERM, which produced more meltwater at Fool Creek and Fraser HQ. However, at St. Louis Creek, less accurate NSM SWE estimates also resulted from smaller energy fluxes to the snowpack by the NSM in comparison to SNTHERM, which produced less meltwater. At Buffalo Pass, more accurate NSM SWE estimates during ablation resulted from smaller energy fluxes (lower meltwater estimates) to the snowpack compared to SNTHERM. Yet, at Walton Creek, more accurate NSM estimates of SWE also resulted from greater energy fluxes to the snowpack than SNTHERM, which created less meltwater.

The specific reasons for the different behaviors between energy fluxes and meltwater production in the two models are unknown. Although both were forced with the same hydrometeorological data over a wide range of physical settings influencing radiative and turbulent energy exchange, small differences between the model representations of liquid water, and perhaps differences in layer structure, were sufficient to cause divergence between the models over brief periods, which ultimately lead to differences in melt-out times of up to several days. Neither model readily enables the tracking of liquid water production and movement within, and runoff from snowpacks, which may be necessary to better understand the production, movement, and fate of liquid water in snow models.

6. Conclusions

The NSM was evaluated using meteorological and snowpack observations at five sites in Colorado. Model validation focused on comparison of mass and energy fluxes derived from the NSM (run in a one-dimensional mode) with in situ observations and output from another one-dimensional snowpack model (SNTHERM).

Comparison of all snowpit SWE observations at all sites with estimates from the NSM showed a good agreement (RMSD = 0.073 m), relative to the average observed maximum SWE from all sites of 0.694 m, where the NSM consistently overestimated SWE during snowpack accumulation and both over- and underestimated SWE during snowpack ablation. SNTHERM exhibited only a slightly better agreement with observed SWE (RMSD = 0.066 m).

Before each snowpack became isothermal at 273.15 K, comparison of hourly thermocouple observations of average snowpack temperature at all sites with modeled estimates indicated that both the NSM (RMSD = 3 K) and SNTHERM (RMSD = 2 K) ran significantly cooler than observed temperatures. Comparison of snowpit surface temperatures at all sites with modeled estimates showed differences of 4 K for both the NSM and SNTHERM.

Periods of divergence (5–21 days) occurred between observed SWE and estimates from the NSM and SNTHERM around the time of peak seasonal accumulation when snowpacks were isothermal at 0°C. Differences that occurred during these periods of divergence continued to persist throughout ablation, creating a range in melt-out times of 0.2–7.2 days between depth observations and modeled estimates.

Evaluation of mass fluxes indicated that differences in modeled estimates of meltwater were the main cause of divergence in modeled estimates of SWE. The difference in relative volumes of meltwater estimated by both models did not always directly correspond to the difference in magnitude of energy fluxes at each site. It is suggested that differences in volumes of modeled meltwater were a consequence of liquid water fractions within a snowpack being estimated using internal energy by the NSM and using a semiempirical temperature-based approach by SNTHERM. Potentially, meltwater estimates were also influenced by the amount of time that the surface of the snowpack was dry (<−273.15 K) during periods of divergence, when SNTHERM accounted for the small fraction of liquid water that coexists in equilibrium with snow while the NSM did not. More detailed analyses of the vertical profiles of liquid water fractions estimated by the NSM and SNTHERM will be the focus of future work to further assess the cause of the differences in meltwater estimates. In particular, a sensitivity analysis is required of 1) Tsnow and af in Eq. (2) to see how the total liquid water content varies close to 273.15 K and 2) energy balance components to determine why there are differences in the duration of snow surface temperature at 273.15 K in key periods of SWE divergence between models.

Acknowledgments

We would like to acknowledge the NASA Terrestrial Hydrology Program, the NASA EOS Program, Kelly Elder (USFS) for precipitation data in Fraser and logistical support in maintenance of the meteorological towers, George Leavesley (USGS) for precipitation data at Walton Creek, and the National Resources Conservation Service (USDA) for precipitation data at Buffalo Pass. We thank Susan Frankenstein, Ian Howat, and Jeff Dozier for valuable comments and suggestions that greatly improved the manuscript. Also, special thanks go to Gus Goodbody (USFS) for downloading data from the meteorological towers and making the regular snowpit measurements at each site.

REFERENCES

REFERENCES
Andreas
,
E. L.
,
R. E.
Jordan
, and
A. P.
Makshtas
,
2004
:
Simulations of snow, ice, and near-surface atmospheric processes on Ice Station Weddell.
J. Hydrometeor.
,
5
,
611
624
.
Carroll
,
T.
,
D.
Cline
,
G.
Fall
,
A.
Nilsson
,
L.
Li
, and
A.
Rost
,
2001
:
NOHRSC operations and the simulation of snow cover properties for the coterminous U.S. Proc. 69th Annual Meeting of the Western Snow Conf., Sun Valley, ID, Western Snow Conference, 1–14
.
Cline
,
D. W.
,
1997
:
Snow surface energy exchanges and snowmelt at a continental, midlatitude Alpine site.
Water Resour. Res.
,
33
,
689
701
.
Cline
,
D. W.
, and
Coauthors
,
2003
:
Overview of the NASA Cold Land Processes field experiment. Microwave Remote Sensing of the Atmosphere and Environment III, C. D. Kummerow, J. Jiang, and S. Uratuka, Eds., International Society for Optical Engineering (SPIE Proceedings, Vol. 4894), 361–372
.
Colbeck
,
S. C.
,
1972
:
A theory of water percolation in snow.
J. Glaciol.
,
11
,
369
385
.
Elder
,
K.
, and
A.
Goodbody
,
cited
.
2005
:
CLPX-Ground: ISA main meteorological data. [Available online at http://nsidc.org/data/nsidc-0172.html.]
.
Elder
,
K.
,
D.
Cline
,
A.
Goodbody
,
P.
Houser
,
G. E.
Liston
,
L.
Mahrt
, and
N.
Rutter
,
2008a
:
NASA Cold Land Processes Experiment (CLPX 2002–2003): Ground-based and near-surface meteorological observations.
J. Hydrometeor.
,
in press
.
Elder
,
K.
,
D.
Cline
,
G. E.
Liston
, and
R.
Armstrong
,
2008b
:
NASA Cold Land Processes Experiment (CLPX 2002–2003): Field measurements of snowpack properties and soil moisture.
J. Hydrometeor.
,
in press
.
Frei
,
A.
,
D. A.
Robinson
, and
M. G.
Hughes
,
1999
:
North American snow extent: 1900–1994.
Int. J. Climatol.
,
19
,
1517
1534
.
Gerald
,
C. F.
,
1978
:
Applied Numerical Analysis.
2nd ed. Addison Wesley, 7 pp
.
Glendinning
,
J. H. G.
, and
E. M.
Morris
,
1999
:
Incorporation of spectral and directional radiative transfer in a snow model.
Hydrol. Processes
,
13
,
1761
1772
.
Groffman
,
P. M.
,
J. P.
Hardy
,
S.
Nolan
,
R. D.
Fitzhugh
,
C. T.
Driscoll
, and
T. J.
Fahey
,
1999
:
Snow depth, soil frost and nutrient loss in a northern hardwood forest.
Hydrol. Processes
,
13
,
2275
2286
.
Grundstein
,
A. J.
, and
D. J.
Leathers
,
1997
:
Factors influencing the variability of midwinter snow-depth decrease in the northern Great Plains of the United States.
Phys. Geogr.
,
18
,
408
423
.
Guryanov
,
I. E.
,
1985
:
Thermal-physical characteristics of frozen, thawing and unfrozen grounds. Proc. Fourth Int. Symp. on Ground Freezing, Sapporo, Japan, 225–230
.
Gustafsson
,
D.
,
M.
Stahli
, and
P. E.
Jansson
,
2001
:
The surface energy balance of a snow cover: Comparing measurements to two different simulation models.
Theor. Appl. Climatol.
,
70
,
81
96
.
Hardy
,
J. P.
,
R.
Melloh
,
P.
Robinson
, and
R.
Jordan
,
2000
:
Incorporating effects of forest litter in a snow process model.
Hydrol. Processes
,
14
,
3227
3237
.
Hellström
,
R. A.
,
2000
:
Forest cover algorithms for estimating meteorological forcing in a numerical snow model.
Hydrol. Processes
,
14
,
3239
3256
.
Jin
,
J.
,
X.
Gao
,
S.
Sorooshian
,
Z-L.
Yang
,
R.
Bales
,
R. E.
Dickinson
,
S-F.
Sun
, and
G-X.
Wu
,
1999
:
One-dimensional snow water and energy balance model for vegetated surfaces.
Hydrol. Processes
,
13
,
2467
2482
.
Jordan
,
R.
,
1991
:
A one-dimensional temperature model for a snowcover: Technical documentation for SNTHERM.89. Special Rep. 91-16, U.S. Army Corps of Engineers Cold Regions Research and Engineering Laboratory, Hanover, NH, 64 pp
.
Jordan
,
R.
,
E. L.
Andreas
, and
A. P.
Makshtas
,
1999
:
Heat budget of snow-covered sea ice at North Pole 4.
J. Geophys. Res.
,
104
,
7785
7806
.
Koivusalo
,
H.
, and
M.
Heikinheimo
,
1999
:
Surface energy exchange over a boreal snowpack: Comparison of two snow energy balance models.
Hydrol. Processes
,
13
,
2395
2408
.
Koivusalo
,
H.
,
M.
Heikinheimo
, and
T.
Karvonen
,
2001
:
Test of a simple two-layer parameterisation to simulate the energy balance and temperature of a snow pack.
Theor. Appl. Climatol.
,
70
,
65
79
.
Leathers
,
D. J.
,
D. R.
Kluck
, and
S.
Kroczynski
,
1998
:
The severe flooding event of January 1996 across north-central Pennsylvania.
Bull. Amer. Meteor. Soc.
,
79
,
785
797
.
Li
,
L.
, and
J. W.
Pomeroy
,
1997
:
Estimates of threshold wind speeds for snow transport using meteorological data.
J. Appl. Meteor.
,
36
,
205
213
.
Melloh
,
R. A.
,
T. J.
Hall
, and
R.
Bailey
,
2004
:
Radiation data corrections for snow-covered sensors: Are they needed for snowmelt modelling?
Hydrol. Processes
,
18
,
1113
1126
.
Mote
,
T. L.
,
A. J.
Grundstein
,
D. J.
Leathers
, and
D. A.
Robinson
,
2003
:
A comparison of modeled, remotely sensed, and measured snow water equivalent in the northern Great Plains.
Water Resour. Res.
,
39
.
1209, doi:10.1029/2002WR001782
.
NSIDC
,
cited
.
2005
:
State of the cryosphere. [Available online at http://nsidc.org/sotc/snow_extent.html.]
.
Pomeroy
,
J. W.
,
D. M.
Gray
, and
P. G.
Landine
,
1993
:
The Prairie Blowing Snow Model: Characteristics, validation, operation.
J. Hydrol.
,
144
,
165
192
.
Schulz
,
O.
, and
C.
de Jong
,
2004
:
Snowmelt and sublimation: Field experiments and modelling in the High Atlas Mountains of Morocco.
Hydrol. Earth Syst. Sci.
,
8
,
1076
1089
.
Semadeni-Davies
,
A.
,
D.
Marechal
,
O.
Bruland
,
Y.
Kodama
, and
K.
Sand
,
2004
:
Estimating latent heat over a melting arctic snow cover.
Nord. Hydrol.
,
35
,
175
190
.
Tarboton
,
D. G.
, and
C. H.
Luce
,
1996
:
Utah Energy Balance Snow Accumulation and Melt Model (UEB). Utah Water Research Laboratory, Utah State University, and USDA Forest Service Intermountain Research Station, 63 pp
.
Watson
,
F.
,
W.
Newman
,
J.
Coughlan
, and
R.
Garrott
,
2006
:
Testing a distributed snowpack simulation model against spatial observations.
J. Hydrol.
,
328
,
453
466
.
Wiesmann
,
A.
,
C.
Fierz
, and
C.
Matzler
,
2000
:
2000: Simulation of microwave emission from physically modeled snowpacks.
Ann. Glaciol.
,
31
,
397
405
.
Williams
,
M. W.
,
D.
Cline
,
M.
Hartman
, and
T.
Bardsley
,
1999
:
Data for snowmelt model development, calibration, and verification at an alpine site, Colorado Front Range.
Water Resour. Res.
,
35
,
3205
3209
.
Yang
,
Z. L.
, and
Coauthors
,
1999
:
Simulation of snow mass and extent in general circulation models.
Hydrol. Processes
,
13
,
2097
2113
.

Footnotes

Corresponding author address: Nick Rutter, Department of Geography, University of Sheffield, Sheffield, S10 2TN, United Kingdom. Email: n.rutter@sheffield.ac.uk

This article included in the The Cold Land Processes Experiment (CLPX) special collection.