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SnowSTAR2002 Transect Reconstruction Using a Multilayered Energy and Mass Balance Snow Model XIAOGANG SHI Department of Civil and Environmental Engineering, University of Washington, Seattle, Washington

MATTHEW STURM U.S. Army Cold Regions Research and Engineering Laboratory, Fort Wainwright, Alaska

GLEN E. LISTON Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

RACHEL E. JORDAN U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire

DENNIS P. LETTENMAIER Department of Civil and Environmental Engineering, University of Washington, Seattle, Washington (Manuscript received 15 September 2008, in final form 28 February 2009) ABSTRACT The lateral and vertical variability of snow stratigraphy was investigated through the comparison of the measured profiles of snow density, temperature, and grain size obtained during the Snow Science Traverse— Alaska Region (SnowSTAR2002) 1200-km transect from Nome to Barrow with model reconstructions from the Snow Thermal Model (SNTHERM), a multilayered energy and mass balance snow model. Model profiles were simulated at the SnowSTAR2002 observation sites using the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) as meteorological forcing. ERA-40 precipitation was rescaled so that the total snow water equivalent (SWE) on the SnowSTAR2002 observation dates equaled the observed values. The mean absolute error (MAE) of measured and simulated snow properties shows that SNTHERM was able to produce good simulations for snowpack temperature but larger errors for grain size and density. A spatial similarity analysis using semivariograms of measured profiles shows that there is diverse lateral and vertical variability for snow properties along the SnowSTAR2002 transect resulting from differences in initial snow deposition, influenced by wind, vegetation, topography, and postdepositional mechanical and thermal metamorphism. The correlation length in snow density (42 km) is quite low, whereas it is slightly longer for snow grain size (125 km) and longer still for snow temperature (130 km). An important practical question that the observed and reconstructed profiles allow to be addressed is the implications of model errors in the observed snow properties for simulated microwave emissions signatures. The Microwave Emission Model for Layered Snowpacks (MEMLS) was used to simulate 19- and 37-GHz brightness temperatures. Comparison of SNTHERM–MEMLS and SnowSTAR2002–MEMLS brightness temperatures showed a very good match occurs at 19 GHz [a root-mean-square error (RMSE) of 1.5 K (8.7 K) for vertical (horizontal) polarization] and somewhat larger [5.9 K (6.2 K) for vertical (horizontal) polarization] at 37 GHz. These results imply that the simulation of snow microphysical profiles is a viable strategy for passive microwave satellite–based retrievals of SWE.

Corresponding author address: Dennis P. Lettenmaier, Department of Civil and Environmental Engineering, University of Washington, 164 Wilcox Hall, Box 352700, Seattle, WA 98195-2700. E-mail: [email protected] DOI: 10.1175/2009JHM1098.1 Ó 2009 American Meteorological Society

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1. Introduction Throughout northwestern Alaska, almost all winter precipitation falls in solid form. The winter snow cover affects atmospheric and soil temperatures by moderating conductive, sensible, and latent energy transfers between the atmosphere, snow cover, and ground (e.g., Hinzman et al. 1998; Nelson et al. 1998; Liston 1999). The lateral and vertical variability in the resulting snowpack strongly affects hydrological and meteorological processes in the region. During the snow accumulation period, snow properties vary vertically in the snowpack as a result of the heterogeneity introduced by the initial deposition, which may be influenced by wind, vegetation, topography, and other land surface properties, and postdepositional mechanical and thermal metamorphic processes. This heterogeneity is widely recognized but only rarely has it been quantified or discussed (Sturm et al. 2004). The layered character resulting from sequences of weather events has been noted by observers of snow covers as early as the work of Seligman (1936). Nevertheless, most snow studies (e.g., Verseghy 1991; Xue et al. 1991; Tarboton and Luce 1996; Kite 1995) have treated the snow cover as a single layer with a simple statistical distribution for each property, and they have not explicitly represented its stratification and the interactions among the layers. The motivation for these simplifications is apparent given the complicated nature of snow stratigraphy, which is influenced not only by the intricate physics of the layered media but also by the abovementioned lateral and vertical variability. Colbeck (1991), among others, has argued that the layered nature of snowpacks should not be ignored because essentially all physical properties of snow are affected by layering and other internal structures that layering causes to happen. To determine the lateral and vertical variability of snow cover characteristics across northwestern Alaska, the second and third authors led a transect known as Snow Science Traverse—Alaska Region (SnowSTAR2002) from 24 March to 26 April 2002 (Douglas and Sturm 2004). The expedition covered roughly 1200 km, starting from Nome and proceeding northeast through the Brooks Range to Barrow (Fig. 1). Snow pits (snow profile samples) were collected at 76 stations along the route. These measurements were taken within a few weeks of the onset of the spring snowmelt period and are considered to represent end-of-winter conditions. In this paper, we evaluate simulations of some of the same snow microphysical properties that were observed in SnowSTAR2002 snow pits using the multilayered one-dimensional Snow Thermal Model (SNTHERM)

FIG. 1. SnowSTAR2002 transect including all sampling sites and four index sites as well as two SNOTEL validation sites.

(Jordan 1991; Jordan et al. 1999). SNTHERM accounts for the snowpack mass and energy balance in multiple layers, and simulates, in addition to snow water equivalent (SWE), profiles of snow microphysical properties, such as temperature, density, and grain size. The model uses meteorological observations as the upper-boundary conditions and assumes a steady state at the lower boundary. SNTHERM is driven by external meteorological data and is initialized with information about the snowpack and underlying soil layer. The mass and energy balances within the snowpack are driven by surface mass and energy fluxes. The surface fluxes are determined from user-supplied meteorological data, which include air temperature, humidity, wind speed, precipitation, incoming and outgoing shortwave radiation, and incoming longwave radiation. A numerical solution is found for the governing equations of energy and mass balance for each of the layers. Snow hydrology models [e.g., the snow-evolution model (SnowModel) of Liston et al. (2006) and Mernild et al. (2008), and the image version of the snowcover energy and mass-balance model (ISNOBAL) of Marks et al. (1999, 2002)] have been used to simulate snowpack properties over large areas for a variety of purposes, ranging from the representation of the land surface in coupled land– atmosphere models for weather and climate prediction, the simulation of snowpack microwave emissions (in

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offline applications for purposes of recovering, from satellite sensors, estimates of SWE), to water management. The SnowSTAR2002 transect provides a unique opportunity to evaluate model simulations of snowpack properties over a spatial scale similar to the continental scales at which these models are applied. In this study, we used the public version of the snowpack model SNTHERM.89 (Jordan 1991), which has been previously applied in northern Finland (Koivusalo et al. 1996, 1999); Greenland (Nolin and Stroeve 1997); Saskatchewan and Manitoba, Canada (Davis et al. 1997); California (Colee et al. 2000); and Vermont (Hardy et al. 2000), as the basis for comparison with the SnowSTAR2002 observations.

2. Data and model The study domain is the SnowSTAR2002 transect in northwestern Alaska. Detailed snow pit measurements of snow temperature, snow density, snow grain size, and other snow parameters (e.g., snow depth and SWE) were taken along the SnowSTAR2002 transect (Sturm and Liston 2003). Following quality control based on the availability of snow variables and data records, field measurements at 49 sites along the SnowSTAR2002 transect, which have all the variables described earlier with full records, were used in this study. Figure 2 shows summary histograms of observed SWE, snow depth, snowpack temperature, snow density, and grain size from these 49 sites. There are substantial variations for all properties but especially for snow density and grain size. Figure 3 shows the measured profiles of snowpack temperature, snow density, and grain size with a normalized snow depth (0–1) for the 49 snow pit locations. Figure 3a shows the signature of differences in air temperature along the Nome–Barrow transect on snowpack temperature profiles. At each snow pit, there is fairly high similarity along the measured vertical temperature profiles. However, it should be noted that there are substantial differences for temperature profiles among the sites from Nome to Barrow. Figure 3b shows high lateral and vertical variability in snow density. On the other hand, the lateral variability of snow grain size is somewhat smaller because stratigraphic layers retain some similarities at relatively large (hundreds of kilometers) spatial scales.

a. Estimation of SNTHERM forcing data SNTHERM was used to simulate the observed snow profiles at the measurement sites, including their history from the beginning of the winter season to the observation dates. Meteorological forcings to SNTHERM include air temperature, precipitation, relative humidity, wind speed, downward and reflected solar radiation,

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and downward longwave radiation. Using these, the model computes the snowpack water and energy balances as well as the profiles of snowpack temperature, density, and grain size. We forced SNTHERM with hourly meteorological input, starting from the end of September (prior to snowfall) through the SnowSTAR2002 observation dates. The initial soil thermal condition for the soil profile was adjusted based on measured data from Welker et al. (2003), and the barometric pressure was set as 990 mb (Jordan 1991). Lacking a detailed time series for the model forcing variables at the measurement sites, 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data (Uppala et al. 2005) were interpolated to the measurement locations from their native spatial resolution of about 1.1258 3 1.1258. The Synagraphic Mapping System (SYMAP) method (Shepard 1984), based on the inverse square of the distances to the target grid cell, was used for this purpose, at a daily time step. Because the ERA-40 data are derived from a global model, inevitably there are mismatches between local and interpolated conditions. In general, particularly during the winter season, the greatest mismatches are in precipitation. Therefore, we used a rescaling approach (described in more detail in section 3) in which we adjusted the ERA-40 precipitation from the beginning of the winter to the time of observation in such a way that the SNTHERM simulation of SWE matched the observations. All other SNTHERM forcings (air temperature, relative humidity, downward solar radiation, longwave radiation, upward solar radiation, and surface wind) are included in or can be derived from the ERA-40 dataset. SNTHERM also requires forcings at an hourly time step. We therefore interpolated daily rescaled precipitation data to hourly steps by dividing by 24 (Bowling et al. 2003). Wind speed was treated as uniform throughout the day, as in Maurer et al. (2002). The disaggregation of other variables is discussed later. Hourly temperature data were estimated as follows. On each day, the daily maximum and minimum 6-hourly air temperatures were extracted from ERA-40, and the ratio of the range from the 6-hourly values to the range from observed hourly data at Barrow and Nome was computed. These two adjustment factors were linearly interpolated to the location of each observation site (using distances of the site from Barrow and Nome) and were used to produce adjusted Tmin and Tmax temperature values at the observation sites. To evaluate the procedure, we applied it to snowpack telemetry (SNOTEL) sites at Indian Pass and Munson Ridge (see Fig. 1), where observed daily maximum and minimum temperature data are available, using the same linear interpolation approach (based on distances of the SNOTEL sites from

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FIG. 2. Histograms of SWE, snow depth, snow density, snowpack temperature, and long and short snow grain size, at 49 sites along the SnowSTAR2002 transect.

Barrow and Nome). These SNOTEL sites, operated by the U.S. Department of Agriculture’s (USDA) Natural Resources Conservation Service, are located at 61.078N, 149.498W (Indian Pass) and at 64.858N, 146.218W (Munson Ridge). Figure 4 shows that the observed Tmin and Tmax values and the adjusted (adjustment factor interpolated from Barrow and Nome) ERA-40 Tmax and

Tmin correlate well with r2, typically in the range from 0.90 to 0.92, and the mean bias between 0.258 and 1.758C (Table 1). Once the daily Tmin and Tmax values were estimated from ERA-40, a disaggregation method was used to produce hourly air temperatures, based on a modified sine curve following the method of Running et al. (1987) and Parton and Logan (1981). The detailed

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FIG. 3. Measured profiles of (a) snow temperature, (b) snow density, (c) snow grain size with a normalized snow depth at 49 snow pits along the SnowSTAR2002 transect.

calculation procedure for daytime and nighttime air temperatures is given by Waichler and Wigmosta (2003). Relative humidity was calculated by the method described in Maurer et al. (2002), which essentially sets the dewpoint to the daily minimum temperature. Downward longwave radiation was estimated using Eq. (2.42) from Bras (1990), which is based on hourly air temperature and a function for emissivity from TVA (1972). In the calculation of downward shortwave radiation, a solar geometry model (Gates 1980) was applied first to obtain

the total daily solar radiation incident at the top of the atmosphere based on the latitude and time of year. Next, the Bristow and Campbell (1984) model was applied to obtain the daily atmospheric transmittance based on daily maximum and minimum air temperatures from ERA-40. Then, the downward solar radiation to level ground was calculated by the product of solar radiation incident at the top of the atmosphere and atmospheric transmittance. The reflected downward solar radiation was determined from the above downward

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FIG. 4. Comparison of daily adjusted maximum and minimum ERA-40 and observed air temperature at (a) Indian Pass and (b) Munson Ridge.

solar radiation and albedo calculated from the albedo model in SNTHERM.

b. Microwave emissions model and forcings Passive microwave remote sensing methods offer the possibility of retrieving SWE remotely. The underlying principle is that snow dielectric properties, and in particular water content, affect the naturally emitted radiation from the earth, with the signature particularly strong at microwave frequencies. However, the retrieval of SWE (generally, the snowpack variable of greatest hydrologic interest) is complicated by the dependence of the signal on snow microphysical properties (specifi-

cally, temperature, density, grain size, and liquid water) as well. This is an issue that will have to be addressed by proposed satellite missions, such as the European Space Agency’s Cold Regions Hydrology High-resolution Observatory (CoReH2O) mission concept and the notional Snow and Cold Land Processes (SCLP) mission (National Academy of Sciences 2007). As a practical matter, there is no current method for measuring snow microphysical properties at large scales. Instead, physically based retrieval algorithms will have to be used to simulate these properties. We therefore used an existing multilayer microwave emissions model, the Microwave Emission Model of Layered Snowpacks (MEMLS) of

TABLE 1. Correlation of daily adjusted maximum and minimum ERA-40 temperatures and observed values at two validation sites.

Station name

Latitude (8N)

Longitude (8W)

Elevation (m)

Tmax correlation

Tmin correlation

Tmax mean bias (8C)

Tmin mean bias (8C)

Indian Pass Munson Ridge

61.07 64.85

149.49 146.21

716 945

0.92 0.91

0.92 0.90

0.96 1.75

1.51 0.25

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Wiesmann and Ma¨tzler (1999), to compute the emissions at the two frequencies (19 and 37 GHz, which are the two frequencies used in most SWE retrieval algorithms), in both horizontal (H) and vertical (V) polarizations. Here we refer to these frequencies as 19V, 19H, 37V, and 37H. These computations were performed using both the observed profiles of snow temperature, grain size, and the density from each of the 49 transect sites and those predicted by SNTHERM. We emphasize that these simulations are intended for the limited purpose of evaluating the feasibility of simulating microphysical properties of the snowpack at large scales. MEMLS is based on radiative transfer theory using the 6-flux (streams in all space directions along and opposed to the three principle axes) formulation to describe multiple volume scattering and absorption. The scattering coefficient is a function of correlation length, snow density, and frequency, whereas the absorption coefficient is a function of snow density, frequency, and snow temperature. The total emissivity (snowpack and ground) for horizontal and vertical polarizations is calculated as described in Wiesmann and Ma¨tzler (1999) as well as the numerical relationship of how ambient temperature relates to snowpack surface brightness temperature. MEMLS has been applied successfully to simulate emissivity from layered snowpacks over land (Ma¨tzler et al. 1999) and sea ice (Powell et al. 2006). The input data to MEMLS includes snow temperature (K), volumetric liquid water content (0–1), snow density (kg m23), snow salinity (parts per thousand, ppt), and correlation length (used to characterize the size of the snow particles within a snow layer) for each of a number of user-defined snow layers. The snow grain size in SNTHERM is the optical grain diameter (do; Jordan 1991), which has a linear relation with exponential correlation length (Pex) given by Pex 5 do 3 0.16

(1)

(Wiesmann et al. 2000). The observed ‘‘long grain size’’ from the SnowSTAR2002 snow pits is typically regarded as what Colbeck et al. (1990) titled the maximum diameter (Dmax). For a spherical snow particle, Ma¨tzler (2002) suggests a relationship between Dmax and Pex of the form Pex 5 0.5D(1

y),

(2)

where y 5 (rs/ri) is the volume fraction of ice, rs is the snow density, ri 5 917 kg m23 is the ice density, and D 5 Dmax. MEMLS was designed for application to the frequency range 5–100 GHz.

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FIG. 5. Cumulative precipitation comparison between the ERA-40 and observed data at Indian Pass. OBS_P is observed cumulative precipitation; ERA-40 is cumulative ERA-40 precipitation.

3. Precipitation scaling approach and evaluation Among the meteorological variables that force the SNTHERM model, precipitation is of paramount importance. As noted before, we adjusted the interpolated ERA-40 precipitation to match observed SWE on the observation dates in a manner similar to Liston and Sturm (2002). We first tested this method at the Indian Pass and Munson Ridge SNOTEL sites where continuous records of precipitation exist as well as other variables required to force SNTHERM (or from which forcing variables can be derived) and where SWE is observed as well. Figure 5 shows the accumulated precipitation for winter 2001/02 from ERA-40 interpolated to the Indian Pass site and from the local observations. The figure shows that although there were substantial differences in the magnitudes of the ERA-40 and observed values, the timing of major snow events was reasonably consistent. This general consistency in the timing of precipitation events in ERA-40 with observations motivated our approach to rescale the ERA-40 precipitation as follows: 1) For the day of a SnowSTAR2002 observation, such as 1 April, we defined a ratio R* of the observed SWE to the accumulated ERA-40 precipitation P* (interpolated spatially to the measurement site, as described in section 2a) up to the measurement date, R* 5 SWE*/P*. 2) This ratio R* was applied to rescale the ERA-40 precipitation on all days starting with the beginning of the winter season so as to produce a rescaled ERA-40 precipitation time series.

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FIG. 6. Observed and simulated SWE at (a) Indian Pass from 9 Oct 2001 to 1 Apr 2002 and (b) Munson Ridge from 6 Oct 2001 to 15 Apr 2002 using the rescaled ERA-40 precipitation.

3) We assume that all winter precipitation either adds to SWE or is sublimated (i.e., we assume that the effect of winter melt is negligible); therefore, SWE on the measurement date is given by SWE 5

åP åS,

(3)

where S is the sublimation rate and the summation is from the beginning of the winter season. The rescaled precipitation at any time is therefore given by   (4) P 5 DSWE 3 1 1 S/SWE ,

å

where S is the sublimation rate (which, in this case, we assume is constant for each site). Here DSWE is the successive difference of SWE over the time step (e.g., daily). Adjusting the ratio of the sublimation to snow water equivalent (åS/SWE) allows for the solution for the rescaled precipitation from ERA-40, and in particular, we force the predicted SWE to match on the observation date. Implementation of the earlier iterative process yielded the precipitation input time series required by SNTHERM. All other model forcing variables were taken from ERA-40, interpolated spatially to the measurement sites as described in section 2a. We tested the approach outlined earlier at both the Indian Pass and Munson Ridge SNOTEL sites where daily precipitation was recorded. Figures 6a,b show the results.

4. Results and discussion For purposes of examining the results, we focus on 4 of the 49 index sites (see Fig. 1). These index sites are

identified as CB-04T, AI-02F, CO-02, and AB-03L and are spaced more or less equally along the route of the SnowSTAR2002 transect.

a. Similarity analysis and simulation of snowpack microphysical properties In addition to the simulations of SWE (Fig. 7), which were essentially constrained to match observations, we compared SNTHERM simulations of snow depth with the SnowSTAR2002 observations. In general, the simulations of snow depth matched the observations quite well, as shown in Fig. 8, which compares the simulated snow depth with the observed values along the transect on the measurement dates.

1) SNOWPACK TEMPERATURE PROFILES Because our study domain in northwestern Alaska is fairly cold and windy in the winter, the effect of wind pumping (e.g., Clark et al. 1987; Colbeck 1989; Cunningham and Waddington 1993), which is not considered by the standard version of SNTHERM, can have a significant effect on heat transfer within the snowpack. We therefore used a modified version of SNTHERM that includes a wind pumping algorithm (see Jordan et al. 2003 for details), which essentially accounts for heat flux resulting from movement of air within the snowpack. Figure 9 shows the vertical variations of observed and simulated snowpack temperatures from the improved version of SNTHERM. Table 2 shows the mean absolute error (MAE) between the observed and simulated snow temperature profiles. It shows that the simulated snow temperature profiles matched observed values quite well. SNTHERM is a high physical fidelity snow model (Jordan et al. 1999). However, its soil model

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FIG. 7. Simulated SWE using adjusted ECMWF forcings at four index sites along the SnowSTAR2002 transect, terminating with observed SWE and date of observation (See Fig. 1 for index site locations).

is simple and does not include many of the energy transport processes common to soils. Therefore, in Fig. 9, it appears that errors of the snow temperature profiles increase closer to the snow–soil interface as a result of the simplified energy transport across the snow–soil interface, which only includes the thermal conduction and excludes the significant vapor diffusion. In particular, Fig. 9a also shows the initial simulation (without the wind pumping algorithm) of the in-snow temperature profile at the site of CB-04T. By applying the wind pumping routine, which treats heat convection resulting from 10-m wind speed interpolated from the lowest ERA-40 model level using surface layer profile functions (ECMWF 2004), the downward flow of cold air cooled the snow. The average temperature gradient, defined as the difference between the basal and surface temperatures of the snow cover divided by the thickness of the snowpack (Sturm 2003), provides a general index to microphysical processes in the snowpack. Previous research (e.g., Akitaya 1974; Armstrong 1980; Marbouty 1980) shows that the average temperature gradient plays an important role in the growth of snow grain size and the formation of depth hoar. Experimental work has shown that for dry snow, when the temperature gradient exceeds approximately 258C m21, kinetic growth will occur

in the snowpack, whereas for lower temperature gradients, equilibrium growth will take place (Marbouty 1980; Colbeck 1983). The sites with higher temperature gradient (e.g., site CO-02) generally have larger grain

FIG. 8. (a) Elevation of snow pits and (b) observed and simulated snow depth along the transect on the observation dates.

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FIG. 9. Comparison of observed and simulated profiles of snow temperature at four index stations shown in Fig. 1.

sizes and deep depth hoar, as shown in the profiles of snow density and snow grain size described in sections 4a(2) and 4a(3). Figure 10 shows the empirical semivariograms for the contributing site pairs at each lag for snow temperature, snow density, and snow grain size. We estimated the correlation length of snow properties with a nugget of zero based on a best-fit exponential semivariogram model. Given that the interval between sample sites is of the same order as the inferred correlation length and that the nugget effect is ignored, the correlation lengths are probably somewhat overestimated but nonetheless give a rough idea of the spatial coherence of the data. Using this approach, we found that the correlation length of snow temperature is about 130 km (Fig. 10a). This covariability is primarily related to spatial persistence in air temperature excursions, as shown in Fig. 3a.

2) SNOW DENSITY PROFILES Many physical processes occurring in snowpacks are related to snow density (Mellor 1975). The semivariogram in Fig. 10b shows that the spatial correlation length in snow density is quite short (42 km). This short TABLE 2. MAE of measured and modeled profiles of snow temperature, snow density, and snow grain size at four Index stations.

Index station CB-4T AI-02F CO-02 AB-03L

Latitude Longitude (8N) (8W) 65.3 67.4 69.1 70.8

162.1 157.5 155.6 157.1

Snow temperature (8C)

Snow density (kg m23)

Snow grain size (mm)

0.7 1.3 0.4 1.2

106.7 79.3 75.8 41.9

0.5 1.2 1.4 0.3

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tation during melt events, they usually result in a signature in the snow stratigraphy. Table 2 shows the MAE between the observed and simulated snow density profiles. Overall, SNTHERM was able to provide a better simulation of the snow density profiles. Figure 11 shows the simulated and observed snow density profiles for the four index stations. The figure does, however, show some evidence of basal depth hoar layers along the transect, which are not represented in SNTHERM. These layers of deep depth hoar may result from the strong temperature gradient across the snow due to the heat fluxes from the ground and extremely low air temperatures. By the time of the observations in early spring, these residual early season effects were modulated to some extent, however, by metamorphic processes occurring throughout the winter. The simulated snow density profiles at the four index sites also show that SNTHERM fails to capture the hard and thin wind slab because of the limitation of point model structure in representing the wind action (e.g., wind compaction effect). In addition, when a strong wind starts to blow, a wind slab can be generated within minutes and may form in extremely localized areas. For these reasons, it is difficult to simulate wind slab very well, even when using current distributed snow models.

3) SNOW GRAIN SIZE PROFILES

FIG. 10. Semivariograms with a best-fit exponential model (a) snow temperature, (b) snow density, and (c) snow grain size for 49 sites along the SnowSTAR2002 transect.

correlation length reflects high lateral variability in the intersite means as well as vertical variability, which is also suggested by Fig. 3b. Generally, the melting of the snow surface, which results in strong density layering, is due to either or both turbulent energy transfer (warm overlying air) and net radiation. If the maximum daily temperature is above the melting point, then precipitation falling as rain, although infrequent, is almost certain to be evidenced in the snow stratigraphy, and even if there is no precipi-

Snow grain size is the primary parameter that controls snow albedo and infiltration as well as microwave emission. Because the rate of grain growth depends not only on snow temperature but also on the temperature gradient, changes in snow grain size are also important indicators of thermodynamic processes. Snow grain size measurements along the SnowSTAR2002 transect were made using a stereo microscope (Nikon Fieldscope) with reticule graduations of 0.5 mm. Visual estimates of multiple grains were made to measure the mean short and long axes of the grains. In the calculation of exponential correlation length (Fig. 10c), the measurement of long grain size is referred to as Dmax. Figure 12 shows the simulated vertical variations of snow grain size at the four index stations, from CB-04T at the southern end of the transect to AB-3L, which is near the north end. Snow grain size generally increases with depth. At each site, the snowpack consists of a bottom layer of thickness generally less than 5.0–15.0 cm. For some sites, the basal depth hoar was well developed with mean snow grain size up to 6.0 mm. For the layers at which there had been wet snow metamorphism, the grain size was about 1.0–20.0 mm in diameter. The new snow layer at the top of the profiles is generally characterized by small nonspherical particles with a characteristic dimension that is usually less than 1.0 mm, as

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FIG. 11. Same as Fig. 9 but for snow density.

shown in Fig. 3c. The semivariogram in Fig. 10c shows a correlation length of 125 km in snow grain size. This is slightly smaller than the correlation length for snow temperature (130 km) but about triple the correlation length for snow density (42 km).

b. MAE evaluation of snow profiles The modeled profiles from SNTHERM have a much higher vertical resolution than the observed profiles from snow pit measurements. Therefore, before comparing the modeled and observed profiles, the first step was to adjust for differences in the simulated and observed snow depth. We did this by stretching or compressing the modeled profiles linearly to match the corresponding observed snow depth. To ensure mass consistency caused by the snow depth adjustment, we used a stretch factor defined

by Lehning et al. (2001) to adjust the snow density. Because of the differences between the modeled and observed snow microphysical properties (e.g., snow density), there are some differences in snow depth in some sites, although the simulations of snow depth in general matched the observations quite well. Along the SnowSTAR2002 transect, the relative RMSE of snow depth was 9.8% for the SNTHERM simulations. For the sites that have a small difference (less then 1%) between the measured and modeled snow depth, the adjustment of snow density was neglected. Then, we mapped the model profile layers onto the layers of the observed profile using the depth-weighted linear interpolation and compared the snow grain size, snow temperature, and snow density of each layer. This procedure ensures a realistic comparison between model and observed profiles.

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FIG. 12. Same as Fig. 9 but for snow grain size.

We also calculated the MAE between the simulated and observed snow density, snow temperature, and snow grain size (after the depth adjustment) at each measurement location. Figure 13 shows the envelope of maximum and minimum temperature, density, and grain size and MAE values along the SnowSTAR2002 transect. The mean MAE for snow temperature along the SnowSTAR2002 transect is 1.88C, with a mean value of snow temperature profiles of 10.68C. For snow density, the mean MAE is 76 kg m23, whereas the mean density profile is 294 kg m23; for grain size, the MAE is 1.2 mm with a mean of 2.2 mm. The MAE of the measured and simulated snow properties at each of the measurement locations shows that SNTHERM was able to produce simulations for temperature that matched observations quite closely, with larger errors for grain size and density.

c. Comparison of microwave signatures As stated earlier, the microwave emission signature of snow is dominated by microphysical snow properties, such as snow grain size, snow density and snowpack temperature, in addition to SWE. For purposes of the simulations described in section 2b, the exponential correlation length parameter was determined using Eqs. (1) and (2), except that the constants were changed to 0.1 and 0.05, respectively. The original constants in equations generated unrealistically large correlation lengths that resulted in erroneous brightness temperatures using MEMLS. We then simulated brightness temperatures at 19 and 37 GHz using MEMLS for both the observed and SNTHERM simulations of snowpack temperature, density, and grain size profiles. On all of the measurement

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wave Radiometer (SMMR; 508) instruments, for the period of SnowSTAR2002 observations from 24 March to 26 April. Compared with other sources of errors in estimates of snowpack microwave emissions (e.g., spatial variations in snowpack properties, vegetation, and other land cover variations over typical satellite footprints) that result in microwave brightness temperature (Tb) discrepancies of 10 K or more, the results are encouraging. The best match is an RMSE of 1.5 K at the 19-GHz vertical polarization, whereas the RMSE is 8.7 K for the 19-GHz horizontal polarization. At 37 GHz, the RMSE is 5.9 K for the 37-GHz vertical polarization and 6.2 K for the 3-GHz horizontal polarization. The larger errors in RMSE at 19H and 37H may be due to wind slab effects near the top of the snowpack and depth hoar or ice layering at the bottom (especially for 19 GHz, which has a greater penetration depth than 37 GHz), which have a large influence on the horizontally polarized brightness temperatures (Durand et al. 2008) as well as surface roughness, as described by Stroeve et al. (2006). The effect of depth hoar on microwave emissions is also consistent with the results of Sturm et al. (1993).

5. Conclusions FIG. 13. (left axis) MAE of measured and modeled profiles and (right axis) minimum and maximum observed values of snow temperature, snow density, and snow grain size for each profile at 49 sites along the SnowSTAR2002 transect.

dates, dry snow conditions prevailed, which is a key assumption for microwave emission retrievals using models like MEMLS. In addition, we assumed that the brightness temperature calculated by MEMLS using field measurements from the SnowSTAR2002 transect is the ‘‘true’’ value in evaluating the differences. We emphasize that the simulations capture only the sensitivity of MEMLS to differences in the simulated and observed snowpack microphysical properties; no observations of the microwave brightness temperature were available. Nonetheless, the availability of the snow profiles over such a long transect, and over a range of conditions, affords a unique opportunity to evaluate the magnitude of one important source of error in microwave retrieval algorithms (e.g., Chang et al. 1987a; Goodison 1989; Tait 1998). Figure 14 shows the simulated brightness temperatures at a 538 incidence angle, which is identical to the incidence angle of the Special Sensor Microwave Imager (SSM/I) and close to those of the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E; 558) and the Scanning Multichannel Micro-

Field measurements of snow properties show that there is significant lateral and vertical variability along the SnowSTAR2002 transect. Using the spatial similarity analysis, we found correlation lengths of measured profiles in snowpack temperature, snow density, and snow grain size of 130, 42, and 125 km, respectively. The short correlation length in snow density indicates that the spatial similarity is low and reflects high lateral and interprofile variability. This large variation in snow density over relatively short distances may be attributable to the effects of wind slabs, which are not represented in SNTHERM. The longer correlation length in snow grain size reflects both spatial similarities in mean (depth integrated) values and similarities in the profile shapes. The relatively long correlation length of snowpack temperatures mostly reflects spatial persistence in air temperatures, which propagate through the snowpacks. The MAE of the measured and simulated snow properties at each of snow pits shows that SNTHERM has the ability to recover observed microphysical structures (snow states, including snow depth, density, and snow grain size, among others) of snow cover along the SnowSTAR2002 transect at the point scale and capture most of snowpack characterization. In particular, it does quite well for profile simulations of snow temperature, less well for snow density, and the worst for snow grain size.

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FIG. 14. Comparison simulated brightness temperatures using MEMLS model with SNTHERM simulation of profile microphysical properties (temperature, grain size, and density) and observed (on SnowSTAR2002 measurement dates) for 19V, 19H, 37V, and 37H.

Moreover, a quantitative assessment of the consistency of passive microwave emissions signatures at 19 and 37 GHz predicted using observed and simulated temperature, density, and grain size profiles showed the differences were quite small. The comparison of simulated brightness temperatures using the two sources of snow profile data showed quite good agreement between SNTHERM–MEMLS and SnowSTAR2002–MEMLS. The best matches were at 19 GHz, with an RMSE of 1.5 K for H polarization and 8.7 K for V, whereas at 37 GHz the RMSEs were 5.9 K for V and 6.2 K for H. These errors are generally lower than the effects of, for instance, mixed land cover types over the relatively large satellite footprints, and although they do not account for model and other sources of error, they do give encouragement to strategies that would extract snowpack microphysical profile information from model simulations. Also, this work has great potential for the global prediction of the snow properties (snow density, temperature, and grain size) that are needed for microwave remote sensing retrievals of snow water equivalent and snow extent. Although the results are of course limited to the range of conditions we encountered, as a practical matter, the passive microwave retrieval of SWE is most feasible under cold, dry snowpack conditions similar to those in Alaska; therefore, within those constraints, the work is clearly adaptable.

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