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Keywords:

  • mass balance;
  • remote sensing of snow;
  • Sierra Nevada;
  • snow albedo;
  • snow water equivalent;
  • snowmelt modeling

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[1] Two commonly used snow surface albedo models were evaluated using albedo data from the Airborne Visible/Infrared Imaging Spectroradiometer (AVIRIS), and their influence on snowmelt timing and magnitude was assessed using a net radiation/temperature index snowmelt model, a series of satellite-based snow covered area scenes, and on-site snow surveys. Albedo estimates using an explicit representation of snow surface temperature, snow age, and solar illumination angle, based on the Biosphere Atmosphere Transfer Scheme (BATS), were within the 0.02 AVIRIS measurement error for 78% of the snow-covered portions of the watershed. Conversely, albedo values estimated using a simple model based solely on snow surface age underestimated AVIRIS-observed albedo. Correlations between the timing of snowmelt and observed runoff using the BATS albedo model (R2 = 0.69) were significantly better than those using the age-based approach (R2 = 0.59) and were comparable to using AVIRIS data (R2 = 0.73). Snow extent was simulated most accurately with the AVIRIS parameterization; average map accuracy was 79 and 10% greater than when using the age-based and BATS albedo parameterizations, respectively. The error in snow water equivalent for April was 14% for BATS versus 39% for the age-based albedo; however, it was less than 1% for simulations using AVIRIS albedo data. Thus the BATS albedo estimates performed better than the age-based albedo but did not outperform simulations using AVIRIS albedo data.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[2] In many semiarid mountainous regions the mountain snowpack is the fundamental hydrologic driver, with downstream hydrologic processes (e.g., groundwater recharge) and water-ecosystem interactions being controlled by processes at higher elevations. The processes controlling the extent of snow coverage, the accumulation of snow water equivalent and patterns of snowmelt are highly variable in time and space, as gradients in physiography (e.g., topography and vegetation) combine to create nonlinear mosaics in energy fluxes, precipitation, and wind fields. In alpine regions, energy exchange between the snowpack and the atmosphere is dominated by radiative fluxes, accounting for as much as 75% of melt energy in some cases [Cline, 1997; Marks and Dozier, 1992]. Hence the representation of snow surface albedo is particularly important for hydrologic simulations [Blöschl, 1991].

[3] Snow-age-based albedo estimates [e.g., U.S. Army Corps of Engineers, 1956] have been widely applied in hydrology [Blöschl, 1991; Blöschl and Kirnbauer, 1991; Cline et al., 1998; Molotch et al., 2004], due in part to their computational simplicity. Albedo parameterizations that explicitly represent snow grain size and the effect of solar illumination angle on albedo, such as the two-stream radiative transfer model of Warren and Wiscombe [1980], are not widely transferable given the computational expense of representing snow grain size within physically based models, e.g., SNTHERM [Jordan, 1991] and CROCUS [Brun et al., 1989, 1992]. A compromise between the age-based approach and that of Warren and Wiscombe [1980] are albedo parameterizations that approximate metamorphic state as a function of snow age and snow surface temperature and include impacts of solar illumination angle on albedo. Although developed for use in land surface models (e.g., the Biosphere Atmosphere Transfer Scheme (BATS) [Dickinson et al., 1993]), this type of parameterization has also found use in hydrologic applications [Tarboton and Luce, 1997]. However, spatial evaluations of these albedo models are lacking, because detailed spectral measurements of radiation are rare in remote snow-covered regions [Marks and Dozier, 1992]. Recent advances in airborne hyperspectral remote sensing have afforded the ability to make accurate spatial estimates of snow surface albedo [Painter et al., 2003]. Spaceborne systems (e.g., Landsat) have also been used to measure the spatial distribution of snow surface albedo over glaciated terrain [Greuell and Oerlemans, 2004; Klok and Oerlemans, 2004].

[4] Using a relatively simple snowmelt model, Molotch et al. [2004] showed that estimates of the timing and magnitude of snowmelt can be improved using remotely sensed snow surface albedo data from the aircraft-based Airborne Visible/Infrared Imaging Spectroradiometer (AVIRIS) [Painter et al., 2003] as compared to a widely used snow-age-based albedo parameterization [U.S. Army Corps of Engineers, 1956]. However, AVIRIS is a research instrument with limited capability for covering large areas yielding frequent data. Although satellite-based albedo data are available from the Moderate Resolution Imaging Spectrometer (MODIS), scenes are often obscured by clouds and temporal resolution is dramatically reduced. Forest cover further limits the utility of remotely sensed albedo data in that viewable gap fractions are dramatically reduced for operational sensors with high scanning angles [Liu et al., 2004].

[5] The aim of the research reported in this paper is to evaluate a more physically based albedo parameterization for optically thick snow [Dickinson et al., 1993] versus an age-based approach [U.S. Army Corps of Engineers, 1956] using albedo data from AVIRIS. We compare the effect of the different albedo parameterizations on snowmelt simulations using a temperature index model that explicitly accounts for radiative fluxes. We also address the question of what are the physiographic and meteorological controls on the spatial and temporal differences in albedo estimates and snowpack mass balance model accuracies.

2. Study Area

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[6] This research was performed in the Tokopah Basin of the Sierra Nevada, California (36°36′N, 118°40W) (Figure 1), which has an area of 19.1 km2 and an elevation range of 2629–3487 m. Granitic bedrock is exposed at the surface throughout much of the watershed, with thin soils and forest cover restricted to small areas of the valley floor. The 1.2 km2 Emerald subbasin is a north facing cirque with an average slope of 26° and an elevation range of 2801–3372 m [Tonnessen, 1991]. The topography of the 1.5 km2 Topaz subbasin is relatively homogeneous and south facing, with an average slope of 11° and an elevation range of 3188–3487 m. Both subbasins contain streamflow gages at the respective basin outflows and meteorological stations that record hourly air temperature, wind speed, incoming solar and thermal radiation, and relative humidity (Figure 1). The hydrology of the watershed is typical of the alpine Sierra Nevada, with most of the annual precipitation inputs occurring between October and April in the form of snowfall, and with snowmelt beginning in early April and extending into June and sometimes August.

image

Figure 1. Tokopah basin with a 50-m contour interval. Streamflow gauges, meteorological stations, and the Emerald and Topaz subbasins are also shown.

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3. Methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

3.1. Snow Surface Albedo

[7] Albedo was estimated throughout the snowmelt season (i.e., 6 April to 27 July 1997) using three approaches: (1) a pixel-specific albedo decay function based on 3 AVIRIS scenes (5 May, 21 May, and 18 June 1997) [Molotch et al., 2004], (2) a decay function developed from first principles for the BATS model, and based on solar zenith angle, snow temperature, and snow age [Dickinson et al., 1993], and (3) an empirically derived standard albedo decay function (SADF) based solely on snow surface age [U.S. Army Corps of Engineers, 1956].

[8] Snow surface albedo was obtained from the AVIRIS scenes using a spectral unmixing model that has a measurement error of 0.02 [Painter et al., 2003]. The 17-m resolution AVIRIS data were degraded to 30 m to match that of the digital elevation model. During time periods without snowfall between two AVIRIS acquisitions, daily pixel-specific albedo estimates were obtained by linearly interpolating albedo as a function of time. When snowfall occurred between two acquisitions and after the final acquisition, albedo was estimated using a linear AVIRIS albedo decay function (AADF) that we derived using the AVIRIS-observed pixel-specific albedo and the snow age at the time of observation. Snow age was determined from precipitation and temperature data from the meteorological stations in the catchment (Figure 1); snow age was set to 0 when precipitation occurred at temperatures below 0°C. Pixel-specific albedo estimates were obtained from the AADF as follows:

  • equation image

where αAh is the estimated albedo for snow age xh, αi and αk are AVIRIS-observed albedo values for acquisitions corresponding to snow ages xi and xk respectively. After a snowfall event the AADF was reset to the maximum AVIRIS-observed albedo value of the 3 acquisitions (i.e., 0.84); snow albedo tends to be fairly uniform immediately after snowfall, becoming spatially heterogeneous as metamorphic processes occur at different rates across a basin. Here we applied a single decay function for each pixel and thus we assumed that the spatial variability in albedo decay rates were relatively consistent after each snowfall event.

[9] The SADF estimates daily albedo using:

  • equation image

where, αsh is the SADF snow surface albedo estimate for snow age xh.

[10] Hourly pixel-specific BATS albedo estimates, αb were obtained using [Dickinson et al., 1993; Yang et al., 1997]:

  • equation image
  • equation image
  • equation image
  • equation image

where αVIS is snow albedo for wavelengths <0.7 μm, αIR is snow albedo for wavelengths >0.7 μm, and fage is dimensionless snow age. We assume that snowfall events deposited at least 10 mm of water equivalent and therefore set ts and fage = 0 at the time of snowfall. After snowfall ts is calculated as:

  • equation image

where N indicates the current time step; and r1 represents the impact of vapor diffusion on snow surface grain growth:

  • equation image

where Tsn (K) is snow surface temperature. The effect of meltwater refreeze is represented by r2:

  • equation image

The effect of dust and soot on snow surface albedo is represented by r3 and is set to 0.3. The factor of solar illumination angle, fz was calculated as

  • equation image

where b is adjustable based on observations but was set to 2 (as per BATS) and θz is the pixel-specific solar illumination angle determined using the method of Dozier and Frew [1990].

[11] We mapped the spatial differences between the two ground-based parameterizations and AVIRIS-observed albedo on 5 and 21 May and 18 June 1997. Because the BATS parameterization includes terms for solar illumination angle and snow temperature we compared BATS albedo estimates corresponding to the specific hour of each AVIRIS acquisition as snow temperature and illumination angles vary during the day.

[12] Multivariate linear regressions were used to relate differences between AVIRIS-observed albedo and modeled albedo to elevation, slope, aspect, average incident solar radiation, and maximum upwind slope (i.e., variables that potentially influence spatial variability in snow surface metamorphic processes and therefore albedo). Elevation, slope and aspect were derived from the level 1 standard U.S. Geological Survey digital elevation model (DEM). Average incident solar radiation throughout the snowmelt season was calculated from the hourly solar radiation surfaces described below. Maximum upwind slope, a terrain-based parameter designed to account for the effect of wind redistribution on snow accumulation [Winstral et al., 2002], is included because wind can significantly alter snow surface roughness and grain size. Molotch et al. [2005] provide a more detailed explanation of the derivation of these variables.

[13] Meteorological influences on albedo differences were also estimated using multivariate linear regressions relating albedo differences in each pixel to corresponding pixel values of accumulated degree days and accumulated incident solar radiation. Accumulated degree days were calculated as the summation of the average daily air temperature above 0°C for each day between the last snowfall event and the AVIRIS acquisition date. Accumulated incident solar radiation was calculated as the summation of average daily incident solar radiation over the same period. These two variables were used as solar radiative and sensible heat fluxes account for the majority of energy exchange between the snowpack and the atmosphere [Cline, 1997; Marks and Dozier, 1992] and therefore snowpack metamorphism and snow surface albedo. The techniques used to distribute air temperature and solar radiation observations over the basin are described in the next section.

3.2. Snowmelt and Snowpack Mass Balance

[14] Precipitation inputs to the snowpack during the ablation season were small and therefore we calculate snow water equivalent as:

  • equation image

where Mj is the melt flux at time step j, SWEn is the SWE of each pixel at time step n, and SWE0 is the initial SWE or SWE at the time step corresponding to the field campaigns. By knowing any two of the three terms in the above expression the mass balance can be closed. We manipulated this expression in two independent simulations to estimate snow water equivalent (case 1) and snow extent (case 2). Field measurements of SWE were held out of case 1 simulations and then used as an independent check on model performance. In the case 2 simulations field measurements of SWE were used to initialize the model and remotely sensed snow covered area (SCA) data, held out of the simulation, were used to evaluate model performance. This approach allows us to evaluate model performance with respect to snowpack mass balance using two measurements that are independent of streamflow. Previous work has primarily used streamflow observations to evaluate snowmelt model performance, potentially misinterpreting results since streamflow incorporates the combined processes of snowmelt, sublimation, infiltration and evapotranspiration integrated over a range of conditions throughout a watershed. Here, we used streamflow only to evaluate model performance with respect to the timing of snowmelt.

[15] SWE was measured during three intensive field campaigns (6–12 April, 8–15 May, and 16–18 June, 1997) involving over 300 snow depth measurements and over 50 snow density measurements on average. Binary regression trees were used to interpolate point observations across the basin at 30-m resolution [Molotch et al., 2005].

[16] Case 1 simulations, aimed at reconstructing SWE at the time of each snow survey, were performed by solving equation (4) for initial SWE:

  • equation image

Here the daily vertical melt flux, Mvj was calculated following Brubaker et al. [1996]:

  • equation image

where S[DOWNWARDS ARROW]j (W m−2) is incoming solar radiation, αj is the snow surface albedo, L[DOWNWARDS ARROW]j (W m−2) is incoming thermal radiation, L[UPWARDS ARROW]j (W m−2) is outgoing thermal radiation, Mq (0.026 cm day−1 W−1 m2) is an energy to water depth conversion, Tdj (°C) is the average daily air temperature above 0°C, ar is the restricted degree day coefficient (0.09 cm °C−1) [Brubaker et al., 1996]. Hereafter we refer to the product of Tdj and ar as “turbulent transfer” although it is actually a parameterization rather than an explicit calculation. SCAj (values range from 0 to 1) was obtained using pixel-specific snow cover depletion curves:

  • equation image

where SCAj is the estimated fractional SCA at time step j, SCAi and SCAk are remotely sensed fractional SCA values derived from Landsat TM data (described below) preceding and subsequent to time step j, respectively, and equation imageMvi and equation imageMvk are the vertical melt flux summation values corresponding to the remote sensing acquisition time steps i and k, respectively.

[17] The initial SWE estimates were then compared with the interpolated observations of SWE from Molotch et al. [2005]. Pixel-specific absolute errors for simulations using the different albedo parameterizations were determined and multivariate regression models, as previously described for albedo differences, were used to assess physiographic influences on model performance.

[18] In case 2, snow extent was simulated by subtracting equation imageMvj from the interpolated observations of SWE from Molotch et al. [2005]; when equation imageMvj equals SWE0, SWEj and SCAj are equal to zero. Errors of omission were determined as the percentage of observed snow covered pixels (i.e., % SCA > 0) simulated to be snow-free. Errors of commission were determined as the percentage of observed snow-free pixels simulated to be snow covered. Map accuracies (percent) were then determined by subtracting from 100 the sum of the omission and commission errors.

[19] Model forcings were distributed over the terrain, using a combination of geometric models and interpolation between point measurements. Air temperature surfaces were created by deriving an environmental lapse rate in the basin for each hour of the model run using air temperature data from three meteorological stations. We then applied the lapse rate to every pixel in the basin using the DEM [Colee et al., 2000; Daly et al., 2000; Raskin et al., 1997; Thornton et al., 1997; Willmott and Matsuura, 1995].

[20] TOPORAD [Dozier, 1980; Dozier and Frew, 1990] was used to model incoming solar radiation at the Emerald and Topaz Lake meteorological stations (Figure 1). Using LOWTRAN7 [Dubayah, 1991; Kneizys et al., 1988], we calculated the atmospheric transmission parameters that caused TOPORAD to match the observed incoming solar radiation values at the meteorological stations. This was done for 5 different atmospheric conditions, ranging from clear sky to cloud cover. Using these atmospheric parameters, TOPORAD was then used to model the incoming solar radiation across the basin.

[21] We modeled incoming thermal radiation using a method similar to that of Colee et al. [2000] and Cline et al. [1998]. Using the interpolated temperature surfaces (as described above) and relative humidity surfaces (interpolated using the same method as the temperature surfaces) we applied the equations of Idso [1981] to the modeled relative humidity and temperature of each pixel to compute the incoming longwave radiation. The RMSE over the modeling period was 34 W m−2 at the Emerald Lake meteorological station and 40 W m−2 at the Topaz Lake station. A detailed evaluation of the techniques used to distribute model forcings is presented by Colee et al. [2000].

[22] Outgoing thermal radiation was estimated as

  • equation image

where ɛs is snow emissivity and is set to 0.99, and δ is the Stefan-Boltzmann constant (5.67 × 10−8 W K−4 m−2). Snow temperature, Tsn at each pixel was set to the air temperature value two hours before the current time step (i.e., a 2-hour lag function) constrained to a maximum of 273.15 K.

[23] Seven satellite images from the Landsat Thematic Mapper (TM) acquired on 6 and 22 April, 8 May, 9 and 25 June, and 11 and 27 July 1997 were used to construct fractional SCA maps across the basin using the spectral mixture analysis algorithm of Rosenthal and Dozier [1996]. AVIRIS scenes on 5 and 21 May were also used to obtain fractional SCA using a spectral mixture analysis model for subpixel SCA, grain size, and albedo [Painter et al., 2003]. AVIRIS SCA surfaces were also degraded to 30-m resolution from their native resolution of 17-m.

4. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

4.1. Snow Surface Albedo

[24] Differences between BATS albedo estimates and AVIRIS-observed albedo ranged from −0.15 to 0.05 on 5 May 1997 (Figure 2a), with BATS being higher by 0.005 on average; differences were below the AVIRIS measurement error of 0.02 [Painter et al., 2003] for 78% of the snow-covered portions of the watershed. BATS albedo was greater than AVIRIS-observed albedo in isolated areas, predominantly in the upper portions of the Topaz subbasin. BATS albedo was below AVIRIS-observed albedo in relatively small areas of the lower elevations of the Tokopah basin. Conversely, SADF-albedo values were −0.32 to −0.1 lower than AVIRIS-observed albedo (Figure 2b), with a mean difference of −0.17.

image

Figure 2. AVIRIS-observed albedo subtracted (a, b) from BATS albedo and (c, d) from albedo estimates of the SADF on 5 and 21 May 1997.

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[25] BATS-albedo values were consistently greater than AVIRIS-observed albedo on 21 May, 1997 (Figure 2c), with only 2% of BATS-albedo values within the 0.02 AVIRIS measurement error. Differences were particularly pronounced in the Topaz subbasin, where 60% of BATS-albedo values exceeded AVIRIS-observed albedo by 0.09 or more. On the same day SADF-albedo values were within the AVIRIS measurement error for 13% of the snow-covered portions of the watershed (Figure 2d).

[26] BATS-albedo estimates were within the AVIRIS measurement error for 13% of the snow-covered portions of the watershed on 18 June 1997; 82% of differences were above the measurement error. Differences ranged from −0.09 to 0.08 with a mean difference of 0.035. SADF-albedo estimates were considerably lower than observed albedo values; differences ranged from −0.28 to −0.11, with an average difference of −0.15.

[27] Although statistically significant, physiographic explanations for albedo differences within multivariate regression models were minimal. For example, the highest correlation between physiographic variables and albedo differences occurred on 5 May 1997, at which time elevation and average incident solar radiation explained 28% of variability (Figure 3a); including slope and maximum upwind slope increased this to 33%. The BATS albedo parameterization underestimated AVIRIS-observed albedo at lower elevations and in areas exposed to greater amounts of solar radiation.

image

Figure 3. Three-dimensional plot of elevation (x axis), average incident solar radiation (y-axis), and the difference between BATS albedo and AVIRIS observed albedo (z axis) (a) in the Tokopah basin and (b) in the Topaz subbasin. (c) As in Figure 3b but for the SADF. Multivariate linear regression model planar fits are shown.

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[28] Physiographics explained less of the variability in SADF versus AVIRIS-observed albedo differences (i.e., R2 = 0.26). On 21 May and 18 June physiographics explained only 14% of the differences between both SADF and BATS-albedo and AVIRIS-observed albedo.

[29] Multivariate regression models on 5 May showed stronger correlations between physiographic variables and the BATS minus AVIRIS albedo in the Topaz subbasin (R2 = 0.22) (Figure 3b) than in the Emerald subbasin (R2 = 0.01) (not shown). Correlations between physiographics and albedo differences within the two subbasins were weak (maximum R2 = 0.002) on 21 May and on 18 June for Topaz. The Emerald subbasin had cloud cover on 18 June that prevented comparisons. As with the BATS versus AVIRIS albedo, differences in SADF versus AVIRIS-observed albedo were positively correlated with elevation (slope = 0.06) and the solar radiation index (slope = 0.13) (Figure 3c). The absolute differences between the AVIRIS-observed albedo and the BATS albedo increased with increasing elevation and solar radiation while SADF differences increased toward lower elevation and average incident solar radiation (Figures 3b and 3c).

[30] The five snowfall events during the melt season corresponded to the highest albedo values for all three parameterizations (i.e., AADF, SADF, and BATS) (Figure 4a). Differences between BATS and AADF albedo estimates were greatest immediately after snowfall events due to the slower initial decay rate of BATS relative to AADF (Figure 4b). Owing to the strong agreement between the two parameterizations for older snow, BATS albedo values were within 0.02 of the AADF values for 53% of the melt season. Conversely, SADF values were within 0.02 of AADF for 11% of the snowmelt season. Air temperature measured at the Emerald meteorological station increased by 10 and 12°C during the snowfall-free periods preceding the May 5 and 18 June acquisitions, respectively (Figure 4c). Conversely, the 21 May acquisition occurred within 48 hours after a snowfall event, a time period in which temperature was decreasing.

image

Figure 4. (a) Variation of mean basin albedo with time using the AADF, SADF, and the BATS albedo parameterization. (b) Temporal variability in SADF – AADF) and BATS – AADF mean basin albedo differences. (c) The 24-hour running mean of air temperature measured at the Emerald meteorological station. Stars indicate snowfall events and circles indicate the dates of AVIRIS acquisition.

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[31] The BATS albedo parameterization and the SADF provided uniform albedo distributions across the watershed at the time of the 21 May and 18 June AVIRIS acquisitions; snow surface temperatures were 0°C and solar illumination angles across the watershed were below 60°. Therefore, for 21 May and 18 June we investigated the ability of the independent variables to explain the spatial distribution of AVIRIS-observed albedo, which is analogous to analyzing albedo differences. The spatial distribution of the accumulated degree days and accumulated incident solar radiation explained 20% of the variability in AVIRIS-observed albedo on 5 May 1997. As single-variable predictors, accumulated degree days and accumulated incident solar radiation explain 18 and 10%, respectively; with 14% of AVIRIS albedo on 21 May explained by a multivariate regression with accumulated degree days and accumulated incident solar radiation as explanatory variables. Unlike the 5 May relationship, accumulated incident solar radiation explained more of the variability in albedo than accumulated degree days (13 and 10%, respectively). These differences are consistent with the observed meteorology prior to the two acquisitions in that air temperature was relatively cold prior to the 21 May acquisition; therefore incident solar radiation played a larger role in snow metamorphism prior to the overpass.

[32] Although statistically significant (p value = 0), R2 was only 0.07 for the multivariate regression model relating 18 June AVIRIS-observed albedo to accumulated degree days and accumulated incident solar radiation. Similarly, the maximum R2 value for all dates at the Emerald subbasin was 0.03 (p value = 0). Fourteen percent of the 5 May AVIRIS albedo variability at the Topaz subbasin was explained by the two meteorological variables. Variability in AVIRIS albedo in the Topaz subbasin was not explained by regression models for 21 May or 18 June 1997.

4.2. Energy Fluxes and Snowmelt

[33] Energy exchange at the snow-atmosphere interface was dominated by net solar radiation (Figure 5). Solar radiation calculated using BATS-albedo closely matched those using the AADF. During the modeling period average over-snow radiative fluxes accounted for 74, 80, and 71% of total energy fluxes when the AADF, SADF and BATS albedo parameterizations were used, respectively. Turbulent exchange remained relatively low, reaching a maximum near 40 W m−2 late in the snowmelt season. Net thermal radiation accounted for 29, 26 and 30% of total radiative fluxes when the AADF, SADF, and BATS albedo treatments were applied, respectively. Net thermal radiation was negative throughout the snowmelt season but approached 0 during various time periods in late May–July. Over-snow net solar radiation using the BATS and SADF parameterizations were 5% and 35% greater than net solar radiation estimates using the AADF, respectively. Average BATS- and AADF-derived net solar radiation values agreed particularly well during the periods 30 April to 20 May and 19 June until the end of snowmelt; the longest duration periods without snowfall (Figure 4a).

image

Figure 5. Average daily net turbulent and net thermal radiative (3.5–50 μm) fluxes, with net solar radiative (0.3–3 μm), Sn, over snow fluxes for the three models for the Tokopah basin.

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[34] Modeled snowmelt using the BATS albedo parameterization explained 69% (R2 = 0.69) of the temporal variability in observed daily outflow volumes from the Tokopah. This compares well with snowmelt estimates obtained using the AADF (R2 = 0.73) and improves dramatically upon the estimates obtained using the SADF (R2 = 0.59) [Molotch et al., 2004]. As with the SADF, peak snowmelt using BATS albedo occurred 18 days before the observed peak despite clear indication of considerable improvement over the SADF (Figure 6a).

image

Figure 6. Observed and simulated hydrographs using the SADF, AADF, and the BATS albedo parameterization for the 1997 snowmelt season (a) in the Tokopah basin and in the (b) Emerald and (c) Topaz subbasins. Stars indicate modeled peak snowmelt and observed peak runoff. Note the difference in magnitude between modeled snowmelt and observed runoff was much lower at Emerald, foregoing the need for a secondary y axis.

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[35] The model was able to explain more of the variability in runoff at the Topaz subbasin versus the Emerald subbasin, with R2 values decreasing from 0.64, 0.56, and 0.60 to 0.51, 0.46, and 0.52 for the AADF, SADF, and BATS simulations, respectively. The magnitude difference between observed runoff and all snowmelt simulations was considerably lower for the Emerald subbasin versus the Topaz subbasin or the Tokopah (Figures 6a–6c). Observed runoff at the Tokopah and Topaz subbasin outflows were consistently below modeled snowmelt volumes (Figures 6a and 6b); runoff incorporates loss terms such as evapotranspiration, change in storage, and ground water recharge not accounted for by the snowmelt model. After 30 May observed runoff at the Emerald subbasin outflow frequently exceeded modeled snowmelt volume (Figure 6b) indicating that snowmelt flux was underestimated at Emerald during the latter half of the snowmelt season.

4.3. Snow Extent

[36] The low albedo values estimated by the SADF, and related overestimation of energy input to the snowpack, resulted in dramatic underestimation of SCA and widespread omission errors (Figure 7). SADF omission errors were particularly prevalent on 21 May and 9 June 1997 (Figure 7). BATS and AADF simulations improved model performance substantially, resulting in SCA estimates that closely resembled observations early in the melt season. On 9 and 25 June simulations using the BATS albedo parameterization reduced omission errors considerably relative to SADF simulations (Figure 7) and produced SCA maps with accuracies above AADF and SADF simulations (Table 1). Widespread omission errors were present on 25 June regardless of the representation of albedo.

image

Figure 7. Measured snow covered area from the Landsat TM (grayscale) and omission and commission errors for simulations using the SADF, BATS albedo parameterization, and the AADF. Colors in the middle legend correspond to areas where errors existed for more than one of the simulations. For example, turquoise indicates errors for both the SADF and the AADF. Omission errors are those where snow was detected from satellite but was simulated as snow-free. Commission errors are those where no snow was detected from satellite but are simulated as snow covered.

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Table 1. Snow Extent Map Accuracies and Omission (OE) and Commission (CE) Errors for 1997 Using BATS, AADF, and the SADF Albedo Parameterizationa
 BATSAADFSADF
OECEAccuracyOECEAccuracyOECEAccuracy
  • a

    Values are in percent.

5-May010001603926038
8-May188112673146333
21-May2692955045242947
9-Jun14503640293179714
25-Jun5819237411159433
11-Jul80515813169802
27-Jul95148911010000
Average364717423226572320

[37] Early in the snowmelt season commission errors were restricted to the lower elevations along the transition from snow-free to snow covered portions of the watershed. Commission errors were higher when the BATS albedo parameterization was used (Figure 7 and Table 1); higher albedo values reduced energy input to the snowpack and increased estimates of SCA. Commission errors were particularly widespread in the Emerald subbasin; energy input to the snowpack was underestimated. Average omission and commission errors over the snowmelt season were lower using the AADF; with an average map accuracy 63 and 37% higher than SADF and BATS albedo parameterizations respectively (Table 1). However, during the period 21 May to 27 July 1997, the period with greatest changes in SCA, the BATS average map accuracy was 62% greater than the SADF and was only 10% lower than the AADF (Table 1).

4.4. Snow Water Equivalent

[38] Reconstructions of the spatial distribution of April SWE using the BATS albedo parameterization and the AADF were similar. Comparisons with the regression tree SWE estimates [Molotch et al., 2005] showed similar patterns in SWE errors using the BATS albedo and the AADF (Figure 8). The BATS albedo parameterization improved model performance relative to the SADF (Table 2); April error decreased from 39% to 14% for the SADF and BATS model simulations, respectively. AADF simulations were most accurate for April and May (Figure 8) with errors less than 2% (Table 2). June SWE was simulated most accurately using the SADF with an average error less than 5% of observed SWE.

image

Figure 8. Error in reconstructed snow water equivalent using the AADF, the BATS albedo parameterization, and the SADF. White areas are those within one standard deviation of the mean observed SWE. Green and orange areas correspond to model underestimates and overestimates, respectively.

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Table 2. Average SWE for Simulations Using the AADF, BATS Albedo Parameterization, SADF, and the Regression Tree Interpolation of the Field Observationsa
 AADFBATSSADFRegression Tree
Tokopah
April10490144104
May70619071
June16162223
 
Emerald
April9688139136
May82669499
June22223044
 
Topaz
April1209616389
May726910366
June17152221

[39] A multivariate regression model using elevation and average incoming solar radiation explained 37% of the variability in BATS model improvement (i.e., absolute April SWE error using the SADF minus that using BATS albedo) (Table 3). The BATS model improved with increasing elevation and increased exposure to solar radiation (Table 3). Lower correlations were found between May model improvement, obtained by using BATS albedo instead of the SADF, and the explanatory variables. June correlations (not shown) were lower than May's in all cases. The improvement in April SWE estimates obtained by using the AADF instead of the BATS albedo (i.e., absolute April SWE error using the BATS albedo minus that using AADF) was not as strongly correlated with physiographics (Table 3).

Table 3. Statistics for Multivariate Regression Models Relating the Difference in SWE Model Performance to Average Incident Solar Radiation and Elevation
 BATS - AADFSADF - AADFSADF - BATS
AprilMayAprilMayAprilMay
Tokopah
R20.20.10.33a0.180.370.18
Slope: srad−0.12−0.070.37a0.120.480.19
Slope: elev−0.03−0.010.06a0.030.10.04
 
Emerald
R20.040.010.280.050.270.05
Slope: srad−0.03−0.010.410.10.440.11
Slope: elev−0.0100.080.020.10.03
 
Topaz
R20.090.040.060.030.10.04
Slope: srad−0.75−0.220.750.321.580.53
Slope: elev0.08−0.02−0.060.01−0.150.03

[40] The SADF provided the most accurate simulations of SWE in the Emerald subbasin (Figure 8 and Table 2). Conversely, April and May SWE in Topaz were estimated most accurately using the BATS albedo parameterization. The spatial distribution of model improvement obtained by using the BATS albedo in Topaz was not explained well by physiographics (maximum R2 for April, May and June = 0.10) (Table 3). Conversely, model improvement associated with using the SADF instead of the BATS albedo in the Emerald subbasin increased with decreasing elevation and average incident solar radiation.

5. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[41] Wiscombe and Warren [1980] showed that their albedo parameterization, which provides the basis for the BATS albedo parameterization, overestimated albedo, particularly for larger snow grains. This source of error may be considerable after late spring snowfall events in the Sierra Nevada, where grain size is relatively large relative to midwinter snowfall events; e.g., the fresh snow albedo in equations (3b) and (3c) may be too high. Jin et al. [1999] also showed that BATS albedo overestimated observations, especially after snowfall. Another limitation of the BATS parameterization is the use of a universal impurity factor (r3 = 0.3) for all applications outside of Antarctica. A larger value for the impurity factor may be needed in the Tokopah basin given the high dust and soot deposition rates to the snow surface relative to other areas where BATS has been applied. Further effort in calibrating the optimal impurity factor is needed in a variety of alpine environments where observations are available. Nevertheless, the results presented here have shown that overall BATS outperforms the SADF without calibration of the impurity factor.

[42] During May–July, the BATS and AADF albedo estimates resulted in net thermal to net radiation ratios that reasonably matched two point estimates from a previous study (Table 4) [Marks and Dozier, 1992]. However, we would expect our ratios to be greater, as they are averaged over a north facing cirque, and the meteorological towers used by Marks and Dozier [1992] were placed in areas with relatively greater exposure to direct insolation (Figure 9) [Marks et al., 1992]. Further, our estimates of incoming thermal radiation may be low, as we have not considered thermal energy exchange along the vertical interface between the snowpack and rock, a potentially large source of energy late in the snowmelt season when direct beam solar insolation warms exposed bedrock. During the series of snow surveys at Emerald it was observed that the distance between vertical cliffs and adjacent snowpacks increased, indicating considerable melt along the interface. This may be relatively unique to the Emerald subbasin, where avalanche activity from steep cliffs deposits snow onto relatively flat benches [Elder, 1995]. This can result in highly variable deposition patterns, where snowpacks can accumulate to depths above 10 m.

image

Figure 9. Average incident solar radiation over the Emerald subbasin, 6 April to 27 July 1997. Locations of the meteorological stations used by Marks and Dozier [1992] are shown.

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Table 4. Proportions of Net Thermal to Net Radiation and Turbulent Fluxes to Total Energy Exchange
MonthNet Thermal/Net RadiationaTurbulent Flux/Total Flux
AADFSADFBATSMarks and DozierbAADFSADFBATSMarks and Dozierb
Emerald
April0.510.500.530.39, 0.340.360.230.470.70, 0.46
May0.330.270.340.35, 0.360.320.210.350.16, 0.08
June0.270.230.270.26, 0.260.330.270.330.27, 0.18
July0.210.160.200.20, 0.210.350.250.320.32, 0.19
 
Topaz
April0.470.440.44n/a0.250.10.12n/a
May0.320.250.3n/a0.190.140.19n/a
June0.280.230.26n/a0.250.210.23n/a

[43] The common presence of commission errors (Figure 7) in the Emerald subbasin could be due to either overestimates in the maximum SWE used to initialize the model or due to underestimates in energy input to the snowpack. The difference in magnitude between observed runoff and modeled snowmelt was considerably lower at Emerald relative to the Topaz subbasin or the Tokopah basin as a whole (Figures 6a–6c), with observed runoff exceeding modeled snowmelt volume at times. This indicates that the persistence of commission errors in the Emerald subbasin were likely due to underestimates in energy input to the snowpack; likely a result of the aforementioned underestimates in thermal energy.

[44] Using our approach, lower energy input to the snowpack results in lower SWE (Figure 8 and Table 2). Additional error is introduced when SCA data are unavailable for long time periods. In this research nine remotely sensed estimates of fractional SCA were used, substantially greater than the 3 acquisitions used in previous applications of this technique [Cline et al., 1998]. Hence our reduction of this error source is probably a best case scenario, as it is unusual to acquire 10 high-resolution, cloud-free scenes within one snowmelt season. Error is also introduced by misregistration of remotely sensed SCA data. In our study, over 30 ground control points were used to georegister the images, with a root mean square error below 0.5 pixels over the Tokopah basin. Errors associated with pixel misregistration may be greater in the topographically heterogeneous Emerald subbasin; snow cover patterns are also relatively heterogeneous. The combination of the error sources resulted in SWE underestimates in the Emerald subbasin. These error sources may not be unique to our study period or modeling approach, as previous studies [Cline et al., 1998] also underestimated initial SWE in the Emerald subbasin.

[45] The results presented here focused on spatially explicit representations of snow surface albedo and evaluating the impact of albedo representation on snowpack mass balance simulations. Previous works aimed at improving the representation of albedo within snowmelt models have largely been performed at the point to plot scales where detailed spectral albedo data are available [Hardy et al., 1997; Melloh et al., 2002]. These efforts largely focused on the effect of forest litter on snow surface albedo and are therefore complimentary in that remotely sensed snow surface albedo data are not available in forested regions. Future research aimed at improving the accuracy of remotely sensed snow surface albedo in forested environments is needed to facilitate application of the techniques presented here to forested regions. In this regard, an ensemble of albedo parameterizations, developed in different topographic environments, climates, and forest types, may be needed for regional-scale applications.

[46] In previous applications of the modeling techniques applied here [Cline et al., 1998] model accuracy was evaluated using basin-mean SWE from relatively sparse point observations and through comparison with distributed estimates of SWE from other years. Here, we are more rigorous in our error assessment in that we compare modeled SWE estimates to temporally coincident field observations interpolated using binary regression tree models, e.g., the best spatial SWE estimate available [Erxleben et al., 2002]. We have also expanded on the work of Molotch et al. [2004] by evaluating modeled SWE distribution using two melt season field campaigns in addition to maximum accumulation. Further building on previous works, we use remotely sensed SCA data and runoff observations from two subbasins to validate model results.

[47] To ensure transferability of our approach to areas where detailed meteorological data are not available, we used the net radiation and temperature index snowmelt algorithm of the snowmelt runoff model (SRM) [Brubaker et al., 1996]. The SRM has been widely used to forecast runoff in relatively uninstrumented watersheds [Rango, 1988]. An explicit representation of net radiation within the SRM has shown considerable utility in situations where snow surface albedo is measured [Brubaker et al., 1996]. However, operational use of the net radiation version of the SRM for runoff forecasting has been restricted, in part, by the lack of real-time albedo data and the difficulty of forecasting changes in albedo [Kustas et al., 1994]. The results presented here indicate that remotely sensed albedo data dramatically improve snowmelt estimates. Further, this research has shown that, in the absence of remotely sensed albedo data, more complex treatments of snow surface albedo improve snowmelt model performance to accuracy levels comparable with those obtained from simulations using the remotely sensed data. These results are critical for advancing applications of the net radiation version of the SRM from runoff simulations to runoff forecasts. Use of these spatial albedo data, parameterized (e.g., BATS) or based on remotely sensed data (e.g., AVIRIS and MODIS), is particularly suited for the SRM, as the model is equipped to make use of spatially distributed data.

6. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[48] The BATS albedo model more closely matched observed albedo and provided values that improved snowmelt model performance relative to the snow-age-based SADF; and was able to simulate snowpack mass balance at levels of accuracy comparable to those using the site-specific AADF. Thus using the BATS albedo parameterization on a pixel-by-pixel basis may be a relatively straightforward way to improve estimates of snowmelt magnitude and timing across alpine basins. The BATS albedo parameterization is particularly suited for applications where snow cover persists for long periods of time in the presence of relatively high air temperatures, but performs less well in the days immediately after snowfall. BATS and SADF albedo values were within 0.02 of those from AADF, which were based on values measured during the period studied, for 53% and 11% of the snowmelt season, respectively. Over-snow net solar radiation using the BATS and SADF albedo values were 5% and 35% greater than estimates using the AADF, respectively. Estimates of the timing of snowmelt using the BATS albedo parameterization (R2 = 0.69) improved considerably over the SADF (R2 = 0.59) and were comparable to the AADF (R2 = 0.73). During late May to late July, the period with greatest changes in SCA, the average snow extent map accuracy using the BATS albedo parameterization was 62% greater than the SADF and was only 10% lower than the AADF. The error in SWE for April, the period of initial snowmelt, was 14% for BATS versus 39% for the SADF; however, it was less than 1% for the AADF. Thus BATS performed better than SADF but did not outperform simulations using AVIRIS albedo data. The BATS model improved over the SADF more at higher elevation (slope = 0.1) and with increased exposure to solar radiation (slope = 0.48).

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[49] This research was supported by a visiting fellowship at the Cooperative Institute for Research in Environmental Sciences (CIRES), a joint institute of the University of Colorado at Boulder and the National Oceanic and Atmospheric Administration (NOAA). Additional support was provided by SAHRA (Sustainability of semi-Arid Hydrology and Riparian Areas) under the STC Program of the National Science Foundation. Data collection was made possible by NASA grant NAG5-4514. Michael Colee, Thomas Painter, Walter Rosenthal, and Jeff Dozier provided technical support. The authors are indebted to all who participated in the data collection. We thank Bert Davis and two anonymous reviewers for comments that improved this manuscript.

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  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Study Area
  5. 3. Methods
  6. 4. Results
  7. 5. Discussion
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information
FilenameFormatSizeDescription
wrcr10592-sup-0001-t01.txtplain text document1KTab-delimited Table 1.
wrcr10592-sup-0002-t02.txtplain text document0KTab-delimited Table 2.
wrcr10592-sup-0003-t03.txtplain text document1KTab-delimited Table 3.
wrcr10592-sup-0004-t04.txtplain text document1KTab-delimited Table 4.

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