Snow water equivalent along elevation gradients in the Merced and Tuolumne River basins of the Sierra Nevada

Manuscript for Water Resource Research Rice et al. May 2011 Snow water equivalent along elevation gradients in the Merced and Tuolumne River basins of the Sierra Nevada Robert Rice Sierra Nevada Research Institute University of California, Merced Roger C. Bales Sierra Nevada Research Institute University of California, Merced Thomas H. Painter Jet Propulsion Laboratory California Institute of Technology Jeff Dozier Bren School of Environmental Science & Management University of California, Santa Barbara Corresponding Author and Address Robert Rice Sierra Nevada Research Institute University of California 5200 N. Lake Road Merced, CA95343 Phone: 209/228-4397 Email: rrice@ucmerced.edu

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Abstract We used daily remotely sensed fractional snow-covered area (SCA) at 500-m resolution to estimate snow water equivalent (SWE) across the Upper Merced and Tuolumne River basins of the Sierra Nevada of California for 2004 (dry and warm) and 2005 (wet and cool). From 1800 to 3900 m, each successively higher 300 m elevation band consistently melts out 2-3 weeks later than the one below it. We compared two methods of estimating SWE from SCA: (i) blending the fractional SCA with SWE interpolated from snow-pillow measurements; and (ii) retrospectively estimating cumulative snowmelt based on a degree-day calculation after the snow disappeared. The interpolation approach estimates a lower snowmelt volume above 3000 m and a higher snowmelt contribution at elevations between 1500-2100 m. Snowmelt timing from the depletion approach matches observed streamflow timing much better than snowmelt estimated by the interpolation method. The snow-pillow sites used in the interpolation method do not cover the highest elevations and melted out several weeks before the basin itself was free of snow. Middle elevations (2100-3000 m) contributed 40-60% of the annual snowmelt in both basins, the lower elevations (1500-2100 m) 10-15%, and elevations above 3000 m the remaining 30-40%. The presence of snow in the highest elevations highlights their critical buffering effect in accumulating snow every year. Variability in lower-elevation snow illustrates its susceptibility to climate variability and change. 20 21 Index terms: snowmelt (0740), snow and ice (1863), estimation and forecasting (1816), remote sensing (1855)

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 Introduction In mid-latitude montane regions, snow is critical for seasonal storage of water, releasing winter precipitation in spring and summer to provide the soil moisture and streamflow needed to sustain ecosystems and human populations. In the semi-arid western United States, snowmelt runoff accounts for up to 80% of annual streamflow [Daly et al., 2001]. Historically, most forecasts of seasonal runoff across this region have been based on statistical relationships between historical runoff and snow water equivalent (SWE) measured at manual snow courses and automatically telemetered sites, but these relationships have been developed during a period when climate was changing so their reliability will degrade as climate continues to change. Moreover, these index sites (i.e. snow courses) often fail to provide spatially representative measures of SWE and do not capture the physiographic variability across a basin [Molotch and Bales, 2005; Dressler et al., 2006; Rice and Bales, 2010]. Snowfall dominates precipitation in the mountains of the western U.S.; and snow accumulation varies because of topography, vegetation cover, and larger-scale synoptic processes [Bales et al., 2006], resulting in snow measurements that exhibit considerable variability, even between sites that are close together [Carroll et al., 1999]. Therefore, accurate estimates of the actual volume of snow and its spatial distribution are needed to provide quantitative estimates for more robust water-supply estimates, flood forecasts, and resource-management decisions. Blending spatial SWE estimates developed from interpolation of ground-based sensors with satellite-derived estimates of snow-covered area (SCA) potentially provides a more representative estimate of SWE across a basin than interpolation alone, because the snow-cover information constrains the interpolation [Bales et al., 2008; Bavera and De Michele, 2009; Harshburger et al., 2010]. Both the SCA interpolation and the surface measurements can be 1

45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 made available in near real time, offering a promising way to provide spatial snow data to drive hydrologic forecast models. In this approach, snowmelt is computed as the difference between successive interpolated spatial SWE estimates. However, these SWE interpolations have not been evaluated at the basin scale, owing to the lack of spatially distributed ground truth estimates. Fractional SCA from NASA s Moderate Resolution Imaging Spectroradiometer (MODIS), and in the future with the Visible Infrared Imaging Radiometer Suite (VIIRS), makes possible a real-time product for operational hydrology [Dozier and Frew, 2009; Painter et al., 2009]. Martinec and Rango [1981] developed an alternate approach for estimating the spatial distribution of SWE, by combining a retrospective time series of snowmelt estimates with a time series of spatial SCA, and back-calculating the amount of SWE that was present earlier in the melt season. Because snowfall sometimes occurs during the snowmelt season, the SWE can be estimated only back to the last significant snowfall. This depletion approach provides an independent spatial SWE and snowmelt time series, which, although available only after the snow is gone, can be compared to the interpolation approach. Subsequent investigations using energy-balance snowmelt models have validated the accuracy of the method [Cline et al., 1998; Liston, 1999], and Molotch et al.[2004] point out that the energy-balance estimates are sensitive to accurate measurements of snow albedo. Homan et al. [2011] recently showed that an energybalance snowmelt model, together with a simple estimate of fractional SCA from MODIS based on a normalized difference snow index, can reproduce single-pixel values of SCA and SWE observed in the field over a snowmelt season, supporting this approach for estimating basin-wide snowmelt depletion curves. In an earlier study, Shamir and Georgakakos [2006] developed 2

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 basin-wide depletion curves for the American River using a temperature-index model and showed that model results compare well with a binary SCA product from MODIS. The aims of the research reported in this paper are to: (i) determine the patterns of snowcovered area in two Sierra Nevada basins based on a fractional SCA product, (ii) evaluate the adequacy of blending ground-based measurements with the fractional SCA to produce estimates of spatially distributed SWE and snowmelt; and (iii) determine the relative importance of different elevation zones within a basin to seasonally integrated snowmelt generation. Methods and data We carried out the study for 2004 and 2005 in the upper Tuolumne and Merced River basins, located in the Sierra Nevada above the foothill reservoirs of Don Pedro (Tuolumne) and Lake McClure (Merced) (Figure 1). These two years represent one below- and one above-normal year. In 2004, SWE measured at snow courses in the Tuolumne (Merced) was 83% (84%) of the historical April 1 records, where as in 2005 the values were 163% of normal in both basins. The Tuolumne basin s area is 4182 km 2 with elevations of 58-3980 m, while the Merced s is 2844 km 2 with elevations of 95-3929 m. Both rivers drain into the San Joaquin River in the Central Valley. Further, both basins are largely free from current human influences like dams, diversions, and major land-use changes, and the basins steep slopes and shallow soils make the hydrology straightforward [Slack and Landwehr, 1992; Jeton et al., 1996]. We restricted this analysis to seasonally snow-covered areas, which start at the rain/snow transition of 1500 m, representing 58% (2420 km 2 ) and 50% (1403 km 2 ) of the Tuolumne and Merced basins above their foothill reservoirs. Much of the snowfall lies within Yosemite National Park. Using topographic data from the Shuttle Radar Topography Mission at 30-m spatial sampling [Farr et 3

89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 al., 2007], the study area was partitioned into eight elevation bands of 300-m increments, beginning at 1500 m and extending to 4000 m (Table 1). Daily fractional SCA maps at 500-m resolution were generated from the MODIS surfacereflectance product MOD09. SCA is retrieved with a spectral mixing model, through which the snow, soil, and vegetation fractions in each grid cell on each day are estimated [Dozier and Painter, 2004; Painter et al., 2009]. The MODIS snow-cover products were produced from the daily Terra satellite with a morning overpass about 10:30 am local time. Because cloud cover and low viewing angle limit the availability of quality data in some scenes, an interpolation scheme was applied to develop a spatially and temporally continuous snow product [Dozier et al., 2008]. No adjustment of snow cover was made for the occlusion by tree canopy, so the SCA values represent projected snow cover, i.e. snow cover that the satellite s sensor can detect. The fractional SCA threshold was set at 0.15, i.e. values below 15% were set to zero to prevent identification of spurious snow. Spatially distributed snowmelt was estimated daily for 2004 and 2005 by both methods described in the Introduction: interpolation and snow-cover depletion. The interpolation involved point SWE measurements from snow-pillows, operated by the California Department of Water Resources and U.S. Natural Resource Conservation Service, followed by masking with the MODIS fractional SCA product [Fassnacht et al., 2003; Bales et al., 2008]. Masking involves multiplying the pixel-by-pixel MODIS SCA product by the interpolated SWE product. SWE for each 500-m grid cell was interpolated using a linear regression between elevation and SWE for all snow-pillows within a 200-km radius of that pixel, including those outside the basin. A residual was obtained at each grid cell where an observing snow pillow was located by removing the observed value from the analysis (i.e. jack-knifing) and subtracting the observed 4

112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 SWE from the computed SWE. Elevation-dependent biases in the residuals were removed by regressing residuals to a fixed datum of 5000 m using a lapse rate. Once regressed to the common datum, the lapsed residuals were spatially distributed using inverse distance squared weighting. The gridded residual surface was then regressed back to the basin surface using the same lapse rate and subtracted from the hypsometrically derived SWE grid in order to derive the SWE surface, thus preserving the SWE observation at each station. Daly et al. [2001] used a similar approach but computed one hypsometric relationship for each sub-basin instead of using a moving search radius to compute the hypsometric relationship at each pixel. Daily snowmelt was calculated by the daily grid cell differences in SWE. The alternate depletion approach to estimating snowmelt combined remote sensing, groundbased SWE and temperatures, and a temperature-index model [Anderson, 1968; Rango and Martinec, 1995; Ohmura, 2001]: M = a (T a T b ) (1) M is daily snowmelt, a is a degree-day coefficient (mm deg -1 day -1 ), T a is average daily temperature, T b = 0 o C; when T a <T b, no melt occurs. In this method, the ground-based SWE data were used to estimate degree-day coefficients. The approach provides an index of the average energy flux, but does not explicitly consider the individual fluxes and controlling factors that influence snowmelt (e.g. solar radiation, albedo, topography, turbulent-energy exchanges). Since temperature and SWE vary from year to year, producing different interannual daily melt rates, a daily degree-day coefficient for each year was calculated for both the Tuolumne and Merced using each of the nine co-located snow-pillow and temperature measurements (Figure 1); data were from the California Data Exchange Center (CDEC, http://cdec.water.ca.gov/snow/current/snow/). Daily average temperature and SWE 5

135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 were calculated from hourly and daily CDEC data for each of the nine snow pillows. The daily degree-day coefficient was calculated as the ratio of the daily decrease in snowmelt and the daily degree day [Anderson, 1968]. Our method of parameterizing the daily degree-day coefficient is similar to such semidistributed runoff models as the Snowmelt Runoff Model [Kustas et al., 1994] and Snow-17 [Anderson, 1973]. The degree-day coefficient increased over the ablation period in both years (Figure 2). As the two basins are adjacent and have similar physiographic characteristics, the same set of daily values was used for both. However, since the snow covered part of the basin extends over more than 2000 m, daily coefficients were calculated for 4 of the 8 elevations bands between 1800-3000 m, where station data were available (Figure 3). Stations were grouped by elevation band and a linear trend fit to the values. In addition, in order to reduce the effects of possible site-specific differences (i.e. local shading, vegetation) snow pillow-stations within ±80 m of an elevation band were included to increase the sample size and reduce the bias. Below 1800 m and above 3000 m, daily coefficients from the adjacent elevation band were applied; above 2700 m no station data are available in the Merced, so the Tuolumne data were used. Two snow pillows were not used because the data were incomplete in 2004-2005. The temperature-index calculation used daily average temperature for each 300-m elevation band. Stations within an elevation band were used to estimate degree days for that band. A simple lapse rate based on a linear fit to the daily station data was used to estimate the temperature in elevation bands with no station data. The calculated fixed lapse rates across the full elevation range for both basins were -6.0 and -7.0 o C per km for 2004 and 2005. We recognize that a simple lapse rate may not fully describe the spatial structure of temperature across complex terrain; a more involved interpolation scheme can improve spatially distributed 6

158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 models incorporating microclimates [Lundquist and Cayan, 2007; Lundquist et al., 2008]. However, for whole-basin calculations integrating the full range of physiographic variability, a simple fixed lapse rate should not bias results. Daily snowmelt, M, was calculated for each elevation band using equation (1) and the average fractional SCA for each band was applied to correct for snow-free area. That is, if an elevation band had snow, we assumed it contributed a melt volume equal to the snowmelt rate times SCA. Results The degree-day coefficient, a, increased over the ablation season, with values for 2004 (2005) ranging from 1.2 (3.4) mm day -1 deg -1 at the onset of snowmelt to 7.8 (6.1) mm day -1 deg -1 by the end of the ablation season, but showed a high degree of daily variability (Figure 2). The different patterns for the degree-day coefficients in 2004 versus 2005 reflect the differing timing of melt. Snowmelt at the snow-pillow sites started much earlier in 2004 (early March) and was largely complete in mid-may, a month earlier than in 2005. Following Anderson [1968], the degree-day coefficient increased up to the summer solstice (June 21), with values afterward decreasing. In 2004 the degree-day coefficients show a distinct increase in elevation along the 4 elevation bands between 1800-3000 m, where the snow-pillow sites are located (Figure 3). In 2005, the degree-day coefficients differed across the 4 elevation bands, but the elevation dependence was not as strong as it was in 2004, with the 2700-3000 m elevation band showing a lower coefficient than the 2400-2700 m elevation band. The daily degree-day coefficients were used to back calculate snowmelt at each snow-pillow site to determine whether these values were representative of the snowmelt. At all snow-pillow sites the elevation-dependent degree-day coefficient, a, overestimated snowmelt for both 2004 and 2005 (Figure 4). The mean absolute 7

180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 errors (MAE) were 130 and 210 mm in 2004 and 2005, respectively. Relative differences between measured and calculated values at each site averaged 15 and 18%. On April 1, 2004 and 2005, the snow courses, which provide manual monthly snow measurements and are near the snow pillows, measured more SWE as compared to the snow pillows in those respective years. The MAE between the snow pillows and snow courses throughout the Tuolumne and Merced River basins were 120 and 240 mm in 2004 and 2005 (18 and 25% average relative differences). Therefore part of the error in our snowmelt calculations might be attributed to uncertainty in the snow-pillow measurements. The fractional SCA just prior to snowmelt in each 300-m elevation band was similar for 2004 and 2005, ranging from near 1.0 at the highest elevations bands to under 0.4 in the lowest band (Figure 5). The lowest band showed large fluctuations associated with snowfall and melt through the winter and spring, while at higher elevations these variations are smaller, but still indicate periods of snowmelt and snowfall. Near depletion of snow-covered area in 2004, identified here as SCA<0.1, occurred by March 15 in the lowest band, and occurred an average of 2-3 weeks later in each successively higher 300-m band. In 2005 SCA depletion occurred on average about five weeks later than in 2004 at the same elevation. There was little difference between the two basins in the timing of snow depletion, except in 2005 at the two highest elevation bands where the Merced melted out 3-5 weeks later than the Tuolumne. Interpolation of SWE from snow pillows and unconstrained by SCA gives estimates across elevation bands that during the accumulation period are fairly close together, with values becoming different during snowmelt (Figure 6). Note that melt at the snow pillows started in early March in both years, with further March accumulation in 2005. The spread in SWE values during snowmelt reflects greater melt at the lower snow pillows. 8

203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 Masking interpolated SWE with the fractional SCA results in differences in SWE with elevation that reflect the SCA with elevation (Figure 7). Masking accounts for the interpolated SWE for areas with no snow, which is especially important at the lower to mid elevations. Note that while decreases in SCA indicate that snowmelt does occur early in the year at lower elevations, this is not reflected in the interpolated SWE of Figure 6 because there are no snow pillows at the lower elevations. Integrating the decline from peak SWE over time for each of the elevation bands in Figure 7 provides an estimate of the cumulative snowmelt volume (Figure 8). By this method, in 2004 snowmelt began in January, with more significant contributions beginning in February, and snowmelt was nearly complete by mid-may. Using the depletion approach to back-calculate snowmelt from the SCA patterns in Figure 5 gives the second estimate of snowmelt by elevation band (Figure 8). In 2004, this method shows no snowmelt in either the Tuolumne or Merced until March. That is, even though SCA decreased in the lower elevations early in the year, daily average temperature was below zero and thus snowmelt was calculated to be zero. Basin-total January-September snowmelt volumes estimated by the interpolation method were greater than that estimated by depletion: 42-44% higher in the Merced, 30-34% higher in the Tuolumne. The depletion method accounts for snow at elevations above that of all pillows, so it continues to estimate snowmelt above 2700 m in July and estimates a greater contribution to basin-wide melt from these higher elevations than does interpolation, whereas interpolated estimates of snowmelt contributions by elevation were approximately proportional to basin areas. Compared to the interpolation method, Table 2 and Figure 9 show that the depletion method shifts snowmelt contributions to higher elevations, especially in the drier year 2004. 9

225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 Using values from the depletion method, elevations 1500-2100 m contributed about 20% (24%) of the March 2004 snowmelt for the Tuolumne (Merced), declining to 19% (15%) and near zero in April (Table 3). Mid elevations (2100-3000 m) contributed about 54% (70%) of March snowmelt, increasing to 61% (75%) in April, declining to 54% (66%) in May and dropping to about 25% (31%) by June and nearly disappearing by July. Elevations above 3000 m contributed only 22% (10%) of the monthly total in March, increasing to 43% (32%) in May and 95% in July. Trends were similar in March 2005, however, by April 1 the pattern of relative snowmelt contributions was about 1 month later than in 2004, with elevations 1500-2100 m providing about 32-68% of the April snowmelt. Elevations 2100-3000 m contributed 29% to 74% of the April, May and June snowmelt, declining to about 10% in August. At elevations above 3000 m snowmelt volume increased as the lower-elevation snow melted; and in July and August these upper elevations accounted for most of the monthly snowmelt (Table 3). For comparison with streamflow at Pohono Bridge in Yosemite National Park in the Merced basin (Figure 10), the per unit area potential snowmelt values were adjusted for vapor losses (sublimation + evapotranspiration) of 0.54 m yr -1 [Dettinger et al., 2004; Christensen et al., 2008]. Vapor losses were adjusted based on the distinct seasonality, nearly zero in November, increasing in February, and peaking in June. Figure 11 shows the comparison of the cumulative March-August streamflow averaged by depth over the basin (0.37 m in 2004 and 0.85 m in 2005) with the interpolation and depletion methods. The interpolation method overestimated the snowmelt by 9.4% in 2004 and 11% in 2005. In the calculation, snowmelt was nearly complete by May 1, 2004 and June 1, 2005, almost 2 months before the stream gauge at Pohono Bridge returned to baseflow levels. The depletion method overestimated the total snowmelt by 4.3% in 10

247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 2004 and underestimated by 8.8% in 2005, with the end of snowmelt delayed until mid-june in 2004 and July in 2005. Compared to traditional operational models, which use of regression models to predict seasonal streamflow volumes, the depletion method provides reasonable estimates, given that it is not calibrated against streamflow. The forecasts from the California Department of Water Resources in the same years over-predicted the April-July streamflow by 8.9% in 2004 and under-predicted it by 2.2% in 2005. It should be noted that CDWR had forecasted the total streamflow volume on April 1 for the 4 months (April-July); achieving this level of accuracy in forecast mode is impressive and should be acknowledged. The forecasts from 1990-present are available each year from February through May at http://cdec.water.ca.gov/snow/bulletin120/. Discussion Some possible reasons for differences in snowmelt estimates by the two methods include uncertainty in the degree-day factors, lack of representative ground-based measurements on which to base estimates, and uncertainties in SCA values for forested terrain. The degree-day factor (Figure 3), a, generally increases over the melt period because of seasonal increases in solar radiation [Granger and Male, 1978]. Previous studies have shown that in most circumstances the degree-day factor ranges between 1.8 and 6.5 mm deg -1 day -1 [Kuusisto, 1980; Kustas et al., 1994; Seidel and Martinec, 2004]. In this study, however, the degree-day factor showed significant day-to-day variations, likely a result of daily variations in the radiation flux. In 2004 snowmelt started on or before March 1; unseasonably high degreeday coefficients were calculated, as the average daily temperatures were low compared to the daily snowmelt rates. Since solar radiation, albedo, and turbulent-energy fluxes dominate snowmelt, day-to-day variations in the energy balance resulting from topography and landcover 11

270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 can make the degree-day approach an unreliable estimate of daily melt, and can contribute to daily variability in the coefficient. However, over time the approach can provide a good measure of the average energy flux and melt, smoothing the day-to-day variations [Anderson, 1968; Ohmura, 2001]. Where sufficient data are available, the depletion method should be based on an energy-balance approach [Cline et al., 1998; Molotch et al., 2004], which can account for early season melt above treeline and topographic effects over the full snow season. The SCA values show clear increases with elevation during winter and steady decreases at all elevations during snowmelt despite small day-to-day variations resulting from patchy cloud cover, satellite view angle, occasional instrument noise from the MODIS sensor, and occasional late-season snowfalls that melt quickly (Figure 5). Although data from the sparse network of snow pillows contain less noise, they also contain less information about basin-scale distribution patterns of snow. Snow pillows were placed in elevations that are representative of the waterproducing regions of a watershed, in order to provide indices of streamflow for statistical watersupply outlooks [Farnes, 1967], not to calculate the water volume in a basin s snowpack. Locations are on flat or nearly flat ground, and thus do not represent the range of physiographic conditions in the surrounding catchments. Because of the multi-variant relationships between the geophysical variables and snowpack properties, interpolation schemes generally explain about only 50% of the SWE variability [Erickson et al., 2005; Molotch and Bales, 2006]. The snow pillows fail to sample the higher elevations (Figure 1). The MODIS images showed that the upper elevations were not snow free until August 2004 and never fully depleted of snow in 2005 (Figure 5), whereas the snow pillows showed complete snow depletion by June 2004 and July 2005 (Figure 6). Although the interpolation method uses observed SCA in the snowmelt estimations, all the input snow-pillow values are zero so the snow-volume estimate is zero. 12

293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 Therefore, a spatial statistical model that uses the snow-pillow data will miss late-season melt unless one guesses at the SWE in the elevations above the snow-free pillows. Streamflow measured at Pohono Bridge on the Merced River in Yosemite Valley showed a snowmelt response beginning in early March in both years (Figure 10) with a return to baseflow by early July and August for 2004 and 2005, respectively. This suggests that snowmelt in both years began around the beginning of March. Comparing the snowmelt for just the March to September period, the interpolation and depletion methods give basin totals that are much closer, within about 5-25% (Figure 11; Tuolumne data not shown). Although snowmelt continues through July and August at the higher elevations, as shown by the depletion approach, the volume contribution was small. This lateseason contribution is, however, important for streamflow, soil moisture and ecosystem services. Because the MODIS fractional snow-cover product estimates the projected snow area, which is the snow not hidden by the forest canopy, during winter the snow cover is underestimated in the middle and lower elevation bands, but the effects of the trees diminish as snow melts. Discrepancies between SCA and canopy openings and the ability of the satellite to determine the amount of snow underneath the canopy [Liu et al., 2004], especially in highly forested areas, is problematic at elevations below 2100 m. At higher elevations, steep slopes keep SCA below 1.0. These issues of forest canopy and steep slopes apply the same bias to both the interpolation and depletion methods because SCA is used in both. To reduce this bias, other studies have used a vegetation gap fraction correction to account for more SCA than the satellite observes [Dressler et al., 2006; Durand et al., 2008]. If the fractional snow-covered area is greater than the gap fraction, then the satellite is likely measuring snow in the canopy, whereas fractional SCA less than the gap fraction may indicate that the canopy has hidden the snow from the sensor 13

316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 (Figure 12). It should be noted that there is good correlation between canopy openings and fractional SCA as the R 2 was 0.91 for both the Tuolumne and Merced in 2004 and 2005. During the accumulation seasons of 2004 and 2005, vegetation may have caused underestimations of SWE by 18-30% at elevations below 2100 m, but when considering the total snowmelt volume, the underestimate represents only 2-4% of the total snowmelt volume. While the majority of the total snowmelt (50-60%) was derived from the 2100-3000 m elevation range, after June the main source of snowmelt was above 3000 m. In 2004, less than 10% of the total snowmelt was derived from elevations of 1500-2100 m, while elevations above 3000 m contributed more than 33% of the basin-wide snowmelt. During 2005, the 1500-2100 m elevations contributed 11-17% of the overall snowmelt volumes, with elevations above 3000 m contributing a smaller fraction of the total, about 36% in the Tuolumne and 25% in the Merced. However, the actual volumes of snowmelt from the higher elevations were basically the same in both years, for the Merced and Tuolumne combined, equivalent to an area-weighted value of about 2.0 m in 2004 versus 2.2 m in 2005 (calculated from Table 1). Much of the difference between the total snowpack volume in the drier (2004) versus wetter (2005) year was in the 2100-3000 m elevation range. For the two basins combined in this elevation range, this translated to an area-weighted average of about 0.60 m in 2004 versus 1.73 m in 2005. Note that 2005 was 47 degree days warmer than 2004 in January-February, so the difference in snow accumulation likely reflects a difference in precipitation, not a difference in temperature. Finally, it is important to consider the elevation dependence of the various methods. The depletion method gives a relatively steep elevation increase for snowmelt, about 1.5 m per 1000 m of elevation in the 2550-3450 elevation range (Figure 13). The interpolation method gives SWE increases with elevation of about 0.1 m per 1000 m elevation (Figure 6); when masked 14

339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 with SCA, this difference becomes about 0.2 m per 1000 m of elevation (Figure 7). In contrast, the commonly used PRISM data show essentially no increase in elevation for October to March precipitation (Figure 13). PRISM precipitation values are higher than snowmelt estimated by depletion. We have not used the snowmelt estimates to back calculate precipitation, as this would require an estimation of rainfall, which is currently not independently measured in these basins. Conclusions The MODIS fractional SCA product at 500-m resolution provides a consistent estimate of basin-scale snow-distribution patterns over mountainous terrain. Noise introduced by off-nadir viewing angles and cloud cover is generally small relative to trends, allowing for a spatially and temporally continuous snow product. Analysis of snowcover by 300-m elevation bands, which averages pixels with a range of slope, aspect and thus energy balance and melt rate, shows decreasing snow cover during the snowmelt season in each elevation band. The 2-3 weeks delay in melt in each successively higher elevation band represents a 2 o C decline in average temperature (based on average ground-surface lapse rate of 6.5 o C per 1000 m). Comparing the interpolated time series with that from the depletion calculation highlights the weakness in the ground-based SWE measurement network, particularly above 3000 m. Despite their smaller area, the high elevations will become more important as seasonal storage decreases at lower elevations with warming of the climate. For estimating a snowmelt time series, it is better to use the snow-pillow data to estimate degree-day factors for melt, i.e. basin-wide daily melt rates, than as absolute measures of SWE in a basin. The resulting back-calculated snowmelt time series using the depletion method provides basin-scale estimates of snowmelt that are consistent with spatially distributed observations of snow depletion. In the two basins 15

362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 studied, about 55% of the snowmelt resulted from the 2100-3000 m elevation bands in both drier (2004) and wetter (2005) years. The approximate one-third of the snowmelt from elevations above 3000 m, whose magnitude is not accurately estimated from ground measurements, contributes significantly to late-season runoff, baseflow and basin recharge. The 10-20% of seasonal snowmelt from below 2100-m elevation is most susceptible to falling as rain rather than snow and melting earlier in a warmer climate. These lower elevations also contribute to the inconsistency in January-February melt between the two methods, i.e. too little melt in the depletion method and too much melt in the interpolation approach. Though MODIS is a research instrument, and past its design lifetime, it is well suited to provide operational snow products with daily temporal resolution and large spatial coverage, and sets the stage for future snow products from VIIRS and GOES-R Advanced Baseline Imager. It is crucial that accurate fractional SCA products are available from these instruments, and the use of the MODSCAG product demonstrates the ability to estimate the spatial and temporal variability of snowmelt at research and operational scales for hydrologic modeling. Acknowledgements Support for this research was provided by NASACooperative AgreementNNG04GC52A and NSF Grant EAR 0610112.We also acknowledge the contributions of X. Meng and P. Slaughter. Comments from the four anonymous reviewers greatly improved this manuscript. 380 16

381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 References Anderson, E. A. (1968), Development and testing of snow pack energy balance equations, Water Resour. Res., 4, 19-37, doi: 10.1029/WR004i001p00019. Anderson, E. A. (1973), National Weather Service River Forecast System snow accumulation and ablation model, Technical Memorandum NWS HYDRO-17, 217 pp, NOAA. Bales, R. C., N. P. Molotch, T. H. Painter, M. D. Dettinger, R. Rice, and J. Dozier (2006), Mountain hydrology of the western United States, Water Resour. Res., 42, W08432, doi: 10.1029/2005WR004387. Bales, R. C., K. A. Dressler, B. Imam, S. R. Fassnacht, and D. J. Lampkin (2008), Fractional snow cover in the Colorado and Rio Grande basins, 1995-2002, Water Resour. Res., 44, W01425, doi: 10.1029/2006WR005377. Bavera, D., and C. De Michele (2009), Snow water equivalent estimation in the Mallero basin using snow gauge data and MODIS images and fieldwork validation, Hydrol. Proc., 23, 1961-1972, doi: 10.1002/hyp.7328. Carroll, S. S., T. R. Carroll, and R. W. Poston (1999), Spatial modeling and prediction of snow water equivalent using ground-based, airborne, and satellite snow data, J. Geophys. Res., 104, 19623-19630, doi: 10.1029/1999JD900093. Christensen, L., C. L. Tague, and J. S. Baron (2008), Spatial patterns of simulated transpiration response to climate variability in a snow dominated mountain ecosystem, Hydrol. Proc., 22, 3576-3588, doi: 10.1002/hyp.6961. Cline, D. W., R. C. Bales, and J. Dozier (1998), Estimating the spatial distribution of snow in mountain basins using remote sensing and energy balance modeling, Water Resour. Res., 34, 1275-1285, doi: 10.1029/97WR03755. 17

404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 Daly, S. F., R. Davis, E. Ochs, and T. Pangburn (2001), An approach to spatially distributed snow modelling of the Sacramento and San Joaquin basins, California, Hydrol. Proc., 14, 3257-3271, doi: 10.1002/1099-1085(20001230)14:18<3257::AID-HYP199>3.0.CO;2-Z. Dettinger, M. D., D. R. Cayan, M. K. Meyer, and A. E. Jeton (2004), Simulated hydrologic responses to climate variations and change in the Merced, Carson, and American River Basins, Sierra Nevada, California, 1900-2099, Climatic Change, 62, 283-317. Dozier, J., and T. H. Painter (2004), Multispectral and hyperspectral remote sensing of alpine snow properties, Ann. Rev. Earth Planet. Sci., 32, 465-494, doi: 10.1146/annurev.earth.32.101802.120404. Dozier, J., T. H. Painter, K. Rittger, and J. E. Frew (2008), Time-space continuity of daily maps of fractional snow cover and albedo from MODIS, Adv. Water Res., 31, 1515-1526, doi: 10.1016/j.advwatres.2008.08.011. Dozier, J., and J. Frew (2009), Computational provenance in hydrologic science: A snow mapping example, Phil. Trans. Royal Soc. A, 367, 1021-1033, doi: 10.1098/rsta.2008.0187. Dressler, K. A., G. H. Leavesley, R. C. Bales, and S. R. Fassnacht (2006), Evaluation of gridded snow water equivalent and satellite snow cover products for mountain basins in a hydrologic model, Hydrol. Proc., 20, 673-688, doi: 10.1002/hyp.6130. Durand, M., N. P. Molotch, and S. A. Margulis (2008), A Bayesian approach to snow water equivalent reconstruction, J. Geophys. Res., 113, D20117, doi: 10.1029/2008JD009894. Erickson, T. A., M. W. Williams, and A. Winstral (2005), Persistence of topographic controls on the spatial distribution of snow in rugged mountain terrain, Colorado, United States, Water Resour. Res., 41, W04014, doi: 10.1029/2003WR002973. 18

426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 Farnes, E. F. (1967), Criteria for determining mountain snow-pillow sites, Proc. Western Snow Conf., 35, 59-62. Farr, T. G., P. A. Rosen, E. Caro, R. Crippen, R. Duren, S. Hensley, M. Kobrick, M. Paller, E. Rodriguez, L. Roth, D. Seal, S. Shaffer, J. Shimada, J. Umland, M. Werner, M. Oskin, D. Burbank, and D. Alsdorf (2007), The Shuttle Radar Topography Mission, Rev. Geophys., 45, RG2004, doi: 10.1029/2005RG000183. Fassnacht, S. R., K. A. Dressler, and R. C. Bales (2003), Snow water equivalent interpolation for the Colorado River Basin from snow telemetry (SNOTEL) data, Water Resour. Res., 39, 1208, doi: 10.1029/2002WR001512. Granger, R. J., and D. H. Male (1978), Melting of a prairie snowpack, J. Appl. Meteorol., 17, 1833-1842, doi: 10.1175/1520-0450(1978)017<1833:MOAPS>2.0.CO;2. Harshburger, B. J., K. S. Humes, V. P. Walden, T. R. Blandford, B. C. Moore, and R. J. Dezzani (2010), Spatial interpolation of snow water equivalency using surface observations and remotely sensed images of snow-covered area, Hydrol. Proc., 24, 1285-1295, doi: 10.1002/hyp.7590. Jeton, A. E., M. D. Dettinger, and J. L. Smith (1996), Potential effects of elimate change on streamflow, eastern and western slopes of the Sierra Nevada, California and Nevada, Water Resources Investigations Rep. 95 4260., U. S. Geological Survey. Kustas, W., A. Rango, and R. Uijlenhoet (1994), A simple energy budget algorithm for the snowmelt runoff model, Water Resour. Res., 30, 1515-1527, doi: 10.1029/94WR00152. Kuusisto, E. (1980), On the values and variability of degree-day melting factor in Finland, Nordic Hydrol., 11, 235-242, doi: 10.2166/nh.1980.018. 19

447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 Liston, G. E. (1999), Interrelationships among snow distribution, snowmelt, and snow cover depletion: Implications for atmospheric, hydrologic, and ecologic modeling, J. Appl. Meteorol., 44, 1474-1487 doi: 10.1175/1520-0450(1999)038<1474:IASDSA>2.0.CO;2. Liu, J., R. A. Melloh, C. E. Woodcock, R. E. Davis, and E. S. Ochs (2004), The effect of viewing geometry and topography on viewable gap fractions through forest canopies, Hydrol. Proc., 18, 3595-3607, doi: 10.1002/hyp.5802. Lundquist, J. D., and D. R. Cayan (2007), Surface temperature patterns in complex terrain: Daily variations and long-term change in the central Sierra Nevada, California, J. Geophys. Res., 112, D11124, doi: 10.1029/2006JD007561. Lundquist, J. D., N. Pepin, and C. Rochford (2008), Automated algorithm for mapping regions of cold-air pooling in complex terrain, J. Geophys. Res., 113, D22107, doi: 10.1029/2008JD009879. Martinec, J., and A. Rango (1981), Areal distribution of snow water equivalent evaluated by snow cover monitoring, Water Resour. Res., 17, 1480-1488, doi: 10.1029/WR017i005p01480. Molotch, N. P., T. H. Painter, R. C. Bales, and J. Dozier (2004), Incorporating remotely sensed snow albedo into spatially distributed snowmelt modeling, Geophys. Res. Lett., 31, L03501, doi: 10.1029/2003GL019063. Molotch, N. P., and R. C. Bales (2005), Scaling snow observations from the point to the grid element: implications for observation network design, Water Resour. Res., 41, W11421, doi: 10.1029/2005WR004229. Molotch, N. P., and R. C. Bales (2006), SNOTEL representativeness in the Rio Grande headwaters on the basis of physiographics and remotely sensed snow cover persistence, Hydrol. Proc., 20, 723-739, doi: 10.1002/hyp.6128. 20

469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 Ohmura, A. (2001), Physical basis for the temperature-based melt-index method, J. Appl. Meteorol., 40, 753-761, doi: 10.1175/1520-0450(2001)040<0753:PBFTTB>2.0.CO;2. Painter, T. H., K. Rittger, C. McKenzie, R. E. Davis, and J. Dozier (2009), Retrieval of subpixel snow-covered area, grain size, and albedo from MODIS, Remote Sens. Environ., 113, 868 879, doi: 10.1016/j.rse.2009.01.001. Rango, A., and J. Martinec (1995), Revisiting the degree-day method for snowmelt computations, Water Resour. Bull., 31, 657-669, doi: 10.1111/j.1752-1688.1995.tb03392.x. Rice, R., and R. C. Bales (2010), Embedded sensor network design for snowcover measurements around snow-pillow and snow-course sites in the Sierra Nevada of California, Water Resour. Res., 46, W03537, doi: 10.1029/2008WR007318. Seidel, K., and J. Martinec (2004), Remote Sensing in Snow Hydrology: Runoff Modeling, Effect of Climate Change, 172 pp., Springer-Verlag, Berlin. Shamir, E., and K. P. Georgakakos (2006), Distributed snow accumulation and ablation modeling in the American River basin, Adv. Water Res., 29, 558-570, doi: 10.1016/j.advwatres.2005.06.010. Slack, J. R., and J. M. Landwehr (1992), Hydro-climatic data detwork (HCDN): A U.S. Geological Survey streamflow data set of the United States for the study of climate variations, 1874-1988, Open-File Rep. 92-129, U. S. Geological Survey. 487 21

488 Tables Table 1. Areas of Tuolumne and Merced River basins above 1500 m, and snowmelt estimates a Merced Tuolumne elevation band, m Avg snowmelt, m Avg snowmelt, m area, km 2 area, km 2 midpoint range 2004 2005 2004 2005 1650 1500-1800 179 0.10 0.25 447 0.13 0.33 1950 1800-2100 197 0.20 0.51 350 0.17 0.64 2250 2100-2400 327 0.28 0.97 375 0.17 0.47 2550 2400-2700 321 0.38 0.83 418 0.31 0.58 2850 2700-3000 223 1.01 1.39 459 1.01 1.39 3150 3000-3300 114 1.68 2.08 276 1.68 2.08 3450 3300-3600 37 2.08 2.56 82 2.88 2.44 3750 3600+ 5 2.02 2.36 15 3.86 3.02 489 a Snowmelt values based on end-of-season volumes from Figure 8 by the depletion method. 22

490 491 Table 2. Snowmelt contributions in elevation bands by interpolation and depletion methods Elevation band, m 1500-2100 2100-3000 Catchment area, % Contributions by interpolation (depletion) method, % Tuolumne Merced Tuolumne Merced 2004 2005 2004 2005 32 26 30 (8) 28 (17) 28 (7) 31 (11) 53 63 51 (43) 55 (47) 62 (57) 61 (64) >3000 15 11 19 (49) 17 (36) 10 (36) 8 (25) 23

492 Table 3. Monthly snowmelt contribution by elevation band, calculated by depletion method Elevation band, m Tuolumne 1500-2100 2100-3000 Contribution for 2004 (2005), % March April May June July August 24 (54) 19 (68) 3 (16) 0 (3) 0 (0) 0 (0) 54 (42) 61 (29) 54 (60) 25 (59) 5 (25) 5 (25) >3000 22 (4) 20 (3) 43 (24) 75 (38) 95 (75) 95 (75) Merced 1500-2100 2100-3000 20 (27) 15 (32) 2 (11) 0 (2) 0 (0) 0 (0) 70 (70) 75 (65) 66 (74) 31 (69) 5 (29) 5 (29) >3000 10 (3) 10 (3) 32 (15) 69 (29) 95 (71) 95 (71) 493 494 495 496 497 24

498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 Figure captions Figure 1. Upper Tuolumne and Merced River basins with the MODIS fractional snow-covered area for April 1, 2005 at 500-m resolution. Elevations of the 9 snow sensors are also shown. Figure 2. Degree-day coefficients for sites in Figure 1. Figure 3. Elevation dependent degree-day coefficients across 4 of 8 elevation bands in 2004 and 2005. Values are shown for period of snowmelt at each elevation. Figure 4. Observed snowmelt as measured at the snow-pillow and the back-calculated snowmelt in 2004 and 2005 using the elevation-dependent degree-day coefficients, a. Figure 5. Daily snow-covered area in the eight 300-m elevation bands. Figure 6. Daily interpolated snow water equivalent in 8 elevation bands in the Tuolumne and Merced River basins for 2004 and 2005. Figure 7. Interpolated snow water equivalent masked with fractional snow-covered area in the eight elevation bands. Figure 8. Cumulative snowmelt for January-September in 2004 and 2005; solid lines represent the interpolation method and dotted lines the depletion method. Note that each curve is cumulative over both time and elevation. Figure 9. Distribution of catchment area and elevation contributions of snowmelt for Tuolumne and Merced basins for January- September, calculated by both the interpolation and depletion methods. Figure 10. Streamflow for Water Years 2004 and 2005 at Pohono Bridge on the Merced River in Yosemite National Park measured by the United States Geological Survey (site 11266500). Figure 11. Cumulative streamflow depth at Pohono Bridge on the Merced River in Yosemite National Park and the cumulative per unit area potential snowmelt depth from the interpolation 25

521 522 523 524 525 526 527 528 529 530 and depletion methods minus sublimation and evapotranspiration (ET) for March September 2004 and 2005. Figure 12. Mean snow-covered area across the eight elevation bands during the accumulation period plotted with the mean canopy openings across for each elevation band, averaged across all pixels in that elevation band. The error bars show the standard deviation from the mean for both SCA and canopy openings. Vegetation data from J. Van Wagtendonk, USGS, based on aerial photography gridded at 10m. Figure 13. Comparison of the PRISM 4 km precipitation (Oct-Mar) across the 8 elevation bands in the Merced and Tuolumne River basins versus the estimated depth of SWE derived from the depletion method. 26

Figure 1. Upper Tuolumne and Merced River basins with the MODIS fractional snow-covered area for April 1, 2005 at 500-m resolution. Elevations of the 9 snow sensors are also shown. 27

531 Figure 2. Degree-day coefficients for sites in Figure 1 28

Figure 3. Elevation dependent degree-day coefficients across 4 of 8 elevation bands in 2004 and 2005. Values are shown for period of snowmelt at each elevation. 532 29

Figure 4. Observed snowmelt as measured at the snow-pillow and the back-calculated snowmelt in 2004 and 2005 using the elevation dependent degree-day coefficients, a. 30

533 Figure 5. Daily snow-covered area in the eight 300-m elevation bands. 31

Figure 6. Daily interpolated SWE in 8 elevation bands in the Tuolumne and Merced River basins for 2004 and 2005. 534 32

535 536 Figure 7. Interpolated snow water equivalent masked with fractional snow-covered area in the eight elevation bands. 33

Figure 8. Cumulative snowmelt for January-September in 2004 and 2005; solid lines represent the interpolation method and dotted lines the depletion method. Note that each curve is cumulative over both time and elevation. 34

537 538 539 Figure 9. Distribution of catchment area and elevation contributions of snowmelt for Tuolumne and Merced basins for January- September, calculated by both the interpolation and depletion methods. 540 35

541 542 543 Figure 10. Streamflow for Water Years 2004 and 2005 at Pohono Bridge on the Merced River in Yosemite National Park measured by the United States Geological Survey (site 11266500). 544 36

545 546 547 548 549 Figure 11. Cumulative streamflow depth at Pohono Bridge on the Merced River in Yosemite National Park and the cumulative per unit area potential snowmelt depth from the interpolation and depletion methods minus sublimation and evapotranspiration (ET) for March September 2004 and 2005. 550 551 37

552 553 554 555 556 Figure 12. Mean snow-covered area across the eight elevation bands during the accumulation period plotted with the mean canopy openings across for each elevation band, averaged across all pixels in that elevation band. The error bars show the standard deviation from the mean for both SCA and canopy openings. Vegetation data from J. Van Wagtendonk, USGS, based on aerial photography gridded at 10m. 557 38