Embedded sensor network design for snow cover measurements around snow pillow and snow course sites in the Sierra Nevada of California

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1 Click Here for Full Article WATER RESOURCES RESEARCH, VOL. 46,, doi: /2008wr007318, 2010 Embedded sensor network design for snow cover measurements around snow pillow and snow course sites in the Sierra Nevada of California Robert Rice 1 and Roger C. Bales 1 Received 30 July 2009; revised 28 August 2009; accepted 3 November 2009; published 31 March [1] The design of sensor networks for measuring the mean and spatial distribution of snow depth at the scale of 1 16 km 2 was evaluated by deploying an embedded sensor network consisting of ultrasonic snow depth sensors to capture the variable physiographic features around an operational snow course in Yosemite National Park in the Sierra Nevada of California. Manual snow surveys were also carried out during accumulation and ablation periods. Four years of continuous data from the embedded sensor network showed that snow depths during both accumulation and ablation periods can vary as much as 50% based on variability in topography and vegetation across a 0.4 ha study area. Spatial snow surveys showed that such a sensor network can be deployed so as to capture both the variability and mean for accumulation and ablation periods across a 1 km 2 area surrounding the sensor network, with a broader network required to extend this to 4 and 16 km 2 areas. In forested areas, higher canopy densities, greater than 60% closure, were associated with the lowest snow depths. Analysis of historical snow course records from 14 sites in Yosemite, including the 10 spatial measurements made during each monthly snow course survey, showed snow depths across the 300 m snow course transects to be relatively uniform, with 68% of all monthly values having standard deviations no more than 10% of the mean. Although existing snow courses do little to help define the spatial patterns of snow distribution at the 1 16 km 2 scales, it is feasible to extend the representativeness of current operational networks by deploying low cost embeddedsensor networks nearby. Such networks should be strategically located to also capture elevational differences in snow accumulation and melt, as well as local scale variability in canopy cover and aspect. Citation: Rice, R., and R. C. Bales (2010), Embedded sensor network design for snow cover measurements around snow pillow and snow course sites in the Sierra Nevada of California, Water Resour. Res., 46,, doi: /2008wr Introduction [2] Ground based observations of snow have long supported operational water resources management, yet for emerging physically based modeling and forecasting tools, historical point measurements leave montane catchments undersampled. The spatial distribution of snow, expressed as snow water equivalent (SWE), is particularly important, given that snow provides the majority of the water input to the mountains of the western United States and dramatically influences energy exchange between the land surface and the atmosphere. Advances in ground based measurements are being outpaced by remote sensing and modeling, and strategic intensification of in situ measurements will provide the means to reduce uncertainty in estimates of hydrologic fluxes and processes [Bales et al., 2006]. [3] Estimations of both physical processes and snowrelated quantities are subject to considerable uncertainty in 1 Sierra Nevada Research Institute, University of California, Merced, California, USA. Copyright 2010 by the American Geophysical Union /10/2008WR mountainous regions because of subgrid variability. The ideal spatial resolution for estimating SWE is one that reduces subgrid element heterogeneity to a level at which most of the variability in the system can be modeled explicitly [Blöschl, 1999]. While the strong relationships between distributed SWE, point snow depth measurements, distributed energy balance, and spatial snow cover depletion observations are well established, use of these relationships for a predictive rather than retrospective analysis of basinwide SWE depletion and snowmelt patterns requires representative, distributed in situ measurements of depth and/or SWE [Cline et al., 1998; Liston, 1999]. Similarly, how physiographic variables and vegetation influence snow distribution has been established for a number of systems [Essery and Pomeroy, 2004; Pomeroy et al., 2004; Elder et al., 1998; Erxleben et al., 2002; Balk and Elder, 2000; Molotch et al., 2005; Molotch and Bales, 2005; Erickson et al., 2005; Sturm and Benson, 2004; Schweizer et al., 2008; Kronholm and Birkeland, 2007; Anderton et al., 2004; Marchand and Killingtveit, 2005]. [4] SWE is measured at over 1700 real time snow sensor stations and manual snow courses in the western United States from a combination of monthly manual snow surveys and continuously telemetered snow pillows. While these 1of13

2 Table 1. Summary of Snow Courses in Yosemite National Park, Merced and Tuolumne River Basins a Established Elevation (m) 1 April Mean/CV (m) Terrain Merced Snow Flat /0.35 grassy meadow Ostrander Lake /0.38 open meadow Tenaya Lake /0.37 grassy meadow, scattered timber Peregoy Meadow /0.37 grassy meadow, encroaching pine Gin Flat b /0.49 grassy meadow Tuolumne Dana Meadow /0.32 large meadow along highway, surrounded by timber Rafferty Meadow /0.32 open meadow New Grace Meadow /0.39 grassy meadow Grace Meadow c /0.31 grassy meadow Tuolumne Meadow /0.39 open meadow Wilma Lake /0.39 open meadow Paradise Meadow /0.42 large meadow in canyon, along creek Vernon Lake /0.56 grassy meadow Beehive Meadow /0.46 grassy meadow a CV is the average coefficient of variation over the period of record within each snow course, considering each of the 10 measurements within a course an independent record. b On ridge between basins. c Ended in Others are still being measured. points provide regional indices of snow amounts, they are insufficient to resolve the volume and distribution of snow at the basin scale [Molotch and Bales, 2005]. Improving and resolving the small scale variability of snow properties will complement the grid scale variability currently available from remote sensing, for example, the 500 m fractional snow covered area (SCA) product from the Moderate Resolution Imaging Spectroradiometer on EOS [Painter et al., 2009]. [5] Snow courses were placed in areas that are representative of the water producing regions of a watershed in order to provide indices of streamflow for statistical water supply outlooks. Many snow courses were installed in the 1930s, and others were installed later, using relatively empirical methods of site selection, with the main criteria being site accessibility and protection from public disturbance (M. Gillespie, National Resources Conservation Service, personal communication, 2004). Moreover, they must be accessible during winter without exposing the surveyors to avalanche danger. Locations are on flat or nearly flat ground, and thus they do not represent the range of physiographic conditions in the surrounding catchments [Dressler et al., 2006]. Therefore snow courses and automated snow stations were not designed to provide SWE values that are representative of the average values within a grid element. Nevertheless, the network has been used to estimate the spatial distribution of SWE [Bocchiola and Rosso, 2007; De Michele and Rosso, 2007; Molotch et al., 2004; Fassnacht et al., 2003; Daly et al., 2000; Carroll and Cressie, 1996; Ling et al., 1995; Carroll and Carroll, 1993], blend with satellite snow cover data for basin scale SWE estimates [Bales et al., 2008], and update snowpackmodel state variables within data assimilation schemes [Brubaker and Menoes, 2001; Carroll et al., 2001; Shafer et al., 1979]. The use of snow measurement network data in these applications implicitly assumes that the SWE values are representative of the grid elements encompassing them, which is not a good assumption [Molotch and Bales, 2006; Schneebeli and Laternser, 2004]. [6] Three questions were addressed in the research reported here. First, how representative of snow variability across the surrounding terrain are monthly snow course measurements, specifically the 10 spatially distributed sampling points that comprise the monthly mean SWE? Second, can a distributed, embedded sensor network, designed and installed in optimal locations based on snow surveys and knowledge of physiographic features, reliably capture the snow distribution patterns during both accumulation and ablation periods? Third, how indicative are the observations within a dense cluster of snow depth measurements of the spatial mean and also variability of snow within grid elements at various spatial scales? 2. Methods [7] The study area was in Yosemite National Park, which includes most of the upper Merced and Tuolumne river basins in the California Sierra Nevada. Two approaches were used to estimate the spatial variability of snow. The first was to examine historical snow course records, which involve making 10 point measurements of snow depth, SWE, and density with a Mt. Rose sampler along a 300 m transect [Church, 1933]. The second approach used an embedded sensor network consisting of 10 ultrasonic snow depth sensors that were placed on the basis of physiographic features (e.g., elevation, solar radiance, slope, aspect, vegetation density) within a 0.4 ha study plot. Manual surveys of snow depth and density were performed across 1 and 4km 2 grids around the sensor network and snow course in order to evaluate the ability of fixed measurements to estimate the spatial mean and variability of snow depth. The locations in Yosemite were chosen for their long snow records, physiographic variability, complementary ongoing measurements, and ease of access. [8] Historical snow course field notes were obtained from the California Department of Water Resources for all 14 snow courses in Yosemite and manually digitized. Only averages of the 10 snow depth measurements made on each survey are generally reported by the snow survey cooperators. Each snow course is situated below timberline on flat or nearly flat terrain (Table 1). Snow surveys occur on or close to the first day of the month, February May, with yearly sampling frequency depending on ease of access; nearly all years have at least a 1 April survey, and most have 2of13

3 Figure 1. Gin Flat is located in Yosemite National Park along Highway 120, Tioga Pass Road, at an elevation of 2100 m in the upper Merced River basin. The embedded sensor network consisting of nine ultrasonic depth sensors is deployed across a mixed conifer 0.4 ha study site within 61 m of Highway 120. The California Department of Water Resources (DWR) operates a snow pillow and snow course at Gin Flat with historical records dating back to 1980 for the snow pillow and 1930 for the snow course. In spring 2005 a second embedded sensor network (Sensor Web) was installed and tested. other months. The 1 April date is also the survey date when most snow courses had maximum seasonal SWE. Prior to 1950, snow courses involved sampling points, but since then, only 10 points have been sampled. We did not use the discontinued points in our analysis. [9] The sensor network was established in November 2003 near the Gin Flat snow course ( N, W) in a mixed conifer forest, where tree canopy densities often exceed 60% (J. van Wagtendonk, U.S. Geological Survey, unpublished data, 1997) and significantly influence snow distribution patterns (Figure 1). In addition to the snow course (1930 to present), Gin Flat is also the location of a snow pillow (1980 to present), and is representative of mid elevation mixed conifer forests in the central and southern Sierra Nevada. The sensor network consisted of 10 ultrasonic snow depth sensors (Judd Communications), each mounted atop a 3 m steel mast on an arm that extended outward 0.61 m from the top. Snow depth and air temperature were logged hourly. The 3 m height represented a 20% exceedence probability based on the snow course records, and provisions were made to extend the mast and raise the height of the snow sensor if snow was deeper. The mast was bolted to a U post that was driven 0.6 m into the ground to provide stability and added strength for snow creep and glide. A centrally located data logger (Campbell Scientific CR10X) with external battery and 12 V photovoltaic power supply was housed in a weather proof enclosure and mounted to one mast. Wires extended from this central point to the sensors to a maximum distance of 55 m (distance limited by resistance and signal loss). [10] In spring 2005 we installed and tested a wireless sensor network located about 500 m northeast and consisting of 10 snow depth sensors connected by wireless pods (Figure 1). This solved two problems with the 10 node wired network: (1) restricted spacing due to signal loss in wires and (2) rodents chewing wires placed in the soil, requiring either conduit or placement of wires above the soil in the snow. These pods (Sensor Web) were advanced versions of those currently being developed and tested by a number of companies [Delin et al., 2005]. This initial test focused on the technical aspects of placement and communications of this self organizing array. Self organizing refers to the lack of a preferred direction or focusing of information flow, where each measuring node determines its unique information flow independent of every other node without the knowledge of previous direction, although there is a main access point in and out of the Sensor Web. This allows the flow of information to continue throughout the network if a node drops out of the network due to, for example, power failure. The snowpack was already well developed before the pods were installed and the snow was disturbed during installation, so only system performance/reliability and not snow depths are reported. 3of13

4 Figure 2. Mean monthly snow depths at 4 of the 14 snow courses in Yosemite National Park over the period of record. These four snow courses provide an elevational transect from 2988 to 1982 m and are representative of the interseasonal and interannual variability that is evident at the other 10 snow courses. The circles represent the monthly mean snow depth measured at the snow course, and the lines connect those measurements within a given year. Snow courses higher in the basin, such as Dana Meadow and Tenaya Lake, might only have one sample point for a given year due to difficult winter access, especially in the early period of record. [11] Field surveys of snow depth and density were performed on 7 10 February 2006 and again on 4 7 April In the 1 km 2 study area, which was centered on the snow pillow, depths were measured at 20 points in each of four cardinal directions at 25 m intervals. The 4 km 2 area involved measuring depths at an additional 8 points spaced 250 m apart, beginning immediately outside the 1 km 2 area along the same cardinal directions. Snow density was measured at four locations in the 1 km 2 grid, locations being 250 m from the snow pillow in each of the four cardinal directions, and at an additional four locations in the 4 km 2 area, at the center of each 1 km 1 km quadrant. Snow pits were excavated and density was measured at 0.10 m vertical intervals using a 1000 cm 3 stainless steel snow cutter. Snow samples were weighed using a digital scale with 1 g precision. Locations of the 144 points were defined in a geographic information system (GIS) and stored in a handheld computer equipped with a GPS receiver and GIS software. On the handheld unit, the 144 points were overlaid on a U.S. Geological Survey (USGS) 7.5 min topographic map. The GPS unit was used to navigate to each point where snow depth was recorded. At each sampling point, four depth measurements were taken within 5 m around a central point, recorded, and averaged. [12] Binary regression tree analysis was used to identify the five independent physiographic variables (elevation, slope, aspect, solar radiation, and vegetation) that affect the distribution of snow depth and SWE and provided the basis for interpolation across the grids [Molotch and Bales, 2005; Molotch et al., 2004; Erxleben et al., 2002; Balk and Elder, 2000; Elder et al., 1998; Breiman et al., 1984]. The regression tree model uses binary recursive portioning to bin 4of13

5 Figure 3. The historical mean 1 April snow depths and coefficients of variation (CVs) for the individual sample points within each snow course. The three lowest elevation sites (Beehive Meadow, Vernon Lakes, and Gin Flat) are highlighted because they show a higher degree of interannual variability than do the other 11 sites. data into increasingly homogeneous subsets. For each combination of independent variables a tree was overgrown to overfit the data, and tree size selection was guided by 100 iterations of 10 fold cross validation procedures. The optimal tree size was located when the model deviance was minimized. Cross validation was used to compare the estimated values with the measured values. Cross validation was accomplished by removing each data point and then using the remaining observations to estimate the data value. Residuals resulting from the difference between the measured and calculated values were evaluated to assess the performance of the model. [13] Elevation, slope, and aspect were taken from a 10 m U.S. Geological Survey digital elevation model (DEM) derived from the standard level min topographic map series provided by the Yosemite National Park. The initial DEM was cast to a Universal Transverse Mercator projection and was referenced to the North American Datum of This projection was chosen because it respects the cardinal directions (extending from the center of the projections). The DEM was then upscaled to a 20 m resolution, resulting in 10,000 records for a 4 km 2 area. A solar radiation index was calculated across visible and nearinfrared wavelengths ( mm) using the TOPQUAD algorithm [Dozier, 1980] with clear sky conditions. Daily solar irradiance was calculated for the15th of each month over the 20 m grid. For the February survey, radiation was summed for November January; for April, the sum was for November March. The average vegetation density data noted above were used as reported in six classes: 0% 2%, 2% 10%, 10% 25%, 25% 40%, 40% 60%, and >60%. 3. Results 3.1. Snow Courses [14] Mean 1 April snow depths over the period of record at the 14 courses ranged from 1.40 to 2.86 m. Four representative snow courses illustrate interannual and interseasonal variability (Figure 2). The maximum 1 April snow depth for the higher elevation sites (Dana, Tenaya, and Gin) occurred in 1983; however, the maximum depth at the lower elevation Beehive site occurred in 1952, when temperatures were below average. The historical 1 April low for all 14 sites was in [15] Standard deviations and coefficients of variation (CVs) of 1 April snow depths were computed for each of the 10 individual locations within the 14 snow courses (140 total locations) over the period of record. Across the 14 snow courses, the average of the 10 standard deviations (CVs) for the 10 points making up the snow course ranged from 0.59 to 1.12 m ( ) (Table 1), with the highest average CVs of 0.56, 0.46, and 0.49 occurring at Vernon, Beehive, and Gin, respectively. The highest standard deviations were generally associated with the snow courses with the highest accumulations. The individual and average 1 April CVs both decreased with increasing snow depth, with lower elevation sites showing a higher degree of variability relative to the site mean depth than those at higher elevation; CVs for individual survey points reached 0.7 (Figure 3). [16] Survey records for each month at all snow courses revealed limited within course variability, as measured by the CV relative to the monthly mean at that site (Figure 4), except for the lowest mean snow depths. Again, CVs were lower for sites with higher mean monthly snow depth, with the highest CVs being reported at the lower elevation sites of Beehive and Vernon. Standard deviations did not show such a distinct pattern as on Figure 4, although Vernon and Beehive did generally have higher standard deviations than other sites. CVs were lower and snow depths higher for 1 February, during the accumulation period; for example, mean CV at Beehive, Vernon, and Gin was 0.11, and mean CV was 0.09 at the 11 other snow courses. The Beehive, Vernon, and Gin CV was also 0.11 for 1 March, but as the record moves toward the ablation period, the CV increased to 0.20 in April and 0.42 by 1 May. The mean CV for the other 11 snow courses remained 0.09 through 1 April, with a slight increase to 0.14 by 1 May. Over all months and snow courses, 68% of the CVs were 0.10; 89% were 0.20; and 97% were 0.5 (Figure 5). The lower elevation Vernon and Beehive sites showed greater variability Snow Surveys [17] The 7 10 February survey was during a 3 week period with unseasonably warm temperatures. For the 32 day period leading up to 10 February the average daily temperature at Gin Flat was 0 C or higher for 21 of the days, the maximum daily temperature was 0 C or higher for 30 of those days, and the minimum daily temperature was at or above 0 C for 15 of the days. By 1 March courses across the Sierra Nevada showed the snowpack to be 85% of the historical average, with the upper Merced basin at 75%. Thus the February survey was done during a winter ablation period. The average snow depth across both the 1 and 4 km 2 sampling grids was 0.67 m, with a mean density of 384 kg m 3. The 4 7 April surveys at Gin Flat began with a rain on snow event up to 2300 m on 4 April; on 5 April, 0.50 m of high density snow fell, and the survey was deferred until the next day because of falling trees. The following 2 days provided stable weather conditions, but 5of13

6 Figure 5. Cumulative distribution of the coefficient of variation for all the monthly measurements at each snow course over the period of record. Note the higher variability at the lower elevation snow courses of Vernon Lakes and Beehive Meadow. at 124%. Therefore, the April snow survey was during an accumulation period. The CV was 0.40 for the February survey for both the 1 and 4 km 2 study areas; in April the respective CVs were 0.20 and Snow depth rather than SWE was used for analysis of optimal measurement locations in part because the embedded sensor network measured only snow depth. Although density was relatively stationary across the survey, using average values would introduce additional uncertainty into the analysis. Note that denser snow was encountered in the 4 km 2 than in the 1 km 2 area Modeled Gridded Snow Depth [18] Results from the cross validation showed that the optimal tree sizes were located when the model deviance was minimized, determining the number of terminal nodes to be 15 and 10 for the February and April simulations, respectively (Figure 6). To assess small scale variability, the Moran I test confirmed (p > 0.05) that the spatial autocorrelation and cross correlation were constant, proving a random distribution of the snow depth residuals and no cross correlation with the independent variables. Thus, the use of Figure 4. CVs across the snow sampling transect for each monthly measurement over the period of record. warm temperatures and melting fresh snow provided difficult travel conditions; hence, 16 depth measurements in the northern section of the grid could not be surveyed. The average snow depth was 1.87 m, with an average density of 315 kg m 3 (Table 2). Despite the rain on 4 April, significant March snowfall resulted in the Sierra Nevada level being 125% of the historical average, with the upper Merced Table 2. February and April 2006 Snow Survey Results 1km 2 4km 2 Density (kg m 3 ) Depth (m) Density (kg m 3 ) Depth (m) February Minimum Maximum Mean CV N Snow pillow April Minimum Maximum Mean CV N Snow pillow of13

7 for the 1 km 2 area (Figure 8), reflecting lower vegetation density, higher elevation, and greater northwest versus smaller southwest aspect compared to the 4 and 16 km 2 areas Embedded Sensor Network [20] Snow depths across the sensor network varied by as much as 50% (Figure 9), with high tree canopy density (>60%) influencing distribution patterns the most. Sensor 2 (in dense canopy) recorded the lowest snow depth, while Figure 6. February and April model deviance versus number of terminal nodes for regression tree models. kriging to distribute the snow depth residuals did not significantly improve the model fit, contrary to reported increases in accuracies of 4% 8% [Molotch et al., 2005; Elder et al., 1998]. [19] The February prediction tree explained 60% of the initial variance. Residuals from the cross validation procedure were normally distributed, and the mean absolute error (MAE) and the root mean square error (RMSE) calculated from the residuals were 0.12 and 0.17 m, respectively. In April, slope, aspect, solar radiation, and elevation were important, as well as, to a lesser extent, vegetation density, suggesting that deeper snow was associated with orographic enhancement, areas with low canopy density, and lower solar irradiance. The April prediction tree explained 55% of the initial variance, and residuals from the cross validation procedure were normally distributed; MAE and RMSE calculated from the residuals were 0.24 and 0.29 m, respectively. It should be noted that variables in the two periods are similar, as radiation is correlated with slope (r 2 = ) and, to a lesser, extent elevation. Other variables were less well linearly correlated (r 2 = ) (Table 3). Using the regression tree for predictions, it was found that modeled snow depths across the 1, 4, and 16 km 2 landscapes surrounding Gin Flat were similar for all three scales, with a minimum of 0.38 m, a maximum of 1.16 m, and a mean across the 1, 4, and 16 km 2 areas of 0.69, 0.64, and 0.62 m, respectively. CVs were also relatively similar across the 1, 4, and 16 km 2 modeled areas at 0.30 for February and 0.18 for April; that is, they were higher for the winter ablation period. One might expect the snow variability to increase as the modeled area increases owing to the greater elevation range (Figure 7). Slightly higher snow depths were modeled Table 3. Correlation r 2 of Independent Variables Used in the Regression Tree Analysis a Solar Radiation Slope Elevation Aspect Vegetation Density Solar radiation Slope Elevation Aspect Vegetation density a February r 2 is given above the diagonal; April r 2 is given below the diagonal. Figure 7. Cumulative distributions of the physiographic variables across the 1, 4, and 16 km 2 study areas surrounding Gin Flat. The distribution associated with each of the sensors is shown. 7of13

8 Figure 8. Distribution of measured and modeled snow depths from the February and April 2006 snow surveys. The horizontal dotted lines give the depth at the snow pillow. The vertical lines represent the range of measured and modeled values, the rectangular boxes represent the 25th and 75th percentiles and thus the middle half of the snow distributions, and the solid lines represent the spatial means. The circles are the outlier values that extend beyond the 10th and 90th percentiles. sensors 4 and 10 (open forest) routinely recorded the highest snow depths for both accumulation and ablation. The Gin Flat snow course mean and snow pillow were at least 25% higher than the sensor network mean. In addition, the embedded sensor network was depleted of snow as much as 4 weeks earlier than the snow pillow each year. [21] For the February period the mean snow depth of the embedded sensor network (0.65 m) was within 5% of means for the modeled 1, 4, and 16 km 2 grids, and the sensor network matched the 25th and 75th percentiles over the 1km 2 area (Figure 8). For the 4 and 16 km 2 grids the sensor network captured the 75th percentile but not the 25th percentile or outliers. Note that the 25th and 75th quartiles of the 4 and 16 km 2 modeled areas coincide because the distributions of physiographic features in both areas are similar. For April the sensor network captured the lowest nonoutlier snow depth value of 1.34 m for the 1, 4, and 16 km 2 and snow survey grids and measured within 3% of the highest nonoutlier for the 1 km 2 grid, as well as an outlier in the 4 and 16 km 2 grids of 2.27 m. However, the sensor network failed to capture the outliers for the snow survey and overestimated the spatial mean. The standard deviation was 0.22 m for the embedded sensor network, indicating a slightly greater spread of snow depths than the modeled 8of13 Figure 9. Hourly snow depth measurements for ultrasonic depth sensors, snow pillow data, and monthly snow course. The vertical lines represent the range of snow depths measured across the snow course transect, the rectangular boxes represent the 25th and 75th percentiles and thus the middle half of the snow distributions, and the solid lines represent the spatial means. The circles are the outlier values that extend beyond the 10th and 90th percentiles.

9 however, software problems limited analysis of data and deployment in subsequent years. Unfortunately, these pods are no longer supported by the manufacturer. Figure 10. Communication reliability of 10 self organizing pods within a Sensor Web during spring The circles represent the average number of pods, and the vertical lines show the spread of pods communicating during a 5 min sampling interval throughout a 24 h period. values of 0.19, 0.19, and 0.08 m for the 1, 4, and 16 km 2 areas, respectively; however, the sensor network failed to capture the shallower depths in the first quartile of the modeled values. Note that some upper and lower bounds for the modeled areas coincide with the quartiles; adding two additional nodes to the regression tree would extend the range, but it would also increases the deviance and provide a poor fit for the remaining snow depths. For April, the sensor network overestimated the spatial mean by 5% for the 1 km 2 area and by 10% and 12% for the 4 and 16 km 2 areas, respectively. The standard deviation for the embedded sensor network was 0.26 m, 20% lower than values for the modeled areas. However, the embedded sensor network was unable to capture the distribution of snow depths modeled over the 1, 4, and 16 km 2 areas for the April accumulation period. It does capture an observation near the lowest modeled value for both 4 and 16 km 2, but the sensor values were skewed toward higher depths and were more representative of the 1km 2 modeled depths. The Gin Flat snow course and snow pillow recorded mean snow depths that were 17% and 25%, respectively, above the sensor network mean (Figure 8) Sensor Network Reliability [22] The wireless pods maintained good connectivity during much of the test but lost connectivity due to heavy snowfall (Figure 10). Two things affected communications. First, a heavy snowfall and resulting snowdrifts immediately after initiating the test prevented some pod to pod line ofsight communications, and only 7 of the 10 pods were reporting; this was alleviated by manually increasing the height of the pods 0.30 m so that they were again above the snow surface. Second, all connectivity was lost during a subsequent snowfall event, in part owing to drifting, but also possibly because antennas accumulated snow and become covered, thereby limiting their ability to transmit a signal, and without internal memory, data were lost. During the mid March to mid May period of maximum accumulation, communication was sporadic. Communications would drop with additional snowfall but recover when snow ablated. Finally, around mid May, when the accumulated snow dropped below 2.50 m, all pods consistently reported. The next year 20 pods were deployed with similar results; 4. Discussion 4.1. Spatial Variability [23] Greater variability within snow courses was associated with later season measurements and lower elevation sites, when melt patterns influence snow distribution. The possible influence of vegetation is apparent below 1.0 m of snow, with lower accumulation years in general exhibiting greater variability, as measured by the CV. Individual snow depths within a single snow course survey showed little deviation from the reported mean (CV mean of 0.07 and range of ) at 11 of the 14 snow courses, indicating little variation in snow cover along these 300 m transects across a wide range of snowfall timing and amounts interannually. Although 11 of the 14 snow courses exhibit less variability than at the Gin Flat snow course, the variability at Gin Flat is not anomalous. Studying spatial patterns of snow depths in the area around Gin Flat should thus yield results that can be applied to other areas. Given the complex terrain surrounding snow courses, it is unlikely that a 300 m snow course transect with no slope, aspect, or significant vegetation will capture the spatial mean and local pattern of snow distribution. [24] The snow survey CVs ( ) (Table 2) are lower than the values of reported for Green Lakes Valley in the Colorado Front Range [Erickson et al., 2005], the reported for Emerald Lake basin in the Sierra Nevada [Elder et al., 1991], and the reported for the headwaters of the Rio Grande in Colorado s San Juan Mountains [Molotch and Bales, 2005]. However, these prior surveys were above tree line and thus likely were subjected to more wind redistribution of snow than in the heavily forested area surrounding Gin Flat. Average annual wind speed at the Emerald Lake basin was reported to be 4.5 m s 1 in the lower part of the basin and 7 m s 1 on a ridge higher up in the basin [Marks et al., 1992]. In contrast, the average wind speed at Gin Flat is about 1.1 m s 1 (data downloaded from the California Data Exchange Center, [25] Partitioning of the snow survey data sets using regression tree analysis showed that a significant fraction of the variation in snow depth at Gin Flat during the snow surveys was explained by the independent variables for both the spring accumulation and winter ablation periods (r 2 = 0.65 and 0.55, respectively), similar to prior work [Molotch et al., 2005; Erxleben et al., 2002; Elder et al., 1998]. Although our snow surveys were performed during a single accumulation and ablation season, they reflect quite different conditions. In nonforested areas, physiographic features are constant year to year, so snow tends to collect in similar areas and melt in similar patterns [Erickson et al., 2005; Deems et al., 2008], suggesting that intense initial sampling within a single accumulation and ablation year may be adequate to characterize the effects of the topographic parameters on snow distribution. At forested sites, active management of vegetation may mean that some variables will change over time, and snow distribution may change in response. 9of13

10 Figure 11. Optimal locations for measuring the mean spatial snow depth across the 1, 4, and 16 km 2 modeled snow depth area at Gin Flat. (left) The ablation period in February. (right) The accumulation period in April. The diamonds represent the locations of the 10 nodes of the embedded sensor network, and the crosses show the locations of the snow pillow and snow course. The shaded areas represent areas with values within 10% of the mean modeled snow depth. 10 of 13

11 Figure 12. Number of snow depth sensors required, within a 95% confidence interval, to improve the accuracy of obtaining the spatial mean. The greatest improvement occurs within the first four snow depth sensors, reducing the uncertainty by 20% for February and April [26] An attempt was also made to assess the variation within each grid cell, using the four measurements made within each cell, but several statistical tests showed that the variance of the measurements was not homogeneous. A Bartlett test rejected the hypothesis of homogeneity, and a linear regression of the point variance against the spatial coordinates gave coefficients significantly different from zero, but these results indicated that sample size was insufficient to provide a statistically significant outcome. Small scale variability is most likely driven by vegetation (>60% canopy density was common) due to canopy interception and subsequent sublimation of snowfall and vegetation induced variability generated by longwave radiation [Essery et al., 2008;Pomeroy et al., 2002; Hedstrom and Pomeroy, 1998; Gray and Male, 2004] Measurement Design [27] Optimal locations to estimate the spatial mean for both the February and April survey dates for the 1, 4, and 16 km 2 modeled areas (Figure 11) are those grid elements with modeled snow depth within 10% of the spatial mean. In February, 34% of the grid cells were optimal in both the 1 and 4 km 2 modeled area, with 19% in the 16 km 2 area. In April, 61% of the grid cells were optimal within the 1 km 2 grid, while 19% and 6% of the areas were optimal for the 4 and 16 km 2 modeled areas, respectively. The snow pillow and snow course did fall within optimal grid cells for either date, but the embedded sensor network was located in optimal locations to capture the mean for both periods. Even if the snow pillow was within an optimal grid cell, as a point measurement it would not necessarily reflect the grid cell mean. Note that Molotch and Bales [2005] identified optimal locations for accumulation and ablation, but they did not deploy a measurement system to test the design. [28] A single point measurement within the sensor network is a poor estimator of the spatial mean for the network, but four or more measurement points can improve the accuracy by more than 20%, while additional sensors provide only minor improvement across the 0.4 ha area (Figure 12). A similar reduction in uncertainty for the first four or five versus additional measurements was found for near surface soil temperature sensors [Lundquist and Lott, 2008]. Thus a network of four or five nodes placed at optimal locations is sufficient to capture the 1 km 2 spatial mean within ±20% in February and ±25% in April. A broader network is needed to represent the 4 and 16 km 2 areas because of elevational and other physiographic differences at these larger scales. [29] For both survey periods, the sensor network failed to represent the distribution of snow depths in the larger grids (4 and 16 km 2 ) and failed for 1 km 2 in April. Though the distributed sensors were located in areas that were optimal for the spatial mean, the independent variables that control the distribution of snowfall and interception, sublimation, and melt were not adequately sampled (Figure 7). [30] To highlight the importance of the canopy structure on accumulation and the limitations of the sensor network as currently configured to capture the patterns of snow depth, the distribution of depths was examined across the m elevation band in the 4 km 2 modeled area (Figure 13), which extended 30 m above and below the elevations of the sensor network. In February and April, the modeled spatial mean was within 6% of the observed mean for the sensor network; however, the area of the sensor network had a higher range of snow depths than the area modeled. The main difference between the two areas was Figure 13. Comparison of the snow distribution patterns in February and April 2006 at the embedded sensor network and the elevation band ranging from 2090 to 2170 m within the 4 km 2 modeled study area. The elevation range extends 30 m below and above the embedded sensor network. The vertical lines represent the range of snow depth values, and the rectangular boxes represent the represent the 25th and 75th percentiles. The circles are the outliers. 11 of 13

12 canopy density, with 45% of the modeled area canopy having a closure of >60% versus 22% of the sensor network area having a canopy closure of >60% (Figure 7). Because ranges of snow depths, both modeled and measured, differ with scale, we could not definitively determine how many sensors are needed to capture variability at the larger scales modeled. 5. Conclusions [31] At Gin Flat, neither individual snow course measurements nor the snow pillow represent the 1, 4, or 16 km 2 scale spatial mean from the snow surveys to within 20% 30%. As the snow course is not representative of the surrounding physiographic features, the 10 individual measurements within it are unable to resolve the spatial variability over distances greater than those observations. Individual point measurements that comprise the monthly snow course surveys in Yosemite showed little variability within the snow course transects, in contrast to the much greater variability in snow depths in the terrain surrounding the snow course. [32] Acoustic snow depth sensors strategically placed so as to sample the independent variables controlling snow distribution and melt can capture the spatial mean snow depth in a forested, mountain area during both accumulation and ablation periods, with greater uncertainty during accumulation. Sensor networks especially need to be distributed so as to capture elevational differences, vegetation, and canopy structures, which influence snow accumulation and ablation patterns. In order to capture the variability across 4 or 16 km 2 areas, sensors need to be deployed at those scales in order to better assess the ability of a smaller area to represent the variability in a larger area. Based on surveys, measurements over an area between 1 and 4 km 2 may be adequate to capture variability over larger areas on the order of 16 km 2. Use of wireless mote networks is essential for extending these sensing platforms beyond traditional wired capabilities, making it possible to extend sensors over greater distances from a central communications hub and to eliminate common wildlife damage. [33] The first priority for operational hydrology should be to augment existing snow courses and snow telemetry sites with sensor networks to extend the spatial representativeness of these point measurements. Our study site in Yosemite National Park was limited to the 122 m wide nonwilderness corridor centered on Tioga Pass Road. While many features of physiographic variability can be captured in nonwilderness areas, measurements will also need to be located in designated wilderness areas that encompass much of the snow producing terrain in the Sierra Nevada. Distributing these networks across a basin has the potential to transform snow cover estimates and enable the use of advanced modeling tools for more accurate hydrologic forecasting, particularly when blended with full basin satellite snow products. [34] Acknowledgments. Support for this research was provided by NASA REASoN (NASA grant NNG04GC52A) and the National Science Foundation (NSF EAR ) observatory design. Additional support was provided by the University of California, Merced, Resources Management and Science Division at Yosemite National Park, and Kevin Delin at SensorWare Systems, Inc. We would also like to acknowledge the contributions of T. Bouffon, X. Meng, R. Dewit, S. Martin, N. Molotch, L. Elits, and F. Baggett. Comments from three anonymous reviewers greatly improved this manuscript, and they are acknowledged with thanks. References Anderton, S. P., S. M. White, and B. 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