SNOTEL representativeness in the Rio Grande headwaters on the basis of physiographics and remotely sensed snow cover persistence

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1 HYDROLOGICAL PROCESSES Hydrol. Process. 2, (2) Published online in Wiley InterScience ( DOI: 1.12/hyp.128 SNOTEL representativeness in the Rio Grande headwaters on the basis of physiographics and remotely sensed snow cover persistence Noah P. Molotch 1 * and Roger C. Bales 2 1 Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 839, USA 2 Division of Engineering, University of California, Merced, CA 95344, USA Abstract: In this study we identify the physiographic and snowpack conditions currently represented by snowpack telemetry (SNOTEL) stations in the Rio Grande headwaters. Based on 8 years of advanced very high-resolution radiometer data ( ) a snow cover persistence index was derived. Snow cover persistence values at the seven SNOTEL sites ranged from 3Ð9 to 4Ð75, with an average 14% greater than the mean persistence of the watershed. Using elevation, western barrier distance, and vegetation density, a 32-node binary classification tree model explained 75% of the variability in average snow cover persistence. Terrain classes encompassing the Lily Pond, Middle Creek, and Slumgullion SNOTEL sites represented 4Ð1%, Ð4%, and 4Ð% of the watershed area respectively. SNOTEL stations do not exist in the spatially extensive (e.g. 11% of the watershed) terrain classes located in the upper elevations above the timberline. The results and techniques presented here will be useful for spatially distributed hydrologic analyses, in that we have identified the physiographic conditions currently represented by SNOTEL stations (i.e. the snowpack regimes at which snow water equivalent estimation uncertainty can be determined). Further, we outlined a statistically unbiased approach for designing future observation networks tailored for spatially distributed applications. Copyright 2 John Wiley & Sons, Ltd. KEY WORDS snow cover; snow water equivalent; SNOTEL; observation network design; binary regression tree INTRODUCTION Ground-based snow water equivalent (SWE) observations from the snowpack telemetry (SNOTEL) network have been used to evaluate, initialize and update grid-element SWE estimates within spatially distributed snowmelt models (Rango, 1988; Carroll et al., 21). Additional spatial applications of these data include the development of remotely sensed SWE detection algorithms (Chang et al., 1991) and estimation of the spatial distribution of SWE using statistical models (Carroll and Cressie, 199; Fassnacht et al., 23; Molotch et al., 24b). Although SNOTEL stations (and snow courses) were placed in areas intended to be representative of the water-producing regions of a watershed (US Soil Conservation Service, 1972), the main criteria actually used to locate sites were accessibility and protection from public disturbance (Mike Gillespie, US Natural Resource Conservation Service, personal communication, 24). Thus, SNOTEL locations may not represent the full range of physiographic and snowpack conditions found within the watersheds in which they are located; more likely they represent only a small subset of these conditions. Future development of spatially distributed hydrologic models and remotely sensed SWE detection algorithms will increase demand for ground-based observations of SWE. The observations used to evaluate spatial snowpack estimation techniques need to represent a variety of physiographic (e.g. vegetation and * Correspondence to: Noah P. Molotch, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 839, USA. molotch@cires.colorado.edu Received 21 June 25 Copyright 2 John Wiley & Sons, Ltd. Accepted September 25

2 724 N. P. MOLOTCH AND R. C. BALES topography) and snowpack (e.g. variability in snow accumulation and ablation rates conditions), as these conditions can control algorithm performance in non-linear ways (Beven, 1995). Identifying the physiographic controls on SWE is particularly challenging over larger watersheds (i.e. >1 km 2 ) as remotely sensed SWE data are not available at sufficiently fine resolutions, i.e. <25 km 2 (Chang et al., 1991). Additionally, the spatial variability in snow distribution at these scales cannot be resolved using current ground observations, as the distance between observations is greater than the correlation length scale (Blöschl, 1999). Previous work has suggested that SNOTEL SWE values are inherently biased toward overestimates of mean basin-wide SWE (e.g. Daly et al., 2). However, the aforementioned SWE measurement challenges prohibit quantification of these biases. Furthermore, designing future observation networks intended to capture the variability in snow distribution patterns is difficult given our inability to characterize SWE distribution over these scales. The relatively long temporal record of the advanced very high-resolution radiometer (AVHRR) permits quantification of interannual snow cover persistence (Bales et al., 23). Analysis of the physiographic controls on snow cover persistence may be useful for classifying zones of snowpack processes as snow cover persistence varies as a function of both snow accumulation and snowmelt processes. Statistically significant relationships between snow accumulation and physiographic variables exist at the hillslope scale (Elder et al., 1998; Molotch et al., 25) and at the regional scale (Solomon et al., 198; Fassnacht et al., 23; Molotch et al., 24b). Regression-tree snow depth models have been used to explore these relationships at the hillslope scale (Elder et al., 1995, 1998; Balk and Elder, 2; Erxleben et al., 22; Winstral et al., 22; Molotch et al., 25), but they have not been used at larger scales (i.e. >1 km 2 ) owing to the inadequate spatial density of ground observations at these scales. Physiographic conditions also control the spatial patterns of snow ablation, as vegetation and topography influence the distribution of solar radiation (Dozier, 198; Davis et al., 1997), snow-surface albedo (Molotch et al., 24a), net longwave radiation (Sicart et al., 24), wind speed, and turbulent fluxes (Cline and Carroll, 1999). In this study, binary classification-tree models are used to relate physiographics (i.e. independent variables) to AVHRR-derived estimates of snow cover persistence (i.e. dependent variable). These relationships are then used to identify the snowpack regimes (i.e. areas with unique relationships between physiographics and snow cover persistence) currently represented by SNOTEL stations. Three questions are addressed. First, what are the physiographic and snowpack conditions (i.e. snow cover persistence) currently represented by the SNOTEL sites relative to the watershed? Second, what are the relationships between physiographics and snow cover persistence across the watershed and how do these relationships control SNOTEL representativeness? Finally, what are the optimal locations for future observations of SWE for the purpose of evaluating grid-element SWE estimates? STUDY AREA This study was conducted in an area surrounding the Rio Grande headwaters in the San Juan Mountains of southern Colorado (Figure 1). The Rio Grande headwaters basin encompasses an area of 3419 km 2, with a minimum elevation of 2434 m and a maximum elevation of 4233 m. Approximately 5% of the watershed is covered with coniferous forests. Herbaceous grasslands of the valley floor and alpine zones cover approximately 35% of the watershed; the remaining 15% is covered by deciduous forests, shrublands and bare ground. The watershed is surrounded by the Continental Divide on its western, northern and southern boundaries, separating it from the San Juan and Gunnison River basins to the southwest and north respectively. Draining to the east, runoff from the basin provides the primary source of surface water for the highly productive agricultural lands in the San Luis Valley and for meeting the water allocation requirements to the downriver states under the Rio Grande Compact. Precipitation in the San Luis Valley is less than 25 cm on

3 SNOTEL REPRESENTATIVENESS IN THE RIO GRANDE 725 Colorado 1 Del Norte gage 38 N New Mexico 2 3 elevation, m Center meteorological station N km 17 W 7 Figure 1. The Rio Grande above Del Norte and the Slumgullion (1), Beartown (2), Upper Rio Grande (3), Middle Creek (4), Upper San Juan (5), Wolf Creek Summit (), and Lily Pond (7) SNOTEL sites. Location of the Center meteorological station is also indicated Table I. Attributes of the seven SNOTEL in the Rio Grande headwaters used in the analysis Site a Forest density b (%) Elevation c (m) Installed d Maximum SWE e (cm) 1. Slumgullion Beartown Upper Rio Grande Middle Creek Upper San Juan Wolf Creek Summit Lily Pond a Site numbers as shown in Figure 1. b US Forest Service (USDA, 1992). c NRCS National Water and Climate Center. d NRCS National Water and Climate Center; installation year indicates the first year of archived SWE data. e NRCS National Water and Climate Center; values are average annual maximum SWE over the period of record. average, but a substantial aquifer provides storage of snowmelt-derived recharge from the Sangre de Cristo and San Juan Mountains. The elevation, vegetation density, year of installation and average annual maximum SWE over the period of record are shown for each of the seven SNOTEL stations in Table I. Additional meteorological data used in this study (i.e. relative humidity, wind speed and direction) were obtained from the Colorado State University San Luis Valley Research Center at Center, CO (hereafter referred to as the Center meteorological station; W, N) (Figure 1), as it is the closest available observation location. STUDY PERIOD During the period the measured maximum SWE accumulation at the seven SNOTEL sites ranged from 38% of average in 22 to 139% of average in 1997 (Figure 2). Significant variability existed between SNOTEL sites during some water years: e.g. the maximum SWE at Lily Pond was 12% of normal in 21, whereas the Upper Rio Grande was 1% of normal (Figure 2). Conversely, in 1998 the percentage of mean

4 72 N. P. MOLOTCH AND R. C. BALES Slumgullion Beartown Upper Rio Grande Middle Creek Upper San Juan Wolf Creek Summit Lily Pond Figure 2. The maximum SWE measured at the seven SNOTEL sites as a percentage of the mean maximum SWE over the period of record. SNOTEL sites numbered 1 7 in Figure 1 are shown from left to right for each year values at the SNOTEL sites ranged by only 11% (Figure 2). The range of percent of mean values during the period averaged 37%. METHODS Physiographic variables Using a geographical information system, the topographic variables of elevation, slope and aspect were obtained from the level-1 standard 7Ð5, 3 m resolution, US Geological Survey (USGS) digital elevation model. A solar radiation index was calculated assuming clear-sky conditions using the TOPQUAD algorithm (Dozier, 198). This algorithm permits calculation of daily-integrated solar radiation in complex terrain and explicitly represents topographically induced variability in local solar illumination angles, incident radiation reflected from adjacent terrain, and shading from adjacent terrain. Incoming solar radiation (Ð3 3Ð µm) was calculated for each 3 m pixel within the study area on the 15th day of each month for the 21 snow accumulation/snowmelt season (i.e. November 2 June 21). The solar radiation index was obtained by taking the average of the daily-integrated incoming solar radiation surfaces from 15 November to the 15th of the respective month at which snow cover persistence was calculated. Given that the solar radiation index was calculated with clear-sky atmospheric parameters, we assumed transferability of the index to other water years. Mean maximum upwind slope is a terrain-based parameter designed to capture the variability in snow deposition as a result of wind redistribution (Winstral et al., 22). Wind speed data in the higher elevations of the Rio Grande are not available. Data from the Center meteorological station obtained from November to April, water years 21 and 22, were used to identify conditions conducive to redistribution of snow by wind. These two water years were chosen based on data availability and the high variability between the two water years (Figure 2). Relative frequency histograms of wind speed, wind direction, and relative humidity were used to define the wind direction corresponding to events most likely to redistribute snow. Redeposition of snow by wind is most likely to occur during and immediately after snowfall and when wind speeds are high. The prevailing precipitation-event wind direction indicated by the data (i.e. 255 ) is consistent with previous studies in the San Juan Mountains that found westerly air movement during precipitation events (e.g. Marwitz, 198). Relative humidity data were included as an indication of snowfall. A pie-shaped area centred on the upwind direction with a radius of 1 m was used to define the upwind area of each 3 m source pixel

5 SNOTEL REPRESENTATIVENESS IN THE RIO GRANDE 727 (Winstral et al., 22; Molotch et al., 25). The maximum upwind slope Sx m was then calculated as ( { }) ELEV xv,y v ELEV x i,y i Sx m x i,y i D max tan [ x v x i 2 C y v y i 2 ] Ð5 1 where a is the azimuth of the directional search vector, ELEV is elevation, (x i,y i ) are the coordinates of the source cell, and (x v,y v ) are the coordinates of all cells along the directional search vector. The mean maximum upwind slope of the source cell Sx m is the average maximum value of each vector within the area defined by the maximum and minimum azimuths within the pie-shaped area in the upwind direction: Sx m x i,y i admax admin D 1 admax Sx m,a x i,y i n v where n v is the number of search vectors within the search area. All 3 m resolution variables were resampled to 1 km to match the resolution of the AVHRR data. Vegetation density plays a role in snow distribution by altering the energy balance at the snow atmosphere interface, intercepting snowfall and by influencing the surface roughness and the wind fields that transport snow (Gray and Male, 1981). Vegetation density data, derived from AVHRR at 1 km resolution, were obtained from the US Forest Service (USDA, 1992). The western barrier distance bar d is an index of orographics and was calculated as the distance between each 1 km 2 cell within the study region and the highest point between that cell and a significant moisture source (Fassnacht et al., 21). In this study, the moisture source was considered to be the Pacific Ocean and, therefore, bar d was determined to be the distance to the highest point between the source cell and the Pacific Ocean along a vector of 27 from north. The physiographic conditions at the SNOTEL sites were compared with the basin-wide statistical distribution of the physiographic variables described above. Snow cover persistence Assessing the representativeness of SNOTEL SWE observations relative to the SWE distribution of the Rio Grande headwaters is difficult because obtaining ground-truth estimates of SWE over large areas (i.e km 2 ) is logistically prohibitive. Therefore, for the purposes of assessing the representativeness of the snowpack characteristics measured at SNOTEL sites relative to the watershed, snow-covered area (SCA) persistence maps were derived. This approach is valid given that patterns of snow cover depletion vary as a function of both snow accumulation and snowmelt processes. Recent advancements in the ability to detect SCA from the moderate resolution imaging spectroradiometer (MODIS; Hall et al., 22) drive the need to study snowpack processes using time series of these data. MODIS data are not yet available over the period of record analysed in this study, but our use of AVHRR data is intended to show proof of concept for future use of other remotely sensed snow cover products as their record length becomes sufficient. Fractional SCA data (i.e. the percentage of each pixel covered by snow) were generated with a spectral mixture analysis (Rosenthal, 199) of AVHRR imagery for cloud-free acquisitions from 1995 to 22 (Bales et al., 23). Images were georegistered and calibrated using various reference images as outlined in Daly et al. (2). Radiance values were atmospherically corrected to apparent surface reflectance (Vermote et al., 1997). The 1Ð1 km 2 native AVHRR resolution was resampled to 1 km 2 using a nearest-neighbour assignment. Channel 1 (Ð58 to Ð8 µm) and channel 2 (Ð72 to 1Ð1 µm) surface reflectance values were derived using the methods of Rosenthal (199). Channel 3 (3Ð55 to 3Ð93 µm) surface reflectance was separated from emittance with the aid of channel 4 (1Ð3 to11ð3 µm). Channel 4 was also used in the determination of brightness temperatures for the image. Manual interpretation of images and an image analysis technique (Simpson et al., 1998) were used to avoid misinterpretation of cloud-covered pixels as snow. Highly reflective land-surface features, such as water, were also masked to prevent interpretation as snow. Brightness temperatures were used admin 2

6 728 N. P. MOLOTCH AND R. C. BALES to further discriminate pixels that potentially contained snow (Rosenthal, 199). Derived surface reflectance and brightness temperatures were used as input to a binary decision-tree algorithm to determine which pixels were likely to contain snow. Pixels determined to contain snow were then processed using a regression heuristic to estimate the fractional SCA within each pixel. The fractional SCA grids were resampled to binary SCA based on the condition that any detectable amount of snow (SCA > %) is a snow-covered pixel and assigned a value of unity, with all other cloud-free pixels assigned a value of zero (Molotch et al., 24b). Given that we use a binary representation of SCA, we did not account for the effects of vegetation on fractional SCA estimates. These effects can be considerable, because viewable gap fraction (i.e. the percentage of a given pixel where the ground can be seen) decreases rapidly as a function of viewing angle (Liu et al., 24) and because the spectral unmixing algorithm has trouble separating the spectra of dirty snow from snow-free end-members (Rosenthal, 199). Snow cover persistence maps were derived for the months of April, May and June, where values of 1 8 were assigned to each 1 km 2 pixel based on the number of years during the period where snow cover was detected during a given month. Additionally, annual snow cover persistence maps were calculated as the number of months (January June) in which snow was observed during any acquisition date within a given month. The average annual persistence for years was used as the dependent variable in the classification tree model. Fractional SCA estimates from the Landsat 7 Enhanced Thematic Mapper (ETMC) acquired on 1 April 21, 17 April 21, 19 March 22, and 4 April 22 were used to estimate the accuracy of the AVHRR SCA estimates. Additional ETMC acquisitions were not used in the error analysis because of the presence of cloud cover and budgetary constraints. The accuracy assessment from 21 and 22, two dramatically different water years (Figure 2), are assumed to be transferable to the other water years of this study. Fractional SCA estimates from ETMC data were derived using the spectral mixture analysis algorithm of Painter et al. (23). Cloud masks for the ETMC data were not necessary, because selected scenes were cloud free. To match the resolution of the AVHRR data, the 3 m ETMC data were aggregated to 99 m resolution. The mean value of all 3 m pixels within a given 99 m pixel was used to determine the aggregated pixel value. The 99 m resolution grids were then resampled to 1 km resolution using a nearest-neighbour assignment. The higher spatial and spectral resolution of ETMC permits more accurate determination of SCA by using a direct spectral unmixing algorithm instead of the regression heuristic approach used to process the AVHRR data. ETMC data were considered truth estimates of SCA relative to AVHRR, and erroneously omitted pixels were determined as those in which AVHRR detected no snow whereas ETMC detected snow (Cline and Carroll, 1999). Erroneously committed pixels were determined as those in which AVHRR detected snow whereas ETMC did not. Omission errors were summarized as the percentage of snow-covered pixels erroneously omitted. Conversely, commission errors were summarized as the percentage of snow-free pixels erroneously committed. Binary classification trees Binary classification-tree models classify dependent variables from a suite of independent variables in a non-linear hierarchical fashion. These models have been successfully used to predict snow cover persistence at the hillslope scale (Anderton et al., 24). The use of these models to identify zones of snowpack processes (i.e. snow accumulation and snowmelt) is appropriate given the non-linear relationships between snowpack processes and physiographic variables. Binary classification-tree models partition the dependent variable (i.e. average snow cover persistence) into increasingly homogeneous subsets with the overall objective of minimizing model deviance. Various combinations of the aforementioned independent variables were included into separate tree models to ensure the proper variable set was used (Molotch et al., 25). For each of these combinations, a classification tree was intentionally grown to overfit the data with the intention of minimizing the deviance within each class of the classification tree (Chambers and Hastie, 1993). The classification-tree

7 SNOTEL REPRESENTATIVENESS IN THE RIO GRANDE 729 models were then pruned to avoid overfitting the data. Mean model deviance (i.e. the sum of the within-class deviance values) from 1 iterations of 1-fold cross-validation procedures were plotted as a function of the number of terminal nodes, i.e. terminal classes (Molotch et al., 25). Tree sizes that minimized model deviance were examined for further consideration. The coefficients of determination R 2 for classification trees ranging from 2 to 4 terminal nodes were plotted versus number of terminal nodes. The tree model that minimized deviance and maximized model fit (i.e. R 2 ) was selected as the best model and was used to categorize the watershed into classes of average snow cover persistence. A detailed description of the tree-fitting, pruning and cross-validation procedures can be found in Breiman et al. (1984), and applications to snow hydrology are given in Elder et al. (1995, 1998). We defined optimal areas for observing snowpack processes to be those that represented the largest proportion of the watershed. Therefore, the spatial extent of the tree model classes (i.e. terminal nodes) was the main criterion for optimality. Snowpack observations made within classes with low deviance are more transferable across the respective class than point observations made in classes with higher deviance. Hence, we also show the distribution of within-class deviance to determine the relative transferability of point observations across individual classes. RESULTS Physiographic variables Owing to the topographic complexity of the watershed, the spatial distribution of the solar radiation index was highly variable (Figure 3a), ranging from 151 to 33 W m 2. Vegetation density was greatest near the southern boundary of the watershed (Figure 3b), with a basin-wide mean of 53% and coefficient of variation of Ð4. The spatial distribution of mean maximum upwind slope Sx m (Figure 3c) exhibited a relatively repeating structure with prominent ridges which divide negative Sx m values from positive values organized in a north south orientation. Western barrier distance decreased toward the western end of the watershed (Figure 3d). Decreases in western barrier distance were also apparent in the southeastern portions of the watershed due to the northwestern southeastern orientation of the southern watershed boundary. The mean western barrier distance was 48 km, with a coefficient of variation of Ð. Given that the western barrier distance approached zero at the western edges of the watershed, the largest barriers between grid cells within the watershed and the Pacific Ocean are the immediate watershed divides, as opposed to mountain ranges outside the basin to the west. SNOTEL sites in and around the Rio Grande headwaters basin are fairly representative of the watershed distribution of maximum upwind slope, and solar radiation (Figure 4a and b). The watershed distribution of elevation is largely represented by the stations, with the exception of the lowest and highest elevations (Figure 4c). Stations preferentially represent flatter slopes (Figure 4d), north- and south-facing slopes (Figure 4e), densely forested areas (Figure 4f), and areas close to the western barrier (Figure 4g). Snow cover persistence Intuitively, snow cover persistence decreased toward the lower elevations of the watershed (Figure 5a c). During April, eight AVHRR scenes were processed for SCA on average for the period ; processing additional scenes was unwarranted given the cloud cover and poor viewing geometry. Six scenes were processed per month for May and June on average. Snow cover persisted into the month of April at every grid cell in the watershed in at least one of the years (Figure 5a). The mean value of the average snow cover persistence map (not shown) was 3Ð7, with a standard deviation of Ð7. SNOTEL stations are located in areas with relatively persistent May and June snow cover (Figure a and b). Average snow cover persistence values at the SNOTEL sites ranged from 3Ð875 at Lily Pond to 4Ð75 at Beartown. The mean value of the average snow cover persistence at the seven SNOTEL sites was 4Ð22,

8 73 N. P. MOLOTCH AND R. C. BALES (a) solar radiation, W m -2 (b) vegetation density, % (c) maximum upwind slope, degrees (d) distance to western barrier, km km N Figure 3. (a) The solar radiation index is the average daily-integrated modelled incoming solar radiation from 15 November to 15 May, water year 21. (b) Vegetation density data (derived from AVHRR) were obtained from the US Forest Service (USDA, 1992). (c) Mean maximum upwind slope Sx m is a terrain-based parameter designed to represent the variability in snow deposition as a result of wind redistribution. (d) Western barrier distance is an index intended to account for orographics and was computed as the distance to the highest point between each source cell and potential moisture sources to the west or 14% greater than the watershed mean. The statistical distribution of snow cover persistence was skewed toward more persistent snow cover at shorter distances to the western barrier and toward less persistent snow cover at greater distances (Figure 7a and b). The statistical distribution of June snow cover persistence was particularly skewed in areas less than 19 km from the western barrier (Figure 7b). SCA estimates derived from AVHRR data underestimated snow extent in the lower elevations of the watershed (Figure 8a and b); hence, omission errors were 1Ð9 times greater than commission errors on average (Table II). These omission errors seem to be more prominent south of the valley floor, which is likely due to the combined effect of terrain illumination (Figure 3a) and vegetation density (Figure 3b), both of which can increase omission errors (Rosenthal, 199). A detailed assessment of the controls on SCA algorithm accuracy is beyond the scope of this research. Average map accuracies were 2% for the four image comparisons. Map accuracies were greatest at time periods when snow cover was relatively continuous. Given the relatively low commission errors, snow cover persistence estimates were considered conservative, because snow cover persisted at least as long as detectable from AVHRR.

9 SNOTEL REPRESENTATIVENESS IN THE RIO GRANDE 731 (a) 3 3 4,5,,7 18 1, Sx m, degrees 45 1,2,3,4, (b) 5, solar radiation, W m ,7 4 (c) 3 5 1, elevation, m ,3,5 2 (d) slope, degrees (e) 5, ,4 (f) 3, , 4 (g) aspect, degrees vegetation density, percent distance to western barrier, km Figure 4. The watershed statistical distribution of physiographic variables that potentially influence snow distribution. (a) The mean maximum upwind slope Sx m is a terrain-based parameter designed to represent the variability in snow deposition as a result of wind redistribution. (b) The solar radiation index is the average daily-integrated modelled incoming solar radiation from 15 November to 15 May, water year 21. Elevation (c), slope (d), and aspect (e) were derived from the standard USGS 3 m digital elevation model. (f) Vegetation density data (derived from AVHRR) were obtained from the US Forest Service (USDA, 1992). (g) Western barrier distance is an index intended to account for orographics and was computed as the distance to the highest point between each source cell and potential moisture sources to the west. Numbers 1 7 correspond to the SNOTEL site numbers presented in Figure 1. Stars indicate the mean value and vertical dotted lines indicate plus/minus one standard deviation. Two stars are shown in (e), corresponding to a mean cosine transformation of aspect equal to zero (i.e. 9 and 27 ) SNOTEL (a) April (b) May (c) June N years of observed snow cover: km Figure 5. The spatial distribution of snow cover persistence for (a) April, (b) May and (c) June Values are the number of years during the 8 year period in which snow cover was observed by AVHRR during the respective month. Stars indicate SNOTEL site locations. This figure is available in colour online at Binary classification trees The cross-validation showed that model deviance was minimized using the solar radiation index, elevation, western barrier distance and vegetation density in the model development. Deviance was minimized using a 32 terminal-node classification tree (Figure 9a). Minimum model deviance increased substantially with the exclusion of western barrier distance (Figure 9a). Slight increases in minimum deviance resulted from the

10 732 N. P. MOLOTCH AND R. C. BALES (a) May 7 1, 2,3,4, (b) June 3,4,7 1,2, number of years Figure. Histograms of snow cover persistence for (a) May and (b) June Abscissa bins are the number of years during the 8 year period in which snow cover was observed by AVHRR. Numbers indicated on each panel correspond to the SNOTEL sites listed in Figure (a) May (b) June distance to western barrier, km distance to western barrier, km Figure 7. (a) May and (b) June snow cover persistence (for the same 8 year period as Figure 2) at different distances from the western barrier. Series classes ( 8) are the number of years during the 8 year period in which snow cover was observed by AVHRR during the respective month. Histograms for shorter distances are skewed toward more persistent snow cover; greater distances are skewed toward less persistent snow cover inclusion of slope, aspect and maximum upwind slope; therefore, these variables were excluded in the final model development. Model fit improved notably with the inclusion of western barrier distance (Figure 9b). Using elevation, western barrier distance, and vegetation density, the 32-node tree model (Figure 1) explained 75% of the variability in snow cover persistence, which is a considerable improvement over the explanatory ability of either elevation (%) or western barrier distance (5%). Snow cover persistence was greatest at the higher elevations and toward the western barrier. Elevation played the most important role, as indicated by its presence in the first partition of the classification-tree model (Figure 1). Although elevation and western barrier distance were significantly correlated (R 2 D Ð15, p D ), the control of western barrier distance on snow cover persistence was considerable, as indicated by the frequent appearance of the variable at upper tree model levels (Figure 1) (Elder, 1995). Within the unique areas defined by each successive model split (i.e. as the classification tree grows), different independent variables minimized the deviance of subsequent nodes. For example, in the fifth row of the classification-tree model, vegetation density, elevation and western barrier distance were all used to split different dependent variable sets. The solar radiation index was not present in the 32-node classification-tree model; terrain-induced variability in solar radiation was negligible at 1 km resolution.

11 SNOTEL REPRESENTATIVENESS IN THE RIO GRANDE 733 (a) Landsat 7 Enhanced Thematic Mapper (b) Advanced Very High Resolution Radiometer N % SCA 17 April km omission errors commission errors Figure 8. Fractional SCA estimates for 17 April 21 derived from (a) ETMC and (b) AVHRR data. Areas misclassified as snow free by AVHRR (i.e. omission errors) are also shown. This figure is available in colour online at Table II. Error statistics and map accuracies for four AVHRR SCA images with ETMC data used to estimate errors 1 April April March 22 4 April 22 Commission error (%) 29Ð9 13Ð5 1Ð1 1Ð3 Omission error (%) 12Ð2 25Ð4 51Ð7 17Ð3 Map accuracy (%) 57Ð9 1Ð1 47Ð2 81Ð (a) without bar_d with bar_d number of terminal nodes (b) Figure 9. (a) Model deviance and (b) coefficient of determination R 2 versus number of terminal nodes for snow cover persistence classification-tree models developed with and without western barrier distance (bar d). Other variables included were elevation, the solar radiation index, vegetation density, maximum upwind slope, slope, and aspect Of the 32 classes (i.e. terminal nodes), only two encompassed an area greater than 5% of the watershed (Figure 11a). The terminal node with a persistence value of 4Ð5 covered 11% of the watershed, restricted to above-timberline areas in the west. As an example application of these results for observation network design, the 1 largest classes were identified (Figure 11a). Class size was not significantly correlated with any of the independent variables; hence, substantial variability in physiographics was represented by the 1 classes shown in Figure 11a. Lily Pond (4Ð1%), Middle Creek (Ð4%), and Slumgullion (4Ð%) SNOTEL sites were located within these 1 priority classes. Upper San Juan was located in a class that encompassed 3Ð5% of the watershed area, with all other SNOTEL sites located in classes covering less than 2% of the watershed area. None of the SNOTEL sites were binned into the same class, indicating that the classification-tree model

12 734 N. P. MOLOTCH AND R. C. BALES 3.9 elev<38 elev> bar_d<59 bar_d>59 bar_d<43 bar_d> elev<2832 elev>2832 bar_d<1 bar_d>1 elev<3471 elev>3471 elev<3491 elev> elev<297 bar_d<2 elev>297 bar_d>2 bar_d<83.5 bar_d<15 bar_d>84 bar_d>15 elev<3587 bar_d<1 elev<348 elev>3587 bar_d>1 elev> veg<74 bar_d<9 veg<13 elev<3257 bar_d<13 elev<3332 bar_d<95 veg>74 bar_d>9 veg>13 elev>3257 bar_d>13 elev>3332 bar_d> bar_d<38 elev<288 veg<1 bar_d<27 veg<7 bar_d>38 elev>288 veg>1 bar_d>27 veg>7 veg<83 elev<335 veg>83 elev> elev<282 elev>282 bar_d<78 bar_d<8 bar_d>78 bar_d> veg<1 veg> Figure 1. The 32-node binary classification-tree model relating independent variables of elevation (elev), western barrier distance (bar d), and vegetation density (veg) to the dependent variable, average snow cover persistence (decimal months) over the period Units for the three independent variables are metres, kilometres, and percent respectively was able to decipher relatively subtle differences between sites that are close together (e.g. Wolf Creek and Upper San Juan). The mean size of the seven classes corresponding to the SNOTEL sites was 4% larger than the mean size of the 32 classes across the watershed. However, the mean size of these seven classes was 38% below the mean class size of the 1 largest classes, indicating that a larger proportion of the watershed would be represented by observations placed in the 1 optimal classes rather than in the current classes represented by the SNOTEL stations. Within-class deviance was lowest in the grasslands of the valley floor (Figure 11b); spatial variability in snow cover persistence was relatively low. Conversely, within-class deviance was greatest in the middle elevations, where spatial variability in snow cover persistence was relatively high. Within-class deviance at higher elevations in the southeast was low relative to other high-elevation portions of the watershed (Figure 11b); relatively high snow accumulation may have reduced spatial variability in snow cover persistence. The spatial extent of the classes explained 58% of the variability of within-class deviance across the watershed, i.e. larger classes had relatively greater within-class deviance (Figure 11a and b). Hence, the within-class deviance of the 1 largest classes was 45% greater than the mean within-class deviance of

13 SNOTEL REPRESENTATIVENESS IN THE RIO GRANDE 735 (a) 1 (b) % watershed area N km *Persistence class within class deviance x 1 3 Figure 11. (a) Snow cover persistence classification-tree model result. The 1 largest classes are shown as unique values with smaller classes shown in greyscale. (b) The spatial distribution of class deviance (a measure of within-class heterogeneity in snow cover persistence). 9 km 2 areas surrounding each SNOTEL site are numbered as in Figure 1. Ł Values correspond to the terminal nodes shown in Figure basin (a) (b) (c) standard deviation 8 7 mean 5-1 standard 4 deviation 3 basin (d) (e) (f) 9 8 basin 7 5 basin 4 3 basin elevation, m western barrier distance, km forest density, % Figure 12. Cumulative probability distribution of elevation, western barrier distance, and vegetation density within the 1 largest classes of the classification-tree model (a c), and within the seven classes corresponding to the SNOTEL sites (d f). The basin distribution of each variable is also shown. Squares represent the mean value and horizontal hash marks indicate the bounds of the standard deviation. Classes with persistence values equal to 3Ð and3ð74 are shown in (a) and (b)

14 73 N. P. MOLOTCH AND R. C. BALES all 32 classes across the watershed. Mean within-class deviance of the seven classes corresponding to the SNOTEL sites was 8% below the mean within-class deviance of all 32 classes. The 1 largest classes represented a broad range of the basin-wide distribution of elevation (Figure 12a); only the lowest 5% of elevations within the basin were not represented. The basin-wide distribution of western barrier distance was also well represented by the 1 classes: 4 of the 1 classes had a mean distance greater than the mean over the basin and two classes extended to the maximum distance from the western barrier (Figure 12b). Relative to elevation and western barrier distance, the within-class statistical distribution of vegetation density was similar from class to class (Figure 12c): 7 of 1 classes contained vegetation density values greater than 9% and all 1 classes had vegetation densities below 3%. Mean vegetation density within the 1 classes was within one standard deviation of the basin-wide mean vegetation density (Figure 12c). In some cases the within-class statistical distribution of individual physiographic variables was similar for two different classes (e.g. class 3Ð74 and 3Ð in Figure 12a). However, classes did not exhibit similarities for multiple variables (e.g. class 3Ð74 and 3Ð in Figure 12b); therefore, each class was unique. The distribution of elevation within the seven classes corresponding to the SNOTEL sites (Figure 12d) was comparable to the 1 largest classes (Figure 12a); discrete elevation bands between 28 and 3 m were represented. These seven classes preferentially represented areas closest to the western barrier, with particular representation of portions of the watershed less than 1 km from the western barrier and those ranging from 15 to 3 km (Figure 12e). The distribution of vegetation density within each of the seven SNOTEL classes (Figure 12f) did not represent the basin as well as the 1 largest classes (Figure 12c). Densely forested areas were preferentially represented; mean within-class vegetation density was greater than the basin mean for six of the seven classes. DISCUSSION Of the physiographic variables studied here, SNOTEL sites were least representative of western barrier distance and vegetation density. Including the station locations of the US National Weather Service Cooperative Observer network (COOP) in our analyses would have altered our results, as these stations are located in areas with relatively sparse vegetation (i.e. vegetation density <4%) and are further from the western barrier (i.e. average distance of 52 km) than the SNOTEL sites considered here. Because SWE observations are not made at COOP stations, they were excluded from our analysis. Adding SWE observations to COOP stations may improve the representativeness of the current SWE observing network. Exhaustive treatment of the independent variables used in this study may further improve the ability of the physiographic variables to explain the distribution of snow cover persistence. For example, the use of western barrier distance as an index of orographics assumes that the only moisture source is the Pacific Ocean and that the prevailing storm track is from the west. Consideration of synoptic-scale weather patterns may be useful for improving the representation of orographics within classification-tree models, as variability in storm-track direction does exist. Here, we used a prevailing storm direction from the west as a first-order estimate based on the work of Marwitz (198). Representation of the interactions between vegetation geometry and the wind fields that redistribute snow may improve the explanatory ability of maximum upwind slope. We did not have the detailed vegetation data needed to consider these interactions and, thus, suggest future research in locales where data are available. We present the first use of maximum upwind slope at the watershed scale (i.e. >1 km 2 ) and, hence, a first-order estimate of the optimal upwind search radius (i.e. 1 m) was used within Equation (1) (Winstral et al., 22). The scale at which independent and dependent variables are measured or estimated is worthy of significant attention as technological advances in the observation capabilities at various scales emerge. A concept for addressing these scaling issues was posed by Wood et al. (199, 1988), in which they

15 SNOTEL REPRESENTATIVENESS IN THE RIO GRANDE 737 assert the need to identify a representative elementary area at which a model element (or subcatchment) contains a sufficient sample of the continuum of hillslope and soil characteristics such that the pattern of those characteristics can be ignored. Estimating this continuum requires information at the next smallest scale (Beven, 1995). Our approach does not allow for explicit separation between the processes that control snow accumulation and snowmelt. However, our use of optical remotely sensed data allows us to determine the spatial continuum in snowpack processes (i.e. dependent variable) at a higher resolution than afforded by remotely sensed SWE data (i.e. 25 km; Chang et al., 1991), and over a much greater spatial extent than permitted by ground observations from intensive field campaigns (e.g. <1 km 2 ). The large dependent variable sample size (i.e. 339) used within the classification-tree model resulted in a much larger tree (i.e. 32 terminal nodes) than previous studies at the hillslope scale (i.e. ¾1 2 terminal nodes); increased sample size allowed classification-tree model complexity to increase without overfitting the data. Model fit (R 2 D Ð75) was also substantially greater than previous studies at the hillslope scale (average R 2 ³ Ð4). Differences in tree model structure were also revealed, as the watershed-scale controls on snowpack processes, e.g. proximity to the western barrier, are distinctly different from those important at the hillslope scale, e.g. solar radiation (Elder et al., 1995; Balk and Elder, 2; Erxleben et al., 22; Winstral et al., 22; Molotch et al., 25). Hydrologic studies that estimate SWE based on rates of snow cover depletion within watershed clusters of elevation (Rango and Martinec, 1982; Rango, 1988; Martinec, 1991; Lee et al., 25) may benefit from more complex basin clustering schemes, as we have shown that elevation does not fully explain snow cover persistence patterns. Efforts aimed at estimating large-scale SWE variability using remote sensing (Chang et al., 1991; Foster et al., 1991; Chang and Rango, 2) and modelling (Martinec, 1991; Carroll et al., 21) will also benefit from the results presented here, as we have identified the unique areas currently represented by the SNOTEL network, e.g. the environments in which uncertainty in modelled and remotely sensed grid-element SWE estimates can be identified. Equally important, we have identified the snow cover environments not represented by SNOTEL observations, e.g. those where uncertainty in grid-element SWE estimates cannot be obtained. Given the global coverage of the satellites used in this study and the global availability of topographic data at 1 km resolution, the techniques presented here are widely transferable and may be particularly useful in countries where development of observation networks is ongoing. However, we do not assert that the classification-tree model results presented here are transferable to other locations, nor do we suggest that SNOTEL stations within the current network be moved. Complementary efforts aimed at scaling point observations to grid elements based on hillslope-scale relationships between snowpack processes and physiographics (Molotch and Bales, 25) can be used to identify the optimal location for observations within the grid elements identified here. Thus, the combination of these watershed- and hillslope-scale techniques will result in observation networks that are ideally suited for evaluating spatially distributed estimates of snowpack properties. CONCLUSIONS SNOTEL stations preferentially represent densely forested areas (i.e. vegetation densities >5%) and those close to the western barrier (i.e. <3 km). Snow cover persistence at SNOTEL stations ranged from 3Ð9 to 4Ð75, with an average 14% greater than the mean persistence of the watershed. Using elevation, western barrier distance, and vegetation density, a 32-node classification-tree model explained 75% of the variability in snow cover persistence, with persistence increasing with elevation and decreasing with distance to the western barrier. The 1 largest classes predicted by the model were determined as optimal for future observations. The basin-wide distribution of western barrier distance and vegetation density was better represented by these 1 optimal classes relative to the seven classes corresponding to the SNOTEL sites. The results and

16 738 N. P. MOLOTCH AND R. C. BALES techniques presented here will be useful for spatially distributed snowpack modelling and remote sensing, as we have identified the physiographic conditions currently represented by SNOTEL stations, i.e. areas in which uncertainty can be estimated. Further, we have outlined a statistically unbiased approach for designing future observation networks based on variability in physiographics and snowpack processes. ACKNOWLEDGEMENTS S. Fassnacht, R. Brice, R. Davis, W. Rosenthal, C. McKenzie, S. Leake, M. Gillespie, T. Pagano and others are thanked for technical support. This research was supported by a visiting fellowship at the Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado at Boulder, National Oceanic and Atmospheric Administration (NOAA). Additional support was provided by SAHRA (Sustainability of semi- Arid Hydrology and Riparian Areas) under the STC Program of the National Science Foundation, agreement no. EAR-9878 and by the Climate Assessment for the Southwest (CLIMAS), Institute for the Study of Planet Earth. Comments from Andrew Klein, Shirley Kurk and three anonymous reviewers improved this work. REFERENCES Anderton SP, White SM, Alvera B. 24. Evaluation of spatial variability in snow water equivalent for a high mountain catchment. Hydrological Processes 18: Bales RC, Brice R, Imam B, Lampkin D. 23. Seasonal and interannual variability in Colorado River and Rio Grande snowcover patterns: Eos Transactions, American Geophysical Union 84: C41B 99. Balk B, Elder K. 2. Combining binary decision tree and geostatistical methods to estimate snow distribution in a mountain watershed. Water Resources Research 3: Beven K Linking parameters across scales: subgrid parameterizations and scale dependent hydrological models. Hydrological Processes 9: Blöschl G Scaling issues in snow hydrology. Hydrological Processes 13: Breiman L, Friedman J, Olshen R, Stone C Classification and Regression Trees. Wadsworth and Brooks: Pacific Grove, CA. Carroll SS, Cressie N A comparison of geostatistical methodologies used to estimate snow water equivalent. Water Resources Bulletin 32: Carroll TR, Cline DW, Fall G, Nilsson A, Li L, Rost A. 21. NOHRSC operations and the simulation of snow cover properties for the coterminous U.S. In Proceedings of the 9th Western Snow Conference; Chambers J, Hastie T Statistical Models in S. Chapman and Hall: London, UK. Chang A, Foster J, Rango A Utilization of surface cover composition to improve the microwave determination of snow water equivalent in a mountain basin. International Journal of Remote Sensing 12: Chang ATC, Rango A. 2. Algorithm theoretical basis document for the AMSR-E snow water equivalent algorithm, Version3Ð1. NASA Goddard Space Flight Center: Greenbelt, MD, USA. Cline DW, Carroll TR Inference of snow cover beneath obscuring clouds using optical remote sensing and a distributed snow energy and mass balance model. Journal of Geophysical Research 14: Daly SF, Davis RE, Ochs E, Pangburn T. 2. An approach to spatially distributed snow modelling of the Sacramento and San Joaquin basins, California. Hydrological Processes 14: Davis RE, Hardy JP, Ni W, Woodcock CE, McKenzie JC, Jordan R, Li X Variation of snow cover ablation in the boreal forest: a sensitivity study on the effects of conifer canopy. Journal of Geophysical Research 12: Dozier J A clear-sky spectral solar radiation model for snow-covered mountainous terrain. Water Resources Research 1: Elder K Snow distribution in alpine watersheds. PhD thesis, Department of Geography University of California, Santa Barbara. Elder K, Michaelsen J, Dozier J Small basin modeling of snow water equivalence using binary regression tree methods. In Biogeochemistry of Seasonally Snow-Covered Catchments, Tonnessen KA, Williams MW, Tranter M (eds). IAHS Publication No IAHS Press: Wallingford; Elder K, Rosenthal W, Davis R Estimating the spatial distribution of snow water equivalence in a montane watershed. Hydrological Processes 12: Erxleben J, Elder K, Davis R. 22. Comparison of spatial interpolation methods for estimating snow distribution in the Colorado Rocky Mountains. Hydrological Processes 1: Fassnacht SR, Dressler KA, Bales RC. 21. Physiographic parameters as indicators of snowpack state for the Colorado River basin. In Proceedings of the 58th Eastern Snow Conference; Fassnacht SR, Dressler KD, Bales RC. 23. Snow water equivalent interpolation for the Colorado River basin from snow telemetry (SNOTEL) data. Water Resources Research 39: DOI: 1Ð129/22WR1512. Foster J, Chang A, Hall D, Rango A Derivation of snow water equivalent in boreal forests using microwave radiometry. Arctic 44: