We present a quantitative framework by which to assess the number of required samples (sensors), as well as their respective locations, to most optimally estimate spatial SWE patterns using sensor networks across the 5000 sq. km American River basin of California. To inform the selection of future sensor locations, 11 years of reconstructed, spatially dense (500 x 500 m resolution) SWE data were used to develop metrics of historical SWE distributions. The historical data were split into eight years of training and three years of validation data, clustering the data set to derive spatial regions which share similar SWE characteristics. Rank-based clustering was compared to geographically-based clustering (sub-basin delineation) to determine the existence of stationary covariance structures within the overall SWE dataset. Within each cluster, a quantitative sensor-placement algorithm, based on maximizing the metric of Mutual Information, was implemented and compared to a randomized placement approach. Gaussian process models were then trained to evaluate the efficacy of each placement approach. Rank based clusters remained stable inter-annually, suggesting that rankings of pixel-by-pixel SWE exhibit stationary features that can be exploited by a sensor-placement algorithm. Rank-based clustering yielded 200 mm average root mean square error (RMSE) for twenty randomly selected sensing locations, outperforming geographic and basin-wide placement approaches, which generated 460 mm and 290 mm RMSE, respectively. Mutual Information-based sampling provided the best placement strategy, improving RMSE between 0 and 100 mm compared to random placements. Increasing the number of rank-based clusters consistently lowered average RMSE from 400 mm for one cluster to 175 mm for eight clusters, for twenty total sensors placed. To optimize sensor placement, or to inform future sampling or surveying strategies, we recommend a strategy that couples rank-based clustering with Mutual Information-based sensor placement.
Kerkez, B., Welch, S.C., Bales, R.C., Glaser, S.D., Rittger, K.E., and R. Rice (2012): Sampling design and optimal sensor placement strategies for basin-scale SWE estimation. Fall Meeting, American Geophysical Union, December 2012. Abstract C33C-0683..