Abstract

An 11-year dataset of spatially distributed snow water equivalent (SWE) was used to inform a quantitative, near-optimal sensor placement methodology for real-time SWE estimation in the American River basin of California. 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. The historical SWE data, at 500 x 500 m resolution, were split into eight years of training and three years of validation data. Within each cluster, a quantitative sensor-placement algorithm, based on maximizing the metric of Mutual Information, was implemented and compared to random placement. Gaussian Process models were then built from validation data points selected by the algorithm 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, yielding a 200 mm average root mean square error (RMSE) for twenty randomly selected sensing locations. This outperformed 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 we recommend a strategy that couples rank-based clustering with Mutual Information-based sampling design.

Citation

Welch, S., Kerkez, B., Bales, R., Glaser, S., Rittger, Rice, R. (2013): Sensor placement strategies for SWE estimation in the American River basin. Water Resources Research, 49 (2). DOI: 10.1002/wrcr.20100