Spatio-temporal prediction of snow water equivalent using the Kalman filter

Consider a spatio-temporal stochastic process {Z(s; t): s is an element of D; t = 1, 2,...} and suppose it is of interest to predict {Z(s; t(0)): s is an element of D} at some fixed time point t(0). Purely spatial methods use data Z(s(1); t(0)),...,Z(s(n); t(0)) to construct a spatial predictor (e.g., kriging). But, when data {Z(s(i); t): i = 1,..., n; t = 1, 2,..., t(0)} are available, it is advantageous to treat the problem as one of spatiotemporal prediction. The US National Weather Service now use current snow water equivalent (SWE) data and a purely spatial model to predict SWE at sites where no observations are available. To improve SWE predictions, we introduce a spatio-temporal model that incorporates the SWE data from the past, resulting in a Kalman-filter prediction algorithm. A simple procedure for estimating the parameters in the model is developed and an example is presented for the Animas River basin in southwest Colorado.