Abstract
Consider a spatio-temporal stochastic process {Z(s; t): s ∈ D; t = 1, 2, ... } and suppose it is of interest to predict {Z(s;t 0 ): s ∈ 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 spatio-temporal 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.