A Moving Average Approach for Spatial Statistical Models of Stream Networks

Abstract

In this article we use moving averages to develop new classes of models in a flexible modeling framework for stream networks. Streams and rivers are among our most important resources, yet models with autocorrelated errors for spatially continuous stream networks have been described only recently. We develop models based on stream distance rather than on Euclidean distance. Spatial autocovariance models developed for Euclidean distance may not be valid when using stream distance. We begin by describing a stream topology. We then use moving averages to build several classes of valid models for streams. Various models are derived depending on whether the moving average has a “tail-up” stream, a “tail-down” stream, or a “two-tail” construction. These models also can account for the volume and direction of flowing water. The data for this article come from the Ecosystem Health Monitoring Program in Southeast Queensland, Australia, an important national program aimed at monitoring water quality. We model two water chemistry variables, pH and conductivity, for sample sizes close to 100. We estimate fixed effects and make spatial predictions. One interesting aspect of stream networks is the possible dichotomy of autocorrelation between flow-connected and flow-unconnected locations. For this reason, it is important to have a flexible modeling framework, which we achieve on the example data using a variance component approach.