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Abstract:
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We present moving average approaches, by integrating kernels over white noise, to develop new classes of models 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, as those developed for Euclidean distance may not be valid. We begin by describing a stream topology. Various models are derived, using moving average constructions, depending on whether the moving average has a "tail-up" stream, a "tail-down" stream, or a "two-tail" construction. There is a 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 by using a variance component approach. Equivalent basis functions based on spectral decomposition are shown and reduced rank approaches are discussed. These models can also account for the volume and direction of flowing water. We estimate parameters using likelihood and Bayesian methods. Spatial predictions are possible in the usual generalized linear model setting.
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