Abstract:

Statistical methods for spatial prediction (kriging) have long been available for environmental variables on Euclidean domains.  A key precursor to prediction of such a variable is the characterization of the statistical dependence among observed values of the variable over space, as quantified by the semivariogram.  Recently, ecologists and other environmental scientists have begun applying these methods to variables on non-Euclidean domains, including stream networks.  In particular, some semivariogram models have been developed for stream network variables, but methods for selecting among the available models are lacking.  I will introduce a graphical diagnostic called the Torgegram for characterizing the spatial dependence of a stream network variable.  The Torgegram consists of four component empirical semivariograms, each one corresponding to a particular combination of flow-connectedness within the network and model type (tail-up/tail-down).  I will show how an overall strategy for fluvial variography can be based on a systematic analysis of the Torgegram.