ABSTRACT
Spatial statistical models are broadly applied within the fields of geology, geography, ecology, real estate, and medicine, just to name a few. Spatial statistical models often have two broad goals: to describe how covariates affect a response variable, and to make predictions at unsampled locations. Organisms that live in streams and rivers are ectothermic and so temperature profoundly affects their ecology. Concerns about climate change and habitat alteration that degrade thermal environments have led to extensive stream temperature monitoring in decades by dozens of natural resources agencies throughout North American and Europe. Many researchers have called for using stream distance, rather than Euclidean distance, when developing spatial statistical models for stream networks. There is a problem, however, if simply use stream distance, rather than Euclidean distance, in a standard geostatistical autocovariance model. The stream network topology requires some preliminaries in notation and distance concepts and computation, which give prior to actually building models.
