Comparing Geostatistical Models for River Networks

Abstract

Geostatistical methods have become popular in various fields of hydrology, and typical applications include the prediction of precipitation events, the simulation of aquifer properties and the estimation of groundwater levels and quality. Until recently, surprisingly little effort has been undertaken to apply geostatistics to stream flow variables. This is most likely because of the tree-like structure of river networks, which poses specific challenges for geostatistical regionalization. Notably, the shape of catchments (irregular block support), the nestedness of catchments along the river network (overlapping support), and the definition of a relevant distance measure between catchments pose specific challenges. This paper attempts an annotated survey of models proposed in the literature, stating contributions and pinpointing merits and shortcomings. Two conceptual viewpoints are distinguished: one-dimensional models which use covariances along a river network based on stream distance, and two-dimensional models where stream flow is conceptualized as the integral of the spatially continuous local runoff process over the catchment area. Both geostatistical concepts are evaluated relative to geostatistical standard methods based on Euclidean distances. It is shown how the methods perform in various examples including spatial prediction of environmental variables, stream flows and stream temperatures.