Incorporating landscape characteristics in a distance metric for interpolating between observations of stream water chemistry

Spatial patterns of water chemistry along stream networks can be quantified using synoptic or 'snapshot' sampling. The basic idea is to sample stream water at many points over a relatively short period of time. Even for intense sampling campaigns, the number of sample points is limited and interpolation methods, like kriging, are commonly used to produce continuous maps of water chemistry based on the point observations from the synoptic sampling. Interpolated concentrations are influenced heavily by how distance between points along the stream network is defined. In this study, we investigate different ways to define distance and test these based on data from a snapshot sampling campaign in a 37-km(2) watershed in the Catskill Mountains region (New York State). Three distance definitions (or metrics) were compared: Euclidean or straight-line distance, in-stream distance, and in-stream distance adjusted according characteristics of the local contributing area, i.e., an adjusted in-stream distance. Using the adjusted distance metric resulted in a lower cross-validation error of the interpolated concentrations, i.e., a better agreement of kriging results with measurements, than the other distance definitions. The adjusted distance metric can also be used in an exploratory manner to test which landscape characteristics are most influential for the spatial patterns of stream water chemistry and, thus, to target future investigations to gain process-based understanding of in-stream chemistry dynamics.