The Torgegram for Fluvial Variography: Characterizing Spatial Dependence on Stream Networks

ABSTRACT

We introduce a graphical diagnostic called the Torgegram for characterizing spatial dependence among observations of a variable on a stream network. 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). We show how an overall strategy for fluvial variography can be based on a careful examination of the Torgegram. An analysis of water temperature data from a stream network within the Columbia River basin of the northwest United States illustrates the diagnostic value of the Torgegram as well as its limitations. Additional uses and extensions of the Torgegram are discussed.

KEYWORDS:

• Geostatistics
• Semivariogram
• Spatial covariance
• Tail-down model
• Tail-up model

Acknowledgments

The project received financial support from the Center for Global and Regional Environmental Research at the University of Iowa, and from NOAA’s National Marine Fisheries Service, Alaska Fisheries Science Center. The findings and conclusions in this article are those of the authors and do not necessarily represent the views of the National Marine Fisheries Service.

Software

Functions computing FUSD, FUDJ, FCSD, FCSD-0, and FCSD-1 have been incorporated into the SSN R package, available on CRAN. An R package containing additional functions, scripts, and data supporting the simulations, analyses, and figures in this article can be found at https://github.com/jayverhoef/fluvgrm.