Spatial statistical models that use flow and stream distance
- 813 Downloads
We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.
KeywordsStream networks Valid autocovariances Geostatistics Variogram Block kriging
Unable to display preview. Download preview PDF.
- Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Second International Symposium on Information Theory. Akademiai Kiado, Budapest, pp 267–281Google Scholar
- Chiles, J-P, Delfiner, P 1999Geostatistics: modeling spatial uncertaintyJohn Wiley and SonsNew York695Google Scholar
- Cressie, N 1993Statistics for spatial data, revised editionJohn Wiley and SonsNew York900Google Scholar
- Curriero F (1996) The use of non-euclidean distance in geostatistics. Ph.D. Thesis, Kansas State UniversityGoogle Scholar
- Higdon D, Swall J, Kern J (1999) Non-stationary spatial modeling. In Bayesian statistics 6, Oxford Univ Press, Oxford 761–768Google Scholar
- Littell, RC, Milliken, RC, Stroup, WW, Wolfinger, R 1996SAS system for mixed modelsSAS publishingCary, NC656Google Scholar
- Schwarz, G 1978Estimating the dimension of a modelAnn Stat6461464Google Scholar
- Torgersen CE, Gresswell RE, Bateman DS (2004) Pattern detection in stream networks: quantifying spatial variability in fish distribution. In: Nishida, T. (ed), Proceedings of the Second Annual International Symposium on GIS/Spatial Analyses in Fishery and Aquatic Sciences. Fishery GIS Research Group, Saitama, JapanGoogle Scholar
- Hoef, JM, Barry, RP 1998Constructing and fitting models for cokriging and multivariable spatial predictionJ Stat Planning Inference69273294Google Scholar