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  1. Spatial Autocorrelation in Streams and Rivers: Tobler’s first law of geography states that, ‘‘Everything is related to everything else, but near things are more related than distant things.’’ In the field of spatial statistics, this phenomenon is referred to as spatial autocorrelation. Spatial statistical models tend to make more accurate predictions when data are spatially correlated. However, in rivers and streams there’s an extra complication because both Euclidean and in-stream distances can be used to describe patterns of spatial autocorrelation. For example, some variables like water temperature are physically connected by flow; while others, such as land use or rainfall, may be similar in neighboring locations – even when they don’t share flow. Statistical modelers often assume spatial independence, but in highly connected systems like streams this may not be a valid modeling assumption – even when working with sparse data locations that are not connected by stream flow. Statisticians have developed sophisticated spatial statistical stream-network models that account for 1) spatial autocorrelation using both Euclidean and in-stream distance, 2) the branching structure of the network, and 3) directional flow. Now, we’ve provided software to help users integrate the geospatial processing undertaken in GIS with the statistical analyses: the STARS ArcGIS custom toolset and the SSN package for R Statistical software. STARS: ArcGIS Custom Toolset for more information and downloads of tools: http://blogs.esri.com/esri/arcgis/2013/01/29/ssn-stars-tools-for-spatial-statistical-modeling-on-stream-networks/ Tutorials, Vignettes, and Example Datasets http://www.fs.fed.us/rm/boise/AWAE/projects/SpatialStreamNetworks.shtml Downloads SSN & STARS:http://www.fs.fed.us/rm/boise/AWAE/projects/SSN_STARS/software_data.html FLoWS:http://www.fs.fed.us/rm/boise/AWAE/projects/SSN_STARS/other_software.html R: statistical software: http://cran.r-project.org/
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