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    A geostatistical model based on Brownian motion to Krige regions in R2 with irregular boundaries and holes

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    Author
    Bernard, Jordy
    Chair
    McIntyre, Julie
    Barry, Ron
    Committee
    Goddard, Scott
    Metadata
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    URI
    http://hdl.handle.net/11122/10945
    Abstract
    Kriging is a geostatistical interpolation method that produces predictions and prediction intervals. Classical kriging models use Euclidean (straight line) distance when modeling spatial autocorrelation. However, for estuaries, inlets, and bays, shortest-in-water distance may capture the system’s proximity dependencies better than Euclidean distance when boundary constraints are present. Shortest-in-water distance has been used to krige such regions (Little et al., 1997; Rathbun, 1998); however, the variance-covariance matrices used in these models have not been shown to be mathematically valid. In this project, a new kriging model is developed for irregularly shaped regions in R 2 . This model incorporates the notion of flow connected distance into a valid variance-covariance matrix through the use of a random walk on a lattice, process convolutions, and the non-stationary kriging equations. The model developed in this paper is compared to existing methods of spatial prediction over irregularly shaped regions using water quality data from Puget Sound.
    Description
    Master's Project (M.S.) University of Alaska Fairbanks, 2019
    Date
    2019-05
    Type
    Master's Project
    Collections
    Mathematics and Statistics

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