A method for the interpolation of nonnegative functions with an application to contaminant load estimation |
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| Authors: | A M Michalak P K Kitanidis |
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| Institution: | (1) Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305-4020, USA;(2) Climate Monitoring and Diagnostics Laboratory (CMDL), National Oceanic and Atmospheric Administration (NOAA), Mailcode R/CMDL1, 325 Broadway, Boulder, Colorado 80305-3328, USA |
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| Abstract: | The objective of this work is to extend kriging, a geostatistical interpolation method, to honor parameter nonnegativity. The new method uses a prior probability distribution based on reflected Brownian motion that enforces this constraint. The work presented in this paper focuses on interpolation problems where the unknown is a function of a single variable (e.g. time), and is developed both for the case with and without measurement error in the available data. The algorithms presented for conditional simulations are computationally efficient, particularly in the case with no measurement error. We present an application to the interpolation of dissolved arsenic concentration data from the North Fork of the Humboldt River, Nevada. |
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| Keywords: | Inference under constraints Nonnegativity Reflected Brownian motion Geostatistics Kriging Gibbs sampler |
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