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A method for the interpolation of nonnegative functions with an application to contaminant load estimation

Authors
  • Michalak, A. M.1, 2
  • Kitanidis, P. K.1
  • 1 Stanford University, Department of Civil and Environmental Engineering, Stanford, CA, 94305-4020, USA , Stanford
  • 2 National Oceanic and Atmospheric Administration (NOAA), Climate Monitoring and Diagnostics Laboratory (CMDL), Mailcode R/CMDL1, 325 Broadway, Boulder, Colorado, 80305-3328, USA , Boulder
Type
Published Article
Journal
Stochastic Environmental Research and Risk Assessment
Publisher
Springer-Verlag
Publication Date
Feb 01, 2005
Volume
19
Issue
1
Pages
8–23
Identifiers
DOI: 10.1007/s00477-004-0189-1
Source
Springer Nature
Keywords
License
Yellow

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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