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


DOI: 10.1007/s00477-004-0189-1

Cite this article as:
Michalak, A. & Kitanidis, P. Stoch Environ Res Ris Assess (2005) 19: 8. doi:10.1007/s00477-004-0189-1


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.


Inference under constraintsNonnegativityReflected Brownian motionGeostatisticsKrigingGibbs sampler

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringStanford UniversityStanfordUSA
  2. 2.Climate Monitoring and Diagnostics Laboratory (CMDL)National Oceanic and Atmospheric Administration (NOAA)BoulderUSA