Uncertainty propagation of arbitrary probability density functions applied to upscaling of transmissivities

Aris Lourens, F.C. van Geer

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In many fields of study, and certainly in hydrogeology, uncertainty propagation is a recurring subject. Usually, parametrized probability density functions (PDFs) are used to represent data uncertainty, which limits their use to particular distributions. Often, this problem is solved by Monte Carlo simulation, with the disadvantage that one needs a large number of calculations to achieve reliable results. In this paper, a method is proposed based on a piecewise linear approximation of PDFs. The uncertainty propagation with these discretized PDFs is distribution independent. The method is applied to the upscaling of transmissivity data, and carried out in two steps: the vertical upscaling of conductivity values from borehole data to aquifer scale, and the spatial interpolation of the transmissivities. The results of this first step are complete PDFs of the transmissivities at borehole locations reflecting the uncertainties of the conductivities and the layer thicknesses. The second step results in a spatially distributed transmissivity field with a complete PDF at every grid cell. We argue that the proposed method is applicable to a wide range of uncertainty propagation problems.

Original languageEnglish
Pages (from-to)237-249
Number of pages13
JournalStochastic Environmental Research and Risk Assessment
Volume30
Issue number1
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • Error propagation
  • Kriging
  • Monte Carlo simulation
  • Piecewise linear
  • Probability density function
  • Upscaling transmissivity

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