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

Author: Lourens, A. · Geer, F.C. van
Publisher: Springer New York LLC
Source:Stochastic Environmental Research and Risk Assessment, 1, 30, 237-249
Identifier: 533281
doi: DOI:10.1007/s00477-015-1075-8
Keywords: Geosciences · Error propagation · Probability density function · Piecewise linear · Kriging · Upscaling transmissivity · Monte Carlo simulation · Geological Survey Netherlands · 2015 Energy · Geo · GM - Geomodelling · ELSS - Earth, Life and Social Sciences


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. © 2015, The Author(s).