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

• Published in: Stochastic environmental research and risk assessment Vol. 30; no. 1; pp. 237 - 249
• Main Authors: Lourens, A, van Geer, F. C
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2016; Springer Nature B.V
• Subjects: Approximation; Aquatic Pollution; aquifers; Boreholes; Chemistry and Earth Sciences; Computational Intelligence; Computer Science; Computer simulation; Density; Earth and Environmental Science; Earth Sciences; Environment; Geology; Hydrogeology; Hydrology; Interpolation; Math. Appl. in Environmental Science; Mathematical analysis; Monte Carlo method; Monte Carlo simulation; Original Paper; Physics; Probability; Probability density functions; probability distribution; Probability Theory and Stochastic Processes; Propagation; Statistics for Engineering; Transmissivity; Uncertainty; Waste Water Technology; Water Management; Water Pollution Control; Probability density function; Piecewise linear; Upscaling transmissivity; Error propagation; Kriging; Monte Carlo simulation
• DOI: 10.1007/s00477-015-1075-8
• ISSN: 1436-3240

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.