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

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...

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Veröffentlicht in:Stochastic environmental research and risk assessment Jg. 30; H. 1; S. 237 - 249
Hauptverfasser: Lourens, A, van Geer, F. C
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2016
Springer Nature B.V
Schlagworte:
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
ISSN:1436-3240, 1436-3259
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Zusammenfassung: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.
Bibliographie:http://dx.doi.org/10.1007/s00477-015-1075-8
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ISSN:1436-3240
1436-3259
DOI:10.1007/s00477-015-1075-8