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Stochastic analysis of one‐dimensional steady state unsaturated flow: A Comparison of Monte Carlo and Perturbation Methods
Author(s) -
Andersson Johan,
Shapiro Allen M
Publication year - 1983
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr019i001p00121
Subject(s) - monte carlo method , perturbation (astronomy) , hydraulic conductivity , water content , stochastic process , statistical physics , infiltration (hvac) , mathematics , stochastic modelling , boundary value problem , mathematical analysis , soil water , physics , soil science , geotechnical engineering , statistics , environmental science , thermodynamics , geology , quantum mechanics
The stochastic nature of moisture content in a soil profile under steady state, unsaturated infiltration is examined, where the saturated hydraulic conductivity is taken as a stationary stochastic process. Two different techniques are employed in determining the stochastic output. These are Monte Carlo simulations and an analytic derivation from a first‐order perturbation solution. In comparing the two techniques, the liability of the perturbation expressions is investigated if the Monte Carlo results are assumed to exactly represent the stochastic nature of the moisture content. In four test examples a relatively good comparison is obtained between the results of the two techniques. The analytic nature of the perturbation solution then readily provides information concerning the general stochastic properties of the moisture content, and in this way, additional Monte Carlo runs are avoided. From this analysis it is shown that the moisture content is a stationary stochastic process at distances far from boundary regions. The distance from the boundary to regions of stationarity is dependent upon soil properties and the boundary conditions imposed.