Morris method with improved sampling strategy and Sobol’ Variance-based method, as validation tool on Numerical Model of Richard’s Equation

Sunny Goh

doi:10.24294/jgc.v4i1.763

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Morris method with improved sampling strategy and Sobol’ Variance-based method, as validation tool on Numerical Model of Richard’s Equation

Sunny Goh

Journal of Geography and Cartography 2021, 4(1), 21-35; https://doi.org/10.24294/jgc.v4i1.763

Submitted：13 Jan 2021

Accepted：26 Feb 2021

Published：06 Mar 2021

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Abstract

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil^[1]. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method has resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at p = 2 , r = 2 and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures (μ^*, σ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters β and θ_s is suggesting a greater significant digits to reduce its input uncertainty range.

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References

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