A new two‐step stochastic modeling approach: Application to water transport in a spatially variable unsaturated soil

A new two-step stochastic modeling approach based on stochastic parameter inputs to a deterministic model system is presented. Step I combines a Stratified sampling scheme with a deterministic model to establish a deterministic response surface (DRS). Step II combines a Monte Carlo sampling scheme with the DRS to establish the stochastic model response. The new two-step approach is demonstrated on a one-dimensional unsaturated water flow problem at field scale with a dynamic surface flux and two spatially variable and interdependent parameters: The Campbell [1974] soil water retention parameter (b) and the saturated hydraulic conductivity (Ks). The new two-step stochastic modeling approach provides a highly time efficient way to analyze consequences of uncertainties in stochastic parameter input at field scale. The new two-step approach is competitive in analyzing problems with time consuming deterministic model runs where the stochastic problem can be adequately described by up to two spatially variable parameters.

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