Abstract. 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.
IntroductionThe concept of soil as an inhomogeneous media was established already at the turn of the century [Vieira et al., 1981]. Despite this, only a limited number of studies focusing specifically on the spatially variable nature of soil were published until approximately 2• decades ago. Since then, however, research within this field has increased dramatically, and the results find applications within, for example, water resource management, pollution control, and agriculture. In recent years, there seems to be an increased bias toward development and validation of predictive modeling tools accounting for the effect of spatial variability.An accurate description of both water and solute transport in the unsaturated zone relies upon good descriptions of the soil-water retention properties and unsaturated hydraulic conductivity of the soil. In recognition of this many studies have dealt with the characterization of natural variability in parameters describing soil hydraulic properties [e.g., Nielsen et al., [1994a] point out that the equations arising from application of the stochastic theory are very complicated to solve (even numerically) because of intercoupling, nonlinearity, and high dimensionality. Furthermore, the estimation of the necessary statistics from measured field data, namely, correlation lengths and covariance functions between parameters, often requires larger data sets than the ones typically available at this point [Jensen and Mantoglou, 1992;Mantoglou, 1992]. Together with the fact that the stochastic theory is very mathematically complex, these points of critique have limited the practical use of the theory to a very small number of studies.Comparatively, there have been a much higher number of applied studies based on deterministic modeling with statistical sampling. Most often, these studies are based on a numerical or analytical solution to the governing partial differential equation of unsaturated water flow subject to appropriate initial and boundary conditions....