Application and assessment of a multiscale data integration method to saturated hydraulic conductivity in soil

Abstract

Saturated hydraulic conductivity (Ks) is one of the most important physical properties of the soil. Inherent spatial variability of soil properties makes it necessary to obtain sufficient and reliable Ks in order to reduce the uncertainty in hydrological modeling. In this study, we employ a Bayesian hierarchical modeling framework combined with upscaling techniques and an efficient adaptive Markov Chain Monte Carlo (MCMC) method, namely, Delayed Rejection Adaptive Metropolis (DRAM), for spatial modeling of fine-scale Ks in soil conditioned on coarse-scale Ks data and some prior information. Within this hierarchical framework, the posterior distribution of the fine-scale Ks field is formulated to incorporate all of the conditional information from different scales, which involves upscaling operators of non-explicit form and especially is high dimensional. The computational challenge of exploring the posterior distribution with complicated structure is solved by means of the DRAM algorithm. Two synthetic examples involving integration of two or three different scales of conductivity data are used to illustrate the implementation of these approaches. Further validation is provided using distributed in situ measurements of Ks from soils in northwest China. Subsequently, a series of representative numerical experiments are conducted to demonstrate the power and utility of these approaches under a range of soil conditions with varying levels of spatial heterogeneity, correlation length, and anisotropy. Overall, the Bayesian hierarchical modeling framework combined with upscaling techniques and DRAM sampling strategies was shown to be a viable tool for reconciling different scales of saturated hydraulic conductivity in soil. Our numerical investigations provide a comprehensive numerical validation of the method, illustrating its applicability and limitations. Copyright 2010 by the American Geophysical Union.