UC Berkeley

Abstract

Efficient Numerical Implementation and Vadose Zone Application of the Method of Anchored Distributions

by

Matthew William Over

Doctor of Philosophy in Civil & Environmental Engineering

University of California, Berkeley

Professor Yoram Rubin, Chair

The method of anchored distributions (MAD) is a Bayesian model inversion technique with a high level of flexibility. MAD can jointly invert multiple types of parameter fields conditional on multiple types and scales of measurement data. Moreover, MAD permits simultaneous analysis of macroscopic characteristics of spatial heterogeneity, e.g. correlation scale, and point characteristics within the parameter field. This dissertation focuses on MAD.

MAD is formulated with a completely generalized, assumption-free likelihood function - a feature that sets it decidedly apart from other inversion and estimation procedures. However, this advantage comes with a considerable increase in computational cost relative to more assumption-laden model inversion techniques. Thus, a section of the following work derives a theoretical approximation to reduce the computational cost of inversion with MAD that has minimal impacts on the accuracy of the results. The approximation utilizes clustering algorithms to combine simulations on a basis of parameter similarities and ultimately limits the computational expense of evaluating the likelihood function, which has significant impact on overall computational cost. The approach is validated in a characterization of a synthetic transmissivity field using concentration data obtained under natural gradient conditions.

MAD is formulated generically and hence is widely applicable to a variety of scientific practice areas. However, previously there has been no software platform for implementing MAD available to the scientific community. Thus, a section of the following work is dedicated to the design and development of the MAD software, which generically evaluates Bayes' rule for different modeling tools, different physical processes, different random physical parameters, and with different statistical tools. The section, focuses on the creation of a graphical user interface (GUI) that helps users define the necessary aspects of the MAD analysis, but is sequenced in a manner that all dependencies are exploited to reduce the possibility of user error in the set up. The flexibility and ease of using the GUI is validated with successful application in a variety of synthetic case studies.

With the existence of a free and publicly available software, the number of studies that could employ MAD has grown substantially. However, MAD, thus far, has never been applied without geostatistics or outside of saturated groundwater studies. Thus, a section of the following work is dedicated to the derivation of MAD with statistical, rather than geostatistical structural models, and application of the framework to a vadose zone soil column characterization. The MAD software is used for the first time on field data (not synthetic) and reasonable conditional results of the Mualem - van Genuchten parameters. The important outcome of the experiment is the first ever validation of a likelihood function in vadose zone parameter inversion.

In total, this dissertation has focused on generic and rapid numerical implementation of MAD. The case studies in saturated and vadose zone flow and transport are used to provide experimental confidence that the generalization and computational gains are successful.