a b s t r a c tEstimation of spatial random fields (SRFs) is required for predicting groundwater flow, subsurface contaminant movement, and other areas of environmental and earth sciences modeling. This paper presents an inverse modeling framework called MAD# for characterizing SRFs, which is an implementation of the Bayesian inverse modeling technique Method of Anchored Distributions (MAD). MAD# allows modelers to "wrap" simulation models using an extensible driver architecture that exposes model parameters to the inversion engine. MAD# is implemented in an open source software package with the goal of lowering the barrier to using inverse modeling in education, research, and resource management. MAD# includes an intentionally simple user interface for simulation configuration, external software integration, spatial domain and model output visualization, and evaluation of model convergence. Four test cases are presented demonstrating the novel functionality of this framework to apply inversion in order to calibrate the model parameters characterizing a groundwater aquifer. Software availabilityMAD# is made available through collaboration with the Consortium of Universities for the Advancement of Hydrologic Science (CUAHSI) Hydrologic Data Center. MAD# source code and documentation can be accessed at the MAD code repository website http://mad.codeplex.com. MAD# and its source code are released under the New Berkeley Software Distribution (BSD) License which allows for liberal reuse of the software and code.

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This paper introduces a hierarchical simulation and modeling framework that allows for inference and validation of the likelihood function in Bayesian inversion of vadose zone hydraulic properties. The likelihood function or its analogs (objective functions and likelihood measures) are commonly assumed to be multivariate Gaussian in form; however, this assumption is not possible to verify without a hierarchical simulation and modeling framework. In this paper, we present the necessary statistical mechanisms for utilizing the hierarchical framework. We apply the hierarchical framework to the inversion of the vadose zone hydraulic properties within a multilayer soil profile conditioned on moisture content observations collected in the uppermost four layers. The key result of our work is that the goodness-of-fit validated likelihood function form provides empirical justification for the assumption of multivariate Gaussian likelihood functions in past and future inversions at similar sites. As an alternative, the likelihood function need not be assumed to follow a parametric statistical distribution and can be computed directly using nonparametric methods. The nonparametric methods are considerably more computationally demanding, and to demonstrate this approach, we present a smaller dimension synthetic case study of evaporation from a soil column. The main drawback of our work is the increased computational expense of the inversion.

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