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Year of publication:

Yoram Rubin1, Daniel P. Ames2, Matthew Over1, Carlos Osorio2

1 Department of Civil and Environmental Engineering

University of California Berkeley

Berkeley, CA 94720


2 Department of Civil and Environmental Engineering

Brigham Young University

Provo, UT 84602





The Method of Anchored Distributions (MAD): Principles and Implementation as a Community Resource

In 2010, we proposed to develop a community-based, open-source computational platform for Bayesian characterization of uncertain parameter fields. It was motivated by the need to provide easily-accessible tools for applications and a platform for broad-based, long-term development, built to meet the challenges brought upon by the ever increasing complexity of modern computational tools, the diversity of data types and the breadth and depth of the subject matters needed for applications. The initiation of such an effort was intended to emulate the success experienced by other communities with a long tradition of community-based development efforts, and our hope was that it could lead to a transformative change in hydrology. The absence of such an approach had been hurting the science discovery process. 

Our project was to construct a modular, open-source computational platform for application and testing of the general statistical framework for parameter field characterization.  Our approach was built around two concepts that make it applicable to a wide range of data types and computational tools. The first concept is a classification of data into two broad categories. The second concept is a strategy for localization of data using anchors (hence Method of Anchored Distributions, or MAD) that captures the relevant information contained in a local or non-local process, respectively, and presents it in terms relevant for the parameter field(s). 

We have constructed a modular computational platform, with 2 distinct modules, which deliver the capabilities necessary to support the aforementioned concepts: namely, a pre-processing block and a post-processing block. The modules comprise the MAD kernel. The design of the user-interface allows users and developers to easily link the kernel with their models via a driver. Many of the decisions over assumptions to be adopted or computational tools to be employed are at the user’s discretion and are not hard-wired into the kernel. The kernel is built using open-source architecture.

Eventually, two versions of MAD will be available: a super-computing version (for large-scale applications - in development) and a desktop application (for educational purposes and smaller-scale applications). Also, the kernel will be eventually interoperable with a wider array of community-based resources (such as CUAHSI’s hydrologic information systems) and is already interoperable with some libraries (such as R). With this framework for generic application of the concepts and principles of MAD in place, further types of data can be introduced, simplifying assumptions can be added or removed at the user’s discretion, and powerful numerical models and analytical tools, current or under development, can be integrated much more easily in future analyses under long-term community-based development to follow. 

We have developed and secured a plan for the continuity of this effort after the development phase of the project is concluded. We will deliver the final product to CUAHSI. CUAHSI has agreed to act as the custodian of the MAD computational platform. This implies securing the integrity of the kernel, updating it and making it available to users and developers. This effort is in line with CUAHSI overall strategy, and CUAHSI has the infrastructure to see this goal carried out. 

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Scientific articles

Rubin, Y., X. Chen, H. Murakami, and M. Hahn (2010), A Bayesian approach for inverse modeling, data assimilation,and conditional simulation of spatial random fields, Water Resour. Res., 46, W10523, doi:10.1029/2009WR008799.

H. Murakami, X. Chen, M. S. Hahn, Y. Liu, M. L. Rockhold, V. R. Vermeul, J. M. Zachara, and Y. Rubin (2010) Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area, Hydrol. Eart Syst. Sci., 14, doi: 10.5194/hess-14-1989-2010.

X. Chen, H. Murakami, M. S. Hahn, G. E. Hammond, M. L. Rockhold, J. M. Zachara, and Y. Rubin (2012) Three-dimensional Bayesian geostatistical aquifer characterization at the Hanford 300 Area using tracer test data, Water Resour. Res., 48, W06501, doi: 10.1029/2011WR010675.

Y. Yang, M. Over, and Y. Rubin (2012) Strategic placement of localization devices (such as pilot points and anchors) in inverse modeling schemes, Water Resour. Res., 48, W08519, doi: 10.1029/2012WR011864.

Over, M. W., X. Chen, Y. Yang, and Y. Rubin (2013), A strategy for improved computational efficiency of the method of anchored distributions, Water Resour. Res., 49, 1-19, doi: 10.1002/wrcr.20182.

Osorio-Murillo, C. A., M. W. Over, D. P. Ames, and Y. Rubin (2013 submitted), Introducing an extensible open source inversion modeling and uncertainty characterization software framework, Environ. Modell. Softw.


Technical information

Operating system(s): Windows 7

Licence: BSD

Output(s): Posterior distributions of model parameters

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