Wednesday, April 2, 2008 : 8:40 a.m.
An Example Multi-Model Analysis: Calibration and Ranking
Modeling solute transport is a complex process governed by multiple site-specific parameters like porosity and hydraulic conductivity as well as many solute-dependent processes such as diffusion and reaction. Furthermore, it must be determined whether a steady or time-variant model is most appropriate. A problem arises because over‑parameterized conceptual models may be easily calibrated to exactly reproduce measured data, even if these data contain measurement noise. During preliminary site investigation stages where available data may be scarce it is often advisable to develop multiple independent conceptual models, but the question immediately arises: which model is best? This work outlines a method for quickly calibrating and ranking multiple models using the parameter estimation code PEST in conjunction with the second-order-bias-corrected Akaike Information Criterion (AICc). The method is demonstrated using the twelve analytical solutions to the one-dimensional convective-dispersive-reactive solute transport equation as the multiple conceptual models (van Genuchten M. Th. and W. J. Alves, 1982. Analytical solutions of the one-dimensional convective-dispersive solute transport equation, USDA ARS Technical Bulletin Number 1661. U.S. Riverside , CA 92501.). Each solution is calibrated to five data sets, each comprising an increasing number of calibration points that represent increased knowledge of the modeled site (calibration points are selected from one of the analytical solutions that provides the “correct” model). The AICc is calculated after each successive calibration to the five data sets yielding model weights that are functions of the sum of the squared, weighted residuals, the number of parameters, and the number of observations (calibration data points) and ultimately indicates which model has the highest likelihood of being correct. The results illustrate how the sparser data sets can be modeled accurately using several of the twelve analytical solutions, while more numerous calibration data lead to a clearly defined model ranking.
Scott James, Ph.D., Sandia National Laboratories Scott James received his BS/MS in Mechanical Engineering from UC San Diego with emphases in fluid mechanics and numerical methods. In 2001, he graduated from UC Irvine with a doctorate in Environmental Engineering and thereafter joined Sandia National Laboratories, working to certify the Waste Isolation Pilot Plant, the only operating transuranic nuclear waste repository in the world. Next, he joined the Geohydrology Department and contributed to the Yucca Mountain Project. Scott is currently Principal Member of the Technical Staff in the Thermal/Fluid Science-&-Engineering Department, where he continues to work on a wide variety of environmental flow and transport modeling problems.