Weight Selection by Misfit Surfaces for Least Squares Estimation

Publication Date


Type of Culminating Activity


Degree Title

Master of Science in Mathematics



Major Advisor

Jodi Mead


Current hydrological methods used to predict ground water recharge rates rely on numerical solutions of the Richards equation which models the near-surface unsaturated flow of water in porous soils. To effectively compute these solutions, accurate information of a soil's ability to conduct water, known as hydraulic conductivity, is required. We anticipate that robust and cost efficient methods for measuring hydraulic conductivity are forthcoming, and hence propose a new method of data fitting using a quadratic cost function containing a weighted parameter and data misfit. Mead [4] employs an algorithm to compute the weight on the parameter misfit when the data, data weight, and a priori initial parameter estimate are specified. However, robust numerical codes are in place only for a simplified diagonal matrix on the parameter weight [5]. This diagonal weight is typically chosen to be an approximation to the lth order derivative, and weights each parameter equally. This is insufficient for parameters of differing magnitudes such as those in hydrological models. We propose a new method using misfit surface information of the underlying empirical equation for hydraulic conductivity (Mualem's Equation) to obtain an appropriate diagonal matrix, and exploit the codes in [5] to solve for the weight on the parameter misfit.

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