7/1/2006 - 6/30/2007
- Mary Anderson, UW-Madison
- Haijiang Zhang, UW-Madison
Background/Need: Complex regional groundwater flow models, like the model of the Trout Lake basin in Vilas County, Northern Wisconsin, are used to address a variety of research questions including the impacts of climate, land use changes, and delineation of flow paths. Yet, the level of certainty expected from predictions made by these models is often beyond what most current calibration techniques can provide. Groundwater models are becoming larger and more complex with many more unknown parameters. Current matrix methods that are used in parameter estimation are not able to solve the large matrices associated with these models. For this reason it is important to explore the applicability of new parameter estimation techniques for solving large groundwater problems. LSQR (Paige and Saunders, 1982a, 1982b) is a parameter estimation method that uses an iterative subspace inversion technique that is related to the better known singular value decomposition (SVD). SVD is currently used by the groundwater community. LSQR is widely used by the geophysical community to solve large problems in tomography and is more powerful than SVD in solving large problems.
Objectives: The objectives of this research were to 1) use a synthetic groundwater flow model as a test case to develop a strategy for using LSQR to solve groundwater inverse problems, 2) demonstrate that a technique used to calculate the model resolution matrix, which is necessary to quantify uncertainty, for large seismic tomography inverse problems can be applied to groundwater problems; and 3) use the experience gained from the first objective to demonstrate that LSQR gives comparable results to the SVD method in estimating parameters for a regional groundwater flow model of the Trout Lake basin.