Model Reduction Using Principal Component Analysis and Markov Chain Monte Carlo for Hydrogeological Inverse Problems
Abstract
Inverse problems in hydrogeological applications often require estimation of a large number of unknown parameters ranging from hundreds to millions. Such problems are computationally prohibitive. To efficiently deal with such high-dimensional problems, model reduction techniques are usually introduced to improve computational performance of traditional inversion method. In this study, we explored the feasibility and effectiveness of Principal Component Analysis (PCA) and Markov Chain Monte Carlo (MCMC) for model reduction using error-involved synthetic data. A 1-D groundwater pumping test is implemented on randomly generated hydraulic conductivity field, then computed head distribution adding random errors is treated as available data for inversing the original hydraulic conductivity field. We run full-dimensional inverse method a few times to generate training set for constructing experienced covariance matrix. Principal Component Analysis is implemented on the experienced covariance matrix to reduce dimensionality of the inverse problem. MCMC is implemented to draw samples from the reduced variable space for providing best estimate and quantifying uncertainty. The synthetic data study demonstrates that PCA-MCMC method can successfully provide reasonable estimate of hydraulic conductivity using biased data and effectively reduce computational time and storage usage. It is also noticed that a tradeoff exists between model simplicity and uncertainty quantification - a highly-reduced model causes narrower confidential intervals, sometimes implying insufficient uncertainty quantification. Thus the extent of model reduction should be wisely manipulated in light of specific problem requirements.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFM.H31F1456Z
- Keywords:
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- 1805 Computational hydrology;
- HYDROLOGYDE: 1873 Uncertainty assessment;
- HYDROLOGYDE: 1906 Computational models;
- algorithms;
- INFORMATICSDE: 1942 Machine learning;
- INFORMATICS