Shock capturing data assimilation algorithm for 1D shallow water equations |
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| Institution: | 1. Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya, Barcelona, Spain;2. Associated Unit: Hydrogeology Group (UPC-CSIC), Spain;3. Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA, USA;1. Department of Earth and Environmental Science, Potsdam University, Germany;2. Department of Geography, University of California, Santa Barbara, USA;3. Earth Surface Geochemistry, Helmholtz Centre Potsdam, GFZ German Research Center for Geosciences, Telegrafenberg, 14473 Potsdam, Germany;4. Institute of Geological Sciences, Freie Universität Berlin, 12249 Berlin, Germany;1. Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, United States\n;2. Department of Environmental Science, Barnard College, New York, NY 10027, United States\n;3. Department of Chemistry, Barnard College, New York, NY 10027, United States\n;1. Lawrence Berkeley National Laboratory, Climate and Ecosystem Sciences Division, 1 Cyclotron Road, Berkeley, CA 94720, United States;2. Lawrence Berkeley National Laboratory, Energy Geosciences Division, 1 Cyclotron Road, Berkeley, CA 94720, United States;1. Hydroprose International Consulting, 328 Beech Avenue, Santa Rosa, CA 95409, United States\n;2. University of Applied Sciences Northwestern Switzerland, School of Architecture, Civil Engineering and Geomatics, Institute of Civil Engineering, Gründenstrasse 40, 4132 Muttenz, Switzerland;3. Department of Civil Engineering, CSU Chico, Chico, CA 95929-0930, United States |
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| Abstract: | We propose a new data assimilation algorithm for shallow water equations in one dimension. The algorithm is based upon Discontinuous Galerkin spatial discretization of shallow water equations (DG-SW model) and the continuous formulation of the minimax filter. The latter allows for construction of a robust estimation of the state of the DG-SW model and computes worst-case bounds for the estimation error, provided the uncertain parameters belong to a given bounding set. Numerical studies show that, given sparse observations from numerical or physical experiments, the proposed algorithm quickly reconstructs the true solution even in the presence of shocks, rarefaction waves and unknown values of model parameters. The minimax filter is compared against the ensemble Kalman filter (EnKF) for a benchmark dam-break problem and the results show that the minimax filter converges faster to the true solution for sparse observations. |
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