Gradient-based estimation of Manning's friction coefficient from noisy data

Authors:
Victor M. Calo;Nathan Collier;Matthias Gehre;Bangti Jin;Hany Radwan;Mauricio Santillana
Affiliations:
Applied Mathematics & Computational Science and Earth Science & Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;Applied Mathematics & Computational Science and Earth Science & Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;Center for Industrial Mathematics and Department of Mathematics, University of Bremen, Bremen 28359, Germany;Institute for Applied Mathematics and Computational Science and Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA;Irrigation and Hydraulics Department, Faculty of Engineering, Cairo University, Egypt;School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional models are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory.