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

TL;DR

This paper introduces a conjugate gradient method for estimating Manning's friction coefficient from noisy data in shallow water models, supported by theoretical proofs and numerical experiments.

Contribution

It presents a novel conjugate gradient approach for the inverse problem of estimating Manning's coefficient, including a proof of differentiability and stability analysis.

Findings

Numerical results demonstrate the method's feasibility in 1D models.

Theoretical proof confirms the differentiability of the weak form.

Stability analysis supports robustness under reasonable assumptions.

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 model 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.