One-dimensional bathymetry based on velocity measurements

Gessese, Alelign; Smart, Graeme; Heining, Christian; Sellier, Mathieu

doi:10.1080/17415977.2012.717621

Cited by 7 publications

(3 citation statements)

References 19 publications

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“…In addition to the previous researches reviewed above, there are also other unique methods. For example, the governing equations of physics-based models (PBMs) can be re-written so that the bed bathymetry can be directly solved for (Gessese et al, 2011(Gessese et al, , 2013Gessese & Sellier, 2012).…”

Section: Introductionmentioning

confidence: 99%

Bathymetry Inversion Using a Deep‐Learning‐Based Surrogate for Shallow Water Equations Solvers

Liu,

Song,

Shen

2024

Water Resources Research

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River bathymetry is critical for many aspects of water resources management. We propose and demonstrate a bathymetry inversion method using a deep‐learning‐based surrogate for shallow water equations solvers. The surrogate uses the convolutional autoencoder with a shared‐encoder, separate‐decoder architecture. It encodes the input bathymetry and decodes to separate outputs for flow field variables. Utilizing the differentiability of the surrogate, a gradient‐based optimizer is used to perform bathymetry inversion. Two physically based constraints on the ranges of both bed elevation and slope have to be added as inversion loss regularizations to contract the solution space. Using the “L‐curve” criterion, a heuristic approach is proposed to determine the regularization parameters. Both the surrogate model and the inversion algorithm show good performance. The bathymetry inversion progresses in two distinctive stages, which resembles the sculptural process of initial broad‐brush calving and final fine detailing. The inversion loss due to flow prediction error and the two regularizations play dominant roles in the initial and final stages, respectively. The surrogate architecture (whether with both velocity and water surface elevation or velocity only as outputs) does not have significant impact on inversion result. The methodology proposed in this work, an example of differentiable parameter learning, can be similarly used in the inversion of other important distributed parameters such as roughness coefficient.

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Section: Introductionmentioning

confidence: 99%

Bathymetry Inversion Using a Deep‐Learning‐Based Surrogate for Shallow Water Equations Solvers

Liu,

Song,

Shen

2024

Water Resources Research

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“…A direct numerical approach to reconstruct river bed topography from free surface elevation data is presented in [Gessese et al, 2011]. Then, in [Gessese et al, 2013] the authors consider velocity measurements and assume a steady flow. Bathymetry imaging using depth-averaged quasi-steady velocity observations are carried out in [Lee et al, 2018].…”

Section: Introductionmentioning

confidence: 99%

Bathymetry and friction estimation from transient velocity data for 1D shallow water flows in open channels with varying width

Moreles¹,

Hernández-Dueñas²,

González–Casanova³

2021

Preprint

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The shallow water equations (SWE) model a variety of geophysical flows. Flows in channels with rectangular cross sections may be modelled with a simplified one-dimensional SWE with varying width.Among other model parameters, information about the bathymetry and friction coefficient is needed for the correct and precise prediction of the flow. Although synthetic values of the model parameters may suffice for testing numerical schemes, approximations of the bathymetry and other parameters may be required for applications. Estimations may be obtained by experimental methods but some of those techniques may be expensive, time consuming, and not always available. In this work, we propose to solve the inverse problem to estimate the bathymetry and the Manning's friction coefficient from transient velocity data. This is done with the aid of a cost functional which includes the SWE through Lagrange multipliers. The solution is obtained by solving the constrained optimization problem by a continuous descent method. The direct and the adjoint problems are both solved numerically using a second-order accurate Roe-type upwind scheme. Numerical tests are included to show the merits of the algorithm.

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“…The first proof of concept for bathymetry reconstructions by this technique was proposed by Gessese et al in [8] using a finite difference discretization of a one-dimensional SWE system for stationary sub-and transcritical configurations. A generalization to the 2D case was presented in [7] and further developed in [9,10]. The main objective of the present work is the design of a special finite element discretization that ensures compatibility of the forward and the inverse problems.…”

Section: Introductionmentioning

confidence: 99%

Bathymetry Reconstruction Using Inverse ShallowWater Models: Finite Element Discretization and Regularization

Hajduk

Kuzmin

Aizinger

2020

Lecture Notes in Computational Science and Engineering

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In the present paper, we use modified shallow water equations (SWE) to reconstruct the bottom topography (also called bathymetry) of a flow domain without resorting to traditional inverse modeling techniques such as adjoint methods. The discretization in space is performed using a piecewise linear discontinuous Galerkin (DG) approximation of the free surface elevation and (linear) continuous finite elements for the bathymetry. Our approach guarantees compatibility of the discrete forward and inverse problems: for a given DG solution of the forward SWE problem, the underlying continuous bathymetry can be recovered exactly. To ensure well-posedness of the modified SWE and reduce sensitivity of the results to noisy data, a regularization term is added to the equation for the water height. A numerical study is performed to demonstrate the ability of the proposed method to recover bathymetry in a robust and accurate manner.

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One-dimensional bathymetry based on velocity measurements

Cited by 7 publications

References 19 publications

Bathymetry Inversion Using a Deep‐Learning‐Based Surrogate for Shallow Water Equations Solvers

Bathymetry Inversion Using a Deep‐Learning‐Based Surrogate for Shallow Water Equations Solvers

Bathymetry and friction estimation from transient velocity data for 1D shallow water flows in open channels with varying width

Bathymetry Reconstruction Using Inverse ShallowWater Models: Finite Element Discretization and Regularization

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