Inferrence of effective river properties from remotely sensed observations of water surface
Résumé
The future SWOT mission (Surface Water and Ocean Topography) will provide cartographic measurements of inland water surfaces (elevation, widths and slope) at an unprecedented spatial and temporal resolution. Given SWOT like synthetic data, hierarchical-complexity forward flow models are revisited, then few inverse formulations allowing to infer the river low flow bathymetry, roughness and discharge (A_{0},K,Q) are derived and assessed. The concept of an effective low flow bathymetry A_{0} (the real one being never observed), hence an effective river dynamics description, is introduced. The few inverse models elaborated for inferring (A_{0},K,Q) are analyzed in two contexts: 1) remotely sensed observations of the water surface (surface elevation, width and slope) only are available ; 2) one additional water depth measurement (or estimate) is available. The inverse models elaborated are independent of data acquisition dynamics; they are assessed on 91 synthetic test cases sampling a wide range of steady-state river flows (the Froude number varying between 0.05 and 0.5 for 1 km reaches) and in the case of a flood on the Garonne River (France) characterized by large spatio-temporal variabilities. It is demonstrated that the most complete shallow-water like model which allows to separate the roughness and bathymetry terms is the so-called low Froude model. In Case 1), the resulting RMSE on the inferred discharges are on the order of 15\% for first guess errors larger than 50\% . An important feature of the present inverse methods is the fairly good accuracy of the discharge Q obtained, while the identified roughness coefficient K includes the measurement errors and the misfit of physics between the real flow and the inverse models hypothesis; the later neglecting the unobserved temporal variations of the flow and the inertia effects. A compensation phenomena between the identified values of K and the unobserved bathymetry A_{0} is highlighted, while the present inverse models lead to an effective river dynamics model accurate in the range of the discharge variability observed. In Case 2), the effective bathymetry profile for 80 km of the Garonne River is retrieved with 1\% relative error only. Next, accurate effective topography-friction pairs and also discharge can be inferred. Finally, defining river reaches from the observation grid averages the river properties in each reach, hence tends to smooth the hydraulic variability.
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