Variational data assimilation on a multi-dimensional hydraulic-hydrological model of hydrographic network: inference of large composite control vectors on the DassFlow paltform

Abstract

<div>In a context of climate change and potential intensification of the hydrological cycle, improving representation of water fluxes within river basins is of paramount importance  for hydrological sciences and operational forecasts. To leverage multi-sourced observations (in situ, satellite, drones) of the critical zone, innovative approaches integrating hydraulic-hydrological modeling and multi-variate assimilation methods are needed. They should enable ingesting spatially distributed forcings, physiographic descriptors, hydrodynamic signatures from multi-source observables, and tackle calibration/correction problems in integrated models. Water surface observables are valuable to constrain hydraulic models of river reaches ([1] and references therein) and complex flow zones (confluences, floodplains), forced by spatially distributed inflows ([2], [3]). Since hydraulic large scale modeling can be computationally costly, a combination of effective 1D representations and 2D zooms, completed by hydrological modules, may be useful. This contribution presents the development of a complete multi-dimensional hydraulic-hydrological toolchain, based on the 2D hydraulic model and variational data assimilation platform DassFlow [4,5]. A new method for multi-dimensional hydraulic modeling, relying on a single 2D 2nd order solver applied to 1Dlike-2D meshes, is presented. Inferences of large composite control vectors, including hydrological and hydraulic controls, are carried out on academic and real cases in twin experiments. Accurate results are achieved given sufficient observability of parameters signatures, including information feedback from the river network to upstream hydrological catchments models.</div><div>[1] Larnier et al. "River discharge and bathymetry estimation from SWOT altimetry measurements", Inverse Problems in Science and Engineering 29, 6 (2021), pp. 759-789.</div><div>[2] Pujol et al. Estimation of multiple inflows and effective channel by assimilation of multi-satellite hydraulic signatures: The ungauged anabranching Negro river. Journal of Hydrology, 591:125331, 2020.</div><div>[3] Malou et al. (2021). Generation and analysis of stage-fall-discharge laws from coupled hydrological-hydraulic river network model integrating sparse multi-satellite data. Journal of Hydrology, 603, 126993.</div><div>[4] Data assimilation for free surface flows. Technical report, Mathematics Institute of Toulouse-INSA group-CS corp. CNES-CNRS, 2019.</div><div>[5] Monnier et al. Inverse algorithms for 2D shallow 893 water equations in presence of wet dry fronts. application to flood plain dynamics. Advances in Water Resources, 894 97:11–24, 2016.</div>