Variational estimation of effective channel and ungauged anabranching river discharge from multi-satellite water heights of different spatial sparsity

Multi-satellite sensing of continental water surfaces (WS) represents an unprecedented and increasing potential for studying ungauged hydrological and hydraulic processes from their signatures, especially on complex flow zones such as anabranching rivers. However the estimation of discharge from WS observations only is a very challenging, ill-posed, inverse problem due to unknown bathymetry and friction in ungauged rivers, measurements nature, quality and spatio-temporal resolutions regarding the flow (model) scales. This paper proposes an effective 1D hydraulic modeling approach of sufficient complexity to describe anabranching river flows from sparse multisatellite observations using the HiVDI inverse method presented in Laurier et al. (2019) with an augmented control vector including a spatially distributed friction law K (x, h) depending on the flow depth h. It is shown on 71 km of the Xingu River (anabranching, Amazon basin) with altimetric water height timeseries that a fairly accurate upstream discharge hydrograph and effective patterns of channel bathymetry and friction can be inferred simultaneously. The coherence between the sparse observation grid and the fine hydraulic model grid is ensured in the optimization process by imposing a piecewise linear bathymetry profile b(x), which is consistent with the hydraulic visibility of WS signatures (Garambois et al., 2017; Montazem et al., 2019). The discharge hydrograph Q(t) at observation times and effective bathymetry-friction (b(x), K(x, h)) patterns are retrieved from 8 years of satellite altimetry (ENVISAT) at 6 virtual stations (VS) along flow. Next, the potential of the forthcoming SWOT data, dense in space, is highlighted by inferring a discharge hydrograph and dense patterns of effective river bathymetry and friction; a physically consistent scaling of friction by reaches enables to consider more dense bathymetry controls. Finally a numerical analysis shows: (i) the importance of an unbiased prior information in the inference of a triplet (Q, b(x), K(x, h)) from WS observations; (ii) the clear signatures of river bottom slope break in low flows and width variations in high flows, through the analysis of the friction slope term, which is consistent with the findings of Montazem et al. (2019) from WS curvature analysis.