We present the Hierarchical Variational Discharge Inference (HiVDI) algorithm [1,2] and its capabilities to estimate the discharge and bathymetry of rivers from altimetry measurement, more particularly from the forthcoming SWOT space mission. The last version algorithm is based on hierarchical flow models and hybrid computational approaches : 1) a dedicated satellite-scale low-complexity model relating the discharge Q(x,t), the bathymetry b(x) and the friction parameter K ; 2) an advanced Variational Data Assimilation (VDA) formulation based on a relatively complete physics (Saint-Venant’s equations) [2,4] ; 3) deep neural networks based estimations obtained from recently enriched databases . The resulting algorithm turns out to be robust and relatively accurate. Passed the assimilation of a hydrological cycle (~ 1 year variations, considered as a “learning period) the identified parameters (b(x), K) are identified; next given newly acquired satellite measurements, the low complexity model enables to estimate Q(x,t) in real-time [1,2].
Numerical results on numerous river datasets are analyzed in detail including for relatively complex flows and multi-satellite datasets [1,2,3].
 K. Larnier, J. Monnier. "Hybrid data assimilation - deep learning approaches to estimate rivers discharges from altimetry". Submitted.
 K. Larnier, J. Monnier, P.-A. Garambois, J. Verley. "River discharge and bathymetry estimations from SWOT altimetry measurements". Revised (nov. 2019).
 P.-A. Garambois, K. Larnier, J. Monnier, P. Finaud-Guyot, J. Verley, A. Montazem, S. Calmant. "Variational inference of effective channel and ungauged anabranching river discharge from multi-satellite water heights of different spatial sparsity". J. of Hydrology 2019.
 P. Brisset, J. Monnier, P.-A. Garambois, H. Roux. "On the assimilation of altimetry data in 1D Saint-Venant river models". Adv. Water Ress. 2018.
 "DassFlow: Data Assimilation for Free Surface Flows", open-source computational software. INSA - IMT, CNRS, CNES, CS group. http://www.math.univ-toulouse.fr/DassFlow