## Altimetry Data Assimilation Chain for Multi-resolution River Flow Models

Collaboration between IMT-INSA Toulouse (J. Monnier), ICUBE-INSA Strasbourg (P.-A. Garambois), short terms Engineers (P. Brisset, J. Verley) from CNRS-CNES, CS corp. (K. Larnier, Research Eng.), IMFT-INP Toulouse (H. Roux) and LEGOS (A. Montazem, S. Biancamaria, S. Calmant), France.

### Objectives

This research project aims at inferring unknown or uncertain hydraulic features of worldwide rivers observed by the SWOT mission; more specifically it aims at estimating the rivers discharge. To do this, a complete hydraulic chain (0.5D - 1D - 2D) with state-of-the-art know-hows in Variational Data Assimilation (VDA) has been developed. This multi-resolution approach makes possible to address single "natural" river reaches like demonstrated below; it should makes possible to consider braided flows and floodplains too.

Below are presented the capabilities of the approach on few river tests by inferring simultaneously the discharge, an effective bathymetry and depth-dependent friction laws for 1D rivers portions.

Most of the developed methods and algorithms in the project are available online: the open source computational platform DassFlow [Dass] and toolboxes (e.g. interface with SWOT HR simulator, QGis pluggin).

### Approach

The present key know-hows to infer the observed river properties (discharge, bathymetry and roughness) rely on the following points:

- A multi-scale resolution of the river flows: low-complexity "0.5D", 1D, 2D shallow flow models,
- Advanced know-hows in Variational Data Assimilation (VDA) (derived from the best and most recent know-hows developed in the international meteorology community),
- A fine analysis of the flow line signal,
- Taking into account the prior information into the direct models and the assimilation - inverse model (e.g. data accuracy vs length scales trade-offs),
- Assimilation of the potential local database information e.g. SWOT river database.

The lowest complexity inversions are derived from the Low Froude flow assumption (Manning-Strickler's law is part of it; so-called "0.5D" models). They make possible to:

- Estimate a first guess of the complete set of the hydraulic unknowns (
*Q(x,t),A*) for starting the VDA process, if not (partially) provided by a database;_{0}(x),K(h) - Estimate accurate effective bathymetries
*A*if one (1) pointwise cross-section measurement is available;_{0}(x) - Perform in real-time discharge estimations once the models have been calibrated by VDA (that is after the "learning period" which requires a complete hydrological SWOT data set).

The advanced VDA process applied to the 1D Saint-Venant - low-Froude hierarchical model makes possible to infer a quite accurate discharge *Q(t)* plus an effective bathymetry *b(x)* and an effective friction law *K(h)* depending on the water depth *h*.

A coupling with hydrological model(s), at the catchment scale, is under progress.

This VDA process has been developed for the 2D flow model (shallow-water, flood plains) too. Moreover a two-ways coupling 1D-2D, by superposing local 2D models over a global 1D one has been investigated.

### Results

The inference capabilities obtained from SWOT like data are illustrated on a few test rivers. The considered river portions are taken from the PEPSI-1 dataset. It consists in ~100 km portions of the upstream Garonne river (France), the Po river (Italy) and the downstream Sacramento river (USA).

Two scenarios are considered: a) Cal-Val context (~1 day repeat period with a complete observation of the river portion); b) A real like SWOT dataset provided by the SWOT-HR simulator (~21 days repeat with only one observation per cycle and the expected SWOT spatial sampling).

### Discharge Inversions from Historical Nadir Altimetry Time Series

Below the same approach is applied to 8 years time series of a historical nadir altimetry dataset; Xingu river portion (Amazonia).

###
### 2D Modeling for Inferences on Complex Hydrodynamics

The same upstream Garonne river portion as above is simulated using the 2D model. The VDA approach makes possible to analysis for example the sensitivity of the model in flooded areas with respect to the friction law and/or with respect to the DEM, bathymetry.

### References

[Dass] DassFlow computational software (Data Assimilation for Free Surface flows). Available online upon request since 2005. University of Toulouse & INSA, France.

#### Submitted

P. Brisset, P.-A. Garambois, J. Monnier, H. Roux. "Identifiability and assimilation of sparse altimetry data in 1D Saint-Venant river models". Revised version under review.

Montazem A. S., Garambois, P. -A., Finaud-Guyot, P., Calmant S., Monnier, J., Moreira, D. "Physical basis for river segmentation from water surface observables". Submitted.

#### On-going Drafting (Complete Results Obtained)

K. Larnier, J. Monnier, P.-A. Garambois. "On the identification of rivers features from altimetry". Results fully obtained; on-going drafting.

#### Published

P.-A. Garambois, S. Calmant, H. Roux, A. Paris, J. Monnier, P. Finaud-Guyot, A. Montazem, J. Santos da Silva, "Hydraulic visibility: using satellite altimetry to parameterize a hydraulic model of an ungauged reach of a braided river". Hydrological Processes, Vol. 31, 4, 756-767, 2017.

J. Monnier, F. Couderc, D. Dartus, K. Larnier, R. Madec, J.P. Vila. "Inverse algorithms for 2D shallow water equations in presence of wet dry fronts. Application to flood plain dynamics". Advances in Water Ressources (97), 11-24, 2016.

M. Durand, C.J. Gleason, P.A. Garambois, D. Bjerklie, L.C. Smith, H. Roux, E. Rodriguez, P.D. Bates, T.M. Pavelsky, J. Monnier et al. "An intercomparison of remote sensing river discharge 1 estimation algorithms from measurements of river height, width, and slope". Water Resources Research, 52 (6), 4527-4549, 2016.

P.-A. Garambois, J. Monnier. "Inference of effective river properties from remotely sensed observations of water surface". Advances in Water Ressources, 79, 103-120, 2015.

R. Hostache, X. Lai, J. Monnier, C. Puech. "Assimilation of spatial distributed water levels into a shallow-water flood model. Part II: using a remote sensing image of Mosel river". J. Hydrology Vol. 390, Issues 3-4, pp 257-268, 2010.

E. Fernandez-Nieto, J. Marin, J. Monnier. "Coupling superposed 1D and 2D shallow-water models: source terms and finite volume schemes". Comput. Fluid. Vol.39, Issue 6, pp 1070-1082, 2010.

X. Lai, J. Monnier. "Assimilation of spatial distributed water levels into a shallow-water flood model. Part I: mathematical method and test case". J. Hydrology. Vol. 377, Issue 1-2, pp. 1-11, 2009.

J. Marin, J. Monnier. "Superposition of local zoom model and simultaneous calibration for 1D-2D shallow-water flows". Math. Comput. Simul. 80 (2009), pp. 547-560.

M. Honnorat, J. Monnier, N. Riviere, E. Huot, F.-X. Le Dimet. "Identification of equivalent topography in an open channel flow using Lagrangian data assimilation." Comput. Visu. Sc. (CVS). Vol. 13, Issue 3 (2010), pp 111-119.

M. Honnorat, J. Monnier, F.-X. Le Dimet. "Lagrangian data assimilation for river hydraulics simulations". Comput. Visu. Sc. (CVS). Vol. 12, Issue 5, pp. 235 (2009).

I. Gejadze, J. Monnier. "On a 2D zoom for 1D shallow-water model: coupling and data assimilation". Comp. Meth. Appl. Mech. Engnr. (CMAME). Vol. 196, issues 45-48, pp. 4628-4643, 2007.