Reducing the Dimension of Infered Time-Varying Boundary conditions to Improve Water Levels Prediction in the Gironde Estuary using Telemac2D and an Ensemble Kalman Filter

Abstract

Vanessya Laborie*, Sophie Ricci and Nicole Goutal

In order to better predict high water levels and floods in the Gironde estuary, a Telemac 2D numerical model is combined with a stochastic Ensemble Kalman Filter (EnKF). The hydrodynamic model calculates water depths and velocity fields at each node of an unstructured mesh. The EnKF corrects the inputs of the model, i.e both scalar parameters and timevarying forcings, as it assimilates in situ water levels observations. Upstream, the model fluvial boundaries are respectively located at La R ́eole and Pessac on the Garonne and Dordogne rivers. The maritime boundary is 32 km off the mouth of the Gironde estuary, located at Le Verdon. It is assumed that the uncertainty in time-varying boundary conditions is well approximated by a Gaussian Process (GP) characterized by its autocorrelation function and associated correlation time scale. The coefficients of the truncated Karhunen- Lo`eve decomposition of this GP are further considered in the EnKF control vector, together with the area-prescribed friction coefficients and the wind influence coefficient. The data assimilation strategy performance was assessed with twin- and real experiments which respectively use synthetic water levels observations and in situ water levels measurements. Twin experiments showed that the proposed methodology succeeds in identifying time varying friction, as well as reconstructing the boundary conditions even though the identification of the Karhunen-Lo`eve coefficients for the time-dependent boundary conditions suffers equifinality. Indeed, the results show the proper reconstruction of the maritime forcing and consequently the expected water levels in the estuary, improving water levels prediction in the Gironde Estuary. However, difficulties in estimating the friction parameter in the confluence zone, where the flows are the result of non-linear physical processes, were highlighted. Real experiments showed that, in spite of these limitations, water levels are significantly improved by assimilating in situ observations, as absolute errors remain smaller than 13 cm at high tides (HT) along the estuary, except in the upstream reaches of the Garonne and Dordogne rivers where the model refinement should be improved.

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