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Abstract:

This PhD thesis present research work on data assimilation and multidimensional model coupling in the framework of real-time flood forecasting. The deterministic numerical models proposed to simulate and forecast river flow are limited because of various uncertainties and simplified physics. Data assimilation and coupling approaches allow to over come these limits and extend the forecast lead time while providing a coherent and realistic description of the hydraulic state.

This thesis is composed of 3 parts gathering 9 chapters.

Part one presents the context of flood forecasting and its stakes, the role of SCHAPI and SPCs. A focus is made on the Adour maritim catchment.

The shallow water equations in the context of the dynamic of river flows are then presented in Part two along with numerical methods usually implemented in hydraulic codes such as Mascaret and Telemac which are used in this work. Data assimilation methods are described with a focus on ensemble approach, then model coupling methods are presented. Results are presented in Part three. It was shown, on a flood wave propagation model, that an Emulated Ensemble Kalman filter algorithm provides results that are close to those of the Ensemble Kalman Filter but with a much reduced computationnal cost. The Emulated Ensemble Kalman Filter is built as a Kalman filter algorithm with an invariant covariance function at the observation point. It was also shown that an initially gaussian shaped correlation function at the observing point is transformed into an asymetric function with a shorter correlation length scale downstream of the observation point. In a real case application on the Adour maritim catchment, it was shown that the dynamics of covariance and correlation model state error functions are strongly influenced by the geometrical characteristics of the river. It was also shown that those functions have a great spatial extent. When combined with an inflation method to circumvent under- dispersivity of the ensemble, the correction provided by the EnKF has an important spatial extent that allow to correct water level and discharge away from the observation points. It was shown on synthetical and real cases experiments that data assimilation provides an hydraulic state that is in great agreement with water level observations. As a consequence of the sequential correction of the hydraulic state over time, the forecasts were also greatly improved by data assimilation over the entire hydraulic network for both assimilated and non-assimilated variables, especially for short term forecasts. This study is combined with the a posteriori estimation of the observation error variance using Desroziers criterion. It was finally shown that the quality of ensemble forecast on the Adour maritim network mostly relies on the knwoledge of the upstream forcings.

While the 1D model covers a great spatial domain and describes the mono-dimensional flow, the 2D model provides a focus on the Adour-Nive confluence in the Bayonne area. Two coupling methods have been implemented in this study : a first one based on the exchange of the state variables at the liquid boundaries of the models and a second one where the models are superposed. While simple 1D or chained 1D-2D solutions provide an incomplete or discontinuous (either on water level or on discharge) description of the hydraulic state, both coupling methods provide a full and dynamically coherent description of the hydraulic state for water level and discharge over the entire 1D-2D domain. On the one hand, the interface coupling method presents a much higher computational cost than the superposition methods but the continuity is better preserved. On the other hand, the superposition methods allows to combine data assimilation of the 1D model and 1D-2D coupling. The positive impact of water level in-situ observations in the 1D domain was illustrated over the 2D domain for a flood event in 2014.

Conclusions and perspective towards the operational use of both data assimilation and coupling for flood forecasting in France are given.