Development of an adjoint free 4Dvar and application to storm surge models

In this thesis a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method was proposed. This method works in a similar way to the incremental 4Dvar but avoids adjoint equations, which are difficult to develop and maintain for large scale models. The tangent linear equations are estimated explicitly by running a set of models. Theoretically, this method is equal to the adjoint method in terms of effectiveness and efficiency for low dimensional model parameters. A series of twin experiments indicate that the proposed adjoint free 4Dvar is effective for parameter estimate. It is able to recover the contaminated low dimension model parameters to their true values. The proposed method is then applied to an existing operational coastal forecasting system for the German North Sea. Since storm surges are major threats to the coast of the German Bight, the study is focused on the improvement of storm surge simulation. The data assimilation scheme is applied to a severe storm which occurred in the North Sea on December 5, 2013. Sensitivity tests show that the uncertainties of wind drag coefficient C_d has significant effect on the accuracy of storm surge model. This is probably due to the missing wind-wave coupling process in the storm surge model. Waves during a strong storm also enhance the sea bed shear stress, which would influence the storm surge simulation. Cd and bed drag coefficient are adjusted by the proposed data assimilation, and model skills are improved significantly. Compared to the storm surge model with function of Cd proposed by Smith, the root mean square deviations between model and observations decrease by 60% - 90%. The updated Cd is compared with the Cd calculated from a wave model, showing that Cd after data assimilation are more reasonable than before data assimilation.


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