Data assimilation in hydrological modelling

Data assimilation is an invaluable tool in hydrological modelling as it allows to efficiently combine scarce data with a numerical model to obtain improved model predictions. In addition, data assimilation also provides an uncertainty analysis of the predictions made by the hydrological model. In this thesis, the Kalman filter is used for data assimilation with a focus on groundwater modelling. However the developed techniques are general and can be applied also in other modelling domains. Modelling involves conceptualization of the processes of Nature. Data assimilation provides a way to deal with the uncertainties resulting from the model creation and calibration. It is necessary to balance modelling uncertainties and observation uncertainties to prevent an excessive forcing of the model towards the observations. The popularity of the Kalman filter resulted in the development of various techniques to deal with model non-linearities and biased errors. A literature review analyzes the most popular techniques and their application in hydrological modelling. Since bias is an important problem in groundwater modelling, two bias aware Kalman filters have been implemented and compared using an artificial test case. It resulted in the recommandation of the Colored Noise Kalman filter as the most suitable method. By using bias feedback in the model propagation, the bias variations are represented by their first order approximation. The main contribution of this thesis is the development of a sequential calibration technique whereby the performance of the model and its associated Kalman filter is optimized separately from the uncertainty analysis. Instead of using rules of thumb to estimate the parameters of the covariance matrices, the method relies on an objective automatic calibration method that aims at optimizing the performance without affecting the stability of the system. The application of the technique to an artificial case leads to a Kalman filter setup that generates a minimum overall model error as well as an optimized uncertainty analysis. The sequential calibration scheme has been further developed for the simultaneous calibration of the Kalman filter and the physical model parameters. The procedure was applied to the Danish Karup catchment. It resulted in a significant reduction of the model error and an optimized uncertainty estimation both at assimilation and validation points. However, the analysis showed that care should be taken in the calibration since some parameters may lack physical interpretability.