Biogeochemical Data Assimilation: On The Singular Evolutive Interpolated Kalman-Filter

Data Assimilation is nowadays a fundamental part in any forecasting geoscience model. In the field of marine biogeochemistry, the number and quality of observational systems (e.g. satellites, biogeochemical Argo floats, moorings) is constantly improving, but the available information is still far from picturing per se the true state of the marine ecosystem. Thus, at forecasting and monitoring purpose, Data Assimilation techniques are necessary in order to face the problem of the sea state estimation. Handling the large dimension of the state vector of the system (order of 10^6) remains an issue, and many attempts have been done to reduce the complexity of the problem, adding hypothesis and approximations in order to obtain fast Data Assimilation algorithms. The 3D-VAR, a Data Assimilation method based on the variational approach, is one of these results and it is adopted in the EU Copernicus system for monitoring and forecasting the biogeochemical state of the Mediterranean Sea. Aside from variational, the other main Data Assimilation approach is the Kalman-Filter. This thesis is focused on biogeochemical marine Data Assimilation, and has a double purpose. The first one is to compare the 3D-VAR scheme with the Singular Evolutive Interpolated Kalman-Filter (SEIK). From a theoretical point of view, this is realized using a Bayesian framework to derive differences and similarities as well as strengths and weaknesses of the two methods. This analysis shows that the main differences are in the choice of the state estimator (the mode for the variational and the mean for the Kalman-Filter), and in the Kalman-Filter's capability of keeping and transferring the information through the time steps. A twin experiment has been used to asses the skill performance of the compared schemes. Tests show that the SEIK is one order of magnitude more precise than the 3D-VAR, in terms of root mean squared distance (RMSD). The second objective of this work is to develop a novel Data Assimilation method from the SEIK filter, focusing on the effects of the model error and its estimation. Various strategies have been implemented at this purpose, namely an high order sampling technique, a method to take into account SEIK's neglected part of the model error as noise-like observation error, a data driven maximum likelihood algorithm for model error estimation and, finally, an ad hoc computationally cheap smoother. The twin experiment tests prove that the first two modifications change the behaviour of the SEIK filter only in case of large model error, conferring to the modified SEIK an higher resiliency to divergences. The maximum likelihood strategy estimations obtained good agreement with the estimated real value, with better results if used in pair with the modified version of the SEIK. The smoother further improved the RMSD of the method, with even better results in case of large model error.