Predictive anisotropy is a phenomenon referring to unequal predictability of surface wind components in different directions. This study addresses the question of whether predictive anisotropy resulting from statistical prediction is influenced by physical factors or by types of regression methods (linear vs nonlinear) used to construct the statistical prediction. A systematic study of statistical predictability of surface wind components at 2109 land stations across the globe is carried out. The results show that predictive anisotropy is a common characteristic for both linear and nonlinear statistical prediction, which suggests that the type of regression method is not a major influential factor. Both strong predictive anisotropy and poor predictability are more likely to be associated with wind components characterized by relatively weak and non-Gaussian variability and in areas characterized by surface heterogeneity. An idealized mathematical model is developed separating predictive signal and noise between large-scale (predictable) and local (unpredictable) contributions to the variability of surface wind, such that small signal-to-noise ratio (SNR) corresponds to low and anisotropic predictability associated with non-Gaussian local variability. The comparison of observed and simulated statistical predictability by Regional Climate models (RCM) and reanalysis in the Northern Hemisphere indicates that small-scale processes that cannot be captured well by RCMs contribute to poor predictability and strong predictive anisotropy in observations. A second idealized mathematical model shows that spatial variability in specifically the minimum directional predictability, resulting from local processes, is the major contributor to predictive anisotropy. / Graduate

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In this work, we implemented the GHER hydrodynamic model in the Gulf of Lions (resolution 1/100°). This model is nested interactively in another model covering the North-Western basin of the Mediterranean Sea (resolution 1/20°), itself nested in a model covering the whole basin (1/4°). A data assimilation filter, called the SEEK filter, is used to test in which of those grids observations taken in the Gulf of Lions are best assimilated. Therefore, twin experiments are used: a reference run is considered as the truth, and another run, starting from different initial conditions, assimilates pseudo-observations coming from the reference run. It appeared that, in order to best constrain the coastal model, available data should be assimilated in that model. The most efficient setup, however, is to group all the state vectors from the 3 grids into a single vector, and hence coherently modify the 3 domains at once during assimilation cycles. Operational forecasting with nested models often only uses so-called passive nesting: no data feedback happens from the regional models to the global model. We propose a new idea: to use data assimilation as a substitute for the feedback. Using again twin experiments, we show that when assimilating outputs from the regional model in the global model, this has benecial impacts for the subsequent forecasts in the regional model. The data assimilation method used in those experiments corrects errors in the models using only some privileged directions in the state space. Furthermore, these directions are selected from a previous model run. This is a weakness of the method when real observations are available. We tried to build new directions of the state space using an ensemble run, this time covering only the Mediterranean basin (without grid nesting). This led to a quantitative characterization of the forecast errors we might expect when various parameters and external forcings are affected by uncertainties. Finally, using these new directions, we tried to build a statistical model supposed to simulate the hydrodynamical model using only a fraction of the computer resources needed by the latter. To achieve this goal, we tried out artifficial neural networks, nearest-neighbor and regression trees. This study constitutes only the first step toward an innovative statistical model, as in its present form, only a few degrees of freedom are considered and the primitive equation model is still required to build the AL method. We tried forecasting at 2 different time horizons: one day and one week.

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