PASHA (PedAgogic StocHastic data Assimilation)

The global structure of the package is mainly composed of a model class which implements the model and a DAscheme class which implements the data assimilation method that is used. The model class is composed of a set of methods allowing to initialize the model, to propagate it on one or several consecutive time steps and to update the initial conditions and/or the parameters for the next assimilation cycle. The DAscheme class allows to drive the whole assimilation experiment by performing alternating prediction and analysis steps. Different variants of the Kalman filter are integrated in the form of classes inheriting from DAscheme: EnKF (two integrated variants: Ensemble Transform Kalman Filter (Bishop et al. 2001) and stochastic version of EnKF as proposed in Burgers et al. 1998), ES ES-MDA iEnKS For each of them, the analysis and DAfull methods are redefined according to the strategy used for the analysis and according to the type of assimilation considered (filter or fixed point smoother or fixed interval smoother with fixed interval). No numerical optimization has been done and the algorithms have been kept as compact and transparent as possible, which allows a better overview of the mathematical theory they implement. Moreover, an ObsInfo class allows to provide all the information related to the observations (values, frequency, observation operator, error covariance matrix,) and a Trajectory class allows to extract some values from the state vector to constitute temporal trajectories. The ObsInfo and Trajectory classes also include a set of methods facilitating the visualization of the temporal evolution of the set of observations and their errors. Finally, the PerfStudy class allows to compute a set of of metrics allowing to evaluate the quality of the assimilation results in relation to a reference trajectory (bias, RMSE, dispersion, CRPS).