A Monte Carlo implementation of the nonlinear filtering problem to produceensemble assimilations and forecasts

Knowledge of the probability distribution of initial conditions is central to almost all practical studies of predictability and to improvements in st ochastic prediction of the atmosphere. Traditionally, data assimilation for atmospheric predictability or prediction experiments has attempted to find a single "best" estimate of the initial state. Additional information abou t the initial condition probability distribution is then obtained primarily through heuristic techniques that attempt to generate representative pertu rbations around the best estimate. However, a classical theory for generati ng an estimate of the complete probability distribution of an initial state given a set of observations exists. This nonlinear filtering theory can be applied to unify the data assimilation and ensemble generation problem and to produce superior estimates of the probability distribution of the initi al state of the atmosphere (or ocean) on regional or global scales. A Monte Carlo implementation of the fully nonlinear filter has been developed and applied to several low-order models. The method is able to produce assimila tions with small ensemble mean errors while also providing random samples o f the initial condition probability distribution. The Monte Carlo method ca n be applied in models that traditionally require the application of initia lization techniques without any explicit initialization. Initial applicatio n to larger models is promising, but a number of challenges remain before t he method can be extended to large realistic forecast models.