A method for ensemble expansion and improved definition of forecast distributions from climate simulations

Because of the inherently chaotic nature of the atmosphere, ensemble simulations are required to characterize a model’s response to the prescribed boundary forcing in probabilistic terms, particularly if the focus is on the probabilities of extreme events. At the same time, substantial computer resources are needed to produce routinely ensemble seasonal climate forecasts of sufficient size to make suitably reproducible estimates of such probabilities. We describe a method for artificially expanding the effective number of members in ensemble climate simulations on a seasonal basis, thereby reducing uncertainty in estimated probability distributions. As described here, the method involves calculating seasonal statistics using monthly values from all possible combinations of ensemble members. Under certain assumptions, this method is able to increase the effective ensemble size of an N-member M-month seasonal forecast by a factor of (asymptotically) M. One key assumption in this regard is that, aside from the effects of prescribed boundary conditions, the month-to-month values from a particular ensemble member are linear independent. This paper describes the behaviour of the ensemble expansion technique using both idealized and actual ensemble forecast data under a variety of conditions, drawing comparisons with an alternative parametric approach for ensemble expansion. A method for testing the assumption of linear independence in model simulations is also presented