Deterministic prediction of the error variance of a meteorological forecast

Both internally for data assimilation purposes, and externally for the end users of NWP products, the error variance of a meteorological forecast is a quantity of prime importance. Although the general consensus is that the forecast error variance must somehow depend on the atmospheric state, no presently operational data assimilation system attempts to predict it along with the state itself. Until now two basic state-dependent strategies have been identified, both of which are very expensive from a computational point of view : (I) Monte Carlo, or ensemble prediction methods , and (II) Kalman filter-based methods. In additional to the computational burden each of these strategies entails its own set of further problems to be solved, e.g. in specifying the inititial ensemble of perturbed states, or in specifying the full initial error convariance field. The purpose of the work presented here is to examine the possibility of predicting the forecast error variance along with the atmospheric state by means of a simple partial differential equation. An approximate prognostic equation for the error variance of a barotropic vorticity equation model is derived. The computational cost of this equation is roughly equal to that of the basic forecast equation. Through experimental results it will be shown that this equation tracks the actual spread caclculated over an ensemble of forecasts, both in terms of the temporal growth and the spatial inhomogeneity of the error. In particular, areas of explosive error growth are captured very well by the simple prognostic scheme.