Abstract
The problem of estimating the error variance of a meteorological forecast is important both for data assimilation purposes and in order to increase the value of the forecast to the end user. Current data assimilation systems have no–or at best a severely limited–capability to estimate this quantity. In principle, the prognostic equation for the forecast error covariance is known from the Kalman filter. However, in its full form this equation is prohibitively expensive to implement and solve. In this article, the possibility of evolving a variance‐only estimate is explored. It is shown that for a barotropic vorticity‐equation model, an approximate equation for the error variance evolution can be written in a closed form under certain assumptions. The cost of solving this equation is comparable to that of solving the model equation itself. Through a demonstration experiment, it is shown that the approximate equation tracks the actual variance of a model run–represented by the variance over a randomly perturbed ensemble of forecasts generated by the model–remarkably well, qualitatively as well as quantitatively.