Reducing Forecast Errors Due to Model Imperfections Using Ensemble Kalman Filtering

A method is introduced for reducing forecast errors in an extended-range to one-month forecast based on an ensemble Kalman filter (EnKF). The prediction skill in such a forecast is typically affected not only by the accuracy of initial conditions but also by the model imperfections. Hence, to improve the forecast in imperfect models, the framework of EnKF is modified by using a state augmentation method. The method includes an adaptive parameter estimation that optimizes mismatched model parameters and a model ensemble initialized with the perturbed model parameter. The main features are the combined ensemble forecast of the initial condition and the parameter, and the assimilation for time-varying parameters with a theoretical basis. First, the method is validated in the imperfect Lorenz '96 model constructed by parameterizing the small-scale variable of the perfect model. The results indicate a reduction in the ensemble-mean forecast error and the optimization of the ensemble spread. It is found that the time-dependent parameter estimation contributes to reduce the forecast error with a lead time shorter than one week, whereas the model ensemble is effective for improving a forecast with a longer lead time. Moreover, the parameter assimilation is useful when model imperfections have a longer time scale than the forecast lead time, and the model ensemble appears to be relevant in any time scale. Preliminary results using a low-resolution atmospheric general circulation model that implements this method support some of the above findings.