Development of Prediction Model Using Ensemble Forecast Assimilation in Nonlinear Dynamical System

In this study a new type of ensemble forecast assimilation technique is developed in order to improve the forecast skill in the nonlinear dynamical system. The forecast assimilation is an analysis technique in which a true value contained in each ensemble forecast is accumulated into a single assimilated forecast such as a data assimilation. For the experiments, we used a Lorenz model, and a Kalman filter is applied for the forecast assimilation. The experiments are started by calculating 101 members of the ensemble forecast in which the initial error with Gaussian distribution is superimposed around the truth, and one of the members is arbitrarily selected as a control forecast. The experiments of the forecast assimilation are repeated 5000 times for different sectors of the solution trajectory to obtain the statistical significance of the results. The distribution of the ensemble members is stretched by a linear error growth at the beginning of the forecast. After that, the nonlinear effect becomes dominant to distort the distribution. The forecast assimilation is then started when the errors of the ensemble forecasts have grown to a certain threshold. It is demonstrated that the forecast skill of the assimilated forecast is always superior to the control forecast. In the range of the small root mean square error (RMSE) of the ensemble forecast, the skill of the assimilated forecast is inferior to the ordinary ensemble mean. However, for the sufficiently large RMSE before the saturation, it is shown that the skill of the assimilated forecast is superior to the ensemble mean. The result suggests that the forecast assimilation is one of the viable approaches to the medium or extended range forecast.