Compression for Freedom Degree in Numerical Weather Prediction and the Error Analogy

A substantial improvement in the skill of numerical weather prediction has been achieved in recent years. Useful skill typically extends numerical weather prediction from present day to about 6 days. But for longer timescale, such as 6—15 days, the forecast quality is poor. It is necessary to improve the quality of the results. Utilizing useful information in historical data to improve the prediction skill of numerical model has been considered as a goal. The analogue dynamical method is one of these optimum methods to combine dynamical methods and statistical methods together. However, the analogue selection is very hard due to broad freedom in traditional analogue selection methods. So an analogue selection method under small degree of freedom is proposed. By the method degree of freedom on low dimensional climate attractor is reduced, and small scale components are filtered. This method is based on the theory that the high dimensional phase space in a forced dissipative nonlinear system eventually evolves into a low dimensional attractor, while small scale high frequency patterns are dissipated. Based on compression for degree of freedom of the initial field, an analogue index is defined. In order to further develop the analogue dynamical method, the regularity of the error similarity is investigated. Analyses show that similar initial conditions lead to analogical characteristics of forecast errors. Compared with the system error, the error under analogical initial condition is more close to actual forecast error. Meanwhile, in the spatial scale, forecast errors between analogical initial conditions are well consistent. The preliminary results of the forecast experiments on a complicated T63 Dynamical Extended Range Forecasting model of NCC/CMA show that the analogue dynamical method can effectively reduce the model error. Results provide support for further developing the analogue dynamical method. Evidently, further theoretical and more prediction experiments are necessary for improving the performance of analogue dynamical method. Meanwhile, the model predictable components should be reasonably obtained. These problems will be studied in further work.