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数值预报中自由度的压缩及误差相似性规律
Compression for Freedom Degree in Numerical Weather Prediction and the Error Analogy
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摘要: 利用历史资料的有用信息提高数值模式预报水平是长期以来人们努力的目标。该文提出了一种在气候吸引子上缩小初始场自由度的相似选取方法, 有效滤除了小尺度分量，避开了原有相似选取中自由度太大，相似选取困难的问题。分析表明：相似初值间的模式预报误差存在相似性，依此估计的预报误差与实际预报误差很接近。在空间分布特征上，相似初值间的模式预报误差也有很好的一致性。这为发展相似 动力方法，利用历史资料改进数值模式提供了支持。Abstract: 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.
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图 1 1 5d预报误差的相似指数随初值相似程度的演变
Fig. 1 The evolution of analogue index of forecast error with the analogue degree of initial value
图 2 2008年1月16日12：00及其4个最相似个例在η=7层 (约453hPa) 的24h温度场预报误差
Fig. 2 24-hour forecast error of temperature at η=7 (about 453 hPa) at 12: 00 16 January 2008 and its first 4 analogues
图 3 2008年1月16日12：00及其4个最相似个例估计的24h温度场预报误差
(η=4层，约216hPa; η=10层，约735hPa)
Fig. 3 24-hour forecast error of temperature at 12:00 16 January 2008 and its first 4 analogues
(η=4, about 216hPa; η=0, about 735 hPa)
图 4 5个个例平均的500hPa高度场的逐日预报与实况的距平相关系数 (a)，均方根误差 (b) 和500hPa温度场的逐日预报与实况的距平相关系数 (c)，均方根误差 (d)
Fig. 4 The daily ACC averaged over 5 cases of 500hPa geopotential height (a) andtemperature (c), and thedaily RMS Eaveraged over 5 cases of 500hPa geopotential height (b) and temperature (d)
表 1 起始个例预报误差与相似个例预报误差、系统误差的相似指数随预报时长的演变
Table 1 The evolution of analogue index of forecast error on initial case, analogue case and system error with leading time
表 2 两种相似选取方案估计的预报误差与实际预报误差相似指数随预报时长演变
Table 2 The comparison of the evolution of analogue index of estimated forecast error and real forecast error with leading time
表 3 5个个例平均的全球6~15d平均500hPa高度场和温度场的预报评分
Table 3 6—15-day average score of 5 cases of 500hPa geopotential height and temperature
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