切比雪夫判据与常用相似判据的比较及应用

Comparison of Chebyshev Polynomials with Conventional Similarity Criteria in the Proximity Filtering and Its Application

为了提高相似预报效果,首先剖析了相似预报中常用的几个相似判据的特点和性能,发现它们都不能同时准确刻画样本之间振幅(能量)和位相(流型)的差异,在此基础上,利用切比雪夫多项式展开的归一化低阶时间权重系数构造出一种能综合反映样本之间振幅和位相差异的相似性判据(切比雪夫判据)。然后,利用T213模式数值预报产品,使用不同判据对2011年1-3月锦州、绥中和兴城3站的气温进行相似试预报对比试验。结果表明,切比雪夫判据对形势场的相似过滤效果明显好于其他判据,能为相似天气形势的选取提供一个更好的依据。

The characteristics and functions of several conventional similarity criterions in analog forecast were analyzed, it turned out that they cannot accurately depict the differences of samples in amplitude（en- ergy） and phase （flow pattern） simultaneously, then a new similarity criterion which can synthetically ex- press the differences of samples in amplitude and phase is presented, i.e. Chebyshev criterion constructed by uniformized and low-level time-weighting coefficients which are expanded from Chebyshev polynomials. Afterwards, the different criteria are used to do analogue prediction and contrast experiments of the tem- perature at Jinzhou, Xingcheng and Suizhong stations by utilizing the 24 h height forecast field of T213 nu- merical forecast products from January to March 2011. The experimental results show that Chebyshev cri- teria has significantly better filtering effect than other criteria. Chebyshev criteria provide a better basis for selecting the similar synoptic situation to seek weather processes which are more similar and improve the quality and accuracy of the analog forecast. The research in this paper can provide some references for re- lated scientific research departments and some operating departments when choosing the similarity criteria.