灰色模型的改进及其在气象干旱预测中的应用

针对传统GM( 1, 1) 模型在数据预处理阶段存在的不足, 分析模型误差的产生原因, 提出新的数据预处理方法。依据峡江县1958- 2018 年降水量资料, 通过计算其SPI 指数( 标准化降水指数) 得到干旱年时间序列。在真实的时间序列数据集上对经典灰色模型GM0 、平移转换预处理灰色模型GM1 、基于平移转换的平均弱化缓冲算子预处理灰色模型GM2 进行了对比测试, 结果表明: 平移转换结合平均弱化缓冲算子弥补了预处理阶段的不足, 有效地降低传统模型的误差, 改进后的GM2 模型的平均预测误差为3.32%, 相较于其它两种模型分别降低了44.16%和16.24%。证明了该模型具有更好的预测精度, 可应用于干旱年的预测, 为区域干旱预测和干旱防治工作提供理论依据。 In view of the shortcomings of the traditional Grey Model ( 1, 1) ( GM ) ( 1, 1) in the data prepr ocessing stage, a new data preprocessing method was proposed by analyzing the causes of model errors. Based on the annual precipitation data of Xiajiang County from 1958 to 2018, drought year time series was obtained by calculating SPI index ( standardized precipitation index ) . The classical gray model GM0 , the translational conversion preprocessing gray model GM 1 , and the average weakening buffer operator pr eprocessing gray model GM 2 based on translation transformation were compared on the real-time series data set. The results showed that the translational conversion combined with the average weakening buffer operator compensated the shortcomings of the prepr ocessing stage and effectively reduced the error of the traditional model. The average prediction error of the improved GM 2 model w as 3.32% , which was 44.16 and 16.24 percentage points lower than the other two models. It is proved that the model has better prediction accuracy . It can be applied to the prediction of dry years, providing a theoretical basis for regional drought pr ediction and drought control. 江西省研究生创新专项资金项目( YC20182S 121)