改进的最优窗宽理论对年径流量的插值预测研究——以黄河利津等站为例

The research on interpolation and prediction of annual runoff of improved theory of optimal window width——An example of Lijin hydrologic station of the Yellow River

针对小样本数据造成年径流量预测效果不理想的情况,以及非对称和非正态资料的处理问题,引入信息扩散和模糊映射思想,同时运用遗传算法改进最优窗宽理论,建立了新的扩散插值模型。该模型通过对零散数据点的信息进行模糊扩散,进而实现对有限数据点信息向其邻近区域点的概率插值。选取黄河利津站为例,根据其近70 a(1942—2011年)径流量实测数据,进行了缺损数据的插值和预测试验,同时与正态扩散插值模型进行对比分析,结果表明:1)预测值能较好地模拟实际径流序列的波形变化,对丰水年(如2007年)和枯水年(如2009年)的预报都比较准确;2)中长期预报(10a)平均相对误差仅为11.59%,相较传统方法有较大的改进;3)以黄河流域2个站点(花园口和兰州)和长江流域的3个站点(朱沱、宜昌和大通)年径流量预测试验以及海温资料的插值试验作为补充,验证了该算法的有效性和普适性。该模型可为实际水文数据资料的客观分析和中长期预报提供参考。

For the case of using small sample data to predict the annual runoff which caused unsatisfactory results,and the case of trying to deal with asymmetric and non-normal data.The thought of information diffusion and fuzzy mapping were introduced in this paper.At the same time,we tried to set up a new diffusion interpolation model by using genetic algorithm to improve the theory of optimal window width.The model achieved probability interpolation of limited data point information to its neighboring regions point by improving the theory of optimal window width based on genetic algorithm.In order to verify the practicability of the model,this paper took Li Jin hydrological station of the Yellow River as an example,and its runoff data from 1942 to 2011 were interpolated and prediction experiments were conducted.After comparing with the normal diffusion interpolation model,the following conclusions can be drawn:(1)In the interpolation and prediction of the runoff data in some non symmetric and non normal data,the results of interpolation is approximate to the actual and the predictive value which can well simulate the waveform changes of actual runoff series,especially accurate in both wet years(such as 2007)and dry years(such as 2009);(2)The average relative error of long-term forecasts(usually 10 years)is only 11.59%,which met the requirements and achieved greater improvement when compared with traditional information diffusion method whose average relative error is 55.23%;(3)Finally,the prediction experiment of annual runoff of two hydrologic stations in the Yellow River Basin(Huayuankou and Lanzhou)and three hydrologic stations in the Yangtze River Basin(Zhutuo,Yichang and Datong)and the interpolation experiment of sea surface temperature data as a complement,which can verify the effectiveness of the proposed method and the general applicability.Owing to the transformation from sample points into fuzzy sets,the new algorithm can partially make up for the information gaps due to incomplete data.It can not only be applicable to the estimation and prediction of annual runoff of hydrological stations with different geographical positions,different underlying surfaces and different catchment areas,but also can be extended to the interpolation prediction field of sparse data,especially in the field of atmosphere and ocean.This new interpolation model which is proposed by this paper is intended to provide a reference for objective analysis and long-term forecasts of actual hydrological data.