洪峰流量与流域面积幂函数关系最优拟合方法探讨  

Optimal fitting for discharge-area power law relationship

作　　者：马春英 杜鹃 郑璟[3] 陈波[1,2] MA Chunying;DU Juan;ZHENG Jing;CHEN Bo(Academy of Disaster Reduction and Emergency Management,Ministry of Civil Affairs & Ministry of Education, Faculty of Geographical Science,BNU,100875,Beijing,China;Key Laboratory of Environmental Change and Natural Disaster,MOE,BNU,100875,Beijing,China;Guangdong Climate Center,510080,Guangzhou,Guangdong,China)

机构地区：[1]北京师范大学民政部/教育部减灾与应急管理研究院,北京师范大学地理科学学部,北京100875 [2]北京师范大学环境演变与自然灾害教育部重点实验室,北京100875 [3]广东省气候中心,广东广州510080

出　　处：《北京师范大学学报（自然科学版）》2019年第3期408-414,共7页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(41501020);国家自然科学基金创新研究群体资助项目(41621061)

摘　　要：基于78场洪水的实测数据,使用非线性与常用的双对数线性回归方法拟合了洪峰流量与流域面积的幂函数关系,分析了所得幂函数模型的差异,探讨了拟合方法的适当性.结果表明:2种方法拟合的洪峰流量与流域面积幂函数关系差异显著(P <0.01);80%情况下双对数线性推求的模型的拟合误差大于非线性;双对数线性拟合中的对数变换虽保持了原始数据的大小次序,但改变了数据点间的相对距离,从而根本上改变了洪峰流量与流域面积关系的特征.因此,建议在拟合洪峰流量与流域面积幂函数关系时,尽量采用非线性方法而慎用对数变换.Discharge-area power law relationship has been widely used to estimate flood peak flows for ungauged basins.This relationship could be fitted with nonlinear and log-log linear regressions.To compare differences in peak-discharge power-law models estimated by these regressions,78peak-discharge events were studied.The estimated models by these two methods were found to be statistically significant(P<0.01).For 80%chances,the model obtained by log-linear regression produced modeling errors larger than by nonlinear regression.Log-transformation retained the order of un-transformed data but altered the relative distance between data points,leading to fundamental changes in the nature of the variables of peak discharge and drainage area.Nonlinear,rather than log-linear regression should be applied for peak-discharge power-law analysis.

关 键 词：洪峰流量 幂函数 非线性拟合 对数变换 

分 类 号：TV11[水利工程—水文学及水资源]