洪峰流量与流域面积幂函数关系最优拟合方法探讨
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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,78 peak-discharge events were studied.The estimated models by these two methods were found to be statistically significant(P<0.01).For80% 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.
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,78 peak-discharge events were studied.The estimated models by these two methods were found to be statistically significant(P<0.01).For80% 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.
引文
[1]O'CONNELL P P L.On the relation of the freshwater floods of rivers to the areas and physical features of their basins and on a method of classifying rivers and streams with reference to the magnitude of their floods[J].Minutes of the Proceedings of the Institution of Civil Engineers,1868,27(1868):204
[2]芮孝芳,蒋成煜.流域水文与地貌特征关系研究的回顾与展望[J].水科学进展,2010,21(4):444
[3]叶守泽.美国无资料地区洪水频率计算的现状和动向[J].水文,1983(2):57
[4]熊立华,郭生练,王才君.国外区域洪水频率分析方法研究进展[J].水科学进展,2004,15(2):261
[5]DAWDY D R,GRIFFIS V W,GUPTA V K.Regional flood-frequency analysis:how we got here and where we are going?[J].Journal of Hydrologic Engineering,2012,17(9):953
[6]郭生练,刘章君,熊立华.设计洪水计算方法研究进展与评价[J].水利学报,2016,47(3):302
[7]张尚义,阳妍,邵知宇,等.美国洪水风险地图编制技术分析及对我国的启示[J].中国给水排水,2017,33(21):124
[8]宫兴龙,付强,王敏,等.洪峰流量与流域面积的幂函数研究[J].广西大学学报(自然科学版),2014,39(2):253
[9]许文涛,张平仓,任斐鹏,等.金沙江下游地区山洪灾害防治非工程措施适宜性评价[J].中国水利,2016(3):50
[10]朱秀迪,王志刚,任斐鹏,等.西南岩溶区小流域划分与水文特征分析[J].中国水土保持,2017(2):25
[11]周芬,郭生练,方彬,等.区域回归法对无资料地区设计洪水的估算[J].水力发电,2004,30(7):10
[12]刘昌明,白鹏,巩同梁,等.西藏稀缺资料地区洪峰流量推求[J].南水北调与水利科技,2013,11(1):1
[13]刘昌明,白鹏,王中根,等.稀缺资料流域水文计算若干研究:以青藏高原为例[J].水利学报,2016,47(3):272
[14]OGDEN F L,DAWDY D R.Peak discharge scaling in small Hortonian watershed[J].Journal of Hydrologic Engineering,2003,8(2):64
[15]EASH D A,BARNES K K,VEILLEUX A G.Methods for estimating annual exceedance-probability discharges for streams in iowa,based on data through water year 2010,scientific investigations report 2013-5086[R].Reston,VA:U.S.Geological Survey,2013
[16]陈华,何加伟,栗飞,等.湘江流域区域洪水频率分析计算[J].水资源研究,2013,2(1):20
[17]宋斌.阿坝州岷江及大渡河流域洪峰流量与流域面积关系指数的初步分析[J].科技与企业,2014(5):123
[18]AYALEW T B,KRAJEWSKI W F,MANTILLA R.Analyzing the effects of excess rainfall properties on the scaling structure of peak discharges:Insights from a mesoscale river basin[J].Water Resources Research,2015,51(6):3900
[19]王春华.九寨沟流域设计洪峰流量与面积关系指数的研究[J].陕西水利,2018(5):59
[20]幸新涪,周火明,秦维,等.基于流量-面积比值的小流域设计洪水计算方法对比研究[J].长江科学院院报,2018,35(1):57
[21]MCCUEN R H,LEAHY R B,JOHNSON P A.Problems with logarithmic transformations in regression[J].Journal of Hydraulic Engineering,1990,116(3):414
[2]芮孝芳,蒋成煜.流域水文与地貌特征关系研究的回顾与展望[J].水科学进展,2010,21(4):444
[3]叶守泽.美国无资料地区洪水频率计算的现状和动向[J].水文,1983(2):57
[4]熊立华,郭生练,王才君.国外区域洪水频率分析方法研究进展[J].水科学进展,2004,15(2):261
[5]DAWDY D R,GRIFFIS V W,GUPTA V K.Regional flood-frequency analysis:how we got here and where we are going?[J].Journal of Hydrologic Engineering,2012,17(9):953
[6]郭生练,刘章君,熊立华.设计洪水计算方法研究进展与评价[J].水利学报,2016,47(3):302
[7]张尚义,阳妍,邵知宇,等.美国洪水风险地图编制技术分析及对我国的启示[J].中国给水排水,2017,33(21):124
[8]宫兴龙,付强,王敏,等.洪峰流量与流域面积的幂函数研究[J].广西大学学报(自然科学版),2014,39(2):253
[9]许文涛,张平仓,任斐鹏,等.金沙江下游地区山洪灾害防治非工程措施适宜性评价[J].中国水利,2016(3):50
[10]朱秀迪,王志刚,任斐鹏,等.西南岩溶区小流域划分与水文特征分析[J].中国水土保持,2017(2):25
[11]周芬,郭生练,方彬,等.区域回归法对无资料地区设计洪水的估算[J].水力发电,2004,30(7):10
[12]刘昌明,白鹏,巩同梁,等.西藏稀缺资料地区洪峰流量推求[J].南水北调与水利科技,2013,11(1):1
[13]刘昌明,白鹏,王中根,等.稀缺资料流域水文计算若干研究:以青藏高原为例[J].水利学报,2016,47(3):272
[14]OGDEN F L,DAWDY D R.Peak discharge scaling in small Hortonian watershed[J].Journal of Hydrologic Engineering,2003,8(2):64
[15]EASH D A,BARNES K K,VEILLEUX A G.Methods for estimating annual exceedance-probability discharges for streams in iowa,based on data through water year 2010,scientific investigations report 2013-5086[R].Reston,VA:U.S.Geological Survey,2013
[16]陈华,何加伟,栗飞,等.湘江流域区域洪水频率分析计算[J].水资源研究,2013,2(1):20
[17]宋斌.阿坝州岷江及大渡河流域洪峰流量与流域面积关系指数的初步分析[J].科技与企业,2014(5):123
[18]AYALEW T B,KRAJEWSKI W F,MANTILLA R.Analyzing the effects of excess rainfall properties on the scaling structure of peak discharges:Insights from a mesoscale river basin[J].Water Resources Research,2015,51(6):3900
[19]王春华.九寨沟流域设计洪峰流量与面积关系指数的研究[J].陕西水利,2018(5):59
[20]幸新涪,周火明,秦维,等.基于流量-面积比值的小流域设计洪水计算方法对比研究[J].长江科学院院报,2018,35(1):57
[21]MCCUEN R H,LEAHY R B,JOHNSON P A.Problems with logarithmic transformations in regression[J].Journal of Hydraulic Engineering,1990,116(3):414