含零值水文序列频率计算方法研究
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摘要
针对常规水文频率分析方法无法进行含零值水文序列频率计算的问题,研究3种含零值水文序列频率的计算方法。选用Gamma分布,推导极大似然法(ML)、最大熵原理(POME)和概率权重矩法(PWM)非零和含零值序列参数估计公式,研究非零值序列和含零值序列参数转换关系和设计值计算。应用蒙特卡洛试验,研究零值序列长度对参数估计方法不同重现期设计值的影响。以陕西省6个测站枯水期1月份月降水资料为例,研究不同参数估计方法的适用性,计算高尾部设计值的累积误差平方和,进行拟合优度评价。结果表明:最大熵原理和极大似然法对含零值降水序列均具有较好的拟合效果,研究结果可为含零值水文序列频率计算提供依据。
This paper presents a study on frequency analysis method of hydrological samples with zero values, focusing on the derivation of parameter estimation formulas of Gamma distribution for the nonzero values and full series using maximum likelihood method(ML), the principle of maximum entropy(POME), and probability weight moment method(PWM). We also discuss the relationship between nonzero values and full series and the calculation of design values of hydrological samples. Monte-Carlo simulations are conducted to examine the influence of different sample lengths on the design values calculated using different methods of parameter estimation. Applicability of these methods are evaluated through a case study of six monthly precipitation samples observed in Shaanxi, including the effect and calculation error of fitting large sample events. The results indicate that both the principle of maximum entropy and maximum likelihood method have a good fitting effect, forming a theoretical basis for frequency analysis of the hydrological samples with zero values.
This paper presents a study on frequency analysis method of hydrological samples with zero values, focusing on the derivation of parameter estimation formulas of Gamma distribution for the nonzero values and full series using maximum likelihood method(ML), the principle of maximum entropy(POME), and probability weight moment method(PWM). We also discuss the relationship between nonzero values and full series and the calculation of design values of hydrological samples. Monte-Carlo simulations are conducted to examine the influence of different sample lengths on the design values calculated using different methods of parameter estimation. Applicability of these methods are evaluated through a case study of six monthly precipitation samples observed in Shaanxi, including the effect and calculation error of fitting large sample events. The results indicate that both the principle of maximum entropy and maximum likelihood method have a good fitting effect, forming a theoretical basis for frequency analysis of the hydrological samples with zero values.
引文
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[2]Wang S X,Singh V P.Frequency estimation for hydrological samples with zero values[J].Journal of Water Resources Planning and Management,1995,121(1):98-108.
[3]Jennings M E,Benson M A.Frequency curves for annual flood series with some zero events or incomplete data[J].Water Resources Research,1969,5(1):276-280.
[4]金光炎.水文系列中有几项为零时的频率计算[J].水利水电技术,1962(10):39-42.JIN Guangyan.Frequency analysis of hydrological samples with several zero values[J].Water Resources and Hydropower Engineering,1962(10):39-42.(in Chinese)
[5]毛赛珠.具有零项系列的中值适线法[J].水文,1985(6):27-29.MAO Saizhu.Plotting position fitting curves for hydrological samples with zero values[J].Journal of China Hydrology,1985(6):27-29.(in Chinese)
[6]杨力行.Ⅱ型乘法分布在干旱资料含零系列统计分析中的应用[J].水文,1992(3):21-24.YANG Lixing.Applying power type II to statistical analysis for hydrological samples with zero values in arid region[J].Journal of China Hydrology,1992(3):21-24.(in Chinese)
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[8]张良,刘鑫杨.含零序列水文频率计算方法在张北水文站的应用探讨[J].海河水利,2017(1):36-38.ZHANG Liang,LIU Xinyang.Discussion on application of hydrologic frequency calculation method with zero sequence in Zhangbei hydrologic station[J].Haihe Water Resources,2017(1):36-38.(in Chinese)
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[10]宋松柏,康艳.含零值水文序列频率的计算原理与应用[J].水文,2012,32(5):22-26.SONG Songbai,KANG Yan.Principle and application of hydrological series frequency analysis with zero values[J].Journal of China Hydrology,2012,32(5):22-26.(in Chinese)
[11]Weglarczyk S,Strupczewski W G,Singh V P.Threeparameter discontinuous distributions for hydrological samples with zero values[J].Hydrological Processes,2005,19(15):2899-2914.
[12]Strupczewski W G,Weglarczyk S,Singh V P.Impulse response of the kinematic diffusion model as a probability distribution of hydrologic samples with zero values[J].Journal of Hydrology,2003,270(3-4):328-351.
[13]濮晓龙.概率论与数理统计教程[M].北京:高等教育出版社,2011.PU Xiaolong.Probability theory and mathematical statistics[M].Beijing:Higher Education Press,2011.(in Chinese)
[14]Zhang L,Singh V P.Frequency analysis of flood damage[J].Journal of Hydrologic Engineering,2005,10(2):100-109.
[15]张元林.积分变换[M].4版.北京:高等教育出版社,2003.ZHANG Yuanlin.Integral transformation[M].4th ed.Beijing:Higher Education Press,2003.(in Chinese)
[16]陈元芳,黄振平.水文统计学[M].北京:中国水利水电出版社,2011.CHEN Yuanfang,HUANG Zhenping.Hydrological statistics[M].Beijing:Water Resources and Hydropower Press,2011.(in Chinese)
[17]Rao A R,Hamed K H.Flood frequency analysis[M].Boca Raton:CRC Press,2000:143.
[18]Singh V P,Singh K.Derivation of the gamma distribution by using the principle of maximum entropy[J].Water Resources Bulletin,1985,21(6):941-952.
[19]Singh V P,Singh K.Derivation of the Pearson type(PT)III distribution by using the principle of maximum entropy(POME)[J].Journal of Hydrology,1985,80(3-4):197-214.
[20]Greenwood J A,Landwehr J M,Matalas N C,et al.Probability weighted moments:definition and relation to parameters of several distributions expressable in inverse form[J].Water Resources Research,1979,15(5):1049-1054.
[21]Phiena H N,Nguyenb V.Derivation of the Pearson type(PT)III distribution by using the principle of maximum entropy(POME)—comment[J].Journal of Hydrology,1987,90(3-4):351-355.
[2]Wang S X,Singh V P.Frequency estimation for hydrological samples with zero values[J].Journal of Water Resources Planning and Management,1995,121(1):98-108.
[3]Jennings M E,Benson M A.Frequency curves for annual flood series with some zero events or incomplete data[J].Water Resources Research,1969,5(1):276-280.
[4]金光炎.水文系列中有几项为零时的频率计算[J].水利水电技术,1962(10):39-42.JIN Guangyan.Frequency analysis of hydrological samples with several zero values[J].Water Resources and Hydropower Engineering,1962(10):39-42.(in Chinese)
[5]毛赛珠.具有零项系列的中值适线法[J].水文,1985(6):27-29.MAO Saizhu.Plotting position fitting curves for hydrological samples with zero values[J].Journal of China Hydrology,1985(6):27-29.(in Chinese)
[6]杨力行.Ⅱ型乘法分布在干旱资料含零系列统计分析中的应用[J].水文,1992(3):21-24.YANG Lixing.Applying power type II to statistical analysis for hydrological samples with zero values in arid region[J].Journal of China Hydrology,1992(3):21-24.(in Chinese)
[7]水利部长江水利委员会水文局.水利水电工程设计洪水计算手册[M].北京:水利电力出版社,1995.Hydrological Bureau of the Changjiang Water Resources Commission of Ministry of Water Resources.Flood calculation manual of water conservancy and hydropower engineering design[M].Beijing:Water Resources and Electricity Press,1995.(in Chinese)
[8]张良,刘鑫杨.含零序列水文频率计算方法在张北水文站的应用探讨[J].海河水利,2017(1):36-38.ZHANG Liang,LIU Xinyang.Discussion on application of hydrologic frequency calculation method with zero sequence in Zhangbei hydrologic station[J].Haihe Water Resources,2017(1):36-38.(in Chinese)
[9]Woo M K,Wu K.Fitting annual floods with zero-flows[J].Canadian Water Resources Journal,1989,14(2):10-16.
[10]宋松柏,康艳.含零值水文序列频率的计算原理与应用[J].水文,2012,32(5):22-26.SONG Songbai,KANG Yan.Principle and application of hydrological series frequency analysis with zero values[J].Journal of China Hydrology,2012,32(5):22-26.(in Chinese)
[11]Weglarczyk S,Strupczewski W G,Singh V P.Threeparameter discontinuous distributions for hydrological samples with zero values[J].Hydrological Processes,2005,19(15):2899-2914.
[12]Strupczewski W G,Weglarczyk S,Singh V P.Impulse response of the kinematic diffusion model as a probability distribution of hydrologic samples with zero values[J].Journal of Hydrology,2003,270(3-4):328-351.
[13]濮晓龙.概率论与数理统计教程[M].北京:高等教育出版社,2011.PU Xiaolong.Probability theory and mathematical statistics[M].Beijing:Higher Education Press,2011.(in Chinese)
[14]Zhang L,Singh V P.Frequency analysis of flood damage[J].Journal of Hydrologic Engineering,2005,10(2):100-109.
[15]张元林.积分变换[M].4版.北京:高等教育出版社,2003.ZHANG Yuanlin.Integral transformation[M].4th ed.Beijing:Higher Education Press,2003.(in Chinese)
[16]陈元芳,黄振平.水文统计学[M].北京:中国水利水电出版社,2011.CHEN Yuanfang,HUANG Zhenping.Hydrological statistics[M].Beijing:Water Resources and Hydropower Press,2011.(in Chinese)
[17]Rao A R,Hamed K H.Flood frequency analysis[M].Boca Raton:CRC Press,2000:143.
[18]Singh V P,Singh K.Derivation of the gamma distribution by using the principle of maximum entropy[J].Water Resources Bulletin,1985,21(6):941-952.
[19]Singh V P,Singh K.Derivation of the Pearson type(PT)III distribution by using the principle of maximum entropy(POME)[J].Journal of Hydrology,1985,80(3-4):197-214.
[20]Greenwood J A,Landwehr J M,Matalas N C,et al.Probability weighted moments:definition and relation to parameters of several distributions expressable in inverse form[J].Water Resources Research,1979,15(5):1049-1054.
[21]Phiena H N,Nguyenb V.Derivation of the Pearson type(PT)III distribution by using the principle of maximum entropy(POME)—comment[J].Journal of Hydrology,1987,90(3-4):351-355.