以洪水分期为条件的管运洪水直接推求法
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摘要
管运洪水是水库工程运用管理时所考虑的一种洪水,事关工程防洪安全和经济效益。当前推求管运洪水的途径分为2类:第1类是以Copula函数为基础的途径,第2类是以全概率原理为基础的途径。作者探讨了第2类途径中的直接法。将洪水资料分为充足、相对充足和不足3种情况,充足情况为主汛期的年最大洪水样本容量为30年以上,而前汛期和后汛期的样本容量分别为20年以上;相对充足情况为主汛期的年最大洪水样本容量为30年以上,而前汛期和后汛期的样本容量之和为20年以上;不足3种情况为主汛期的年最大洪水样本容量为30年以上,而前汛期和后汛期的样本容量之和少于20年。基于3种资料情况,提出了管运洪水计算的全概率直接推求方法。资料充足情况下,根据全概率公式直接采用频率分析推求管运洪水,提出了直接利用数学期望公式计算经验频率的思路;资料相对充足情况下,采用前汛期和后汛期的样本合并手段基于全概率公式采用频率分析推求管运洪水;资料不足情况下,提出了反算手段,建立了基于全概率公式的管运洪水推求方法。以多个流域洪峰流量序列为例对不同资料情况的管运洪水进行了推求,给出了各流域管运洪水计算成果,并与Copula函数法计算成果进行了对比。研究表明,以全概率原理为基础的管运洪水直接推求途径思路清晰,结果合理,因此建议途径是可行的,具有优势。
The manage-flood is very important for flood control safety and economic effectiveness of reservoir engineering. There are two approaches which can be used to calculate the manage-flood at present, i.e., one is based on Copula functions, and the other is based on the principle of total probability. The latter can be divided into direct method and indirect method. The direct method based on the principle of total probability is explored in this article. The flood data for calculation of manage-flood have been divided into three condition:Sufficient data condition, relatively sufficient data condition and insufficient data condition. For sufficient data conditions, the length of flood data series in main flood season is greater than 30 years and the length of flood data series in pre-main flood season and post-main flood season is no less than 20 years, respectively;For relatively sufficient data condition, the length of flood data series in main flood season is greater than 30 years and the length of flood data series in non-main flood season is no less than 20 years; For insufficient data condition, the length of flood data series in main flood season is greater than 30 years and the length of flood data series in non-main flood season is less than 20 years. The calculating methods of manage-flood for three flood data conditions have been presented based on the principle of total probability in this paper. For sufficient data condition, the mathematical expect formula of total probability has been adopted with frequency analysis; for relatively sufficient data condition, the mathematical expect formula of total probability with combined data in non-main flood season was applied; for insufficient data condition, the back calculation approach was presented, and the formula of manage-flood based on the principle of total probability has been suggested. The case studies for calculating of manage-flood in different flood data conditions have been given for different basins. The comparison of the suggested method to the method of Copula function has been discussed. The results have showed that the suggested method is better than the method of Copula function,and the designed value of manage-flood is reasonable.
The manage-flood is very important for flood control safety and economic effectiveness of reservoir engineering. There are two approaches which can be used to calculate the manage-flood at present, i.e., one is based on Copula functions, and the other is based on the principle of total probability. The latter can be divided into direct method and indirect method. The direct method based on the principle of total probability is explored in this article. The flood data for calculation of manage-flood have been divided into three condition:Sufficient data condition, relatively sufficient data condition and insufficient data condition. For sufficient data conditions, the length of flood data series in main flood season is greater than 30 years and the length of flood data series in pre-main flood season and post-main flood season is no less than 20 years, respectively;For relatively sufficient data condition, the length of flood data series in main flood season is greater than 30 years and the length of flood data series in non-main flood season is no less than 20 years; For insufficient data condition, the length of flood data series in main flood season is greater than 30 years and the length of flood data series in non-main flood season is less than 20 years. The calculating methods of manage-flood for three flood data conditions have been presented based on the principle of total probability in this paper. For sufficient data condition, the mathematical expect formula of total probability has been adopted with frequency analysis; for relatively sufficient data condition, the mathematical expect formula of total probability with combined data in non-main flood season was applied; for insufficient data condition, the back calculation approach was presented, and the formula of manage-flood based on the principle of total probability has been suggested. The case studies for calculating of manage-flood in different flood data conditions have been given for different basins. The comparison of the suggested method to the method of Copula function has been discussed. The results have showed that the suggested method is better than the method of Copula function,and the designed value of manage-flood is reasonable.
引文
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[3]Liu Pan,Guo Shenglian,Yan Baowei,et al.Supplementary of relationship between seasonal flood frequency and flood control standard[J].Journal of Hydroelectric Engineering,2011,30(1):187-192.[刘攀,郭生练,闫宝伟,等.再论分析设计洪水频率与防洪标准的关系[J].水力发电学报,2011,30(1):187-192.]
[4]Zhang Na,Guo Shenglian,Yan Baowei,et al.Seasonal design flood based on Copula function[J].Journal of China Hydrology,2008,28(5):28-32.[张娜,郭生练,闫宝伟,等.Copula函数在分期设计洪水中的应用研究[J].水文,2008,28(5):28-32.]
[5]Zhang Na,Guo Shenglian,Liu Pan,et al.Seasonal design floods and flood control water levels based on Copula[J].Journal of Wuhan University(Engineering Science),2008,41(6):33-36.[张娜,郭生练,刘攀,等.基于Copula函数法推求分期设计洪水和汛限水位[J].武汉大学学报(工学版),2008,41(6):33-36.]
[6]Chen Lu,Guo Shenglian,Yan Baowei,et al.A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence[J].Hydrological Sciences Journal,2010,55(8):1264-1280.
[7]陈璐.Copula函数理论在多变量水文分析计算中的应用研究[M].武汉:武汉大学出版社,2013.
[8]中华人民共和国水利部.水利水电工程设计洪水计算规范:SL44-2006[S].北京:中国水利水电出版社,2006.
[9]国家技术监督局,中华人民共和国住房和城乡建设部.防洪标准:GB50201-2014[S].北京:中国计划出版社,2014.
[10]中华人民共和国水利部.水利水电工程等级划分及洪水标准:SL252-2017[S].北京:中国水利水电出版社,2017.
[11]Song Songbai,Jin Juliang.Research on the calculation principle and method of the return period of univariate independent and identically distributed hydrological event[J].Journal of North China University of Water Resources and Electric Power,2017,38(4):43-46.[宋松柏,金菊良.单变量独立同分布水文事件重现期的计算原理与方法[J].华北水利水电大学学报(自然科学版),2017,38(4):43-46.]
[12]盛骤,谢式千,潘承毅.概率论与数理统计[M].北京:高等教育出版社,2008.
[13]水利水电规划设计总院.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.
[14]詹道江,徐向阳,陈元芳,等.工程水文学[M].北京:中国水利水电出版社,2010.
[15]Li Shenqi.The preliminary study of manage-flood[D].Chengdu:Sichuan University,2016.[李深奇.管运洪水的初步研究[D].成都:四川大学,2016.]