Analysis of runoff and sediment characteristics of Datong Station based on Copula function
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摘要: 长江口受人类活动影响较为强烈,其水沙序列一致性遭到破坏。以大通站1965—2019年逐月径流量和来沙量资料为基础,采用滑动窗口算法结合Copula理论的方法,研究长江口来水来沙变化特征及丰枯一致性问题,并分析水沙联合分布模型边缘函数选取不确定性问题。结果表明:(1)受人类活动的影响,大通站水沙组合在1965—2019年间均呈减少趋势,并且在1979和2000年发生突变,水沙序列1965—1979年和1980—2000年阶段最优函数模型均为Clayton模型,2001—2019年则为Frank模型;(2)大通水文站3个阶段水沙序列同步频率分别是84.52%、84.40%和83.20%,远大于丰枯异步频率,揭示了长江上游来水来沙条件具有较强的一致性;(3)PE3-PE3边缘分布组合的95%置信区间小于PE3-GPD组合,说明采用PE3-PE3组合可以减少函数选取的不确定性。通过探讨大通站来水来沙联合变化特征,可为长江口水域水资源管理、河道整治等工作提供参考。Abstract: The Yangtze River estuary has been strongly influenced by human activities, and the consistency of its runoff-sediment sequence has been damaged. Based on the monthly runoff and sediment data from 1965 to 2019 at Datong Station, a sliding window algorithm based on Copula is applied to investigate the variation characteristics of runoff and sediment in the Yangtze estuary and the consistency of its abundance-depletion, and the uncertainty of the marginal distribution selection for the joint runoff-sediment distribution model is also analyzed. The results show that: (1) The runoff-sediment combination at Datong Station shows a decreasing trend from 1965 to 2019 due to human activities, and changes abruptly in 1979 and 2000. The optimal function models for the runoff-sediment series in 1965—1979 and 1980—2000 are Clayton, while 2001—2019 is best modeled by Frank; (2) the synchronous frequencies of the runoff-sediment series in the three periods are 84.52%, 84.40% and 83.20% respectively, which are much greater than the asynchronous frequencies of abundance-depletion, revealing the strong consistency of the incoming runoff-sediment in the upper reaches of the Yangtze River; (3) the 95% confidence interval of the PE3-PE3 marginal distribution combination is smaller than that of the PE3-GPD combination, indicating that the PE3-PE3 combination would reduce the uncertainty of function selection. By exploring the joint variation characteristics of incoming runoff and sediment at Datong station, this study provides a reference for water resources management and river regulation in the Yangtze estuary.
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表 1 4种不同的Copula 函数
Table 1. Four different Copula functions
类型 函数表达式 Clayton $C\left(u,v;\theta \right)={({u}^{-\theta }+{v}^{-\theta }-1)}^{(-1/\theta )},\theta \in (0,\infty )$ Frank $C\left(u,v;\theta \right)=-\dfrac{1}{\theta }\mathrm{ln}\left\{1+\dfrac{\left[\mathrm{exp}\left(-\theta u\right)-1\right]\left[\mathrm{exp}\left(-\theta v\right)-1\right]}{\mathrm{exp}\left(-\theta \right)-1}\right\},\theta \in R$ G-H $C\left(u,v;\theta \right)=\mathrm{exp}\left\{ {-[{(-\mathrm{l}\mathrm{n}u)}^{\theta }+{(-\mathrm{l}\mathrm{n}v)}^{\theta }]}^{\frac{1}{\theta } }\right\},\theta \in [1,\infty ]$ Gaussian $C\left(u,v;\theta \right)={\displaystyle\int }_{-\infty }^{ {{\textit{ø}} }^{-1}\left(u\right)}{\displaystyle\int }_{-\infty }^{ {{\textit{ø}} }^{-1}\left(v\right)}\dfrac{1}{2{\text{π} } \sqrt{1-{\theta }^{2} } }{\rm{exp} }\left[\dfrac{ {x}_{1}^{2}-2\theta {x}_{1}{x}_{2}+{x}_{2}^{2} }{2\left(1-{\theta }^{2}\right)}\right]{\rm {d} }{x}_{1}{ {\rm {d} }x}_{2},\theta \in [-\mathrm{1,1}]$ 注:表中Copula函数参数θ的取值均采用Kendall秩相关系数方法求解。 表 2 水沙关系突变前后特征值分析
Table 2. Analysis of eigenvalues before and after the mutation of runoff-sediment relationship
设计重现期/a 月径流量/亿m3 月输沙量/万t 1965—1979年 1980—2000年 2001—2019年 1965—1979年 1980—2000年 2001—2019年 2 677.72 720.23 657.74 2652.03 2389.41 837.82 5 927.69 1048.81 986.92 6068.86 5241.05 1962.10 10 1082.74 1255.17 1201.09 8668.20 7215.87 2825.71 20 1224.00 1444.40 1401.03 11273.70 9046.30 3700.80 50 1397.71 1678.36 1651.86 14723.83 11262.24 4875.47 100 1522.38 1846.96 1834.63 17336.35 12796.82 5777.79 表 3 水沙边缘分布选取
Table 3. Selection of marginal distribution of runoff and sediment
阶 段 变量 评价准则 PE3 GPD GLO 1965—1979年 径流 AIC −299.285 −249.523 −297.387 RMSE 0.428 0.492 0.431 来沙量 AIC −292.955 −280.809 −290.845 RMSE 0.436 0.451 0.438 1980—2000年 径流 AIC −444.970 −289.279 −417.867 RMSE 0.409 0.557 0.431 来沙量 AIC −405.640 −463.132 −445.233 RMSE 0.442 0.394 0.409 2001—2019年 径流 AIC −409.383 −252.618 −371.375 RMSE 0.402 0.567 0.437 来沙量 AIC −368.871 −463.444 −444.361 RMSE 0.440 0.357 0.373 表 4 水沙联合模型选取
Table 4. Selection of runoff-sediment joint model
阶 段 Copula函数 参数θ 欧氏距离 1965—1979年 Clayton 8.151 0.0457 Frank 18.497 0.0692 G-H 5.076 0.0666 Gaussian 0.953 0.3157 1980—2000年 Clayton 8.066 0.0456 Frank 18.324 0.0573 G-H 5.033 0.0644 Gaussian 0.952 0.2516 2001—2019年 Clayton 7.066 0.0745 Frank 16.302 0.0526 G-H 4.533 0.0580 Gaussian 0.941 0.4963 表 5 大通水文站水沙丰枯遭遇计算
Table 5. Calculation of flood and drought of runoff and sediment at Datong Hydrological Station
类型 组合 1965—1979年 1980—2000年 2001—2019年 水沙异步
频率/%X≥${x_{ {p_{\rm{f} } } } },\;{y_{ {p_{\rm{k} } } } }$<Y<${y_{ {p_{\rm{f} } } } } $ 5.70 5.74 4.20 X≥${x_{ {p_{\rm{f} } } } } $, Y≤${y_{ {p_{\rm{k} } } } } $ 0 0 0 ${x_{ {p_{\rm{k} } } } } $<X<${x_{ {p_{\rm{f} } } } } $, Y≥${y_{ {p_{\rm{f} } } } } $ 5.70 5.74 4.20 ${x_{ {p_{\rm{k} } } } } $<X<${x_{ {p_{\rm{f} } } } } $, Y≤${y_{ {p_{\rm{k} } } } } $ 2.04 2.06 4.20 X≤${x_{ {p_{\rm{k} } } } } $, Y≥$ {y_{ {p_{\rm{f} } } } } $ 0 0 0 X≤${x_{ {p_{\rm{k} } } } } $, ${y_{ {p_{\rm{k} } } } } $<Y<${y_{ {p_{\rm{f} } } } } $ 2.04 2.06 4.20 总计 15.48 15.60 16.80 水沙同步
频率/%X≥${x_{ {p_{\rm{f} } } } } $, Y≥$ {y_{ {p_{\rm{f} } } } } $ 19.30 19.26 20.80 ${x_{ {p_{\rm{k} } } } } $<X<${x_{ {p_{\rm{f} } } } } $, ${y_{ {p_{\rm{k} } } } } $<Y<$ {y_{ {p_{\rm{f} } } } } $ 42.26 42.20 41.60 X≤${x_{ {p_{\rm{k} } } } } $, Y≤${y_{ {p_{\rm{k} } } } } $ 22.96 22.94 20.80 总计 84.52 84.40 83.20 表 6 边缘分布选取不确定性评价指标的95%置信区间取值
Table 6. Values of 95% confidence interval of uncertainty evaluation index selected by marginal distribution
阶 段 组合 参数θ 参数
变幅/%置信区间面积
S95% /(亿 m3·万 t)1965—1979年 PE3-PE3 [8.248, 8.379] 1.588 2.643×105 PE3-GPD [8.220, 8.346] 1.533 1.432×106 1980—2000年 PE3-PE3 [8.078, 8.183] 1.300 1.404×105 PE3-GPD [8.082, 8.187] 1.299 1.923×106 2001—2019年 PE3-PE3 [16.288, 16.434] 0.896 4.756×105 PE3-GPD [16.296, 16.442] 0.896 6.983×105 -
[1] 李艺珍, 岳春芳, 曹伟. 基于滑动Copula函数的金沟河流域径流-气温关系变异诊断[J]. 长江科学院院报,2020,37(11):33-39 doi: 10.11988/ckyyb.20190932 LI Yizhen, YUE Chunfang, CAO Wei. Variation diagnosis of runoff-temperature relation in Jingou River basin based on sliding Copula function[J]. Journal of Yangtze River Scientific Research Institute, 2020, 37(11): 33-39. (in Chinese) doi: 10.11988/ckyyb.20190932 [2] 陈广才, 谢平. 水文变异的滑动F识别与检验方法[J]. 水文,2006,26(2):57-60 doi: 10.3969/j.issn.1000-0852.2006.02.014 CHEN Guangcai, XIE Ping. Slide F test of change-point analysis[J]. Journal of China Hydrology, 2006, 26(2): 57-60. (in Chinese) doi: 10.3969/j.issn.1000-0852.2006.02.014 [3] 武连洲, 白涛, 哈燕萍, 等. 水文序列变异对水库调度运行的影响研究[J]. 水资源与水工程学报,2016,27(4):88-92 doi: 10.11705/j.issn.1672-643X.2016.04.16 WU Lianzhou, BAI Tao, HA Yanping, et al. Effect of hydrological sequence variation on operation reservoir[J]. Journal of Water Resources and Water Engineering, 2016, 27(4): 88-92. (in Chinese) doi: 10.11705/j.issn.1672-643X.2016.04.16 [4] 谢平, 陈广才, 雷红富. 基于Hurst系数的水文变异分析方法[J]. 应用基础与工程科学学报,2009,17(1):32-39 doi: 10.3969/j.issn.1005-0930.2009.01.004 XIE Ping, CHEN Guangcai, LEI Hongfu. Hydrological alteration analysis method based on Hurst coefficient[J]. Journal of Basic Science and Engineering, 2009, 17(1): 32-39. (in Chinese) doi: 10.3969/j.issn.1005-0930.2009.01.004 [5] 李彬彬, 谢平, 李析男, 等. 基于Hurst系数与Bartels检验的水文变异联合分析方法[J]. 应用基础与工程科学学报,2014,22(3):481-491 LI Binbin, XIE Ping, LI Xi’nan, et al. Joint analysis method for hydrological variation based on Hurst coefficient and bartels test[J]. Journal of Basic Science and Engineering, 2014, 22(3): 481-491. (in Chinese) [6] 刘丽芳, 王中根, 姜爱华, 等. 近50年济南三川流域降雨-径流关系变化分析[J]. 南水北调与水利科技,2018,16(1):22-27, 56 LIU Lifang, WANG Zhonggen, JIANG Aihua, et al. Analysis of rainfall-runoff relationship variation characteristics in Sanchuan watershed in Jinan city over recent 50 years[J]. South-to-North Water Transfers and Water Science & Technology, 2018, 16(1): 22-27, 56. (in Chinese) [7] 甘富万, 张华国, 黄宇明, 等. 基于二次重现期的桂平航运枢纽水闸设计洪水组合研究[J]. 水文,2020,40(2):48-54 GAN Fuwan, ZHANG Huaguo, HUANG Yuming, et al. Study on design flood combination of Guiping shipping hub sluice based on secondary return period[J]. Journal of China Hydrology, 2020, 40(2): 48-54. (in Chinese) [8] 李艳玲, 畅建霞, 黄强, 等. 基于滑动Copula函数的降水和径流关系变异诊断[J]. 水力发电学报,2014,33(6):20-24, 60 LI Yanling, CHANG Jianxia, HUANG Qiang, et al. Diagnosis of abrupt changes in precipitation and runoff relation based on sliding Copula function[J]. Journal of Hydroelectric Engineering, 2014, 33(6): 20-24, 60. (in Chinese) [9] 郭爱军, 黄强, 畅建霞, 等. 基于Copula函数的泾河流域水沙关系演变特征分析[J]. 自然资源学报,2015,30(4):673-683 doi: 10.11849/zrzyxb.2015.04.013 GUO Aijun, HUANG Qiang, CHANG Jianxia, et al. Variation of relationship between runoff and sediment based on Copula function in the Jinghe River basin[J]. Journal of Natural Resources, 2015, 30(4): 673-683. (in Chinese) doi: 10.11849/zrzyxb.2015.04.013 [10] 何兵, 高凡, 唐小雨, 等. 基于滑动Copula函数的新疆干旱内陆河流水文气象要素变异关系诊断[J]. 水土保持研究,2019,26(1):155-161 HE Bing, GAO Fan, TANG Xiaoyu, et al. Diagnosis of variation of the relationship between hydrological and meteorological elements in arid inland rivers of Xinjiang based on the sliding Copula function[J]. Research of Soil and Water Conservation, 2019, 26(1): 155-161. (in Chinese) [11] SKLAR A. Fonctions de repartition an dimensions et leurs marges[J]. Universite Paris, 1959, 8: 229-231. [12] SALVADORI G, DE MICHELE C, DURANTE F. On the return period and design in a multivariate framework[J]. Hydrology and Earth System Sciences, 2011, 15(11): 3293-3305. doi: 10.5194/hess-15-3293-2011 [13] 赵德招, 刘杰, 程海峰, 等. 长江口深水航道疏浚土处理现状及未来展望[J]. 水利水运工程学报,2013(2):26-32 ZHAO Dezhao, LIU Jie, CHENG Haifeng, et al. Current situation and future prospect of dredged material disposal in the Yangtze estuary deepwater navigation channel[J]. Hydro-Science and Engineering, 2013(2): 26-32. (in Chinese) [14] 刘杰, 程海峰, 韩露, 等. 流域水沙变化和人类活动对长江口河槽演变的影响[J]. 水利水运工程学报,2021(4):1-9 LIU Jie, CHENG Haifeng, HAN Lu, et al. New trends of river channel evolution of the Yangtze River estuary under the influences of inflow and sediment variations and human activities[J]. Hydro-Science and Engineering, 2021(4): 1-9. (in Chinese) [15] 窦希萍, 缴健, 储鏖, 等. 长江口水沙变化与趋势预测[J]. 海洋工程,2020,38(4):2-10 DOU Xiping, JIAO Jian, CHU Ao, et al. Review of hydro-sediment change and tendency in Yangtze estuary[J]. The Ocean Engineering, 2020, 38(4): 2-10. (in Chinese) [16] 武旭同, 王腊春, 李娜. 近60 a来长江干流输沙量变化及原因分析[J]. 长江流域资源与环境,2018,27(1):116-124 doi: 10.11870/cjlyzyyhj201801024 WU Xutong, WANG Lachun, LI Na. Analysis on the change of sediment discharge of the Yangtze River in recent 60 years[J]. Resources and Environment in the Yangtze Basin, 2018, 27(1): 116-124. (in Chinese) doi: 10.11870/cjlyzyyhj201801024 [17] 周念清, 赵露, 沈新平. 基于Copula函数的洞庭湖流域水沙丰枯遭遇频率分析[J]. 地理科学,2014,34(2):242-248 ZHOU Nianqing, ZHAO Lu, SHEN Xinping. Copula-based probability evaluation of rich-poor runoff and sediment encounter in Dongting Lake Basin[J]. Scientia Geographica Sinica, 2014, 34(2): 242-248. (in Chinese) [18] MOU S Y, SHI P, QU S M, et al. Uncertainty analysis of two copula-based conditional regional design flood composition methods: a case study of Huai River, China[J]. Water, 2018, 10(12): 1872. doi: 10.3390/w10121872 -