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Study on Flood Season Segmentation of Dongting Lake Basin
DOI: 10.12677/JWRR.2022.114040, PDF, HTML, XML, 下载: 81  浏览: 128  国家科技经费支持

Abstract: Flood season segmentation is the basis for estimating seasonal design flood and seasonal flood limit water levels. The cause analysis method and five mathematical statistics methods were applied to the flood season segmentation of Xiangjiang, Zijiang, Yuanjiang and Lishui rivers in the Dongting Lake basin. The results illustrated that the flood season (1 May~31 October)could be segmented into the early flood season, the main flood season and the late flood season. The main flood seasons of Xiangjiang, Zijiang, Yuan- jiang and Lishui rivers are 15 June~23 July, 14 June~28 July, 20 June~2 August and 22 June~9 August, respectively. These results are reasonably characterized the flood seasonality and could provide support for exploiting the potential of flood water resources utilizing.

1. 引言

2. 研究方法

2.1. 变点分析法

$\begin{array}{cc}{X}_{i}={\mu }_{i}+{e}_{i},& i=1,2,\cdots ,n\end{array}$ (1)

${\mu }_{1}={\mu }_{2}=\cdots ={\mu }_{{m}_{1}-1}={b}_{1},{\mu }_{{m}_{1}}={\mu }_{{m}_{1}+1}=\cdots ={\mu }_{{m}_{2}-1}={b}_{2},\cdots ,{\mu }_{{m}_{q}}={\mu }_{{m}_{q}+1}=\cdots ={\mu }_{n}={b}_{q+1}$ (2)

${y}_{j}=\frac{{x}_{m}{}_{{}_{j-1}}+{x}_{{m}_{j-2}}+\cdots +{x}_{{m}_{j}}{}_{-1}}{{m}_{j}-{m}_{j-1}}$ (3)

$\begin{array}{cc}{W}_{j}=\underset{i={m}_{j-1}}{\overset{{m}_{j}-1}{\sum }}{\left({x}_{i}-{y}_{j}\right)}^{2}+\underset{i={m}_{j}}{\overset{{m}_{j+1}-1}{\sum }}{\left({x}_{i}-{y}_{j+1}\right)}^{2},& j=1,2,\cdots ,q\end{array}$ (4)

${\sigma }^{2}=\frac{{W}_{j}}{N-2\mathrm{log}\mathrm{log}N-\mathrm{log}\mathrm{log}\mathrm{log}N-2.4}$ (5)

${C}_{\alpha }={\sigma }^{2}\left(2\mathrm{log}\mathrm{log}N+\mathrm{log}\mathrm{log}\mathrm{log}N-\mathrm{log}\pi -2\mathrm{log}\left(-0.5\mathrm{log}\left(1-\alpha \right)\right)\right)$ (6)

$T=\underset{i={m}_{j-1}}{\overset{{m}_{j+1}-1}{\sum }}{\left({x}_{i}-\stackrel{¯}{X}\right)}^{2}$ (7)

$T-{W}_{j}>{C}_{\alpha }$，则认为在显著性水平 $\alpha$ 上，变点 ${m}_{j}$ 存在。

$L=\underset{i=1}{\overset{{m}_{1}-1}{\prod }}{C}_{n}^{{x}_{i}}{p}_{1}^{{x}_{i}}{\left(1-{p}_{1}\right)}^{n-{x}_{i}}\underset{i={m}_{1}}{\overset{{m}_{2}-1}{\prod }}{C}_{n}^{{x}_{i}}{p}_{2}^{{x}_{i}}{\left(1-{p}_{2}\right)}^{n-{x}_{i}}\cdots \underset{i={m}_{q}}{\overset{{m}_{q+1}-1}{\prod }}{C}_{n}^{{x}_{i}}{p}_{q+1}^{{x}_{i}}{\left(1-{p}_{q+1}\right)}^{n-{x}_{i}}$ (8)

${p}_{i}=\frac{1}{n\left({m}_{i}-{m}_{i-1}\right)}\underset{j={m}_{i-1}}{\overset{{m}_{i}-1}{\sum }}{x}_{j}$ (9)

${L}^{\prime }=\underset{i=1}{\overset{q+1}{\sum }}\underset{j={m}_{i-1}}{\overset{{m}_{i}-1}{\sum }}{x}_{j}\mathrm{log}{p}_{i}+\underset{i=1}{\overset{q+1}{\sum }}\underset{j={m}_{i-1}}{\overset{{m}_{i}-1}{\sum }}\left(n-{x}_{j}\right)\mathrm{log}\left(1-{p}_{i}\right)$ (10)

2.2. 有序聚类法

${S}_{j}=\underset{i={m}_{j}}{\overset{{m}_{j+1}-1}{\sum }}{\left({X}_{i}-{\stackrel{¯}{X}}_{j}\right)}^{2}$ (11)

${S}^{*}=\underset{j=1}{\overset{k}{\sum }}{S}_{j}$ (12)

2.3. 信息熵法

$\begin{array}{cc}{S}_{j}=\underset{i={m}_{j}}{\overset{{m}_{j+1}-1}{\sum }}{X}_{i},& j=1,2,\cdots ,k\end{array}$ (13)

$\begin{array}{cc}{P}_{i}=\frac{{X}_{i}}{{S}_{j}},& i={m}_{j},{m}_{j}+1,\cdots ,{m}_{j+1}-1\end{array}$ (14)

${H}_{j}=-\underset{i={m}_{j}}{\overset{{m}_{j+1}-1}{\sum }}{P}_{i}\mathrm{log}{P}_{i}$ (15)

${P}_{{m}_{j}}={P}_{{m}_{j}+1}=\cdots ={P}_{{m}_{j+1}-1}⇒{H}_{\mathrm{max},}{}_{j}=\mathrm{log}\left({m}_{j+1}-{m}_{j}\right)$ (16)

${U}_{j}=\frac{{H}_{j}}{{H}_{\mathrm{max},}{}_{j}}$ (17)

${U}_{j}$ 描述了分期内流(洪)量时间序列的均匀程度， ${U}_{j}$ 越大，代表该分期的均匀程度越高 [13]。如果某一分期持续时间更长，则该分期对汛期整体均匀程度的影响更大 [13]，因此以分期长度为权重计算总体的加权均匀度：

$U=\frac{{m}_{1}}{n}{U}_{1}+\frac{{m}_{2}-{m}_{1}}{n}{U}_{2}+\cdots +\frac{n-{m}_{j-1}}{n}{U}_{k}$ (18)

2.4. 圆形分布法

${\alpha }_{i}=\frac{2\pi {D}_{i}}{T}$ (19)

$\left({x}_{i},{y}_{i}\right)=\left\{\begin{array}{ll}\left(\mathrm{cos}{\alpha }_{i},\mathrm{sin}{\alpha }_{i}\right)\hfill & 不考虑洪水量级\hfill \\ \left({q}_{i}\mathrm{cos}{\alpha }_{i},{q}_{i}\mathrm{sin}{\alpha }_{i}\right)\hfill & 考虑洪水量级\hfill \end{array}$ (20)

$\stackrel{¯}{\alpha }=\left\{\begin{array}{ll}\mathrm{arctan}\frac{\stackrel{¯}{y}}{\stackrel{¯}{x}}\hfill & x>0\hfill \\ 2\pi +\mathrm{arctan}\frac{\stackrel{¯}{y}}{\stackrel{¯}{x}}\hfill & x<0\hfill \end{array}$ (21)

$r=\left\{\begin{array}{ll}\sqrt{{\stackrel{¯}{x}}^{2}+{\stackrel{¯}{y}}^{2}}\hfill & 不考虑洪水量级\hfill \\ \frac{\sqrt{{\stackrel{¯}{x}}^{2}+{\stackrel{¯}{y}}^{2}}}{Q}\hfill & 考虑洪水量级\hfill \end{array}$ (22)

$s=\sqrt{-2\mathrm{ln}r}$ (23)

${D}_{s}=\frac{\stackrel{¯}{\alpha }-s}{2\pi }T$ (24)

${D}_{e}=\frac{\stackrel{¯}{\alpha }+s}{2\pi }T$ (25)

2.5. 相对频率法

$\begin{array}{cc}R{F}_{i}=\frac{{b}_{i}}{n},& i=1,2,\cdots ,T\end{array}$ (26)

$\begin{array}{cc}R{F}_{i}=R{{F}^{\prime }}_{i}\cdot \frac{s}{{s}^{\prime }},& i=1,2,\cdots ,T\end{array}$ (27)

3. 研究区域

3.1. 流域概况

Figure 1. Sketch map of the Dongting Lake basin and hydrologic stations

Table 1. Basic information of the Four Rivers basin and main reservoirs

3.2. 取样方法

Table 2. The sampled series of each segmentation method

4. 结果分析

4.1. 天气成因分析

Figure 2. Monthly average of Western Pacific subtropical high ridge line index

4.2. 汛期洪水分布与径流分析

4.2.1. 汛期洪水年内分布分析

Table 3. Flood distribution of Taoyuan station in Yuanjiang River during flood season from 1951 to 2020

4.2.2. 汛期径流统计分析

Figure 3. Daily maximum peak flow series of flood season in the Four Rivers basin

(a) 1988~2020年湘江(湘潭站) AM洪峰流量散点图 (b) 1951~2020年资江(桃江站) AM洪峰流量散点图(c) 1951~2020年沅江(桃源站) AM洪峰流量散点图 (d) 1950~2020年澧水(石门站) AM洪峰流量散点图

Figure 4. Scatter diagrams of AM peak flows in the Four Rivers basin

Table 4. Flood season segmentation based on annual flood distribution and runoff analysis

4.3. 汛期分期结果分析

Table 5. Flood season segmentation in the Four Rivers basin of Dongting Lake

(a) 湘江流域(湘潭站)(b) 资江流域(桃江站)(c) 沅江流域(桃源站) (d) 澧水流域(石门站)

Figure 5. Flood season segmentation based on circular distribution method

Table 6. Flood season segmentation schemes of the Four Rivers basin

5. 结语

 [1] 谢康, 张晓菁, 卫晓婧, 等. 洞庭湖流域未控区间水量平衡分析[J]. 水资源研究, 2019, 8(1): 44-55. XIE Kang, ZHANG Xiaojing, WEI Xiaojing, et al. Water balance analysis in the uncontrolled area of Dongting Lake basin. Journal of Water Resources Research, 2019, 8(1): 44-55. (in Chinese) [2] 胡毅鸿, 李景保. 1951-2015年洞庭湖区旱涝演变及典型年份旱涝急转特征分析[J]. 农业工程学报, 2017, 33(7): 107-115. HU Yihong, LI Jingbao. Analysis on evolution of drought-flood and its abrupt alternation in typical year from 1951 to 2015 in Dongting Lake area. Transactions of the Chinese Society of Agricultural Engineering, 2017, 33(7): 107-115. (in Chinese) [3] 刘培亮, 毛德华, 周慧, 等. 1990-2013年湖南四水入洞庭湖汛期径流量的变化规律[J]. 水资源保护, 2015, 31(4): 52-61. LIU Peiliang, MAO Dehua, ZHOU Hui, et al. Variation law of runoff in flood seasons into Dongting Lake from Four Rivers in Hunan Province during 1990-2013. Water Resources Protection, 2015, 31(4): 52-61. (in Chinese) [4] 余玉聪, 李雯晴, 刘招, 等. 金沙江下游梯级水库汛期分期及汛限水位合理性研究[J]. 长江科学院院报, 2020, 37(9): 39-44. YU Yucong, LI Wenqing, LIU Zhao, et al. Rational flood season staging and limit flood levels of cascade reservoirs in downstream Jinsha River. Journal of Yangtze River Scientific Research Institute, 2020, 37(9): 39-44. (in Chinese) [5] 蒋海艳, 莫崇勋, 韦逗逗, 等. 水库汛期分期研究综述[J]. 水利水电科技进展, 2012, 32(3): 75-80. JIANG Haiyan, MO Chongxun, WEI Doudou, et al. Review of reservoir flood season staging. Advances in Science and Technology of Water Resources, 2012, 32(3): 75-80. (in Chinese) [6] 李妍清, 郭生练, 周研来, 等. 汉江安康水库流域汛期分期研究[J]. 水资源研究, 2013, 2(1): 64-69. LI Yanqing, GUO Shenglian, ZHOU Yanlai, et al. Identification of flood seasonality for the Ankang Reservoir basin. Journal of Water Resources Research, 2013, 2(1): 64-69. (in Chinese) [7] 方彬, 郭生练, 郭富强, 等. 汛期分期的圆形分布法研究[J]. 水文, 2007, 27(5): 7-11. FANG Bin, GUO Shenglian, GUO Fuqiang, et al. Identification of seasonality by circular distribution method. Journal of China Hydrology, 2007, 27(5): 7-11. (in Chinese) [8] CUNDERLIK, J. M., OUARDA, T. and BOBÉE, B. Determination of flood seasonality from hydrological records. Hydrological Sciences Journal, 2004, 49(3): 511-526. https://doi.org/10.1623/hysj.49.3.511.54351 [9] 刘攀, 郭生练, 方彬, 等. 汛期分期变点分析方法的原理及验证[J]. 长江科学院院报, 2006, 23(6): 27-31. LIU Pan, GUO Shenglian, FANG Bin, et al. Change point analysis methods for flood seasonality determination. Journal of Yangtze River Scientific Research Institute, 2006, 23(6): 27-31. (in Chinese) [10] LIU, P., GUO, S., XIONG, L., et al. Flood season segmentation based on the probability change-point analysis technique. International Association of Scientific Hydrology Bulletin, 2010, 55(4): 540-554. https://doi.org/10.1080/02626667.2010.481087 [11] 郭金城, 郭倩, 武学毅. 基于模糊集合分析法与圆形分布法的水库汛期分期研究[J]. 水电能源科学, 2013, 31(3): 50-53. GUO Jincheng, GUO Jing and WU Xueyi. Study on flood season staging based on fuzzy set analysis method and circle distribution method. Water Resources and Power, 2013, 31(3): 50-53. (in Chinese) [12] 崔巍, 顾圣平, 肖聪, 等. 分形分析方法在汛期分期中的参数优选与应用[J]. 水电能源科学, 2014, 32(3): 75-79. CUI Wei, GU Shengping, XIAO Cong, et al. Parameter optimization and application of fractal analysis method in division of flood season. Water Resources and Power, 2014, 32(3): 75-79. (in Chinese) [13] XIONG, F., GUO, S., CHEN, L., et al. Identification of flood seasonality using an entropy-based method. Stochastic Environmental Research and Risk Assessment, 2018, 32(11): 3021-3035. https://doi.org/10.1007/s00477-018-1614-1 [14] 钟逸轩, 林凯荣, 李俊. 北江乐昌峡水库流域汛期分期研究[J]. 水资源研究, 2014, 3(4): 351-359. ZHONG Yixuan, LIN Kairong and LI Jun. Identification of flood seasonality for the Lechang Gorge Reservoir basin. Journal of Water Resources Research, 2014, 3(4): 351-359. (in Chinese) [15] 刘攀, 李立平, 吴荣飞, 等. 论水库旱限水位分期控制的必要性与计算方法探讨[J]. 水资源研究, 2012, 1(3): 52-56. LIU Pan, LI Liping, WU Rongfei, et al. Necessity and methods for reservoir seasonal drought control water level. Journal of Water Resources Research, 2012, 1(3): 52-56. (in Chinese) [16] 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): 302-314. GUO Shenglian, LIU Zhangjun and XIONG Lihua. Advances and assessment on design flood estimation methods. Journal of Hydraulic Engineering, 2016, 47(3): 302-314. (in Chinese) [17] 喻婷, 郭生练, 刘攀, 等. 水库汛期分期方法研究及其应用[J]. 中国农村水利水电, 2006(8): 24-26+56. YU Ting, GUO Shenglian, LIU Pan, et al. Study on method and application of reservoir flood season staging. China Rural Water and Hydropower, 2006(8): 24-26+56. (in Chinese) [18] 胡光伟, 毛德华, 李正最, 等. 60年来洞庭湖区进出湖径流特征分析[J]. 地理科学, 2014, 34(1): 89-96. HU Guangwei, MAO Dehua, LI Zhengzui, et al. Analysis on the runoff characteristics in and out Dongting Lake in recent 60 years. Scientia Geographica Sinica, 2014, 34(1): 89-96. (in Chinese) [19] 周如瑞, 梁国华, 周惠成, 等. 大伙房水库汛期分期研究[J]. 水资源与水工程学报, 2013, 24(6): 145-148. ZHOU Rurui, LIANG Guohua, ZHOU Huicheng, et al. Study on separation of flood season of Dahuofang Reservoir. Journal of Water Resources and Water Engineering, 2013, 24(6): 145-148. (in Chinese) [20] 李慧, 周顺武, 王亚非. 西太平洋副热带高压异常与中国长江中下游夏季降水关系研究综述[J]. 气象与环境学报, 2013, 29(1): 93-102. LI Hui, ZHOU Shunwu and WANG Yafei. A review on relationship between subtropical high anomaly over West Pacific and summer precipitation in the middle-lower reaches of the Yangtze River. Journal of Meteorology and Environment, 2013, 29(1): 93-102. (in Chinese)