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 水利水运工程学报   2019 Issue (6): 132-138.  DOI: 10.16198/j.cnki.1009-640X.2019.06.015 0

### 引用本文 [复制中英文]

[复制中文]
LIU Jiahong, SHAO Weiwei, WANG Hao, et al. Spectrum analysis method for assessing water use efficiency[J]. Hydro-science and Engineering, 2019(6): 132-138. (in Chinese) DOI: 10.16198/j.cnki.1009-640X.2019.06.015.
[复制英文]

### 文章历史

1. 中国水利水电科学研究院 流域水循环模拟与调控国家重点实验室，北京 100038;
2. 辽宁师范大学 地理科学学院，辽宁 大连 116029;
3. 大连理工大学水利工程学院，辽宁 大连 116024

1 研究数据

 图 1 全国GDP体量及平均万元GDP用水量变化 Fig.1 Changes of total amount of GDP and water consumption of average ten thousand yuan GDP in China
2 研究方法

 $\varGamma(x)=\int\limits_{0}^{+\infty} t^{x-1} \exp (-t) \mathrm{d} t$ (1)

 $\varGamma(z)=\int\limits_{0}^{+\infty} t^{z-1} \exp (-t) \mathrm{d} t$ (2)

 $f(x)=\left\{\begin{array}{cc} {\frac{\lambda^{\alpha}\left(x-x_{0}\right)^{\alpha-1} \exp \left(-\lambda\left(x-x_{0}\right)\right)}{\varGamma(\alpha)}, } & {x \geqslant x_{0}} \\ {0, } & {x 式中：x0为位置参数，保留对基准点或基准时刻的预示；α为形状线束，以保持与伽马分布的一致；λ为尺度参数，以保持与指数分布的一致性。其中，当α=1且x0=0时对应的分布正好是参数为λ的指数分布；当α < 1时为递减函数；当α>1时为单峰函数，可以反映经济和技术驱动下水资源利用效率的先锋和群聚特征。因此，本研究选择伽马分布函数作为水资源利用效率频谱分析的基础函数。 本研究基于1998—2016年全国各省的万元GDP用水量(Wi)和对应的GDP量(Pi)数据，按Wi的升序编排数组(W1P1)，(W2P2)，…，(W31P31)；在每一个年份内以一定的用水效率步长(ΔW)进行分段，对数组(WiPi)进行分类，具体如下：第1组：∀(Wk1Pk1)，其中Wk1∈[0, ΔW)，第2组：∀(Wk2Pk2)，其中Wk2∈[ΔW, 2ΔW)，……，第n组：∀(WknPkn)，其中Wkn∈[ΔW, nΔW)。 按照上述分组方法，将所有省份的数据组无一遗漏地分配到相应的区间，然后对各区间的GDP累加起来除以当年的GDP总量∑P，得到各区间的GDP占总GDP的比例p1p2，…，pn。根据前面的定义和计算过程，很容易得到：$\sum\limits_{j=1}^{n} p_{j}=1, p_{1}, p_{2}, \cdots, p_{n} \$满足全域上所有区间概率之和为1的性质，因此可视作区间概率密度。将p1p2，…，pn以柱状图的形式绘制在坐标轴上，并用伽马分布函数去拟合这些数据点，得到的曲线称之为水资源利用效率频谱曲线。由于有些国家或地区的水资源效率分布会出现双峰或多峰特征，这时就要根据具体情况采用两个或多个伽马分布函数的线性组合进行拟合，拟合得到的两个或多个伽马分布函数实际上反映了水资源利用效率内部的不均匀性，以及相应的聚合特征。

3 结果分析

 图 2 1998—2016年水资源利用效率频谱曲线簇 Fig.2 Frequency spectrum curve cluster of water resources utilization efficiency from 1998 to 2016
3.1 水资源利用效率频谱特征分析

 图 3 2000—2016年平均万元GDP用水量空间分布 Fig.3 Spatial distribution of average ten thousand yuan GDP water consumption in 2000—2016
3.2 京津冀地区水资源利用效率变化

 图 4 京津冀地区水资源利用效率在频谱图中分布 Fig.4 Distribution of water resources utilization efficiency in the spectrum of Beijing-Tianjin-Hebei region

 图 5 京津冀地区万元GDP用水量变化 Fig.5 Change of water consumption of ten thousand yuan GDP in Beijing-Tianjin-Hebei region
3.3 水资源高效利用精准调控建议

4 结语

 [1] 王红瑞, 钱龙霞, 赵自阳, 等. 水资源风险分析理论及评估方法[J]. 水利学报, 2019, 50(8): 980-989. ( WANG Hongrui, QIAN Longxia, ZHAO Ziyang, et al. Theory and assessment method of water resources risk[J]. Journal of Hydraulic Engineering, 2019, 50(8): 980-989. (in Chinese)) [2] 夏军, 石卫. 变化环境下中国水安全问题研究与展望[J]. 水利学报, 2016, 47(3): 292-301. ( XIA Jun, SHI Wei. Perspective on water security issue of changing environment in China[J]. Journal of Hydraulic Engineering, 2016, 47(3): 292-301. (in Chinese)) [3] 冯保清.我国不同尺度灌溉用水效率评价与管理研究[D].北京: 中国水利水电科学研究院, 2013. (FENG Baoqing. Study on the evaluation and management of irrigation water use efficiency for different scales in countrywide[D]. Beijing: China Institute of Water Resources & Hydropower Research, 2013. (in Chinese)) [4] 王浩, 刘家宏. 引汉济渭工程在国家水资源战略布局中的作用[J]. 中国水利, 2015(14): 47-50, 59. ( WANG Hao, LIU Jiahong. Hanjiang-to-Weihe River Water Diversion Project plays an important role in China strategy of water resources[J]. China Water Resources, 2015(14): 47-50, 59. (in Chinese)) [5] 胡四一. 《国务院关于实行最严格水资源管理制度的意见》出台背景和主要内容答记者问[EB/OL]. [2019-09-10]. http://www.china.com.cn/zhibo/2012-02/16/content_24625548.htm. (HU Siyi. The background and main contents of Opinions of the State Council on Implementing the Strictest Water Resources Management System[EB/OL]. [2019-09-10]. http://www.china.com.cn/zhibo/2012-02/16/content_24625548.htm. (in Chinese)) [6] 国家发展改革委, 水利部, 住房城乡建设部, 等.全民节水行动计划[EB/OL]. (2016-11-02)[2019-09-10]. http://www.miit.gov.cn/n1146295/n1652858/n1652930/n4509650/c5335420/content.html. (National Development and Reform Commission, Ministry of Water Resources, Ministry of Housing and Urban-Rural Development, et al. Action plan on water conservation for all[EB/OL]. (2016-11-02)[2019-09-10]. http://www.miit.gov.cn/n1146295/n1652858/n1652930/n4509650/c5335420/content.html. (in Chinese)) [7] 孙付华, 陈汝佳, 张兆方. 基于三阶段DEA-Malmquist区域农业水资源利用效率评价[J]. 水利经济, 2019, 37(2): 53-58, 78. ( SUN Fuhua, CHEN Rujia, ZHANG Zhaofang. Evaluation of utilization efficiency of regional agricultural water resources based on three-stage DEA-Malmquist model[J]. Journal of Economics of Water Resources, 2019, 37(2): 53-58, 78. (in Chinese)) [8] 朱燕飞, 陈智和, 金远征. 金华市水资源利用效率评价研究[J]. 人民长江, 2016, 47(21): 43-47. ( ZHU Yanfei, CHEN Zhihe, JIN Yuanzheng. Evaluation on utilization efficiency of water resources in Jinhua City[J]. Yangtze River, 2016, 47(21): 43-47. (in Chinese)) [9] 崔东文. 文山州近10年水资源利用效率评价SLC-PP模型及应用[J]. 河海大学学报(自然科学版), 2017, 45(2): 129-136. ( CUI Dongwen. SLC-PP model and its application to evaluation of water use efficiency in Wenshan Prefecture in last ten years[J]. Journal of Hohai University (Natural Sciences), 2017, 45(2): 129-136. (in Chinese)) [10] 王震, 吴颖超, 张娜娜, 等. 我国粮食主产区农业水资源利用效率评价[J]. 水土保持通报, 2015, 35(2): 292-296. ( WANG Zhen, WU Yingchao, ZHANG Nana, et al. Evaluation on agricultural water utilization efficiency in major grain producting areas[J]. Bulletin of Soil and Water Conservation, 2015, 35(2): 292-296. (in Chinese)) [11] 高雄, 王红瑞, 高媛媛, 等. 基于迭代修正的水资源利用效率评价模型及其应用[J]. 水利学报, 2013, 44(4): 478-488. ( GAO Xiong, WANG Hongrui, GAO Yuanyuan, et al. A model based on iteration-correction for water resources utilization efficiency evaluation and its application[J]. Journal of Hydraulic Engineering, 2013, 44(4): 478-488. (in Chinese)) [12] 温笑寒. 水资源利用效率评价方法及发展方向探讨[J]. 地下水, 2017, 39(3): 116-117. ( WEN Xiaohan. Discussion on evaluation method and development direction of water resources utilization efficiency[J]. Ground Water, 2017, 39(3): 116-117. (in Chinese)) [13] 苏茂林. 黄河水资源管理制度建设与流域经济社会的可持续发展[J]. 人民黄河, 2015, 37(11): 1-3, 7. ( SU Maolin. Water resources management system construction and sustainable socioeconomic development of the Yellow River Basin[J]. Yellow River, 2015, 37(11): 1-3, 7. (in Chinese)) [14] 张国玉, 谢晨, 李舒, 等. 2000年以来我国用水效率指标变化趋势研究[J]. 人民黄河, 2018, 40(10): 36-39, 60. ( ZHANG Guoyu, XIE Chen, LI Shu, et al. Study on water use efficiency indicators variation trend in China since 2000[J]. Yellow River, 2018, 40(10): 36-39, 60. (in Chinese)) [15] 陆国锋.常熟市暴雨强度公式编制及应用研究[D].苏州: 苏州科技大学, 2016. (LU Guofeng. The establishment and application of rainstorm intensity formula in Changshu City[D]. Suzhou: Suzhou University of Science and Technology, 2016. (in Chinese)) http://cdmd.cnki.com.cn/Article/CDMD-10332-1017020312.htm [16] 龚谊承.基于频率类别的洪水过程模拟和广义洪水风险分析与模拟[D].武汉: 武汉大学, 2012. (GONG Yicheng. A flood simulation based on the types of flood frequencies and the generalized flood risk analysises with their simulations[J]. Wuhan: Wuhan University, 2012. (in Chinese)) http://cdmd.cnki.com.cn/article/cdmd-10486-1013151905.htm [17] 唐忠辉. 关于国家节水新政的分析与建议[J]. 中国水利, 2015(19): 9-12. ( TANG Zhonghui. Analysis and suggestion of national new policy on water-saving[J]. China Water Resources, 2015(19): 9-12. (in Chinese))
Spectrum analysis method for assessing water use efficiency
LIU Jiahong 1, SHAO Weiwei 1, WANG Hao 1, LI Yuanfei 2, LI Weijia 3
1. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China;
2. School of Geographic Sciences, Liaoning Normal University, Dalian 110629, China;
3. School of Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China
Abstract: Efficient utilization of water resources is one of the key measures to alleviate the contradiction between supply and demand of water resources in the water-deficient areas. Therefore, how to evaluate the utilization efficiency of water resources in a country or a region is a basic scientific problem to be solved in water resources management. Existing water resources utilization efficiency evaluation indicators mainly include water consumption per ten-thousand-yuan GDP, agricultural irrigation water utilization coefficient and so on. However, these indicators represent the comprehensive water use level of a country or a region. They cannot reflect the imbalance of water use efficiency within the region, nor can they express the economic volume supported by different water use efficiency levels. Therefore, they cannot identify low-efficiency water users and it is difficult to make precise regulation for the low-efficiency water users. This paper presents a spectrum analysis method for water resources utilization efficiency. Based on the Gamma function, this study analyzes the different water use efficiency and its corresponding economic scale, and then calculates the proportion of the economic volume corresponding to different water use efficiency to the total economic volume (as the probability density) and draws the spectrum curves of water use efficiency. Using this method, the research on the spectrum of water resources utilization efficiency in China is carried out. Based on the water consumption per ten-thousand-yuan GDP in different provinces and corresponding GDP data from 1998 to 2016, the spectrum curves of water resources utilization efficiency are drawn, and the evolution trend of regional water resources utilization efficiency in China is revealed. The spectrum analysis method of water use efficiency reflects the imbalance of water use efficiency within the region by analyzing the distribution of water use efficiency and its corresponding probability density, which can provide a scientific basis for water resources management and precise regulation of efficient utilization.
Key words: efficient utilization of water resources    spectrum analysis method for assessing water use efficiency    water consumption per ten-thousand-yuan GDP    water demand regulation    water saving