Ecological flow analysis method based on the comprehensive variation diagnosis of Gini coefficient

Abstract

Owing to climate change, human activities and underlying surface change in the basin, a series of hydrological factors have not only changed in the annual form, but also changed the distribution trend of monthly hydrological factors in a year. This phenomenon has seriously affected the ecological water demand in the river channel. The calculation and analysis of ecological water demand will be affected by runoff sequence after variations. This paper proposed a distribution trend model of runoff by using Gini coefficient, which was used to identify the variation points of runoff at Ga Datan station in the Da Tong River basin. Then the monthly ecological water demand in the river channel was calculated. Finally, through comparing the mean flow before and after variation, in addition to ecological water demand and broken frequency of ecological flow, the study analyzed the effects of hydrological variations on ecological flow.

Keywords

Gini coefficient comprehensive diagnosis system ecological flow

1 Introduction

With the development of the social economy, the intensity of human developing and utilizing water resources and the degree of interference with the ecosystem are increasing [8 , 13]. Moreover, many water-related ecological problems appeared. Therefore, more and more scholars begin to study catchment ecological water demand. The study of ecological water demand, involving theories and methods of ecology, hydrology, environmental science and many other disciplines, has become a hot topic in recent years [7, 10]. Ecological water demand of channels is the minimum flow in the channel to maintain the structure and basic ecological functions of a particular ecosystem, such as the balance of water and sand of river, the balance of water and salt and ecological environment balance of estuary area. The methods of calculating ecological water demand of channels are roughly divided into four categories according to data type and reference standard, including hydrological methods, hydraulics methods, habitat methods and holistic methods. The hydrological methods established the relationship between river hydrological characteristics (such as runoff) and the biology and its living environment in the channel based on field investigation, data collection and statistical analysis. The representative hydrological methods are methods of Tennant [11], 7Q10 [1], NGPRP [2], minimum monthly average flow [5], ABF [6], monthly frequency calculation [3 , 12], minimum continuous 30-day average flow, flow duration curve and so on. Among these methods, the Tennant method, estimating the ecological demand water with giving a fixed proportional interval, is the most representative method. However, the fixed proportional interval has limitations for the application in different regions. However, characteristics of a fixed river reach a certain flow distribution. Application of these distribution characteristics to calculate ecological flow of rivers can avoid the limitations of fixed proportion. Therefore, the monthly frequency calculation is also widely used. The calculation basis of hydrological method is the historical measured runoff data. Hydrological variation appeared in the river because many reservoirs and dams were built and the water resources were developed with high intensity in the study area [9]. Therefore, the measured runoff cannot simply and approximately equal to the natural runoff. In this paper, variation of annual runoff and ecological water demand in Ga Ditan hydrometric station were studied in the study area of Datong river. In the process of introducing the Gini coefficient, the uniformity of annual runoff distribution was analyzed and the variation points were founded. The runoff sequence before the variation points were used to determine the monthly ecological water demand in the river. And the influence of hydrological variation on ecological flow was analyzed through the broken frequency of ecological flows and the comparison between ecological water demand and the average flow before and after variability point.

2 Evaluation model of annual distribution uniformity based on Gini coefficient

Gini coefficient is the index used to judge the degree of fair income distribution by American economist Albert Hirschman in 1943 based on Lorenz curve. The essence of Gini coefficient is to evaluate the distribution uniformity degree of a set of data, which can be used to analyze the influence of water conservancy projects on the annual distribution uniformity of hydrological elements (precipitation, runoff et al.) in a year [11]. This paper chose runoff distribution uniformity in a year as the research object. The model building steps based on Gini coefficient are shown as follows:

Divide monthly historical runoff into groups with unit of years and then rank the runoff of each group in an ascending order;

Corresponding with time accumulation (based on month), accumulate monthly runoff data respectively;

Choose the ratio between time accumulation and a group of time (one year) as the horizontal coordinate and the ration between monthly runoff accumulation and a group of total runoff as the vertical coordinate, then draw the area graph with data in 1956 (shown in Fig. 1);

Solve Gini coefficient (GI): $GI = S_{B} / (S_{A} + S_{B})$ (1)

Where S_A and S_B represent the area of A and B, respectively.

Fig.1

Lorenz curve of annual distribution for monthly runoff in 1956 (GI = 0.799).

3 Variation analysis of distribution uniformity in a year based on Gini coefficient

Hydrological elements variation involves trend variation and jumping variation. Aimed at the two kinds of variation, the variation diagnosis of hydrological elements can be divided into trend diagnosis and variation diagnosis. The main methods of trend diagnosis include correlation coefficient method, Spearman rank correlation test and Kendall rank correlation method. Jumping diagnosis methods usually involve Lee-Heghinan method, moving runs testing method, BSYES method and so on [12]. As single diagnosis method has limits, Xie Ping [12] proposed a comprehensive diagnosis system aimed at hydrological elements variation, which increased the accuracy and reliability of variation diagnosis. The comprehensive variation diagnosis system includes primary diagnosis, detailed diagnosis and comprehensive diagnosis, whosespecific methods are shown in Table 1. This paper used hydrological diagnosis system to take variation diagnosis on monthly runoff GI series and annual runoff average value series of Ga Datan hydrological station in Da Tong River basin, choosing the first confidence level as α= 0.05 and the second confidence level as β= 0.02. The diagnosed results and processes are displayed as follows.

Table 1
Results of variation in diagnosis of GI series and annual runoff average

Diagnosis method GI series Annual runoff average

Primary diagnosis Hurst coefficient 1956–2010 1956–2010

0.813 0.572

Variation degree Strong variation No variation

Detailed diagnosis Jumping diagnosis Moving F test 1997(0) –

Moving T test 1997(+) –

Lee-Heghinan method 1997(+) –

Ordered cluster method 1997(0) –

Standard deviation RS 2002(+) –

Brown-Forsythe 1997(+) –

Moving run test 1983(0) –

Moving rank sum test 1997(+) –

The optimal information second segmentation 1997(0) –

Mann-kendall 1993(+) –

BSYES method 1997(+) –

Trend diagnosis Trend variation degree strong –

Correlation coefficient method + –

Spearman + –

Kendall + –

Jumping point 1997 –

Jumping Comprehensive weight 0.76 –

Comprehensive significance 5(+) –

Trend Comprehensive significance 3(+) –

Comprehensive diagnosis Choice Efficiency coefficient (%) Jumping 48.33 –

Trend 35.16 –

Conclusion 1997(+) ↑ –

Diagnosis method	GI series	Annual runoff average
Primary diagnosis		Hurst coefficient	1956–2010	1956–2010
			0.813	0.572
		Variation degree	Strong variation	No variation
Detailed diagnosis	Jumping diagnosis	Moving F test	1997(0)	–
		Moving T test	1997(+)	–
		Lee-Heghinan method	1997(+)	–
		Ordered cluster method	1997(0)	–
		Standard deviation RS	2002(+)	–
		Brown-Forsythe	1997(+)	–
		Moving run test	1983(0)	–
		Moving rank sum test	1997(+)	–
		The optimal information second segmentation	1997(0)	–
		Mann-kendall	1993(+)	–
		BSYES method	1997(+)	–
	Trend diagnosis	Trend variation degree	strong	–
		Correlation coefficient method	+	–
		Spearman	+	–
		Kendall	+	–
		Jumping point	1997	–
	Jumping	Comprehensive weight	0.76	–
		Comprehensive significance	5(+)	–
	Trend	Comprehensive significance	3(+)	–
Comprehensive diagnosis	Choice	Efficiency coefficient (%) Jumping	48.33	–
		Trend	35.16	–
	Conclusion		1997(+) ↑	–

3.1 Primary diagnosis

The primary diagnosis of variation diagnosis system adopted hydrograph method, moving average method and Hursts efficient method to test variations on monthly runoff GI series and annual runoff series. Figure 2 is the hydrograph of monthly runoff GI series and its moving average. From this figure we can see that GI series of Ga Datan station was smaller than its average value before 1997, but bigger than average value after 1997. So we can deem that there was a variation for GI series in 1997 and its variation type was increasing or upward jumping. Figure 3 is the hydrograph of annual runoff average series and its moving average value, from which we found that there was no obvious variation point of this series. The coefficient value h of the two kinds of series were 0.813 and 0.572, respectively. After primary diagnosis we can conclude that there existed variation point for GI series, however, for annual runoff average series, there was no variation.

Fig.2

The GI series and its moving average.

Fig.3

The series of annual runoff average and its moving series.

3.2 Detailed diagnosis

The primary diagnosis showed that monthly runoff GI series had variation, while annual runoff average series had no variation. Consequently, we only need to take detailed diagnosis for GI series. By using jumping diagnosis method and trend diagnosis method of the hydrological variation diagnosis system, we got conclusions as follows: (1) Five methods diagnosed that GI series had an obvious jumping in 1997 and two methods diagnosed obvious jumpings in 2003 and 1993, respectively; (2) during trend diagnosis and under the condition of confidence level α= 0.05, three diagnosis methods all showed increasing trends. The detailed results are displayed in Table 1.

3.3 Comprehensive diagnosis

Jumping comprehensive diagnosis involves comprehensive weight and comprehensive significance, among which the weight is calculated through vector similarity method. After taking jumping comprehensive diagnosis, we found that the comprehensive weight of GI series variation point in 1997 was 0.76 and the comprehensive significance was 5, which was much bigger than the weights of variation point in 2002 and 1993. So jumping comprehensive diagnosis confirmed the variation point was 1997. During trend comprehensive diagnosis process, the comprehensive significance was 3, indicating that GI series had an obvious tendency. Finally, by using efficiency coefficient method we got that the efficiency coefficients of jumping variation and trend variation were 48.33% and 35.16%, respectively. As a result, we can conclude that GI series had a jumping variation in 1997. Specific results are displayed in Table 1.

3.4 Variation analysis

The reason of monthly runoff GI series existing jumping variation can be divided into two types: climate changing impact and human activity impact. Climate change has impacts on runoff mainly through precipitation, temperature and mete-orological factors, which inevitably causes total runoff and annual average runoff having variations. However, comprehensive diagnosis system diag-noses that average runoff does not have an obvious variation. So the influence of climate change on GI series can be excluded. Human activities influence runoff mainly through changing the underlying surface, water conservancy projects construction and so on. The influence degree of human activities on the underlying surface of the upstream of Da Tong River basin was very small, so the impacts on annual runoff distribution uniformity were mainly through building water conservancy projects. Form Fig. 4 we can see that monthly average runoff changed from “tall-thin type” into “short-fat type”, which was mainly caused by regulation and storage effects of reservoirs. Besides, by calculating the number of hydropower stations and accumulative changes of installed capacity of Da Tong River basin we found that since water conservancy projects were built in 1996, monthly runoff GI series of Da Datan hydrological station began varying in 1997 (Fig. 5). The time was consistent, so we can deem that water conservancy projects construction in Da Tong River basin caused the variation of monthly runoff GI series.

Fig.4

Comparison of monthly runoff mean flow before and after variation.

Fig.5

Number and installed capacity of hydropower station in Da Tong River basin.

4 Ecological water demand calculation

4.1 Data selection

The results of variation diagnosis system and variation analysis showed that monthly runoff GI of Da Datan station occurred variations under the influence of human activities. Before and after the variation point, the overall distribution of all kinds of hydrological elements showed changes. Varied hydrological elements distribution had adverse effects on stable local ecological system and impacted ecological water demand calculation. So hydrological series after the variation point should be excluded when calculating ecological water demand. This paper chose monthly runoff of Da Datan station between 1986 and 1996 as the basic data to calculate river ecological flow.

4.2 Calculation method of ecological flow

We adopted monthly runoff frequency method to calculate ecological flow, namely, choosing runoff with the largest frequency in monthly runoff distribution as channel ecological flow and monthly ecological flow making up the annual ecological flow. Before confirming the largest runoff frequency, firstly, we chose suitable probability distribution function, such as PIII distribution, GEV distribution and so on. Li Jianfen et al. [13] tested mean probability value to compare and analyze fitting effects of PIII distribution and GEV distribution with monthly runoff, finding that GEV distribution was more suitable for monthly runoff. Consequently, this paper chose GEV distribution as the distribution function of monthly runoff.

GEV probability density distribution function is: $f (x) = \frac{1}{σ} t {(x)}^{ξ + 1} e^{- t (x)}$ (2) $t (x) = {\begin{matrix} {(1 + ζ \frac{x - μ}{σ})}^{- \frac{1}{ζ}} & ζ \neq 0 \\ e^{- \frac{x - μ}{ω}} & ζ = 0 \end{matrix}$ (3)

Estimate parameters of GEV probability distribution function with linear moment method and calculate linear moment l1, l2, l3 and GEV parameters as follows: $l_{1} = n^{- 1} \sum_{j = 1}^{n} x_{j}$ (4) $l_{2} = 2 n^{- 1} \sum_{j = 2}^{n} \frac{(j - 1)}{n - 1} x_{j} - n^{- 1} \sum_{j = 1}^{n} x_{j}$ (5) $\begin{matrix} l_{3} & = & 6 n^{- 1} \sum_{j = 3}^{n} \frac{(j - 1) (j - 2)}{(n - 1) (n - 2)} x_{j} \\ - 6 n^{- 1} \sum_{j = 2}^{n} \frac{(j - 1)}{n - 1} x_{j} + n^{- 1} \sum_{j = 1}^{n} x_{j} \end{matrix}$ (6) $t_{3} = \frac{l_{3}}{l_{2}}$ (7) $ζ \approx - [\begin{matrix} 7.8590 (\frac{2}{3 + t_{3}} - \frac{log 2}{log 3}) \\ + 2.9554 {(\frac{2}{3 + t_{3}} - \frac{log 2}{log 3})}^{2} \end{matrix}]$ (8) $σ = \frac{l_{2} ζ}{(1 - 2^{- ζ}) Γ (1 + ζ)}$ (9) $μ = l_{1} + \frac{σ [Γ (1 + ζ) - 1]}{ζ}$ (10)

Where, n represents the length of monthly runoff series; x_j represents the monthly runoff in the jth year; ζ, σ, μ are shape parameter, scale parameter and location parameter of GEV distribution respectively. ζ < 0, ζ = 0, ζ > 0 correspond to Frechet distribution, Gumbel distribution and Weibull distribution respectively. Ecological flow x, namely, the flow with the largest frequency in GEV distribution: $x = \frac{σ}{ζ} [{(ζ + 1)}^{- ζ} - 1] + μ$ (11)

4.3 Ecological flow analysis

Choosing monthly runoff at Da Datan station between 1956 and 1996 as the basic data, we used the above ecological flow calculation methods to analyze ecological flow from January to December at Da Datan and compared it with monthly average value. The results are shown as follows:

Table 2 shows that before variation, monthly average flow was bigger than ecological flow; after variation, mean flow during non-flood season (October to May in the following year) increased, while in flood season (Jun to September) the mean flow decreased, and in May and June the mean flow was smaller than ecological flow.

Table 2
Ecological flow and average flow at Ga Datan station

Month Ecological flow Average flow Month Ecological flow Average flow

Before variation After variation Before variation After variation

Jan 3.82 4.97 7.96 Jul 109.24 131.59 91.39

Feb 3.45 4.71 7.92 Aug 91.30 113.51 95.30

Mar 6.17 8.91 31.23 Sept 72.50 95.40 88.22

Apr 25.17 28.36 48.47 Oct 38.06 44.76 83.01

May 47.70 55.04 62.88 Nov 16.37 18.09 33.97

Jun 66.98 81.08 61.71 Dec 6.27 7.46 10.58

Month	Ecological flow	Average flow	Month	Ecological flow	Average flow
Jan	3.82	4.97	7.96	Jul	109.24	131.59	91.39
Feb	3.45	4.71	7.92	Aug	91.30	113.51	95.30
Mar	6.17	8.91	31.23	Sept	72.50	95.40	88.22
Apr	25.17	28.36	48.47	Oct	38.06	44.76	83.01
May	47.70	55.04	62.88	Nov	16.37	18.09	33.97
Jun	66.98	81.08	61.71	Dec	6.27	7.46	10.58

Unit: m³/s.

If monthly flow is bigger than ecological flow, and then we can deem that this flow satisfies ecological water demand, otherwise, ecological water demand suffers destruction. The ratio between the number of broken ecological flow and the length of month series is called ecological flow broken frequency. From Table 3 we can see that before and after the variation point 1997, there were opposite changes for ecological flow broken frequency in flood season and non-flood season, respectively. Before variation, the broken frequency of ecological flow in each month except May all stayed below 42%, indicating that over 58% time of one year could satisfy ecological water demand before variation. After variation, the broken frequency of ecological flow increased during flood season, especially in June and July, the increasing range reached 88.26% and 75.70%, respectively. However, in non-flood season the broken frequency of ecological flow decreased, especially from January to March, there was no broken ecological flow after variation. This is because water conservancy project holds up some upstream incoming flow in flood season and stores water in non-flood season. Due to the small channel ecological flow in non-flood season, water conservancy project plays important regulation and storage role for ecological flow. But for flood season, water conservancy project avoids to destroy channel ecological flow through optimize regulation rules.

Table 3

Ecological flow failure frequency at Ga Datan station

Month	Before variation	After variation	Month	Before variation	After variation
Jan	36.59%	0.00%	Jul	36.59%	64.29%
Feb	34.15%	0.00%	Aug	36.59%	42.86%
Mar	26.83%	0.00%	Sept	41.46%	42.86%
Apr	36.59%	14.29%	Oct	39.02%	14.29%
May	41.46%	28.57%	Nov	29.27%	14.29%
Jun	34.15%	64.29%	Dec	29.27%	7.14%

5 Conclusions

This paper used Gini coefficient to study uniformity changes of monthly flow distribution in the year. Through comprehensive diagnosis system analyzing monthly GI series, we found that there was an obvious upward jumping for annual distribution uniformity of monthly flow in 1997. After comparing variation results of annual average runoff in Da Datan station and researching water conservancy projects in Da Tong River basin, we deemed that this variation was mainly caused by human activities.

Based on variation point analysis, we confirmed that the calculation series of ecological water demand was between 1956 and 1996. Then we used current moment method to calculate GEV distribution function and maximum flow of probability density function in each month, and regarded it as ecological flow.

After comparing monthly average flow and ecological flow before and after variation point we found that before variation, monthly average flow was bigger than ecological flow; after variation, in May and June the mean flow was smaller than ecological flow. Through analyzing ecological water demand broken frequency, we found that the broken frequency of ecological flow increased after variation in flood season, especially in June and July, the increasing range reached 88.26% and 75.70%, respectively; while in non-flood season, the failure frequency of ecological flow decreased.

Footnotes

Acknowledgments

This study was jointly supported by Intergov-ernmental Key International S&T Innovation Coop-eration Program (No. 2016YFE0102400), the National Key Technology R&D Program of China (2016YFC0402208, 2016YFC0401903, 2016YFC0400903, 2017YFC0404305, 2017YFB0203104, 2016YFC0402204, 2016YFC0402201), National Key Technology R&D Program (2015BAB07B03), the National Science Foundation of China (41701076), and State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (2016CG05).

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