Temporal–Spatial Variations in the Economic Value Produced by Environmental Flows in a Water Shortage Area in Northwest China

Abstract

Scientific and accurate assessments of the economic value produced by environmental flows are an important basis for the protection of environmental flows by means of economics. Because of the temporal and spatial variation characteristics of environmental flows, it is more appropriate to study the economic value produced by environmental flows using a temporal–spatial scale rather than static calculations. In the present study, we combine the major influencing factors to establish the temporal–spatial calculation methods of the economic value produced by environmental flows using the assessment techniques of resources and environmental economics. The results obtained for the Wei River show that the annual variation range of the total economic value is CNY 0.30–0.42 billion, and the unit economic value is 0.86–6.40 CNY/m³ during the non-flood season ranging from the years 1980 to 2017. In general, the monthly variation in the total economic value ranges from CNY 0.04 to 0.08 billion, and the unit economic value is 0.94–14.34 CNY/m³. Based on this result, the variation tendency of the total economic value is consistent with the changing trend of the environmental flows occurring in the river; however, the unit economic value presents a reverse pattern. Furthermore, the deficiency of environmental flows can lead to a significant increase in its unit economic value. This method presents a dynamic, small temporal–spatial scale assessment of the economic value produced by environmental flows. It can also provide theoretical support for the ecological compensation of environmental flow protection in rivers present in water shortage areas.

1. Introduction

Environmental flows (e-flows) are described in the Brisbane Declaration as “the quantity, timing, and quality of water flows required to sustain freshwater and estuarine ecosystems and the human livelihoods and well-being that depend on these ecosystems” [1]. E-flows provide great ecological benefits to human beings [2]; however, these benefits are difficult to observe directly in the economic data [3,4]. As a result of this, human beings often ignore e-flows when diverting river water resources for the purpose of economic development [5], especially during the non-flood season. Decreased e-flows lead to a series of river ecosystem degradation [6], such as water contamination, biodiversity loss, and water and soil erosion [7]. Therefore, it is important for e-flow protection practices to accurately assess the economic value (EV) produced by e-flows and integrate this into water resource management practices [8,9,10].

A river’s flow changes with the climate, and the physical, chemical, and biological elements in river flows exhibit periodic variations [11]. As a part of river flows, e-flows present differentiation and non-equilibrium characteristics during different periods [12,13]. Meanwhile, affected by underlying surface and water diversions, e-flows also vary in different sections of the same river [14]. All of these factors determine that the EV produced by e-flows has the characteristics of temporal and spatial variations. Hence, studies conducted on the EV produced by e-flows should be based on temporal and spatial scales, and they should shift from static, regime-based metrics to dynamic, time–space varying characterizations [15,16,17].

In the research being conducted at present, researchers mainly use a water resource value model or ecosystem services value model to calculate the EV produced by e-flows. Ojeda et al. [18] estimated that the EV of e-flows occurring in the water-scarce Yaqui River Delta in Mexico adopted a contingent valuation method. Akter et al. [19] provided an integrated socio-economic and hydro-ecological modeling approach for water allocation decisions across a wide range of uses based on the estimation of environmental water price. Crespo et al. [20] used a hydro-economic model to analyze the effects of different water allocation policies in e-flow scenarios. Sisto [21], Perona et al. [22], and Cheng et al. [23] proposed the allocation and management of e-flows in a river based on the EV produced by e-flows. Bejarano et al. [24] evaluated the environmental and economic benefits of implementing different hydrology-based e-flow restrictions. These studies were mainly static evaluations at some point in time. Only Zhao [25], Xu [26], and Cheng [27] utilized the Wei River as an example, and preliminarily discussed the dynamic change features of the EV produced by e-flows on an annual scale. This research direction required further study.

Ecosystem service value scientists mainly assess the occurrence of dynamic changes using remote sensing technology based on land-use change during different periods of time [28,29]; however, the time frame generally utilized in the research is over five years. In addition, Xie et al. [30] initiated a dynamic assessment method of ecosystem service values by modifying and developing the method of equivalence factor per unit area, and they realized the estimation of the monthly values of ecosystem services in a dynamic manner. This dynamic research provided the references used in the present study. We combined the assessment techniques of environmental economics and the temporal–spatial variation coefficients produced by influencing factors to establish the calculation method of temporal–spatial variations in the EV produced by e-flows. Then, we used this method to assess the EV produced by e-flows in the Shaanxi section of the Wei River (SWR). Based on the research results, it can provide economic leverage in terms of economic value when coordinating the disagreement between supply and demand and optimizing the allocation of water resources in rivers in water shortage areas. The results can also provide theoretical support for the establishment of a long-term e-flow protection/compensation mechanism.

2. Materials and Methods

2.1. Study Area

The Wei River is the largest tributary in the Yellow River, exposed to a typical temperate, continental, monsoon climate [31]. The SWR is located in this river’s middle and lower sections (Figure 1). It is the most economically developed and densely populated area in Northwest China. There are 8 large irrigation areas present along the SWR with surface values of 9.11 × 10³ km² [32]; however, the per capita water resource is less than 400 m³, only one-tenth of the international standard value (3000 m³). It is commonly believed in the research that the SWR has water scarcity issues.

In the SWR, the annual precipitation distribution is uneven, and natural runoff has the characteristics of alternating between flood and dry seasons with a relatively long dry-season period [33]. Most precipitation occurs from July to October for 4 months, accounting for 60% of the annual precipitation [34]. During this period, the requirements of e-flows in the cross section are satisfied. In the dry season, from December to March, the natural runoff decreases, but the increased demand for irrigation causes a severe lack of e-flows. Therefore, the dry season is a crucial period for e-flow protection practices.

2.2. Temporal–Spatial Scale

We used different sections of the river to represent the spatial scale. Figure 1 presents the six hydrological stations used as generalized points to divide the SWR into five sections: Sections 1 (Tuoshi–Linjiacun), 2 (Linjiacun–Weijiabu), 3 (Weijiabu–Xianyang), 4 (Xianyang–Lintong), and 5 (Lintong–Huaxian). Linjiacun, Weijiabu, Xianyang, Lintong, and Huaxian stations are the cross sections of each section, respectively.

Temporal variations included annual and monthly variations. As for the annual variation, we selected the non-flood season (November–June) from the years 1980 to 2017 as the period based on the previous analysis. As for the monthly variation, we utilized a typical-year method to perform the assessment. According to the annual runoff data for the six hydrological stations in the SWR from the years 1980 to 2017, provided by the Annual Hydrological Report of the Yellow River, we selected 1989 as wet, 1991 as normal, 2008 as dry, and 2001 as very-dry years, based on runoff-frequency analysis.

2.3. Research Methods

2.3.1. Influencing Factors

Under the interaction of various factors, the EV produced by e-flows exhibits dynamic change characteristics. According to the literature concerning the influence factors of e-flows and water price [35,36,37,38], we selected “precipitation”, “river flow”, “water quality”, “water consumption”, and “ability to pay” as the influencing factors of EV produced by e-flows. Due to the different units of these five factors, we expressed them in an equivalent form.

(1)

Precipitation

The number of e-flows is closely related to precipitation [39]. In the wet season, water resources in the river are abundant, water consumption for human use reduces, and e-flows are relatively easy to protect. On the contrary, natural inflows occurring in the river are limited in the dry season, but the surging demand for irrigation water causes a contradiction between e-flows and water for human use.

The water price reflects its scarcity [40]. The more water that is available, the lower its EV, and vice versa. As a special kind of water resource, e-flows also fit this feature. In the areas or during the periods presenting high precipitation values, the EV produced by e-flows is reduced, whereas it becomes higher in the areas or during periods with poor precipitation values.

$${\mathit{f}}_1=\overline{\mathit{P}}/{\mathit{P}}_{\mathit{j}}$$

(1)

Here, f₁ is the influence of precipitation on the EV produced by e-flows; $\overline{\mathit{P}}$ is the multi-year average precipitation over the study period (mm); and P_j is the precipitation level during the jth period (mm).

(2)

River flow

The difficulty concerning e-flow protection affects the EV produced by e-flows. When e-flows are easy to protect due to higher river-flow rates, the EV is low, whereas the decrease in the river’s flow significantly increases the difficulty of e-flow protection, and its EV is high.

$${\mathit{f}}_2{=\mathit{E}\mathit{F}}_{\mathrm{B}}/{\mathit{Q}}_{\mathit{j}}$$

(2)

Here, f₂ is the influence of the river’s flow on the EV produced by e-flows; EF_B is the baseline value of e-flows (m³/s); and Q_j is the river’s flow during the jth period (m³/s).

(3)

Water quality

We adopted a comprehensive pollution index (I) to assess the water quality of the river [41]:

$$\mathit{I}=\frac{1}{\mathit{m}}{\sum }_{\mathit{i}=1}^{\mathit{m}}\frac{{\mathit{C}}_{\mathit{i}}}{{\mathit{S}}_{\mathit{i}}}$$

(3)

Here, C_i is the mean-measured concentration of the ith pollutant in the river (mg/L); S_i is the standard concentration of the ith pollutant in the river (mg/L); and m is the pollutant type.

For this index, 0 < I ≤ 1 shows that the river’s water quality meets the established criterion, and I > 1 means that the river’s water quality does not. The river’s pollution level becomes more severe as the value of I increases. The EV produced by e-flows should increase as the water quality improves.

$${\mathit{f}}_3=1/{\mathit{I}}_{\mathit{j}}$$

(4)

Here, f₃ is the influence of water quality on the EV produced by e-flows; and I_j is the comprehensive pollution index during the jth period.

(4)

Water consumption

Human beings divert water from the river, mainly for the purpose of agricultural irrigation [42]. We selected water consumption per square kilometer as the indicator of f₄. Based on the average water consumption rate per square kilometer in China, we assumed that the area where water consumption per square kilometer was lower than the national average value presented the risk of irrigation water shortage. Although the quantitative calculation of the EV produced by e-flows is beneficial for e-flow protection purposes, a high EV in an agricultural water shortage area may affect a farmer’s enthusiasm to divert water due to the low price of agricultural products [43]. This effect threatens food security [44]. Therefore, we appropriately adjusted the EV produced by e-flows to balance the water demand between e-flows and agricultural irrigation.

$${\mathit{f}}_4{=\mathit{W}}_{\mathit{j}}/\overline{\mathit{W}}$$

(5)

Here, f₄ is the influence of water consumption on the EV produced by e-flows; W_j is the water consumption per square kilometer in the calculated region during the jth period (m³/km²); and $\overline{\mathit{W}}$ is the average water consumption per square kilometer in China during the study period (m³/km²).

(5)

Ability to pay

We selected GDP per capita as the indicator of f₅. According to this indicator, an area with a GDP per capita lower than the national value is an undeveloped region in China. The EV produced by e-flows requires an adjustment to provide a practical compensation mechanism.

$${\mathit{f}}_5{=\mathit{GDP}}_{\mathit{j}}/\overline{\mathit{GDP}}$$

(6)

Here, f₅ is the influence of one’s ability to pay for the EV produced by e-flows; GDP_j is the regional GDP per capita during the jth period (CNY); and $\overline{\mathit{GDP}}$ is the national GDP per capita in China during the study period (CNY).

(6)

Temporal–spatial variation coefficient

We adopted the entropy method to determine the weight of each influencing factor. The detailed procedures are as follows [45]:

(i) The original matrix of the influencing factors is

$${\mathit{X}}_{\mathit{ij}}=\left[\begin{array}{ccc}{\mathit{x}}_{11}& {\mathit{x}}_{12}& \begin{array}{cc}\begin{array}{cc}\dots & \begin{array}{cc}{\mathit{x}}_{\mathit{i}1}& \dots \end{array}\end{array}& {\mathit{x}}_{\mathit{m}1}\end{array}\\ {\mathit{x}}_{21}& {\mathit{x}}_{22}& \begin{array}{cc}\begin{array}{cc}\dots & \begin{array}{cc}{\mathit{x}}_{\mathit{i}2}& \dots \end{array}\end{array}& {\mathit{x}}_{\mathit{m}2}\end{array}\\ \begin{array}{c}\begin{array}{c}\dots \\ \begin{array}{c}{\mathit{x}}_{1\mathit{j}}\\ \dots \end{array}\end{array}\\ {\mathit{x}}_{1\mathit{n}}\end{array}& \begin{array}{c}\begin{array}{c}\dots \\ \begin{array}{c}{\mathit{x}}_{2\mathit{j}}\\ \dots \end{array}\end{array}\\ {\mathit{x}}_{2\mathit{n}}\end{array}& \begin{array}{c}\begin{array}{cc}\begin{array}{c}\begin{array}{cc}\dots & \begin{array}{cc}\dots & \dots \end{array}\end{array}\\ \begin{array}{c}\begin{array}{cc}\dots & \begin{array}{cc}{\mathit{x}}_{\mathit{ij}}& \dots \end{array}\end{array}\\ \begin{array}{cc}\dots & \begin{array}{cc}\dots & \dots \end{array}\end{array}\end{array}\end{array}& \begin{array}{c}\dots \\ \begin{array}{c}{\mathit{x}}_{\mathit{mj}}\\ \dots \end{array}\end{array}\end{array}\\ \begin{array}{cc}\begin{array}{cc}\dots & \begin{array}{cc}{\mathit{x}}_{\mathit{in}}& \dots \end{array}\end{array}& {\mathit{x}}_{\mathit{mn}}\end{array}\end{array}\end{array}\right]$$

(7)

Here, X_ij is the original matrix of the influencing factors; x_ij represents the value of the ith influencing factor during the jth period; m is the number of influencing factors; and n is the number of periods.

The evaluation matrix of the ith influencing factor (X_i) is

$${\mathit{X}}_{\mathit{i}}=\left\{{\mathit{x}}_1{, \mathit{x}}_2, \dots {, \mathit{x}}_{\mathit{j}}, \dots {, \mathit{x}}_{\mathit{n}}\right\}$$

(8)

(ii) The standardized process of original data is as follows:

For positive factors:

$${\mathit{Y}}_{\mathit{ij}}=\frac{{\mathit{x}}_{\mathit{ij}}{-\mathit{min}(\mathit{X}}_{\mathit{i}})}{{\mathit{max}(\mathit{X}}_{\mathit{i}}{)-\mathit{min}(\mathit{X}}_{\mathit{i}})}$$

(9)

For negative factors:

$${\mathit{Y}}_{\mathit{ij}}=\frac{{\mathit{max}(\mathit{X}}_{\mathit{i}}{)-\mathit{x}}_{\mathit{ij}}}{{\mathit{max}(\mathit{X}}_{\mathit{i}})-{\mathit{min}(\mathit{X}}_{\mathit{i}})}$$

(10)

Here, max(X_i) is the maximum value of the ith influencing factor; and min(X_i) is the minimum value of the ith influencing factor.

The positive factor has a positive effect on the EV produced by e-flows. Conversely, the negative factor is negatively correlated with the variations in the EV produced by e-flows.

(iii) The information entropy of influencing factor (E_i) is

$${\mathit{E}}_{\mathit{i}}=-{\mathit{ln}\left(\mathit{n}\right)}^{-1}{\sum }_{\mathit{j}=1}^{\mathit{n}}{\mathit{p}}_{\mathit{ij}}{\mathit{lnp}}_{\mathit{ij}}$$

(11)

$${\mathit{p}}_{\mathit{ij}}=\frac{{\mathit{Y}}_{\mathit{ij}}}{{\sum }_{\mathit{j}=1}^{\mathit{n}}{\mathit{Y}}_{\mathit{ij}}}$$

(12)

If ${\mathit{p}}_{\mathit{ij}}=0$, then

$$\underset{{\mathit{p}}_{\mathit{ij}}\to 0}{\mathit{lim}}{\mathit{p}}_{\mathit{ij}}{\mathit{lnp}}_{\mathit{ij}}=0$$

(13)

(iv) The weight of influencing factor (w_i) is

$${\mathit{w}}_{\mathit{i}}=\frac{{1-\mathit{E}}_{\mathit{i}}}{\mathit{m}-\sum {\mathit{E}}_{\mathit{i}}}$$

(14)

(v) The temporal–spatial variation coefficient of the EV produced by e-flows is

$$\mathit{f}={\sum }_{\mathit{i}=1}^{\mathit{m}}{\mathit{w}}_{\mathit{i}}{\mathit{f}}_{\mathit{i}}$$

(15)

Here, f is the temporal–spatial variation coefficient; w_i is the weight of the ith influencing factor; and f_i is the ith influencing factor.

2.3.2. Temporal–Spatial Variation of the EV Produced by E-Flows

(1)

Basic sub-values

To adequately analyze the function of e-flows, we proposed its EV composition by referencing river ecosystem service functions [30,46]. This included the EV of the hydrologic cycle (V_HC), sediment transport (V_ST), sustaining floodplain wetland ecosystem (V_FW), nutrient transport (V_NT), water purification (V_WP), increasing soil organic matter content (V_SO), fishery production (V_FP), recreation (V_RV), and improving the quality of human life (V_LQ). On this basis, we established quantitative calculation methods for each sub-value using the assessment techniques of resource and environmental economics, as presented in

Table 1. The EV composition produced by e-flows.

Sub-Values	Calculation Methods	Calculation Equations	Meanings	Equations Numbers
Hydrologic cycle	Market valuation method	${\mathit{V}}_{\mathrm{HC}}{ =\mathit{W}\times \mathit{P}}_{\mathrm{W}}$	VHC is the EV of the hydrologic cycle; W is the water amount of e-flows; and PW is the resident water price.	(16)
Sediment transport	Replacement cost method	${\mathit{V}}_{\mathrm{ST}}{ =\mathit{G}}_{\mathit{ST}}{\times \mathit{P}}_{\mathrm{ST}}$	VST is the EV of sediment transport; GST is the sediment transport quantity by e-flows; and PST is the cost of sediment removal using manpower.	(17)
Sustaining floodplain wetland ecosystem	Shadow project method	${\mathit{V}}_{\mathrm{FW}}{ =\mathit{V}}_{\mathrm{AW}}$	VFW is the EV of sustaining a floodplain wetland ecosystem; and VAW is the construction cost of an artificial wetland.	(18)
Nutrient transport	Replacement cost method	${\mathit{V}}_{\mathrm{NT}}{ =\mathit{c}}_{\mathrm{N}}{\times \mathit{W}\times \mathit{P}}_{\mathrm{N}}$	VNT is the EV of nutrient transport; cN is the nutrient concentration in e-flows; and PN is the organic fertilizer price.	(19)
Water purification	Replacement cost method	${\mathit{V}}_{\mathrm{WP}} =\left({\mathit{G}}_{\mathrm{COD}}{\times \mathit{P}}_{\mathrm{COD}}\right)$ $+\left({\mathit{G}}_{\mathrm{NH}}{\times \mathit{P}}_{\mathrm{NH}}\right)$	VWP is the EV of water purification; GCOD and GNH are the removal quantities of COD and NH3-N by e-flow purification methods, respectively; and PCOD and PNH are the treatment costs of COD and NH3-N, respectively.	(20)
Increasing soil organic matter content	Replacement cost method	${\mathit{V}}_{\mathrm{SO}}{ =\mathit{G}}_{\mathrm{SO}}{\times \mathit{P}}_{\mathrm{N}}$	VSO is the EV of increasing soil organic matter content; and GSO is the amount of organic fertilizer required for increasing soil organic matter content.	(21)
Fishery production	Market valuation method	${\mathit{V}}_{\mathrm{FP}}{ =\mathit{G}}_{\mathrm{F}}{\times \mathit{P}}_{\mathrm{F}}$	VFP is the EV of fishery production; GF is the fish weight in the river; and PF is the fish price.	(22)
Recreation	Travel cost method	${\mathit{V}}_{\mathrm{RV}}{ =\mathit{Z}}_{\mathrm{R}}{\times \mathit{P}}_{\mathrm{R}}$	VRV is the EV of recreation; ZR is the number of tourists who consider the river as a destination for recreation; and PR is the average travel expense per tourist.	(23)
Improving the quality of human life	Hedonic price method	${\mathit{V}}_{\mathrm{LQ}}{ =\mathit{A}}_{\mathrm{H}}\times \Delta {\mathit{P}}_{\mathrm{H}}$	VLQ is the EV of improving the quality of human life; AH is the residential area within the influence range; and △PH is the increased residence price within the influence range.	(24)

.

Based on EF_B, we can obtain basic sub-values produced by e-flows (V_Bi) according to the calculation methods for each sub-value presented in Table 1. V_Bi is expressed by unit basic sub-values (v_Bi) to facilitate the subsequent temporal–spatial variation calculations.

$${\mathit{v}}_{\mathrm{B}\mathit{i}}{=\mathit{V}}_{\mathrm{B}\mathit{i}}/{\mathit{W}}_{\mathrm{B}}$$

(25)

Here, W_B is the corresponding baseline water amount of e-flows (m³) calculated by EF_B (m³/s).

(2)

Temporal–spatial variation of sub-values

We divided the study area into several sections. k exhibits the spatial location and j is the period. We can acquire the temporal–spatial variation value of the sub-values (V_ijk).

$${\mathit{V}}_{\mathit{ijk}}{=\mathit{f}}_{\mathit{jk}}{\mathit{v}}_{\mathrm{B}\mathit{i}}{\mathit{W}}_{\mathit{jk}}$$

(26)

Here, f_jk is the temporal–spatial variation coefficient of the kth section during the jth period; and W_jk is the water amount of e-flows in the kth section during the jth period (m³).

W_jk is the corresponding water amount of EF_jk, implying the e-flows in the kth section during the jth period. The calculation method suggests that if the actual river flow is greater than EF_B in a cross section, EF_jk is equal to EF_B. If the actual river flow is lower than EF_B, then EF_jk is the actual river flow.

(3)

Temporal–spatial variation of the total and unit EVs produced by e-flows

We used the total and unit EVs to indicate the temporal–spatial variations present. The total EV produced by e-flows (V_jk) is

$${\mathit{V}}_{\mathit{jk}}=\sum {\mathit{V}}_{\mathit{ijk}}$$

(27)

Then, the unit EV produced by e-flows (BV_jk) is as follows:

$${\mathit{BV}}_{\mathit{jk}}=\frac{{\mathit{V}}_{\mathit{jk}}}{{\mathit{W}}_{\mathit{jk}}}$$

(28)

2.3.3. Correlation and Regression Analysis

(1)

Correlation analysis

We used the Pearson correlation coefficient (r) to analyze the abovementioned variables.

$$\mathit{r}=\frac{{\sum }_{\mathit{i}=1}^{\mathit{n}}{(\mathit{x}}_{\mathit{i}}{- \overline{\mathit{x}} \left)\right(\mathit{y}}_{\mathit{i}}- \overline{\mathit{y}} )}{\sqrt{{\sum }_{\mathit{i}=1}^{\mathit{n}}{{(\mathit{x}}_{\mathit{i}}- \overline{\mathit{x}} )}^2}\sqrt{{\sum }_{\mathit{i}=1}^{\mathit{n}}{{(\mathit{y}}_{\mathit{i}}- \overline{\mathit{y}} )}^2}}$$

(29)

For this coefficient, r > 0 represents a positive linear correlation, r < 0 represents a negative linear correlation, and r = 0 implies no linear correlation between the two variables. The linear correlation has four levels: $\left|\mathit{r}\right|\le 0.3$ represents a very weak correlation; $0.3<\left|\mathit{r}\right|\le 0.5$ signifies a weak correlation; $0.5<\left|\mathit{r}\right|\le 0.8$ indicates a medium correlation; and $\left|\mathit{r}\right|>0.8$ denotes a good correlation.

(2)

Multiple nonlinear regressions

Based on the results of the Pearson correlation analysis, we applied the multiple nonlinear regression method to obtain the regression model of the unit EV. The regression model can predict the unit EV produced by e-flows.

2.4. Original Data

Precipitation: There were 11 meteorological stations in the SWR. P_j was the mean precipitation value of the meteorological stations in each section during the non-flood season in the jth year. $\overline{\mathit{P}}$ was the multi-year average precipitation value of the abovementioned meteorological stations in the non-flood season during 1980–2017. The meteorological data were obtained from the National Meteorological Information Center of China. We used Equation (1) to obtain f₁ in each section.

River flow: Based on the recommended baseline of e-flows in the SWR (EF_B), Linjiacun was 5 m³/s, Weijiabu was 6 m³/s, Xianyang was 8 m³/s, Lintong was 12 m³/s, and Huaxian was 20 m³/s [47]. The data for Q_j were the measured flows in the cross sections of each section during the non-flood season in the jth year, provided by the Annual Hydrological Report of the Yellow River. We used Equation (2) to obtain f₂ in each section.

Water quality: According to the Water Function Zoning of Shaanxi Province, Sections 1 and 2 should meet the III-class water quality standard of the Environmental Quality Standards for Surface Water in China, and Sections 3, 4, and 5 should satisfy the IV-class standard. From the Environmental Statistics Bulletin of Shaanxi Province, we adopted Equation (3) to calculate I_j in each section in the jth year, and then obtained f₃ in each section using Equation (4).

Water consumption: The water consumption per square kilometer in each section (W_j) and the average water consumption per square kilometer in China ($\overline{\mathit{W}}$) in the jth year were obtained from the Water Resources Bulletin of China. We used Equation (5) to attain f₄ in each section.

Ability to pay: The GDP per capita in each section (GDP_j) and the national GDP per capita in China ($\overline{\mathit{GDP}}$) in the jth year were obtained from the Statistical Yearbook of China. We used Equation (6) to acquire f₅ in each section.

3. Results

3.1. Temporal–Spatial Variation Coefficient

We adopted the entropy method to treat the original data in each section of the SWR and obtained the weight of each factor. The weight values of precipitation (w₁), water consumption (w₄), and ability to pay (w₅) were all 0.19. The weight values of river flow (w₂) and water quality (w₃) were 0.23 and 0.20, respectively. The weight values of these five factors were relatively similar, implying a reasonable selection of factors. Therefore, the equation for the temporal–spatial variation coefficient in the SWR based on Equation (15) is as follows:

$${\mathit{f}}_{\mathit{jk}}=0{.19\mathit{f}}_{\mathit{jk}1}+0{.23\mathit{f}}_{\mathit{jk}2}+0{.20\mathit{f}}_{\mathit{jk}3}+0{.19\mathit{f}}_{\mathit{jk}4}+0{.19\mathit{f}}_{\mathit{jk}5}$$

(30)

3.2. Basic Sub-Values

Sections 1 and 2 belonged to Baoji city, Section 3 belonged to Xianyang city, Section 4 belonged to Xi’an city, and Section 5 belonged to Weinan city. We obtained the relevant data of each section from the Annual Hydrological Report of the Yellow River, the Water Resources Bulletin of China, the Statistical Yearbook of China, the Environmental Statistics Bulletin of Shaanxi Province, the Wastewater Comprehensive Discharge Standard of the Wei River (Shaanxi Section), and the Water Function Zoning of Shaanxi Province. Then, we adopted Equations (16)–(24) to calculate the basic sub-values produced by e-flows (V_Bi) in these five sections. According to the e-flows in each cross section, we used Equation (25) to express the values by v_Bi (

Table 2. Basic sub-values produced by e-flows in the SWR. The V_Bi unit represents CNY one million, and the v_Bi unit represents CNY/m³.

Sub-Values	Section 1		Section 2		Section 3		Section 4		Section 5
	VB1	vB1	VB2	vB2	VB3	vB3	VB4	vB4	VB5	vB5
VHC	36	0.228	36	0.190	39	0.155	14	0.037	14	0.022
VST	3	0.019	2	0.011	1	0.004	8	0.021	18	0.029
VFW	872	5.519	520	2.751	896	3.556	432	1.143	672	1.065
VNT	0.06	0.0004	0.02	0.001	0.2	0.001	0.9	0.002	0.8	0.001
VWP	32	0.203	41	0.217	107	0.425	174	0.460	269	0.426
VSO	29	0.184	18	0.095	30	0.119	15	0.040	23	0.036
VFP	2	0.013	1	0.005	4	0.016	0.7	0.002	3	0.005
VRV	2	0.013	5	0.026	7	0.028	25	0.066	5	0.008
VLQ	0	0	162	0.857	176	0.698	3.65	0.966	0	0

).

3.3. Annual Variation

According to the original data for precipitation, river flow, comprehensive pollution index, water consumption per square kilometer, and GDP per capita values in the five sections of the SWR, we can use Equation (30) to obtain f_jk for each section. Then, we combined v_Bi, f_jk, and W_jk to obtain the annual variation results for the sub-values in each section using Equation (26). Finally, we employed Equations (27) and (28) to acquire the temporal–spatial results of the total and unit EVs for each section during the non-flood season in 1980–2017 (Figure 2).

Figure 2 shows that the change in the total and unit EVs in Section 1 is more extensive than that occurring in the other sections due to the deficiency of e-flows in Section 1. The e-flows in Sections 2–5 can basically meet the requirements of EFB, and their total and unit EVs only present a minor fluctuation. There is also an uptrend in the total and unit EVs of each section due to the remarkable improvement in the water quality in the Wei River since the year 2011.

The total EV produced by e-flows in the SWR ranged from CNY 81 to 764 million during the non-flood season between 1980 and 2017. Generally, the total EV in Section 3 was the highest (CNY 424 million for the long-term average value) because this section was the longest one in the SWR, at 112 km. The second-highest total EV belonged to Section 5 (CNY 346 million for the long-term average value) since EFB in this section was 20 m³/s, the maximum baseline value of e-flows in the SWR.

The unit EV produced by e-flows in the SWR ranged from 0.64 to 22.12 CNY/m³. Section 1 shows that the maximum unit EV (22.12 CNY/m³) and its corresponding e-flows were at only 0.35 m³/s, a value much lower than the baseline value presented in Section 1 (5 m³/s). The minimum unit EV (0.64 CNY/m³) appeared in Section 5 since the corresponding e-flow value reached its baseline value (20 m³/s). Overall, the e-flows increased from the upper to lower sections of the river, and the unit EV gradually decreased. Hence, the unit EV had an inverse relationship with the e-flow value.

3.4. Monthly Variations

The calculation procedure utilized for the monthly variation was the same as the annual variation. We assessed the monthly total and unit EV produced by e-flows in Sections 1, 2, 3, 4, and 5 by typical years. We only presented the results for Section 1 in the figures to analyze the monthly variation characteristics (Figure 3).

Figure 3a illustrates that the e-flows attained a baseline value of 5 m³/s, except in December and January in a wet year, and the monthly average total EV was CNY 66 million. The maximum EV occurred in October (CNY 95 million), and the minimum EV in January (CNY 36 million). The monthly average unit EV was 6.20 CNY/m³. The highest value appeared in January (12.10 CNY/m³) and the lowest in April (3.75 CNY/m³). Figure 3b shows that the number of months with insufficient e-flows increased to four (November–February) in a normal year. The monthly average total EV decreased to CNY 60 million, but the monthly average unit EV increased to 7.50 CNY/m³.

Figure 3c,d show that the e-flows in Section 1 are less than 5 m³/s in December–May during the dry year and November–August during the very-dry year, or even less than 1 m³/s throughout the non-flood season. The monthly average total EV during the dry year was CNY 62 million, and in the very-dry year drastically decreased to CNY 42 million. The monthly average unit EV was 14.34 CNY/m³ during the dry year and 12.59 CNY/m³ during the very-dry year.

3.5. Comparison to Similar Studies

Akter et al. [19], Xu [26], Li et al. [48] and Pang et al. [49], estimated the unit EV produced by e-flows in their studies. We directly compared these results to the average unit EV of the relevant sections calculated using this method (

Table 3. Comparisons of the unit EV produced by e-flows in similar studies. The unit is CNY/m³.

Data Sources	Area	Section 2	Section 3	Section 4	Section 5
This study	Wei River	3.40	3.37	1.52	1.09
Xu [26]	Wei River	5.53	2.50	1.76	1.16
Li et al. [48]	Wei River	3.01	3.30	2.01	2.11
Pang et al. [49]	Yellow River	1.16
Akter et al. [19]	Macquarie Marshes, Australia	0.5–1.4 AUD/m3, equivalent to 2.3–6.4 CNY/m3

).

Based on the comparison we performed, the unit EV produced by e-flows in the current research was relatively similar to the results obtained by Xu [26] and Li et al. [48], and all variation trends gradually decreased when flowing from upstream to downstream. Compared to the results obtained by Akter et al. [19] and Pang et al. [49], the calculation results in this study were within a reasonable range.

4. Discussions

4.1. Contribution of Influencing Factors tableDriving Temporal–Spatial Variations

4.1.1. Samples

Each sample group included one dependent and five independent variables. The dependent variable was the unit EV (CNY/m³) calculated by the methods proposed in this paper. Independent variables were the calculation data corresponding to the dependent variable of the same group, containing precipitation (mm), river flow (m³/s), comprehensive pollution index, water consumption per square kilometer (m³/km²), and GDP per capita (CNY) values.

We assessed the unit EV of five sections during the non-flood season (November–June) in 1980–2017 for 190 sample groups in an annual variation. Meanwhile, we calculated the unit EV of five sections in January–December in 4 typical years, approximately 240 sample groups in a monthly variation. We grouped the data of the annual and monthly variations together for the results analysis using a total of 430 sample groups.

4.1.2. Correlation Analysis

We entered 430 samples into SPSS 20 and gained the output results for the Pearson correlation analysis (

Table 4. Correlations between the unit EV and influencing factors in the SWR. ** or * imply a significant correlation at 0.01 or 0.05 levels, respectively.

	Unit EV	Precipitation	River Flow	Comprehensive Pollution Index	Water Consumption per Square Kilometer	GDP per Capita
Unit EV	1	−0.229 **	−0.437 **	−0.315 **	−0.029	0.144 *
Precipitation	−0.229 **	1	0.379 **	−0.158 **	0.177 *	−0.129
River flow	−0.437 **	0.379 **	1	0.108 *	0.019	−0.023
Comprehensive pollution index	−0.315 **	−0.158 **	0.108 *	1	0.091	−0.352 **
Water consumption per square kilometer	−0.029	0.177 *	0.019	0.091	1	0.046
GDP per capita	0.144 *	−0.129	−0.023	−0.352 **	0.046	1

). According to the results, the unit EV has a significantly negative correlation with the values of precipitation (−0.229), river flow (−0.437), and comprehensive pollution index (−0.315) at a 0.01 level. The coefficients presented a weak linear correlation. In addition, the unit EV had a significantly positive correlation with GDP per capita at a 0.05 level, and their linear correlation coefficient was 0.144, which was extremely weak. Finally, the unit EV showed no significant correlation with water consumption per square kilometer.

4.1.3. Unitary Regression Analysis

We scattered the plots with the dependent variable and each independent variable (Figure 4). We selected a suitable function to establish a fitted relationship between unit EV and each independent variable according to the distribution pattern of discrete points.

In Figure 4a–c, the distribution patterns of their discrete points are similar, and the variation tendency of their fitting curve is also analogous. The unit EV and river flow show the strongest relationship with a high R² value of 0.87. With the increase in the precipitation value, river flow, or comprehensive pollution index, the unit EV rapidly decreased, approaching 0 CNY/m³. Figure 4d,e scattered the discrete points without apparent regularities, not fitting very well. The correlation between the unit EV and water consumption per square kilometer or GDP per capita was insignificant, which was consistent with the Pearson correlation analysis.

4.2. Results Analysis

In this study, according to the characteristics of e-flows, we proposed sub-values produced by e-flows and established a quantitative calculation method for each sub-value using the assessment techniques of resource and environmental economics. Among all sub-values, the ecological sub-values were dominant, such as sustaining a floodplain wetland ecosystem, hydrologic cycle, water purification, etc., mainly for the indirect use value. This indicated that e-flows are not a service for human beings, and they hardly provide direct economic benefits to humans, which is unlike the valuable components of rivers. Quantitive calculation of indirect use value remains a challenge at present. We simplified the relative equations based on the convenience and authority of data sources. Therefore, it can be considered that the EV estimated using this method should be the minimum value.

For the total EV, we calculated the total EV during the non-flood season (November–June) from 1980 to 2017. The multi-year average total EVs during the non-flood season were CNY 317 million (Section 1, 109 km), 322 million (Section 2, 65 km), 424 million (Section 3, 112 km), 299 million (Section 4, 54 km), and 346 million (Section 5, 84 km), respectively. The total EV for Section 4 was the highest, and Section 5 was in second place. This was because Section 4 was the longest, and the baseline e-flow in Section 5 was the greatest (20 m³/s). There was a positive correlation between total EV and the river length or amount of e-flows. This showed that the EV produced by e-flows belonged to a kind of ecosystem service value directly related to the number of services available.

For the unit EV, the multi-year average unit EVs were 6.40 CNY/m³ (Section 1), 2.65 CNY/m³ (Section 2), 2.61 CNY/m³ (Section 3), 1.20 CNY/m³ (Section 4), and 0.86 CNY/m³ (Section 5), respectively. The e-flows in the SWR gradually increased from upstream to downstream locations, and the unit EVs gradually decreased. Combined with the monthly variation results, the variation tendency of unit EVs was opposite to the changing trend of the river’s flow, increased in the dry season, and decreased in the wet season. It was also determined that the deficiency of e-flows could lead to a significant increase in unit EVs.

Among the influencing factors, precipitation, river flow, or water quality were more evident than that of water consumption per square kilometer or GDP per capita for the EV produced by e-flows. This was because the factors of water consumption per square kilometer or GDP per capita mainly played a regulating, but not a determining, role in the EV produced by e-flows. Their prominent role was to prevent calculation results from being impractical due to an EV that was too high. When precipitation was less than 50 mm, river flow was less than 10 m³/s, or when the comprehensive pollution index was less than 1, the unit EV produced by e-flows would increase, similar to a power function. This kind of change reflected the scarcity feature of the unit EV produced by e-flows, similar to the scarcity economic value of water resources.

4.3. Policy Recommendations

4.3.1. Prediction Model

In order to apply the theoretical research results to the practices, we obtained the prediction model of the unit EV produced by e-flows in the Wei River based on multivariate nonlinear regression analysis results.

$$\left\{\begin{array}{c}\mathit{BV}={3.544\mathit{e}}^{-0.063\mathit{P}}+{9.905\mathit{Q}}^{-0.771}+{1.791\mathit{I}}^{ -0.916}+{0.148 (\mathit{R}}^2=0.95) (\mathrm{a})\\ \mathit{BV}={11.4\mathit{Q}}^{-0.679}+{1.249\mathit{I}}^{-1.09}+{0.856 (\mathit{R}}^2=0.92) (\mathrm{b})\\ \mathit{BV}={14.55\mathit{Q}}^{-0.47}{ (\mathit{R}}^2=0.87) (\mathrm{c})\end{array}\right.$$

(31)

Here, BV is the unit EV produced by e-flows (CNY/m³); P is the precipitation (mm); Q is the river flow (m³/s); and I is the comprehensive pollution index.

The prediction model consisted of three prediction equations. These can be selected according to the available data. For example, if precipitation, river flow, and water quality monitoring data were available, Equation (31a) was used to perform simulations and predictions; however, if only river flow data were available, we could select Equation (31c). Among the three prediction equations, the predicting effects of Equation (31a) were relatively good, and its correlation coefficient between simulation and actual values could reach 0.95 (Figure 5). Considering that the correlation between the unit EV and water consumption per square kilometer or GDP per capita was insignificant, we did not use these two influencing factors in the prediction model. It achieved relatively accurate prediction results using simplified data.

4.3.2. Recommended Values

On the basis of monthly average river flows in the SWR, we used the prediction model to forecast the unit EV produced by e-flows in each section (January–December). Then, based on this, we proposed the recommended unit EV produced by e-flows occurring in the Wei River (

Table 5. Recommended unit EV produced by e-flows in the SWR. The unit is CNY/m³.

Sections	Section 1	Section 2	Section 3	Section 4	Section 5
Cross sections	Linjiacun	Weijiabu	Xianyang	Lintong	Huaxian
Prediction unit EV	4.54–10.22	1.34–4.50	1.15–2.94	0.91–2.04	0.88–2.19
Recommended unit EV	4–10	1–5	1–3	1–2	1–2

).

4.3.3. Recommendations

The Wei River is a typical water shortage area in China, and its e-flows often cannot be satisfied. The calculation of the EV produced by e-flows can make humans realize the importance of e-flows intuitively. In the critical period (dry season), the government improves the enthusiasm of water users in the river to protect e-flows through economic compensation. The recommended values presented in this study were theoretic foundations used to establish a rational protection/compensation plan, and to coordinate the relationship between e-flows and water for human use by economic means. The research methods can also provide theoretical support for the precise management of river water resources in similar water shortage areas.

5. Conclusions

In this study, we used the number of e-flows in the water shortage area as the research object and established a dynamic method to assess the EVs they produced. We utilized the SWR as an example to apply this theoretical method and revealed the temporal–spatial variation characteristics of the EV produced by e-flows. The main conclusions were as follows:

(1)

We proposed the EV composition of e-flows and established quantitative calculation methods for each sub-value using the assessment techniques of resource and environmental economics. Then, we selected the influencing factors and proposed the temporal–spatial variation coefficient. By combining the coefficient, we established the temporal–spatial calculation methods for the EV produced by e-flows. This method realized the dynamic calculation of the EV produced by e-flows;

(2)

In the Wei River, the annual variation range of the total EV was CNY 0.30–0.42 billion, and the unit EV was in the range of 0.86–6.40 CNY/m³. The monthly variation range of the total EV was CNY 0.04–0.08 billion, and the unit EV was 0.94–14.34 CNY/m³. The pattern of change of total and unit EVs was roughly the opposite. In the dry season, the total EV decreased, but the unit EV increased; in the wet season, the reverse occurred. Moreover, the deficiency of e-flows can lead to a significant increase in its unit EV;

(3)

Based on the contribution of the influencing factors driving temporal–spatial variations, we established a model to predict the unit EV produced by e-flows, which only required precipitation, river flow, and water quality data. According to the prediction results, our preliminary recommendations for the unit EVs for the Wei River were 4–10 CNY/m³ (Tuoshi–Linjiacun), 1–5 CNY/m³ (Linjiacun–Weijiabu), 1–3 CNY/m³ (Weijiabu–Xianyang), 1–2 CNY/m³ (Xianyang–Lintong), and 1–2 CNY/m³(Lingtong–Huaxian), respectively.