Dynamic Simulation of Ecological Flow Based on the Variable Interval Analysis Method

Abstract

Ecological flow is an important basis for maintaining the structure and function of river ecosystems, and ensuring the sustainable development of economies and societies in river basins. In order to solve the problems of unclear concepts of ecological flow, difficulty in adapting to dynamic changes in demands, and the hydrological conditions and poor operability of calculated results of a practical application, a variable interval analysis method (VIAM) was proposed to calculate the ecological flow. The method comprehensively considered a variety of variable factors, such as spatial–temporal scale changes, hydrological condition changes, ecological service object changes, and calculation method changes. On the basis of a relatively fixed ecological base flow, a variable lifting amount was added to determine the ecological flow, and the ecological flow was a variable interval. Taking the Wei River as an example, the VIAM was validated and applied. With the support of a knowledge visualization integrated platform, the ecological flow simulation system of the Wei River was constructed. The results show that: (1) the VIAM makes the ecological flow calculation more scientific and reasonable, and the ecological flow of the Wei River from the upper reaches to the lower reaches increases gradually under the influence of water inflow, sewage discharge, and erosion and deposition of sediment, and the annual total water demand of the upper limit of ecological flow in a dry year is 1.04 billion m³, 1.63 billion m³, 2.29 billion m³, 4.09 billion m³, and 4.66 billion m³; (2) the variable interval is used to describe the ecological flow, which has strong applicability and operability; (3) the simulation system can quickly adapt to the demand changes in practical application, and provide visual decision support for managers. The VIAM provides new ideas and references for comprehensively promoting the control of the ecological flow.

1. Introduction

With the acceleration of the urbanization process, river ecosystems are currently facing prominent problems, such as water resources shortage, water area shrinking, water pollution, and the destruction of biological habitats. The healthy life of rivers is threatened, which is a severe challenge for human economic and social development [1]. Ecological flow is one of the quantitative indexes for creating healthy rivers and realizing human–water harmony. It is particularly important to scientifically determine the ecological flow of rivers, which is the basic element for maintaining the structure and function of river ecosystems and controlling the intensity of water resource development, as it is an important basis for coordinating ecological–production–living water use, and is related to the health of rivers, ecological civilization construction, and high-quality development [2].

The concept of ecological flow can be traced back to the studies of low flow [3] and base flow [4] in river channels in the early 1940s. In the 1950s, experts began to study river ecological flow based on the relationship between flow, velocity, water level, and aquatic organisms [5]. In the 1960s and 1970s, scholars started to research on the evaluation and calculation methods of river ecological flow [6]. After the 1980s, the concept of ecological flow developed rapidly in different disciplines and industries, and evolved into different concepts and definitions. It can be roughly divided into two categories: one is the conceptual system that uses the total water in a period to express the flow, such as the ecological water demand [7,8], environmental water demand, and eco-environmental water demand [9]. In addition, from the perspective of water management, concepts such as ecological water use [10], environmental water use [11], and eco-environmental water use [12] are proposed. The other is the conceptual system expressed by instantaneous flow, such as ecological flow [13] and environmental flow [14].

At present, the ecological flow calculation includes four methods, as shown in

Table 1. Categories of ecological flow calculation methods.

Categories	Methods	Source	Applications	Advantages	Disadvantages
Hydrology methods	Tennant method	Tennant, 1976 [16]	Jia et al., 2019 [17], Wu et al., 2022 [18]	The methods are simple and convenient and do not require on-site monitoring.	The accuracy of the methods is low, due to single factor.
	Texas method	Matthews et al, 1991 [19]	Jia, 2021 [20]
	FDC method	Stalnaker and Arnette, 1976 [21]	Tian et al, 2019 [22]
	RVA method	Richter et al., 1996 [23]	Zhang et al., 2018 [24], Ban et al., 2019 [25]
	7Q10 method	Bovee, 1982 [26]	Wei et al., 2019 [27]
	Annual distribution method	Pan et al., 2013 [28]	Lin et al., 2021 [29]
	Monthly frequency calculation method	Yu et al., 2004 [30]	Li et al., 2007 [31]
	Monthly guarantee rate method	Yang et al., 2003 [32]	Wang et al., 2021 [33]
	Minimum monthly average flow method	Wang et al., 2002 [34]	Wu et al., 2020 [35]
	NGPRP method	Dunbar et al., 1998 [36]	Wang, et al., 2015 [37]
Hydraulic methods	Wetted perimeter method	Gippel and Stewardson, 1998 [38]	Cheng et al., 2019 [39], Prakasam et al, 2021 [40]	The methods take account of the hydraulic factors.	The methods do not reflect seasonality and needs a large number of river topographic data.
	R2-CROSS method	Mosley, 1983 [41]	Guo et al., 2009 [42]
Habitat simulation methods	IFIM	Richter et al., 1997 [45]	Pan et al., 2015 [46]	The theoretical basis is sufficient, and meet the requirements of representative species.	The methods consider limited river biological species, and find it difficult to reflect the overall situation of river ecosystem.
	CASIMIR	Clayton, 2002 [47]	Munoz-Mas et al., 2012 [48]
	PHABSIM	Willians, 1996 [49]	Fu et al., 2021 [50], Wang et al., 2020 [51]
Holistic methods	BBM	King and Louw, 1998 [52]	Yang et al., 2005 [53]	The methods take into account economy, society, ecology, and environment.	The methods require a large amount of data support, with complex calculation.
	DRIFT	King et al., 2003 [54]	King et al., 2014 [55]
	SPAM	Thoms et al., 1996 [56]	Cottingham et al., 2002 [57]
	ELOHA	Poff et al., 2010 [58]	Ge et al., 2018 [59]

: hydrological methods, hydraulic methods, habitat simulation methods, and holistic methods [15]. Among them, hydrological methods are based on a long series of historical run-off data, and take a fixed flow percentage as the required flow process of the river; these are generally used for reference or method comparison, including the Tennant method [16,17,18], Texas method [19,20], flow duration curve (FDC) method [21,22], range of variability approach (RVA) [23,24,25], minimum average 7 day (consecutive) flow expected to occur once every 10 years (7Q10) method [26,27], annual distribution method [28,29], monthly frequency calculation method [30,31], monthly guarantee rate method [32,33], minimum monthly average flow method [34,35], and the Northern Great Plains Resources Program (NGPRP) method [36,37]. The hydrological methods are simple and convenient, and do not require on-site monitoring, but the accuracy is low, due to single factor. The hydraulic methods mainly adopt the hydraulic models to analyze the relationship between the flow process and key ecological processes, and the premise is to include the historical flow data and river section parameters (such as hydraulic radius, roughness, hydraulic gradient, etc.); these include the wetted perimeter method [38,39,40], and the region 2 cross (R2-CROSS) method [41,42]. Although the hydraulic methods take hydraulic factors into account, they do not reflect seasonality, and need a large number of measured data, which makes realization difficult. On the basis of hydraulic methods, Tharme [43] and Dunbar et al. [44] propose the habitat simulation methods, to meet the requirements of representative species. Starting from the suitable habitat characteristics and the eco-environmental conditions, the habitat simulation methods establish the response relationship between a habitat area and flow through numerical simulation, such as the Instream Flow Incremental Methodology (IFIM) [45,46], Computer-Aided Simulation Model for Instream Flow Requirements in Diverted Stream (CASIMIR) [47,48] and physical habitat simulation model (PHABSIM) [49,50,51]. The methods consider limited river biological species, and encounter difficulty in reflecting the overall situation of a river ecosystem. With the comprehensive utilization of water resources, and the diversified development of water environment, the related research on ecological flow gradually shifted from the single factor to the holistic methods considering multi-discipline integration, such as building block methodology (BBM) [52,53], downstream response to imposed flow transformations (DRIFT) [54,55], scientific panel assessment method (SPAM) [56,57], and ecological limits of hydrologic alteration (ELOHA) [58,59]. The holistic methods regard rivers as an ecosystem, and recommend a flow process that can simultaneously meet the requirements of aquatic habitat, water quantity and quality balance, water landscape, pollution control, and scouring and silting balance, with high precision but complicated calculation. The above methods have their own applicable conditions, with different emphases when calculating the ecological flow, and should be reasonably selected according to the river conditions and data collection in practical application.

In addition, scholars’ research on ecological flow turned to the coupling of multiple methods to overcome the defects of a single method. Zhang et al. [60] propose a simple, practical, and easy-to-manage comprehensive method, by combining the hydraulic wetted perimeter method and R2-CROSS method with the hydrological Tennant method. Jiang et al. [61] propose a new method, namely flow recovery method, which combines the hydrological method with the habitat simulation method. Li et al. [62] consider different protection targets at different stages, and couple various calculation methods to determine the river ecological flow. Huang et al. [63] propose the ME–Tennant method, which couples the matter–element analysis method with the Tennant method to evaluate river ecological flow process. Xu et al. [64] calculate the ecological flow by using the eco-hydraulic method according to the flow velocity range of fish migration. Yang et al. [65] combine the monthly guarantee rate method with the hydrological index method, and propose a calculation method of dynamic eco-environmental water demand.

It is seen that the concept and calculation methods of ecological flow are not unified, and there is a lack of systematic and universal calculation methods. The main reason is that there are obvious spatial–temporal differences in the water cycle. The uneven spatial–temporal distribution of run-off, and the dynamic characteristics of the hydrological elements of rivers, leads to the dynamic characteristics of ecological flow. At the same time, the uncertainties of the water inflow process and the water demand process determine that the ecological flow is dynamic, and difficult to accurately quantify [66]. At present, most scholars at home and abroad calculate the ecological flow for a specific river reach under specific hydrological conditions, and using specific methods. The calculation results are often one or a set of specific values, which are obviously inconsistent with the dynamic characteristics of ecological flow, and are not conducive to the implementation and supervision of ecological flow, with poor acceptance and operability. Actually, ecological flow is not only a scientific concept, but also a management tool. The determination of ecological flow should be gradually changed from static to dynamic, in order to better adapt to development and change in demands and hydrological conditions.

In this study, a variable interval analysis method (VIAM) for ecological flow calculation was proposed, based on the concept analysis of ecological flow. The method comprehensively considered various variable factors, such as spatial–temporal scale changes, water inflow changes, ecological service object changes, and calculation method changes. The Wei River was selected as a study area to test the verification and application of the VIAM. Based on the knowledge visualization integrated platform, the ecological flow simulation system of the Wei River was built. The dynamic simulation of ecological flow was realized through the dynamics of spatial–temporal scale, hydrological conditions, ecological service objects, and calculation methods. The calculation results of VIAM can solve the problems of the inaccurate quantification of ecological flow, weak adaptability, and poor operability caused by various uncertainties. The method and system could supply the technical support and decision basis for managers.

2. Study Area and Data

The Wei River is the biggest tributary of the Yellow River in China, with a basin area of 67,100 km² and a mainstream of 512 km in Shaanxi Province. The Wei River originates from the Niaoshu Mountain in Weiyuan County of Gansu Province, and flows into the Yellow River in Tongguan County of Shaanxi Province. The Wei River Basin is located in the transition zone between an arid region and a humid region, with an average annual rainfall of 566 mm. Affected by the topography, the rainfall in the whole basin is less, and the spatial–temporal distribution is uneven. In term of space, there is a trend of more in south and less in north, more in mountainous areas and less in basins. In term of time, the inter-annual variation of rainfall is large, with a C_v value of about 0.21–0.29. The precipitation during flood seasons (from July to October) is large, accounting for about 60–70% of the total annual precipitation. The intra-annual variation of flow is similar to that of precipitation.

The distribution of major water systems, and some hydrological stations of the Wei River in Shaanxi Province, is shown in Figure 1. The river passes through five cities: Baoji, Yangling, Xianyang, Xi’an, and Weinan, and plays an important role in the regional economy. However, with the rapid development of the economy and society along the river since the 1980s, the river suffered from various problems, including water resources insufficiency, water pollution, and severe water channel blockage, which led to a disquieting decline of the river ecosystem. To maintain river health and realize man–water harmonization with insufficient water resources, many ecological protection measures were taken, aiming to reconstruct parts of the river ecosystem of the Wei River. Therefore, how to determine a reasonable and feasible ecological flow is an urgent problem to be solved.

The eco-environmental function zones are the basis of implementing watershed eco-environmental zoning management and control, and are an important basis for determining ecological service objects in different river reaches, and identifying ecological problems and their causes. Based on the fish zones, soil zones, and water function zones of the Wei River Basin, the Wei River in Shaanxi Province is divided into 14 eco-environmental function zones from upstream to downstream [67], corresponding to 14 river reaches. In this study, five hydrological stations in the mainstream of the Wei River, namely, Linjiacun, Weijiabu, Xianyang, Lintong, and Huaxian, were selected as key sections, corresponding to eco-environmental function zones 2, 5, 8, 11, and 13, respectively. The hydrological, sediment, and water function zone data of Shaanxi Province from 1950 to 2018 were used to calculate the ecological flow of each section, as shown in Figure 1 and

Table 2. The eco-environmental function zones of the Wei River in Shaanxi Province.

ID	Name of Eco-Environmental Function Zones	ID	Name of Eco-Environmental Function Zones
1	Agricultural and fishery water-use area of Baoji reaches	8	Landscape water-use area of Xianyang reaches
2	Landscape water-use area of Baoji reaches	9	Sewage discharge control area of Xianyang reaches
3	Sewage discharge control area of Baoji reaches	10	Transition area of Xianyang and Xi’an reaches
4	Transition area of Baoji reaches	11	Agricultural and fishery water-use area of Lintong reaches
5	Industrial and agricultural water-use area of Baoji and Meixian reaches	12	Agricultural water-use area of Lintong reaches
6	Agricultural water-use area of Yangling reaches	13	Agricultural water-use area of Weinan reaches
7	Industrial water-use area of Xianyang reaches	14	Buffer area of Huayin reaches

.

3. Methodology

3.1. Traditional Method

The traditional ecological flow calculation methods and their applications have made some progress. However, most of the calculation methods have their specific constraints, and are only applicable to a narrow range. There are few studies on the systematic and universal framework for determining the ecological flow, ignoring the adaptability and operability of the ecological flow. After systematic analysis and simulation experiments, it is not difficult to find that there are many problems in traditional ecological flow calculation:

(1) The concept of ecological flow is not unified, and is continuously developing. There are many definitions of ecological flow, and different regions, industries, departments, and professions have different demands for ecological flow, which brings great difficulties to the ecological flow calculation;

(2) The traditional methods have limitations. Different calculation methods have different applicable conditions and emphases. When selecting methods, different countries/regions should not only consider their own national conditions, but are also limited by data, time, funds, and related technologies, resulting in many methods being limited, lacking universality, and not being widely applicable;

(3) The traditional methods cannot adapt to development and change. Due to the obvious spatial–temporal differences in the water cycle, the spatial–temporal distribution of river run-off is uneven, and other hydrological factors and natural factors of rivers show dynamic characteristics. The variable factors, such as spatial–temporal scale changes, water inflow changes, water demand changes, and calculation method changes, determine that ecological flow is a dynamic value. The traditional methods are difficult to adapt to the dynamic changes in demands and hydrological conditions, leading to difficulty in accurately quantifying the ecological flow;

(4) The calculation results are not operable. The traditional methods often adopt specific methods to calculate the ecological flow for a specific river reach, specific temporal scale, and specific hydrological conditions. The calculation results are often a value or a set of values, which are difficult to deal with in the complex and changeable environment, and cannot reflect the dynamic characteristics of ecological flow.

3.2. Variable Interval Analysis Method

3.2.1. Basic Concept

The variable interval analysis method comprehensively considers various variable factors, such as spatial–temporal scale changes, hydrological condition changes, ecological service object changes, and calculation method changes. The method improves and repairs the ecosystem function of rivers on the basis of maintaining their continuous flow. On the basis of a relatively fixed ecological base flow, a variable lifting amount is added to determine the ecological flow. The lifting amount is a variable interval, and the resulting ecological flow is also a variable interval. Under different spatial–temporal scales, different hydrological conditions, different ecological service objects, and different calculation methods, the ecological flow is different, which conforms to the dynamic characteristics of ecological flow. Therefore, it is called the variable interval analysis method (VIAM).

The VIAM redefines the ecological flow from an operational and manageable point of view. According to the definition of ecological base flow, the ecological base flow is the minimum flow needed to maintain the continuous flow of rivers, and avoid unrecoverable destruction of the aquatic biological community. The focus is to meet the natural attributes of the river, such as water sources, river water transmission, etc., without additional consideration of the water demand for various ecological service objects. The ecological base flow represents the basic benefits of the river ecosystem and must be met.

The lifting amount is the water needed to increase on the basis of the ecological base flow, in order to maintain the structure and function of the river ecosystem, and meet the water demand for various ecological service objects. The ecological service object includes two categories: the ecological service objects in the river, and the ecological service objects outside the river. The former is divided according to the eco-environmental function to be maintained, including the basic morphology of rivers, basic habitats, fish, water landscape, self-purification, and sand transport, etc.; the latter is divided according to various construction requirements of the eco-environment, including wetland, urban green space, environmental sanitation, and ecological forest and grass, etc.

Under the situation of competitive water use, it is difficult to meet the water demand for all ecological service objects. On the premise of ensuring the continuous flow of rivers, the water demand for each ecological service object should be satisfied according to its priority. The magnitude of the lifting amount can be expressed by a variable interval; the lower limit of the lifting amount is zero, and the upper limit of the lifting amount can be dynamically determined according to the hydrological conditions and the water demand for ecological service objects in a specific river reach. The satisfactory degree of the lifting amount reflects the management level of rivers and the capacity for the restoration and improvement of the river ecosystem. The resulting ecological flow is also a variable interval; the lower limit of the ecological flow is the ecological base flow, and the upper limit of ecological flow is the sum of the ecological base flow and the upper limit of the lifting amount.

The VIAM has the following characteristics: (1) Dynamic changes of spatial–temporal scales. Considering the hydrological characteristics of the upper, middle, and lower reaches of rivers, the eco-environmental function zones, and the impact of human activities, the control sections are increased or deleted flexibly. An appropriate temporal scale for ecological flow is selected, such as yearly scale and monthly scale. (2) Dynamic changes of hydrological conditions. The hydrological process is a dynamic process that changes in time and space, with uncertainty and randomness. The typical year with different water inflow frequency can be selected for ecological flow calculation, such as wet year, normal year, and dry year. (3) Dynamic changes of ecological service objects. The requirements of national economic development for ecological function planning and water quality protection objectives are different. For specific river reach, the water demand combination for different ecological service objects can be expressed by the lifting amount needed to adapt to the dynamic changes of ecological service objects. (4) Dynamic changes of calculation methods. Due to different spatial–temporal scales, different hydrological conditions, and different service objects, the required flow processes have their own characteristics. The dynamic adjustment of calculation methods can adapt to dynamic changes in demands and hydrological conditions.

In addition, in order to better coordinate the water demand for different water users, and ensure the better implementation of ecological flow, the interval of the lifting amount can be further subdivided into small intervals, considering the water demand priorities of ecological service objects; the interval of ecological flow will change accordingly. When the water inflow is sufficient, it can meet the water demand for all ecological service objects, corresponding to a large interval of lifting amount and ecological flow. When the water inflow is insufficient, it can only meet the water demand for some ecological service objects, according to the priorities of water demand for them, corresponding to a small interval of lifting amount and ecological flow.

3.2.2. Overall Framework

The overall framework of ecological flow calculation based on the VIAM is shown in Figure 2. The specific steps are as follows: (1) Select the control sections of rivers. Considering the inflow of tributaries, water intake from sections, eco-environmental function zone, upstream and downstream characteristics, and other factors, the representative control sections are selected. The catchment area controlled by each section or node can be regarded as an independent unit, which serves a specific ecological service function. (2) Identify the ecological service objects corresponding to each control section or node, including the ecological service objects inside the river and the ecological service objects outside the river. (3) Determine the ecological base flow. According to the characteristics of rivers and existing data, the appropriate methods are selected to calculate the ecological base flow of each control section or node, and its rationality is analyzed. (4) Determine the lifting amount. According to the ecological service objects determined in step 2, the calculation methods of water demand for different types of ecological service objects are determined. Comprehensively considering the mutual satisfaction relationship between various types of water demand, the upper and lower limit of the lifting amount are determined, which is a variable interval. (5) The upper and lower limit of ecological flow is determined, which is also a variable interval.

3.2.3. Calculation Method

• Calculation method of ecological base flow

The hydrological method is the earliest and most widely used method, which is suitable for setting the primary objectives of rivers and making national strategic decisions [68,69]. Therefore, this study adopts a variety of hydrological methods to calculate the ecological base flow. The expressions and characteristics of each method are shown in

Table 3. Expressions and characteristics of hydrological methods.

Methods	Expressions	Characteristics
Tennant method	Total of 10% of the annual average flow is selected as ecological base flow.	The method is simple to operate and has macroscopic and qualitative guiding significance.
Texas method	According to the monthly flow frequency curve, the specific percentage of monthly flow with 50% guarantee rate is selected as ecological base flow.	The specific percentage is 20%, which is more suitable for the calculation of river ecological base flow in northern China.
7Q10 method	The average measured run-off of the continuous lowest seven days under the 90 % guarantee rate is taken as ecological base flow.	The method considers the water quality requirements of rivers.
Method of driest monthly average flow with 90% guarantee rate	According to the frequency curve of the driest monthly average flow, the flow with 90% guarantee rate is selected as ecological base flow.	The method is suitable for rivers with a small water volume and high degree of exploitation and utilization.
Hoppe method	The flow duration curve is drawn according to the daily flow data, and the flow with 90% guarantee rate is selected as ecological base flow.	The method is simple and fast, and needs to analyze the daily average flow data for at least 20 years.
Minimum monthly average flow method	The annual average of the minimum monthly average flow is selected as ecological base flow.	The method is suitable for rivers less affected by human activities.
NGPRP method	The flow with 90% guarantee rate of normal years is selected as ecological base flow.	The method considers the difference among wet, normal, and dry years, but lacks biological basis.
Annual distribution method	The ratio of annual average run-off to minimum annual average run-off multiplied by monthly average run-off is used as ecological base flow.	The method is suitable for large and medium-sized rivers with a continuous run-off process.

. The applicability and rationality of each method is compared and analyzed, and the ecological base flow is finally determined.

2.

Calculation method of water demand for ecological service object

(1) Water demand for basic morphological of rivers

The water demand for basic morphological of rivers is usually calculated by the riverbed morphology analysis method, and can be analyzed according to the wet years, normal years, and dry years, or flood seasons and non-flood seasons. The focus is to analyze the water amount (flow) of the river channel in dry seasons or dry years.

(2) Water demand for basic habitat

The water demand for basic habitat can be calculated by the wetted perimeter method. By collecting the river channel size of aquatic habitat and its corresponding flow, the wetted perimeter to flow relationship curve is established. The flow corresponding to the inflection point in the curve is regarded as the water demand for basic habitat. The relationship between the wetted perimeter and flow is established by the Chezy formula and Manning formula [67]:

$$v=C\sqrt{RJ}$$

(1)

$$Q=AC\sqrt{RJ}$$

(2)

$$C=\frac{1}{n}{R}^{1/6}$$

(3)

$$Q=\frac{J^{1/2}{A}^{5/3}}{n{P}^{2/3}}$$

(4)

where $v$ is the flow velocity, m³/s; $n$ is the roughness; $R$ is the hydraulic radius, m; $C$ is the Chezy coefficient; $A$ is the wetted area, m²; $P$ is the wetted perimeter, m; $J$ is the hydraulic slope; and $Q$ is the flow required by basic habitat, m³/s.

(3) Water demand for fish survival

By investigating the key environmental factors required for fish survival, such as flow velocity, water temperature, water depth, water surface width, and wetted area, etc., the suitability curves of different environmental factors for target fish are constructed. The suitable water temperature, water depth, and flow velocity required for different life stages of fish are analyzed to determine the flow process required for fish survival [70].

(4) Water demand for water landscape

The water demand for water landscape is generally the water amount consumed and replenished to maintain the ecological and environmental functions of the landscapes or lakes. The water exchange cycle method can be used to calculate the water demand for water landscape. The water exchange cycle refers to water exchange cycle of other similar artificial landscapes and lakes. The calculation formula is as follows [71]:

$$Q=\frac{W}{T}$$

(5)

where $T$ is the water exchange cycle, s; $W$ is the annual average water storage, which can be determined by water depth and water surface area of the landscapes, m³; and $Q$ is the flow required for water landscape, m³/s.

(5) Water demand for self-purification

The water demand for self-purification refers to the minimum water amount required to ensure the river achieves the water quality target determined by the water function zone, on the premise of strengthening the prevention and control of urban pollution sources. In this study, the width–depth ratio of the river channel is small, the river pollutants can be quickly and evenly mixed at each section, and only change in the flow direction. Thus, the one-dimensional water quality model can be used to calculate the self-purification water demand. According to the section-end control method, only when the flow at the terminal section is $Q_{i-1}^{\prime }$ can the water quality target be achieved. The calculation formula is as follows [72]:

$$\begin{array}{c}{Q}_{i-1}^{\prime }=\frac{Q_{i-1}{C}_{i-1}\exp \left(-k\frac{L_i}{u_i}\right)+q_i{s}_i\exp \left(-k\frac{L_i}{2u_i}\right)}{C_{si}}-q_i\end{array}$$

(6)

where $L_i$ is the length of the river reach of a certain water function zone, km; $C_{i-1}$ is the pollutant concentration at the initial section of the water function zone, mg/L; $Q_{i-1}$ is the designed flow at the initial section without considering self-purification of the river; $u_i$ is the average velocity of the river reach under design flow, m/s; $k$ is the comprehensive attenuation coefficient of pollutants, 1/s; $q_i$ is the discharge of waste water in the river reach, m³/s; and $s_i$ is the concentration of waste water, mg/L. Here, several sewage outlets in the river reach are generalized as a centralized sewage outlet, which is located at the midpoint of the river reach and equivalent to a centralized point source. The actual self-purification length of the centralized point source is half of the length of the river reach; $C_{si}$ is the target water concentration at the terminal section, mg/L.

(6) Water demand for sediment transport

The water demand for sediment transport refers to the water amount required in a specific river reach to transport all or part of the sediment to the next river reach under certain conditions of water inflow and sediment. The sediment transport efficiency must be considered when calculating the water demand for sediment transport, which is closely related to the erosion and deposition of the river. If scouring occurs in the whole river reach, the water demand for sediment transport is less than the net water amount. If the erosion and deposition of the whole reach is balanced or silted, all the net water amount is used for sediment transport. The calculation formula is as follows [73]:

$$W^{\prime }={\eta }^{\alpha }{W}_w$$

(7)

$$W_w=W-\frac{W_s}{{\gamma }_s}$$

(8)

$$\eta =\frac{S_{\mathrm{in}}}{S_{\mathrm{out}}}$$

(9)

where $W^{\prime }$ is the water demand for sediment transport, m³; $\eta$ is the sediment transport efficiency; $\alpha$ is the index, which is determined by $\eta$; $W_w$ is the net water amount, m³; $W$ is the run-off, m³; $W_s$ is the sediment transport, t; ${\gamma }_s$ is bulk density of sediment, which is usually 2.65 t/m³; $S_{\mathrm{in}}$ is the sediment concentration flowing into the river reach, kg/m³; and $S_{\mathrm{out}}$ is the sediment concentration flowing out the river reach, kg/m³. When $\eta$ < 1, $S_{\mathrm{in}}$ < $S_{\mathrm{out}}$, the river is scoured, and $\alpha$ = 1. When $\eta$ ≥ 1, $S_{\mathrm{in}}$ ≥ $S_{\mathrm{out}}$, the river reach is erosion–deposition equilibrium or silted, and $\alpha$ = 0.

(7) Water demand for ecological service object outside the river

The direct calculation method or indirect calculation method can be used to calculate the water demand for ecological service objects outside the river. The direct calculation method takes the area of a certain type of vegetation in a certain area multiplied by its ecological water quota as the water demand. This method is suitable for areas with better basic conditions and vegetation types, such as shelter forest and grass, artificial oasis, etc. The calculation formula is as follows [74]:

$$W_1=A_{1}q$$

(10)

where $W_1$ is the water demand for ecological service object outside the river, m³; $A_1$ is the area corresponding to vegetation, hm²; and $q$ is the annual average irrigation quota of vegetation, m³/hm².

The indirect calculation method is based on the area of a certain vegetation type at a certain phreatic water level multiplied by the phreatic evaporation under the phreatic water level and vegetation coefficient as the water demand. The calculation formula is as follows [75]:

$$W_2=A_2{q}_{g}K$$

(11)

where $W_2$ is the water demand for ecological service object outside the river, m³; $A_2$ is the area of vegetation at a certain phreatic water level, hm²; $q_g$ is the phreatic evaporation of vegetation under this phreatic water level, m; and $K$ is vegetation coefficient.

3.

Calculation method of ecological flow

The VIAM is used to determine the ecological flow based on the known boundary conditions, such as hydrological conditions, ecological service objects, and calculation methods, etc. If any boundary condition changes, the ecological flow changes accordingly. Taking river reach $L$ as an example, Figure 3 shows the control sections of river reach $L$ and the corresponding ecological service objects of each control section. Taking Section $A_1$ as an example, the corresponding river reach is $L_1$, and the VIAM is adopted to calculate the ecological flow of Section $A_1$. The detailed steps are shown in Algorithm 1.

Algorithm 1: Determination of ecological flow based on the VIAM

Input: Control sections, long series hydrological, sediment and water function zone data, hydrological condition, parameters, ecological service objects, temporal scale, constraints.

Output: $Q_{1,t}^{basic}, \left[0,Q_{1,t}^{lift}\right],\left[Q_{1,t}^{basic},Q_{1,t}^{basic}+Q_{1,t}^{lift}\right]\leftarrow$ Ecological base flow, interval of lifting amount, and interval of ecological flow for Section $A_1$.

Step1: Determine the control sections of river reach $L$

1.1 $L_1,L_2,\cdots ,L_n, n$ is the number of eco-environmental function zones $\leftarrow$ Determine the eco-environmental function zones according to other types of zones.

1.2 $A_1,A_2,\cdots ,A_m,m$ is the number of control sections $\leftarrow$ Select the control sections according to the upstream and downstream characteristics, and the impact of human activities.

Step 2: Identify the ecological service objects of Section $A_1$

2.1 $Q_{11}^{in},Q_{12}^{in},\dots ,Q_{1p}^{in},$ $p$ is the number of ecological service objects inside the river reach $L_1\leftarrow$ Identify the ecological service objects inside the river reach $L_1$.

2.2 $Q_{11}^{out},Q_{12}^{out},\dots ,Q_{1q}^{out},q$ is the number of ecological service objects outside the river reach $L_1\leftarrow$ Identify the ecological service objects outside the river reach $L_1$.

Step 3: Determine the ecological base flow of Section $A_1$

3.1 $Q_{11,t}^{basic},Q_{12,t}^{basic},\cdots ,Q_{1s,t}^{basic},t=1,2,\dots T,$ $T$ is the total number of periods, $s$ is the number of calculation methods of ecological base flow $\leftarrow$ Multiple methods are used to calculate the ecological base flow of Section $A_1$.

3.2 $Q_{1,t}^{basic}\leftarrow$ Determine the cological base flow of Section $A_1$ based on rationality analysis.

Step 4: Calculate the water demand for ecological service objects of Section $A_1$

4.1 $Q_{11,t}^{in}, Q_{12,t}^{in},\cdots ,Q_{1p,t}^{in}\leftarrow$ Water demand process of each ecological service object inside the river reach $L_1$.

4.2 $Q_{1,t}^{in}=\max (Q_{11,t}^{in},Q_{12,t}^{in},\cdots ,Q_{1p,t}^{in})\leftarrow$ Water demand process of all ecological service objects inside the river reach $L_1$.

4.3 $Q_{11,t}^{out},Q_{12,t}^{out},\cdots ,Q_{1q,t}^{out}\leftarrow$ Water demand process of each ecological service object outside the river reach $L_1$.

4.4 $Q_{1,t}^{out}=Q_{11,t}^{out}+Q_{12,t}^{out}+\cdots +Q_{1q,t}^{out}\leftarrow$ Water demand process of all ecological service objects outside the river reach $L_1$.

Step 5: Determine the lifting amount of Section $A_1$

5.1 For each $t\in T$ If $Q_{1,t}^{in}>Q_{1,t}^{basic},Q_{1,t}^{lift}=Q_{1,t}^{in}-Q_{1,t}^{basic}+Q_{1,t}^{out}$; else $Q_{1,t}^{lift}=Q_{1,t}^{out}$. 5.2 $[0, Q_{1,t}^{lift}]\leftarrow$ Determine the lifting amount of Section $A_1$.

Step 6: Determine the ecological flow of Section $A_1$

6.1 $[Q_{1,t}^{basic},Q_{1,t}^{basic}+Q_{1,t}]\leftarrow$ Determine the ecological flow of Section $A_1$.

4. Simulation System of Ecological Flow

The ecological flow has dynamic characteristics, and its calculation results are different under different spatial–temporal scales, different hydrological conditions, different ecological service objects, and different calculation methods. In practical application, the traditional method has a large amount of data and complex calculation process. It is difficult to adapt to dynamic changes, with poor universality and operability. Therefore, it is necessary to build a simulation system based on information technology in order to realize the dynamic calculation of the ecological flow under different conditions.

From the perspective of the dynamics and operability of ecological flow, the ecological flow simulation system is supported by the knowledge visualization integrated platform [76,77,78], which is designed and constructed based on the water conservancy information processing platform technical specification (SL 538-2011) of the water conservancy industry standard, and provides effective technical support and a working platform for the application of ecological flow calculation methods. The framework of the platform is designed based on service-oriented architecture (SOA), and all business applications are implemented using SOA and Web Service technology through knowledge maps and components. The knowledge map technology was used to visualize the control sections of rivers in the form of nodes. The ecological flow calculation methods were componentized by using components, Web Service, and SOA technology. The simulation system was rapidly constructed in the form of application themes, knowledge maps, and business components. The calculation process of ecological flow for key sections could be displayed dynamically and visually through the simulation system.

The main interface of ecological flow simulation system of the Wei River is shown in Figure 4. The red inverted triangles represent the main hydrological stations, including Linjiacun, Weijiabu, Xianyang, Lintong, and Huaxian hydrological stations. The blue lines represent the main streams of the Wei River, and the light blue lines represent the primary tributaries of the Wei River, including the Qian River, Qishui River, Jing River, and so on. The short lines in different colors marked with numbers on the main stream of the Wei River represent the 14 eco-environmental function zones. The orange ellipses represent the calculation condition selection buttons and the result statistics buttons. The calculation condition selection buttons include the temporal scale selection button, the calculation method selection button, the parameter setting button, and the hydrological condition selection button. The statistical buttons included the ecological base flow statistics button, the lifting amount statistics button, the ecological flow statistics button, and the result statistics button. Through clicking the selection buttons, the temporal scale, hydrological condition, calculation method, and parameter can be selected, according to different demands. Once the calculation conditions change, the statistical tables and graphs change accordingly. In addition, when the river needs to be extended or shortened, a new ecological flow simulation system can be rapidly constructed, by adding or deleting the corresponding section nodes and components on the knowledge map, which reflects the dynamics of spatial scale.

Figure 5 shows the interface of the ecological flow calculation results. Taking the Lintong section as an example, after selecting the calculation conditions of the section (ss shown on the top left of Figure 5), the relevant statistical results are displayed in a table or graph by clicking the result statistics button. The first table on the left of Figure 5 shows the ecological base flow calculated by various hydrological methods, such as the Tennant method, Texas method, method of driest monthly average flow with 90% guarantee rate, minimum monthly average flow method, and annual distribution method in normal year of the Lintong section. Meanwhile, the table also gives the recommended values of the ecological base flow of the Lintong section through comparative analysis of various methods. The second table on the left of Figure 5 shows the water demand for different ecological service objects in a normal year of the Lintong section, including water demand for fish survival, sediment transport, self-purification, and wetland. In addition, the table also gives the lower and upper limit of the lifting amount of the Lintong section. The table on the right of Figure 5 shows the upper and lower limit of the ecological flow. The figure on the right of Figure 5 is the processes of ecological base flow, lifting amount, and the upper limit of ecological flow.

5. Results and Discussion

5.1. Results of Certain Control Sections

Through the simulation system, it is more convenient to calculate the ecological flow of different control sections under different temporal–spatial scales, different hydrological conditions, different ecological service objects, and different calculation methods. In this study, the Linjiacun section upstream and the Lintong section downstream of the Wei River are selected to verify the rationality and applicability of the VIAM. Taking a normal year as an example, the Linjiacun section corresponds to three ecological service objects inside the river, and one ecological service object outside the river, which are fish survival, water landscape, self-purification and wetlands. The Lintong section corresponds to three ecological service objects inside the river and one ecological service object outside the river, which are fish survival, self-purification, sediment transport, and wetlands.

The VIAM is applied to calculate the ecological base flow, water demand for ecological service objects, lifting amount, and ecological flow of the two sections mentioned above, as shown in

Table 4. Ecological base flow, water demand for ecological service objects, lifting amount, and ecological flow of Linjiacun section in a normal year (m³/s).

Items	Jan.	Feb.	Mar.	Apr.	May	Jun.	Jul.	Aug.	Sept.	Oct.	Nov.	Dec.
Ecological base flow	0.42	0.67	0.57	3.52	3.81	4.48	6.46	4.73	5.24	4.64	1.60	0.35
Water demand for fish survival	4.70	4.70	4.70	4.70	16.00	16.00	7.83	7.83	7.83	7.83	4.70	4.70
Water demand for water landscape	0.68	0.68	0.68	0.68	0.68	0.68	0.68	0.68	0.68	0.68	0.68	0.68
Water demand for self-purification	24.35	26.62	36.11	44.57	52.47	54.53	107.63	100.75	104.58	90.02	49.18	27.98
Water demand for wetland	0.37	0.37	0.37	0.37	0.37	0.37	0.37	0.37	0.37	0.37	0.37	0.37
Lower limit of lifting amount	0	0	0	0	0	0	0	0	0	0	0	0
Upper limit of lifting amount	24.30	26.31	35.90	40.22	48.21	51.37	101.54	97.31	99.70	85.91	47.95	28.00
Lower limit of ecological flow	0.42	0.67	0.57	3.52	3.81	4.48	6.46	4.73	5.24	4.64	1.60	0.35
Upper limit of ecological flow	24.72	26.99	36.48	43.74	52.01	55.85	108.00	102.04	104.95	90.54	49.55	28.35

and

Table 5. Ecological base flow, water demand for ecological service objects, lifting amount, and ecological flow of Lintong section in a normal year (m³/s).

Items	Jan.	Feb.	Mar.	Apr.	May	Jun.	Jul.	Aug.	Sept.	Oct.	Nov.	Dec.
Ecological base flow	5.10	6.27	8.35	14.22	16.68	19.35	26.30	21.32	33.05	22.58	13.89	7.39
Water demand for fish survival	5.73	5.73	5.73	5.73	5.73	5.73	9.55	9.55	9.55	9.55	5.73	5.73
Water demand for self-purification	55.80	63.38	80.90	122.44	165.31	114.21	288.16	255.78	341.99	251.54	159.34	67.08
Water demand for sediment transport	56.73	73.48	188.08	223.87	365.12	150.39	548.63	327.42	441.64	327.81	121.45	62.44
Water demand for wetland	0.34	0.34	0.34	0.34	0.34	0.34	0.34	0.34	0.34	0.34	0.34	0.34
Lower limit of lifting amount	0	0	0	0	0	0	0	0	0	0	0	0
Upper limit of lifting amount	51.97	67.55	180.06	209.99	348.78	131.38	522.66	306.44	408.94	305.57	145.78	60.03
Lower limit of ecological flow	5.10	6.27	8.35	14.22	16.68	19.35	26.30	21.32	33.05	22.58	13.89	7.39
Upper limit of ecological flow	57.07	73.82	188.42	224.21	365.46	150.73	548.97	327.76	441.98	328.15	159.68	67.42

. It is seen that the recommended ecological base flow better reflects the changes of the ecological base flow in flood seasons (from July to October) and non-flood seasons (from November to June next year). The average ecological base flow of the Linjiacun section in flood seasons and non-flood seasons is 5.27 m³/s and 1.93 m³/s, respectively. The average ecological base flow of the Lintong section in flood seasons and non-flood seasons is 25.81 m³/s and 11.41 m³/s, respectively. The ecological base flow of the Lintong section downstream is generally larger than that of the Linjiacun section upstream. According to the climatic characteristics of the Wei River Basin, the rainfall mainly concentrates in July to October, and the maximum of the ecological base flow also occurs in these periods, which is consistent with the actual situation of the Weihe River Basin.

Table 4 shows the water demand processes of ecological service objects for the Linjiacun section. The intra-annual variation of water demand for self-purification changes the most. The main reason is that the water quality of the main stream of the Wei River is poor at present, and the phenomenon of illegal discharge of pollutants still occurs. Moreover, the water inflow varies greatly throughout the year, and the pollutant emissions are different in each month. The annual total water demand for self-purification is 1.89 billion m³, and the water demand for self-purification in flood seasons accounts for 56.1% of the whole year. The intra-annual variation of water demand for fish survival takes second place. The flow required for fish survival in flood seasons and non-flood seasons is 7.83 m³/s and 4.70 m³/s, respectively. The Linjiacun section corresponds to the spawning ground for fish reproduction. In addition to meeting the water demand for normal fish survival, it also needs to meet the flow pulse process during the spawning periods (from May to June). The flow required during the spawning periods is 16.00 m³/s. In addition, the Linjiacun section corresponds to one water landscape and three wetlands; the water demand processes for the water landscape and wetlands are relatively stable.

Table 5 shows the water demand processes of ecological service objects for the Lintong section. The intra-annual variation of water demand for sediment transport changes most dramatically, which is mainly due to the sharp decrease in the flood-carrying capacity of the main channel, caused by sediment deposition of the Wei River downstream. The oscillation of the river channel intensifies the further deterioration of the river regime downstream. The annual total water demand for the sediment transport is 7.58 billion m³, and the water demand for sediment transport in flood seasons accounts for 57.0% of the whole year. The intra-annual variation of water demand for self-purification takes second place. The annual total water demand for self-purification is 5.16 billion m³, and the water demand for self-purification in flood seasons accounts for 57.9% of the whole year. Compared with the Linjiacun section, the water demand for self-purification increases gradually from upstream to downstream, which is closely related to the waste water discharge generated by the economic development along the Wei River. The Lintong section does not involve spawning ground. The water demand process for fish survival is relatively stable. The flow required in flood seasons and non-flood seasons is 9.55 m³/s and 5.73 m³/s, respectively. In addition, the Lintong section corresponds to four important wetlands; the water demand process for the wetlands has little change.

On the basis of the ecological base flow and the water demand for each ecological service object, the lifting amount of the two sections is obtained, as shown in Table 3 and Table 4. The lower limit of the lifting amount is zero, and the upper limit of the lifting amount mainly depends on the water demand for ecological service objects. For the Linjiacun section, the water demand processes for all ecological service object are relatively stable; the intra-annual variation of the upper limit of lifting amount changes little. The maximum and minimum of the upper limit of the lifting amount are 101.54 m³/s and 24.3 m³/s, respectively. The annual total water demand for the upper limit of the lifting amount is 1.80 billion m³, which is mainly determined by the water demand for self-purification. For the Lintong Section, the water demand processes for some ecological service objects change significantly, resulting in great differences in the upper limit of the lifting amount. The maximum and minimum of the upper limit of lifting amount are 548.97 m³/s and 57.07 m³/s, respectively. The annual total water demand for the upper limit of the lifting amount is 7.19 billion m³, which is mainly determined by the water demand for sediment transport. It is seen that the annual total water demand of the upper limit of the lifting amount of the Lintong section downstream is generally greater than that of the Linjiacun section upstream, which is closely related to water inflow and the ecological service objects of sections.

On the basis of the ecological base flow and the lifting amount, the ecological flow of the two sections is obtained, as shown in Table 3 and Table 4. The lower limit of ecological flow is the ecological base flow, and the upper limit of ecological flow is the sum of the ecological base flow and the upper limit of the lifting amount. The average of the upper limit of ecological flow for the Linjiacun section in flood seasons and non-flood seasons is 101.38 m³/s and 39.71 m³/s, respectively. The average of the upper limit of ecological flow for the Lintong section in flood seasons and non-flood seasons is 411.71 m³/s and 160.85 m³/s, respectively. It is seen that the upper limit of the ecological flow of the two sections in flood seasons is greater than that in non-flood seasons. The annual total water demand of the upper limit of ecological flow of the two sections is 1.90 billion m³ and 7.71 billion m³, respectively. The annual total water demand of the Lintong Section downstream is larger than that of the Linjiacun Section upstream.

The intervals of the lifting amount and ecological flow mentioned above are the corresponding intervals when all ecological service objects of the two sections are considered. At this time, when the upper limit of the lifting amount reaches the maximum, so does the upper limit of ecological flow. However, the above-mentioned ecological flow processes are difficult to achieve when water resources are scare in the basin. In order to better coordinate the water demand for different water users, the interval of the lifting amount can be further subdivided into small intervals, according to the water demand priorities of ecological service objects. Taking the ecological flow of the Lintong section in flood seasons (from July to October) as an example, if only considering sediment transport and self-purification, when the priority of sediment transport is greater than that of self-purification, it only needs to meet the water demand for sediment transport, and the upper limit of the lifting amount from July to October is 522.33 m³/s, 306.10 m³/s, 408.59 m³/s, and 305.23 m³/s, while the upper limit of the ecological flow is 548.63 m³/s, 327.42 m³/s, 441.64 m³/s, and 327.81 m³/s, respectively. As the water demand for sediment transport from July to October is greater than that for self-purification, when the water demand for sediment transport is met, the water demand for self-purification is also met simultaneously. When the priority of self-purification is greater than that of sediment transport, it only needs to meet the water demand for self-purification, and the upper limit of the lifting amount from July to October is 261.86 m³/s, 234.46 m³/s, 308.94 m³/s, and 228.96 m³/s, while the upper limit of the ecological flow is 288.16 m³/s, 255.78 m³/s, 341.99 m³/s, and 251.54 m³/s, respectively. When the water demand for self-purification is met, the water demand for sediment transport is not met.

5.2. Results of the Wei River

According to the comprehensive treatment targets of the Wei River Basin, the ecological service objects of other sections were analyzed. The VIAM and the simulation system were used to calculate the ecological flow of other sections. Figure 6 shows the ecological base flow, the lifting amount, and the upper limit of the ecological flow of five key sections in a wet year, a normal year, and a dry year. In Figure 6, the blue histograms represent the ecological base flow of each section, the orange histograms represent the lifting amount of each section, and the gray broken lines represent the upper limit of the ecological flow of each section.

For the ecological base flow, the average ecological base flow of all sections in flood seasons is greater than that in non-flood seasons. Taking the Weijiabu section as an example, the average ecological base flow in flood seasons in a dry, normal, and wet year is 4.67 m³/s, 9.67 m³/s, and 24.17 m³/s, respectively; the average ecological base flow in non-flood seasons is 1.95 m³/s, 3.72 m³/s, and 4.78 m³/s, respectively. The annual total water demand of the ecological base flow in a dry, normal, and wet year increases in turn. Taking the Xianyang section as an example, the annual total water demand of the ecological base flow in a dry, normal, and wet year is 0.16 billion m³, 0.30 billion m³, and 0.49 billion m³, respectively. The annual total water demand of the ecological base flow shows an increasing trend from upstream to downstream. Taking the wet year as an example, the annual total water demand of the ecological base flow from the Linjiacun section to the Huaxian section is 0.19 billion m³, 0.35 billion m³, 0.49 billion m³, 0.80 billion m³, and 0.82 billion m³, respectively.

For the lifting amount, affected by the water inflow and ecological service objects, the intra-annual and inter-annual variations of the upper limit of the lifting amount of different sections varies greatly. The upper limit of the lifting amount of all sections in flood seasons is greater than that in non-flood seasons. Taking the Weijiabu section as an example, the average of the upper limit of the lifting amount in flood seasons in a dry, normal, and wet year is 89.01 m³/s, 214.45 m³/s, and 383.80 m³/s, respectively; the average of the upper limit of the lifting amount in non-flood seasons is 28.65 m³/s, 62.49 m³/s, and 125.27 m³/s, respectively. This feature is particularly prominent for the Lintong and Huaxian sections, because both sections contain water demand for sediment transport. The amount of sediment in the Wei River mainly concentrates in flood seasons, which has the characteristics of "more incoming, more discharged." The annual total water demand of the upper limit of the lifting amount in a dry, normal, and wet year increases in turn. Taking the Xianyang section as an example, the annual total water demand of the upper limit of the lifting amount in a dry, normal, and wet year is 2.13 billion m³, 4.23 billion m³, and 7.54 billion m³, respectively. The annual total water demand of the upper limit of the lifting amount increases gradually from upstream to downstream. Taking the dry year as an example, the annual total water demand of the upper limit of the lifting amount from the Linjiacun section to the Huaxian section is 1.00 billion m³, 1.54 billion m³, 2.13 billion m³, 3.73 billion m³, and 4.32 billion m³, respectively.

For the ecological flow, the upper limit of the ecological flow of five sections in different typical years is greatly increased, and the intra-annual and inter-annual variations of the upper limit of ecological flow are consistent with the upper limit of the lifting amount. The upper limit of the ecological flow of all sections in flood seasons is greater than that in non-flood seasons. Taking Weijiabu section as an example, the average of upper limit of ecological flow in flood seasons in a dry, normal, and wet year is 93.68 m³/s, 224.12 m³/s, and 407.97 m³/s, respectively; the average of the upper limit of ecological flow in non-flood seasons is 30.60 m³/s, 66.22 m³/s, and 130.05 m³/s, respectively. The annual total water demand of the upper limit of ecological flow in a dry, normal, and wet year increases in turn. Taking Xianyang section as an example, the annual total water demand of the upper limit of ecological flow in a dry, normal, and wet year is 2.29 billion m³, 4.51 billion m³, and 8.00 billion m³, respectively. The annual total water demand of the upper limit of ecological flow increases gradually from upstream to downstream. Taking the dry year as an example, the annual total water demand of the upper limit of ecological flow from the Linjiacun section to the Huaxian section is 1.04 billion m³, 1.63 billion m³, 2.29 billion m³, 4.09 billion m³, and 4.66 billion m³.

The above is the calculation process of the ecological flow of five key sections in Shaanxi section of the Wei River under certain boundary conditions. When the variable factors, such as hydrological conditions, ecological service objects, and calculation methods, change, a new conditional combination is immediately generated, corresponding to a new interval of lifting amount interval, and a new interval of ecological flow.

Some previous studies only focus on the ecological base flow of the Wei River [79,80], and some studies carry out research on the ecological flow of the Wei River [72,81]. The study [72] divides the ecological flow into three parts: sediment transport, self-purification, and ecological base flow and proposes an ecological flow calculation model of the Wei River Basin in Shaanxi province considering inter-annual, intra-annual, and river partition variation. The study [81] puts forward the methodology of holistic eco-environmental flow assessment in semi-arid and semi-humid regions (HEFASS). The method calculates each sub-item of ecological flow, and finally determines the ecological flow of the Wei River, considering the opinions of stakeholders.

It is seen that previous studies calculate the ecological flow for specific river reach under specific hydrological conditions, and using specific methods. The calculation results are a set of specific values, which are inconsistent with the dynamic characteristics of ecological flow, and not conducive to the implementation and supervision of ecological flow. The VIAM proposed in this study comprehensively considers various variable factors, with strong adaptability and operability. The simulation system can both quickly adapt to the demand changes in practical application and provide visual decision support for managers.

6. Conclusions

The ecological flow is an important scientific basis for maintaining the ecological health of rivers, and realizing the optimal allocation of water resources. In this study, the new concept of ecological flow was given, and the VIAM for ecological flow calculation was proposed. Based on the knowledge visualization integrated platform, the ecological flow simulation system was constructed, using the knowledge graph and components. The Wei River was simulated through the method and system. The results validate the rationality and feasibility of the method. By analyzing the results of the application, the following conclusions are obtained:

(1) The VIAM determines the ecological flow through ecological base flow and lifting amount, which solves the problem of unclear concepts and difficult quantification of ecological flow, and makes the calculation results of ecological flow more scientific and reasonable;

(2) The lifting amount varies with variable factors, such as spatial–temporal scale, hydrological conditions, ecological service objects, and calculation methods. The lifting amount can be described as a variable interval, which determines that ecological flow is also a variable interval, with strong applicability and operability;

(3) The simulation system quickly adapts to changes in practical application. The different spatial–temporal scales, different hydrological conditions, different service objects, and different calculation methods can be adjusted by the visual human–machine interface. The system provides a visualization tool for the calculation of ecological flow, and offers decision support for managers

Although some achievements were made in this study, due to the complexity of the determination and control of ecological flow, there are still many shortcomings, which should be further explored. For the regions/basins with water shortages, ecological base flow intervals should be set up, in order to maintain the continuous flow of rivers and guarantee the most basic requirements of rivers. There is a normalized and long-term competitive water-use situation among multi-stakeholders. Research on the interval coordination mechanism of multi-stakeholders will be carried out to balance the interests of all stakeholders [82,83,84]. In addition, we will build a dynamic simulation and process management and control system for ecological flow, in order to increase the adaptability and operability of the system, and improve the quality of decision-making service.