Abstract

Drought is one of the major natural disasters affecting the development of economies and society. Drought early warning is the primary step and most important non-engineering measure for drought relief. This paper took Yuqiao Reservoir in Tianjin as a case study and analysed inter-annual changes of the drought limit water level. First, the causality between variables in the water supply–demand system was analysed, and a structural diagram of water sources allocation was drawn. Coupled with the parameters and a structural diagram, a system dynamics (SD) model of the water supply volume was established. Secondly, simulation results were tested to ensure that the model was valid. The water supply volume from 2003 to 2020 was simulated by using the model. Finally, based on the inflow process and the water supply volume, the drought limit water level was calculated. The results showed the water supply volume of Yuqiao Reservoir has changed remarkably. The drought limit water levels in 2003–2012 and in 2016–2020 were 16.70 m and 16.30 m, respectively: a difference of 0.40 m. The regulation curve of guarantee for water supply during 2016–2020 is significantly lower than that of 2003–2012. This research is of great significance for drought resistance, disaster mitigation and reservoir management.

Introduction

Given that almost half of the earth's terrestrial surfaces are susceptible to it, drought is a widespread phenomenon that has significant social, economic and environmental impacts (Kogan, 1997). Drought affects more people than any other kind of natural disaster owing to its large-scale and long-lasting nature (WMO, 2013). Drought warning is a critical component of drought hydrology, which plays a major role in risk management, drought preparedness and mitigation (Mishra & Singh, 2011). Developing fast predictive results will help in defining strategies and measures to minimise its effects. Water managers make use of monitoring systems in order to characterise and assess drought risk by means of indices and indicators (Haro-Monteagudo et al., 2017).

Drought preparedness planning has become a widely accepted tool to reduce the risks of future events (Wilhite & Svoboda, 2000) and reservoirs play an important role in it. Reservoirs can modify the distribution of water over space and time (Wurbs, 1993; Nandalal & Sakthivadivel, 2002). To mitigate drought impacts on water users, reservoir operation policies should consider the inclusion of drought-based parameters. Huang & Yuan (2004) proposed a drought early warning system (DEWS) for reservoir operation to aid water authorities in the decision-making process while confronting drought threats. On this basis, Huang & Chou (2005) revised the DEWS for reservoir operation and used a drought alert index (DAI) to characterise the drought severity alert level. Nicolosi et al. (2009) carried out a risk evaluation by means of an optimisation model based on genetic algorithms and defined thresholds for the implementation of mitigation measures tested through Monte Carlo simulation that made use of a stochastic generation of streamflow. Rossi et al. (2012) analysed the relationship between the risk of failure of water supply systems and the available water stored in reservoirs, and developed operating rules for drought mitigation by defining some threshold values. The drought threshold values proposed in the above research were expressed in probabilistic terms and its complexity was inconvenient to regulate practically for reservoir managers.

Flood limit water level is a key regulation level for flood control in reservoir operation (Chen et al., 2013; Jiang et al., 2015). Managers lower the water level of a reservoir to the flood limit water level before the arrival of the flood season, thus keeping adequate storage capacity for flood control. For reservoir managers, it is convenient to control a flood using a flood limit water level. The same method could be applied for drought prevention/management, adopting a key control level to cope with drought situations. When reservoir water level continues to be low and inflow continues to be less than normal, managers must guarantee that the water level of a reservoir is not less than the drought limit water level to ensure water supply for production and living. Therefore, for reservoir managers, it is convenient to regulate a drought by the drought limit water level.

The water inflow volume and water demand are important factors to determine the drought limit water level of a reservoir. The water inflow volume can be obtained from the reservoir hydrologic station, so the key of determining the drought limit water level is to confirm the water supply volume of the reservoir (namely, the users' water demand). The change of water supply volume is relatively steady, but if the water supply configuration changes, such as with the construction of a water transfer project, the water supply volume will have a marked change.

It is obvious that water demand development will affect drought (Rossi & Cancelliere, 2013). When the water supply volume increases, the drought limit water level will rise. When the water supply volume decreases, the drought limit water level will fall. Therefore, it is necessary to carry out research on inter-annual changes of water supply volume, thereby identifying the inter-annual change of the drought limit water level.

This paper took Yuqiao Reservoir in Tianjin as a case study – the main water source of Tianjin. In recent years, with the development of the social economy in Tianjin and the completion of the South to North Water Diversion Project (SNWDP) in 2015, the water supply configuration of Yuqiao Reservoir has changed greatly. In this paper, a system dynamics (SD) model was used to simulate and predict the change trend of reservoir water supply volume by using VensimPLE software. Combining the water inflow process, the drought limit water level of Yuqiao Reservoir was calculated. On this basis, the inter-annual change of drought limit water level was analysed.

Materials and methods

Study area

Tianjin city is located at longitude 116°42′05″–118°03′31″ east and latitude 38°33′57″–40°00′07″ north. It measures 172 km (south to north) and 104 km (east to west). Yuqiao Reservoir is located in Ji County, northern Tianjin (Figure 1), where the average annual precipitation is 750 mm and average annual evaporation is 1,000 mm. The precipitation is mainly concentrated in the flood season from June to September, accounting for 67–76% of the annual precipitation, while winter precipitation accounts for less than 2%. Therefore, serious drought often happens in winter and spring. Yuqiao Reservoir is the largest reservoir in Tianjin with a total storage capacity of 1.56 × 109 m3, a flood control storage capacity of 1.26 × 109 m3, an active storage capacity of 3.85 × 108 m3, a dead storage capacity of 0.36 × 108 m3, a flood limit water level of 19.87 m, and a normal water level of 21.16 m at the end of the flood season.

Fig. 1.

Schematic diagram of water supply from Yuqiao Reservoir to Tianjin.

Fig. 1.

Schematic diagram of water supply from Yuqiao Reservoir to Tianjin.

At present, the main water supply sources of Tianjin include the diversion water from Yuqiao Reservoir, surface water, groundwater and diversion water from the Yangtze River, as well as reclaimed water and desalinated seawater. Yuqiao Reservoir supplies mainly domestic water, industrial water and eco-environmental water, and the scope of water supply almost covers the whole of Tianjin. The water supply network of Yuqiao Reservoir is shown in Figure 1.

As the water supply of Yuqiao Reservoir can only meet the partial water demand of Tianjin, a water supply–demand contradiction in Tianjin still exists. In order to solve the problem, groundwater in Tianjin has been in a state of over-extraction for a long time, resulting in a series of geological and hydrological problems such as ecological environment degradation, saline intrusion and land subsidence. To ease the water shortage in Northern China, China implemented the SNWDP and the middle route of the project was put into operation in 2015. The water supply configuration in Tianjin is composed of seven water sources: diversion water from the middle route of the SNWDP, diversion water from Yuqiao Reservoir, local surface water, local groundwater, desalinated seawater, reclaimed water and emergency diversion water from the Yellow River.

Water uses in Tianjin include domestic water, industrial water, agricultural water and eco-environmental water. The eco-environmental water in Tianjin has been squeezed by domestic water and production water in the past. With the improvement of living standards, eco-environmental water will increase gradually.

The economic and social development data in Tianjin from 2003 to 2015 were obtained from the Tianjin Statistics Bureau (Tianjin Statistics Bureau, 2015). The water inflow data from 1990 to 2009 of Yuqiao Reservoir station in dry season (from October to May) and the water level–capacity relation curve of Yuqiao Reservoir were obtained from Yuqiao Reservoir Management Agency (Feng et al., 2011). The water demand data of Yuqiao Reservoir were obtained from Tianjin Water Conservancy Bureau (Hong et al., 2017).

Research methods

Determination of drought limit water level

Water shortage in a region can have a tremendous destructive effect on the local economy and society. In drought situations, water managers would rather incur a sequence of smaller shortages than one catastrophic shortage (Shih & Revelle, 1994). Therefore, a correct indicator needs to be determined to trigger a timely warning to prevent larger shortages later. A change of storage (water level) clearly reflects a reservoir's operation during previous periods, whilst its present status defines any future use possibilities (Haro-Monteagudo et al., 2017). Therefore, it is necessary to set reservoir storage (water level) as an indicator to trigger a drought warning. This paper adopts reservoir water level as an early warning index.

In this paper, the drought limit water level was determined by the supply–demand balance method. First, the design dry year was determined based on the guaranteed probability of inflow rate. Based on the known design probability, a typical dry year was chosen as the design typical dry year. Secondly, according to the water inflow, water demand and loss of water in the reservoir, the monthly water deficit was calculated by the supply–demand balance method. Lastly, the drought limit water level was determined based on the water level corresponding to the sum of the dead capacity and the maximum monthly water deficit.

A probability of 75% was taken for the design dry year in Yuqiao Basin. Based on the inflow series from 1990 to 2009 in the dry season (from October to May), the design inflow process Q(k) (P = 75%) was obtained by typical year method. The reservoir water supply volume W(k) was obtained by simulation results from an SD model.

The calculation equation for the drought limit water level is as follows: 
formula
(1)
where D(k) is the water deficit in the kth month; W(k) is the water supply volume in the kth month; L(k) is the loss of water (evaporation, leakage, etc.); Q(k) is the inflow in the kth month.
In a dry year, the worst situation is that the reservoir water level drops to the dead water level at the beginning of the flood season. If the inflow continues to be less than the water demand in the flood season, a severe drought may occur. In general, the inflow in a flood season can meet water demand under normal conditions. This paper adopts the beginning of the flood season in a dry year as the starting point of the regulation calculation, and the dead water level as the initial regulating water level. The monthly guarantee for water supply was calculated by the supply–demand balance method in a monthly reverse sequence, which can be measured as: 
formula
(2)
where , and V(k) and V(k + 1) are the storage that should be reached at the beginning of kth month and (k + 1)th month, respectively; Vmin and Vmax are the storage corresponding to the dead water level and the normal water level, respectively.

The regulation curve of guarantee for water supply can be depicted by Equation (2), which reflects the lowest water level under continuous dry conditions in the non-flood season.

Analysis of reservoir water supply volume

Generally, there are multiple water sources and multiple water users in a region. The relationships between them often do not satisfy one-to-one correspondence. Therefore, in order to calculate accurately the water supply volume undertaken by the reservoir, the water supply–demand balance of the study area should be analysed. Firstly, the topological relationship of water sources–water plants–water users was plotted based on the distribution configuration of water resources and users (Figure 1). Then, the water supply volume undertaken by the reservoir can be extracted from the total water supply systems.

In order to analyse the change of reservoir water supply volume, the future water supply configuration of multiple water sources and water users should also be taken into full consideration. The future predictable changes of supply water sources in this region should be considered, such as mining plans for groundwater, development plans for unconventional water sources, and so on. In terms of water demand, changes caused by the development of the regional industrial structure, population and economy should all be considered. This paper used an SD method to construct the water supply–demand relationships in Tianjin and predict the change of water supply volume of Yuqiao Reservoir.

System dynamics model

SD, as proposed by Forrester (1961, 1968), aims to solve the simulation problems of large-scale systems by integrating cybernetics, systems theory, information theory, decision–making theory and computer technology (Wang, 1995). The basis of SD is the recognition of complex interrelationships existing among different objects within a system (Elshorbagy et al., 2005). Though SD was initially designed for the analysis and modelling of large-scale socioeconomic systems, with its ability to explain complexity, it has now been applied in many areas, such as energy system planning, solid waste management, project management, etc. (Naill et al., 1992; Dyson & Chang, 2005; Lyneis & Ford, 2007; Aoyama & Osakaya, 2009; Fong et al., 2009). Similarly, the SD method has been widely used in water demand prediction (Zhang et al., 2008; Nawarathna & George, 2009; Zhai et al., 2009; Qi & Chang, 2011; Qin et al., 2012; Wang et al., 2015; Li & Zhang, 2016) in recent years. Following this research, it was concluded that the SD model can provide reliable technical support for water demand prediction.

An SD model is composed of two parts: flow chart drawing and structure equations building. For this paper, VensimPLE software was used to build an SD model; causal loop, stock and flowchart models can be built easily using Vensim. When building an SD model, the relationships between variables are depicted using arrows with a positive (+) or negative (−) sign placed besides the arrow heads to indicate link polarity. Thus, Vensim automatically established the causal relationship between the variables. Then, applying the equation function provided by Vensim, the quantitative relationships between the parameters and variables were entered into the model.

The modelling steps of the water supply system are as follows:

  1. Make the study purpose clear. Here, the purpose is to simulate a water supply–demand system in a given area for a specified period, and to extract the water supply volume of the reservoir from the system.

  2. Determine the study boundaries. Generally speaking, an SD model sets the study area as the spatial boundary and the simulation period of the model as the time boundary.

  3. Analyse causality. The system feedback process is the core of SD and feedback relations are the basis of the system structure. Causality analysis aims to clarify the causal relationship between variables within a system and express the relationship through causal loop diagrams. The main cause–effect chain of the water supply–demand system is: regional economic development →+ water resources demand →+ imbalance between supply and demand → regional economic development.

  4. Establish the model. By depicting a flow chart and establishing the structural equations, the internal mechanism of the system is defined clearly and the relations among the variables are quantified. The major constraints in the equations are water supply constraints, economic and social development constraints and water quota constraints.

  5. Simulate the model. The value of each parameter was substituted into the structural equations and the simulation process was performed with Vensim software. The rationality of the simulation results was analysed, and then the model was adjusted accordingly.

  6. Test the model. The purpose of a model test is to ensure that the model is highly consistent with the behaviour of the real system.

Results and discussion

Water supply volume of Yuqiao Reservoir based on an SD model

SD model building

In this paper, the borders of Tianjin were set as the spatial boundary, whilst the time boundary was set from 2003 to 2020, for which historical statistics were used for the years 2003–2014 and model predictions were used for 2015–2020.

Based on the basic principle of water allocation in Tianjin, the causality relationships between multiple water sources and multiple water users were built; these relationships (except those including diversion water from Yuqiao Reservoir) can be seen in the cause–effect diagram in Figure 2. Based on the principle of water balance, the water supply deficit can be defined as the water supplied by the Yuqiao Reservoir. Thus, the water supply volume of Yuqiao Reservoir can be extracted from the total water supply system.

Fig. 2.

Model causality diagram.

Fig. 2.

Model causality diagram.

The water supply SD model of Tianjin was constructed based on Tianjin's water supply configuration, internal system structure and the balance of water supply and demand. The water sources mainly included transferred water, unconventional water, groundwater and surface water. Water uses were mainly urban, rural, industrial, ecological and agricultural. Because Yuqiao Reservoir only provides water for urban, industrial and ecological use, the deficit of urban domestic water, industrial water and ecological water was regarded as the water supply volume of Yuqiao Reservoir. The structure diagram of the water resources allocation model in Tianjin is shown in Figure 3.

Fig. 3.

Structure diagram of the water resources allocation model for Tianjin.

Fig. 3.

Structure diagram of the water resources allocation model for Tianjin.

For the SD model, results are determined mainly by the model structure, whilst the parameters of the model have relatively little influence. Although parameter estimation requirements are not very strict, it is still necessary to accurately estimate some parameters that have significant impacts on system results. Also, in the process of running the model, the parameters need to be constantly modified so as to make them conform to the actual situation.

The main parameters used included: state variables (city population, rural population, industrial output, ecological-environmental water demand, surface water resources), rate variables (city population growth rate, urbanisation rate, industrial growth rate, change rate of cultivated land area), auxiliary variables (urban domestic water deficit, industrial water deficit, ecological water deficit) and table functions (groundwater exploitation plan, reclaimed water plan, desalinated water plan, water supply plan of the SNWDP). (Table functions are user-defined functions in SD programs which are usually represented by charts and are generally used to reflect the special nonlinear relationship between two variables).

Testing the SD model

First, the model was intuitively tested and it was found that the variable setting, causality construction, equation expression and layout of the flow chart structure were reasonable. Then, the dimensions in the equations were found to be consistent. Finally, Vensim-PLE software was used to simulate the model, and the model ran successfully without any ill-conditioned results.

The industrial output, urban population and water supplied by Yuqiao Reservoir from 2003 to 2014 were simulated by using the SD model. The simulation results were compared with actual statistical data to test the reliability, as shown in Tables 13.

Table 1.

Consistency test on industrial output.

Year Statistics (108 yuan) Simulation (108 yuan) Relative error (%) 
2003 4,370.00 4,374.00 0.09 
2004 5,763.93 5,336.28 –8.01 
2005 6,774.10 6,510.26 –4.05 
2006 8,527.70 7,942.52 –7.37 
2007 10,502.91 9,689.87 –8.39 
2008 12,506.83 11,821.60 –5.80 
2009 14,758.05 14,422.40 –2.33 
2010 17,016.01 17,595.30 +3.29 
2011 21,523.32 21,466.30 −0.27 
2012 24,017.18 24,256.90 +0.99 
2013 27,169.14 27,410.30 +0.88 
2014 30,055.12 30,973.70 +2.97 
Year Statistics (108 yuan) Simulation (108 yuan) Relative error (%) 
2003 4,370.00 4,374.00 0.09 
2004 5,763.93 5,336.28 –8.01 
2005 6,774.10 6,510.26 –4.05 
2006 8,527.70 7,942.52 –7.37 
2007 10,502.91 9,689.87 –8.39 
2008 12,506.83 11,821.60 –5.80 
2009 14,758.05 14,422.40 –2.33 
2010 17,016.01 17,595.30 +3.29 
2011 21,523.32 21,466.30 −0.27 
2012 24,017.18 24,256.90 +0.99 
2013 27,169.14 27,410.30 +0.88 
2014 30,055.12 30,973.70 +2.97 
Table 2.

Consistency test on urban population.

Year Statistics (104 person) Simulation (104 person) Relative error (%) 
2003 1,009.0 1,009.0 0.00 
2004 1,021.5 1,049.4 +2.66 
2005 1,040.5 1,091.3 +4.65 
2006 1,072.6 1,135.0 +5.50 
2007 1,115.0 1,180.4 +5.54 
2008 1,176.1 1,227.6 +4.20 
2009 1,228.3 1,276.7 +3.79 
2010 1,299.5 1,327.8 +2.13 
2011 1,354.5 1,380.9 +1.91 
2012 1,413.0 1,436.1 +1.61 
2013 1,464.9 1,493.6 +1.92 
2014 1,516.8 1,553.3 +2.35 
Year Statistics (104 person) Simulation (104 person) Relative error (%) 
2003 1,009.0 1,009.0 0.00 
2004 1,021.5 1,049.4 +2.66 
2005 1,040.5 1,091.3 +4.65 
2006 1,072.6 1,135.0 +5.50 
2007 1,115.0 1,180.4 +5.54 
2008 1,176.1 1,227.6 +4.20 
2009 1,228.3 1,276.7 +3.79 
2010 1,299.5 1,327.8 +2.13 
2011 1,354.5 1,380.9 +1.91 
2012 1,413.0 1,436.1 +1.61 
2013 1,464.9 1,493.6 +1.92 
2014 1,516.8 1,553.3 +2.35 
Table 3.

Consistency test on water supplied by Yuqiao Reservoir.

Year Actual water supply (108 m3Simulation value (108 m3Relative error (%) 
2003 7.63 6.96 –9.63 
2004 7.52 7.89 +4.69 
2005 8.82 8.09 –9.02 
2006 8.58 8.14 –5.41 
2007 8.53 7.95 –7.30 
2008 8.13 7.40 –9.86 
2009 8.13 7.81 –4.10 
2010 8.39 8.18 –2.57 
2011 7.66 8.46 +9.46 
2012 9.06 8.85 –2.37 
2013 9.87 10.15 +2.76 
2014 10.87 11.45 +5.07 
Year Actual water supply (108 m3Simulation value (108 m3Relative error (%) 
2003 7.63 6.96 –9.63 
2004 7.52 7.89 +4.69 
2005 8.82 8.09 –9.02 
2006 8.58 8.14 –5.41 
2007 8.53 7.95 –7.30 
2008 8.13 7.40 –9.86 
2009 8.13 7.81 –4.10 
2010 8.39 8.18 –2.57 
2011 7.66 8.46 +9.46 
2012 9.06 8.85 –2.37 
2013 9.87 10.15 +2.76 
2014 10.87 11.45 +5.07 

Tables 13 show that the simulation values of all variables were basically consistent with the historical values, and the relative error was controlled within ±10%. Thus, the simulation results of the model were in good agreement with the actual values and the SD model showed high accuracy. Complicated interactions and unknown factors affect simulations of the water resources allocation system. Specifically, government policies and other external factors vary from year to year and affect the results. The fluctuating range of relative errors is normal.

Among the procedures underlying water supply volume forecasting, the selection of affecting factors and the development of a causal loop diagram are the most important procedures. This research is focused on the forecasting of the water supply volume of Yuqiao Reservoir. The middle route of the SNWDP, unconventional water, groundwater, and urban, industrial and ecological-environmental water demand were identified as major factors affecting the water supply volume of Yuqiao Reservoir. We applied some policy decisions (such as the transferred water quota, water allocation plans of unconventional water and groundwater) to the SD model to provide applicable information for planners and to simulate the potential effects on their choices. Thus, the SD model built on paper has obvious advantages for solving dynamic problems, reflecting the process of water supply structure adjustment, and analysing the influence of policy decisions on the water supply volume of Yuqiao Reservoir.

Scenarios and result analysis

After model validation and assuring accuracy and precision, results obtained after applying different scenarios could be evaluated.

The middle route of the SNWDP has been in operation since 2015. Therefore, the water supply configuration of Tianjin should consider the transferred water. In 2015, the water transferred to Tianjin from the middle route was 4 × 108 m3. In 2016, the transferred water increased to 8.6 × 108 m3.

In the water supply subsystem, the table functions of the unconventional water and groundwater were set according to the relevant plans (Table 4). The unconventional water included reclaimed water and desalinated seawater, and groundwater included shallow groundwater and deep groundwater.

Table 4.

Water allocation plans for unconventional water and groundwater; in 100 million m3 (108 m3).

Year Reclaimed water Desalinated seawater Shallow groundwater Deep groundwater 
2003 2.80 2.00 
2011 0.23 0.28 2.99 2.40 
2015 0.31 0.59 3.09 1.98 
2020 0.47 1.61 2.83 0.25 
Year Reclaimed water Desalinated seawater Shallow groundwater Deep groundwater 
2003 2.80 2.00 
2011 0.23 0.28 2.99 2.40 
2015 0.31 0.59 3.09 1.98 
2020 0.47 1.61 2.83 0.25 

In the water consumption subsystem, the middle route of the SNWDP mainly supplies water to the City Centre Waterworks and Jinbin Waterworks, and water uses partially overlap with Yuqiao Reservoir water uses. Therefore, part of Yuqiao Reservoir water uses (urban and industrial) has been converted into the middle route of the SNWDP water use. The natural growth rate of the urban population was set at 4%, and the annual growth rate of industrial output was set at 13% from Tianjin Statistics Bureau (Tianjin Statistics Bureau, 2015). The eco-environmental water demand is shown in Table 5.

Table 5.

Eco-environmental water demand in Tianjin; in 100 million m3.

Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 
Water demand 0.73 0.74 0.76 0.77 0.79 0.80 0.82 0.83 0.84 
Year 2012 2013 2014 2015 2016 2017 2018 2019 2020 
Water demand 0.85 1.77 2.68 3.26 3.85 3.66 3.47 3.28 3.09 
Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 
Water demand 0.73 0.74 0.76 0.77 0.79 0.80 0.82 0.83 0.84 
Year 2012 2013 2014 2015 2016 2017 2018 2019 2020 
Water demand 0.85 1.77 2.68 3.26 3.85 3.66 3.47 3.28 3.09 

According to the water supply subsystem and the water consumption subsystem, the change trend of the water supply volume of Yuqiao Reservoir was predicted by using the SD model. The results are shown in Figure 4.

Fig. 4.

Water supply volume of Yuqiao Reservoir.

Fig. 4.

Water supply volume of Yuqiao Reservoir.

As can be seen in Figure 4, before 2015 the water supply of Yuqiao Reservoir showed a rising tendency in fluctuation, with a change trend which was the same as for industrial water demand. The urban domestic water demand showed a steady rising trend. The eco-environmental water remained nearly constant from 2003 to 2012, but it increased greatly in 2013 and 2014, due largely to the implementation of river pollution control projects in Tianjin from 2013. As the middle route of SNWDP was not completed, pollution control projects increased the extra water supply of Yuqiao Reservoir, but the extra water supply did not belong to the normal water supply for Yuqiao Reservoir. In 2015, the middle route of SNWDP was put into operation, and Yuqiao Reservoir could provide more water to guarantee the eco-environment water, but the water supply capacity of middle route of SNWDP had not yet reached its design value. Therefore, water use fluctuated remarkably in the period 2013–2015.

After 2015, the water supply capacity of middle route of SNWDP had reached its design value. The water supply of Yuqiao Reservoir stabilised, relatively. Compared to before, the urban domestic water and industrial water reduced greatly, and the ecological environmental water was greatly increased.

In order to analyse the inter-annual change of the drought limit water level, the time series (2003–2020) was divided into 2003–2012 (stabilisation period), 2013–2015 (transition period) and 2016–2020 (stabilisation period).

Analysis of the inter-annual change of the drought limit water level

According to the water supply of Yuqiao Reservoir (Figure 4), the water supply volume obviously changed after the middle route of the SNWDP was put into operation. Therefore, it is necessary to analyse the inter-annual change of the drought limit water level.

Using the water inflow data from 1990 to 2009 of Yuqiao Reservoir station in dry season (from October to May), the design inflow process Q(k) (P = 75%) was obtained by the typical year method, as shown in Table 6.

Table 6.

Design inflow data of Yuqiao Reservoir; in 100 million m3.

Month JAN FEB MAR APR MAY JUN JUL AGU SEP OCT NOV DEC 
Inflow 0.15 0.15 0.33 0.42 0.30 0.63 1.27 1.84 1.09 0.57 0.38 0.18 
Month JAN FEB MAR APR MAY JUN JUL AGU SEP OCT NOV DEC 
Inflow 0.15 0.15 0.33 0.42 0.30 0.63 1.27 1.84 1.09 0.57 0.38 0.18 

The water supply volume of Yuqiao Reservoir from 2016 to 2020 was obtained by the SD model. Because water users of Yuqiao Reservoir do not include agriculture water, water users' water consumption does not change much, month to month. The annual and monthly (annual divided by 12) water supply volumes are shown in Table 7.

Table 7.

The water supply volume of Yuqiao Reservoir from 2016 to 2020; in 100 million m3.

Year 2016 2017 2018 2019 2020 
Annual water supply volume 5.93 6.15 6.32 6.44 6.49 
Monthly water supply volume 0.49 0.51 0.53 0.54 0.54 
Year 2016 2017 2018 2019 2020 
Annual water supply volume 5.93 6.15 6.32 6.44 6.49 
Monthly water supply volume 0.49 0.51 0.53 0.54 0.54 

The loss of water in Yuqiao Reservoir is mainly from reservoir evaporation, while reservoir leakage is very small, so can be ignored. The reservoir evaporation in a dry year is shown in Table 8.

Table 8.

Annual mean evaporation from Yuqiao Reservoir; in 100 million m3.

Month OCT NOV DEC JAN FEB MAR APR MAY JUN 
Evaporation 0.07 0.04 0.03 0.02 0.02 0.04 0.06 0.07 0.03 
Month OCT NOV DEC JAN FEB MAR APR MAY JUN 
Evaporation 0.07 0.04 0.03 0.02 0.02 0.04 0.06 0.07 0.03 

In this paper, we have only considered drought limit water levels in stabilisation periods. Using the determination method of the drought limit water level, the monthly water deficit was calculated by Equation (1). The calculation results are shown in Table 9. The maximum monthly water deficits in 2003–2012 and in 2016–2020 were 0.55 and 0.39, respectively. Based on the dead capacity (0.36 × 108 m3), the maximum monthly water deficit and the storage-capacity curve map of Yuqiao Reservoir (Figure 5), the drought limit water levels in 2003–2012 and in 2016–2020 are 16.70 m and 16.30 m, respectively. The difference between these two water levels is 0.40 m. It follows that the change of water supply volume has an obvious effect on the drought limit water level.

Table 9.

Calculation of drought limit water level in Yuqiao Reservoir; in 100 million m3.

Month Water demand
 
Water Inflow Water evaporation Water deficit
 
2003–2012 2016–2020 2003–2012 2016–2020 
JUN 0.68 0.52 0.63 0.03 0.08 −0.08 
MAY 0.68 0.52 0.30 0.07 0.45 0.29 
APR 0.68 0.52 0.42 0.06 0.32 0.16 
MAR 0.68 0.52 0.33 0.04 0.39 0.23 
FEB 0.68 0.52 0.15 0.02 0.55 0.39 
JAN 0.68 0.52 0.15 0.02 0.55 0.39 
DEC 0.68 0.52 0.18 0.03 0.53 0.37 
NOV 0.68 0.52 0.38 0.04 0.34 0.18 
OCT 0.68 0.52 0.57 0.07 0.18 0.02 
Month Water demand
 
Water Inflow Water evaporation Water deficit
 
2003–2012 2016–2020 2003–2012 2016–2020 
JUN 0.68 0.52 0.63 0.03 0.08 −0.08 
MAY 0.68 0.52 0.30 0.07 0.45 0.29 
APR 0.68 0.52 0.42 0.06 0.32 0.16 
MAR 0.68 0.52 0.33 0.04 0.39 0.23 
FEB 0.68 0.52 0.15 0.02 0.55 0.39 
JAN 0.68 0.52 0.15 0.02 0.55 0.39 
DEC 0.68 0.52 0.18 0.03 0.53 0.37 
NOV 0.68 0.52 0.38 0.04 0.34 0.18 
OCT 0.68 0.52 0.57 0.07 0.18 0.02 
Fig. 5.

The storage capacity curve map of Yuqiao Reservoir.

Fig. 5.

The storage capacity curve map of Yuqiao Reservoir.

The monthly guarantee for water supply was calculated using Equation (2). The calculation results are shown in Table 10 and Figure 6.

Table 10.

Calculation of monthly guarantee for water supply; in 100 million m3.

Month Water demand
 
Water inflow Water evaporation Reservoir storage/level (m)
 
2003–2012 2016–2020 2003–2012 2016–2020 
JUL 0.68 0.52 1.27 0.04 0.36/15.00 -- 
JUN 0.68 0.52 0.63 0.03 0.44/15.32 0.36/15.00 
MAY 0.68 0.52 0.30 0.07 0.89/16.65 0.65/16.02 
APR 0.68 0.52 0.42 0.06 1.21/17.27 0.81/16.46 
MAR 0.68 0.52 0.33 0.04 1.60/17.96 1.04/16.97 
FEB 0.68 0.52 0.15 0.02 2.15/18.80 1.43/17.66 
JAN 0.68 0.52 0.15 0.02 2.70/19.51 1.82/18.30 
DEC 0.68 0.52 0.18 0.03 3.23/20.20 2.19/18.86 
NOV 0.68 0.52 0.38 0.04 3.57/20.60 2.37/19.11 
OCT 0.68 0.52 0.57 0.07 3.75/20.81 2.39/19.14 
Month Water demand
 
Water inflow Water evaporation Reservoir storage/level (m)
 
2003–2012 2016–2020 2003–2012 2016–2020 
JUL 0.68 0.52 1.27 0.04 0.36/15.00 -- 
JUN 0.68 0.52 0.63 0.03 0.44/15.32 0.36/15.00 
MAY 0.68 0.52 0.30 0.07 0.89/16.65 0.65/16.02 
APR 0.68 0.52 0.42 0.06 1.21/17.27 0.81/16.46 
MAR 0.68 0.52 0.33 0.04 1.60/17.96 1.04/16.97 
FEB 0.68 0.52 0.15 0.02 2.15/18.80 1.43/17.66 
JAN 0.68 0.52 0.15 0.02 2.70/19.51 1.82/18.30 
DEC 0.68 0.52 0.18 0.03 3.23/20.20 2.19/18.86 
NOV 0.68 0.52 0.38 0.04 3.57/20.60 2.37/19.11 
OCT 0.68 0.52 0.57 0.07 3.75/20.81 2.39/19.14 
Fig. 6.

The regulation curve of guarantee for water supply.

Fig. 6.

The regulation curve of guarantee for water supply.

As can be seen from Figure 6, when the water level is below the regulation curve of guarantee for water supply, water supply cannot be guaranteed. The regulation curve of guarantee for water supply during 2016–2020 is significantly lower than for 2003–2012. The water levels at the end of the flood season were 20.81 m and 19.14 m in 2003–2012 and in 2016–2020, respectively. The normal water level at the end of flood season is 21.16 m. If the reservoir water level reaches the normal water level at the end of flood season, water supply can meet demands, even if the reservoir encounters continuous dry in the non-flood season.

If the inflow is low in the flood season, the pressure on water supply of the reservoir in 2016–2020 is alleviated compared with that of 2003–2012. In terms of practical reservoir regulation, managers can regulate the water level in real time based on the inflow and the regulation curve of guarantee for water supply, thus guaranteeing urban domestic, industry and eco-environment water uses.

With the development of the social economy and the construction of the water diversion project, the water supply configuration in some areas have changed. Therefore, it was necessary to research the inter-annual change of water supply volume, and thereby identify the inter-annual change of the drought limit water level. The research methods and ideas applied could provide necessary guidance for the determination of drought limit water level in other areas, and the research results are of great significance to drought prevention, disaster reduction and reservoir management.

At present, a great many studies on drought preparedness planning of reservoirs have been made in different parts of the world, which could provide plentiful basic data for the calculation of drought limit water level. On this basis, the analysis of inter-annual changes of drought limit water levels could easily be implemented by the method presented in this paper. Thus, the findings of this paper have a wide applicability.

Conclusions

The drought limit water level is an important index for drought warning. With a change of water supply volume, the drought limit water level of a reservoir will also change.

An SD model was used to simulate and predict the change trend of reservoir water supply volume by using VensimPLE software. The simulation values of all variables were basically consistent with the historical values, and the relative error was controlled within ±10%. The simulation results of the model were in good agreement with the actual values, and the SD model had high reliability.

Applying the SD model, the water supply of Yuqiao Reservoir was simulated and predicted. Before 2015, the water supply of the reservoir showed a rising tendency for fluctuation. After 2015, the water supply capacity of the middle route project of the SNWDP had reached its design value and the water supply of Yuqiao Reservoir stabilised relatively.

The drought limit water levels in 2003–2012 and in 2016–2020 were 16.70 m and 16.30 m, respectively, giving a difference between the two levels of 0.40 m. It follows that the change of water supply volume had an obvious effect on the drought limit water level.

The regulation curve of guarantee for water supply during 2016–2020 is significantly lower than that of 2003–2012. The water levels at the end of the flood seasons were 20.81 m and 19.14 m in 2003–2012 and in 2016–2020, respectively. The normal water level at the end of a flood season is 21.16 m. If the reservoir water level reaches the normal water level, water supply can meet demands, even if the reservoir encounters a continuous dry period in the non-flood season.

Acknowledgments

The authors would like to acknowledge the financial support for this work provided by the National Key R&D Program of China (Grant no. 2016YFC0401407), the National Natural Science Foundation of China (Grant no. 51579169), and the Ministry of Water Resources Special Funds for Scientific Research on Public Causes (Grant no. 201401041).

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