In the current study, to investigate the impacts of the wetness–dryness encountering of the upstream inflow and downstream salt intrusion on the water supply of the Pearl River Delta, we developed a water evaluation and planning (WEAP)-based water resources allocation model to calculate water supply schemes for the Pearl River Delta under 10 different scenarios. The impact of the scenarios on the water supply scheme of the Pearl River Delta was investigated. The results showed that (1) the water shortage of the Pearl River Delta is highly dependent upon the dryness combination of the upstream runoff during the dry period, in particular to the cities at the Pearl River Delta estuary, the water shortages are seriously influenced by saltwater intrusion; and (2) the water transfer projects could alleviate the water supply pressure of the Pearl River Delta when there is an extreme or more dryness encounter of upstream runoff. However, when extreme dryness events are impacting the upstream runoff of the West River, the impact of the water transfer projects is weakened and much of the critical upstream runoff for saltwater suppression cannot be satisfied, which largely impacts water withdrawals at the downstream cities in the Pearl River Delta estuary.

  • A water evaluation and planning (WEAP)-based water allocation model was developed for coastal urban agglomerations like the Pearl River Delta (PRD).

  • Water allocation schemes under different scenarios of upstream inflow and downstream salt intrusion were worked out.

  • The response of the water allocation scheme to the wetness–dryness encountering of the upstream inflow and downstream salt intrusion was revealed.

Graphical Abstract

Graphical Abstract
Graphical Abstract

Coastal urban agglomerations host a dense population, have developed economies, and usually are the economic growth poles of a nation or region (Ren et al., 2019; Wang et al., 2021). A steady and sustainable resource supply is the prerequisite of urban agglomeration development, with water resources being one of the strategic natural resources and foundational for socio-economic development. A safe water supply is vital for the domestic, productive, and ecological water demands of urban agglomerations (Wang et al., 2020a, 2020b; Saucedo-Ramirez et al., 2022). However, due to climate change and human-environmental system dynamics, the water supply for coastal urban agglomerations is challenged by the uncertainty of available water resources and the often-ineffective layout of water infrastructure (Ashofteh et al., 2017; Pienaar & Hughes, 2017; Saharwardi & Kumar, 2021). Coastal urban agglomerations are usually located downstream of large rivers, where the river meets the coastal region. The upstream inflows and downstream salt tides are the two chief factors influencing the available water resources within these regions (Gong et al., 2022), and the decrease of upstream runoff is also one of the causes of salt tides (Munia et al., 2018; Tang et al., 2020). Therefore, incorporating changes in upstream inflows and salt intrusion into water resource allocation models is crucial for developing effective and reasonable water supply schemes. This is particularly important given the great uncertainty of hydro-climate change on coastal urban agglomerations.

Allocation of water resources can be conducted at various spatial scales (e.g., basin, region, and city) and several simulation and modeling technologies have been proposed to obtain the optimal water supply scheme at various time scales (e.g., daily, monthly, and yearly). However, modeling of water allocation within coastal urban agglomerations considered with saltwater intrusion is still not sufficient. In addition, traditional water allocation models usually choose long time series for the runoff input and water supply schemes are chosen and analyzed under several frequencies (e.g., 97, 90, and 50%) (Fu et al., 2018; Li et al., 2018; He et al., 2019). Spatiotemporal variation of runoff is being intensified as the compound impacts of climate change and human activities continue to advance. Analysis of the wetness–dryness encountering of runoff in different rivers is a good alternative to promote a more comprehensive understanding of runoff characteristics within a basin and to help refine the input of available water resources for water resource allocation models. The copula function is widely used in the analysis of wetness–dryness encountering of runoff (Wang et al., 2022), and compared to other multivariate hydrological analysis methods (e.g., joint distribution, multiple normal distribution, and non-parametric methods), has the advantage of having the same adaptability to variables with different distribution characteristics (Liu et al., 2015, 2020a, 2020b; Fan et al., 2018). The multiple copula function can better portray the randomness and dependence of hydrological variables and simplifies the joint probability problem in multidimensional analysis. For example, it has been used to construct two- and three-dimensional runoff combinations of rivers and then to estimate the wetness–dryness encountering of the runoff as an input for the water allocation model (Chen et al., 2019; Wu et al., 2020).

The water evaluation and planning (WEAP) model is one of the most useful water modeling systems and has the advantage of analyzing and simulating different water systems for policy analysis of water resource systems at the regional- or basin-scale (Li et al., 2015). WEAP can provide an integrated water resource planning framework for water management under various scenarios and has been successfully applied to evaluate the sustainability of limited water resource management strategies in coastal zones (Kou et al., 2018). The Pearl River Delta is one of China's three largest coastal urban agglomerations with a dense population, developed economy, and complicated water networks. The uneven distribution of water resources and high dependence on upstream runoff poses a great challenge to water supply security within the Pearl River Delta. In addition, the water supply within this region is threatened by salt intrusion downstream during the dry period (Yao et al., 2016; Payo-Payo et al., 2022). Given these factors, it is necessary to work out strategic water supply schemes of the Pearl River Delta that consider the wetness–dryness encountering of the upstream inflow and downstream salt intrusion, for guaranteeing water supply security.

The current study aims to explore the impacts of wetness–dryness encountering of upstream inflow and downstream salt intrusion on the water supply scheme of the Pearl River Delta via a WEAP-based water allocation model. Different from the previous studies, the input of available water resources for the water allocation model is deduced from wetness–dryness encountering instead of long time series for the runoff, and the critical upstream runoff for saltwater suppression, reflecting downstream salt intrusion, is estimated and taken as the river flow requirement in the model. The objectives of this study are to: (1) develop a WEAP based water allocation model for the Pearl River Delta considering the wetness–dryness encountering of upstream inflow quantified by the multiple copula function and downstream salt intrusion; (2) work out reasonable water supply schemes of the Pearl River Delta under different scenarios of upstream inflow and downstream salt intrusion; and (3) reveal the response of the water supply scheme of the Pearl River Delta to the wetness–dryness encountering of the upstream inflow and downstream salt intrusion and based on which the corresponding policy recommendations are put forwards for the local government to reduce the water shortage risk of the Pearl River Delta in dry periods. This study has the potential to provide policy structure and solutions for water resource planning within coastal urban agglomerations in a changing environment.

The Pearl River Delta is located in the central and southern parts of the Guangdong Province (Figure 1). It is situated at the lower reaches of the East River, North River, and West River, and has a total drainage area of 450,000 km2 (Deng et al., 2018; Zhang et al., 2019). The Pearl River Delta is an impingement plain formed by a complex river network. The river network has a high density of 0.8 km2. The Pearl River Delta experiences a subtropical marine monsoon climate with a mean annual precipitation of approximately 1,600–2,300 mm. The total water resources amount to 374.2 billion m3 and the upstream runoff from the East River, North River, and West River accounts for approximately 78.6% of the total water resources (Tang et al., 2017; Liu et al., 2018a, 2018b). The Pearl River Delta covers nine cities, namely Guangzhou, Shenzhen, Zhuhai, Foshan, Jiangmen, Zhaoqing, Dongguan, Huizhou, and Zhongshan, with a total area of 5, 6,000 km2. The Pearl River Delta hosts a population of 58 million and the Gross Domestic Product (GDP) in 2019 was 8,104 billion RMB (Liu et al., 2018a, 2018b; Li et al., 2020). Per capita GDP within the Pearl River Delta is much higher than the national average. The Pearl River Delta region has the highest degree of economic and social openness and the strongest degree of activity in China, with this region playing an important role in the national development strategy. The growing population and rapidly developing economy of the Pearl River Delta require huge amounts of water resources for domestic, productive, and ecological water use, resulting in an increasing pressure on the water supply. Severe saltwater intrusion has impaired the drinking water supply in the densely populated estuary of the Pearl River Delta during the dry season (Sun et al., 2017; Lin et al., 2019) and higher dependence on the upstream runoff has increased the risk to the water supply (Yan et al., 2018). Both saltwater intrusion and the high dependence on the upstream runoff could be exacerbated by increasing extreme weather events and intensive anthropogenic activities. Therefore, it is essential to investigate reasonable water resource schemes for the water supply security of the Pearl River Delta, which considers changes to upstream inflow and downstream salt intrusion.
Fig. 1

Sketch map of the Pearl River Delta.

Fig. 1

Sketch map of the Pearl River Delta.

Close modal
A 50-year time series (1959–2008) of the monthly average discharge at three hydrological stations (Makou, Shijiao, and Boluo) was used for the analysis of the wetness–dryness encountering of the runoff of the East River, North River, and West River. Hourly chlorinity at three pumping stations (Pinggang, Guangchang, and Zhuzhoutou) (Figure 2) was selected from the observed data from 2010 to 2015 for the estimation of the critical upstream runoff for saltwater suppression.
Fig. 2

The locations of Pinggang, Guangchang, and Zhuzhoutou pumping stations.

Fig. 2

The locations of Pinggang, Guangchang, and Zhuzhoutou pumping stations.

Close modal

Multidimensional copula function

Copulas have been widely used to deal with multivariate extremes (e.g., flood peak, volume, and duration) in hydrology in recent years (Lilienthal et al., 2018; Worland et al., 2019) because they do not require a uniform distribution of random variables. Copulas can illustrate the correlation of each random vector and therefore, are known as the multivariate joint distributions that connect the marginal distributions of the random variables, where H is a n-dimensional distribution function with the marginal distributions of a function () verifies a copula as:
formula
(1)

Dependence between random variables can be modeled by the C function, while several functions such as NORM, POISS, EV, GEV, GAMMA, WBL, and GP are chosen to describe the marginal distributions of the random variables. Copulas have to be chosen and the dependence under the given marginal distributions is compared, to derive better multivariate joint distributions. Well-known copulas are the Gaussian copula, t-Copula, and Archimedean copulas including the Clayton Copula, Frank Copula, and the Gumbel Copula.

In the current study, the multidimensional copula functions were compared and chosen for the analysis of the wetness–dryness encountering of the monthly runoffs of the East River, North River, and West River. Parameters in the marginal distributions of the runoffs of the East River, North River, and West River were estimated by the Maximum Likelihood Method (MLE) and a goodness of fit test for the copulas was conducted by examining the Root Mean Square Error (RMSE), and Akaike Information Criterion (AIC).

The runoff was divided into five categories according to the cumulative frequency (p): extreme dryness (), more dryness (), normal (), more wetness (), and extreme wetness (). These categories are according to the rules for survey and statistical analysis of surface water resources and are used by the Ministry of Water Resources (Shi et al., 2019). The joint probability of the three-dimensional Copula is calculated as:
formula
(2)
where X, Y, and Z are the runoff of the West River, North River, and East River, respectively; are the upper runoff intervals given the frequency p, while are the lower runoff intervals; u, v, and w are the corresponding marginal distributions.

Consequently, there are 125 groups of three-dimensional wetness–dryness combinations for the monthly runoff of the East River, North River, and West River. The three-dimensional wetness–dryness combinations are numbered sequentially to facilitate the distinction (Table 1).

Table 1

Serial number of the three-dimensional wetness–dryness combinations for the monthly runoff of the East River, North River, and West River.

The monthly runoff of the West RiverThe monthly runoff of the North River
ED
MD
NOR
MW
EW
The monthly runoff of the East River
The monthly runoff of the East River
The monthly runoff of the East River
The monthly runoff of the East River
The monthly runoff of the East River
EDMDNORMWEWEDMDNORMWEWEDMDNORMWEWEDMDNORMWEWEDMDNORMWEW
ED 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 
MD 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 
NOR 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 
MW 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 
EW 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 
The monthly runoff of the West RiverThe monthly runoff of the North River
ED
MD
NOR
MW
EW
The monthly runoff of the East River
The monthly runoff of the East River
The monthly runoff of the East River
The monthly runoff of the East River
The monthly runoff of the East River
EDMDNORMWEWEDMDNORMWEWEDMDNORMWEWEDMDNORMWEWEDMDNORMWEW
ED 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 
MD 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 
NOR 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 
MW 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 
EW 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 

Note: ED, extreme dryness; MD, more dryness; NOR, normal; MW, more wetness; EW extreme wetness. The numbers with bold represent the synchronous wetness–dryness combinations.

WEAP system model

WEAP was proposed by Paul Raskins in 1988 and provides a comprehensive, user-friendly, and flexible framework for planning and policy analysis of complex water systems (Hollermann et al., 2010). In WEAP, a network is formed with links that connect and deliver water from the resource's node to the demand sites. This network creates a generalized structure of the water supply system, which consists of the water sources, reservoirs, and waterworks, such as pumping stations, sluice gates, and pipelines (Li et al., 2015). WEAP evaluates the sustainability of the water resource supply and demand balance over a long time scale according to the principle of water balance. It operates at a monthly step on the basic principle of water balance accounting, which means the total amount of water resources entering a node (e.g., a city in the Pearl River Delta) should be equal to the sum of the amounts of water resources flowing out and being lost in the node. Each node and link follows the mass conservation equation expressed as (Yates et al., 2005):
formula
(3)
where , , and represent the total amount of water resources entering, flowing out, and being lost in each node or link in the model, respectively.

The application of WEAP involves several steps. First, the time-span, spatial boundaries, system components, and problem structure are set. Simulations of the status quo benchmark can then be conducted, which provide the present-day water demand, water resources, and supply of the system. Alternative simulations of ‘future assumptions’ can subsequently be carried out, which are based on policies, costs, technological advances, and other factors that affect demand, supply, and hydrology. The water supply scheme is based on a set of alternative assumptions or policies. Finally, the adequacy of water and its sensitivity to the uncertainty of key variables are evaluated.

In WEAP, a demand site is a point where several water users share one or more water sources in a specific space and time (Amin et al., 2018).
formula
(4)
where i represents the sequence of demand site, n represents the amount of demand site, represents the annual water demand of demand site, and and represent the activity level and water use rate of the demand site, respectively.
When the model takes the month as the time step to carry out simulation calculations, monthly water demand can be obtained by setting the monthly water consumption ratio.
formula
(5)
where represents the monthly water demand and represents the water consumption ratio of the month (Gao et al., 2017).

Two user-defined priority systems are used to determine the distribution priority from the water source to the demand site and the catchment basin (for irrigation purposes), for in-channel flow requirements and reservoir storage. The priorities range from 1 to 99, where 1 is the highest priority and 99 is the lowest.

Establishing a ‘status quo baseline’ requires users to ‘calibrate’ system data and assumptions to accurately reflect the actual operation of the system. The ‘status quo baseline’ includes monthly supply and demand data (including reservoirs, pipe networks, treatment plants, pollution generated, etc.) for the first year of the study. Scenario analysis is the core of WEAP modeling. A preplan is a self-consistent description of how the future system will evolve under a specific socio-economic background and a set of specific policy and technical conditions. Using WEAP, plans can be generated and compared to evaluate the water requirements, costs, and environmental impacts of different plans. The plan includes any factors that can change over time, including factors that may change due to specific policy interventions and factors that reflect different socio-economic assumptions. A sensitivity analysis can also be performed by varying the values of uncertainties within the range of possibilities and comparing the results.

Inputs to the WEAP model mainly consist of (1) upstream runoff, (2) current water use and water demand predictions of cities, (3) water transfer and diversion projects, and (4) the boundary condition of the downstream. The WEAP schematic view is shown in Figure 3.
Fig. 3

The WEAP schematic view.

Fig. 3

The WEAP schematic view.

Close modal

Boundary conditions set for the WEAP model

The boundary conditions set for the WEAP model included the water supply and demand, and a combination of the upstream runoff and different levels of the critical upstream runoff for saltwater suppression to create 10 scenarios. Current water uses and water demand predictions were obtained from the water resources bulletin of Guangdong Province and the total constrained water use was issued by the regulation of the strictest water resources management system for Guangdong Province (Table 2). Four water transfer and diversion projects (Table 3) are considered in the WEAP model and the downstream boundary conditions are represented by the estimated critical upstream runoff for saltwater suppression. The spatial relationship between supply and demand of the Pearl River Delta was generalized (Figure 4) according to the geographical locations of the reservoirs and demand sites, and the hydraulic connections of the downstream and upstream. The flow requirement of the West River is the critical upstream runoff required for saltwater suppression, while the flow requirements of the North River and East River are from the ecological base flow issued by the comprehensive water resources planning of Guangdong Province, China.
Table 2

Water demand prediction of the Pearl River Delta in 2020 and 2030 (109 m3).

YearWater demand (109 m3)
GuangzhouShenzhenZhuhaiFoshanJiangmenZhao QingHuizhouDongguanZhongshan
2018 57.17 14.8 4.26 28.19 26.55 18.01 18.79 16.04 12.68 
2020 49.52 21.13 6.84 30.52 28.73 21 21.94 22.07 16.53 
2030 49.52 16.25 8.24 31. 76 33.39 28.33 25.77 19.54 16.27 
YearWater demand (109 m3)
GuangzhouShenzhenZhuhaiFoshanJiangmenZhao QingHuizhouDongguanZhongshan
2018 57.17 14.8 4.26 28.19 26.55 18.01 18.79 16.04 12.68 
2020 49.52 21.13 6.84 30.52 28.73 21 21.94 22.07 16.53 
2030 49.52 16.25 8.24 31. 76 33.39 28.33 25.77 19.54 16.27 
Table 3

Total amount of water resources provided by the water supply project of the Pearl River Delta.

Water supply projectWater resources allocation project of the Pearl River Delta
Water intake project for North RiverWater intake project for West RiverWater intake project for Foshan
GuangzhouDongguanShenzhen
Total water amount (108 m35.31 3.3 8.47 2.16 12.6 3.6 
Water supply projectWater resources allocation project of the Pearl River Delta
Water intake project for North RiverWater intake project for West RiverWater intake project for Foshan
GuangzhouDongguanShenzhen
Total water amount (108 m35.31 3.3 8.47 2.16 12.6 3.6 
Fig. 4

The generalized spatial relationship between water supply and demand of the Pearl River Delta.

Fig. 4

The generalized spatial relationship between water supply and demand of the Pearl River Delta.

Close modal

In the current study, the upstream runoff was from the monthly runoffs of the West River, North River, and East River under the wetness–dryness encountering. The 5 groups of dryness combinations with higher joint probabilities were selected among the 125 groups of three-dimensional wetness–dryness combinations for the runoff of the West River, North River, and East River. The 5 groups of three-dimensional wetness–dryness combinations of the runoff were combined with high and low levels of the critical upstream runoff for saltwater suppression (i.e., high level of the critical upstream runoff is combined in scenarios 1, 3, 5, and 7 and the low level of the critical upstream runoff is combined in scenarios 2, 4, 6, and 8) and formed the 10 scenarios. With these scenarios, the water supply scheme under different combinations of upstream runoff and levels of critical upstream runoff for saltwater suppression were calculated with the WEAP model. This modeling enabled the future changing satisfactory rate of water demand within the Pearl River Delta to be detected and revealed the impact of the wetness–dryness encountering of the runoff of the West River, North River, and East River on the water supply scheme of the Pearl River Delta.

The flowchart of the current study is shown in Figure 5.
Fig. 5

The flowchart of the current study.

Fig. 5

The flowchart of the current study.

Close modal

Wetness–dryness encountering of the runoff of the West River, North River, and East River

Several marginal distribution functions were used to fit the 50-year time series of monthly average runoff of the West River, North River, and East River. The marginal distributions with the best fit are shown in Figure 6 (i.e., normal distribution, general extreme value distribution, Weibull distribution, and gamma distribution). Goodness of fit tests and parameter estimation were done for the joint distributions based on three copulas (i.e., Clayton Copula, Frank Copula, and Gumbel Copula), according to the combined monthly runoff of the West River, North River, and East River (Table 4). As shown in Table 4, the Frank Copula had the lowest RMSE and AIC, and therefore, was chosen for the analysis of the wetness–dryness encountering of the runoff.
Table 4

Parameter estimation and test of three-dimensional Copula joint distribution functions.

MouthsParameter3D Copula (West River, North River and East River)
FrankClaytonGumbel
Jan θ 22.665 9.134 9.382 
RMSE 0.04299 0.05286 0.03372 
AIC 134.660 −125.686 − 145.216 
Feb θ 36.149 6.598 6.228 
RMSE 0.04302 0.07238 0.05193 
AIC − 134.635 −112.039 −126.459 
Mar θ 31.818 8.411 9.445 
RMSE 0.05734 0.06828 0.05424 
AIC −122.152 −114.570 − 124.567 
Apr θ 32.510 10.061 8.223 
RMSE 0.04679 0.05450 0.04875 
AIC − 130.982 −124.363 −129.201 
May θ 34.205 9.006 7.347 
RMSE 0.03859 0.05702 0.04375 
AIC − 139.355 −122.394 −133.900 
Jun θ 33.838 7.567 6.792 
RMSE 0.03622 0.06048 0.04569 
AIC − 142.110 −119.841 −132.022 
Jul θ 34.242 10.242 7.869 
RMSE 0.04663 0.05268 0.05076 
AIC − 131.131 −125.833 −127.448 
Aug θ 23.148 7.550 6.136 
RMSE 0.05242 0.06845 0.05473 
AIC − 126.049 −114.465 −124.178 
Sep θ 26.782 6.977 8.198 
RMSE 0.05014 0.06996 0.04600 
AIC −127.979 −113.514 − 131.725 
Oct θ 29.383 9.140 7.334 
RMSE 0.04704 0.05770 0.04933 
AIC − 130.749 −121.883 −128.693 
Nov θ 34.111 6.946 7.115 
RMSE 0.04563 0.06801 0.05142 
AIC − 132.078 −114.744 −126.885 
Dec θ 30.240 4.610 6.009 
RMSE 0.04750 0.08759 0.05771 
AIC − 130.332 −103.753 −121.876 
MouthsParameter3D Copula (West River, North River and East River)
FrankClaytonGumbel
Jan θ 22.665 9.134 9.382 
RMSE 0.04299 0.05286 0.03372 
AIC 134.660 −125.686 − 145.216 
Feb θ 36.149 6.598 6.228 
RMSE 0.04302 0.07238 0.05193 
AIC − 134.635 −112.039 −126.459 
Mar θ 31.818 8.411 9.445 
RMSE 0.05734 0.06828 0.05424 
AIC −122.152 −114.570 − 124.567 
Apr θ 32.510 10.061 8.223 
RMSE 0.04679 0.05450 0.04875 
AIC − 130.982 −124.363 −129.201 
May θ 34.205 9.006 7.347 
RMSE 0.03859 0.05702 0.04375 
AIC − 139.355 −122.394 −133.900 
Jun θ 33.838 7.567 6.792 
RMSE 0.03622 0.06048 0.04569 
AIC − 142.110 −119.841 −132.022 
Jul θ 34.242 10.242 7.869 
RMSE 0.04663 0.05268 0.05076 
AIC − 131.131 −125.833 −127.448 
Aug θ 23.148 7.550 6.136 
RMSE 0.05242 0.06845 0.05473 
AIC − 126.049 −114.465 −124.178 
Sep θ 26.782 6.977 8.198 
RMSE 0.05014 0.06996 0.04600 
AIC −127.979 −113.514 − 131.725 
Oct θ 29.383 9.140 7.334 
RMSE 0.04704 0.05770 0.04933 
AIC − 130.749 −121.883 −128.693 
Nov θ 34.111 6.946 7.115 
RMSE 0.04563 0.06801 0.05142 
AIC − 132.078 −114.744 −126.885 
Dec θ 30.240 4.610 6.009 
RMSE 0.04750 0.08759 0.05771 
AIC − 130.332 −103.753 −121.876 

Note: Bold numbers indicate that the copula function fits best.

Fig. 6

The marginal distributions fit with monthly average runoff of West River, North River, and East River.

Fig. 6

The marginal distributions fit with monthly average runoff of West River, North River, and East River.

Close modal
The monthly three-dimensional wetness–dryness encounter combination by Frank Copula was shown in Figure 7. In the three-dimensional combination, numbers 1, 32, 63, 94, and 125 are the synchronized wetness–dryness combinations, and their probabilities are 0.0039, 0.0199, 0.0165, 0.0212, and 0.0052, respectively. As shown in Figure 7, the probability of synchronized wetness–dryness combinations is higher than other combinations, especially in the flood period (from April to September). However, due to the large number of asynchronous combinations, the overall probability of synchronized wetness–dryness is low. In the dryness year, ‘extreme dryness-extreme dryness-more dryness’ and ‘extreme dryness-more dryness-more dryness’ are more likely to happen.
Fig. 7

The monthly three-dimensional wetness–dryness encounter combinations from January to December.

Fig. 7

The monthly three-dimensional wetness–dryness encounter combinations from January to December.

Close modal
The monthly runoff for the West River, North River, and East River under the synchronous wetness–dryness encounter was obtained (Figure 8) according to the marginal distributions and the joint probability of the three-dimensional Copula. Figure 8 shows that the West River, North River, and East River have similar distributions of monthly runoff under each synchronous wetness–dryness combination. The West River has the largest monthly runoff, followed by the North River and East River and the monthly runoff from May to September of each river accounts for a larger proportion of its total yearly runoff, suggesting an uneven spatiotemporal distribution of the upstream runoff. Dryness encountering of the runoffs with bigger probabilities and extreme situation were chosen for the input of the WEAP model.
Fig. 8

The monthly runoffs of the West River, North River, and East River under the synchronous wetness–dryness encounter.

Fig. 8

The monthly runoffs of the West River, North River, and East River under the synchronous wetness–dryness encounter.

Close modal

Estimation of the critical upstream runoff for saltwater suppression

Daily excessive chlorinity hours were counted according to the observed data at the three pumping stations from 2010 to 2015. As the upstream runoff is identified as the dominant factor affecting saltwater intrusion downstream and excessive chlorinity in the pumping stations (Liu et al., 2017), a correlation analysis was conducted based on the excessive chlorinity hours and the average monthly streamflow of Makou station in the West River. The quadratic function fitting method was used to analyze the correlation between the daily excessive chlorinity hours of the three pumping stations and the average monthly streamflow at the Makou station (Figure 9).
formula
(6)
formula
(7)
formula
(8)
Fig. 9

The correlation between daily excessive chlorinity hours of Pinggang, Guangchang, and Zhuzhoutou pumping stations and the average monthly streamflow of Makou station.

Fig. 9

The correlation between daily excessive chlorinity hours of Pinggang, Guangchang, and Zhuzhoutou pumping stations and the average monthly streamflow of Makou station.

Close modal

Equations (6)–(8) show the relationship between the upstream flow () of West River and the daily excessive chlorinity hours (, and ) of Pinggang, Guangchang, and Zhuzhoutou pumping stations, respectively.

It was found that as the upstream flow increased, the excessive chlorinity hours of the pumping station gradually decreased and trended toward zero. Moreover, the relationship of Q and the daily excessive chlorinity hours varied according to the different geographical locations of the pumping stations.

To guarantee the water supply security of the downstream cities in the Pearl River Delta, the daily excessive chlorinity at the pumping station should be less than 18 h. Therefore, the average monthly streamflow of Makou station should be equal to or more than 1,650 m3/s for Pinggang, 2,500 m3/s for Guangchang, and 1,400 m3/s for Zhuzhoutou, according to Equations (6)–(8). Three levels (i.e., high, medium, and low) of the critical upstream runoff for saltwater suppression were defined according to the distances between the three pumping stations and the Pearl River estuary. High critical upstream runoff (2,500 m3/s) guarantees water withdrawals for all three pumping stations; medium critical upstream runoff (1,650 m3/s) guarantees water withdrawals for pumping stations at Pinggang and the upstream stationsand low critical upstream runoff (1,400 m3/s) guarantees water withdrawals for pumping stations at Zhuzhoutou and stations upstream.

The calibration of the WEAP model

The WEAP model was calibrated with the upstream runoff and water use data for the year 2018. The simulated runoff was compared (Figure 10) with the observed runoff of the Sanshui station, one of the main hydrological stations of the Pearl River Delta. As shown in Figure 10, the simulated runoff displayed a similar trend with the observed runoff, and the Nash-Sutcliffe efficiency (NSE) coefficient was 0.93, suggesting the WEAP model had a good performance and the parameters of the model reflected well the exploitation of the water resources of the Pearl River Delta.
Fig. 10

Comparison of the observed simulated monthly average flow at Sanshui station.

Fig. 10

Comparison of the observed simulated monthly average flow at Sanshui station.

Close modal

Water supply scheme based on the WEAP model

According to the results of three-dimensional wetness–dryness combinations joint probabilities, five groups of dryness combinations were selected: ‘extreme dryness-extreme dryness-extreme dryness’ with a probability of 0.0039 (scenarios 1 and 2); ‘extreme dryness-more dryness-more dryness’ with a probability of 0.0109 (scenarios 3 and 4); ‘more dryness-extreme dryness-extreme dryness’ with a probability of 0.0064 (scenarios 5 and 6); ‘more dryness-more dryness-more dryness’ with a probability of 0.0199 (scenarios 7 and 8); and ‘more dryness-more dryness-normal’ with a probability of 0.0172 (scenarios 9 and 10). Ten scenarios were shown in Figure 11.
Fig. 11

The 10 scenarios exhibiting different sets of boundary conditions.

Fig. 11

The 10 scenarios exhibiting different sets of boundary conditions.

Close modal
Figure 12 shows the monthly water supply schemes in 2020 and 2030 of the Pearl River Delta for the 10 scenarios. These scenarios represent different combinations of dryness in the upstream runoff for the Pearl River Delta. It was found that the water demand of the Pearl River Delta can be satisfied by the upstream runoff in the flood period, while there are still water shortages in the dry period. During the dry period, the reservoirs of each city and water transfer projects serve as water resource suppliers. Water shortages in each city vary according to their water demand and geographical location. The water supply of each city is influenced by the level of the critical upstream runoff for saltwater suppression. For instance, high critical upstream runoff reduces the upstream water resources available for the cities, while low critical upstream runoff negatively impacts the water supply security of the Pearl River Delta estuary.
Fig. 12

Monthly water supply schemes in 2020 and 2030 of the Pearl River Delta under the 10 sets of boundary conditions (a–j). Note: GZ = Guangzhou, SZ = Shenzhen, ZH = Zhuhai, FS = Foshan, JM = Jiangmen, ZQ = Zhaoqing, HZ = Huizhou, DG = Dongguan, and ZS = Zhongshan.

Fig. 12

Monthly water supply schemes in 2020 and 2030 of the Pearl River Delta under the 10 sets of boundary conditions (a–j). Note: GZ = Guangzhou, SZ = Shenzhen, ZH = Zhuhai, FS = Foshan, JM = Jiangmen, ZQ = Zhaoqing, HZ = Huizhou, DG = Dongguan, and ZS = Zhongshan.

Close modal

Monthly water demand satisfaction rate

The average monthly water demand satisfaction rate of each city between 2020 and 2030 is shown in Figure 13, according to the water allocation results for the 10 different scenarios. As shown in Figure 13, the water demand of the Pearl River Delta can be fully satisfied with the upstream runoff of the dryness combination during the flood period, however, during the dry period, the average monthly water demand satisfaction rate is only 60–80%. Particularly for Zhuhai City, which is at the Pearl River Delta estuary, the monthly water demand satisfaction rate is only 40% due to saltwater intrusion. In addition, the monthly water demand satisfaction rate decreases from January to February and October to December for the Pearl River Delta cities. During these periods, the water supply of the cities is mainly provided by the reservoirs due to the extreme dryness; the capacity of the reservoirs, however, cannot be replenished effectively under the condition of low inflow, resulting in a decreasing water supply. The reservoir storage and inflow decrease from October to December, contributing to a significant reduction in the water demand satisfaction rate.
Fig. 13

The average monthly water demand satisfaction rate of each city in 2020 (a) and 2030 (b).

Fig. 13

The average monthly water demand satisfaction rate of each city in 2020 (a) and 2030 (b).

Close modal
The average monthly water demand satisfaction rate of the Pearl River Delta between 2020 and 2030 is shown in Figure 14, according to the water allocation results from the 10 scenarios. It can be concluded from Figure 14 that the water demand of the Pearl River Delta can be fully satisfied during the flood period, however, the water demand satisfaction rate decreases to 60–80% in the dry period. The lowest monthly water demand satisfaction rate for the Pearl River Delta occurs in February and December, and there is little difference in the satisfaction rate between 2020 and 2030. This result suggests that the water shortage of the Pearl River Delta in 2020 and 2030 is highly dependent upon the dryness combination of the upstream runoff. In particular, water withdrawals at the downstream cities in the Pearl River Delta estuary are seriously influenced by saltwater intrusion, and water supply security is aggravated in the dry period. In order to suppress the saltwater intrusion, water withdrawals by the upstream cities would need to be reduced, which, therefore, would impact the entire water supply networks of the Pearl River Delta.
Fig. 14

The average monthly water demand satisfaction rate of the Pearl River Delta in 2020 (a) and 2030 (b) under the 10 scenarios.

Fig. 14

The average monthly water demand satisfaction rate of the Pearl River Delta in 2020 (a) and 2030 (b) under the 10 scenarios.

Close modal

The impact of the wetness–dryness combination of the upstream runoff on water supply in the Pearl River Delta

Scenarios 1 and 3 had the same critical upstream runoff for saltwater suppression, while the combination of the upstream runoff from West River, North River, and East River differed from ‘extreme dryness-extreme dryness-extreme dryness’, respectively, in scenario 1 to ‘extreme dryness-more dryness-more dryness’ in scenario 3. From scenarios 1 to 3, the monthly water demand satisfaction rates of Guangzhou, Shenzhen, Dongguan, Huizhou, and Foshan, whose water supplies are largely impacted by the upstream runoff from the North River and East River, increased by 7, 24, 34, 6, and 24% in the dry period in 2020, respectively, an average increase of 19%. The monthly water demand satisfaction rates of the cities whose water supply is largely impacted by the upstream runoff from West River, however, did not change with the change in the wetness–dryness combination of the upstream runoff of the North River and East River, because their water supplements are mainly from West River and the local reservoirs. This was similar to the differences between scenarios 2 and 4. When the combination of the upstream runoff transferred from ‘extreme dryness-extreme dryness-extreme dryness’ in scenario 1 to ‘more dryness-extreme dryness-extreme dryness’ in scenario 5, the monthly water demand satisfaction rates of Zhuhai, Zhongshan, Jiangmen, and Zhaoqing, whose water supplies are largely impacted by the upstream runoff from the West River, increased by 24, 15, 15, and 22% in the dry period in 2020, respectively, an average increase of 19%. The monthly water demand satisfaction rate of Guangzhou was also influenced by the wetness–dryness combination of the upstream runoff of the West River and exhibited an average increase of 3%, due to the West River water transfer project and the Nanzhou water withdrawal project. This is similar to scenarios 2 and 6. The combination of the upstream runoff transferred from ‘extreme dryness-extreme dryness-extreme dryness’ in scenario 1 to ‘more dryness-more dryness-more dryness’ in scenario 7, and the monthly water demand satisfaction rates of the Pearl River Delta increased by 9% in Guangzhou, 24% in Shenzhen, 24% in Zhuhai, 33% in Dongguan, 6% in Huizhou, 31% in Zhongshan, 31% in Foshan, 15% in Jiangmen, and 22% in Zhaoqing, respectively, with an average increase of 22%, which is similar to scenarios 2 and 8.

The monthly water demand satisfaction rates of the cities in 2030 were not quite similar to those in 2020. First, different scenarios for the wetness–dryness combination of the upstream runoff impacted the water supplies and water demand satisfactions, which is like 2020. Second, due to the different development plans of each city, the water demand of each city would increase or decrease, respectively, compared to 2020, thus affecting the water demand satisfaction rates (Table 2). Third, Shenzhen and Dongguan will receive water supply from West River through the Pearl River Delta water division engineering in 2030, while Guangzhou will receive more water supply from West River in 2030. For example, compared to 2020, the monthly water demand satisfaction rate of Shenzhen in scenarios 1 and 5 was increased by 29–33%, in Dongguan by 34–35%, in Guangzhou by 2–1%, and in Huizhou by 3–4%. While the satisfaction in Jiangmen decreased from 4 to 2%, and in Zhaoqing from 8 to 5%. The results showed the influence by water demand and water division engineering. From 2020 to 2030, Shenzhen and Dongguan decreased their water demand and water division engineering began to supply water, thus their water demand satisfaction rates were greatly increased. On the contrary, because of the increased water demand in Jiangmen and Zhaoqing (Table 2), the water demand satisfaction rate would decrease in the same wetness–dryness combination scenario and monthly runoff. The water demand was also increased in Huizhou, and Huizhou did not get the water supply from water division engineering. However, due to the water division engineering from West River to Shenzhen and Dongguan, the pressure of water supply in ER was eased; therefore, the satisfaction in Huizhou has also been increased. This result has shown the regional impact of water division engineering on the water demand satisfaction rates of the cities in the Pearl River Delta.

As shown in Figure 12, the water transfer projects provided water supply, easing pressure during the dry period. However, as the runoff of the West River accounts for the largest proportion of the upstream runoff of the Pearl River Delta (Figure 8), the impact of the water transfer project on the water supply of the Pearl River Delta is weakened when there is an extreme dryness event impacting the upstream runoff of the West River. Changes in the wetness–dryness combination of the upstream runoffs from the West River, North River, and East River demonstrate that the upstream runoffs have a significant impact on the water demand satisfaction rates of the Pearl River Delta. The upstream runoffs of the West River, North River, and East River cannot be fully utilized in the flood period, even if the city reservoirs have the largest storage capacity before the dry period, water shortages will occur when there is extreme/more dryness of events impacting the upstream runoff, and the water demand satisfaction rate of the Pearl River Delta will decrease month by month in the dry period as the reservoir storage capacity cannot be effectively replenished. In particular, the water withdrawal of the cities along the river is directly influenced by the upstream runoff, and a reduction in the upstream runoff would cause a significant decrease in the water demand satisfaction rates. Our results demonstrate that water transfer projects are necessary to reallocate water resources in regions like the Pearl River Delta, in which the water supply is dominated by the upstream runoff and its wetness–dryness combination.

The impact of the critical upstream runoff for saltwater suppression on the monthly water demand satisfaction rate

As shown in Table 5, the average saltwater suppression passing rate in the dry period is only 75.8% under extreme dryness and 85% under more dryness of the upstream runoff of the West River. Furthermore, the saltwater suppression passing rate is only 60–70% in January and February, suggesting that much of the critical upstream runoff for saltwater suppression cannot be satisfied when there is an ‘extreme’ or ‘more dryness’ event affecting the upstream runoff of the West River.

Table 5

Rate of reaching the standard of estuary discharge of West River under the high level of the critical upstream runoff for saltwater suppression.

Runoff from West RiverJanFebMarAprMayJunJulAugSepOctNovDec
Extreme dry 0.63 0.63 0.77 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.86 0.66 
More dry 0.72 0.77 0.89 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.83 
Runoff from West RiverJanFebMarAprMayJunJulAugSepOctNovDec
Extreme dry 0.63 0.63 0.77 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.86 0.66 
More dry 0.72 0.77 0.89 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.83 

In the scenarios with a high level of critical upstream runoff for saltwater suppression, even if the average saltwater suppression passing rate is 70–80%, the monthly water demand satisfaction rates of Zhuhai, Zhongshan, and Jiangmen are largely impacted. For instance, comparing the scenarios with low-level critical upstream runoff (i.e., scenarios 2, 4, 6, 8, and 10) to their paired scenarios with high-level critical upstream runoff (i.e., scenarios 1, 3, 5, 7, and 9), the monthly water demand satisfaction rate of Zhuhai in 2020 decreased by 23, 23, 2, 2, and 2%, respectively. In Zhongshan, the water demand satisfaction rates decreased by 23, 23, 2, 2, and 2%, respectively, and for Jiangmen they decreased by 21, 23, 13, 15, and 15%, respectively. However, the impact of the critical upstream runoff for saltwater suppression on the monthly water demand satisfaction rate could be alleviated as the upstream runoff increases.

Policy implications

The current study proposes further implications for water resource management in the coastal urban agglomeration of the Pearl River Delta. The higher guarantee of water supply security is one of the important prerequisites for the sustainable development of the region, and water shortages will affect human life and normal social development, especially in the Pearl River Delta, which has a growing population and rapidly developing economics. Although uncertainty about water resources increases under changing conditions, the risks and stresses of water scarcity can be minimized by taking anthropogenic measures.

In an extreme dryness year, the reservoirs’ water storage decreased, and the impact of the water transfer project on the water supply of the Pearl River Delta was weakened, mainly because of the significant decrease of the upstream inflow. New water transfer projects require long-term construction and involve administrative communication issues across basins and regions. Therefore, the water shortage problem in the Pearl River Delta during the extreme dryness period cannot be properly solved by the construction of more new water transfer projects in a short period. Due to the shortage of land resources in the Pearl River Delta, it is also unrealistic to build more reservoirs in the short term (Hu et al., 2019). However, the capacity of the existing reservoirs can be expanded as much as possible to store more water during flood periods and supply more water resources during extremely dry years. In addition, the most effective management strategy in the near future should be to strengthen the rational allocation of water resources between the upstream and downstream of the Pearl River Basin by administrative methods, so as to supply more water for the Pearl River Delta during dry periods (Huang & Zhang, 2020; Liu et al., 2020a, 2020b; Ren et al., 2021). Moreover, cities at the Pearl River Delta estuary should accelerate the construction of emergency backup water source projects, so as to gradually form the strategic reserve system of water resources and reduce the water shortage risk, particularly in an extreme dryness year.

In an extreme or more dryness event, the critical upstream runoff for saltwater suppression could not be satisfied. Under the premise of a serious reduction of upstream runoff, for satisfying the rigid water demand in coastal cities during the saltwater intrusion, it is necessary for water resources management departments to build effective saltwater intrusion forecasting systems (Lu et al., 2021), and draw as much fresh water as possible into reservoir storage before the saltwater arrives, in particular to cities at the Pearl River Delta estuary. Moreover, the coastal cities should enhance water conservation measures on the basis of China's strictest water resource management system, to reduce the water demand gap under the influence of saltwater intrusion (Wang et al., 2020a, 2020b; Bai et al., 2021).

In short, it is suggested that, considering both water demand and supply sides, the local government should strengthen the unified planning and management of water resources, guarantee the capital investment in the construction of an emergency backup water source project, scientific and technological research on the development of an alarm forecasting system and water-saving renovation, so as to ensure the safety of water supply in the Pearl River Delta during the dry period.

In the current study, a WEAP-based water resource allocation model was developed to investigate the water supply schemes of the coastal urban agglomeration of the Pearl River Delta and reveal the impacts of the wetness–dryness encountering of the upstream inflow and downstream salt intrusion. The following main conclusions were drawn:

  • (1)

    The upstream runoff is highly correlated with the daily excessive chlorinity hours of the pumping stations in the downstream of the Pearl River Delta. The estimated high, medium, and low levels of the critical upstream runoff for saltwater suppression are 2,500, 1,650, and 1,400 m3/s, respectively, according to a correlation analysis based on the excessive chlorinity hours and the average monthly streamflow of Makou station in the West River.

  • (2)

    The West River, North River, and East River have stronger synchronous wetness–dryness encountering, and the water shortage of the Pearl River Delta is highly dependent upon the dryness combination of the upstream runoff during the dry period. Particularly for the cities at the Pearl River Delta estuary, the water shortages would be aggravated due to saltwater intrusion during the dry period. It is essential for the local government to tap the regulation potential of existing reservoirs of the Pearl River Delta and operate the unified regulation and management of water resources across the entire Pearl River Basin.

  • (3)

    The water transfer projects could alleviate the water supply pressure of the Pearl River Delta when there is an extreme or more dryness encounter of upstream runoff, however, the impact of the water transfer projects is weakened and much of the critical upstream runoff for saltwater suppression cannot be satisfied when there is an extreme dryness event of the West River. It is necessary to develop the emergency backup water source project, particularly in cities at the Pearl River Delta estuary, and advance the effectiveness of the saltwater intrusion forecasting system.

The current study reveals the impacts of the wetness–dryness encountering of the upstream inflow and downstream salt intrusion on water supply in the Pearl River Delta, based on which reasonable water allocation considering regional and industrial water distribution priorities can be further studied in the Pearl River Delta, according to the different aims of development, function positioning, and the level of economic and social development for each city.

The authors would like to express their gratitude to all of the reviewers for their valuable recommendations. This study was financially supported by the National Natural Science Foundation of China (Grant No. 51979043, 51861125203, U1911204), and the Natural Science Foundation of Guangdong Province (Grant No. 2021A1515010723).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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