Abstract
Systematic domestic water demand prediction is of great importance for social and economic sustainable development. To explain the system of domestic water demand prediction more completely, a system dynamic model based on the social-hydrology method was proposed in this paper. The key natural and socio-economic factors that affect the domestic water demand most were identified and investigated. The prediction equations of water price considering the feedback between humans and nature were deduced. The expressions of water-saving consciousness were proposed for the first time. Furthermore, the differential and difference equations for domestic water demand prediction were established to realize the future domestic water demand forecasts considering the natural and social driving forces. Finally, three scenarios were designed to investigate the impact of climate change and economic development on the domestic water demand. The upper and middle Pearl River Basin was selected as a case study. The predicted domestic water demand is consistent with the historical results, which demonstrates that the proposed model can be well used for the prediction of the domestic water demand. Under the three scenarios, the domestic water demand increased by 33, 27 and 18% in 2050 compared with that in 2017, respectively.
HIGHLIGHTS
This study combined a system dynamic model with social-hydrology methods.
The mechanism of water price formation considering the feedback between humans and water resources was deduced.
The expressions of water-saving consciousness were proposed for the first time.
Three scenarios were designed to investigate the impact of climate change and economic development on the domestic water demand.
INTRODUCTION
It is widely recognized that the demand for water resources is growing around the world with the rapid development of the world economy, the expansion of the global population and the acceleration of urbanization (Mall et al. 2006; Vairavamoorthy et al. 2008). Around one-third of the world's population currently lives under physical water scarcity, and water shortage has become a significant bottleneck that affects the world's political structure, economic development and social progress (Vörösmarty et al. 2000; Alcamo et al. 2003; Oki & Kanae 2006; Kummu et al. 2010). The United Nations (UN) estimates that human water demand has changed dramatically in the two centuries. In the early 20th century, global water consumption was only 400 billion m³ per year, but by the end of the 20th century it had risen to 3,900 billion m³ per year, among which domestic water consumption is an important part and vital to humans. Therefore, it is of great practical significance to predict future domestic water demand for supporting water management.
In the literature, various models were used to predict long-term water demand. They can be categorized into deterministic models and probabilistic models (Froukh 2001; Almutaz et al. 2013). Deterministic models normally do not consider the uncertainties of the explanatory variables. In fact, it is a simplified probabilistic model. Examples include time series equation (Zhai et al. 2012) and multivariate analysis equation (Babel et al. 2006). However, the factors affecting water demand are stochastic in nature and mutually influenced among themselves. Thus, the deterministic model cannot well describe the mechanism of water demand formation. Most studies using probabilistic models (Almutaz et al. 2013) failed to account for the correlations among factors. Also, the problem can be solved by the concept of the social-hydrology (SH) and system dynamics (SD) methods.
SH was first proposed by Sivapalan et al. (2014), which is characterized through uncovering the dynamic cross-scale interactions and feedbacks between the natural and human processes and aims to formalize the feedbacks between human and water systems in an explicit way that can help us explain the past, understand the present and illuminate sustainable future trajectories of their coevolution. SD and SH are consistent in solving water resource problems from a system perspective and many relevant studies have been conducted in the past several years. Linton & Budds (2014) advanced the concept of the hydro-social cycle as a means of theorizing and analyzing water–society relations. Elshafei et al. (2014) outlined a generic framework for models of socio-hydrology applicable to agricultural catchments, which was made up of six key components that combine to form the coupled system dynamics. Therefore, the future research on water demand prediction can focus on the perspective of SH, by analyzing the dynamic characteristics of human–water coupling system and the mutual feedback relationship among society, water resources and ecological environment. Also, SD can be further used to realize the simulation of complex system relationships.
The SD method, designed for simulating complex socio-economic systems, is a commonly used method for the prediction of water use, since it can well deal with the inherent complexity of water management by considering a feedback-oriented modeling framework (Zhang et al. 2008; Winz et al. 2009). This method is a combination of quantitative and qualitative methods based on the feedback control theory (Wolstenholme 1990). Computer simulation was used to study the relationship between socio-economic systems and water resources systems. It is suitable for dealing with long-term and periodic systems. Generally, an SD modeling process includes the following steps: problem definition, model conceptualization, model formulation, model evaluation and policy analysis (Elmahdi et al. 2007; Wang et al. 2010).
The traditional SD method for predicting the domestic water demand were used in different scales (cities, basins and countries) (Qin et al. 2011; Sun et al. 2017). Population and urbanization rate are two common and important explanatory variables that affect the change of the domestic water demand (Domene & Saurí 2006; Feng et al. 2017). The expansion of population scale has a significant impact on the growth of the domestic water demand (Falkenmark 1990). It is estimated that the domestic water consumption of urban residents will increase by 20.09 × 104 m3 for every 10,000 urban population increase and the rapid urbanization has brought about increasing growth of urban water use, especially for the domestic water consumption (Wu & Tan 2012). However, the explanatory variables of most previous studies are usually not enough. The impacts of natural and socio-economic factors were less taken into account.
Climatic change has an unignored impact on the future changes of water demand (Slavíková et al. 2013; Zubaidi et al. 2020). Thus, climate factors were considered as explanatory variables in many studies of water demand forecasting. For example, Babel et al. (2014) explored the use of five future climate variables – precipitation, maximum temperature, minimum temperature, evaporation and relative humidity in forecasting the water demand. Haque et al. (2014) took temperature and rainfall data under three emission scenarios as input to the water demand forecast model. Rasifaghihi et al. (2020) split water use into base water use and seasonal water use to forecast urban water consumption, on the basis of the correlation between water consumption and air temperature. Between these climate factors, temperature and precipitation are used most. It is predicted that there will be a steady increase in temperature and changes in the rainfall pattern across the world due to climate change (IPCC 2007). The former impacts the water demand. People are likely to use more water when temperature rises. The latter changes the water availability, which in turn leads to changes in the water supply (Guo & Shen 2016). Consequently, the contradiction between the water demand and water supply may sharpen because of the climate change.
In addition, the influence of economic factors on the domestic water demand is far beyond expectations (Arbués et al. 2003). Income is tightly associated with a region's domestic water demand. For example, along with the upgrading of living environment and the improvement of health habits (human consciousness and behavior), the domestic water demand shows an increasing trend at the margin. As a common management tool on the demand side of water resources, the influence of water price also should be considered in water demand prediction although it is only moderate (Kenney et al. 2008; Nawaz et al. 2019). Water supply and water demand impact the water pricing; conversely, water price impacts the behaviors of water consumers (Renwick & Green 2000; Rinaudo et al. 2012).
Furthermore, previous studies show that those people with greater water-saving consciousness will use about 24% less water than people without such concerns (Willis et al. 2011; Wei et al. 2016). There are three main reasons for a decrease in water consumption, including the increased use of water-saving appliances for households, the cultivation of good habits of saving water (such as limiting shower time, reducing detergent use and so on) and reuse of domestic water reasonably.
The objective of this study is, therefore, to realize the future domestic water demand forecasts considering the natural and socio-economic driving forces. Resident population, urbanization rate, disposable income of urban and rural residents, future precipitation, water price and water-saving consciousness were regarded as important factors affecting the domestic water demand in this study. The innovation of this study is that an SD domestic water demand prediction model was proposed, considering the impact of nature and socio-economy as well as the evolution of comprehensive variables. First, the key socio-economic factors that mainly affect the domestic water demand were identified based on a linear regression analysis; second, water supply under the impact of climate change was considered by introducing dynamic water price; third, the evolution law of social and economic factors affecting the domestic water demand was analyzed, and water-saving consciousness was innovatively taken into account in the proposed SD model; fourth, the differential and difference equations for domestic water demand prediction were established; fifth, the proposed method was examined based on the observed data from the Pearl River Basin, and the proposed method was compared with the currently used domestic water demand prediction model; and finally, the water demand results under three scenarios with different economic developments and climate changes were compared in the Pearl River Basin.
METHODOLOGIES
Evolution trend prediction of natural factors
Water supply under the impact of climate change
and 
are coefficients; 
and 
are increment of water supply for the domestic water demand and total water resources, respectively; t is the time. Because the domestic water demand is a part of total water demand, g is the ratio of the increment of the water supply for the domestic water demand to the increment of total water resources.Prediction of socio-economic factors
Factors including population, urbanization rate, disposable income and water-saving consciousness and so on were predicted, and their corresponding prediction model was established. The dynamic water price equation and the water-saving consciousness equation were deduced. The logistic regressions were used for population prediction as well as the urbanization rate. The disposable income prediction model was established based on the linear regression.
The mechanism of water price formation
is the increment of the water supply for the domestic water demand in year t; 
is the increment of the total domestic water demand in year t; 
is the water price in year t. The model supposed that the water supply can meet the water demand at the end of the year. Under this supposition, we can use the relationship of the increment of the domestic water demand and supply to simply judge whether the domestic water demand and supply are balanced. 
is the increment ratio of the water price when the supply was less than the demand, and 
is the reduction ratio of the water price when the supply exceeds the demand.Establishment of the prediction model of water-saving consciousness of residents
Currently, the demand for domestic water will increase with the economic growth and continuous improvement of living standards of residents. However, with the popularization of water-saving education and improvement of the water-saving consciousness of residents, the increase of the domestic water demand can slow down correspondingly. Against this background, a mathematical expression of water-saving consciousness was proposed and the impact of water-saving consciousness on domestic water consumption was simulated effectively in this study.
increases linearly. The annual growth rate of water-saving consciousness 
remains constant, then, and can be written as
is the annual growth rate of water-saving consciousness and M is the upper limit of water-saving consciousness.
, the specific derivation formula is given below
Assume that the upper limit of M is 1, which means that the maximum value of water conservation willingness of residents is 100%, then the water-saving consciousness K is between 0 and 1. Also, the physical interpretation of this equation is that the change rate of water-saving consciousness is 
, which is not fixed. The closer this value is to the upper limit of water-saving consciousness, the smaller will be the rate of change.
Establishment of the population prediction model based on Malthus–Logistic regression
is the initial time; r is the population growth rate; 
is the population at the initial time 
; and 
is the population at time t. However, there is a threshold for population growth, because of the limitation of the living space, food and fertility in a region. Eventually the population of the region will tend to be stable, and in this situation the model is no longer applicable for population calculation. In this paper, we estimated the population by the following formula, since the population growth rate is variable:
Establishment of the urbanization rate prediction model based on logistic regression
is the urbanization rate; C is the integral constant; and d is the parameter to be determined. Assume 
is the base year, then the constant C can be defined as
is the urban population in the base year and 
is the rural population in the base year.Establishment of the disposable income prediction model of residents based on linear regression
and 
are the per capita disposable income of rural and urban residents in the t year; 
and 
are the per capita disposable income of rural and urban residents in the base year 
; 
and 
represent the growth rate of per capita disposable income of rural and urban residents, respectively.SD modeling method with SH factors
SD modeling tools
This paper used the Ventana Simulation Environment Vensim DSS for windows version 5.6a (http://vensim.com/). The Vensim is commonly applied for the development of SD simulation programs. It provides a set of graphical objects with its mathematical functions for easy representation of the system structure and the development of computer code. Simulation models can be easily and quickly developed using this software tool (Wang et al. 2010). The main elements of the SD model include flow, level, rate, auxiliary and constant, which are combined to form the SD flow diagram.
SD modeling method
Following the previous research results, there is a significant correlation between the domestic water demand and purchasing power coefficient of residents, namely the ratio of residents' disposable income to domestic water price (Yang et al. 1999). To project the future domestic water demand, log–log linear models were mostly used. However, this model cannot consider the population changes or other socio-economic issues for forecasting future domestic water demand. Since the socio-economic factors in urban and rural areas are very different, the equations for calculating the domestic water demand in the urban and rural areas were considered separately. In this study, an SD model has been established for predicting the domestic water demand by considering water price, water-saving consciousness, urban and rural per capita disposable income, population scale and urbanization rate.
Skeleton of the domestic water demand (the red arrow displays a negative feedback). Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/nh.2022.051.
Skeleton of the domestic water demand (the red arrow displays a negative feedback). Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/nh.2022.051.
is total water resources; P is the annual average precipitation; 
and 
are coefficients; 
, 
and 
are water price and increment of the water supply for the domestic water demand and total water resources in year t, respectively; 
and 
are water price and increment of total water resources in year t–1 ; g is the ratio of the increment of the water supply for the domestic water demand occupying the increment of total water resources; 
is the ratio of water price in the present year to that in the last year; UPI and RPI are increment of urban population and rural population, respectively; UGR is the growth rate of urbanization; UP is the urban population; IUWD, IRWD and ITWD are increment of the urban domestic water demand, increment of the rural domestic water demand and increment of the total domestic water demand, respectively; 
is the total water demand in year t calculated by 
plus ITWD (increment of the total domestic water demand); UPCI is per capita disposable income of urban residents and RPCI is per capita disposable income of rural residents; 
is the elasticity coefficient of resident income; 
is the adjustment coefficient of rural population increment, which means the impact of rural population changes on the domestic water demand, and 
is the adjustment coefficient of urban population increment, which means the impact of urban population changes on the domestic water demand; 
and 
are the rural and urban elasticity coefficients of domestic water price; and WSC is water-saving consciousness.Equation (15a) estimates the total water resources through precipitation. The increment of domestic water supply and water price was defined by Equations (15b) and (15c). Also, the increment of urban population and rural population was calculated by Equations (15d) and (15e). Equations (15f) and (15g) express the mapping relationship of increment of urban water demand (increment of rural water demand) with various factors, including per capita disposable income of urban residents (per capita disposable income of rural residents), increment of urban population (increment of rural population), water price and so on. Increment of urban population (increment of rural population) and per capita disposable income of urban residents (per capita disposable income of rural residents) show a positive feedback on the domestic water demand, whereas the water price shows a negative feedback on the domestic water demand. Equations (15f) and (15g) can be used to simulate the comprehensive impacts of multiple factors on changes in the domestic water demand. Equation (15h) characterizes the increment of the total domestic water demand equaling the increment of urban water demand plus the increment of rural water demand. In addition, water-saving consciousness was used to revise the increment of urban and rural domestic water demand based on Equation (15h), avoiding large prediction results of the domestic water demand caused by ignoring the water-saving consciousness.
The growth rate of the domestic water demand slows down with the strengthening of water-saving awareness. Based on Equations (15f)–(15h), the total increment of the domestic water demand was predicted. According to Equation (15i), the predicted results of the domestic water demand in year t is calculated by the domestic water demand in year t−1 plus the increment of the domestic water demand.
The SD prediction model of the domestic water demand considering multiple socio-economic and natural factors were conducted by the following steps:
Regression analysis was used to identify the key socio-economic factors that affect the domestic water demand most.
The development trend of key factors affecting the domestic water demand was investigated and predicted.
The differential and difference equations for domestic water demand prediction were established to realize the future domestic water demand forecasts considering the natural and socio-economic driving forces.
The flow diagram for the study case was determined to simulate the trend of the factors and the domestic water demand.
The validity of the model is verified by comparing the predicted water demand with the historical results.
Three scenarios were designed to predict the domestic water demand considering the impact of economic development and climate change.
CASE STUDY
Study area and data
The drainage area and area ratio of the upper and middle reaches of the Pearl River
| Provinces | Drainage area in the province (km2) | The ratio of drainage area in the province to the study area (%) | The ratio of drainage area in the province to the province (%) |
|---|---|---|---|
| Guangxi Province | 164,626.3 | 54.1 | 70.2 |
| Yunnan Province | 93,115.8 | 30.6 | 23.6 |
| Guizhou Province | 40,471.9 | 13.3 | 23 |
| Lang Son (Vietnam) | 6,086 | 2 | – |
| Provinces | Drainage area in the province (km2) | The ratio of drainage area in the province to the study area (%) | The ratio of drainage area in the province to the province (%) |
|---|---|---|---|
| Guangxi Province | 164,626.3 | 54.1 | 70.2 |
| Yunnan Province | 93,115.8 | 30.6 | 23.6 |
| Guizhou Province | 40,471.9 | 13.3 | 23 |
| Lang Son (Vietnam) | 6,086 | 2 | – |
Sketch map of the study area hydrological station.
Socio-economic data series (2007–2017) of annual water demand, population, urbanization rate, disposable income and relevant statistics of the three provinces in the Pearl River basin were collected from the National Bureau of Statistics of China. The relevant geographical, meteorological and hydrological data of the Pearl River basin were collected from the Pearl River Water Resources Commission of the Ministry of Water Resources. The precipitation of the Pearl River basin under different climate scenarios is collected from statistical downscaling of climate model data in the CMIP6 project (https://esgf-node.llnl.gov/).
In this study, the base year is 2007. The verification period is from 2007 to 2017, and the prediction period ranges from 2018 to 2050.
Identification of the socio-economic factors
To describe the correlations between the domestic water consumption and corresponding socio-economic factors, the linear correlation coefficient was calculated. Then, the T-test was applied to characterize the significance of the factors.
is the domestic water demand; 
is an independent variable, which stands for the factors related to the domestic water demand; 
is a constant; 
is the partial regression coefficient; and 
is the random error, which means the changes of 
that cannot be explained by the independent variable 
.The correlation coefficients between the domestic water demand and socio-economic factors are calculated and given in Table 2. Meanwhile, T–test was employed to check whether the correlation coefficients were significant or not and results showed that all correlation coefficients passed at the 95% confidence test. Based on these, the linear regression equations of the domestic water demand and socio-economic factors, including population, urbanization rate and disposable income of urban and rural residents were established. The water-saving consciousness and water price were not considered in this study, because it was hard to quantify the residents' water consciousness and unify the historical water price in the study region. Usually, mixed technology and questionnaire surveys were used to reveal the relationship between the water demand and water-saving consciousness (Willis et al. 2011).
Correlation coefficients and regression equations between key socio-economic factors and the domestic water demand
| Provinces | Socio-economic factors | ||||
|---|---|---|---|---|---|
| Population | Urbanization rate | Disposable income of urban residents | Disposable income of rural residents | ||
| Guangxi | Correlation coefficient | 0.941a | 0.935a | 0.946a | 0.942a |
| Regression equation | y=0.0285x–100.24 | y=35.533x+22.472 | y=0.0003 x+32.264 | y=0.0006 x+33.129 | |
| Yunnan | Correlation coefficient | 0.999a | 0.995a | 0.998a | 0.990a |
| Regression equation | y=0.0077x–14.712 | y=14.13 x+15.592 | y=0.0001 x+18.702 | y=0.0004 x+18.75 | |
| Guizhou | Correlation coefficient | 0.671a | 0.619a | 0.636a | 0.669a |
| Regression equation | y=0.0188x–49.526 | y=14.836 x+10.666 | y=0.0002 x+13.116 | y=0.0005 x+13.071 | |
| Provinces | Socio-economic factors | ||||
|---|---|---|---|---|---|
| Population | Urbanization rate | Disposable income of urban residents | Disposable income of rural residents | ||
| Guangxi | Correlation coefficient | 0.941a | 0.935a | 0.946a | 0.942a |
| Regression equation | y=0.0285x–100.24 | y=35.533x+22.472 | y=0.0003 x+32.264 | y=0.0006 x+33.129 | |
| Yunnan | Correlation coefficient | 0.999a | 0.995a | 0.998a | 0.990a |
| Regression equation | y=0.0077x–14.712 | y=14.13 x+15.592 | y=0.0001 x+18.702 | y=0.0004 x+18.75 | |
| Guizhou | Correlation coefficient | 0.671a | 0.619a | 0.636a | 0.669a |
| Regression equation | y=0.0188x–49.526 | y=14.836 x+10.666 | y=0.0002 x+13.116 | y=0.0005 x+13.071 | |
Note: t0.025(9)=2.262.
aThe correlation coefficient passes the 95% confidence test.
Correlation analysis results show that the four factors, namely population, urbanization rate, disposable income of urban and rural residents, have a significant correlation with the domestic water demand. Therefore, the above factors can be applied to the SD modeling of the domestic water demand.
Establishment of the domestic water demand prediction model
Flow diagrams for the domestic water demand model.
The Malthus–Logistic regression models were used for population prediction, 
was the population in the base year 2007. The natural population growth rate r was determined by referring to the regional population growth planning values. Then, assuming different population growth thresholds, the predicted population was calculated by the natural population growth rate, the population in the base year and the threshold. The population growth threshold N was determined by comparing the observed population with the predicted value. To sum up, the natural population growth rates of Guangxi, Yunnan and Guizhou provinces in the upper and middle reaches of the Pearl River were 8, 7, and 8 ‰, respectively.
The logistic curve regression method was adopted for the prediction model of the urbanization rate. After the base year was determined, the integral constant C of the three areas in the upper and middle reaches of the Pearl River can be determined according to the formula 
, which was the ratio of the initial value of the rural population to the initial value of the urban population in the reference period. The value of the parameter d was estimated based on comparing the historical value with the predicted value.
The future rainfall data were collected from CMIP6 under SSP2-4.5 scenarios. Also, the volume of total water resources was calculated by the regression equation, parameters of which were fitted by the least square method. The variation of water supply for domestic water was set to be 80% of the variation of total water resources according to the historic data and the importance of domestic water. Therefore, when the subtraction of the water demand variation from the water supply variation is negative, the water price rises; when the subtraction of the water demand variation from the water supply variation is positive, the water price falls. The change rate of the water price was calibrated by the historic data.
Simulated and historical socio-economic data related to the domestic water demand prediction in the upper and middle reaches of the Pearl River Basin: (a) population, (b) urbanization rate, (c) urban disposable income per capita and (d) urban disposable income per capita.
Simulated and historical socio-economic data related to the domestic water demand prediction in the upper and middle reaches of the Pearl River Basin: (a) population, (b) urbanization rate, (c) urban disposable income per capita and (d) urban disposable income per capita.
Water-saving consciousness varies among provinces, because of the different water demand growth trends, economic development levels and water resource enrichment levels. The trial-and-error method was used to determine the parameter value of water-saving consciousness, for there was no historical value of water-saving consciousness. The estimation processes of water-saving consciousness were as follows.
The upper limit of water-saving consciousness M was determined. Assume that M=1 at first and the range of M is [0,1].
The parameter A was determined. For the base year, t=0, according to formula (12), K=M–A, assume that the value of A is between [0, M]. Different A values will be corresponding to different K values.
Substituting different K, M and A values into the domestic water demand prediction model, the required A value is obtained, at the situation that the established prediction model shows a better performance by comparing the historical water demand with the simulated water demand values.
If the fitting error is large, the value of M should be re-adjusted. Follow the above steps and re-calibrate the parameters, until the fitting result is optimal.
Simulation diagram of water-saving awareness in the upper and middle Pearl River Basin.
Simulation diagram of water-saving awareness in the upper and middle Pearl River Basin.
Relative errors of simulated values and historical values of the main variables: (a) population, (b) urbanization rate, (c) urban disposable income per capita and (d) rural disposable income per capita.
Relative errors of simulated values and historical values of the main variables: (a) population, (b) urbanization rate, (c) urban disposable income per capita and (d) rural disposable income per capita.
Prediction of the domestic water demand in the upper and middle Pearl River Basin
Parameters of the water demand prediction model
| Factors | Parameters | Guangxi Province | Yunnan Province | Guizhou Province |
|---|---|---|---|---|
| Population | r | 0.008 | 0.007 | 0.008 |
| N | 9,865.9 | 14,429.0 | 10,778.0 | |
| Urbanization Rate | C | 1.76 | 2.17 | 2.54 |
| d | 0.0558 | 0.0596 | 0.0716 | |
| Disposable income for rural and urban residents | K1 | 737.31 | 627.74 | 577.92 |
| K2 | 1,793.3 | 1,964.5 | 1,861.8 | |
| Water-saving consciousness | M | 0.9 | 1.0 | 1.0 |
| A | 0.55 | 0.61 | 0.60 | |
 | 0.050 | 0.027 | 0.028 | |
| Water supply | a1 | 2.3202 | 1.4738 | 0.8789 |
| a1 | −1,072 | −30.04 | −146.07 | |
| g | 0.8 | 0.8 | 0.8 | |
| Water price | f1 | 1.05 | 1.05 | 1.05 |
| f2 | 0.98 | 0.98 | 0.98 |
| Factors | Parameters | Guangxi Province | Yunnan Province | Guizhou Province |
|---|---|---|---|---|
| Population | r | 0.008 | 0.007 | 0.008 |
| N | 9,865.9 | 14,429.0 | 10,778.0 | |
| Urbanization Rate | C | 1.76 | 2.17 | 2.54 |
| d | 0.0558 | 0.0596 | 0.0716 | |
| Disposable income for rural and urban residents | K1 | 737.31 | 627.74 | 577.92 |
| K2 | 1,793.3 | 1,964.5 | 1,861.8 | |
| Water-saving consciousness | M | 0.9 | 1.0 | 1.0 |
| A | 0.55 | 0.61 | 0.60 | |
| | 0.050 | 0.027 | 0.028 | |
| Water supply | a1 | 2.3202 | 1.4738 | 0.8789 |
| a1 | −1,072 | −30.04 | −146.07 | |
| g | 0.8 | 0.8 | 0.8 | |
| Water price | f1 | 1.05 | 1.05 | 1.05 |
| f2 | 0.98 | 0.98 | 0.98 |
Prediction results and error analysis of the domestic water demand in the upper and middle Pearl River
| Year | Guangxi Province | Yunnan Province | Guizhou Province | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Actual value (108 m3) | Simulated value (108 m3) | Relative error (%) | Actual value (108 m3) | Simulated value (108 m3) | Relative error (%) | Actual value (108 m3) | Simulated value (108 m3) | Relative error (%) | |
| 2007 | 27.08 | 24.57 | −9.28 | 4.71 | 4.71 | 0.00 | 3.57 | 3.57 | 0.00 |
| 2008 | 28.06 | 25.46 | −0.09 | 5.27 | 4.79 | −0.10 | 3.58 | 3.63 | 0.01 |
| 2009 | 26.98 | 26.00 | −0.04 | 5.56 | 4.86 | −0.14 | 3.61 | 3.71 | 0.02 |
| 2010 | 25.59 | 26.45 | 0.03 | 5.38 | 4.92 | −0.09 | 3.79 | 3.80 | −0.01 |
| 2011 | 25.65 | 26.83 | 0.05 | 5.77 | 4.99 | −0.15 | 3.42 | 3.89 | 0.12 |
| 2012 | 25.72 | 27.14 | 0.06 | 4.54 | 5.06 | 0.10 | 3.02 | 3.97 | 0.29 |
| 2013 | 26.90 | 27.40 | 0.02 | 4.84 | 5.12 | 0.04 | 3.69 | 4.06 | 0.08 |
| 2014 | 27.55 | 27.61 | 0.00 | 4.60 | 5.17 | 0.10 | 3.81 | 4.14 | 0.06 |
| 2015 | 27.87 | 27.80 | 0.00 | 4.77 | 5.23 | 0.08 | 3.91 | 4.21 | 0.05 |
| 2016 | 27.87 | 27.97 | 0.00 | 4.98 | 5.28 | 0.04 | 4.00 | 4.29 | 0.04 |
| 2017 | 28.22 | 28.12 | 0.00 | 5.12 | 5.33 | 0.02 | 4.32 | 4.37 | −0.02 |
| Year | Guangxi Province | Yunnan Province | Guizhou Province | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Actual value (108 m3) | Simulated value (108 m3) | Relative error (%) | Actual value (108 m3) | Simulated value (108 m3) | Relative error (%) | Actual value (108 m3) | Simulated value (108 m3) | Relative error (%) | |
| 2007 | 27.08 | 24.57 | −9.28 | 4.71 | 4.71 | 0.00 | 3.57 | 3.57 | 0.00 |
| 2008 | 28.06 | 25.46 | −0.09 | 5.27 | 4.79 | −0.10 | 3.58 | 3.63 | 0.01 |
| 2009 | 26.98 | 26.00 | −0.04 | 5.56 | 4.86 | −0.14 | 3.61 | 3.71 | 0.02 |
| 2010 | 25.59 | 26.45 | 0.03 | 5.38 | 4.92 | −0.09 | 3.79 | 3.80 | −0.01 |
| 2011 | 25.65 | 26.83 | 0.05 | 5.77 | 4.99 | −0.15 | 3.42 | 3.89 | 0.12 |
| 2012 | 25.72 | 27.14 | 0.06 | 4.54 | 5.06 | 0.10 | 3.02 | 3.97 | 0.29 |
| 2013 | 26.90 | 27.40 | 0.02 | 4.84 | 5.12 | 0.04 | 3.69 | 4.06 | 0.08 |
| 2014 | 27.55 | 27.61 | 0.00 | 4.60 | 5.17 | 0.10 | 3.81 | 4.14 | 0.06 |
| 2015 | 27.87 | 27.80 | 0.00 | 4.77 | 5.23 | 0.08 | 3.91 | 4.21 | 0.05 |
| 2016 | 27.87 | 27.97 | 0.00 | 4.98 | 5.28 | 0.04 | 4.00 | 4.29 | 0.04 |
| 2017 | 28.22 | 28.12 | 0.00 | 5.12 | 5.33 | 0.02 | 4.32 | 4.37 | −0.02 |
Simulated results of the future domestic water demand.
The proposed model was used for the simulation of the domestic water demand from 2007 to 2050 in the upper and middle Pearl River Basin. Table 5 shows the prediction results of the domestic water demand in 2020, 2030, 2040 and 2050. It is indicated that the domestic water demand in Guangxi Province will increase from 2.822 billion m³ in 2017 to 2.941 billion m³ in 2050. The domestic water demand in Yunnan Province will increase from 512 million m³ to 624 million m³. The domestic water demand in Guizhou Province will increase from 432 million m³ to 596 million m³ in the next three decades. The domestic water demand in the study area will increase by 151 million m³ from 2020 to 2030, and by only 159 million m³ during the two decades from 2030 to 2050, which means that with the economic development to a certain degree, the domestic water demand will not increase uncontrollably with the increase of the population. The growth trend of water demand for living will be restricted by certain factors and be in a relatively stable state. For example, the development of science and technology can improve the utilization of water resources. The improvement of national quality and the increase of water price and water-saving consciousness will reduce the amount of the domestic water demand to a certain extent, which is consistent with China's development plan and the current trend of domestic water use in developed countries.
Prediction results of the future domestic water demand in the upper and middle Pearl River
| Year | 2020 | 2030 | 2040 | 2050 |
|---|---|---|---|---|
| Domestic water demand (108 m³) | 38.52 | 40.02 | 40.96 | 41.61 |
| Year | 2020 | 2030 | 2040 | 2050 |
|---|---|---|---|---|
| Domestic water demand (108 m³) | 38.52 | 40.02 | 40.96 | 41.61 |
Comparisons with currently used models
The water quota method has been widely used in the prediction of the domestic water demand. The water quota method and the proposed method were used to predict the domestic water demand in the upper and middle Pearl River in this study. Table 6 shows the simulated results and their relative errors based on the proposed and currently used methods. The relative error calculated by the water demand quota method is always positive, and the prediction results are systematically higher than the historical values during the inspection period. The average relative errors of the proposed and water quota methods were 3.84 and 7.23%, respectively. Therefore, the performance of the proposed method is better than that of the currently used method.
Prediction results and the relative errors of the proposed and currently used methods
| Year | Historical value (108m³) | Proposed method | Water quota method | ||
|---|---|---|---|---|---|
| Simulated value (108m³) | Relative error (%) | Simulated value (108m³) | Relative error (%) | ||
| 2007 | 35.36 | 32.84 | −7.11 | 37.16 | 5.11 |
| 2008 | 36.91 | 33.88 | −8.21 | 37.50 | 1.60 |
| 2009 | 36.16 | 34.57 | −4.40 | 37.78 | 4.49 |
| 2010 | 34.75 | 35.17 | 1.20 | 38.03 | 9.42 |
| 2011 | 34.84 | 35.71 | 2.48 | 38.25 | 9.77 |
| 2012 | 33.28 | 36.17 | 8.68 | 38.45 | 15.52 |
| 2013 | 35.43 | 36.57 | 3.24 | 38.63 | 9.03 |
| 2014 | 35.96 | 36.92 | 2.68 | 38.79 | 7.87 |
| 2015 | 36.55 | 37.25 | 1.91 | 38.94 | 6.56 |
| 2016 | 36.85 | 37.55 | 1.89 | 39.09 | 6.07 |
| 2017 | 37.67 | 37.82 | 0.41 | 39.22 | 4.13 |
| Average relative error (%) | – | – | 3.84 | – | 7.23 |
| Year | Historical value (108m³) | Proposed method | Water quota method | ||
|---|---|---|---|---|---|
| Simulated value (108m³) | Relative error (%) | Simulated value (108m³) | Relative error (%) | ||
| 2007 | 35.36 | 32.84 | −7.11 | 37.16 | 5.11 |
| 2008 | 36.91 | 33.88 | −8.21 | 37.50 | 1.60 |
| 2009 | 36.16 | 34.57 | −4.40 | 37.78 | 4.49 |
| 2010 | 34.75 | 35.17 | 1.20 | 38.03 | 9.42 |
| 2011 | 34.84 | 35.71 | 2.48 | 38.25 | 9.77 |
| 2012 | 33.28 | 36.17 | 8.68 | 38.45 | 15.52 |
| 2013 | 35.43 | 36.57 | 3.24 | 38.63 | 9.03 |
| 2014 | 35.96 | 36.92 | 2.68 | 38.79 | 7.87 |
| 2015 | 36.55 | 37.25 | 1.91 | 38.94 | 6.56 |
| 2016 | 36.85 | 37.55 | 1.89 | 39.09 | 6.07 |
| 2017 | 37.67 | 37.82 | 0.41 | 39.22 | 4.13 |
| Average relative error (%) | – | – | 3.84 | – | 7.23 |
Sensitivity analysis of the model parameters
If the behavior of the proposed model is too sensitive to the change of parameters within a reasonable range, this means that the model robustness is poor and it will not help to evaluate the merits of different policies. From this point of view, the policy analysis was considered, which is usually comprised of model structure analysis, parameter analysis and boundary analysis (Refsgaard et al. 2007). In this study, the proposed domestic water demand is a mathematical simplification of the water-using system under the dynamic impacts of socio-economics and nature. Thus, there is uncertainty in the simplification process. Considering that the proposed model has fewer boundary conditions and simple structure, the parameter analysis was only considered to evaluate the robustness of the model.
Parameters setting for the sensitivity analysis
| Par. | Guangxi Province | Yunnan Province | Guizhou Province | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Value | Min. | Max. | Value | Min. | Max. | Value | Min. | Max. | |
| r (×10−2) | 0.8 | 0.64 | 0.96 | 0.7 | 0.56 | 0.84 | 0.8 | 0.72 | 0.88 |
| N | 9,866 | 7,893 | 11,839 | 14,429 | 11,543 | 17,315 | 10,778 | 9,700 | 11,856 |
| d (×10−2) | 5.58 | 3.35 | 7.81 | 5.96 | 5.36 | 6.56 | 7.16 | 6.44 | 7.88 |
| K1 | 737.3 | 442.4 | 1,032.2 | 627.7 | 565.0 | 690.5 | 577.9 | 520.1 | 635.7 |
| K2 | 1,793.3 | 1,076.0 | 2,510.6 | 1,964.5 | 1,768.1 | 2,161.0 | 1,861.8 | 1,675.6 | 2,048.0 |
| M | 0.9 | 0.81 | 0.99 | 1 | – | – | 1 | – | – |
| A | 0.55 | 0.44 | 0.66 | 0.61 | 0.488 | 0.732 | 0.6 | 0.48 | 0.72 |
| θ (×10−2) | 5 | 4 | 6 | 2.7 | 2.43 | 2.97 | 2.8 | 2.52 | 3.08 |
| f1 | 1.05 | 1.01 | 1.09 | 1.05 | 1.01 | 1.09 | 1.05 | 1.01 | 1.09 |
| Par. | Guangxi Province | Yunnan Province | Guizhou Province | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Value | Min. | Max. | Value | Min. | Max. | Value | Min. | Max. | |
| r (×10−2) | 0.8 | 0.64 | 0.96 | 0.7 | 0.56 | 0.84 | 0.8 | 0.72 | 0.88 |
| N | 9,866 | 7,893 | 11,839 | 14,429 | 11,543 | 17,315 | 10,778 | 9,700 | 11,856 |
| d (×10−2) | 5.58 | 3.35 | 7.81 | 5.96 | 5.36 | 6.56 | 7.16 | 6.44 | 7.88 |
| K1 | 737.3 | 442.4 | 1,032.2 | 627.7 | 565.0 | 690.5 | 577.9 | 520.1 | 635.7 |
| K2 | 1,793.3 | 1,076.0 | 2,510.6 | 1,964.5 | 1,768.1 | 2,161.0 | 1,861.8 | 1,675.6 | 2,048.0 |
| M | 0.9 | 0.81 | 0.99 | 1 | – | – | 1 | – | – |
| A | 0.55 | 0.44 | 0.66 | 0.61 | 0.488 | 0.732 | 0.6 | 0.48 | 0.72 |
| θ (×10−2) | 5 | 4 | 6 | 2.7 | 2.43 | 2.97 | 2.8 | 2.52 | 3.08 |
| f1 | 1.05 | 1.01 | 1.09 | 1.05 | 1.01 | 1.09 | 1.05 | 1.01 | 1.09 |
Simulation results of sensitivity analysis. Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/nh.2022.051.
Simulation results of sensitivity analysis. Please refer to the online version of this paper to see this figure in color: http://dx.doi.org/10.2166/nh.2022.051.
As shown in Figure 8, the parameters of water-saving consciousness (M, A,
) are identified as the most sensitive parameters that influence the evolution of the domestic water demand. Conversely, the parameters of urbanization rate and residents' disposable income (d, K1, K2) are identified as the least sensitive parameters for the domestic water demand. The results are reasonable according to the structure of the model, and prove that the uncertainty of water-saving consciousness is most likely to lead to the uncertainty of the domestic water demand than other explanatory variables. It is valid to increase water-saving consciousness to reduce the domestic water demand. In addition, all the evolution trajectories of the domestic water demand with varied parameter values exhibit increasing trends. This is mainly due to the stable increment of population and economy. Finally, it is easy to find that the uncertainty of the model output caused by the parameter uncertainty increases with time in Figure 8. This is because the influence of the values of parameters on the model output increases with time.
Scenario design and analysis
Scenarios describe the future states of a system by different parameters, which are valuable references for policy makers. Three scenarios were designed to predict the future water demand of the upper and middle Pearl River Basin under different climate change scenarios and social-economic development speed. First, the business-as-usual (BAU) scenario supposes that the future maintains the present development trends of social-economy corresponding to the SSP2-4.5 climate scenario. Second, the high economic development (HED) scenario assuming higher economic development than the BAU scenario, integrated with the SSP5-8.5 climate scenario. On the contrary, the low economic development (LED) scenario assumes lower economic development than the BAU scenario, matching the SSP1-2.6 climate scenario.
Parameters setting for scenario analysis
| Par. | Guangxi Province | Yunnan Province | Guizhou Province | ||||||
|---|---|---|---|---|---|---|---|---|---|
| LED | BAS | HED | LED | BAS | HED | LED | BAS | HED | |
| r | 0.008 | 0.008 | 0.008 | 0.007 | 0.007 | 0.007 | 0.008 | 0.008 | 0.008 |
| N | 9,000 | 9,865.9 | 11,000 | 13,500 | 14,429 | 15,500 | 10,000 | 10,778 | 12,000 |
| C | 1.76 | 1.76 | 1.76 | 2.17 | 2.17 | 2.17 | 2.54 | 2.54 | 2.54 |
| d | 0.04 | 0.0558 | 0.06 | 0.05 | 0.0596 | 0.07 | 0.06 | 0.0716 | 0.08 |
| K1 | 600 | 737.31 | 800 | 550 | 627.74 | 750 | 450 | 577.92 | 650 |
| K2 | 1,700 | 1,793.3 | 2,000 | 1,900 | 1,964.5 | 2,200 | 1,800 | 1,861.8 | 2,100 |
| M | 1 | 0.9 | 0.9 | 1 | 1 | 1 | 1 | 1 | 1 |
| A | 0.55 | 0.55 | 0.55 | 0.61 | 0.61 | 0.61 | 0.6 | 0.6 | 0.6 |
| θ | 0.06 | 0.05 | 0.04 | 0.04 | 0.027 | 0.02 | 0.04 | 0.028 | 0.02 |
| f1 | 1.04 | 1.05 | 1.06 | 1.04 | 1.05 | 1.06 | 1.04 | 1.05 | 1.06 |
| Par. | Guangxi Province | Yunnan Province | Guizhou Province | ||||||
|---|---|---|---|---|---|---|---|---|---|
| LED | BAS | HED | LED | BAS | HED | LED | BAS | HED | |
| r | 0.008 | 0.008 | 0.008 | 0.007 | 0.007 | 0.007 | 0.008 | 0.008 | 0.008 |
| N | 9,000 | 9,865.9 | 11,000 | 13,500 | 14,429 | 15,500 | 10,000 | 10,778 | 12,000 |
| C | 1.76 | 1.76 | 1.76 | 2.17 | 2.17 | 2.17 | 2.54 | 2.54 | 2.54 |
| d | 0.04 | 0.0558 | 0.06 | 0.05 | 0.0596 | 0.07 | 0.06 | 0.0716 | 0.08 |
| K1 | 600 | 737.31 | 800 | 550 | 627.74 | 750 | 450 | 577.92 | 650 |
| K2 | 1,700 | 1,793.3 | 2,000 | 1,900 | 1,964.5 | 2,200 | 1,800 | 1,861.8 | 2,100 |
| M | 1 | 0.9 | 0.9 | 1 | 1 | 1 | 1 | 1 | 1 |
| A | 0.55 | 0.55 | 0.55 | 0.61 | 0.61 | 0.61 | 0.6 | 0.6 | 0.6 |
| θ | 0.06 | 0.05 | 0.04 | 0.04 | 0.027 | 0.02 | 0.04 | 0.028 | 0.02 |
| f1 | 1.04 | 1.05 | 1.06 | 1.04 | 1.05 | 1.06 | 1.04 | 1.05 | 1.06 |
Future evolution trend of precipitation corresponding to three scenarios.
Simulation results of the domestic water demand under different scenarios.
CONCLUSIONS
In this paper, we presented a SD model considering socio-economic multi-factor for simulating and analyzing the trend of the domestic water demand in the upper and middle Pearl River Basin. The method of combining SD with SH was proposed to solve the complicated and unpredictable problems of the water resources system. The dynamic water price was modeled and the feedback loop between people and water was established. The key socio-economic factors affecting the domestic water demand were identified with the correlation analysis method and the evolution trend of population, urbanization rate and disposable income level were characterized based on the corresponding prediction model. The variable of water-saving consciousness was innovatively taken into account in the proposed SD model and its expressions were derived for the first time. Furthermore, the game relationship between socio-economic systems and water resource systems was analyzed using the kinetic equations. A system dynamic method of the domestic water demand forecasting system considering the natural and socio-economic driving forces was proposed on these bases. The main conclusions are summarized as follows.
Results show that the proposed model can be used for simulating the evolution trend of the social-hydrological factors, which includes water price, water-saving consciousness, population, urbanization rate, income level and so on. The predicted factors are consistent with the historical results.
The prediction results of the domestic water demand dynamic model in the upper and middle Pearl River Basin show that the historical value is consistent with the predicted domestic water demand, and it is reasonable to use this model to predict the future domestic water demand. The domestic water demand in the study area is increasing slowly, and the water consumption situation is generally stable after the 2030s.
The proposed method was compared with the water quota demand method, and results show that the prediction error of the proposed method is small.
The proposed model was simulated for sensitivity analysis of parameters. Results show that the model is robust and the policy sensitivity is low.
Three scenarios were compared and results show that the reasonable decrease of the speed of economic development and population growth and the implementation of climate policies are necessary.
ACKNOWLEDGEMENTS
This research is supported by the National key R&D Program during the Fourteenth Five-year Plan Period (2021YFC3200400), the National Natural Science Foundation of China (51922047; 51879109), Hubei Science Foundation for Distinguished Young Scholars (2020CFA101) and Water Conservancy Science and Technology Innovation Project of the Guangdong Province (2020–23).
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
