Towards Sustainable Energy–Water–Environment Nexus System Considering the Interactions between Climatic, Social and Economic Factors: A Case Study of Fujian, China

Abstract

This study develops a factorial Bayesian least-squares support vector machine-based energy–water–environment nexus system optimization (i.e., FBL–EWEO) model. FBL–EWEO can provide dependable predictions for electricity demand, quantify the interactions among different factors, and present optimal system planning strategies. The application to Fujian Province is driven by three global climate models (i.e., GCMs) under two SSPs, as well as two levels of economic and social factors’ growth rates. Results revealed in the planning horizon: (1) Fujian would encounter rainy and warming trends (e.g., [2.17645, 4.51247] mm/year of precipitation and [0.0072, 0.0073] °C/year of mean temperature); (2) economic, social, and climatic factors contribute 62.30%, 35.50%, and 1.47% to electricity demand variations; (3) electricity demand would grow with time (increase by [64.21, 74.79]%); (4) the ratio of new energy power would rise to [70.84, 73.53]%; (5) authorities should focus on photovoltaic and wind power plants construction (their proportions increase from [0.81, 1.83]% to [9.14, 9.56]%, [1.33, 4.16]% to [11.44, 15.58]%, respectively); and (6) air pollutants/CO₂ emissions would averagely decline [51.97, 53.90]%, and water consumption would decrease [41.77%, 42.25]%. Findings provide technical support to sustainable development.

1. Introduction

Electricity demand (ED) is predicted to increase in the future because of the speed of economic development, rapid population growth, and great improvement in living standards [1]. It is worth noting that climate change encourages people to use air conditioning, refrigerators, and electric water heaters more frequently, causing additional pressure on ED. The extra pressure on ED results in more energy for generating electricity. Coal-fired power is still the world’s dominant energy conversion technology, especially in some developing countries. For instance, in China, coal-fired power contributed 63% (i.e., 4918 TWh) to the total electricity generation in 2020 (SRWE 2021); corresponding SO₂, NO_x, PM, and CO₂ emissions reached about 688.52 × 10³ t (0.14 g/kWh), 1032.78 × 10³ t (0.21 g/kWh), 59.02 × 10³ t (0.012 g/kWh), and 4.62 × 10⁹ t (940 g/kWh) [2]. Water is vital to coal-fired power generation; unit water consumptions for coal extraction, processing, and conversion are about 0.52 m³/t, 0.30 m³/t, and 13.58× 10⁻³ m³/kWh, respectively [3,4]. Under such circumstances, authorities face some challenges: (1) How to accurately know the amount of ED in the future. (2) In order to conserve resources and protect the environment, new energy power (e.g., nuclear power, hydropower, wind power, photovoltaic power, and others) can be adopted to replace coal-fired power. This formulates a problem of optimal energy–water–environment nexus system (EWE) planning [5].

ED prediction is often uncertain and complex since it depends on climatic, social, and economic factors, such as precipitation, temperature, gross domestic product (GDP), industrial outputs, population, etc. Some efforts were made to construct the relationship between climatic–social–economic inputs and ED response [6,7,8,9,10,11,12,13,14]. Ahmed et al. [6] used an MLR (i.e., multiple linear regression) model to forecast per capita ED in Australia; results indicated that ED in summer and spring would rise because of the varied temperature. Günay [7] employed an ANN (i.e., artificial neural network) model to predict the annual ED in Turkey; ED was validated with great precision for years with known values, and it was predicted that ED would reach 460 TWh in 2028. Toktarova et al. [8] introduced an MLR model to project ED for all countries globally; results showed that the model was flexible to provide ED information regarding long-term trends and short-term projections. Mei et al. [9] developed a GCMs (i.e., global climate models) based SVM (i.e., support vector machine) to simulate ED in China; it was found that ED would rise about 58.6% from 2021 to 2050. Wen and Yuan [10] proposed a hybrid back propagation neural network (BPNN) model to predict the future residential ED in China; results presented that residential ED would increase from 9685 TWh in 2018 to 13,171 TWh in 2025. Eshraghi et al. [11] used an MLR model to estimate the variability of residential ED in America; results found that 70% (summer) and 50% (winter) of ED variability was mainly affected by climate. Liu et al. [12] used ANN, MLR, and SVM to predict Hong Kong’s electricity demand considering climatic and socioeconomic changes; results showed that ANN exhibits the lowest accuracy and generalization ability. Pannakkong et al. [13] involved MLR, ANN, SVM, and a hybrid model to predict electricity consumption in Thailand; the computational experiments showed that the hybrid model provided a better mean absolution percentage error. Liu and Li [14] employed MLR, BPNN, and least-squares SVM (LSVM) for UK’s long-term annual ED forecast considering population, GDP, mean temperature, sunshine, rainfall, and frost days; results presented that LSVM has the best performance. The above research used MLR, ANN, BPNN, SVM, and LSVM models to analyze the impacts of climatic–social–economic changes on ED.

Among them, MLR generated a linear relationship between inputs and responses, ignoring the nonlinear relationship. ANN and SVM tackled nonlinear relationships (without a particular function) between inputs and responses. ANN and BPNN have disadvantages of many adjustable parameters, a local minimum to converge, and overfitting; SVM has difficulties in ensuring high computation efficiency by simplifying the process. Least-squares SVM (LSVM), enhanced based on SVM, can overcome the shortage of computation burden. Some researchers applied the LSVM to the field of energy systems [15,16,17,18,19]. One concern of LSVM is the proper choices of regularization and kernel parameters. Bayesian inference is an effective tool to address this problem, which can produce favorable generalization performance, as well as quantify the uncertainty or variability in the parameters [20,21,22]. It is essential to formulate a Bayesian LSVM model. Moreover, factorial analysis (FA), a popular statistical analysis method, can be adapted to identify key parameters and detect their joint effects on ED response [23]. A factorial Bayesian least-squares support vector machine (FBL) model can be developed to simulate ED.

An optimization technique can then be employed to analyze the impact of electricity demand (ED) on EWE planning. Previously, much research was conducted on EWE planning without considering climate change [24,25,26,27,28,29,30,31]. Ji et al. [24] proposed an optimization model for planning EWE; optimal capacity expansion, electricity generation, imported electricity, and water consumption strategies were obtained. Zhen et al. [25] developed a EWE optimization model considering resource availability, electricity demand, pollutants emission, and system cost. Ma et al. [26] established an optimization model for achieving minimum system cost under consideration of available resources, electricity output, electric power balance, pollutant/CO₂ emissions, etc. Tan et al. [27] proposed an optimization model to investigate the regional EWE optimization in China; strategies related to electricity generation, system cost, CO₂ emissions mitigation, water consumption, and wastewater disposal were gained. Tan et al. [28] constructed a model to optimize EWE for electric power planning; results indicated that, under a strict water conservation policy, the electricity supply structure showed a low-carbon transition trend. Gómez-Gardars et al. [29] enhanced an optimization model for managing EWE taking water, CO₂, and energy-related constraints, as well as system cost, into account; results discovered that thermal storage had an effect on reducing 15.5% of water and 67.5% of CO₂, as well as increasing 75% of energy efficiency. Ahmad and Zeeshan [30] optimized concentrated solar power plants from a EWE nexus perspective; results indicated that an additional 6 h of storage for solar tower and trough plants could lead to a 60% and 75% increment in annual electricity generation, and a 5% and 7% decrease in levelized cost of electricity, respectively. Huang et al. [31] proposed a model for holistic optimization of EWE; results indicated that the application of carbon capture and storage could increase energy and water consumption by up to [0.24, 7.35] × 10⁶ tce and [0.16, 1.12] × 10⁸ m³, respectively. These studies indicate the feasibility and practicability of optimization models; an energy–water–environment nexus optimization (EWEO) model can be proposed to make optimal strategies.

This research aims to develop a factorial Bayesian least-squares support vector machine-based energy–water–environment nexus system optimization (i.e., FBL–EWEO) model through integrating multi-GCMs, FBL, and EWEO models within a framework. Each model provides an exclusive contribution to improving the FBL–EWEO model’s abilities in simulation and optimization. The main contribution and novelty of the model can be described as (a) it is first presented to EWE planning under climatic–social–economic changes; (b) it can handle the uncertainty in climate variables projection derived from differences of assumptions and structures of GCMs; (c) it can catch the nonlinear relationship between inputs and ED in the simulation process with high efficiency; (d) it can identify key parameters and quantify their interactions on ED; (e) it can address uncertainties related to energy, water, and environmental elements in the optimization process; (f) it is employed to a case of Fujian Province (in China) with a planning horizon of 2021–2060; and (g) optimal strategies about electricity generation, water consumption, pollutants/CO₂ emissions can be obtained, which provides decision support for achieving the goal of sustainable development.

2. Methodology

2.1. Electricity Demand Simulation

2.1.1. Downscaling Outputs of Multiple GCMs

The data extracted from a GCM usually need to be downscaled to approach the observed data; this deviation is caused by the huge spatial difference between large-scale regions and small-scale regions. Bias correction methods containing transformation algorithms can adjust large-scale climate phenomena to be in line with the local climate phenomena. Research has analyzed the performance of bias correction methods, concluding that suitable methods show good performance [32]. Linear scaling (LS) is adopted to correct the temperature data of GCMs due to its simplicity and effectiveness. For obtaining precise precipitation data, two methods, including LS and distribution mapping (DM), are chosen.

LS is adopted to correct temperature and precipitation data on the basis of the following equations [33]:

$$T_{sim}^{*}(d)=T_{sim}^{}(d)+{\mu }_m(T_{obs}^{}(d))-{\mu }_m(T_{sim}^{}(d))$$

(1)

$$T_{pro}^{*}(d)=T_{pro}^{}(d)+{\mu }_m(T_{obs}^{}(d))-{\mu }_m(T_{sim}^{}(d))$$

(2)

$$P_{sim}^{*}(d)=P_{sim}^{}(d)\times \frac{{\mu }_m(P_{obs}^{}(d))}{{\mu }_m(P_{sim}^{}(d))}$$

(3)

$$P_{pre}^{*}(d)=P_{pre}^{}(d)\times \frac{{\mu }_m(P_{obs}^{}(d))}{{\mu }_m(P_{sim}^{}(d))}$$

(4)

where P and T are the precipitation and temperature of day d within month m, respectively; obs denotes observation; sim means simulation; pre presents prediction; and μ_m is the monthly mean value. P* and T* are the corrected P and T, respectively.

DM amends the distribution function of precipitation, with the empirical cumulative distribution functions (F_cdf) and its inverse ($F_{cdf}^{-1}$) as follows [33]:

$$P_{sim}^{*}(d)=F_{cdf}^{-1}(F_{cdf}^{}(P_{sim}^{}(d)|{\alpha }_{sim,m}^{},{\beta }_{sim,m}^{})|{\alpha }_{obs,m}^{},{\beta }_{obs,m}^{})$$

(5)

$$P_{pre}^{*}(d)=F_{cdf}^{-1}(F_{cdf}^{}(P_{pre}^{}(d)|{\alpha }_{sim,m}^{},{\beta }_{sim,m}^{})|{\alpha }_{obs,m}^{},{\beta }_{obs,m}^{})$$

(6)

where α and β are the parameters of F_cdf. The gained provincial data is capable of reflecting future P and T changes. To investigate future ED, a dependable simulation model is needed.

2.1.2. Bayesian Least Squares Support Vector Machine (BLSVM)

LSVM uses equality constraints and converts quadratic programming problems into linear versions. For the training set {(x_i, y_i) |i = 1, 2, …, n} associated with inputs and electricity demand (ED), the corresponding equation can be presented [34]:

$$y(x)={\omega }^T·\phi (x)+b$$

(7)

where φ(x) maps x into a D-dimensional eigenvector; b means bias term. The weight vector ω is calculated by solving the problem as follows:

$$\underset{\omega ,b,\xi }{\min }J(\omega ,\xi )=\frac{1}{2}{\omega }^T·\omega +\frac{c}{2}{\displaystyle \sum _{i=1}^N{\xi }^2}$$

(8)

subject to:

$$y_i={\omega }^T·\phi (x_i)+b+{\xi }_i, i=1, 2, \dots , n$$

(9)

where min means minimization, c is the penalty parameter, and ξ is training error. The corresponding result is obtained by considering the Lagrange function as:

$$L(\omega ,b,\xi ,\beta )=\frac{1}{2}{\omega }^T\omega +\frac{\gamma }{2}{\displaystyle \sum _{i=1}^N{\xi }^2}-{\displaystyle \sum _{i=1}^N{\beta }_i[{\omega }^T\phi (x_i)+b+{\xi }_i-y_i}]$$

(10)

where β_i is the Lagrange multiplier vector. Based on the Karush Kuhn-Tucker (KKT) conditions, the optimal result can be gained by differentiating ω, b, ξ, and β_i in Equation (10) as:

$$\left\{\begin{array}{l}\frac{\partial L(\omega ,b,\xi ,\beta )}{\partial \omega }=0\Rightarrow \omega ={\displaystyle \sum _{i=1}^N{\beta }_i{y}_i\phi (x_i)}\\ \frac{\partial L(\omega ,b,\xi ,\beta )}{\partial b}=0\Rightarrow {\displaystyle \sum _{i=1}^N{\beta }_i}=0\\ \frac{\partial L(\omega ,b,\xi ,\beta )}{\partial \xi }=0\Rightarrow {\beta }_i=\gamma {\xi }_i\\ \frac{\partial L(\omega ,b,\xi ,\beta )}{\partial {\beta }_i}=0\Rightarrow y_i({\omega }^T\phi (x_i)+\beta )-1+{\xi }_i=0\end{array}\right.$$

(11)

The relationship between inputs and ED is described as follows:

$$y={\displaystyle \sum _{i=1}^N{a}_{i}K(x_i,x)+b}$$

(12)

where K (x_i, x) means kernel function. The radial basis function (RBF) kernel, which can avoid computational difficulty in high-dimension space, is chosen to solve the LSVM problem [19]:

$$K(x_i,x_j)=\exp (-\frac{\left|\right|x_i-x_j\left|\right|}{2{\sigma }^2})$$

(13)

where σ² means the bandwidth of the RBF kernel. Regularization (γ) parameter and kernel (σ) parameter mainly decide the precision and convergence of LSVM.

Bayesian inference is introduced into LSVM (finally BLSVM) for optimizing γ and σ values, as well as improving prediction performance. BLSVM is carried out through three-level reasoning, which includes inference of the parameters ω and b, inference of the optimal hyperparameters μ and ξ, and inference of the parameters of kernel function [34]. Bayesian rules are used to provide a posteriori parameter distribution:

$$P(\left.\theta \right|X,\partial )=\frac{P(\left.X\right|\theta )P(\left.\theta \right|\partial )}{P(\left.X\partial )\right|}\propto P(\left.X\right|\theta )P(\left.\theta \right|\partial )$$

(14)

where X = {x₁, x₂, …, x_m} denotes m observed data points; θ means data point’s distribution parameter; ∂ is the hyperparameter of the parameter distribution; and P(θ|∂) is the prior distribution.

P(X|θ) is the likelihood function, showing the distribution of the observed data conditional on its parameter; P(θ|X, ∂) is the posterior distribution. The optimal parameters and future ED are obtained. Using the BLSVM model, ED under climatic–social–economic changes can be gained.

2.1.3. Factorial Analysis

Factorial analysis (FA) can be used to explore the individual and joint effects of multiple inputs on ED simulation performance. Climatic variables (i.e., P and T), which come from different GCMs, and emission scenarios (SSPs) often aggravate the complexity of the decision-making process. Different GCMs and SSPs are chosen as factors with multiple levels, and climatic variables are chosen as responses. Using Taguchi design (a fractional FA) is adopted to rapidly screen the effects of GCMs and SSPs on climatic variables. Scholars chose a proper experimental matrix based on the inputs’ number [35]. The impact models of different inputs (i.e., GCM and SSP) are summarized as follows:

$$y_{edv}=\mu +{\alpha }_e+{\beta }_d+{(\alpha \beta )}_{ed}+{\epsilon }_{edv}, e=1, \dots , E; d=1, \dots , D; v=1, \dots , V$$

(15)

where y_edv is the total variability in P and T; μ is the overall average effect of all factors; α_e means the effect of eth GCM (e = 1 to 3); β_d means the effect of dth SSP (d = 1, 2); (αβ)_ed is the joint effect between the eth GCM and dth SSP; ε_edv is the random error component. Some equations can be presented as [23]:

$$E_{GCM}=x(e,·)-\overline{X}$$

(16)

$$E_{SSP}=x(·,d)-\overline{X}$$

(17)

$$E_{GCM\times SSP}=x(e,d)+\overline{X}-x(e,·)-x(·,d)$$

(18)

where $E_{GCM}$ and $E_{SSP}$ are individual effects; $E_{GCM\times SSP}$ is the joint effect; X is the overall mean of climate variable; x(e,⋅) and x(⋅, d) are the means of climate variables over the eth GCM (e = 1 to 3) and dth SSP (d = 1, 2); and x(e, d) is the average of the members for eth GCM and dth SSP.

After Taguchi’s design, a two-level factorial analysis is used to detect the effects of n inputs (including climatic, social, and economic inputs) on ED. A set of experiments are conducted to calculate the result of all input combinations. There are low (L) and high (H) levels for each input, leading to 2ⁿ treatment combinations. Each combination’s ED can be gained by operating BLSVM. The sum of squares for inputs’ effects are:

$$S{S}_A=\frac{1}{JT}{{\displaystyle \sum _{i=1}^I\left({\displaystyle \sum _{j=1}^J{\displaystyle \sum _{t=1}^T{Y}_{ijt}}}\right)}}^2-\frac{1}{IJT}{\left({\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{t=1}^T{Y}_{ijt}}}}\right)}^2$$

(19)

$$S{S}_B=\frac{1}{IT}{{\displaystyle \sum _{j=1}^J\left({\displaystyle \sum _{i=1}^I{\displaystyle \sum _{t=1}^T{Y}_{ijt}}}\right)}}^2-\frac{1}{IJT}{\left({\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{t=1}^T{Y}_{ijt}}}}\right)}^2$$

(20)

$$S{S}_C=\frac{1}{IJ}{{\displaystyle \sum _{t=1}^T\left({\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{Y}_{ijt}}}\right)}}^2-\frac{1}{IJT}{\left({\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{t=1}^T{Y}_{ijt}}}}\right)}^2$$

(21)

$$S{S}_{A\times B}=\frac{1}{T}{{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J\left({\displaystyle \sum _{t=1}^T{Y}_{ijt}}\right)}}}^2-\frac{1}{IJT}{\left({\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{t=1}^T{Y}_{ijt}}}}\right)}^2-S{S}_A-S{S}_B$$

(22)

$$S{S}_{A\times C}=\frac{1}{J}{{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{t=1}^T\left({\displaystyle \sum _{J=1}^j{Y}_{ijt}}\right)}}}^2-\frac{1}{IJT}{\left({\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{t=1}^T{Y}_{ijt}}}}\right)}^2-S{S}_A-S{S}_C$$

(23)

$$S{S}_{B\times C}=\frac{1}{I}{{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{t=1}^T\left({\displaystyle \sum _{i=1}^I{Y}_{ijt}}\right)}}}^2-\frac{1}{IJT}{\left({\displaystyle \sum _{i=1}^I{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{t=1}^T{Y}_{ijt}}}}\right)}^2-S{S}_B-S{S}_C$$

(24)

where SS_A, SS_B, and SS_C are inputs’ sums of squares; SS_A×B, SS_A×C, and SS_B×C are two-factor interaction’s sums of squares. Y_ijt is the ED response under the ith, jth, and tth level of input A, B, and C, respectively; I, J, and T are the numbers of levels of A, B, and C; “-” means subtraction sign. Each input’s contribution to ED can be obtained by counting the ratio of its sum of squares to the total values. Ten climatic, economic, and social inputs are selected for ED simulation. All parameters’ descriptions, abbreviations, and changes are listed in Appendix A.

2.2. Energy–Water–Environment Nexus Optimization (EWEO) Model

An energy–water–environment nexus optimization (EWEO) model can then be formulated. Electricity demand (ED) in the future can be obtained using the former methods; then, ED is used as the right-hand side parameter in the EWEO model.

2.2.1. Model Objective

The objective function is to minimize system cost while fulfilling a set of model constraints. It is a linear combination of the costs, including purchasing energy, energy conversion, capacity expansion, electricity import, pollutants and carbon mitigation, electricity transmission, and water resources.

$$\mathrm{Min} f^{}=f_1{}^{}+f_2{}^{}+f_3{}^{}+f_4{}^{}+f_5{}^{}+f_6{}^{}+f_7{}^{}$$

(25)

(1)

Cost of purchasing energy:

$$f_1{}^{}={\displaystyle \sum _{i=1}^2{\displaystyle \sum _{t=1}^{8}EP{M}_{i,t}^{}·P{C}_{i,t}^{}}}$$

(26)

(2)

Cost of energy conversion:

$$f_2{}^{}={\displaystyle \sum _{k=1}^8{\displaystyle \sum _{t=1}^8(EC{M}_{k,t}^{}·C{C}_{k,t}^{}+EC{N}_{k,t}^{}·B_{k,t}^{})}}$$

(27)

(3)

Cost of capacity expansion:

$$f_3{}^{}={\displaystyle \sum _{k=1}^8{\displaystyle \sum _{t=1}^3(A_{k,t}^{}}}·Q_{k,t}^{}+B_{k,t}^{}·Z_{k,t}^{})$$

(28)

(4)

Cost of electricity import:

$$f_4{}^{}={\displaystyle \sum _{t=1}^{8}IE{M}_t^{}·I{C}_t^{}}$$

(29)

(5)

Cost of pollutants and carbon mitigation:

$$\begin{array}{ll}{f}_5& ={\displaystyle \sum _{k=1}^8{\displaystyle \sum _{t=1}^{8}EC{M}_{k,t}^{}·(EHC{N}_{k,t}^{}·PF{S}_{k,t}^{}·\eta s_{k,t}^{}·T{S}_{k,t}^{}+EHC{N}_{k,t}^{}·PF{N}_{k,t}^{}·\eta n_{k,t}^{}·T{N}_{k,t}^{}}}\\ & +EHC{N}_{k,t}^{}·PF{P}_{k,t}^{}·\eta p_{k,t}^{}·T{P}_{k,t}^{})+{\displaystyle \sum _{t=1}^{3}EC{M}_{k,t}^{}·EHC{N}_{k=1,t}^{}·OC·OCN·\zeta ·CC{S}_t^{}·TC{C}_{k=1,t}^{}}\\ & +{\displaystyle \sum _{t=1}^{3}EC{M}_{k,t}^{}·EHC{N}_{k=2,t}^{}·OC·OCF·\zeta ·CC{S}_t^{}·TC{C}_{k=2,t}^{}}\end{array}$$

(30)

(6)

Cost of electricity transmission:

$$f_6{}^{}={\displaystyle \sum _{k=1}^8{\displaystyle \sum _{t=1}^{8}EC{M}_{k,t}^{}·ZD{J}_{k,t}^{}·SPD{R}_{k,t}^{}}}$$

(31)

(7)

Cost of water resources:

$$f_7{}^{}={\displaystyle \sum _{k=1}^8{\displaystyle \sum _{t=1}^{8}EC{M}_{k,t}^{}·EW{D}_{k,t}^{}·KW{C}_{k,t}^{}}}$$

(32)

2.2.2. Model Constraint

A number of constraints are presented to describe the complex activities in the planning processes. The constraints contain energy availability, electricity demand-supply balance, energy conversion capacity, policy, electricity import, air pollutants and CO₂ emissions, and water consumption.

(1)

Constraint for energy availability:

$$EP{M}_{i,t}^{}\le ESP{M}_{i,t}^{},\forall i,t$$

(33)

$$EHC{N}_{k=1,t}^{}·EC{M}_{k=1,t}^{}\le EP{M}_{i=1,t}^{},\forall t$$

(34)

$$EHC{N}_{k=2,t}^{}·EC{M}_{k=2,t}^{}\le EP{M}_{i=2,t}^{},\forall t$$

(35)

(2)

Constraint for electricity demand-supply balance:

$${\displaystyle \sum _{k=1}^{8}EC{M}_{k,t}^{}·\left(1-WS{R}_{k,t}^{}\right)}+IE{M}_t^{}\ge E{D}_t^{},\forall t$$

(36)

(3)

Constraint for energy conversion capacity:

$$EC{N}_{k,t}^{}=EC{T}_k^{}+Z_{k,t}^{}·Q_{k,t}^{}-TY{Z}_{k,t}^{},\forall k,t=1$$

(37)

$$EC{N}_{k,t}^{}=EC{N}_{k,t-1}^{}+Z_{k,t}^{}·Q_{k,t}^{}-TY{Z}_{k,t}^{},\forall k,t=2, \dots , 8$$

(38)

$$EC{N}_{k,t}^{}·C{T}_{k,t}^{}\ge EC{M}_{k,t}^{},\forall k,t$$

(39)

$$Q_{k,t}=\left\{\begin{array}{l}1, \mathrm{if} \mathrm{capacity} \mathrm{expansion} \mathrm{is} \mathrm{undertaken}\\ 0, \mathrm{otherwise}\end{array}\right.$$

(40)

(4)

Constraint for policy:

$$EC{N}_{k,t}^{\pm }\le U{S}_{k,t}^{\pm }, \forall k,t$$

(41)

(5)

Constraint for electricity import:

$$IE{M}_t^{}\le IEM{S}_t^{}, \forall t$$

(42)

(6)

Constraint for air pollutants and CO₂ emissions:

$${\displaystyle \sum _{k=1}^{2}EC{M}_{k,t}^{}·EHC{N}_{k,t}^{}·PF{S}_{k,t}^{}·(1-\eta s_{k,t}^{})}\le PL{S}_t^{}, \forall t$$

(43)

$${\displaystyle \sum _{k=1}^{2}EC{M}_{k,t}^{}·EHC{N}_{k,t}^{}·PF{N}_{k,t}^{}·(1-\eta n_{k,t}^{})}\le PL{N}_t^{}, \forall t$$

(44)

$${\displaystyle \sum _{k=1}^{2}EC{M}_{k,t}^{}·EHC{N}_{k,t}^{}·PF{P}_{k,t}^{}·(1-\eta p_{k,t}^{})}\le PL{P}_t^{}, \forall t$$

(45)

$$\begin{array}{l}EC{M}_{k=1,t}^{}·EHC{N}_{k=1,t}^{}·OC·OCN·\zeta ·(1-CC{S}_t^{})\\ +EC{M}_{k=2,t}^{}·EHC{N}_{k=2,t}^{}·OC·OCF·\zeta ·(1-CC{S}_t^{})\\ \le PL{C}_t^{}, \forall t\end{array}$$

(46)

(7)

Constraint for water consumption:

$${\displaystyle \sum _{k=1}^{8}EC{M}_{k,t}^{}·EW{D}_{k,t}^{}}\le DTQ{W}_t^{}$$

(47)

Appendix B shows nomenclatures for parameters. By integrating multi-GCMs, FBL, and EWEO models into a framework, the GSO-EWEO model can be formulated (Figure 1).

3. Case Study

3.1. Study Area

Fujian Province (latitude 23°33′ to 28°20′ N, longitude 115°50′ to 120°40′ E) is located on the southeast coast of China, covering an area of 124 × 10³ km² in 2020. Fujian has abundant rainfall and sufficient light because of the monsoon circulation and topography. The annual average temperature is 17–21 °C, and the annual average rainfall is 1400–2000 mm [36]. In 2020, Fujian hosted a population of 39.73 million (with a mean annual growth rate of 6.91% since 2015), as well as achieved a regional GDP of RMB 4239.5 billion (with a mean annual growth rate of 9.42% since 2015) [36]. Regional electricity consumption has risen sharply over the past decades. The total electricity consumption in Fujian reached 248.3 billion kWh in 2020, with a mean annual growth rate of 7.02% since 2015. Future electricity demand can be simulated based on uncertain variables, including natural, economic, and social conditions, which can provide reliable information to decision-makers.

In Fujian, coal-fired power accounted for 58.88% of the total electricity supply in 2020. Hydropower, wind power, nuclear power, and others occupied 41.12% of the total electricity supply, while imported electricity from other provinces accounted for 0.09% in 2020. Industrial water consumption was 4.11 billion m³, occupying 22.5% of the total water consumption in 2020 (decreased by 26.6% compared with 2019). The life cycle of coal, including mining, chemical industry, and power generation, is water intensive [37]. It results in sharp competition for water among industries and restricts coal-fired power generation. Moreover, SO₂, NO_x, PM, and CO₂ emissions from energy conversion (mainly from the combustion of coal) were 162.1 × 10³, 141.1 × 10³, 18.43 × 10³, and 49.96 × 10⁶ t, respectively. In order to mitigate air pollutants/carbon emissions and conserve resources (e.g., energy and water), authorities in Fujian have decided to adjust the current electricity supply structures.

3.2. Data Collection

The observed daily data of precipitation (abbreviate as P), minimum temperature (abbreviate as T_min), mean temperature (abbreviate as T_mean), and maximum temperature (abbreviate as T_max) from 1991 to 2020 (as potential predictors for training downscaling approaches) are downloaded from the China Meteorological Data Network (http://data.cma.cn). The future P, T_min, T_mean, and T_max from three GCMs (i.e., CanESM5, GFDL-ESM4, and MIROC6) under two emission scenarios (i.e., SSP2-4.5 and SSP5-8.5, reflecting two distinct paths of human evolution) are extracted from Coupled Model Intercomparison Project Phase 6 (CMIP6) dataset archive (https://esgfnode.llnl.gov/projects/esgf-llnl/ assessed on 1 January 2021). SSP2-4.5, a more sustainable one, assumes a middle-of-the-road scenario with some GHG emission reductions; and SSP5-8.5, a business-as-usual scenario which assumes a fossil-fueled development with very limited actions to decrease GHG emissions [38]. The historical period of GCMs is 1991–2014, and the future period of GCMs is 2021–2060. Numerous research about these GCMs was conducted and showed decent performances. According to recent statistical materials and research reports, economic and social inputs fluctuated within certain ranges [36,39]. For instance, the annual growth rate of the population was higher than 0.6% and lower than 1.2% in recent years, and it was estimated that a slow-growth trend would maintain for a long period; 0.6% (2021–2025), 0.8% (2026–2030), 1.0% (2031–2035), 1.2% (2036–2060) is chosen as slow growth rate and 1.0% (2021–2025), 1.1% (2026–2030), 1.3% (2031–2035), 1.5% (2036–2060) is selected as fast growth rate.

Data on economic and social inputs in the simulation process, as well as data on economic and technical parameters in the optimization process, are collated based on authoritative governmental documents, statistic yearbooks, and relevant references [36,39,40,41,42,43]. In the EWEO model, energy exploitation types are raw coal and natural gas; the planning horizon is 2021–2060, which is divided into eight periods, with each has 5 years; energy conversion technologies are coal-fired power, natural gas-fired power, hydropower, pumped storage power, nuclear power, wind power, biomass power, photovoltaic power; pollutants are SO₂, NO_x, and PM; carbon means CO₂.

4. Results and Discussion

4.1. Precipitation and Temperature

Figure 2 displays the root mean square error (RMSE) for each GCM during 1991–2014. RMSE represents the sample standard deviation of the differences between predicted values and observed values, which is a good measure of accuracy to compare forecasting errors of different models for a particular variable. Results show that LS is effective to correct T bias, but it has little correction effect on P, and DM performs well in correcting P. For example, RMSE increased from 111.82 to 118.49 (GFDL-ESM4) after correcting P data with the LS method; after correcting P data by LS and DM methods, RMSE, respectively, decreased from 218.77 to 183.67 (using LS, CanESM5) and 161.47 (using MD, CanESM5); RMSE, respectively decreases from 134.52 to 132.40 (using LS, MIROC6) and 122.02 (using DM, MIROC6). Thus, the data of projected T corrected by the LS method is adopted, as well as the data of projected P corrected by the DM method is chosen.

Figure 3 presents the projected P, T_min, T_mean, and T_max of each day during 2021–2060. Results show the great variability of P and T projections among the CanESM5, GFDL-ESM4, and MIROC6. For instance, under SSP2-4.5, future P, T_min, T_mean, and T_max on 1 January 2040 would be 0.603 mm, 2.56 °C, 5.21 °C, 10.57 °C (CanESM5), 0.061 mm, 4.21 °C, 7.36 °C, 13.14 °C (GFDL-ESM4), and 3.063 mm, 12.05 °C, 15.15 °C, 19.03 °C (MIROC6), respectively. It is revealed that uncertainty exists in climate projections due to the differences between GCMs. Taking the average results from the three GCMs may be helpful for reducing the uncertainty to provide more reliable information. Under SSP2-4.5, future P, T_min, T_mean, and T_max on 1 January 2040 would change to 0.587 mm, 1.66 °C, 4.88 °C, 10.46 °C (CanESM5), 0 mm, 1.47 °C, 7.29 °C, 17.10 °C (GFDL-ESM4), and 0.786 mm, 5.95 °C, 6.26 °C, 7.45 °C (MIROC6). Compared with each GCM, P, and T derived from GCMs-Ensemble would be neutral.

It is noted that P, T_min, T_mean, and T_max projections are also affected by SSPs. For example, on 1 January 2025, under SSP2-4.5, the projected P, T_min, T_mean, and T_max would be 0.584 mm, 2.60 °C, 3.49 °C, 7.30 °C (CanESM5), 0 mm, 0.97 °C, 3.78 °C, 9.10 °C (GFDL-ESM4), 0.236 mm, 2.51 °C, 5.65 °C, 9.18 °C (MIROC6), and 0.273 mm, 2.03 °C, 4.31 °C, 8.52 °C (GCMs-Ensemble); under SSP5-8.5, the projected P, T_min, T_mean, and T_max would be 0.587 mm, 6.45 °C, 8.93 °C, 14.05 °C (CanESM5), 0.896 mm, 6.86 °C, 8.95 °C, 11.77 °C (GFDL-ESM4), 3.677 mm, 5.81 °C, 7.06 °C, 9.71 °C (MIROC6), and 1.720 mm, 6.37 °C, 8.31 °C, 11.85 °C (GCMs-Ensemble). It has been discovered that carbon emissions could impact the P and T of Fujian Province. Results also indicate that the daily P and T would be featured with randomness in the next 40 years. For example, for GCM-Ensemble on 31 December, under SSP2-4.5, the minimum P, T_min, T_mean, and T_max would be 0.17 mm (2021), 5.00 °C (2047), 8.84 °C (2047), 1.41 °C (2053); the maximum P, T_mean, T_max, and T_min would be 33.37 mm (2027), 14.01 °C (2028), 18.57 °C (2028), 11.13 °C (2028); under SSP5-8.5, the minimum P, T_mean, T_max, and T_min would be 0.17 mm (2060), 5.48 °C (2039), 9.92 °C (2043), 0.92 °C (2058); the maximum P, T_mean, T_max, and T_min would be 14.44 mm (2042),15.49 °C (2060), 20.75 °C (2060), 12.44 °C (2027).

As inputs to simulate future electricity demand (ED), daily P and T should be transformed to yearly P and T. Figure 4 shows the yearly trends of P, T_min, T_mean, and T_max on the basis of Mann–Kendall (M-K) and Sen’s slope estimator tests. The mean values of assessed Sen’s slopes for P, T_min, T_mean, and T_max are 3.34446 mm/year, 0.01028, 0.00072, and 0.00585 °C/year, respectively. The ranges of assessed Sen’s slopes for P, T_min, T_mean, and T_max would be [1.32464, 5.56573] mm/year, [−0.00263, 0.01697], [0.00004, 0.00201] and [−0.00208, 0.02265] °C/year, respectively. This indicates the great uncertainties of future P and T trends in the correction process. Most rising trends of P and T under SSP2-4.5 are important with z-values ≥ 1.64 (i.e., p < 0.05); most rising trends of P, T_mean, and T_max under SSP5-8.5 are very important with z-values ≥ 2.32 (i.e., p < 0.01) as well as rising trends of T_min are not important with z-values < 1.64. It is revealed that the rainy and warming trends are likely occurred in the province (4.51247 mm/year of P, 0.00805 °C/year of T_min, 0.00073 °C/year of T_mean, and 0.00851 °C/year of T_max) under a great greenhouse gas emission (SSP5-8.5); conversely, low greenhouse gas emission (SSP2-4.5) would lead to a slight warming trend (2.17645 mm/year of P, 0.01251 °C/year of T_min, 0.00072 °C/year of T_mean, and 0.00318 °C/year of T_max) for P and T in the province.

4.2. Electricity Demand

In the simulation process, for each GCM, under each SSP, there are 32 scenarios for social-economic parameter combinations, leading to 256 electricity demand scenarios (EDS). Figure 5 describes annual ED during 2021–2060, respectively. ED shows great variability under different scenarios. For example, in 2021, the highest ED would be 270.71 × 10⁹ kWh under EDS65, the lowest ED would be 233.80 × 10⁹ kWh under EDS60; in 2060, the highest ED would be 467.26 × 10⁹ kWh under EDS2, the lowest ED would be 412.04 × 10⁹ kWh under EDS237. It is revealed that future ED would vary significantly across different GCMs, SSPs, and socioeconomic development conditions. In addition, results indicate that ED would increase with time. For instance, under EDS1, the total ED would be 1.31 × 10¹² kWh in period 1 (during 2021–2025); the total ED would be 2.18 × 10¹² kWh in period 8 (during 2056–2060). It is implied that the energy supply pressure of Fujian Province would continuously increase, and authorities should make corresponding optimal planning policies.

To quantify single and joint effects of inputs on ED. Ten inputs are divided as low (L) and high (H) levels corresponding to minimum and maximum values during 2021–2060, respectively. Figure 6(a1–a4) describes the single effects of GCMs and SSPs on P and T. The lines of GCM are steeper than SSP, showing that GCM is very important to P and T projections. For instance, under SSP2-4.5, the largest T_max projection reproduced by CanESM5, GFDL-ESM4, MIROC6 and GCMs-Ensemble are 39.45 °C, 35.88 °C, 41.07 °C and 36.96 °C, respectively; while the largest T_max projection of GFDL-ESM4 reproduced by SSP2-4.5 and SSP5-8.5 are 41.07 °C and 41.14 °C, respectively. Figure 6(b1–b4) describes the joint effects of GCMs and SSPs on P and T projections. Parallel lines mean that there are no joint effects. Results show that the joint effects of GCM and SSP on P and T_max would be obvious. For example, when MIROC6 is chosen in 2060, P would rise from 2218.3 mm to 2768.1 mm with SSP changing from SSP2-4.5 to SSP5-8.5; when CanESM5 is chosen in 2050, T_max will rise from 36.7 °C to 40.2 °C with similar SSP change. The interactions of GCM and SSP weakly affect T_min and T_mean. For example, when GFDL-ESM4 is selected in 2047, T_mean would rise from 19.2868 °C to 19.2869 °C with SSP changing from SSP2-4.5 to SSP5-8.5; when MIROC6 is selected in 2060, T_min will rise from −1.6 °C to −1.3 °C with similar SSP change.

Quantitative results show that the total contribution rate of single inputs would be 99.27%. Figure 7a depicts the single effects of climatic, economic, and social inputs on ED. Take the plot of GDP as an example. ED rise from 338.02 × 10⁹ kWh to 366.54 × 10⁹ kWh, with GDP increasing from its low level of 5.22 × 10¹² RMB to a high level of 305.85 × 10¹² RMB; the slope of the line is positive, indicating that GDP has a positive effect on ED. Compared with other inputs, PO has the steepest slope, implying that PO has the greatest magnitude of a single effect on ED. From the results, GDP, FI, TI, RCL, and PO have obvious positive effects on ED; T_min and T_mean have slightly positive effects. P and T_max still have slightly negative effects on ED, showing that economic and social inputs remain a prominent role. Figure 7b depicts the multiple inputs matrix of the interaction plot. It shows that the interaction of climatic inputs has slight effects; there is little interaction between economic and social inputs. The joint effects would contribute 0.73%, whereas the interaction between P and T_min would contribute the greatest (0.078%).

4.3. System Planning

In the EWEO model, the minimum and maximum values of ED_t under all EDSs are set as low demand and high demand; DTQW_t have data with low-water availability and high-water availability; PLS_t, PLN_t, PLP_t, and PLC_t have data with strict environmental policy and normal environmental policy, respectively; thus, there are 64 combinations of the six parameters. Figure 8 presents the system cost under each combination. It is shown that the system cost would be different under varied combinations because of the changed ED_t, DTQW_t, PLS_t, PLN_t, PLP_t, and PLC_t. The lowest system cost would be 12.71 × 10¹² RMB¥ under C40 (i.e., combination 40, with low electricity demand, high-water availability as well as normal environmental policy), and the highest system cost would be 16.87 × 10¹² RMB¥ under C37 (with high electricity demand, low-water availability as well as strict environmental policy). It is estimated that ED_t is the most significant parameter since it contributes the most (i.e., 88.76%, generated by factorial analysis) to the system cost variations. It has positive effects on system cost, meaning higher ED_t corresponds to higher system cost. When ED_t is set as low electricity demand, system cost will range between 12.71 × 10¹² RMB¥ and 13.33 × 10¹² RMB¥ (under C17); when ED_t is set as high electricity demand, system cost will range between 16.12 × 10¹² RMB¥ (under C5) and 16.87 × 10¹² RMB¥. PLP_t, PLS_t, PLN_t, PLC_t, and DTQW_t contribute −2.92%, −1.75%, −1.21%, −1.06, and −1.04% to the system cost variations. They have negative effects on system cost, denoting higher PLP_t, PLS_t, PLN_t, PLC_t, and DTQW_t, resulting in lower system costs. The above results reveal that the prediction of electricity demand is necessary.

Figure 9 describes the energy conversion structure under typical combinations (i.e., C5, C17, C25, C36, C37, and C40). Coal-fired power would show a declining tendency during 2021–2060; its proportion in the total electricity supply would reduce from [49.41, 58.92]% to [13.93, 16.27]%. Natural gas-fired power would rise during 2021–2060; its proportion in the total electricity supply would change from [8.83, 9.74]% to [12.51, 12.95]%. Coal and natural gas-fired power would still be dominant for electricity supply before 2035; nevertheless, its proportion in the total electricity supply would decrease from [58.31, 68.63]% to [50.44, 60.25]% because of resource scarcity and emission mitigation pressures. To satisfy the increasing ED, electricity converted by new energy would increase with time, and its ratio would surpass that of coal and gas after 2035. Among them, hydropower, nuclear power, and wind power would occupy large shares of the electricity supply, totally occupying [45.2%, 51.54]% during 2036–2040 and [54.57, 57.71]% during 2055–2060, respectively. By 2055–2060, the share of nuclear power would be [23.85, 25.49]% as the largest source of electricity supply. Photovoltaic power would exhibit an obvious upward trend; its ratios would be [0.18, 1.83]% during 2036–2040 and increase to [9.14, 9.56]% during 2055–2060. During the planning horizon, wind power would rise sharply, which would satisfy [1.33, 4.16]% of the total electricity demand during 2022–2025 and [11.44, 15.58]% of the total electricity demand during 2055–2060. The proportion of imported electricity would be relatively low (about [1.34, 1.84]% to [2.12, 2.97]%). It is revealed that Fujian needs to greatly adjust energy conversion structures to overcome the challenges of climate change, economic development, and environmental protection.

Figure 10 shows water, pollutants, and carbon flows under typical combinations. Coal-fired power would consume the vast majority of water resources (>70%) as well as emit large amounts of pollutants (>99%) and CO₂ (>90%). Emissions of PM, NO_x, SO₂, and CO₂ would be [14.1, 15.2] × 10³ ton, [287.8, 310.7] × 10³ ton, [554.7, 598.7] × 10³ ton, and [669.2, 722.4] × 10⁶ ton in 2021–2025, respectively; corresponding emissions would decrease to [6.5, 7.3] × 10³ ton, [132.8, 149.1] × 10³ ton, [255.8, 287.4] × 10³ ton, and [308.7, 346.8] × 10⁶ ton in 2055–2060. It is proved that air pollutants and CO₂ emissions would decline with time due to the optimized energy conversion structure. It is also shown that mitigating CO₂ would still be urgent; decision-makers may adopt carbon emission trading, carbon sink, and other useful measures. For water consumption, the amount would be [8.97, 9.67] × 10⁹ m³ in 2021–2025, and the amount would reduce to [5.18, 5.63] × 10⁹ m³ in 2055–2060. The total share of water consumption by nuclear power, wind power, and photovoltaic power would be about 0.21% (2021–2025), 0.44% (2026–2030), 0.55% (2031–2035), 0.68% (2036–2040), 0.84% (2041–2045), 1.04% (2046–2050), 1.58% (2051–2055), and 1.6% (2056–2060). It is revealed that nuclear power, photovoltaic power, and wind power are water-saving technologies. If possible, decision-makers can develop three energy conversion technologies to conserve water.

5. Conclusions

In this research, an FBL-EWEO model is proposed by integrating multi-GCMs, Bayesian least-squares-support-vector machine factorial-analysis (FBL), and energy–water–environment nexus optimization (EWEO) models within a framework. The model is capable of providing reliable information for climatic variables (i.e., precipitation and temperature), catching the complex nonlinear relationship between inputs (related to climate, society, and economy) and response (i.e., electricity demand, namely as ED) with high efficiency; quantifying the contributions of inputs to ED response; optimizing energy–water–environment nexus system considering uncertainties associated with energy supply, electricity demand, water consumption, pollutants/CO₂ emissions, and system cost. The model is applied to a real case study of Fujian Province, China.

Major findings can be concluded as: (1) Fujian would encounter rainy and warming trends (4.51247 mm/year of P, 0.00805 °C/year of T_min, 0.00073 °C/year of T_mean, and 0.00851 °C/year of T_max) under SSP5-8.5, and a slight warming trend (2.17645 mm/year of P, 0.01251 °C/year of T_min, 0.00072 °C/year of T_mean, and 0.00318 °C/year of T_max) under SSP2-4.5; (2) ED would vary significantly under different scenarios of climatic–social–economic changes and grow with time in the next 40 years (increase by about [64.21, 74.13]%); (3) GCM would affect the climate projections more significantly compared with SSP, while the key inputs affecting ED would be PO (21.03%) > FI (17.07%) > SI (15.59%) > GDP (15.29%) > RCL (14.47%) > TI (14.35%) > T_mean (1.31%) > P (0.08%) > T_min (0.06%) > T_max (0.02%); economic inputs would occupy 62.30% on ED response, followed by social and climatic inputs that would contribute 35.50% and 1.47%, respectively; interactions between inputs would contribute about 0.73%, where the interaction between P and T_mean would be prominent; (4) ED prediction is necessary since it contributes 88.76% (compared with water availability and environmental policy) to the system cost variations in the EWEO model; (5) it is noticed that coal- and gas-fired power would still be dominant for electricity supply before 2035 (the share would decrease from [58.24, 68.66]% to [45.26, 55.01]%), and the share of hydropower, nuclear power and wind power would increase to [54.57, 57.71]% by 2055–2060 (adding wind power capacity would be important for Fujian); (7) air pollutants/CO₂ emissions would averagely decline [51.97, 53.90]%, and water consumption would decrease [41.77, 42.25]%; (8) results quantitively provide potential sustainable development strategies.