Impact of Climate Change on Wind Power Generation Studied Using Multivariate Copula Downscaling: A Case Study in Northwestern China

Abstract

Climate change can modify regional wind power generation ability, as it may affect wind speed. Here, we developed a multivariate copula downscaling (MvCD) approach to statistically downscale the near-surface wind speed of CMIP5 global climate models (GCMs) to the scale of wind farms in Urumqi, China. The low computational cost and high random analysis capability of this approach allowed the rapid assessment of projected changes and randomness from nine GCMs, spanning a range of potential futures under four scenarios. Simulation data from multiple GCMs and historical data of the study area were incorporated into the MvCD to generate a high dimensional multivariate copula. Thereafter, the high dimensional multivariate copula was further used to identify future wind speed patterns based on multiple GCMs under different CO₂ emission scenarios. The estimated amount of wind power generation was obtained using future wind speed data. Results revealed the regional characteristics and periodicity of wind speed for Urumqi in the future. Wind power generation results revealed the impacts of climate changes on regional wind power generation and indicated that high wind speeds would occur from June to September and low wind speeds would occur from December to March in future scenarios. Wind speed would be more extreme under each scenario in the future than before. The highest and lowest wind speeds will increase and decrease, respectively. Sustained high winds would increase the potential of wind power generation in the future. Wind instability based on CO₂ emission increases will lead to wind power being curtailed and low wind-power generation.

1. Introduction

China aims to peak carbon dioxide (CO₂) emissions before 2030 and achieve carbon neutrality before 2060. China will increase the share of non-fossil fuels in its primary energy consumption to approximately 25% and increase its total installed capacity of wind and solar power to over 1.2 GW. Wind power will play an important role in achieving this goal. Wind power is regarded as one of the most important green energies for sustainable development under the target of peaking CO₂ emissions and carbon neutrality [1,2,3]. Nevertheless, there are many uncertainties in the application of wind power, which is affected by different factors. Wind electricity generation directly depends on wind speed, which is highly influenced by the weather and climate conditions [4,5,6]. Wind power is also susceptible to seasons and climate change, similar to several other renewable technologies [7,8]. For example, the climate governs the energy density in the wind and, hence, the power that can potentially be harnessed [9]. Because of anthropological effects, climate change is becoming extreme. Extreme climate will lead to abrupt changes in wind speed, even leading to extreme wind (e.g., strong wind, cyclones, and windstorms). Extreme wind can be damaging to wind farms and can impact the macro layout of wind farm construction. Extreme wind speed might bring risks to wind turbines and power loads. Moreover, high wind speeds lead to changes in the extreme loads of wind turbines [10,11]. Therefore, wind speed variability has several risk consequences for wind power systems [12,13,14,15,16]. In contrast, wind turbines are designed for different conditions of wind speeds in regional wind farms. Thus, analysing the impacts of climate change on wind speed and wind power generation would be important for wind farm planning and construction [17,18]. Simulation and forecasting of wind speed in wind farms under different future climate change scenarios are also important for regional wind power systems.

Global climate models (GCMs) can be used to efficiently study regional climatic factors, such as temperature, rainfall, wind speed, etc. The effects of climate change are generally quantified based on bias correction by extracting higher-resolution projections of GCMs and regional climate models (RCMs). However, the scale of GCMs is too imprecise for regional sites, such as meteorological stations or wind farms. The calculation of RCMs is complicated, and generating robust results using RCMs is challenging because of the small number of models [19,20]. GCMs are generally downscaled to a more appropriate spatial scale using downscaling methods [21]. Therefore, several mathematical methods have been applied to downscale GCM data. For example, support vector machine is a classical method with favourable features for bias correction of GCM data [22,23,24]. Jones and Thornton used a suite of climate models for agricultural modelling applications to generate downscaled weather data [25]. Trotochaud et al. developed a simple technique for obtaining downscaled future climate data output from multiple GCMs [26]. Muhling et al. applied four statistical downscaling methods—bias-corrected quantile mapping, change factor quantile mapping, equidistant quantile mapping, and the cumulative distribution function transform—to output data from four GCMs [27]. Zobel et al. used a weather research and forecast model to evaluate the performance of several dynamical downscaled historical simulations with an area that covers most of North America [28]. Li et al. summarize four main kinds of downscaling methods used in the field of climate change [29]: statistical downscaling [30], dynamic downscaling [31], hybrid dynamic–statistical downscaling [32] and interpolation [33]. Method architecture statistical downscaling would use empirical relationships between local-scale variables and large-scale atmospheric variables, for instance, regression models such as quantile regression [34], multiple regression [35], support vector machine [36], and deep learning neural models [37]. Traditional downscaling methods have definitive results, making the identification of probabilistic features almost impossible. Therefore, it is hard for probabilistic methods to analyse the impacts and risks of climate change to wind speed and wind power generation using traditional downscaling methods.

The risks for wind energy resources are present in wind farms, namely, wind speed uncertainty [38]. Fitting the cumulative behaviour with the distributions of wind to overcome the challenges associated with wind forecasting has been difficult. Several probability distributions have been employed for wind speed studies. Weibull distribution is classical distribution to describe the characteristics of wind behaviour. Although the Weibull distribution is often used for wind speed distribution, it does not fit specific wind speed distributions well, especially the probabilities of strong wind [39,40,41]. Thus, the marginal distribution was chosen as the empirical distribution in this study. Marginal distributions of multiple GCMs and historical wind speed data have been coupled by a joint probability distribution function [42]. A joint probability distribution function of wind speed among multiple GCMs and historical wind speed data was obtained using the pair-copula method, which can use bivariate copula functions to consider dependencies between two arbitrary wind speed sets and overcome the constraints and difficulties of high dimensional copula functions. Copula functions can not only be used to describe dependencies between random input variables but also be applied for an arbitrary marginal distribution of random variables with no constraints of linear dependence. Copula functions are flexible joint distributions that can handle mixed marginal distributions [43,44,45,46]. Different scholars have used higher-dimensional copula functions with respect to hydrological datasets to perform rainfall frequency and flood frequency analyses [47,48,49]. Li and Babovic introduced a new scheme for a multivariate, multisite weather generator based on an empirical copula approach and established a multi-site multivariate downscaling of global climate model outputs, which were combined with quantile mapping, stochastic weather generator and empirical copula approaches [50,51]. Therefore, the copula function has many advantages in terms of constructing a joint probability distribution function in this study.

In this study, a multivariate copula downscaling (MvCD) approach was developed to identify the impacts of climate change on wind power generation in northwestern China. Therefore, we propose a new method to achieve the following aims: (i) develop a statistical multivariate copula function for downscaling regional wind speeds based on the historical observational data and GCM data; (ii) obtain regional wind speed sequences under future climatic conditions; (iii) recognise and estimate the impacts and risks of regional wind power based on wind speed under future climatic conditions. Simulation results from multiple GCMs were incorporated into the MvCD to establish a probabilistic relationship between GCM results and real wind observations. This probabilistic relationship was further used to generate future wind speed patterns based on projects from multiple GCMs. The advantage of this method is that it can capture the common characteristics of different GCMs and integrate them into downscaling. On the other hand, the unique features of each GCMs will be weakened to reduce uncertainty, which is caused by the different GCMs architectures. We obtained downscaled GCM projections, and wind speed was predicted with MvCD using future climate scenarios considering different representative concentration pathways (RCPs). Scenarios of RCPs are RCP2.6, RCP4.5, RCP6.0, and RCP8.5, representing an increase in radiative forcing levels by 2.6 W/m², 4.5 W/m², 6.0 W/m², and 8.5 W/m² by 2100, respectively. Future wind speed patterns were used to analyse the regional wind power generation in Urumqi, China. Studying the complex wind conditions under changing climate conditions because of global warming is important for the regional safety of wind energy resources (

Table 1. The contribution of this study.

1. MvCD was applied to a wind-downscaling study firstly, which will provide new ideas for related research.

2. The development of a stochastic downscaling method (such as MvCD) will provide an analysis path for randomness in downscaling research.

3. The results of this study clearly show the vulnerability of new energy systems to climate change.

4. The findings also point to the wind energy potential associated with climate change.

). In this study, we quantified the wind power potential in Urumqi and estimated the influence of inter-annual variability on wind resources.

The organization of the paper is as follows. Section 2 provides the methodology, which includes survey region, copula theory, theoretical construct of MvCD, evaluation criteria, and a wind energy conversion application. Section 3 provides natural features of the survey region and regional data processing ideas. Section 4 details the wind speed downscaling results based on the copula method and programming results and potential prediction for regional wind power. Finally, Section 5 shows some conclusions.

2. Methodology

2.1. Study Site

The research location was Urumqi, the capital of the Xinjiang Uygur Autonomous Region, which is one of the richest new energy resource provinces in China. Wind power is the main renewable energy source in Urumqi. The instability of wind conditions affects the stability of wind power generation in this area.

2.2. Copula Method

A copula is a joint distribution function of standard uniform random variables. A copula can be represented simply as follows:

$$C:[0,1]\to [0,1]$$

(1)

It must fulfil the following conditions:

$$C(1,u)=C(u,1)=u and C(0,u)=C(u,0)=0$$

(2)

$$C(u_1,u_2)+C(v_1,v_2)-C(u_1,v_2)-C(v_1,u_2)\ge 0 if u_1\ge v_1, u_2\ge v_2 and u_1,u_2,v_1,v_2 \in [0,1]$$

(3)

Subsequently, the n dimensional distribution function F can be written as

$$F(x_1,x_2,\dots ,x_n)=C(F(x_1),F(x_2),\dots ,F(x_n))$$

(4)

The copula function C is unique and has the following representation.

$$C_{gau}(u_1,u_2,...,u_n)=F_k^{-1}\left(u_k\right)=\mathit{inf}\left\{x\in \mathfrak{R}\left|F_k\left(x\right)\ge u_k\right.\right\},k=1,...,n$$

(5)

where F₁,…, F_n are marginal distribution functions.

Gaussian copula, t-Copula, and Archimedean copula are widely applied classes of copula functions [52,53,54,55,56,57]. In this study, bivariate copula functions were employed to structure the connection between the historic data and CMIP5 data.

2.3. Common Copula Functions

(1)

Gaussian Copula

The bivariate copula form of the Gaussian copula can be defined as follows:

$$C^{Gau}(u,v;\rho )={\displaystyle \stackrel{{\varphi }^{-1}(u)}{\int }{\displaystyle \stackrel{{\varphi }^{-1}(v)}{\int }\frac{1}{2\pi \sqrt{1-{\rho }^2}}\exp \left[-\frac{s^2-2\rho st+t^2}{2(1-{\rho }^2)}\right]}}dsdt$$

(6)

(2)

t-Copula

The bivariate copula form of the t-Copula can be defined as follows:

$$C^t(u,v;\rho ,k)={{\displaystyle \stackrel{t^{-1}(u)}{\int }{\displaystyle \stackrel{t^{-1}(v)}{\int }\frac{1}{2\pi \sqrt{1-{\rho }^2}}\left[1+\frac{s^2-2\rho st+t^2}{2(1-{\rho }^2)}\right]}}}^{-(k+1)/2}dsdt$$

(7)

(3)

Archimedean Copula

In general, a bivariate Archimedean copula can be defined as follows:

$$C^{Acr}(u,v)={\phi }^{-1}[\phi (u),\phi (v)]$$

(8)

where $\phi$ is the generating function. The Gumbel copula, Clayton copula, and Frank copula can be defined as follows (

Table 2. Archimedean Copula functions.

Copula	$\begin{array}{c}\mathbf{Generating\; Function}\\ \mathbf{\left[}\mathit{\phi }\mathbf{(}\mathit{\theta }\mathbf{)}=\mathbf{\right]}\end{array}$	${\mathit{C}}^{\mathit{A}\mathit{c}\mathit{r}}\mathbf{(}\mathit{u}\mathbf{,}\mathit{v}\mathbf{)}$	$\begin{array}{c}\mathbf{Parameter}\\ \mathbf{[}\mathit{\theta }\mathbf{\in }\mathbf{]}\end{array}$
Gumbel Copula	${(-\ln t)}^{1/\theta }$	$C(u,v)=e^{-{[{(-\ln u)}^{1/\theta }+{(-\ln v)}^{1/\theta }]}^{\theta }}$	[1,∞)
Clayton Copula	$t^{-\theta }-1$	$C(u,v)={(u^{-\theta }+v^{-\theta }-1)}^{-1/\theta }$	(0,∞)
Frank Copula	$-\ln {\displaystyle \frac{e^{-\theta t}-1}{e^{-\theta t}-1}}$	$C(u,v)=-{\displaystyle \frac{1}{\theta }}\ln \left[1+{\displaystyle \frac{(e^{-\theta u}-1)(e^{-\theta v}-1)}{e^{-\theta }-1}}\right]$	R

):

2.4. MvCD Based on Pair-Copula Method

According to the Sklar theorem [58,59], the multivariate joint distribution function can be determined as follows:

$$C(y_1,y_2,\dots ,y_n)=F(F_1^{-1}(y_1),F_2^{-1}(y_2),\dots ,F_n^{-1}(y_n))$$

(9)

where $F_1,F_2,\dots ,F_n$ are the continuous marginal distribution function of an n group Checkedof random variables $x_1,x_2,\dots ,x_n$, and $F(x_1,x_2,\dots ,x_n)$ is the joint distribution function. $C(y_1,y_2,\dots ,y_n)$ is the suitable copula function for $F(x_1,x_2,\dots ,x_n)$. n is the number of known data series. The suitable copula function can be obtained using the test of goodness fit by the Akaike information criterion (AIC) and Bayesian information criterion (BIC). Model selection should vary according to the data distribution and be able to fit into the framework of statistical reasoning where K is the number of arguments, $f(y|{\theta }_k)$ is the maximum likelihood function, and n is sample quantity. The value of the maximum likelihood function represents the fitting degree of the model to the data, and the number of arguments represents the complexity of the model. Then, the smaller the AIC value shows, the better the fitting effect of the model, and AIC and BIC are indicators used to weigh model fitness and complexity and can be applied to a variety of statistical models, including clustering methods. AIC is one of the most widely used methods for choosing the most suitable approximating model from several competing models [60,61]. The AIC method is based on the Kullback–Leibler divergence, which provides an asymptotically unbiased estimator of the expected Kullback discrepancy between models. In contrast, the BIC method is based on the Bayes factor.

$$AIC=2K-2\ln (f(y|{\theta }_k))$$

(10)

$$BIC=K\log (n)-2\ln (f(y|{\theta }_k))$$

(11)

Then, the multivariate joint distribution function can be described by a high-dimensional copula function. A marginal distribution function can be combined orderly according to a fixed vine-structure. Each marginal distribution function will be combined with another marginal distribution function to form a pair-copula joint distribution function by appropriate copula functions, such as Gaussian copula, t-Copula, and Archimedean copula functions. The pair-copula method with vine construction, which is based on the layer-by-layer merge technique and bivariate copula distribution, was introduced. This method, which is called the vine-copula method, has the advantage that it considers the mutual dependences between two arbitrary random variables, which is a drawback for the common high dimensional distribution function. The vine-copula is an important representation of a high-dimensional copula function. The vine construction can be described as follows:

1.

The first layer pair-copula sequence was constructed by bivariate copula functions of one random variable with other random variables: $\{c_{12}(F_1(x_1),F_2(x_2)),\dots ,c_{1n}(F(x_1),F(x_n))\}$

2.

The second layer condition pair-copula sequence is constructed by distribution functions of (1) as new random variable sequences: $\{c_{2,3|1}(F(x_2|x_1),F(x_2|x_1)),\dots ,c_{2,n|1}(F(x_2|x_1),F(x_n|x_1))\}$

3.

Repeating step (2) until the last one bivariate copula reveals

$$c_{n-1,n|1,2,\dots ,n-2}(F(x_{n-1}|x_1,x_2,\dots ,x_{n-2}),F(x_n|x_1,x_2,\dots ,x_{n-2}))$$

(12)

Then, the joint density function of $x_1,x_2,\dots ,x_n$ can be described as

$$f(x_1,x_2,\dots ,x_n)={\displaystyle \prod _{t=1}^n{f}_t}{\displaystyle \prod _{j=1}^{n-1}{\displaystyle \prod _{i=1}^{n-2}{c}_{j,j+1|1,\dots ,j-1}(F(x_j|x_1,x_2,\dots ,x_{j-1}),F(x_{j+1}|x_1,x_2,\dots ,x_{j-1}))}}$$

(13)

where $f_t$ is probabilistic marginal distribution function of $x_j$.

According to the theorem above, the joint distribution function of MvCD can be determined:

$$C(g_1^t,g_2^t,\dots ,g_{n-1}^t,h_t)=F(F_1^{-1}(g_1^t),F_2^{-1}(g_2^t),\dots ,F_n^{-1}(g_{n-1}^t),F_n^{-1}(h_t))$$

(14)

where $g_1,g_2,\dots ,g_{n-1}$ denote the GCM data; and $h$ is historic data. $t$ is the whole downscaling period, which is divided into three horizons—training horizon, validation horizon, and forecasting horizon. Dates of the training horizon were used to establish the joint distribution function. Dates of the validation horizon were used to verify the validity of the downscaling result. Subsequently, dates of $g_1,g_2,\dots ,g_{n-1}$ in the validation horizon were used to generate the downscaling result.

2.5. Evaluation Criteria

In this study, the coefficient of determination (R²), Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE) were used to test the result. Three different evaluation criteria were used to indicate the mean accuracy of the model, reliability of the model, and dispersion degree of the simulation and forecast results. The range of R² was [0, 1]. If the value of R² is 0, it indicates that the imitative effect of the model is poor. If the value of R² is 1, it indicates that the model is error free. Generally, the model’s fitting effect, which reflects the mean accuracy of the model, is better as the value of R² increases.

(1)

NSE coefficient

The NSE is given as follows:

$$NSE=1-{\displaystyle \frac{{\displaystyle {\sum }_{t=1}^T{(Q_o^t-Q_m^t)}^2}}{{\displaystyle {\sum }_{t=1}^T{(Q_o-\overline{Q_o})}^2}}}$$

(15)

where $Q_o$ is the observed value, $Q_m$ is the value of simulation, and $\overline{Q_o}$ is the general average of $Q_o^t$. The range of NSE is (−∞, 1]. If the value of NSE is close to 1, it indicates that the model’s quality is good, and its reliability is high. If the value of NSE is close to 0, it indicates that the simulation result is close to the average level of the observation value, and the overall result is reliable but the process simulation error is large. If NSE is much less than 0, the model is not credible.

(2)

RMSE

The RMSE is denoted as

$$RMSE=\sqrt{{\displaystyle \frac{{\displaystyle {\sum }_{t=1}^T{(Q_o^t-Q_m^t)}^2}}{T}}}$$

(16)

where $Q_o$ is the observed value, and $Q_m$ is the value of simulation.

The range of RMSE is [0, +∞). If the value of RMSE is 0, it indicates that the predicted value is completely consistent with the observed values. The accuracy of the model increases as the RMSE reduces. The RMSE can show the influential error values because it is more sensitive to outlier data. The RMSE is large if there are several predicted values that are significantly different from the observed values. Therefore, the RMSE is also used to reflect the dispersion degree of simulation and forecast results.

In this study, the historical wind data were obtained from the China International Weather Station (Urumqi Station). The training horizon of MvCD was from 1951 to 2005 (duration of 55 years); the validation horizon of MvCD was from 2006 to 2015 (duration of 10 years) and the forecasting horizon of MvCD was from 2016 to 2030 (duration of 15 years). The confidence intervals were calculated to be 0.95.

2.6. Output Power Function

The relationship between the output power of the wind turbine $P_W$ and wind speed $v$ can be approximated by a piecewise function:

$$P_W=\left\{\begin{array}{c} 0, v\le v_{in} or v\le v_{out} \\ {\displaystyle \frac{v_3-v_{in}^3}{v_r^3-v_{in}^3}}{P}_{rate}, v_{in}\le v\le v_r \\ P_{rate}, v_r\le v\le v_{out} \end{array}\right.$$

(17)

where $P_{rate}$ is the output rating; $v_r$ is the rated wind speed; $v_{in}$ is the cut-in wind speed; and $v_{out}$ is the cut-out wind speed.

3. Case Study

The original data on wind speed were derived from wind farms located in Urumqi, China. Urumqi (43°00′–44°07′ N, 86°45′–87°56′ E) is the capital of the Xinjiang Uygur Autonomous Region with a population of 2.49 million (Figure 1). It covers an area of 14,216.3 km². Urumqi is located in the hinterland of the Eurasian continent, the middle section on the northward slope of the Tianshan Mountains, and the southern margin of the Junggar Basin. The climate of Urumqi is unique because of its unique geographical location and topography. In contrast, Urumqi has been one of the dominant renewable energy bases of China because of the development of renewable energy in the resource-rich region and other advantages. For example, the Dabancheng District of Urumqi is famous because it has a draught climate with an average wind speed of 6.1 m·s⁻¹. The largest wind farm in China is also in Dabancheng District. The wind farm owns 172 wind turbines and generates 182 million KW·h power annually. Wind power is the main power generated using renewable energy in Urumqi. Based on the historical wind data from the China International Weather Station (Urumqi Station), the monthly average values of wind speed over 65 years (1951–2015) were 4.20 m·s⁻¹, 4.24 m·s⁻¹, 6.21 m·s⁻¹, 8.92 m·s⁻¹, 9.08 m·s⁻¹¹, 8.52 m·s⁻¹, 8.37 m·s⁻¹, 8.38 m·s⁻¹, 7.88 m·s⁻¹, 6.51 m·s⁻¹, 5.17 m·s⁻¹, and 4.14 m·s⁻¹ from January to December, respectively (

Table 3. The monthly average values of wind speed from 1951 to 2015.

Month	Wind Speed (m/s)
January	4.20
February	4.24
March	6.21
April	8.92
May	9.08
June	8.52
July	8.37
August	8.38
September	7.88
October	6.51
November	5.17
December	4.14

). High winds usually occur from April to June. Slow winds usually occur from December to February. Slow winds are also one of the main reasons for severe haze in winter in Urumqi.

In this study, nine CMIP5 GCMs (GFDL-CM3, GFDL-ESM2M, GISS-E2-H, GISS-E2-R, HadGEM2-AO, MIROC5, MIROC-ESM, MIROC-ESM-CHEM, and MRI -CGCM3) were utilised to generate a joint distribution function and estimate future climate scenarios. The historical observational data and data of CMIP5 GCMs are monthly data. Over the 660 months (1976–2030) training horizon, training wind data are available to meet the demand of validation. The historical wind observational data were obtained from the China International Weather Station (Urumqi Station). Marginal distribution was used as the empirical function, which is based on the original data. A joint distribution function with pair-copula was established via vine construction. Figure 2 shows the joint distribution function with a canonical-vine structure, which can indicate the marginal distribution function merging order and structure of distribution functions.

Table 4. The differences in MvCD with respect to other existing approaches.

Approaches	Characteristic
MvCD	Simplicity of calculation; stochastic analysis; high dimensional problem-solving ability; nonlinear problem-solving ability; limited application scope
Artificial Neural Network, ANN	Strong distribution processing ability; distributed storage and learning ability; large parameter quantity requirement
Genetic Algorithm, GA	Simple analytical procedure; randomness; easy to combine with other algorithms; complex programming implementation; large parameter quantity requirement
Support Vector Machine, SVM	Generalization performance; high dimensional problem-solving ability; nonlinear problem solving ability; sensitive to missing data; no universal solution

shows the differences in the MvCD with respect to other existing approaches.

4. Result and Discussion

Figure 3 presents the 10-dimensional copula selection diagram of pair-copula joint probability distribution with the R-vine structure of wind speed using historical wind speed data and the nine GCMs under RCP2.6 in the training horizon. The AIC and BIC of the 10-dimensional copula distribution function were −3813.62 and −3602.49, respectively.

The downscaling results of the validation horizon were calculated using the trained 10-dimensional multivariate copula with the data obtained from the nine GCMs. Figure 4 shows the values of R², NSE, and RMSE in the validation period (0.820, 0.709, and 1.227, respectively), implying that the imitative effects of four multivariate copulas are satisfactory for validation. Figure 5 presents the historical wind speed and results of the validation horizon over 1996–2005. Figure 5 shows that the wind speed is influenced by the radiative forcing trajectories. High radiative forcing makes the wind speed more extreme than that observed using original data. For example, wind speeds of RCP2.6, RCP8.5, and historical data were 3.06 m s⁻¹, 4.12 m s⁻¹, and 5.83 m s⁻¹ in March 2006, respectively. The wind speeds of RCP2.6, RCP8.5, and historical data were 7.99 m s⁻¹, 11.0 m s⁻¹, and 7.78 m s⁻¹ in September 2010, respectively. The wind speeds of RCP2.6, RCP8.5, and historical data were 8.44 m s⁻¹, 10.8 m s⁻¹, and 7.50 m s⁻¹ in September 2015, respectively. These findings suggest that the high carbon emission scenario would lead to unstable wind speed with large variations. We also calculated downscaling results by ANN and SVM.

Table 5. Result comparison of MvCD with respect to other existing approaches.

Approaches	R2	NSE	RMSE
MvCD	0.82	0.709	1.227
ANN	0.85	0.34	3.234
SVM	0.771	0.826	4.17

shows the comparison of verification results. The simulation result of ANN is close to the average level of the observation value, and the overall result is reliable, but the process simulation error is large. The simulation result of SVM shows the imitative effect of the observation value is poor, but the process simulation error is small. RMSE of ANN and SVM shows some very different values in the simulation result of ANN and SVM. Therefore, MvCD is the most appropriate method for this study.

The downscaling results of the forecasting horizon were calculated using the trained 10-dimensional multivariate copula using data from the nine GCMs.

Table 6. Results of the forecasting horizon in 2016, 2020, and 2030.

		1	2	3	4	5	6	7	8	9	10	11	12
2016	RCP2.6	6.12	4.04	5.19	4.59	7.39	9.62	11.00	9.48	8.43	10.23	2.58	4.51
	RCP4.5	5.11	3.87	3.61	5.79	7.37	9.41	10.63	11.00	6.58	8.52	3.41	3.22
	RCP6.0	2.23	4.65	3.02	5.78	8.54	2.56	7.17	9.24	9.16	7.43	3.62	3.87
	RCP8.5	3.47	4.49	3.95	5.16	6.52	11.00	8.88	7.93	11.00	8.39	5.25	2.52
2020	RCP2.6	2.93	3.89	3.20	5.46	8.16	10.32	6.63	7.48	10.82	9.65	4.45	2.17
	RCP4.5	3.71	3.69	3.13	5.23	8.03	11.00	10.19	7.64	11.00	7.26	6.03	4.55
	RCP6.0	3.78	1.70	3.42	5.44	9.97	7.53	8.25	9.45	10.65	10.53	4.36	4.07
	RCP8.5	3.46	3.81	3.85	5.79	6.89	8.65	9.04	8.75	10.75	8.27	3.21	5.55
2030	RCP2.6	4.55	1.98	4.53	3.39	9.50	9.48	8.90	11.00	8.55	6.69	3.60	4.16
	RCP4.5	3.91	3.98	3.71	6.97	7.42	9.19	7.56	11.00	9.10	5.85	5.51	4.44
	RCP6.0	2.71	1.83	4.02	5.58	10.70	11.00	8.16	9.30	9.31	8.66	6.31	4.42
	RCP8.5	3.67	0.93	3.71	5.46	8.48	9.03	7.45	11.00	10.81	8.09	4.14	3.34

shows the results of the forecasting horizon in 2016, 2020, and 2030. Figure 6 presents the results of the forecasting horizon for 2016–2030. High radiative forcing will make wind speed more extreme in the forecasting horizon. High winds will occur from June to September, indicating that high-wind weather will be more frequent and sustainable in the future. The rich wind resources show that Urumqi has a high potential for wind power development. Low wind speeds will occur from December to March 2030; however, the average low wind speeds in the future will be lower than that of the historical average. These results indicate that the wind speed will be more extreme in each scenario. Sustained high winds in the future mean high-quality wind resources and will lead to the increased potential for wind power generation.

Our results also show that the wind speed will change with an increase in radiative forcing. The wind power will have great potential in Urumqi. Meanwhile, the instability of wind power can impact wind power in Urumqi. Figure 7 shows the output power of one wind turbine generator monthly, which is calculated based on the output power function and average values of wind speed in Figure 5. Figure 7 shows that the output power will be stable and a high output will be maintained from June to September. This shows that high-quality wind energy can be obtained in these four months. In contrast, four months will be low output power months (December to March), indicating that the wind power curtailing rate will rise from December to March.

The installed capacity of wind power in Urumqi until 2016 was 1.48 × 10⁶ kW. The wind power over 15 years was obtained based on the output power function and downscaling results of the forecasting horizon (2016–2030). Figure 8 shows the result of wind power generation over 15 years in each RCP scenario and historical observation data, respectively. For instance, wind power generation of RCP2.6–8.5 was 64.71 × 10⁹ kW h, 60.70 × 10⁹ kW h, 59.81 × 10⁹ kW h, and 58.05 × 10⁹ kW h, indicating that Urumqi has considerable potential for wind power. The CO₂ emission reduction potential of RCP2.6–8.5 was 54.23 × 10⁶, 50.87 × 10⁶, 50.12 × 10⁶, and 48.65 × 10⁶ tonnes. However, wind power will reduce with an increase in the radiative forcing. This indicates that the instability of wind based on an increase in radiative forcing will lead to wind power generation being curtailed and low wind power generation. For instance, wind power generation from RCP2.6 to 8.5 will reduce by 2.12%, 8.18%, 9.53%, and 12.19%, respectively.

5. Conclusions

In this study, an MvCD approach was developed to establish the probabilistic relationship between GCM results and real wind observations. The results of this study showed that RCP4.5 (representing an increase in radiative forcing levels by 4.5 W/m² by the year 2100) will be the most approximate scenario to the real regional circumstances. Each scenario, corresponding to different radiative forcing trajectories in the future based on the greenhouse effects, was examined.

The results indicated that high winds will occur from June to September, and low wind speeds will occur from December to March. High-quality wind energy can thus be obtained from June to September. In contrast, four months will have a low power output: the wind power curtailing rate will increase from December to March. Moreover, wind speed would be more variable with an increase in the radiative forcing. The results indicate that the highest wind speed will increase and the lowest wind speed will reduce. Wind instability will lead to other problems for the existing wind power system. Sustained high winds in the future will increase the potential of wind power generation. Wind instability caused by an increase in the radiative forcing will lead to wind power being curtailed and low wind power generation. In this method, multiple GCMs can be nested and fused simultaneously, and the common features of the GCM sequences can be preserved. The simplicity of calculation is also one of the advantages of this method. However, this study has a few limitations. The method also preserves simulation problems and architectural flaws common to all GCMs and brings them into the downscaling results. MvCD is a relatively new method, as the downscaling method has been applied to only a few hydraulic engineering studies. MvCD is developed for random-dependent climate factor analysis, which is suitable for downscaling a single climate factor and studying its randomness at the present stage. MvCD is particularly suitable because of the randomness of wind speed in this study. Collaborative stochastic downscaling of multiple climatic factors will be the next focus in the MvCD research direction. The applied copula method has many extensible spaces. Moreover, several other factors can impact the regional wind speed. The integration of multiple factors into the copula method will be an interesting topic in future research. Therefore, further studies are desired to mitigate these limitations.