Future projections of wind and solar energy resources over China from regional climate models based on bias correction

In this study, WRF (V3.6.1; Skamarock et al 2008) and RegCM4 (Giorgi et al 2012) are utilized to conduct historical simulations and future projections under the CORDEX-EA-II framework. Developed by the U.S. National Center for Atmospheric Research (NCAR), WRF is a non-hydrostatic model using a terrain-following vertical coordinate and an Arakawa-C grid. The RegCM4 model is developed by International Centre for Theoretical Physics (ICTP), and adopts a terrain-following σ-pressure vertical coordinate system and an Arakawa-B grid finite differencing algorithm. The outputs of four global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 5 (CMIP5; Taylor et al 2012), that is, CNRM-CM5 (Voldoire et al 2013), GFDL-ESM2M (Dunne et al 2012), EC-EARTH (Hazeleger et al 2010) and MPI-ESM-LR (Jungclaus et al 2010), are applied as the initial and boundary conditions for the downscaling simulations with WRF and RegCM4.

The detailed physical schemes used in the RCM simulations, including land surface, radiation, convection, microphysics and planetary boundary layer (PBL) schemes, are shown in table 1. The historical experiments are conducted during the period of 1981–2005, and the future projections are carried out during 2031–2060 under the RCP 8.5 scenario. All the RCM simulations provide the variables of 10-m wind speed, surface down-welling shortwave radiation and air temperature over China, with a spatial resolution at 0.22°. The simulated 10-m wind speed has been extrapolated to the wind-turbine hub height of 100 m.

The fifth generation of atmospheric reanalysis (ERA5) released by European Centre for Medium-Range Weather Forecasts (ECMWF) is used to calibrate the simulated data and validate the skill of the bias correction method. The spatial and temporal resolution of the ERA5 reanalysis is 0.25° and 3-hourly, respectively. The 100-m wind speed and surface down-welling shortwave radiation data from the ERA5 reanalysis has been proved reliable in the previous studies (Liu et al 2021, He et al 2021). Several studies pointed out that reanalysis datasets exhibit deviation in wind speed and shortwave radiation (Kennedy et al 2011; Fan et al 2021), while ERA5 can reduces the biases compared with other reanalysis (Fan et al 2021; He et al 2021). The station observations sometimes can be inhomogeneous and inaccurate because of anthropic factor and instrument failure, while ERA5 can supply dynamically gridded data, particularly for areas without observations. Thus, ERA5 is selected as reference dataset. The data from ERA5 reanalysis during 1981–1995 and 1996–2005 is utilized to correct the raw simulated data and to verify the bias correction method, respectively. The raw simulated data is interpolated to 0.25° × 0.25° grids for easy calibration and validation, by using simple inverse distance squared weighting.

The bias correction method of quantile mapping based on probability distribution function is applied in this study, assuming that the observational and simulated probability distributions are consistent with each other for a given month during the calibration period. Weibull distribution and normal distribution are adopted for the distribution approximation of 100-m wind speed and surface down-welling shortwave radiation, respectively. The bias correction method is implemented for daily data at each grid point individually:

$$\begin{eqnarray*}&&{X}_{contr}^{* }={F}_{obs}^{-1}[{F}_{contr}({X}_{contr})],\end{eqnarray*}$$

$$\begin{eqnarray*}&&{X}_{evalu}^{* }={F}_{obs}^{-1}[{F}_{contr}({X}_{evalu})],\end{eqnarray*}$$

$$\begin{eqnarray*}&&{X}_{future}^{* }={F}_{obs}^{-1}[{F}_{contr}({X}_{future})],\end{eqnarray*}$$

where ${X}_{contr}^{* },$ ${X}_{evalu}^{* }$ and ${X}_{future}^{* }$ represent the bias-corrected data during the calibration period (1981–1995), validation period (1996–2005) and future period (2031–2060), respectively, and ${X}_{contr},$ ${X}_{evalu}$ and ${X}_{future}$ are the raw simulated data. ${F}_{contr}$ and ${F}_{obs}^{-1}$ are calculated during the calibration period, and indicate the cumulative distribution function of raw simulated data and the inverse cumulative distribution function of observation data, respectively. For 100-m wind speed, Weibull distribution is adopted as the cumulative distribution function:

$$\begin{eqnarray*}&&{\rm{F}}\left({\rm{w}}\right)=1-{{\rm{e}}}^{-{\left(\displaystyle \frac{w}{c}\right)}^{k}},\end{eqnarray*}$$

where k and c are shape parameter and scale parameter, respectively, and w represents wind speed. For shortwave radiation, the cumulative distribution function is expressed as normal distribution:

$$\begin{eqnarray*}&&{\rm{F}}({\rm{x}})=\displaystyle \frac{1}{\sqrt{2\pi }\sigma }\displaystyle {\int }_{-\infty }^{x}{e}^{-\displaystyle \frac{{(x-\mu )}^{2}}{2{\sigma }^{2}}}{\rm{dx}},\end{eqnarray*}$$

where $\mu$ and $\sigma$ are mathematical expectation and standard deviation, respectively. The parameters, k and c in Weibull distribution and $\mu$ and $\sigma$ in normal distribution, are calculated for each grid in a given month to correct the seasonal biases.

Wind power density (WPD) and capacity factor (CF) are employed to quantitatively measure the wind energy resource. Both of them are calculated based on the wind speed at 100 m, which can be extrapolated from 10-m wind speed according to an empirical power law (Gao et al 2019):

$$\begin{eqnarray*}&&W=w{\left(\displaystyle \frac{100\,m}{10\,m}\right)}^{{\rm{\alpha }}},\end{eqnarray*}$$

where w and W represent the wind speed at 10 m and 100 m, respectively, and $\alpha$ is the wind shear exponent, which is equal to $\displaystyle \frac{1}{7}.$

Wind power density is defined as (Pryor & Barthelmie 2010)

$$\begin{eqnarray*}&&{\rm{WPD}}=\displaystyle \frac{1}{2}\rho {W}^{3},\end{eqnarray*}$$

where $\rho$ is the air density at 100 m and equal to 1.213 kg m⁻³.

As in Li et al (2020), the capacity factor of wind energy resource is expressed as the ratio of output power to rated power:

$$\begin{eqnarray*}&&\begin{array}{c}\overline{P\left(W\right)}\,=\\ \left\{\begin{array}{c}0\,kw,\,W\in \left.\left[0,3\right.\right)\,m/s\,\left(below\,cut-in\right)\\ -0.24151\ast {W}^{5}+6.9287\ast {W}^{4}-74.2354\ast {W}^{3}+412.0241\ast {W}^{2}-1049.58726\ast W+956.1936,\\ W\,\in [3,11]m/s\,\left(ramp-up\right)\\ 3000\,kw,\,W\,\in \left(\left.11,25\right]\right.m/s\left(rated\,power\right)\\ 0\,kw,\,W\,\in \left(25,+\infty \right)m/s\left(above\,cut-out\right)\end{array}\,\right.\end{array}\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\rm{CF}}=\overline{P\left(W\right)}/{P}_{rated},\end{eqnarray*}$$

where $\overline{P\left(W\right)}$ is output power, and ${P}_{rated}$ is rated power, which is taken as 3000 kw.

The capacity factor of solar energy resource is calculated as follows (Bett and Thornton 2016).

$$\begin{eqnarray*}&&{T}_{mod}=T+({T}_{NOCT}-{T}_{0})\displaystyle \frac{G}{{G}_{0}},\end{eqnarray*}$$

where ${G}_{0}$ = 800 W m⁻², ${T}_{NOCT}$ = 48 °C and ${T}_{0}$ = 20 °C. ${G}_{0}$ and ${T}_{0}$ are reference values for surface down-welling shortwave radiation and ambient temperature. ${T}_{mod}$ and T represent module temperature and ambient air temperature, respectively, and G is surface down-welling shortwave radiation.

$$\begin{eqnarray*}&&{\rm{\Delta }}{T}_{mod}={T}_{{mod}}-{T}_{STC},\,G^{\prime} =\displaystyle \frac{G}{{G}_{STC}},\end{eqnarray*}$$

$$\begin{eqnarray*}&&{\eta }_{rel}(G,\,T)=\left[1+\alpha {\rm{\Delta }}{T}_{mod}\right]\,\ast \,\left[1+{c}_{1}\,\mathrm{ln}\,{G}^{\text{'}}+{c}_{2}{\mathrm{ln}}^{2}{G}^{\text{'}}+\beta {\rm{\Delta }}{T}_{mod}\right],\end{eqnarray*}$$

where $\alpha$ = 4.2 × 10⁻³ K⁻¹, $\beta$ = −4.6 × 10⁻³ K⁻¹, ${c}_{1}$ = 0.033 and ${c}_{2}$ = −0.0092. ${T}_{STC}$ and ${G}_{STC}$ are air temperature and shortwave radiation under standard test conditions, and equal to 25 °C and 1000 W m⁻², respectively. ${\eta }_{rel}$ is relative efficiency.

Then, the capacity factor of solar energy resource is

$$\begin{eqnarray*}&&{\rm{CF}}={\eta }_{rel}(G,T)\displaystyle \frac{G}{{G}_{STC}}\end{eqnarray*}$$

The variability at different temporal scales can reflect the variation amplitude and change rate of renewable resources (Gao et al 2019). In this study, the robust coefficient of variation (RCoV) is used to measure the variability of wind and solar energy resources. It is defined as

$$\begin{eqnarray*}&&RCoV=\displaystyle \frac{Median(\left|{X}_{i}-median\left({X}_{i}\right)\right|)}{median({X}_{i})},\end{eqnarray*}$$

where ${X}_{i}$ represents wind power density or surface down-welling shortwave radiation. The annual mean, monthly mean and daily mean time series are utilized to calculate the interannual, intra-annual and interdiurnal variability, respectively (Li et al 2020).

Figure 1 shows the bias of annual mean 100-m wind speed in the RCM simulations during the validation period before and after using the bias correction method. Without bias correction, the WRF and RegCM4 simulations driven by four GCMs all generate evident overestimation of wind speed, with little discrepancy among different driven fields. The WRF simulations exhibit great overestimation over southeastern China and northern China, with the bias around 2 m s⁻¹ and 1 m s⁻¹ respectively (figures 1(a)–(d)). The four RegCM4 simulations generate less bias (almost below 2 m s⁻¹) than WRF over southeastern China (figures 1(e)–(h)). By applying bias correction, all the RCM simulations show remarkable improvement in capturing the annual mean wind speed over whole China, with the negligible bias within ±0.5 m s⁻¹.

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The bias of surface down-welling shortwave radiation in the raw and bias-corrected simulations is illustrated in figure S1. Without bias correction, the four WRF simulations consistently overestimate the shortwave radiation, with the bias up to 80 W m⁻² over southeastern China and within 20–60 W m⁻² in other regions (figures S1(a)–(d)). The raw RegCM4 simulations underestimate the shortwave radiation over northern China, with the negative bias ranging from −80 W m⁻² to −20 W m⁻². Overestimation below 60 W m⁻² is located over southeastern China (figures S1(e)–(h)). Generally, the bias-corrected shortwave radiation demonstrates slight bias within ±20 W m⁻² over whole China, and positive bias is mainly located in the western areas and negative bias in the eastern areas (figures S1(i)–(p)).

To comprehensively evaluate the RCMs' skill in capturing the wind speed features, various statistical approaches are adopted, including annual cycle, quantile-quantile plot (Q-Q), probability distribution function (PDF), cumulative distribution function (CDF) and Taylor diagram (figure 2). The raw RCM simulations demonstrate remarkable deficiency in simulating the annual cycle of domain-averaged wind speed, with greater bias in winter than in summer. Specifically, the bias in RegCM4 is about 1.5 m s⁻¹ in summer, while reaches up to 3.5 m s⁻¹ in winter. In addition, almost all RCM simulations prepone the wind speed peak for one month, which occurs in April in the observation (figure 2(a)). The Taylor diagram is further applied to depict the consistency of monthly mean wind speed between the RCMs and observation. The raw RCM simulations can well capture the characteristics of intra-annual variation, with the temporal correlation coefficients (TCCs) above 0.55. However, both WRF and RegCM4 tend to enlarge the variation amplitude, with the ratios of standard deviation around 1.5 and 2.5, respectively (figure 2(e)). The Q-Q plot indicates overestimation at all quantiles in the raw simulated data. Comparing the two RCMs, it is found that the RegCM4 simulations generate smaller bias than WRF for lower quantiles and greater bias for higher quantiles (figure 2(b)). The raw RCM simulations tend to shift the spectrums of both PDF and CDF rightward. For CDF, the deviation of the raw simulations from the observation gets smaller for higher wind speed. It means that the raw simulations underestimate the frequency of lower wind speed and overestimate that of higher wind speed (figures 2(c)–(d)). After bias correction, the simulated data can properly portray the annual cycle, intra-annual variability, quantile distribution, PDF and CDF of wind speed, with the bias-corrected result almostly overlapping with the observation.

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Figure S2 shows the statistical results for surface down-welling shortwave radiation. The ERA5 reanalysis exhibits a unimodal pattern of annual cycle, with the peak around 260 W m⁻² in May. The raw WRF and RegCM4 simulations overestimate and underestimate the domain-averaged shortwave radiation respectively, especially in late spring and summer. Specifically, the positive bias in WRF can reach up to 80 W m⁻² in June and negative bias in RegCM4 are around −50 W m⁻² in May. What's more, WRF and RegCM4 postpone the radiation peak for one and two months, respectively (figure S2(a)). The Taylor diagram shows that the raw WRF and RegCM4 simulations can successfully produce the intra-annual variation characteristics, with the TCCs above 0.9. However, WRF and RegCM4 enlarge and lessen the intra-annual variability respectively (figure S2(e)). As shown in figure S2(b), all the quantiles of daily shortwave radiation are overestimated in the raw WRF simulations and underestimated in RegCM4 (figure S2(b)). The PDF in the ERA5 reanalysis demonstrates a bimodal pattern with the major frequency peak at around 180 W m⁻² and a secondary peak at around 240 W m⁻². The raw WRF simulations can generally capture the bimodal pattern, but shift the spectrum rightward. The RegCM4 simulations falsely produce a unimodal pattern of radiation PDF, and shift the spectrum leftward. As a result, the CDF spectrum is also rightward and leftward shifted in the WRF and RegCM4 simulations respectively (figures S2(c), (d)). As expected, the deviation between RCMs and ERA5 can be greatly corrected after using the bias correction method, and the bias-corrected data exhibits great consistency with the ERA5 reanalysis from the aspects of annual cycle, intra-annual variability, quantile distribution, PDF and CDF.

The bias correction method has been proved to be effective in correcting individual RCM simulations. Furthermore, the applicability of the bias correction method for the multi-model ensemble mean is investigated by using several metrics, including mean absolute error (MAE), root-mean-square error (RMSE) and TCC. Figure 3 displays the spatial distributions of MAE, RMSE and TCC of monthly mean 100-m wind speed and surface down-welling shortwave radiation in both raw and bias-corrected ensemble mean. The MAE and RMSE of raw simulated wind speed are around 2 m s⁻¹ over most parts of China (figures 3(a), (b)), while the bias correction brings obvious improvement to the monthly mean wind, with the MAE and RMSE below 0.5 m s⁻¹ (figures 3(d), (e)). The TCCs of wind speed are below 0.3 over southeastern China and some northwestern areas in the raw simulation, which increase to around 0.5 in the bias-corrected result (figures 3(c), (f)). In terms of surface down-welling shortwave radiation, the raw simulation exhibits distinct bias over southeastern China, with the MAE and RMSE up to 70 W m⁻² (figures 3(g), (h)). By comparison, the MAE and RMSE in bias-corrected ensemble are just within 20 W m⁻² (figures 3(j), (k)). Both the raw and bias-corrected simulations successfully produce the intra-annual variation of monthly mean radiation, with the TCC above 0.8 over most parts of China, and the bias-corrected result improves the TCC over the southern coastal regions (figures 3(i), (l)).

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A clear understanding of future change is vital for exploiting renewable energy. For its satisfactory performance, the bias-corrected ensemble mean is adopted to provide projections of wind and solar energy resources during 2031–2060 under the RCP 8.5 emission scenario. Figure S3 illustrates the relative changes in the seasonal mean 100-m wind speed and surface down-welling shortwave radiation between 2031–2060 and 1981–2005 from the bias-corrected data. The wind speed is projected to decrease in four seasons in the ensemble mean and seven out of the eight individual RCM simulations. The multi-model ensemble projects a relative change of about −2% in spring and around −1% in other seasons. Generally, the RegCM4 simulation downscaled from GFDL-ESM2M shows obvious inconsistence with the other simulations, with a relative decrease of −5% in spring and a increase of 1.5% in autumn (figure S3(a)). The shortwave radiation in the four seasons also tends to decrease in the multi-model ensemble mean and at least six individual simulations, with the relative changes ranging from −2% in autumn to −0.5% in spring in ensemble mean. The RegCM4 simulation driven by GFDL-ESM2M also shows disagreement with the other simulations, with a intensive decrease of −6% in autumn and a increase of 2% in spring and winter (figure S3(b)).

Future projections of annual and seasonal mean wind power density and surface down-welling shortwave radiation from the bias-corrected ensemble mean are shown in figure S4. In the future, the wind energy resource is abundant over northwestern and northeastern China, with the annual mean WPD around 100 W m⁻²(figure S4(a)). Over southeastern China, the annual and seasonal mean WPD is just around 30 W m⁻². Moreover, more plentiful wind energy is found in winter than in summer (figures S4(b), (c)). The WPD is projected to decrease over most areas of China, with the relative changes around −6% over the western regions, while the summer and winter WPD will slightly increase (within 4%) over Southeast China (figures S4(d)–(f)).

The surface down-welling shortwave radiation demonstrates an increasing gradient from southeast to northwest, with the strongest radiation over the Tibetan Plateau (figures S4(g)–(i)). Unlike wind energy, the future solar energy resource is much richer in summer than in winter. For example, the shortwave radiation over Southeast China can be above 180 W m⁻² in summer while only around 100 W m⁻² in winter (figures S4(h), (i)). The annual mean shortwave radiation is generally projected to decrease, with the relative changes ranging from −2% to 0% (figure S4(j)). Over southeastern China, the shortwave radiation is projected to decrease (around 4%) and increase (within 2%) in winter and summer, respectively (figures S4(k), (l)).

The variability of energy at multiple temporal scales plays an important role for the implement of power plants. Thus, the RCoV is used to quantify the interannual, intra-annual and interdiurnal variability of WPD and surface down-welling shortwave radiation (figure 4). The future WPD exhibits more pronounced interdiurnal variability than interannual and intra-annual variability (figures 4(a)–(c)). The interannual RCoV is generally less than 0.05, with large value over the Tibetan Plateau, Inner Mongolia and Guangdong (figure 4(a)). The intra-annual and interdiurnal RCoV demonstrates large value over Northwest China, which can reach up to 0.5 (figures 4(b), (c)). The interannual variability of WPD tends to increase by about 50% over northern China, while decrease by around 40% over Southeast China (figure 4(d)). The intra-annual and interdiurnal variability generally features an irregular pattern of decrease and increase respectively, with the relative changes mostly within ±10% (figures 4(e), (f)).

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The surface down-welling shortwave radiation in the future shows larger interannual variability over southeastern China than northern China, with the RCoV around 0.04 and 0.02, respectively (figure 4(g)). The RCoV of intra-annual and interdiurnal variability demonstrates large value above 0.6 over some areas of China (figures 4(h), (i)). The interannual variability of shortwave radiation shows increase of around 40% over northern China and southeastern coastal areas, while decrease of around 30% over Northwest China and interior Southeast (figure 4(j)). The intra-annual and interdiurnal variability tends to increase over most areas of China, with the relative changes over Southeast China up to 8% and 6%, respectively (figures 4(k), (l)).

The above analysis reveals that the variability of both wind power density and shortwave radiation is more pronounced at short-term scales, while the long-term variability would experience more dramatic change in the future. This conclusion coincides with the characteristics of wind speed and WPD variability in Li et al (2020).

Figure 5 shows the future projections of CF for wind and solar energy resources to quantitatively assess the capacity of the resources. The projected annual and seasonal mean CF of wind energy resource demonstrates similar pattern with that of WPD (figures 5(a)–(c)). Abundant wind resource is located over Northeast and Northwest China, and the CF is higher in winter than summer, with the winter CF above 0.3 in some areas of Northeast China (figure 5(c)). Generally, the CF of wind energy resource is projected to decrease (around −5%) over most areas of China, except for southeastern China (figures 5(d)–(f)). The CF of solar energy resource exhibits similar spatio-temporal features to that of surface down-welling shortwave radiation, with high value over Northwest China (figures 5(g)–(i)). In addition, it indicates higher CF in summer than in winter (figure 5(h)). Overall, the annual and seasonal mean CF of solar energy resource will experience reduction over most areas of China, with the greatest negative change up to −5% over southeastern China in winter (figures 5(j)–(l)).

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Gobiet et al (2015) argued that the bias correction can bring improvement in predictions of climate change. To exhibit the role of bias correction, figure S5 shows future projections and relative changes of RCoV from the raw ensemble mean. Predicted results of RCoV are comparable before and after bias correction, while the RCoV of solar energy in Sichuan Basin from bias-corrected data is larger than raw data (figure 4; figure S5). Before and after bias correction, spatial patterns and relative changes of future resources are generally similar to each other (figure 5; figure S6). However, projections of renewable resources from raw data are richer than the bias-corrected data, especially for wind energy resource, and bias correction tends to intensify the change signals.