Constrained future brightening of solar radiation and its implication for China's solar power

Abstract

As Earth's primary energy source, surface downward solar radiation (R_s) determines the solar power potential and usage for climate change mitigation. Future projections of R_s based on climate models have large uncertainties that interfere with the efficient deployment of solar energy to achieve China's carbon-neutrality goal. Here we assess 24 models in the latest Coupled Model Intercomparison Project Phase 6 with historical observations in China and find systematic biases in simulating historical R_s values likely due to model biases in cloud cover and clear-sky radiation, resulting in largely uncertain projections for future changes in R_s. Based on emergent constraints, we obtain credible R_s with narrowed uncertainties by ∼56% in the mid-twenty-first century and show that the mean R_s change during 2050–2069 relative to 1995–2014 is 30% more brightening than the raw projections. Particularly in North China and Southeast China with higher power demand, the constrained projections present more significant brightening, highlighting the importance of considering the spatial changes in future R_s when locating new solar energy infrastructures.

We narrowed the uncertainties in the projection of surface downward solar radiation by ∼56% based on emergent constraints. We found that the constrained predictions present significant brightening in North and Southeast China with high power demand.

INTRODUCTION

To keep global warming to <2°C by the end of this century, renewable energy resources, such as solar energy generated by solar photovoltaic (PV) systems, have become increasingly important in the total primary energy supply [1–3]. Surface downward solar radiation (R_s, with a wavelength of 0.2–4.0 μm) is the most critical indicator to know about the PV potential. To meet the carbon-neutrality goal, China has invested heavily in PV systems in the last decade. By the end of 2021, the installed capacity of the PV systems nationwide reached 306 GW, ranking first in the world for six consecutive years since 2015. Moreover, China plans 3550 GW of installed PV capacity by 2060, accounting for 45% of the total power generation in China [4]. Thus, robust estimates of future trends and uncertainties in solar radiation are crucial for realizing this promise of energy structure optimization.

Historical ground observations reveal that R_s declined from the 1950s to the 1980s and increased thereafter, known as global dimming and brightening [5]. In China, observational data show significant decadal variations in R_s in China with a dimming during the 1960s to 1990s and flattening thereafter (Supplementary Fig. S1a) [5–9]. Prior studies showed that the models that participated in the Coupled Model Intercomparison Project Phase 6 (CMIP6) overestimate the global mean R_s and underestimate R_s trend in China [10,11], but the underlying drivers of the R_s bias in CMIP6 models remain to be explored further. The CMIP6 experiments offer a unique opportunity for R_s assessment and projections under various emission scenarios that reflect policy impacts and socio-economic risks [12,13]. However, uncertainties in climate projections can arise from internal climate variability, model uncertainty and scenario uncertainty [14–17]. The parametric and structural model uncertainty associated with the model's response to specified forcing agents explains a major part of uncertainty in mid- to long-term climate projection [18]. To improve the reliability of climate projection, emergent constraints (EC) provide a novel approach with a solid physical basis for narrowing the uncertainties of future climate projections through the combination of an ensemble of climate simulations with contemporary measurements [19,20]. While EC have served to narrow down the uncertainty in equilibrium climate sensitivity, atmospheric circulation pattern and air temperature projection, among others [19–26], how to constrain the R_s projection remains to be explored through looking for a robust constraint relationship of R_s.

In this paper, we assess the performance of R_s simulations from 24 CMIP6 climate models and explore whether their R_s biases over China are triggered by model biases in simulating total cloud cover and aerosol radiative effects. Then, we use historical biases of models to constrain the future projections of R_s under three possible future scenarios with different shared socio-economic pathways (SSPs) (SSP1-2.6, SSP2-4.5 and SSP5-8.5) based on EC. Details of our analytical approach are in the ‘Methods’ section. Our results can provide the best estimate and confidence interval of the R_s projection over China in the mid-twenty-first century and have important implications for the investment and construction of PV systems in China.

RESULTS

Model bias in simulating historical R_s

The multi-model mean (MMM) R_s of the CMIP6 historical all-forcing simulations presents a similar spatial pattern with the observations and the spatial correlation coefficient between the simulations and the observations over 2° × 2° grids is 0.93 (P < 0.05; Fig. 1a and b). Peaks of R_s mainly concentrate over the Tibetan Plateau with ∼250 W·m⁻² (Fig. 1a), due to low air mass, short cloud liquid water pathways and low anthropogenic aerosol concentrations. Lower values of R_s mainly distribute in the east of China with the lowest value of ∼150 W·m⁻² (Fig. 1a). The substantial reflection of clouds and the scattering and absorption of anthropogenic aerosols are responsible for low R_s over these regions [27,28].

Figure 1.

Maps of the climatology and model bias in climate simulations. (a) Spatial patterns of the climatology in surface downward solar radiation (R_s, in W·m⁻²) from the ground-based observations (OBS, circle) and the multi-model mean (MMM, shading) of the CMIP6 historical all-forcing simulations averaged from 1961 to 2014 over 2° × 2° grids. (b) Grid-versus-grid comparison of the CMIP6 MMM with R_s observations in China. Orange dots and gray error bars show multi-year means and standard deviations of R_s for each grid, respectively. Correlation coefficient (r), mean bias (MB) and root-mean-square error (RMSE) are shown in the right-bottom. (c)–(e) Spatial patterns of multi-year mean biases in (c) R_s, (d) total cloud cover fraction (TCC, in %) and (e) clear-sky surface downward solar radiation (R_s-clear, in W·m⁻²) of the CMIP6 MMM against the ground-based observations averaged from 1961 to 2014. Black dots indicate that at least two-thirds of models agree on the sign of the mean bias in the CMIP6 MMM over those grids.

However, the CMIP6 MMM R_s in the historical simulations is apparently overestimated at most grids (Fig. 1b), particularly in Northwest China and Southwest China (Fig. 1c). Compared with the observations, the CMIP6 MMM overestimates R_s by 11.39 ± 7.20 W·m⁻² (mean ± 1 standard deviation) averaged in China from 1961 to 2014 (Fig. 1c and Table 1). The performance among CMIP6 models differs greatly, with the inter-model range of the R_s biases averaged in China over 30 W·m⁻² (Table 1), which is larger than those averaged over the globe [11]. Most models exhibit a consistent pattern of overestimation with a spatial correlation of ∼0.7 against the CMIP6 MMM, and only 2 out of 24 models present negative biases in R_s (Table 1).

Table 1.

Overview of the CMIP6 models used in this study, their horizontal grids, multi-year mean biases (MB) of surface downward solar radiation (R_s, in W·m⁻²), total cloud cover fraction (TCC, in %) and clear-sky surface downward solar radiation (R_s-clear, in W·m⁻²) referenced to station observations averaged over China from 1961 to 2014, spatial correlation coefficient (r) of the biases between individual model simulation and the multi-model mean (MMM) of the CMIP6 historical all-forcing simulations over the grids with observations. The rightmost column is the model weight (w_i, in %) estimated for the weighted emergent constraint method (weight-EC).

		MB (r)
CMIP6 models	Model grids	R s	TCC	R s-clear	wi
ACCESS-CM2	192 × 144	7.27 (0.81)	12.53 (0.93)	17.33 (0.81)	0.00
ACCESS-ESM1-5	192 × 145	4.09 (0.47)	11.39 (0.71)	20.24 (0.89)	19.93
AWI-CM-1–1-MR	384 × 192	14.31 (0.72)	–4.80 (0.88)	14.58 (0.86)	0.00
BCC-CSM2-MR	320 × 160	8.27 (0.72)	–7.32 (0.87)	17.68 (0.86)	0.00
CAS-ESM2-0	256 × 128	–1.18 (0.51)	–1.21 (0.64)	14.32 (0.86)	35.56
CESM2-WACCM	288 × 192	13.78 (0.70)	2.95 (0.92)	16.93 (0.70)	0.05
CMCC-ESM2	288 × 192	10.19 (0.72)	–0.06 (0.91)	22.24 (0.89)	0.07
CanESM5	128 × 64	13.45 (0.40)	–10.27 (0.70)	3.72 (0.48)	0.04
EC-Earth3-Veg-LR	320 × 160	10.49 (0.65)	2.62 (0.96)	12.42(0.84)	0.01
EC-Earth3-Veg	512 × 256	13.10 (0.58)	1.50 (0.93)	12.00 (0.88)	0.01
EC-Earth3	512 × 256	13.43 (0.58)	2.15 (0.93)	12.83 (0.76)	0.02
FGOALS-g3	180 × 80	27.72 (0.78)	–7.84 (0.76)	21.80 (0.87)	0.00
GFDL-ESM4	288 × 180	5.11 (0.83)	5.43 (0.95)	14.47 (0.88)	14.21
IITM-ESM	192 × 94	4.48 (0.53)	8.96 (0.82)	21.55 (0.88)	1.47
IPSL-CM6A-LR	144 × 143	22.50 (0.54)	–11.21 (0.89)	14.64 (0.43)	0.00
KIOST-ESM	192 × 96	–2.80 (0.74)	9.26 (0.91)	21.08 (0.88)	27.36
MIROC6	256 × 128	13.17 (0.88)	–10.50 (0.83)	28.03 (0.83)	0.00
MPI-ESM1-2-HR	384 × 192	14.81 (0.72)	–4.33 (0.88)	14.99 (0.87)	0.00
MPI-ESM1-2-LR	192 × 96	7.29 (0.71)	–0.18 (0.84)	14.83 (0.85)	0.83
MRI-ESM2-0	320 × 160	22.61 (0.53)	–7.33 (0.88)	13.05 (0.85)	0.00
NESM3	192 × 96	10.32 (0.64)	–1.44 (0.67)	3.07 (0.69)	0.11
NorESM2-LM	144 × 96	14.41 (0.77)	–6.46 (0.80)	18.56 (0.80)	0.00
NorESM2-MM	288 × 192	18.70 (0.74)	–2.73 (0.86)	19.14 (0.73)	0.00
TaiESM1	288 × 192	7.90 (0.78)	4.48 (0.96)	19.66 (0.92)	0.33
MMM	90 × 180	11.39	–0.60	16.21	–

Drivers of model bias in historical R_s

Clouds and aerosols have been widely regarded as the main controlling factors for changes in R_s [29,30]. The former can regulate R_s by reflecting solar radiation [31] and the latter also play a critical role in R_s changes due to their scattering and absorption of insolation, especially in regions with severe air pollution [32]. Although models have made significant progress in key physical processes of climate change, the biases in simulating these key processes may still be the major contributors to the biases of R_s. The overall pattern of the total cloud cover fraction (TCC) can be simulated with a spatial correlation of 0.81 (P < 0.05) against the observed TCC in China (Supplementary Fig. S2a and b) but with evident spatial heterogeneities. For instance, models underestimate TCC in North China and Southeast China but overestimate in Northeast China, Northwest China and the Tibetan Plateau (Fig. 1d). The spatial pattern of the TCC bias is rather robust among the 24 models and the average value of the spatial correlation with the CMIP6 MMM is ∼0.85 (Table 1). The spatial pattern of the TCC bias in the CMIP6 MMM matches well with that of the R_s bias (Fig. 1c and d), with a spatial correlation of –0.51 (P < 0.05).

The historical simulations of clear-sky surface downward solar radiation (R_s-clear) are also evaluated to identify the impact of aerosols on the simulated R_s. First, the CMIP6 MMM R_s-clear exhibits a similar pattern as observations with a spatial correlation of 0.94 (P < 0.05; Supplementary Fig. S2c and d) but it is positively biased in China, especially in Northeast China and the Tibetan Plateau (Fig. 1e). This pattern of the R_s-clear bias is robust and consistent among the 24 models with a spatial correlation of ∼0.80 on average against the CMIP6 MMM (Table 1). Second, the simulated R_s-clear shows an excessive decline from 1961 to 2014, while both ground-based observations and satellite measurements show an increase after 2008 (Supplementary Fig. S1c). This is probably because the CMIP6 models significantly overload the decadal changes in anthropogenic aerosols in China [33].

Figure 2 shows the sensitivities of model bias in R_s to TCC and R_s-clear biases, where the R_s bias has a larger partial correlation coefficient for the TCC bias in the south and the R_s-clear bias in the north. Overall, the bias of R_s in the CMIP6 MMM at the spatio-temporal scale can be explained by the combined effects of the simulated biases in TCC and R_s-clear. In North China and Southeast China, the underestimation of TCC with high sensitivity to R_s and the overestimation of R_s-clear with low sensitivity to R_s jointly result in the positive bias of R_s (Figs 1c–e and 2). In Northeast China, Northwest China and the Tibetan Plateau, the positive bias of R_s is dominated by the overestimated R_s-clear that is highly sensitive to R_s, completely offsetting the overestimated TCC that is slightly sensitive to R_s (Figs 1c–e and 2).

Figure 2.

Sensitivities of model bias in surface downward solar radiation. (a) and (b) Spatial patterns of the partial coefficients (ρ) of the annual multi-model mean biases of the CMIP6 historical all-forcing simulations in surface downward solar radiation (ΔR_s) against those in (a) total cloud cover fraction (ΔTCC) and (b) clear-sky surface downward solar radiation (ΔR_s-clear) during 1961–2014. Black dots indicate a significance level of 0.05.

The inter-model relationships of the R_s bias against the TCC and R_s-clear biases can also offer additional insights into the possible causes of the R_s bias (Fig. 3). The R_s bias clearly demonstrates a strong inter-model correlation with the TCC bias (r = –0.67, P < 0.01), with a larger underestimation of TCC simulation responding to a larger overestimation of R_s simulation (Fig. 3a), and this relationship is also robust over the grids (Supplementary Fig. S3a). This significant relationship between the R_s and TCC biases suggests that the inter-model differences may have the same underlying physical drivers as the individual model bias has [22]. Although the inter-model relationship between the R_s and R_s-clear biases is weak on the national scale (Fig. 3b), such significantly positive correlations can be seen at most grids in Northwest China and Southeast China (Supplementary Fig. S3b). Most models overestimate R_s-clear to enhance the positive bias in the simulated R_s or partly alleviate the effect of the TCC overestimation (Figs 3 and 1c–e).

Figure 3.

Inter-model relationship of the biases. (a) and (b) Relationship of the simulated biases in surface downward solar radiation (R_s) against those in (a) total cloud cover fraction (TCC) and (b) clear-sky surface downward solar radiation (R_s-clear) for 24 individual model simulations (colored dots) averaged over China from 1961 to 2014. Correlation coefficient (r) with a significance level (p) between them is shown and their least-square linear fit is plotted as red dash line.

Impact of model bias on the R_s projections

The national mean R_s simulated in three future SSP scenarios (SSP1-2.6, SSP2-4.5 and SSP5-8.5) show different levels of upward trends with large uncertainties during China's planned 20-year carbon-neutrality period (2050–2069), relative to the last 20 years of historical simulations (1995–2014) (Supplementary Fig. S1a). The systematic biases in TCC and R_s-clear can cause the historical bias of R_s revealed above and are bound to greatly affect the future projections of R_s and their uncertainty. EC based on this physical relationship allow us to constrain the future projections of R_s and narrow down the projection uncertainty, which can increase our ability and confidence in future solar energy deployment.

Figure 4a–c shows robust linear relationships between the future projections of national mean R_s during 2050–2069 for three future SSP scenarios and the systematic model bias in R_s identified above, with a goodness-of-fit of ∼0.90 (P < 0.05). Such robust relationships also apply to the grid scale under three future SSP scenarios (Supplementary Fig. S4). Leveraging the robust relationships, Fig. 4d–f describes the constrained future projection of R_s during 2050–2069 and their uncertainties based on two types of EC methods (see ‘Methods’ section), i.e. one is based on posterior probability weight (weight-EC) and the other is based on regression (regression-EC). Considering the different advantages of the regression-EC and weight-EC methods, we average their constrained projections of R_s (Fig. 4d–f) for better supporting decision-making in the future. Compared with the raw projections, the constrained projections in 2050–2069 are reduced in the national mean R_s by ∼5%, i.e. from 196 to 185 W·m⁻² in SSP1-2.6, 192 to 182 W·m⁻² in SSP2-4.5 and 191 to 181 W·m⁻² in SSP5-8.5 (Fig. 4d–f). More importantly, the projection uncertainties of R_s are reduced by ∼56%, which significantly improves inter-model agreement in R_s and substantially increases our confidence in the future projections of R_s (Fig. 4d–f). Moreover, we find that the constraints using the combined effect of the TCC and R_s-clear biases can account for ∼81% of the projection uncertainties using R_s (Fig. 4d–f). The constraints are also applied to the grid scale and yield similar results as above.

Figure 4.

Constraining the model projections of surface downward solar radiation. (a)–(c) Constraining the model projections of surface downward solar radiation (R_s) in three possible future scenarios, i.e. (a) SSP1-2.6, (b) SSP2-4.5 and (c) SSP5-8.5, with the help of the observations. The gray dots show the future R_s averaged over all grids in China during 2050–2069 versus the historical bias in R_s during 1961–2014 for the 24 models. Their robust regression fit shown as a gray line represents the constraint relationship for the future R_s, and the dashed lines show the 95% confidence intervals estimated by bootstrap. R² is the goodness-of-fit for the regression. The vertical black line shows that the bias between the simulated and observed R_s is equal to 0 and its probability density function is inferred from the differences between the bootstrap-resampled averages (see ‘Methods’ section) of the observations during 1961–2014 and their mean. (d)–(f) Comparisons of raw and constrained projections of R_s in three future scenarios. Four groups of bars are the raw projections of R_s (gray) averaged over China during 2050–2069, the constrained projections of R_s using the weight-EC and regression-EC methods (see ‘Methods’ section) and their average of the constraint projections, respectively. The projections are constrained based on the historical bias in R_s (red) and its combined effect from total cloud cover fraction (TCC) and clear-sky surface downward solar radiation (R_s-clear) (blue), respectively. The mode (×) and confidence intervals (66% and 95%) estimated from the probability density function of the constrained projections are shown over the bar.

Credible projection of R_s values obtained by the EC with the help of historical observations can yield more realistic estimates for future changes in R_s. Figure 5 shows the spatial patterns of future changes in R_s calculated as the differences of the constrained simulations between 2050–2069 and 1995–2014. Compared with the raw future change, the constrained result of the CMIP6 MMM R_s in SSP1-2.6 shows a higher level of brightening during 2050–2069 relative to the 1995–2014 mean in North China and Southeast China with higher power demand (Fig. 5a and d). The constrained change increases by ∼30% in China referenced to the raw projection in SSP1-2.6 (Fig. 5a and d). With increased anthropogenic forcing in SSP2-4.5 and SSP5-8.5, the constrained future changes become weaker brightening in eastern China and more dimming in western China (Fig. 5b, c, e and f). This could imply that low anthropogenic emissions under the carbon-neutrality actions would increase future changes in R_s and solar energy potential, consequently creating positive feedback for building a climate-resilient society. More importantly, the uncertainties of future changes in R_s are reduced by 70% in North China and Southeast China and by 30% for the rest of China.

Figure 5.

Maps of the constrained future changes in R_s and their uncertainty. (a)–(f) Future changes (shading; in W·m⁻²) in the 20-year mean of surface downward solar radiation (R_s) during 2050–2069 relative to the 1995–2014 mean from the (a)–(c) raw and (d)–(f) constrained values in three possible future scenarios, i.e. SSP1-2.6, SSP2-4.5 and SSP5-8.5, with the 66% confidence interval shown as a contour. The constraints are done for both periods to derive the future change and the results of the weight-EC and regression-EC are averaged in (d–(f).

DISCUSSION

Effectiveness and confidence in the layout of solar PV systems heavily depend on reliable projections of R_s. Considering model bias and scenario uncertainty, the future projections of R_s in the mid-twenty-first century by the CMIP6 models in three possible future emission scenarios are constrained with the help of historical observations in this study. Results show that future increase in the constrained R_s is largest in SSP1-2.6, a low-emission scenario, followed by SSP2-4.5 and SSP5-8.5, median- and high-emission scenarios (Fig. 5). According to the linear relationship between R_s and electrical power by solar (see ‘Methods’ section) [34], the potential electrical power generated by solar in China at SSP1-2.6, SSP2-4.5 and SSP5-8.5 is estimated to be 44.3, 43.6 and 43.3 TW per year on average during 2050–2069, respectively. These results are more favorable for increasing the share of solar energy in the future for phasing out heavily polluting coal as its major energy source, which is conducive to the formation of positive feedback in the producing clean energy—tackling climate change under the carbon-neutrality actions.

In China, there are substantial regional variations in solar power generation potential affected by shortwave radiation, land availability and installation densities, showing a downward trend from northwest to southeast [35,36]. However, most western regions including Xinjiang, Inner Mongolia, Gansu, Qinghai and Tibet with huge solar PV generation potential have relatively low electricity demand and population density [35,37], so it needs huge costs to realize power transmission from west to east. Taking into account the cost of spatial dislocations between the PV power generation potential and electricity demand in China, and the need to improve air quality by reducing coal use in eastern China, the development of PV systems has recently begun to shift from west to east [37]. The higher level of brightening in the future in North China and Southeast China revealed by our constrained projections of R_s in the low-emission scenario (Fig. 5) directly supports the west-to-east shift of the PV systems, which can make better use of future solar energy resources.

Limitations of our analysis are revealed here for better understanding our results. First, sunshine duration data are recorded by visually reading the burned signals on light-sensitive paper and TCC data are observed based on human eye, so the shift work of different meteorological observers may cause problems on the data homogeneity [38,39]. Our homogenization has removed most large

discontinuities contained in these data, which can minimize the impact of the observational uncertainty. In addition, sparse ground-based observations over complex terrain in the Tibetan Plateau may also lack spatial representation compared to the rest of China [6]. Second, our methods work well to obtain the best estimates and their uncertainty of the national average R_s projections by building a robust constraint relationship using model and observational data, but are not able to constrain R_s on those grids without observational data, such as the western Tibetan Plateau (Fig. 5). Third, uncertainties in future projections may suffer from some limitations of different constraint methods. The weight-EC method presents a limitation in the projected R_s because it weights the models by the posterior probabilities of their historical simulations against the observations and consequently 4 out of 24 models have large weights (Table 1). In contrast, the regression-EC method treats each model as equal and independent, and leverages the robust linear relationship to constrain the projections of R_s. Its result may be disturbed by the models that are significantly inconsistent with the observations or that might share some interdependent modules despite being modified among the models [40], while the weight-EC could overcome these disadvantages [26]. On this basis, our result shown above is averaged from their R_s projections constrained by the two methods, considering their different advantages and inherent systematic bias of climate models over China, so we believe that the constrained projections are more credible than the raw projections. Finally, while the relationship between R_s and electrical power by solar is actually complex [41], a simple linear model is able to describe their relationship [34].

In summary, the significant systematic bias in R_s in the CMIP6 models is identified in this study and its drivers are further revealed to be model biases in simulating TCC and R_s-clear. These biases have significant impacts on future projections of R_s and their uncertainties from these models. Observation-based EC through this robust relationship largely reduce the projection uncertainties of future R_s by ∼56% and increase brightening by ∼30% in the future R_s changes during 2050–2069 in China. The constrained projections of R_s show a higher level of future brightening in North China and Southeast China, highlighting the need to consider the spatial changes in future R_s when making policies or decisions associated with future solar energy deployment.

METHODS

Observation and model data

Direct measurements of surface downward solar radiation (R_s) are conducted only at ∼100 stations in China. These direct R_s measurements not only are unevenly located, but also suffer from series inhomogeneity due to instrument aging and instrument sensitivity drift problems [42–44], so that they are

not able to well depict historical R_s and its change in China. Unlike direct R_s measurements, sunshine duration (SunDu) was measured at ∼2200 stations from 1961 to 2014. SunDu has been used to derive R_s (SunDu-derived R_s; Equations (1) and (2)) [6,7] based on the revised Ångström-Prescott equations [45]. The SunDu-derived R_s avoids series inhomogeneities not only due to instrument aging and instrument sensitivity drift problems contained in direct R_s measurements, but also due to large-scale instrument replacements in 1990–1993 across China [42,43,45]. The SunDu-derived R_s can well reproduce monthly R_s values in China with a bias of 2.19 W·m⁻² (1.4%) and a standard deviation of 19.32 W·m⁻² (12.0%) compared with direct R_s measurements and is able to describe monthly to decadal R_s variability well [7,42], which has been used as reference data to assess the performance of R_s in the reanalysis products and climate simulations [27,38,46]. Here, the SunDu-derived R_s data set at ∼2200 stations in He et al. [7] is used as observations for comparisons with the CMIP6 historical all-forcing simulations:

(1)

(2)

where a₀, a₁ and a₂ represent the regression coefficients of the sunshine duration against the R_s observation; n and N represent the observed sunshine duration and theoretical sunshine duration, respectively; τ_c is the radiative transmittance due to cloud extinction; I₀ is the solar irradiance at the top of the atmosphere; t is the time (in seconds); τ_{c_dir} and τ_{c_dif} denote the direct radiation transmittance and the diffuse radiation transmittance under clear skies, respectively, which are calculated through a broad radiative transfer model based on meteorological observations including near-surface air temperature, air pressure and relative humidity and the turbidity coefficient [45].

TCC measured at ∼2200 stations by the China Meteorological Administration (CMA, http://data.cma.cn/en) are used in this study. Noted is that TCC is observed based on the human eye and the number of stations with TCC observations decreased to 800 in 2014. To supplement TCC data for those stations without TCC observations in 2014, we apply inverse distance weighting interpolation to the observations at nearby stations that have a correlation coefficient of >0.7 with the anomaly of the candidate station during 1961–2013 [38,47].

R _s and TCC data in the CMIP6 experiments (https://esgf-node.llnl.gov/search/cmip6/) are used in this study, including historical all-forcing simulations (HIST; 1961–2014) and future projections in three possible scenarios with different shared socio-economic pathways (SSP1-2.6, SSP2-4.5 and SSP5-8.5; 2015–2099). To ensure an equal weight for different CMIP6 models, the ‘rlilp1f1’ realizations are adopted in this study. There are 30 models providing both historical and future data, 24 out of which are selected by comparing the R_s anomalies in the HIST simulations with those of observations via the Kolmogorov–Smirnov test at a significance level of 0.05. This method is often used to filter out some models with apparently inappropriate climate simulations [48]. Information of the models used are listed in Table 1.

We describe the clear-sky surface downward solar radiation (R_s-clear) by using the days with TCC of <15% as the clear-sky data [47]. It has been shown that there is little difference in the monthly R_s climatology under different clear-sky thresholds (e.g. 10% and 15%) with the one under true cloud-free conditions (0%). To reduce the sampling effect of uneven observation sites and ensure spatial consistency between model grids and observation sites, we integrate all the data onto 2° × 2° grid boxes by averaging observations of all the sites within a grid box or bilinearly interpolating model grids. We calculate the national average by weighting the area of each grid.

Statistical analyses

Mean bias (MB), root-mean-square error (RMSE) and Pearson correlation coefficient (r) are used to quantify historical bias in R_s, TCC and R_s-clear of the CMIP6 historical all-forcing simulations against the observations:

(3)

(4)

(5)

where m is the number of the R_s, TCC or R_s-clear data; S_i and O_i denote the i^th data of the CMIP6 simulations and observations, respectively; and are the mean of the simulations and observations, respectively.

To quantify the sensitivities of R_s bias to the TCC or R_s-clear bias, we use partial least squares to statistically exclude the confounding effects of the other variable:

(6)

where is the partial correlation coefficient between x and y after controlling z; x represents the R_s bias; y or z can be the TCC or R_s-clear bias; r is the Pearson correlation coefficient.

EC

Two emergent constraints methods are used to constrain future projection: one is based on posterior probability weight (weight-EC) and the other is based on regression (regression-EC).

Weight-EC

This method is to estimate a posterior probability through an information–theoretic perspective according to how well the models reproduce the observations [26]. The estimated posterior probability is used for weighting the future projections given the climate models to yield robust constraints assuming a robust linear relationship with historical data. To this end, we first calculate the Kullback–Leibler divergence, also known as relative entropy or information divergence, to measure the asymmetry of the probability distributions of R_s between the historical simulation of each model and the observation (Equation (7)) [49]. Then, we estimate the weight (w) by an information–theoretic distance measure (l) between each model and the observation (Equations (8) and (9)), which is also verified by visual comparison between them. The weights for all the models are listed in Table 1. We also identify the robust linear relationship between future projections of R_s and historical R_s bias (Fig. 4a–c) and, based on this relationship, we can obtain the probability density functions (PDF) of the constrained R_s by applying the estimated posterior probability and then use a Gaussian kernel to estimate the mean and uncertainty of the projected R_s:

(7)

(8)

(9)

(10)

where O(x) is the PDF of the observation; s_j(x) is the PDF of the historical simulation in the j^th model; is the Kullback–Leibler divergence of each model; l_j is the information–theoretic distance describing how well the historical simulation reproduces the observation, which is quantified here as the likelihood of the j^th model given the observed distribution; w_j is the normalized weight of the j^th model.

Regression-EC

This method is to leverage the robust inter-model relationship (Equation (11)) to constrain the future projection of R_s with the help of the observation. The parametric uncertainty of the regression model and the observation uncertainty are considered. To account for the parametric uncertainty, we repeat the inter-model regression between future projections of R_s and model biases of R_s via 1000-times bootstraps. To estimate the uncertainty of the observation average, we estimate the PDF of the average via 1000-times bootstraps of annual R_s observations during 1961–2014. The observation uncertainty contained in the R_s bias can be quantified by the PDF of the observation average:

(11)

where Y is the future projection of R_s from CMIP6 models in each of three possible future scenarios and X is the historical model bias in R_s; is the regression slope and is the intercept. The value of Y as X equals 0 is the constrained projection.

To constrain future projections of R_s, we take the bias of 0 and its PDF as input data into each bootstrap regression equation (Equation (11)) to generate a pool of future constrained R_s. As the weight-EC method, we also employ a Gaussian kernel with a bandwidth chosen to minimize the mean integrated squared error of the pool of future constrained R_s, to estimate the mean and uncertainty of the projected R_s. Previous studies [22,50] usually ignore either of them in their EC constraints, thereby weakening the estimated uncertainty.

To verify the validity of the constraint methods, we constrain the recent 20-year mean historical R_s simulations of the CMIP6 models averaged over the grids with the observations in China during 1995–2014 based on the former period of 1961–1994 and compare the constrained results with the 1995–2014 observations. The comparison shows they match well and the uncertainties are significantly reduced (Supplementary Fig. S5).

Estimate of the combined effect of TCC and R_s-clear

To estimate the combined effect of TCC and R_s-clear on R_s in the observations from 1961 to 2014, a multiple linear regression is applied:

(12)

where and are the regression coefficients; is the constant and is the residual. Then, we repeat the constraints using the combined effect of TCC and R_s-clear, instead of R_s, based on the weight-EC and regression-EC methods.

Estimate of electrical power generated by solar

A model [34] to estimate electrical power (EP) generated by solar is used to show its linear relationship with R_s, as the following:

(13)

where S represents the annual average R_s in China during 2050–2069; is the average conversion efficiency set at 26.9% in 2060 where air temperature plays a role [37]; is the panel albedo assumed to be 0.1 [34]; A_p represents the suitable land area for PV power generation, which is set at 0.99 million km² as suggested by Qiu et al. [35] based on the 2015 situation in China.

DATA AVAILABILITY

Climate model outputs from CMIP6 are publicly available at https://esgfnode.llnl.gov/search/cmip6/. Routine meteorological observations at ∼2200 stations are obtained from the CMA (http://data.cma.cn/en). The homogenized meteorological observations and ground-based R_s from sunshine duration used in this study are available upon reasonable request to the corresponding author. The code is available upon request to the corresponding author.

FUNDING

This work was supported by the National Key R&D Program of China (2018YFA0605400), the National Natural Science Foundation of China (42205171), the China Postdoctoral Science Foundation (2021M701839) and the Shuimu Tsinghua Scholar Program.

AUTHOR CONTRIBUTIONS

Y.H. and K.Y. designed the research. Y.H. performed the analysis and wrote the draft. All the authors jointly contributed to interpreting the results and writing the final paper.

Conflict of interest statement. None declared.