In this study, we used CORDEX WAS-22 regional downscaled experiments for all Coupled Model Inter-comparison Panel 5 (CMIP5) models available on the Earth System Grid Federation (ESGF). We focused on three climate variables from CORDEX, namely, near-surface wind speeds (sfcWind) at 10 m height, surface temperature (tas), and downward surface radiation (rsds) at the monthly resolution, and 0.22° (about 22 km) horizontal spacing. We defined the study area in India as 6.70°N to 35.5°N and 68.1°W to 97.3°W. CORDEX simulations are available for a historical period (1979–2005) and future projections starting from 2006 to the end of the century with representative concentration pathway (RCP) scenarios RCP 2.6, the lower emission scenario for CMIP5, and RCP 8.5, the scenario assuming a continued increase in greenhouse gases throughout the end of the century (Riahi et al., 2011). Three RCM families are available for CORDEX WAS-22: 1) the Abdus Salam International Center for Theoretical Physics (ICTP) RegCM system (ICTP-RegCM4-7 (Giorgi et al., 2012), noted RegCM4 hereafter); 2) COSMO-crCLIM-v1-1.v1 (COSMO (Sorland et al., 2021)); and 3) REMO2015.v1 (REMO (Jacob et al., 2012)). Table 1 summarizes RCM names, with their driving GCM parent, scenarios available, and acronyms of CORDEX simulations.

As a necessary prerequisite for this work, we evaluate monthly CORDEX WAS-22 simulations for the three climate variables over the period 1981–2005 with comparison to the ERA5 reanalysis dataset (Sabater, 2019). We examine how well they reproduce the spatial distribution of annual and seasonal means during specified time periods (denoted climatology) and trends at each grid point and the spatial averages.

We analyze the temporal patterns of wind speed at three existing wind sites and radiation and temperature at four solar sites for ERA5 and the individual CORDEX WAS-22 models. Table 2 outlines the name, location, and total capacity in megawatt (MW) of the sites considered in this study. They are selected because they all belong to the CLP Group and are used as a benchmark of a real-life portfolio whose structure will be the model of the portfolios simulated later on in India. On the selected sites, we evaluate the standardized monthly anomalies derived during a 25-year period extending from 1981 to the end of 2005 to examine the seasonal variations.

One way to use RCM projections is to assess the magnitude and degree of consistency in the simulations in terms of changes in 1) climate variables or 2) impacts when the wind speed or solar radiation and temperature are converted to energy estimates (Intergovernmental Panel on Climate Change, 2014). These changes can be expressed in linear trends of annual, seasonal, or monthly mean quantities between certain time periods. For the evaluation of future changes, we analyze annual and seasonal climatology and trends in surface wind speeds, temperature, and radiation from CORDEX WAS-22 models in the Indian subcontinent for RCP 2.6 and RCP 8.5 scenarios during two subperiods; from 2025 to 2055 and from 2065 to 2095. We focus the discussion in the main text on simulations with RCP 8.5 to identify the largest bounds of changes in wind, radiation, and temperatures in the models. The length of the two subperiods simulates the economic lifetime of wind and solar assets. When the seasonality is considered, we refer to winter as the months from December to February, pre-monsoon as the months from March to May, monsoon as the months from June to September (noted JJAS), and the post-monsoon (months of October and November) seasons. We use linear regression and the Theil–Sen (Theil, 1950; Sen, 1968) nonparametric method to analyze trend magnitudes, which are tested for statistical significance using the Mann–Kendall test (Mann, 1945; Kendall, 1948). To illustrate the spread of model projections, we take the most extreme and the median trend values of all considered models at every grid point. Thus, we evaluate the smallest trends; strongest negative or smallest positive trends, the largest trends; strongest positive or smallest negative trends, and the median trends. After analyzing the whole study domain, we divide it into five subregions described in Figure 1 to summarize the regional trends. This step is motivated by the need to identify regions where wind and solar monsoon trends are anti-correlated as this is a binding condition in our work. Once these regions are identified, we focus on two of them for this analysis. In each region, we select three locations for wind assets and four others for solar assets. For the application of portfolio methods, we produce energy time series for wind and solar PV at selected locations according to the method discussed in Section 2.4.

After identifying the regions where wind and solar are anti-correlated during the monsoon season, we pick the locations for the wind and solar sites. Hereafter, we lay out the method used to estimate the returns of the wind and solar PV assets, which then serve as an input in the portfolio analysis explained in Section 2.5. We determine the energy production for each wind and solar asset using CORDEX data and express this return in the form of capacity factors and PV potential as actual production estimates depend on local weather and installations. For wind assets, the capacity factor CF _wind is defined as the fraction of the potential production of wind power at the wind site and the maximum possible energy (P rated, times the amount of time energy was produced, t): C F w i n d = E p r o d u c e d P r a t e d * t . (1)

At the three wind farm locations considered, we assume 30 Suzlon 111 wind turbines installed at a hub height of 90 m, with a turbine diameter equal to 111.9 m and a rated power of 2.1 MW. To project surface wind speed to hub height, we extrapolate wind speed data v ₁ at 10 m height to the 90 m hub height using the power law (Archer and Jacobson, 2005) to obtain v ₂: v 2 = v 1 z 2 z 1 α , (2) where the friction coefficient α is equal to 1 7 . The total energy production of each wind farm is estimated by summing the production (resp. nameplate capacity) of each wind turbine over the life of the asset. We assimilate the life of the turbines to 25 years to align with time periods selected to evaluate the impact of climate change. Our analysis is independent of a specific investment life-cycle. Therefore, we do not assume that all turbines need to be installed at a certain point in time, and the conclusions do not depend on the 25-year assumption.

For solar sites, in order to make a first-order estimate and translate solar radiation and temperature into potential changes in PV generation, we use the methods presented by Jerez et al. (2015) and Crook et al. (2011) to calculate PV _pot , which is defined as the fraction of the power output under standard conditions that a PV module may have according to Eq. 3: P V p o t = P R r s d s r s d s S T C . (3)

PV _pot is unit-less, rsds is the surface downward radiation at each time from ERA5, rsds _STC is radiation under standard conditions which is equal to 1000Wm ⁻², and P _R is the performance ratio calculated from Eq. 4: P R = 1 − γ T c e l l − T S T C , (4) where T _STC is equal to 25°C, γ = 0.005°C ⁻¹ assuming the behavior of monocrystalline silicon solar panels, and T _cell is the temperature of the PV cell calculated with Eq. 5: T c e l l = c 1 + c 2 T + c 3 r s d s − c 4 s f c W i n d (5) sfcWind is surface wind speed, c ₁, c ₂, c ₃ and c ₄ values are listed in Table 3, along with the other variables and constants and their units.

See Supplementary Figure S1 for an illustration of PV potential (PV_pot ) and on-shore wind capacity factors (CF_wind ) in the Indian sub-continent from ERA5 data and the period extending from 1981 to 2006. In Section 2.5, we show how CF _wind and PV _pot estimated from CORDEX data are used in the portfolio analysis framework to investigate the impact of combining wind and solar assets on the uncertainty of portfolio returns.

Portfolio analysis supports the decision-making subject to the tradeoff between the expected return and the volatility of this return. The framework enables the assignment of weights to assets included in a portfolio such that the total return is maximized and the volatility of this return is minimized. Decision makers can evaluate the performance of each optimal portfolio formed by a combination of assets. The optimal solutions of the trade-off in the portfolio analysis are graphically represented on an efficient frontier, which is a plot of optimal returns and their volatility. In the following section, we explain how it is adapted to calculate the uncertainty on returns calculated from climate models. First of all, we use a set of wind and solar sites as an input to the bi-objective function. We consider that these candidates are part of a portfolio whose structure mimics the existing portfolio discussed earlier, with three wind farms and four solar PV assets. The sites selected sit on locations where wind and radiation trends are anti-correlated during the monsoon season. We solve the bi-optimization problem three times for each set of locations in a way that we have 1) only wind sites, 2) only solar sites, and 3) wind and solar sites combined as an input. By doing so, we can compare the efficient frontiers obtained from the standalone perspective with wind-only or solar-only portfolios and the mixed portfolios. The examination of the three efficient frontiers obtained enables us to highlight the effects of the combination of wind and solar energy in the portfolio and its impact on the volatility of the return, as opposed to the nonmixed portfolios. The analysis is repeated for each individual RCM model for a certain RCP scenario. Finally, by doing so, we can measure the spread between the curves of the efficient frontiers for each one of the portfolio types and examine how the combination of asset types affects this spread.

Formally, the mean–variance analysis consists of a bi-optimization problem Eqs 6, 7, where μ _k is the average production of wind or solar power in each location k, and the mean portfolio return μ _p (approximated by its total capacity factor) is maximized while its variance σ p 2 is minimized, subject to the constraints that the sum of the weights w _k is equal to one and that all capacity factors are positive. max μ p = ∑ k w k μ k s . t . ∑ k w k ≤ 1 . (6) min σ p 2 = ∑ k ∑ m w k w m cov k , m s . t . ∑ k w k ≤ 1 . (7)

Hence, we calculate the average production at each location k, namely, the mean μ _wind that is approximated by CF _wind in the case of wind sites and by PV _pot in the case of solar sites. In Eqs 6, 7, w _k is the weight of each asset in the portfolio. For the minimization of the portfolio variance σ p 2 in Eq. 7, we calculate the covariance matrix cov _(k,m) between the different assets k and m based on their geographical distribution using time-series. Furthermore, we limit the weight for each asset in the optimal portfolio, which cannot be larger than 50%. After solving the bi-objective function presented earlier, we obtain the efficient frontiers or the set of optimal portfolios; each point on the frontier is a combination of assets according to certain weights to form a portfolio with a certain return and its corresponding volatility value. The algorithm defines the assets considered in the portfolio.

We simulate returns for five assets to illustrate the concept of the efficient frontier in Figure 2. The five points represent the mean return and standard deviation for each one of the five individual assets. The resolution of the bi-optimization problem described in Eqs. 6, 7 enable finding the combination of assets where returns are maximized for a given level of volatility or minimized volatility for a given level of return. The set of these optimal solutions constitutes the efficient frontier. On this graph, the higher a point is to the left the better an asset is because the expected return is higher and the related volatility is lower.

The results of the comparison between CORDEX WAS-22 models and ERA5 are presented in Figure 3 for sfcWind, Figure 4 for tas, and Figure 5 for rsds.

Regarding the annual climatology of wind speeds, the results in Figure 3A demonstrate that the geographical pattern of CORDEX WAS-22 models resembles the one found for ERA5, although differences exist in the south of Tibet. For the annual trends of surface winds, the comparison in Figure 3B shows that not all individual climate models reproduce the pattern of ERA5. In general, we find that the ensemble mean for wind speed, noted sfcWind _hist (first row and second column in Figure 3C satisfactorily captures wind speed annual trends, and shows similarities in the pattern of the monsoonal trend (Figure 3 D). This result is in general a key finding because it increases confidence in the ability of CORDEX models in reproducing the monsoon pattern, which is a majorly impacting climatological feature on wind energy in India.

We include a similar assessment for temperature and solar radiation as they are used to estimate solar energy time series. We find a strong resemblance in the spatial pattern of annual temperature climatology between ERA5 and CORDEX WAS-22 individual models displayed in Figure 4A. Discrepancies in the annual climatology for temperature are found in mountainous areas toward the Himalayas in northern India because the resolution of climate models cannot capture the complexity of local spatial variability. There is also a good agreement in the annual temperature trends (Figure 4B), and all datasets exhibit trends with a positive slope. According to the results for wind speeds, we find large similarities in the seasonal temperature climatology between ERA5 (Figure 4C) and the historical ensemble (Figure 4D).

We see in Figure 5A that differences exist in the spatial pattern of the annual climatology for radiation, while ERA5 data and the ensemble mean outline a good agreement with only a slight difference in the spatial average (230 Wm ⁻² for ERA5 and 220 Wm ⁻² for the ensemble mean). We notice a high variability between ERA5 and the individual models for the annual radiation trends in Figure 5B. Similar to the annual pattern, we find a significant similarity in the seasonal climatology for radiation between ERA5 (Figure 5C) and the historical ensemble (Figure 5D).

In summary, we conclude that CORDEX WAS-22 models for the three climate variables reproduce ERA5 data with a reasonable degree of fidelity, and the resemblance in the spatial distribution is stronger at the annual level than at the seasonal level. Section 3.3 includes an evaluation of the temporal variability at existing wind and solar sites.

Figure 6A outlines the temporal variability of standardized wind speed at three existing wind-farm sites and compares CORDEX models with ERA5 (black line). In the three sites, the peak in wind speeds reflected by ERA5 coincides with the monsoon season. However, REMO models represented in purple shades outline a peak delayed and occurring later during the year. The delay in the monsoon peak for wind speeds from REMO models is apparent while looking at the plots of the seasonality component. COSMO and RegCM4 models show good correspondence in the seasonal component of the individual models with ERA5. We see that there are differences in the individual models and that in some instances, the individual models are not able to reproduce the peak in wind speed during monsoon.

At the four solar sites, we observe that the peak in radiation (Figure 6B) reported by ERA5 (black line) occurs between March and May. The time of occurrence of the peak for RegCM4 and COSMO models coincides well with that of ERA5. REMO models (lines in the purple shade) fail to reproduce that as the peak of these purple lines occurs later around the monsoon season. This delay in peak radiation for REMO models also appears when we analyze the seasonality component for radiation. In Veltoor, the correspondence in the trends between ERA5 and RegCM4 models is the highest which could indicate that not all available models are equally suitable for a particular location. The differences between the RCMs can be partially explained by the fact that COSMO, for example, has difficulties over domains with a climate substantially different from that of Europe where it has been developed (Sørland et al., 2021). On the other hand, IITM-RegCM4 over South Asia was developed at an Indian institute.

For temperature (Figure 6C), the peak that occurs in June or July according to ERA5 data is accurately reported by RegCM4 models (green) and COSMO ones, while REMO models persistently show delay with a peak occurring only after the monsoon season and toward the end of the year.

The evaluation of the temporal variability between the individual models in wind and solar locations highlights one of the problems when evaluating climate change; these differences between the ERA5 data and CORDEX models can be attributed to differences in the parametrization of the models and shows that uncertainty of climate predictions may still be large. Now that we highlighted some differences in the models, we study the trends for future projections before testing how the combination of wind and solar energy can reduce the variability in the trends.

In this section, we describe the geographical distribution of long-term annual and seasonal climatology and trends for surface wind speed, temperature, and radiation in India under the RCP 8.5 scenario. The results for the annual climatology for the three climate variables are presented in Figure 7.

The evaluation of the climatology between the two periods (2025–2055) and (2065–2095) in Figures 7A,B shows that the median value of the annual wind speed increases by 2.6%. Looking at the seasonal climatology for surface wind in Figure 8, we observe that the minimum seasonal values shown in Figure 8A increase for monsoon and winter winds during the first time period, while pre-monsoon and maximum monsoon wind speeds increased in the later part of the century in Figure 8 F. Regarding the seasonal trends during the first period (Figures 8 G, H, I), we find a positive wind speed trend during the pre-monsoon in the northwest and some southern areas during the monsoon and winter seasons. We also find some increase in the northeast for winter wind speeds from the maximum ensemble. During the second period extending from 2065 to 2095 (Figures 8 J, K, L ), we find a positive trend in the northwest and southeastern coast for pre-monsoon wind speeds. We can also report on some positive trends for monsoon wind speeds in areas located in the northwest and northeast. Looking at the maximum ensemble, we find a positive trend in the north and northeast, indicating an increase in extreme wind speeds.

The spatial distribution of the annual climatology for the downward surface radiation is presented in Figure 9. The highest values are found in the north of India toward the Himalayas and in the northwestern and southwestern parts of India. The annual and seasonal mean climatology remains the same between the first and second periods. Looking at the median ensemble for the first period (Figures 9A–C), we see no significant change in the pre/post-monsoon climatology. During the monsoon season (Figures 9G–I), the northwest and northeast regions near the coast have significant negative trends. During the second period, the results show a positive trend in the north of India during the monsoon that would involve an increase in PV output in the region (Figures 9J–L).

For temperature, we find a higher climatology and positive trend toward the end of the century and extreme temperatures increasing during the monsoon in the whole of India except the South. Assuming that there will be no changes in future solar radiation, these trends would imply decreasing power output for solar PV as solar panel decrease in efficiency with increasing temperatures (Dubey et al., 2013).

Prior to the portfolio analysis, we investigate the seasonal correlation between surface downward radiation and wind speed in the subregions defined earlier in Table 4. This table shows that the two regions where the anti-correlation in wind and radiation is strongly distinguishable and consistent for the two RCP scenarios are the South from 2025 to 2055 and the North from 2065 to 2095. Hence, we select two sets of wind and solar assets in these two regions as candidates for the application of the portfolio analysis.

We apply the portfolio framework in two sets of wind and solar assets in the South and the North where the two solar radiation and wind speed variables are anti-correlated. The characteristics of the two sets are summarized in Table 5. We analyze how the combination of wind and solar energy impacts the uncertainty of prediction on energy returns.

For the analysis of the results, we evaluate how the spread of the efficient frontiers associated with the mixed portfolios differs from the one found for wind- and solar-only portfolios. The results are presented in Figure 10, where the first row depicts the results for the set located in the South from 2025 to 2055 and the second row depicts the ones for the set located in the North for the second time-period.

In the southern region, under RCP 2.6 and during the first time-period, the evaluation of the efficient frontiers obtained for the set of asset in Figure 10A shows that for a return level of 0.25, the standard deviation of the portfolio for solar-only portfolios ranges between 0.035 and 0.045. The efficient frontier of wind-only portfolios has only one optimal solution for the level of return, and the standard deviation converges to a single value of 0.032. Different weight values of the three wind assets currently evaluated cannot improve the optimal return and thus its attached standard deviation. The standard portfolio for mixed portfolios ranges from 0.025 to 0.032. The mixed portfolio reduces the spread of the standard deviation of the portfolio for this return level by 30% compared to the solar-only type. In the same region and time period, under RCP 8.5, Figure 10B shows that for the same return level of 0.25, the reduction of the uncertainty range for the mixed portfolio compared to the solar-only type is also valid as the standard deviation of the portfolio for solar-only varies from 0.035 to 0.049, while it ranges between 0.025 and 0.035 for the mixed type, which also corresponds to a reduction of 30%. In the North, where the seasonal anti-correlation between wind and solar radiation variables extends throughout the year under RCP 2.6 and between 2065 and 2095, Figure 10C highlights that for a return level of 0.31, the spread of the standard deviation of solar-only portfolios ranges from 0.041 to 0.48, from 0.082 to 0.085 for the wind-only type, and from 0.039 to 0.041 for the mixed portfolio. Hence, the reduction obtained with the mixed portfolio reaches a level of 71.4% compared to the solar-only and 33.3% compared to the wind-only type. For this same set, under RCP 8.5, we find that for a return level of 0.34 (Figure 10D), the spread of the standard deviation for solar-only portfolios ranges from 0.052 to 0.097, for wind-only portfolios is between 0.092 and 0.096, and for the mixed portfolios is between 0.047 and 0.490. This entails that the range obtained with the mixed portfolio for the return level evaluated leads to reduction of the uncertainty on the standard deviation by 96% compared to the solar-only portfolio type and 50% compared to the wind-only one. The benefits of the portfolio method are demonstrated in the two regions presented considering the reduction of the spread in the efficient frontiers for a certain return value when the portfolios are mixed compared to the portfolios of solar-only type in the first case and both wind and solar for the second case. We highlight that we also find cases where the reduction of the spread for the mixed portfolios does not hold. Yet, we consistently find that mixed portfolios offer a great advantage in reaching higher return levels for low- to-medium-risk portfolios (efficient frontiers on the left), and this constitutes a desired advantage for investors. The results also indicate that the reduction in the uncertainty is more substantial for the solar-only portfolios than the wind-only ones. The variability at the monthly time-scales is higher for wind than solar portfolios. We investigate the impact of time resolution on the findings and redo the analysis in the same regions with daily data for CORDEX WAS-22 data under both RCP scenarios. We evaluate the differences in the spread of the mixed portfolio compared to the single portfolio types from daily data for the same return levels defined for monthly data. The results are included in Figure 11.

In the South, with daily data, the reduction in the spread of the uncertainty for the mixed portfolio compared to the solar-only type is effective for return levels below 0.22. The efficient frontiers for wind portfolios from daily data have the same characteristics with a single optimal solution. In the North, with daily data, we find that mixed portfolios have a lower uncertainty spread than solar ones for high return levels (above 0.30). The conclusions found at the monthly resolution remain valid with daily data.