What drives historical and future changes in photovoltaic power production from the perspective of global warming?

We isolate the benefits and losses in the potential PV power production associated with climate change. The calculation of the potential of PV power production is based on earlier methods (Jerez et al 2015, Bichet et al 2019) and our own derivation of equations for separating contributions to the changes in PV power production, namely for clouds, air humidity, and aerosols. We calculate the PV power production as a function of time PV(t) following Jerez et al (2015) with:

$$\begin{align} PV\left(t\right) = P_{\mathrm {R}}\left(t\right)\frac{I\left(t\right)}{I_{\mathrm {STC}}}, \end{align} \tag{ 1 }$$

where I(t) is the temporally dependent irradiance at the surface and $I_{\mathrm {STC}} = 1000\,{\text{W}\,\text{m}^{-2}}$ is the irradiance used during standard testing conditions of PV panels. The performance ratio, $P_{\mathrm {R}}(t)$, is calculated as:

$$\begin{align} P_{\mathrm {R}}\left(t\right) = 1 + \gamma \left[T_{\mathrm {cell}}\left(t\right)-T_{\mathrm {STC}}\right]. \end{align} \tag{ 2 }$$

Here, $T_{\mathrm {cell}}(t)$ is the temporally dependent temperature of the PV cell in $^\circ \text{C}$, and $T_{\mathrm {STC}} = 25^{\circ}\text{C}$ is the temperature used during standard testing conditions of the PV panel. We use parameters for present-day monocrystalline silicon solar panels. Their response factor is, $\gamma = -0.005^{\circ}\text{C}^{-1}$, which is taken from Tonui and Tripanagnostopoulos (2008). We compute $T_{\mathrm {cell}}(t)$ following the approach from Jerez et al (2015) with:

$$\begin{align} T_{\mathrm {cell}}\left(t\right) = c_1 + c_2T_{sfc}\left(t\right) + c_3I\left(t\right) + c_4u_{sfc}\left(t\right), \end{align} \tag{ 3 }$$

using the constants c₁ = 4.3 ^∘C, c₂ = 0.943, c₃ = 0.028 ^∘C m² W^–1, and $c_4 = -1.528~^{\circ}$Csm⁻¹ from Chenni et al (2007). All meteorological data, here the near-surface air temperature, T_sfc , the near-surface wind speed, $u_{sfc}(t)$, and the irradiance at the surface, I(t), are taken from CMIP6 output explained in section 2.2. By inserting equations (2) and (3) into equation (1) and rearranging the equation, Jerez et al (2015) obtained:

$$\begin{align} PV = \alpha_{1} I + \alpha_2 I^2 + \alpha_3 I T_{sfc} + \alpha_4 I u_{sfc} \end{align} \tag{ 4 }$$

with the constants $\alpha_1 = 1.1035\times10^{-3}$ m² W⁻¹, $\alpha_2 = -1.4\times10^{-7}$ m⁴ W⁻², $\alpha_3 = -4.715\times10^{-6}$ m² W⁻¹/ ^∘C, $\alpha_4 = 7.64\times10^{-6}$ m sW⁻¹.

The mean change in PV power production potentials, $\Delta PV$, is then computed here as the difference between two thirty-year periods t₁ and t₂ as $\Delta PV = PV(t_1)- PV(t_2)$, written with equation (4) as:

$$\begin{align} \Delta PV& = \underbrace{\Delta I\left(\alpha_1 + \alpha_2 \Delta I + 2\alpha_2 I + \alpha_3 T_{sfc} + \alpha_4 u_{sfc}\right)}_{\Delta PV_{I}} \nonumber \\ &\quad + \; \underbrace{\alpha_3 I \Delta T_{sfc} }_{\Delta PV_{T}} + \; \underbrace{\alpha_3 \Delta I \Delta T_{sfc} }_{\Delta PV_{IT}} \nonumber \\ &\quad + \; \underbrace{\alpha_4 I \Delta u_{sfc} }_{\Delta PV_{u}} + \; \underbrace{\alpha_4 \Delta I \Delta u_{sfc} }_{\Delta PV_{Iu}}. \end{align} \tag{ 5 }$$

The different terms in equation (5) are interpreted according to their physical meaning allowing us to quantify the net contributions from different changes in meteorological variables to the mean change in the potential of PV power production. The five terms are composed of variables describing the mean values for a particular time period, e.g. the present-day temperature, T_sfc , and of variables for mean changes, e.g. changes in irradiance between two time periods, $\Delta I$. The name convention for the terms is chosen such that the variables driving the change in PV power production potentials determine the name, e.g. $\Delta PV_I$ is the change in PV power production potential associated with $\Delta I$. The magnitude of products of two changes in different variables, namely $\Delta PV_{IT}$ and $\Delta PV_{Iu}$, are small compared to the magnitude of the other terms and are, therefore, not shown.

Irradiance can change due to differences in clouds, air humidity, and aerosols between two time periods. These variables do not necessarily change similarly with warming and can be associated with different levels of model agreement. We, therefore, decompose irradiance-associated changes in PV power production, $\Delta PV_{I}$, into net contributions from changes in clouds, aerosols, and humidity, as:

$$\begin{align} \Delta PV_{I} = \Delta PV_{\mathrm {cloud}}+\Delta PV_{\mathrm {aer}}+\Delta PV_{q}, \end{align} \tag{ 6 }$$

describing the sum of changes in the PV power production potential due to irradiance differences associated with clouds, $\Delta PV_{\mathrm {cloud}}$, aerosols, $\Delta PV_{\mathrm {aer}}$, and air humidity $\Delta PV_{q}$. The difference in irradiance between all-sky (I) and clear-sky ($I_{\mathrm {cs}}$) conditions describes the net effect of clouds on radiation. We therefore calculate the influence of clouds on $\Delta PV_{I}$ with:

$$\begin{align} \Delta PV_{\mathrm {cloud}} = \Delta PV_{I}-\Delta PV_{I_{\mathrm {cs}}}. \end{align} \tag{ 7 }$$

The contribution from changes in air humidity to $\Delta PV_{I}$ is estimated using the water vapor content:

$$\begin{align} \Delta PV_{q} = \Delta I_q (\alpha_1 \!+ \!\alpha_2 \Delta I_q \!+\! 2\alpha_2 I_{cs} \!+ \!\alpha_3 T_{sfc} + \alpha_4 u_{sfc}). \end{align} \tag{ 8 }$$

Meteorological data as input for the conceptual model are available from CMIP6 output, except for $\Delta I_q$. We, therefore, compute $\Delta I_q$ with the help of our simulations with the Radiative Transfer Model for Global climate models (RRTMG, Clough et al 2005). For simplicity, and because the tests with other profiles had no substantial impact on the results for the change in PV power potentials, we use the clear-sky U.S. Standard Atmosphere 1976 (COESA 1976). We specifically performed two sensitivity tests for $\Delta PV_q$ with atmospheric profiles for the tropics and the subarctic winter taken from Anderson et al (1986). The mean difference for the global (table 1) and regional (figure 3) $\Delta I_q$ in the tests was ${\lt}0.03$% compared to the RRTMG simulation with the U.S. Standard Atmosphere. We perform multiple RRTMG simulations to create a lookup table (Servera et al 2019) for I_q . The simulation setups differ concerning (1) the water vapor profile scaled by integrated water vapor of 0–90 kg m⁻² with steps of 0.01 kg m⁻², and (2) different solar zenith angles from 0^∘–90^∘ with steps of 0.5 ^∘.

Table 1. Change of potential PV in % ($\Delta PV$) and the contributing terms for PD (1985–2014) against PI (1850), and SSP1-2.6, SSP2-4.5, and SSP5-8.5 (2071–2100) against PD. Shown are the CMIP6 multi-model means ± the model-to-model standard deviation.

Time periods	Average	$\Delta PV$	$\Delta PV_{\mathrm {cloud}}$	$\Delta PV_{\mathrm {aer}}$	$\Delta PV_{q}$	$\Delta PV_{T}$
PD-PI	Global	−1.7 ± 0.5	−0.1 ± 0.3	−1.3 ± 0.4	−0.1 ± 0.5	−0.3 ± 0.2
	Land only	−2.4 ± 0.7	0.0 ± 0.5	−2.0 ± 0.6	−0.1 ± 0.4	−0.3 ± 0.2
SSP1-2.6–PD	Global	0.1 ± 0.5	0.6 ± 0.9	0.8 ± 0.5	−0.6 ± 0.5	−0.6 ± 0.2
	Land only	0.7 ± 0.6	0.7 ± 0.9	1.5 ± 0.5	−0.7 ± 0.5	−0.8 ± 0.3
SSP2-4.5–PD	Global	−1.1 ± 0.5	0.5 ± 0.8	0.3 ± 0.4	−0.9 ± 0.3	−0.9 ± 0.3
	Land only	−0.7 ± 0.6	0.8 ± 0.8	0.8 ± 0.5	−1.0 ± 0.3	−1.3 ± 0.3
SSP5-8.5–PD	Global	−2.4 ± 0.9	1.4 ± 1.6	−0.2 ± 0.6	−1.8 ± 0.6	−1.8 ± 0.5
	Land only	−2.4 ± 1.0	1.9 ± 1.4	0.1 ± 0.8	−1.9 ± 0.6	−2.4 ± 0.6

Values from the lookup table are used for I_q values in $\Delta I_q$ for the calculation of changes in PV power production potentials. All calculations are with monthly mean output in each grid point from CMIP6 output paired with I_q values from the lookup table according to the monthly integrated water vapor content and the mean zenith angle of the latitude and month. The percentage change between two time periods is then used to estimate $\Delta I_{q}$ following:

$$\begin{align} \Delta I_{q} = I_{{\mathrm {cs}}_{1}}*\frac{I_{q_{2}}-I_{q_{1}}}{I_{q_{1}}}, \end{align} \tag{ 9 }$$

where the indices 1, 2 refer to the two time periods for which $\Delta PV$ is computed, e.g. the end of the 21st century against the present. The residual term is ascribed to changes in aerosols from both natural and anthropogenic sources:

$$\begin{align} \Delta PV_{\mathrm {aerosols}} = \Delta PV_{\Delta I_{\mathrm {cs}}}-\Delta PV_{q}. \end{align} \tag{ 10 }$$

We use monthly output from CMIP6 model experiments, listed in table B1, as input for the conceptual model. CMIP6 model experiments were used in the sixth assessment report on climate change by the Intergovernmental Panel on Climate Change (IPCC 2021). We used output for 30 year periods from the pre-industrial control experiments with conditions as of 1850 (PI), the period 1985–2014 from the historical experiments with transient changes of climate forcers (PD), and 2071–2100 from three future scenarios to account for different possible future developments of climate forcers. We selected three future scenarios with Shared Socioeconomic Pathways (SSP), namely SSP1 as a sustainable pathway, SSP2 as a middle-of-the-road pathway, and SSP5 as a fossil-fueled development pathway (O'Neill et al 2016). Those SSPs are combined with future radiative forcing of 2.6 W m⁻² (SSP1-2.6), 4.5 W m⁻² (SSP2-4.5), and 8.5 W m⁻² (SSP5-8.5) by the end of the 21st century and are more recent estimates for projected future developments than were used in CMIP5. The scenarios differ in terms of transient changes in various climate forcers, e.g. for greenhouse gases, aerosols, and their precursors. Due to the different forcings, the scenarios have different magnitudes of warming by the end of the century with global mean temperature increases of around +2 ^∘C (SSP1-2.6), +3 ^∘C (SSP2-4.5), and +5 ^∘C (SSP5-8.5) (Riahi et al 2017). The three scenarios therefore span a range of future warming levels and are useful to document the associated uncertainty in $\Delta PV$ at the end of the 21st century. We use output from experiments with models that have interactive aerosol parameterizations. Dust aerosols and their effects on the irradiance at the surface are for instance represented in the data, such that we account for associated losses in the potential for PV power production.

In total, these are 14 experiments from 14 models for PI, 154 experiments from 18 models for PD, 98 experiments from 14 models for SSP1-2.6, 109 experiments from 12 models for SSP2-4.5, and 92 experiments from 15 models for SSP5-8.5. The larger number of experiments is due to having several realizations of the same experiment type, e.g. there are ensembles of historical experiments from single models. Due to the different ensemble sizes and spatial grids, we pre-processed the CMIP6 output before reading it as input in the conceptual model. For each CMIP6 model, we first compute the mean over all ensemble members of the same model. These model means are then interpolated from their original spatial grid to a $1^\circ \times 1^\circ$ latitude-longitude grid with second-order conservative remapping (Jones 1999). For $\Delta PV$, we first calculate the mean annual cycle of $\Delta PV$ for each model between two time periods and then calculate the CMIP6 multi-model mean. Retaining the information on the temporal changes per model allows us to assess the degree of model agreement in trends across the CMIP6 ensemble. All changes are computed for each SSP against PD and for PD against PI.

Our regional means are computed as spatial averages for seven regions, namely Europe, North America, South America, South Africa, Northwest Africa, India, and Southeast Asia, to allow a more detailed assessment of month-to-month changes. The regions are chosen for their regionally different results in $\Delta PV$. Some of the regions are known for high (dust) aerosol optical depth, which inspired us to use for these cases regions as in Pu and Ginoux (2018). Additionally, we include North America and Europe due to, as we will see in the results, the strong influence of cloud changes. The margins of the regions are listed in table B2 and marked in figure 3.

The globally averaged multi-model mean change in PV power potential for present-day (PD) against the pre-industrial (PI) has decreased and is primarily explained by the reduced surface irradiance due to regionally different pronounced aerosol increases. We list the spatial and temporal mean changes in the PV power potential ($\Delta PV$) and the contributing terms in table 1. From PI to PD, $\Delta PV$ indicates a reduction in the global multi-model mean PV potential by $-1.7\%$. Over land, where the majority of PV modules are located, the multi-model mean of $\Delta PV$ is more pronounced with $-2.4\%$. The dominating contribution to the reduction in the PV potential for PD against PI stems from the increase of aerosols due to anthropogenic activities ($\Delta PV_{\mathrm {aer}}$). For instance, sulfur dioxide, black carbon, and organic carbon emissions increased by several Tg yr⁻¹ from 1850 to 2010 (Zhang et al 2016). Emissions of anthropogenic aerosols led to reduced irradiance at the surface (Wild 2009). We estimate a contribution of the anthropogenic aerosol increase to $\Delta PV$ of $-1.3\%$ in the global mean and $-2.0\%$ to the land-only mean for PD against PI. The strongest effect is seen over East Asia with up to −13.9% (figure A1) for PD against PI, consistent with the spatial patterns of PD emissions for anthropogenic aerosols. In comparison to the global contribution from aerosols, the contribution by the PI to PD changes in temperature, clouds, and humidity is one order of magnitude smaller (table 1).

Projected negative mean $\Delta PV$ at the end of the century in two of the three scenarios are primarily controlled by the degree of future warming that adversely affects the conversion efficiency of PV modules to produce power. Positive contributions from reduced clouds and negative contributions from increased water vapor largely balance each other. For the end of the century, $\Delta PV$ is projected to be $+0.7\%$ over land for SSP1-2.6, but $-0.7\%$ and $-2.4\%$ for SSP2-4.5 and SSP5-8.5. On the one hand, this is due to the negative impact on PV power production from the projected temperature and humidity increases at the end of the 21st century. Their combined negative contributions become stronger from SSP1-2.6 ($-1.8\%$) to SSP5-8.5 ($-4.3\%$). Our estimates for the increased contribution of water vapor with warming are consistent with the fact that a warmer atmosphere can contain more water vapor (Held and Soden 2006) causing more attenuation of shortwave radiation (Mani and Chacko 1980). On the other hand, the positive impact of reduced aerosols decreases as we go from SSP1-2.6 ($+1.5\%$) to SSP5-8.5 ($+0.1\%$), while $\Delta PV_{\mathrm {cloud}}$ increases from $+0.7\%$ in SSP1-2.6 to $1.9\%$ in SSP5-8.5. Interestingly, there are model-to-model standard deviations in $\Delta PV_{\mathrm {cloud}}$ of $0.9\%$ for SSP1-2.6 and $1.4\%$ for SSP5-8.5, which are similar in magnitude to the mean $\Delta PV_{\mathrm {cloud}}$, indicative for relatively large model diversity in representing cloud changes. That result reflects the grand challenge of simulating clouds with CMIP-class models (Bony et al 2015).

The degree of warming to a given radiative forcing is controlled by the climate sensitivity, which remains uncertain in CMIP6 (Zelinka et al 2020). CMIP6 includes models with a higher climate sensitivity than was the case in CMIP5, although the difference in the climate sensitivity between CMIP5 and CMIP6 is statistically insignificant (Zelinka et al 2020). CMIP6 models project warmer climates for a given radiative forcing, e.g. higher summer temperatures over Europe (Palmer et al 2021). One could expect weaker signals for changes in the potential for PV power production from models with smaller climate sensitivity. Specifically, the changes in $\Delta PV$ associated with temperature changes, which are particularly pronounced for the change between SSP5-8.5 against PD, would be weaker for a smaller climate sensitivity. Reasons for the model diversity in climate sensitivity are thought to arise from model differences in cloud feedbacks (Myers et al 2021) and in ocean heat transport (Singh et al 2022). Cloud properties additionally influence the shortwave radiation transfer with an impact on $\Delta PV_{\mathrm {cloud}}$. Model differences in $\Delta PV_{\mathrm {cloud}}$ might arise from differently simulated extra-tropical low-level cloud cover responses associated with the climate sensitivity (Zelinka et al 2020).

The spatial patterns of $\Delta PV$ for the future projections SSP1-2.6, SSP2-4.5, and SSP5-8.5 are mainly explained by the combined impact of $\Delta PV_{\mathrm {cloud}}$ and $\Delta PV_{\mathrm {aer}}$ (figure 1). Changes in temperature and humidity lead to a global reduction in PV potential that does not strongly change from one region to the next. The regional magnitude of $\Delta PV$ rather depends on irradiance changes due to clouds and aerosols that in some regions enhance and in other regions compensate for the adverse impacts on PV power production arising from the temperature and humidity increases. Regionally positive $\Delta PV$ in the northern hemisphere are consistent with other future estimates of changes in PV power potential on land (e.g. Gernaat et al 2021).

Zoom In Zoom Out Reset image size

The pattern of $\Delta PV_{\mathrm {aer}}$ over land is consistent with irradiance changes that one would expect from future changes in anthropogenic aerosols (figures 1(c), (f) and (i)). In all SSPs, the anthropogenic aerosol optical depth (AOD) decreases over East Asia, Europe, North America, and Australia from PD to the end of the 21st century (Gidden et al 2019). This decrease is most pronounced in SSP1-2.6, weaker in SSP2-4.5, and smallest in SSP5-8.5. An exception is the anthropogenic AOD over Central Africa, where the values are similar in SSP1-2.6 and SSP2-4.5 compared to PD but the values increase in SSP5-8.5 (Fiedler et al 2019). Aerosols change the attenuation of shortwave radiation (Eltbaakh et al 2012), i.e. lower (higher) AOD leads to increasing (decreasing) shortwave radiation at the surface. This is broadly consistent with the positive $\Delta PV_{\mathrm {aer}}$ over China, Europe, North America in all SSPs against PD, and with the negative $\Delta PV_{\mathrm {aer}}$ over Central Africa for SSP5-8.5 against PD. Over China, the reduction of $\Delta PV_{\mathrm {aer}}$ seen for PD against PI is projected to be substantially weakened by the end of the 21st century with a positive $\Delta PV$ of up to $+16\%$ in SSP1-2.6 and up to $+12\%$ in SSP5-8.5. Individual CMIP6 models qualitatively agree on the sign of the aerosol contributions due to similarly prescribed anthropogenic aerosol emissions or concentrations, indicated by the spatial correlation coefficients for $\Delta PV_{\mathrm {aer}}$ across the models with values around 0.9 for SSP1-2.6, 0.85 for SSP2-4.5 and 0.8 for SSP5-8.5 (figure 2).

Zoom In Zoom Out Reset image size

Over most land regions, $\Delta PV_{\mathrm {cloud}}$ is positive in all SSPs against PD. Over Europe and South America $\Delta PV_{\mathrm {cloud}}$ increases from SSP1-2.6 to SSP5-8.5 from values around $+1\%$ to more than $+4\%$. The spatial correlation and the root-mean-square-differences (RMSD) across the CMIP6 models for $\Delta PV_{\mathrm {cloud}}$ indicate relatively larger model differences than for the other components affecting $\Delta PV$. These model differences in $\Delta PV_{\mathrm {cloud}}$ become larger with warming, as seen by comparing the different scenarios (figure 2). This behavior indicates model-dependent responses of clouds to future warming with adverse impacts on the capability to assess future PV power from CMIP6 simulations.

Interestingly, there is negative $\Delta PV_{\mathrm {cloud}}$ over polar regions in contrast to positive signs in most other world regions. Around Antarctica, $\Delta PV_{\mathrm {cloud}}$ has values of up to −5%, −7% and −12% for SSP1-2.6, SSP2-4.5, and SSP5-8.5, respectively (figure 1). Moreover, the regional $\Delta PV_{\mathrm {aer}}$ around Antarctica is negative in all SSPs compared again PD, which coincides with higher surface wind speeds in the Southern hemisphere mid-latitude storm track (Priestley and Catto 2022) indicative of more sea spray aerosols (not shown) and therefore regionally higher aerosol optical depth. This regional change in winds could be associated with changes in the large-scale circulation, e.g. the broadening of the Hadley Cells, which is positively correlated with global warming (Frierson et al 2007, Nguyen et al 2015, Zhou et al 2020, Hur et al 2021). Also in the Arctic, negative $\Delta PV_{\mathrm {aer}}$ occur in SSP5-8.5 paired with a particularly strongly negative $\Delta PV_{\mathrm {cloud}}$, indicative for regional changes in $\Delta PV$ being at least in parts driven by irradiance changes due to aerosols and clouds and not primarily the large regional $\Delta PV_{T}$, due to Arctic amplification, through the temperature influence on the conversion efficiency of PV modules (e.g. Kawajiri et al 2011, Gernaat et al 2021).

Taken together, the future spatial patterns of $\Delta PV$ are qualitatively similar to PD, but the regional magnitudes depend on the CMIP6 scenario (compare figure 1 against figure A1). Future mean PV power potentials might most strongly decrease in polar regions, over the tropical oceans, western North America, and northern Africa, while an increasing potential is projected for Europe, eastern North America, and China. Our results for the future $\Delta PV$ are consistent with regional results from other studies. For instance, the positive $\Delta PV$ with warming over European regions is consistent with regional studies (Crook et al 2011, Gaetani et al 2014, Wild et al 2015, Müller et al 2019, Feron et al 2020, Hou et al 2021). For western North America, we find that the PV potential is decreasing for SSP5-8.5 because of the dominating effect of rising temperatures and humidity, consistent with another projected reduction of PV potential (Crook et al 2011).

Understanding seasonal differences in PV power production is important to satisfy the seasonally varying electricity demand, e.g. for heating in winter when irradiance is naturally lower than during summer. We find that regional changes in the annual cycle of $\Delta PV$ from PI to PD is dominated by changes in aerosol-induced changes in irradiance (figure 3). A change in the annual cycle of $\Delta PV_{\mathrm {aer}}$ is evident over Europe, North America, and Northwest Africa, with a maximum absolute change in summer when irradiance and AOD are high (compare figure 3 against figure A2). In contrast to the mid-latitudes, $\Delta PV_{\mathrm {aer}}$ shows a constant offset of −3% to −5% independent of the month over sub-tropical regions of Southeast Asia and India where seasonal changes in irradiance are smaller than at higher latitudes.

Zoom In Zoom Out Reset image size

The reduction of PV by aerosols since PI is reversed in almost all regions for SSP1-2.6 and to a lesser extent for SSP2-4.5 and SSP5-8.5 (figure 3). An exception is Northwest Africa, where the aerosol load increases in SSP5-8.5 and reduces the PV potential, especially in the summer months when the temperatures are the largest and the demand for electricity for cooling is potentially high. Here, dust aerosols play a major role in the regional aerosol burden, yet the response of dust emissions in a warming world is insufficiently understood from CMIP-class models (Evan et al 2014, Kok et al 2023). We infer that our estimate of the regional contribution to the PI to PD change in the $\Delta PV$ over Northwest Africa is conservative, given that observed changes in dust aerosols are larger than simulated by the models (Kok et al 2023).

From PD to the future scenarios for 2070–2100, the change in the annual cycle of $\Delta PV$ due to clouds ($\Delta PV_{\mathrm {cloud}}$) is largest in summer in northern hemisphere mid-latitudes with again impacts scaling with the degree of warming (figure 3). In the mid-latitudes, we also see a summertime negative contribution from humidity ($\Delta PV_{q}$) and temperature ($\Delta PV_{T}$) partially balancing the positive $\Delta PV_{\mathrm {cloud}}$ in Europe, North America, and China. The large contribution of $\Delta PV_{\mathrm {cloud}}$ in the mid-latitudes during summer makes here the response of clouds to warming crucial to project $\Delta PV$ in summer when temperatures are the highest and hence the electricity demand might be increased, e.g. for operating cooling systems during heat waves.