Impacts of solar intermittency on future photovoltaic reliability

As photovoltaic power is expanding rapidly worldwide, it is imperative to assess its promise under future climate scenarios. While a great deal of research has been devoted to trends in mean solar radiation, less attention has been paid to its intermittent character, a key challenge when compounded with uncertainties related to climate variability. Using both satellite data and climate model outputs, we characterize solar radiation intermittency to assess future photovoltaic reliability. We find that the relation between the future power supply and long-term mean solar radiation trends is spatially heterogeneous, showing power reliability is more sensitive to the fluctuations of mean solar radiation in hot arid regions. Our results highlight how reliability analysis must account simultaneously for the mean and intermittency of solar inputs when assessing the impacts of climate change on photovoltaics.

: please elaborate a bit on the climate differences between Romania and UAE (evident in the K distribution).   L. 196: the wording 'wet regions' is inaccurate. For instance Europe and Southeast C hina are not wet in the same way. You should refer to climatic zones, such as Tropics, monsoonal regions, subtropics, mid-latitudes. L. 199-200: your statement about wet regions is too simplistic. For instance, while subtropics are actually projected to be sunnier in the future, higher latitudes are expected to be cloudier because of the shift in the mid-latitude storm track (see e.g. Gaetani et al. 2914Gaetani et al. , https://doi.org/10.1016Gaetani et al. /j.rser.2014. Reviewer #3 (Remarks to the Author): General comments: The paper provides valuable insights into the future projections of solar energy production. The authors proposed to use the "Loss-of-load probability" functional to assess the availability of solar energy at future climate conditions. Based on the satellite observations and IPC C model outputs, they were able to make a PV-panel lifetime (30-year) projection that accounts for the intermittency of the renewable energy source. The paper is well written and could be published after a minor revision.
Specific comments: L50: I think you should talk about the "scattering and absorption" of radiation by all optically active constituents in the atmosphere.   Figure 2 is about 1%. It means that in Figure 4, the effect of different sensitivities is small. Please comment on this.
L323-324: The surface fluxes are not directly measured from the satellite.
L334-336: Dust in the atmosphere will affect incoming solar radiation. This can not be controlled by regular maintenance.
The authors put forward the impacts of solar irradiance variations in relation to the future PV reliability. The intermittent character of solar and wind power is well known. It is not clear if this work will aid scientists since even nowadays large storage projects are increasing in both number and capacity, substantially reducing the impact of solar variability. Forecasting solar irradiance and wind speed hours or days ahead aids the system operators for stable grid operation. Thus, I invite the authors to revise their manuscript to address specific concerns detailed below.
We thank the reviewer for his/her insightful and constructive comments. In general, we agree with the reviewer that power storage and weather forecast can substantially reduce the impacts of intermittent solar power.
However, these solutions apply to existing plants under stationary climatic conditions, where the system operator is called to use solutions like storage, curtailment, or load shaping to mitigate shortterm (from few seconds to days) effects of weather variability and intermittency (Ela et al. 2013;Perez et al. 2016).
In contrast, having simple and robust statistics for the assessment of solar resources at decadal timescales, such as the one proposed here, could help us improve the long-term performance of PVplants, optimize grid-design and operation, and analyze the tradeoff between mitigation practices (power storage, curtailment, load-shaping, geographic dispersion etc.) and reliability.
In the revised manuscript, we stressed the importance of prediction in managing the impact of variability, at least in the short term. We also emphasized the importance of power storage and explained the unique values of our long-term statistical analysis of solar radiation.
This work is practically based upon climate model outputs, but validation data are not detailed. This is clearly important since otherwise this work is not justified. The reader should not search other papers to consider the differences between the models, what were the input parameters, their importance, which is the sensitivity of the models to those parameters, Thanks for the comment. We have better justified our work and detailed our validation. First of all, we better explained the implicit bias corrections already done in the previous version.
Climate model may exhibit systematic biases which usually need to be corrected before being used for climate change impact assessment (Stocker 2014). One of the basic bias-correcting methods is to correct the model outputs by using the differences between historical reference data from the model and observations (Hawkins et al. 2013). This bias correction was implicitly conducted in our analysis as we focus on the change of solar radiation (rather than the absolute values) from climate model outputs. This is now better explained and emphasized in the revised manuscript. Furthermore, in the new version, we provided more information regarding the data accuracy, as the reviewer suggested. To this purpose, we compared the climate model outputs to the satellite-derived products and large-scale reliable datasets. The results show that, while presenting some biases, climate models likely have the same order of accuracy as those reliable data. These results were included in the revised manuscript and reported below.
There are only limited numbers of long-term high-quality observations of solar radiation. For example, Observations of solar radiation from WCRP Baseline Surface Radiation Network (BSRN) collected from 58 stations are highly sparse. Other observational networks are extremely local in nature (e.g., Atmospheric Radiation Measurement Climate Research Facility of US Department of Energy, UO SRML, Sudi Network). Up to date, it is one of the biggest challenges to validate the global solar irradiance and surface energy balance in the climate science community (Trenberth et al. 2009;Wild et al. 2015). For this reason, we used the National Solar Radiation Database (NSRDB), which was produced by using ground observations, satellite data, and/or meteorological models. It covers the whole United States and argued to be one of the most reliable datasets for assessing the long-term spatial and temporal variability of the solar resource (Sengupta et al. 2018).
Two typical outputs with different assimilation models, METSTAT and SUNY, are achieved in NSRDB (https://rredc.nrel.gov/solar/old_data/nsrdb/) and both are recommended by NREL. We compared SUNY and METSTAT during 2001-2010 when both products are available (see Figure 1a and b). Of 1415 sites over the United States (sites with missing data are excluded), the root mean square errors (RMSE) between these two outputs are around 0.05, which may be considered as the systematic biases from NSRDB. When further compared these measurements with satellite data (CERES SYN) in the same locations during the same period (see Figure 1 c, d, e, and f), one finds similar ranges of RMSE, suggesting that the satellite products are as accurate as these reliable data. Next, we compared the long-term clearness index from the satellite data and the climate model outputs during 2006-2015 averaged at 280 km equal-area grids over the world (Table 1, Figure 2, and Figure 3). The RMSE for some climate models (e.g., CCSM, GFDL) are similar to these SUNY-METSTAT differences from NSRDB, while for others the RMSE is at least of the same order of magnitude. For this reason, we use climate model outputs to assess the future power reliability in this study but also remind the readers of the uncertainties in the results. Table 1 Root mean square error (RMSE) between climate model outputs and satellite data as shown in Figure 2 and     Thank you for pointing this out. The period 2041-2050 is chosen to be consistent with the lifespan of solar panels. This was clarified in the revised manuscript.
As shown in Figure 4 below, the sensitivity of loss-of-load probability (L s ) calculated from the data at various time periods is similar. This is accounted for by the relatively invariant  relationships, as shown in Figure 5. The  relationship has long been identified in the solar energy industry and used for sizing the solar system (Liu and Jordan 1960;Klein and Beckman 1987). Here, we further tested this relationship under future climates and used it to inform us how the intermittency of solar radiation would change along with the change of the mean radiation (i.e., L s ). We added these figures in the supplementary materials to explain these invariant characteristics.  Line 62. The adopted K d values are not detailed to the reader.
We added the detail of K d . We explain K d is the value of K that is just enough to satisfy energy demand. The adoption of K d , along with the distribution of K, allows us to define the loss-of-load probability.
Line 99. "While the solar radiation in Europe is projected to decrease in January and increase in July, the radiation in Middle East decreases in both months.". Explain why this happens. (also related to Line 195 below) Thank you for the suggestion. Our research group, in collaboration with Lucarini's group (University of Reading), has analyzed the changes in rainfall seasonality over the world (Feng et al. 2013;Pascale et al. 2015Pascale et al. , 2016. These results help explain the change in solar radiation. In particular, we quantified rainfall seasonality by relative entropy, which has lower values for more evenly distribution rainfall over the year. Figure 3 of Pascale et al. (2016), reported below in Figure  6, shows that the relative entropy tends to increase in the Mediterranean regions. The change of seasonality means more rain in winter and less in summer, which explains the decrease in solar radiation in January and increase in July. Note that understanding the climate seasonality is a challenge for climate science because it requires knowledge of the large-scale weather system such as monsoons, the Hadley Cell, mid-latitude/tropic cyclones, and their responses to the rising greenhouse gas concentration.
The decrease in solar radiation in the Middle East may be associated with large-scale circulation (Gaetani et al. 2014), cloudiness trends (Yousef et al. 2020), or the positive Aerosol Optical Depth (AOD) trend already documented over large parts of the Middle East for the period 2001 to 2012 (Klingmüller et al. 2016). We cited these results to explain the change in solar radiation in the revised manuscript.
  Line 119. Section "Quantifying sensitivity of power reliability to climate change". The authors state "To systematically assess this linkage, we consider in detail satellite data as well as climate model outputs under the historical climate conditions (see dark color curves in Figure 3a and Supplementary Fig. 3)." It is important for the reader to understand the physical causes behind this behavior of the parameters and not just see plots of some parameters.
Great suggestion. We now provide physical interpretation for the distribution of clearness index as detailed below. Solar radiation is reflected, scattered, and absorbed by clouds, aerosols, water vapor, and other optically active constituents. Not all of the scattered radiation is lost and part of it eventually arrives at the surface of the earth in the form of diffuse radiation. The diffuse radiation has maximum intensity when the concentrations of optically active constituents are moderate, neither reflecting too much solar radiation back to the outer space or allow most of radiation reaches the Earth surface as direct radiation (see Fig.5 in Liu and Jordan 1960, reported below in Figure 7). The diffuse radiation also has the largest variations for moderate concentrations of optically active constituents, whose dynamic behaviors control the scattering of solar radiation. Since global horizontal irradiance (GHI) is the sum of direct and diffuse radiation, it is logical to expect largest variations of GHI or clearness index (i.e., ) for moderate monthly mean clearness index (i.e., ) as presented in Figure 3 of the manuscript.

[REDACTED]
In the revised manuscript, we cited the reference and explained the figures by using the relationship between direct and diffuse radiations. Line 166. Fig. 4. Given the nature of the paper and the uncertainty in the climate models, it is not necessary to quote numbers to the third decimal.
Done. Thank you for the reminder.
Line 195 "Discussion". ".. power reliability is less sensitive to mean solar radiation in wet regions (e.g., Europe, Southeast China, Southeast United States) and more sensitive in dry regions (Middle East and Northern Africa).

". It is important to explain this performance and not just quoted. Such information is important to see if mitigation measures can be considered.
We agree. We did not explain this point very well in the original manuscript, but now have clarified it in the revised manuscript. To explain the geographical patterns, we analyzed the behaviors of the reliability sensitivity function (see Figure 4 above). This sensitivity, expressed as a function of  and LOLP at the design period, has higher absolute value for larger  . These characteristics suggest higher sensitivity of power reliability in regions with lower cloud optical depth (e.g., Middle East and Northern Africa) and lower sensitivity of power reliability in regions with higher cloud optical depth (e.g., Europe, Southeast China, and Southeast United States).
Line 342. The authors refer to "For a power system with daily storage capacity, LOLP" but no data are given about the battery model since this is directly related to the input energy (from Sun-PV) and output energy (to the loads). Clarify.
We clarified this and referred to a popular PV software, PVGIS (https://ec.europa.eu/jrc/en/pvgis), which includes the solar radiation input, the energy conversion efficiency, the state of the battery, and loads (Huld et al. 2017;Huld 2017). One of the output variables "percentage of days the battery became fully discharged" has been used to quantify the reliability of the PV system and is the same metrics "LOLP" used in our study. We have revised the manuscript to reflect this point.
Section "Methods". Temperature typically accounts for, roughly, a less than 10% annual energy loss depending on the site. However, since this work performs a global search it should consider temperature effects. Roughly speaking, a 5-7% change between south African countries and northern European countries is expected in normalized energy production.
The reviewer is right. Temperature influences the energy conversion efficiency and can have significant impacts on power generation in hot climates (Dubey et al. 2013) . It is estimated that photovoltaic power output reduces by 0.45% for each degree increase in temperature (Fell et al. 2015;Patt et al. 2013). Therefore, we may treat the temperature rising as equivalent to the increase of power requirement in our original framework and redefine the parameter K D as where the temperature factor, T  , is about 0.0045, T r is the reference temperature, and , Dr K is the specific value of K that is just enough to generate the demanding energy at the reference temperature. With this change, the corresponding LOLP becomes, The change of LOLP from current to future climate conditions can be expressed as where , () 11 This expression suggests that the change of LOLP has two parts. This first part has been analyzed in the original manuscript and the second part can also be obtained analytically once we have the distribution of K. The sensitivity for temperature, L T , is always positive (see Eq. (4)), meaning that rising temperature increases the loss-of-load probability. It should be noted that the temperature impacts on photovoltaic power generation appear much weaker than the solar radiation impacts over the lifespan of photovoltaic modules (Gaetani et al. 2014). However, the rising greenhouse gas concentration may increase the near-air temperature in most of the regions over the world, thus reducing the photovoltaic power generation and the power reliability.
We added these analyses in the Methods section and discussed the impacts of rising temperature on power reliability in the manuscript. Line 78. Change "panels" to "modules" Done. We thank the reviewer again for the constructive comments.

Review of the paper "Impacts of Solar Intermittency 1 on Future Photovoltaic Reliability" by Yin and co-authors, submitted for publication in Nature Communications.
The paper tackles the problem of solar energy availability in future climate, assessing the relative importance of changes in mean and intermittence for photovoltaic power reliability at global scale. Yin and co-authors highlight that the sensitivity of power reliability to fluctuations of mean solar radiation is geographically inhomogeneous. In particular, regions with the highest solar insolation will be affected by largest fluctuations and reduced reliability. The paper is well written in a clear and concise manner, figures are effective in delivering key information. The methodology is well described, mathematics and statistics are properly used, and conclusions follow from evidence. The paper has value, especially in the context of the current and future climate change, with renewable energy playing a crucial role in the effort for mitigating global warming. However, before recommending the paper for publication, I believe that some important issues in the study should be addressed.
We thank the reviewer for the positive comments and encouragement. We have used these suggestions to improve the manuscript as addressed below.

Major point
The estimation of future loss-of-load-probability sensitivity (Ls), which gives an indication of the photovoltaic power reliability, depends on choice of the pdf shape, in this case the beta function. However, the choice of using beta function at the global scale does not appear fully convincing.
Two papers cited as reference in the Methods section (Bendt et al. 1981;Hollands et al. 1983) actually focus on the US. In Fig. 1, two very specific situations are showed. In Fig. 3 and S3, pdfs of daily clearness index (K) in different regions are displayed, without any indication of the regions where PDFs are derived. This way of presenting PDFs has the merit of being visually clear, but it cannot be used to claim that beta function is the correct fit for K pdfs globally.
The authors should provide quantitative evidence for the pdf choice. I suggest to perform a simple goodness-of-fit test at any location, showing that the beta function is a good approximation at the global scale. To make things simpler, the authors could perform the test at the regional scale, but regions must to be selected carefully to represent the main climatic zones on Earth (e.g. Tropics, subtropics, mid-latitudes). Testing at least another pdf shape would be ideal.
We followed the reviewer's suggestion and conducted goodness-of-fit tests for the clearness index over three main climatic zones, tropics, subtropics, and temperate in both January and July as shown in Figure 8 and Table 2. Using the maximum likelihood estimation, we fitted of clearness index data with beta distributions, which shows certain seasonal variations in the locations at the temperate and subtropics. The p values of the Kolmogorov-Smirnov goodness-of-fit tests are larger than the significance level of 0.05, failing to reject the null hypothesis that the clearness index data come from beta distributions.
It is also important to note that this beta distribution is a parsimonious choice which we prefer to other unbounded ones (e.g., Weibull and extreme value distributions) used in the literature (e.g., Markvart et al. 2006;Kaplani and Kaplanis 2012). However, our framework is not limited to the use of beta distribution but can easily adopt other distributions if they appear more suitable in some regions. In the revised manuscript, we added these statistical tests of clearness index for the representative locations; we also commented on the general framework in this study and its application for various types of distributions.

Figure 8
Probability density function of clearness index. The bars are empirical distribution from CERES data in the month of (a, c, e) January and (b, d, f) July around (a, b) Paris, France, (c, d) Qinghai, China, and (e, f) Manus, Brazil, corresponding to the three main climatic zones of temperate, subtropics, and tropics. The black curves are the fits of the beta distributions using the maximum likelihood estimation. Thank you for pushing us to improve the presentation of the manuscript. We explained that Romania and UAE are chosen to show two contrasting climate conditions and drastically different potentials for solar energy production. Romania, located in the temperate continental climatic zone, shows strong seasonal variations of clouds, whereas Dubai, UAE has a hot desert climate with weak seasonality (see Figure 9 left). The contrasting behaviors of cloud seasonality are also evident in the distribution of clearness index as shown in Figure 1 of the manuscript (reported here in Figure 9 right). In Romania, the distributions tend to be positively skewed in January and negatively skewed in July; in Dubai, the distributions are similar in both January and July.
The choice of Southern Romania also helps us to link the change of clearness index to the change of climate seasonality in future climates. In our previous work, we quantified rainfall seasonality by relative entropy, which has lower values for more evenly distributed rainfall over the year. Figure 3 of Pascale et al. (2016), reported below in Figure 10, shows that the relative entropy tends to increase in the Mediterranean region. The change of seasonality may suggest more rain in winter and less in summer, which explains the decrease of solar radiation in January and increase in July as already shown in Fig. 2 of the manuscript.
In the revised manuscript, we added the cloud seasonality plots in the supplementary material and explained the choice of Southern Romania and Dubai is associated with the contrasting climate conditions.  We now present the cloud seasonality in both Romania and UAE to identify the climate differences in the supplementary material of the manuscript (reported here in Figure 9). We also explain how climate seasonality change may influence the solar power generation in mid-latitude temperate regions (Pascale et al., 2016), while several other factors like changes in large-scale circulation [REDACTED] (Gaetani et al. 2014), cloudiness (Yousef et al. 2020), Aerosol Optical Depth (Klingmüller et al. 2016) and dust transport (Prospero and Lamb 2003) may have an influence in solar energy generation hotspots like the Middle East and North Africa (MENA) region. Figure 2: could you also provide the degree of agreement among climate models on the sign of the change? Same for Fig. S1 and S2.

Done.
Over eleven climate models, eight or more have the same sign of change are marked as dots in Figure 11. The corresponding maps for Fig S1 and S2 are reported in Figure 12 and Figure 13. These maps are similar to these t-test results in the original manuscript, corroborating our analysis of climate change impacts on solar radiation and power reliability. We added these maps as the supplementary materials in the revised manuscript.  We followed this suggestion and clarified that all regions over the world with monthly mean clearness index ranging from 0.3 to 0.7 with interval of 0.05 were selected to plot the probability density function of K and the  relationship. These statistics are relatively invariant in response to changing climate in different periods (see Figure 14). Motivated by these features, we then obtained the analytical expression of the sensitivity of the power reliability, which is the key message of the study.
We did not explain this point very well in the original manuscript, but now have clarified how we plot Figure 3 and showed invariant  relationship in the revised manuscript.

Equation 2: why do you add 100% in the formulation?
Since most previous studies reported changes in solar radiation in percentage, we add 100% to be consistent with other reports. We clarified this in the revised manuscript.  Thank you for the suggestion. Actually we already did this, but we did not explain this approach very well in the original manuscript. Figure 2 in the manuscript (also see Figures 11-13 here) show the climate change impacts on LOLP at global scale using the climate model outputs. These geographical patterns were then explained in a theoretical framework in the rest of manuscript with the assumptions of beta distribution of K and invariant  relationships. Specifically, we revisited our results in line 177-186 for Southern Romania from climate model outputs to justify our proposed theoretical framework.
In the revised manuscript, we also changed the second section titles as "theoretical framework of the power reliability under changing climates" to stress the data-to-theory transition and clarify the logical flow of the manuscript. Fig. 5, also the relationship with Ls is unclear. Please elaborate more.

L. 195: referring to cloud climatology pattern comes out of the blue at this point. You only give a reference and no way to compare with
We thank the reviewer for the suggestion. In the revised manuscript we now clarify that L s in Figure 5 is calculated from our theoretical framework (visualized in Figure 4a in the manuscript and reported below in Figure 15), which is expressed as a function of the monthly mean clearness index. This index accounts for the scattered and absorbed radiation by all optically active constituents in the atmosphere such as clouds. Therefore, L s maps are associated with cloud climatology.

Figure 15
Analytical solutions of L s (As in Figure 4a in the manuscript).

L. 196: the wording 'wet regions' is inaccurate. For instance Europe and Southeast China are not wet in the same way. You should refer to climatic zones, such as Tropics, monsoonal regions, subtropics, mid-latitudes.
Thank you for the suggestions. We referred Europe as the Mediterranean climatic zone and temperate continental climatic zone, Southeast China as the humid subtropics, and Middle East as the arid hot regions.
L. 199-200: your statement about wet regions is too simplistic. For instance, while subtropics are actually projected to be sunnier in the future, higher latitudes are expected to be cloudier because of the shift in the mid-latitude storm track (see e.g. Gaetani et al. 2014Gaetani et al. , https://doi.org/10.1016Gaetani et al. /j.rser.2014.
We thank the reviewer for providing this useful reference. We cited it to explain the climate shift and its impacts on the solar radiation and power reliability.

Reviewer #3 (Remarks to the Author):
General comments: The paper provides valuable insights into the future projections of solar energy production. The authors proposed to use the "Loss-of-load probability" functional to assess the availability of solar energy at future climate conditions. Based on the satellite observations and IPCC model outputs, they were able to make a  projection that accounts for the intermittency of the renewable energy source. The paper is well written and could be published after a minor revision.
We thank the reviewer for the positive comments and valuable suggestions.

Specific comments:
L50: I think you should talk about the "scattering and absorption" of radiation by all optically active constituents in the atmosphere.
The reviewer is right. Clearness index accounts for all optically active constituents in the atmosphere. We revised the text accordingly.

L77-93: Please clarify what data have been used to plot Figure 1. Could you give the estimate of the statistical variability of the mean clearness index?
We use the data from the Clouds and the Earth's Radiant Energy System (CERES) SYN1deg. To estimate the variability of the mean clearness index, we follow the center limit law to estimate the 95% confidence intervals as 1.96 / n

 
, where n is the sample size. The estimated intervals are reported here in Table 3 and added in the supplementary material. Aerosol is a key climate component and remains a significant source of uncertainty in climate modeling largely due to the sparse observations (Su et al. 2013;. We discussed this uncertainty in the last paragraph of the manuscript.

L110-118: How did you calculate the standard deviation to apply the t-test?
We performed the t-test as where the bar refers to the sample mean, n is number of climate models (i.e., 11), s refers to the sample standard deviation and is calculated as This statistical test shows the degree of agreement among climate models. To prove this, we also present additional maps, showing the locations where eight or more climate models have the same sign of change (see Figure 16). These maps, similar to these t-test results in the original manuscript, were added in the supplementary materials of the revised manuscript. Agree. To clarify this, we commented that CERES fluxes are based on model estimates and referred these fluxes as the satellite products or satellite data. Corrected. Figure 2 is about 1%. It means that in Figure 4, the effect of different sensitivities is small. Please comment on this.

Figure 4: The relative change of the mean clearness index in
As noticed by the reviewer, the climate change impacts on sensitivity, L s , is small so that we can calculate the change of LOLP as the multiplication of the change of clearness index by the relatively constant L s . This further justifies the use of first order Taylor expansion to approximate  LOLP. We commented this in the Methods section of the revised manuscript.

L323-324: The surface fluxes are not directly measured from the satellite.
We clarified that these fluxes are based on the column model estimates when we first cited these data.

L334-336: Dust in the atmosphere will affect incoming solar radiation. This can not be controlled by regular maintenance.
Thank you for pointing this out. We meant to suggest the dust on the surface PV module (i.e., photovoltaic soiling) can be removed by regular maintenance. We clarified this in the revised manuscript.

REVIEWER C OMMENTS
Reviewer #1 (Remarks to the Author): The current version has been improved following the comments of all reviewers.
I understand that the authors are active in the field of environmental engineering. However, the proposed work inevitably involves the field of electrical engineering. Technology advances and we do expect significant improvements in the near future in the field of energy storage, smart grids, electric cars in a large scale. All this affect the proposed work. It is clear that the Earth's atmosphere is a dynamic system. It was and will always be one. The authors project weather conditions to the future but do not advance accordingly the ability of storage technologies or other approaches to mitigate weather effects upon energy production. As in other cases, the authors may examine scenarios (business as usual or adopt today's technology on mitigating PV power variability which is the current version of the paper, assume a scenario where e.g. 25% of the variability is mitigated and another scenario where 50% is mitigated). It is expected that global maps of LOLP will be smoother.
Section titles seem to be missing (e.g. Introduction, Data, etc) Reviewer #2 (Remarks to the Author): Review of the paper "Impacts of Solar Intermittency on Future Photovoltaic Reliability" by Yin and co-authors, submitted for publication in Nature C ommunications.
I first thanks the authors for taking into account all my comments and providing detailed responses. The authors addressed all the issues I raised, making new analysis and computations also to respond to the other reviewers' requests, and I feel the manuscript substantially improved and is now ready for publication.
Nonetheless, I'd like to highlight a last minor point that could be still addressed to improve the presentation of the results. In my previous review I asked to perform a goodness-of-fit of the beta function, to make sure this is the best shape on a global basis. The authors presented the results of a Kolmogorov-Smirnov test for 3 locations chosen in different climatic zones. When I asked for a test at regional scale, I actually meant to take averages over large regions, which should be selected to be climatically homogeneous. I understand that this is quite a lot of work and is beyond the scope of the paper, but I think that presenting just three locations, even in different climatic zones, is not really representative. The easiest way to present the goodness-of-fit assessment in a convincing and compact way would be to show a global map with the result of the KS test at each grid point, to make sure that the beta function assumption is verified at the global scale.
Reviewer #3 (Remarks to the Author): The paper deals with a potentially very important issue that could affect the future of the planet. The solar energy is the most significant renewable resource that allows reducing greenhouse emissions. However, a wise decision making on planning and implementation phase is extremely important. The most significant achievement of this study in my view is accounting for solar flux intermittency and in reducing the dimensionality of the evaluation problem to only mean solar radiation. The approximation of f(K), which is fundamental for this purpose, appears to be quite accurate. And this results will stay. Only this would warrant the publication. The prediction of LOLP, however, is as good, as is a prediction of solar surface flux. Solar flux changes depend both on change in cloudiness and aerosol radiative effect. Both of these factors are poorly predicted. The authors wisely use the multimodel ensemble to evaluate their changes. All models have to account for the cloudiness effect. What about aerosol prediction? Are all chosen models have interactive aerosols and predict the associated solar deeming? I believe clarifying this minor issue would help to better evaluate the results of this interesting study.

Reviewer #1 (Remarks to the Author):
The current version has been improved following the comments of all reviewers.
We thank the reviewer for his/her insightful comments. We are also glad that the reviewer appreciated our effort in improving the paper.
I understand that the authors are active in the field of environmental engineering. However, the proposed work inevitably involves the field of electrical engineering. Technology advances and we do expect significant improvements in the near future in the field of energy storage, smart grids, electric cars in a large scale. All this affect the proposed work. It is clear that the Earth's atmosphere is a dynamic system. It was and will always be one. The authors project weather conditions to the future but do not advance accordingly the ability of storage technologies or other approaches to mitigate weather effects upon energy production. As in other cases, the authors may examine scenarios (business as usual or adopt today's technology on mitigating PV power variability which is the current version of the paper, assume a scenario where e.g. 25% of the variability is mitigated and another scenario where 50% is mitigated). It is expected that global maps of LOLP will be smoother.
As commented by the reviewer, increasing power storage is an essential approach to mitigate the effects of intermittent solar power. We followed his/her suggestions to provide two scenarios with 25% and 50% reduction of the variability of the clearness index. We then investigated its impacts on the LOLP as reported below.
To address this issue, we proceeded as follows. The impacts of increasing power storage may be modeled by reducing the variability of the clearness index as where the original clearness index K has mean of  and standard deviation of  , and the smoothed clearness index is K b , whose standard deviation becomes where the coefficient b controls the reduction of the variability. Following the reviewer's suggestion, we set b as 0.75 and 0.5 for two scenarios corresponding to the 25% and 50% variability mitigation. We applied Eq. (2) to recalculate the clearness index from 11 climate model outputs during 2041-2050, which were then used to calculate the LOLP numerically. We showed the change of LOLP with no variability mitigation, 25% mitigation, and 50% mitigation in Figure 1. As can be seen, reducing the variability often leads to the decrease of LOLP and thus more reliable power output. These results explain that power storage may mitigate the impacts of intermittent solar power and its uncertainties related to climate change. Note that power storage can only smooth the variability of the power. Regarding the source, when solar power is significantly reduced as in the Middle East, the LOLP also increases even with the variability mitigation (see Figure 1).
We have updated the manuscript to reflect this analysis, adding the variability mitigation scenarios and discussing the effects of power storage. Section titles seem to be missing (e.g. Introduction, Data, etc) Thank you for pointing this out. We added the section titles.

Review of the paper "Impacts of Solar Intermittency on Future Photovoltaic Reliability" by Yin and co-authors, submitted for publication in Nature Communications.
I first thank the authors for taking into account all my comments and providing detailed responses. The authors addressed all the issues I raised, making new analysis and computations also to respond to the other reviewers' requests, and I feel the manuscript substantially improved and is now ready for publication.
We thank the reviewer for taking his/her time to carefully read our manuscript and provide constructive comments. We are also glad that the reviewer appreciated our work.
Nonetheless, I'd like to highlight a last minor point that could be still addressed to improve the presentation of the results. In my previous review I asked to perform a goodness-of-fit of the beta function, to make sure this is the best shape on a global basis. The authors presented the results of a Kolmogorov-Smirnov test for 3 locations chosen in different climatic zones. When I asked for a test at regional scale, I actually meant to take averages over large regions, which should be selected to be climatically homogeneous. I understand that this is quite a lot of work and is beyond the scope of the paper, but I think that presenting just three locations, even in different climatic zones, is not really representative. The easiest way to present the goodness-of-fit assessment in a convincing and compact way would be to show a global map with the result of the KS test at each grid point, to make sure that the beta function assumption is verified at the global scale.
We agree. It is more robust to perform statistical tests of the averages over large regions in different climatic zones over the world. This analysis is now included in the revised manuscript and reported below.
We followed an independent study from Beck et al. (2018) to classify the climatic zones in the 280-km equal-area grids over the world (see Figure 2a). We performed the Kolmogorov-Smirnov tests of the daily clearness index during 2010-2018 in the month of January/July at each grid point averaging over a relatively large area (e.g., within 1000 km radius) and within the same climatic zone. The results show that beta distributions describe well the clearness index in most regions covering 70% of the world (Figure 2 b, c and Table 1). Beta distributions may not be accurate in the Western Sahara in January and in Australia in July. Other distributions tailored for these regions can be directly incorporated into our proposed theoretical framework to analyze the power reliability and will be the subject of future research. Note that the selection of the distributions does not influence the numerical results presented in the first part of the manuscript which directly use the data to calculate LOLP.
We updated the manuscript to add these statistical test results and discuss the adaptation of other distributions for specific locations.  Table 1). (b and c) The black dots show that the clearness index comes from beta distributions as confirmed by the Kolmogorov-Smirnov tests at 0.05 significant levels. The clearness index is collected at daily timescale from CERES satellite products (see Methods) during 2010-2018 in the month of January (b) or July (c) at each grid point averaging over an area within 1000 km radius and within the same climatic zone as identified in (a). We thank the reviewer his/her insightful and constructive comments. As also commented by the reviewer, modelling aerosols and clouds remains the largest sources of uncertainties in climate system ). The future aerosol and greenhouse gas emissions in climate models are prescribed as different Representative Concentration Pathways (RCPs) (Moss et al. 2010). Our results are based on an intermediate scenario of RCP45, which projects the declining of aerosols during the 21th century because of the emission controls (Rotstayn et al. 2014). While future aerosol emissions are prescribed in RCPs, not all models include the indirect effects related to the aerosol-cloud interaction (see Table 2), which could have certain impacts on the prediction of solar radiation (Chylek et al. 2016). However, this aerosol-cloud interaction seems to have limited impacts on the relationship between the mean and standard deviation of the radiation (see Figure 3), which is key to our analysis of power reliability.
We have updated the manuscript to clarify the future aerosol scenarios and the inclusion of indirect aerosol effects in climate models.

REVIEWERS' C OMMENTS:
Reviewer #1 (Remarks to the Author): The manuscript has been improved over the original version and can be accepted for publication.
Reviewer #2 (Remarks to the Author): I thank the authors for taking into account my suggestions and performing more detailed analysis to improve the robustness of their findings. Interestingly, the beta function seems not be fitting for subtropical climates, this could be an aspect to investigate in future research. My last and final request is to report the number of successful KS tests as percentage to facilitate the reading of Table S2. I also suggest to add lines reporting the results for macro climatic zones, namely tropical, arid, temperate, cold and polar. I'm now happy to recommend the paper for publication.
Reviewer #3 (Remarks to the Author): I like the paper and recommend to publish it in its current form Each reviewer comment (italicized) is followed by a response.

REVIEWERS' COMMENTS:
Reviewer #1 (Remarks to the Author): The manuscript has been improved over the original version and can be accepted for publication.
We thank the reviewer for taking his/her time to carefully review our manuscript.

Reviewer #2 (Remarks to the Author):
I thank the authors for taking into account my suggestions and performing more detailed analysis to improve the robustness of their findings. Interestingly, the beta function seems not be fitting for subtropical climates, this could be an aspect to investigate in future research. My last and final request is to report the number of successful KS tests as percentage to facilitate the reading of Table  S2. I also suggest to add lines reporting the results for macro climatic zones, namely tropical, arid, temperate, cold and polar. I'm now happy to recommend the paper for publication.
Thank you for reviewing our manuscript. We have updated the Table S2 to report the percentage and included the macro climatic zones (see the revised table below).