CO2 emissions of nuclear power and renewable energies: a statistical analysis of European and global data

In this paper, we investigate the CO2 emissions caused by nuclear and renewable power generation. The knowledge of the share of coal, gas and oil in electricity generation permits the exact calculation of the related CO2 emissions. In addition, there is a second approach especially within the economic sciences, which applies statistical techniques for the study of the energy-related emissions. The background for these studies is the provision of general political advice and the expectation that political, cultural, or infrastructural considerations guide nations in the preference and choice of specific technologies. In this paper, we are applying both approaches and come to the certain conclusion, that nuclear power is as effective as renewable power in order to reduce the CO2 emissions. Our results are in complete contradiction to a recent publication (Sovacool et al. in Nat Energy 5:928–935, 2020. https://doi.org/10.1038/s41560-020-00696-3). The authors of this paper conclude that nuclear power does not reduce the CO2 emissions, but renewable power efficiently does. In addition, they argue that these two technologies crowd out each other. The possible reason for their claims may result from a specific conditioning of the data. In contrast, our analysis clearly confirms the adequacy of both nuclear and renewable power generation.


Introduction
There are not many technical options for a future carbon-free energy supply. Renewable energies in their different forms will contribute a significant share in a future energy portfolio. Fusion might be a possibility once the development is successfully completed [1]. Realistically, this may happen in the second half of this century. Fossil fuels may still be an option but only in combination with CCS technologies (carbon capture and sequestration), which avoid the release of CO 2 into the atmosphere by storing it underground [2]. However, a global implementation has to overcome many local safety concerns. This is also true for fission, which completes the list of potential CO 2 -free energies. Since decades, fission contributes about 10% to the world electricity demand-less than hydropower but at present, more than wind and solar power together. One major and highly disputed topic is whether CO 2 -free energies-fission together with renewables-can co-exist and jointly form the basis of a future largely carbon-free electricity supply.
Focus Point on The Interplay between Climate and Energy Policies. a e-mail: fritz.wagner@ipp.mpg.de (corresponding author) The nuclear countries are again singled out in the sub-database DBgln. DBgl includes all European countries of DBeu, all nuclear countries outside Europe and has been supplemented by countries listed in the EY Renewable Energy Country Attractiveness Index (Recai) from November 2020 [10] and by those with a high human development index (HDI [11]) and a large population. It is expected that the countries selected along these criteria provide data with specific sensitivity to electricity generating technologies and their characteristics. DBgl also includes the large countries China, USA, India, Russia and Japan, which are the major CO 2 emitters. These countries dominate the statistical analysis because in their frame the parameters of the other countries lump together. DBgl may better allow to reveal secondary drivers searched for by [3], which could influence the evolution of electricity generation technologies beyond their technical specifications.
Like DBeu, DBgl contains data only from 2018. In this sense, we limit ourselves to cross-sectional analyses. Emphasis and interest here are to assess the outcome of the historic development in the country-specific mix of electricity technologies up to the year 2018.

The world database DBw(t)
DBw(t) contains integral world data from the period from 1990 to 2018. The purpose of this database is to carry out a statistical analysis of electricity generation and emission over a longer period of joint evolution.
In the Appendix B, the databases, the data sources, and the data selection procedures are described in detail.

Variables of the databases
Employing correlation and regression analysis the dependencies of CO 2 -emissions on nuclear and renewable power are investigated. In order to avoid a loss of sensitivity regarding renewable versus nuclear electricity generation, we concentrate in this paper on CO 2 emission from electricity production proper. To allow meaningful analysis of widely different countries, CO 2 -emission per capita (CO 2 pc) is defined as response variable; the explanatory variables are the nuclear-and renewable generation fractions f nuc and f res . They are defined in this paper as the ratio of, e.g. annual nuclear energy E nuc /E tot , with E tot being the total electricity consumed in a country in a year. In order to assess possible non-technical actors in the evolvement of electricity supply technologies, the gross domestic product per capita, GDP pc , is traditionally used. In this paper, we additionally involve the fossil fuel fraction f fos for some studies, as fossil fuels are the only source for CO 2 emissions during operation. f fos , f res , and f nuc add up to one.

Analysis of generation and emission data
3.1 CO 2 emissions of key countries Figure 1 introduces into the topic of CO 2 emission and avoidance comparing the emission history of different key countries along with the global development. Plotted is the ratio of CO 2 -emission by electricity generation CO 2_ el and electricity consumption E tot for the period 2000 to 2018. A low value of this ratio (CO 2_ el/E tot ) can be seen as a quality factor of the employed technologies and fuels in electricity generation. The following country-specific observations can be made: Fig. 1 Specific CO 2 emission from electricity generation, CO 2 _el, divided by the total electricity consumption E tot [16] for the countries shown in the legend China: The CO 2 _el/E tot values are high because of the predominant use of coal (at present, about 1000 GW coal power stations are in operation). Nevertheless, this quality factor improves roughly linearly within the considered period. The nuclear and renewable electricity generation increase, in this case predominantly hydroelectricity. Also, the efficiency of fossil power stations improves.
Poland: The use of coal dominates electricity production in Poland (see Fig. 5); the technologies for burning fossil fuels improve, however, and, together with a growing share of renewables, reduce emissions in a rate comparable to the one of China.
Denmark: Denmark started with electricity being predominantly generated by coal but has, as is well known, a successful policy to employ more and more wind energy. This is well borne out by the comparatively steep decrease of CO 2 _el/E tot during the last decade.
Germany: Here CO 2 _el/E tot hardly changed within the 19 years considered in spite of tremendous efforts to expand renewable energies. Indeed, in the period from 2000 to 2018, wind and solar power installations increased from 6 to 104 GW [12]. Unlike the Danish case, this addition of CO 2 -free technologies did not pay-off ecologically because in this period, nuclear power, the other CO 2 -free supply, has been abolished in Germany in steps from 22.4 to 10 GW. Though the electricity mix in Germany changed strongly by nearly 200 TWh of additional renewable energy generation, about half had to be used to compensate the nuclear energy losses (see Sect. 3.3).
UK: A parabolic fit describes the data. The decrease in recent years has been accomplished by the replacement of coal by gas-a process which started already at the beginning of the 90ies and was accelerated by an early introduction of a CO 2 -price system. Now, gas contributes with 40% to UK's electricity generation [13]. The drop of CO 2 _el/E tot in recent years is due to the installation of renewables, favourably offshore wind power.
France: Since decades, electricity generation in France excels with very low CO 2 emission factors thanks to the use of nuclear energy and-to a lesser extent-hydropower (see Sect. 3.3).
World: CO 2 _el/E tot lies slightly above the German quality factor and is similarly constant over the years. Most of the electricity is generated by fossil fuels. In the last 5 years, the coal fraction drops [14]. The world electricity and emission situation will be discussed in Sect. 3.4.3 in more detail.  per capita CO 2  emissions versus tabulated values  made available by IEA [15] for the three data basis of this study. The results from the subsets of nuclear countries are also shown. The solid and dashed lines are fits to the data of DBgl and DBeu. Russia is an outlier Figure 1 demonstrates the reasons for high CO 2 intensities and which measures allow to reduce them. No statistical analysis is necessary for this realisation. UK (like the USA) shows that the replacement of coal by gas is beneficial for the climate-this is obvious and trivial (as long as methane leakage is not considered). The case of Denmark clearly demonstrates the favourable use of renewable energies and the example of France the advantage of nuclear power. Germany demonstrates indirectly the CO 2 reduction effectiveness of both in a case where renewable energy replaces successively nuclear energy thereby mostly nullifying a distinct impact on CO 2 emissions over many years of the transition period.

Calculated CO 2 intensities of the countries in the three databases
With the knowledge of lignite, gas, and oil consumption, the CO 2 intensity of electricity generation can be calculated. Figure 2 compares tabulated per capita CO 2 emissions [15] with calculated ones for the countries of the three databases DBeu, DBgl and DBw(t) and the sub-databases DBeun and DBgln. The calculations are done with fuel-specific CO 2 -intensities (Table 7 of the appendix B). The agreement is very good (apart from Russia), which is not surprising but demonstrates the solidity of the used databases. There is a sufficient understanding of CO 2 emission by fossil fuels, which allows valid predictions and there is no need for statistical assessment to identify the primary agents.

Electricity generation and CO 2 -emission history of France and Germany
France and Germany-neighbours with rather similar economic development, which also share the same basic values and cultural attachments-nevertheless selected totally different technologies for electricity generation in the 70ies of last century. Figure 3 compares primary, unprocessed data for both countries over 30 years, starting with 1970. The three major components of annual generation-fossil, nuclear, and renewable power-are plotted. Long before the year 2000, France reduced the fossil share in electricity generation and replaced it by nuclear power; the remarkable increase in demand after 1980 was predominantly met by The step in the German data at 1979 is an artefact in the sense that from there on-much before German unification-the specifics of electricity generation of the former DDR were included into the public databases nuclear power. In the period considered here, the renewable energy is mostly hydroelectricity with a substantial contribution in case of France (see also Fig. 5). The hydro-share is rather constant indicating that the national potentials are mostly exploited. In contrary to France, Germany met its electricity consumption growth primarily by fossil fuels, mostly by lignite and hard coal.
After 2000 and under the impression of global warming, Germany started to rapidly increase the use of renewable energies, predominantly wind and PV power. As is well known, it was the Fukushima catastrophe-an exogenic shock, which made Germany to change its energy policy again in 2011 with the goal to step out of nuclear energy use till 2022. The corollary of these decisions is that over the last 10 years one CO 2 -free power replaces another one. Only in the last two years the share of fossil power was reduced slightly and the CO 2 emission by power production dropped accordingly. Figure 4 plots the CO 2 emissions from electricity generation of Germany and France over a longer period from 1960 to 2020. This is twice the time span from now to 2050, when the world has to be decarbonised to meet the Paris goals. Compared to Germany, France started this process well ahead and, since decades, avoids the emission of about 300 Mill tons of CO 2 a year. The history of nuclear power development of Germany is compared in Ref. [16].
As national CO 2 emissions can easily be calculated on the basis of fuel-specific emission intensities- Fig. 4 shows also the hypothetical reduction of CO 2 , if Germany had decided to shut down lignite burning power stations in the steps nuclear power was actually abandoned specifically after Fukushima. In 2020, the integral CO 2 savings would have been in the order of 800 Mill tons. Thus, Germany could have avoided the amount of one year of GHG emissions. Fig. 4 Comparison of the CO 2 emission from electricity generation from France and Germany for 60 years. The difference of 300 Mill tons per year is indicated. For Germany, data from two data [35,36] source are plotted. The hypothetical development for the case that electricity production by lignite had been reduced in the steps of nuclear power production is also plotted (red squares)  Figure 6 plots the CO 2 pc emission from electricity generation versus the renewable (res) energy fraction f res . The black dots represent the whole database DBeu; the black solid line is a linear fit to the data. CO 2 pc reduces with increasing f res down to nearly zero emission in case of Norway. The data scatter is high but the coefficient of determination R 2 0.26 tells us that 26% of the variation of CO 2 pc is accounted for by f res . The red dashed line is the fit to the 15 nuclear countries of DBeun. It falls well below the black line. The two blue dashed lines are fits to a reduced number of members from the DBeu database. The dark blue line represents those countries employing a high coal fraction, the lower light blue line countries burning little coal. The border between these two sub-sets is determined by the median of the coal fraction (see Fig. 5). The high-coal line lies above the black trend line of all data of DBeu; the low-coal line is flatter because these countries demonstrate a lower CO 2 level already at a lower f res . Toward f res 1, these curves have to merge, because there is no   The dark blue dotted line is the fit to the subset of DBeu with a coal fraction above and the light blue dashed line with a coal fraction below the median room for the use of coal any longer. This analysis shows that the high variability of the data in Fig. 6 is more systematic than arbitrary. Table 1 summarises the slopes of the fit lines and the R 2 values of Fig. 6-CO 2 pc versus f res -for the total databases DBeu and the one restricted to nuclear countries, DBeun. For both cases, CO 2 pc decreases with increasing renewable fraction.

European databases DBeu and DBeun
We repeat this analysis but now with the nuclear power fraction f nuc as independent variable. This part is restricted to the 15 nuclear countries of DBeun. Figure 7 plots CO 2 pc versus the nuclear fraction, f nuc . Like in case of renewables, we observe a reduction of CO 2 emission by nuclear power with similar slopes and relevance. The key analysis parameters are also summarised in Table 1. Outliers in Fig. 7 are the data points of Czech Republic and Table 1 Linear fits yield slope coefficient and parameter of determination, R 2 , to the relation CO 2 pc versus the renewable fraction f res or the nuclear fraction f nuc , respectively, for the two European databases DBeu and DBeun All European countries, DBeu Nuclear countries, DBeun Switzerland though they share nearly the same nuclear power fraction of f nuc~0 . 35. The high emission value of the Czech Republic is due to a high fossil fraction of 50% whereas Switzerland additionally employs hydropower with a share of 55% (see Fig. 5). The fits to the sub-data sets-high-and low-coal fractions-are also plotted. There is a distinct difference in CO 2 emission between these two classes, which will be picked up again in Sect. 4.5.
We confirm that the scattering of the data is rather systematic and not of statistical origin.
Removing the a-typical countries-three with a coal-share > 30% and Switzerland-increases R 2 from 0.20 to 0.34. Table 2 summarises the correlation coefficients between the different variables. Dependences on the nuclear fraction, f nuc , can only be identified employing DBeun. Otherwise, the data are affected by the variable distribution along the f nuc 0 axis and countries without nuclear power would co-define the relation between CO 2 pc and f nuc . Because of the small sample size and the larger number of independent variables, the results are rather suggestive than significant in some cases. The coefficient of determination, R 2 , and the p value allow qualifying the statistical description of a setting. The obvious correlation between CO 2 emis- The correlation is carried out for the variables of relevance here-CO 2 pc as response variable for the regression analysis and the global domestic product per capita, GDPpc, the nuclear (f nuc ), and renewable fractions (f res ) as independent variables and, for completion, the fossil fraction f fos . This table corresponds to Table 1 of [3]. p values are classified in the standard form: ***p < 0.001; **p < 0.01; *p < 0.05 sion and fossil power fraction, f fos , is clearly reproduced in both databases. The correlation coefficient is positive and about 50% of the variance is caught by the regression with f fos . The p value is lower in case of DBeu because of the larger number of countries in this database.
The following observations are made: (1) The global domestic product per capita, GDPpc, does not correlate with CO 2 pc with any statistical relevance. GDPpc correlates only with f res in a noteworthy manner. The positive correlation can be interpreted in the sense that wealthier European countries could afford to invest more into renewable energies. (2) Like renewable energy, nuclear power correlates negatively with CO 2 pc. The dependence of CO 2 pc on f res is stronger and more significant within DBeu than DBeun with 26 instead of 15 data samples. The analysis of the European nuclear countries yields a fairly symmetric reduction in CO 2 emission by nuclear power or renewable power, respectively. We conclude that both technologies qualify as clean CO 2 -free energies.
(3) f nuc and f res are negatively correlated, which has been interpreted in [3] as "mutual crowding out" of these two technologies. But in case of the European countries the statistical criteria do not attribute any significance to this correlation.
Next, we analyse the databases DBeu and DBeun by linear multiple regression in the hierarchical fashion as adopted in [3]. The dependent variable is in all cases CO 2 per capita emission (CO 2 pc). As independent variables, we single out the gross domestic product per capita (GDPpc) and the generation shares of nuclear (f nuc ) and renewable (f res ) energies. For special issues, we also employ the fossil energy share, f fos . The analysis will be carried out in 4 steps. The first step is the regression with GDPpc, the first independent variable. Though this parameter has turned out not to carry any relevance (see Table 2) we add it to maintain the parallelism to [3]. In the second step f nuc , in the third step f res is added. The ansatz of In this step, two moderators are involved to test the strength of the main effects of f nuc and f res on CO 2 pc. bi are the regression coefficients; e represents the remaining error. All parameters have been z-standardised. Table 3 shows the main results from the regression analysis which can be summarised as follows: (1) GDPpc is not a significant variable for CO 2 pc (see Sect. 4.2); the parameter of determination, R 2 , is small; the p value indicates that the null hypothesis cannot be excluded. A black-box use of standard stepwise regression [17] identifies f nuc and f res as the only significant explanatory variables. Obviously, the selected European countries are representatives of a comparably homogeneous economic region with regard to their energy mix. In order to explore the role of GDPpc in more detail, DBeu was split by the median into two groups. Both groups-characterised by low or high GDPpc-benefit emission-wise from the use of nuclear energy. In all cases, CO 2 pc decreases with f nuc . (2) R 2 increases in a distinct step by R 2 0.23 (DBeun) as soon as the nuclear fraction is included and in another distinct step when f res is additionally added, whereas the dependence of CO 2 pc on GDPpc becomes weaker and loses further significance (p value increases). In case f res instead of f nuc is first to follow GDPpc, R 2 0.08. Both parameters are able to improve the predictability of the dependent variable.  DBeu benefits from the larger number of data samples (26 instead of 15) but suffers from a lack of balance between data contributing to f res and those to f nuc . In this data array, 11 countries show f nuc 0. Nevertheless, the outcomes of DBeun are more-or-less confirmed by the analysis of DBeu.

Global databases DBgl and DBgln
The bar plot Fig. 8 introduces the countries of DBgln (as listed in Appendix A). The parameters selected are f nuc , the hydroelectricity fraction f hydro , the coal and gas fractions f coal and f gas . The graph displays directly the emissions of the different electricity generation technologies. The countries are ordered according to their CO 2 pc emissions in ascending sequence (see top scale). It is obvious that a large hydro and nuclear fraction gives rise to low emissions. The most prominent cases are Brazil with a high renewable and France with a high nuclear fraction. Brazil has a very low nuclear share (2.6%) but the CO 2 pc is nevertheless low thanks to a high f hydro 0.65. Switzerland and Sweden demonstrate that the combination of nuclear and hydro-generation pays-off in low emissions. Coal dominates toward higher CO 2 pc emissions whereas the use of gas with a lower CO 2 emission intensity (see Table 7 in Appendix B) leads to placements more in the middle of the diagram. This is all comprehensible. India represents an exception because its position seems to be wrong as it is on the low-CO 2 pc side with a high coal fraction. The reason is simply that the abscissa is ordered according to CO 2 per capita emissions, the dependent parameter used in many similar studies [26,27, and references therein]. The location of India in this plot is not due to low-CO 2 emission technologies employed rather due to its large population. The choice of CO 2 pc as dependent variable favours large populations with the association of clean electricity generation. Indeed, the ratio of f res /f nuc increases with population introducing a bias favouring f res for low emission. This topic will be picked up again in Sect. 4.2.
The statistical processing of DBgl and DBgln yields the following correlation and regression results:

Correlation results:
In agreement with the analysis of the European countries: (1) CO 2 pc increases clearly with f fos ; (2) both f nuc and f res show a relevant and strongly negative correlation with f fos ; (3) GDPpc is not a relevant variable for per capita CO 2 emission; (4) both for DBgl and DBgln, f fos and GDPpc show a strong and substantial negative correlation: the larger GDPpc is, the lower seems to be the use of fossil power; (5) f res correlates positively with GDPpc-as identified in the European databases and interpreted there; (6) f nuc and f res are not correlated; Unlike the European database, f nuc correlates positively with GDPpc though without statistical relevance. This is only mentioned here to stress the lack of credibility of the sign of correlation coefficients under conditions of missing significance.

Regression results:
(1) The regression coefficients with CO 2 pc as dependent and f nuc and f res as independent variables are negative-as expected; the significance for f nuc is at the 7% level; the one of f res at the 1‰ level. (2) Again, the moderation with GDPpc carries no statistical significance.

Global database DBw(t)
This database compiles parameters of the world electricity generation and the related global CO 2 emissions over the last 30-35 years. In this period, electricity consumption rose by 120% and CO 2 emissions nearly doubled owing to an increase in fossil electricity generation by a factor of 2.2. GDP quadruplicated and GDPpc is-unlike the previous cases-highly correlated now with CO 2 pc (r 0.97) because of the joint evolution over a long period. CO 2 pc showed a moderate increase by 30%. This historical view might help to anticipate the complexity expected for the next 30 years up to 2050, when also electricity has to be generated carbon-free. Figure 9 summarises the temporal development of world electricity parameters related to the question of this paper. The average total CO 2 pc emission increased moderately, the average annual CO 2 pc emission in conjunction with electricity generation increased from 1.5 to 1.9 tons/y. The increase to new levels occurred mostly in the second half of the period considered. Also, GDPpc develops differently in this period with a steep rise in the second half. Both, f nuc , the nuclear share, and f res , the renewable share, hardly move initially. In this period, f res is basically f hydro . There is more dynamic in the second half with f res increasing and f nuc decreasing. To the increase of f res , wind and PV power contribute: with respect to renewables, a technology change happens in the second half of the time window of Fig. 9. Table 4 summarises the hierarchical regression results from DBw(t) for the period 1990-2014. CO 2 pc decreases both with the use of renewable or nuclear power. The relations are significant. The moderators do not change the picture. The major difference to the previous finding is that GDPpc shows a strong and positive correlation with CO 2 pc. Both develop in a period of growing economic prosperity, which, however, is mostly based on the use of fossil fuels and not of CO 2 -free energies. In step 2 of the hierarchical regression, the sign of bi-f nuc is negative but statistically insignificant. This changes in step 3 to the correct Fig. 9 The three graphs show results from the DBw(t) database in the time window from 1985 to 2019. a Shows the world annual per capita CO 2 emission CO 2 pc_tot (black) and the one caused by electricity generation CO 2 pc_el (red); b Plots the world global domestic product per capita, GDPpc, (black) and the world electricity generation (red); in c, the world fossil fraction f fos , the renewable fraction f res , the hydroelectricity fraction f hydro , and the nuclear fraction f nuc are plotted sign, now with high statistical significance. With respect to the credibility of the analysis, it is interesting to note that the sign of bi-f nuc changes and becomes positive in step 2 when the analysis is extended from 2014 up to 2018. This is again mentioned only to illustrate the little robustness of the sign of statistics results under conditions of low significance.

Intermediate summary
The analysis of both European and more global data shows that both renewable and nuclear technologies allow a reduction of CO 2 emissions with comparable efficacy. This is obvious but also revealed by the statistical analysis of many countries grouped for cross-sectional analysis or by the analysis of a time series. As the use of nuclear power does not lead to CO 2 emission, this technology is therefore not subject to the European ETS CO 2 certificate system [18]. No evidence was found that countries using nuclear power systematically employ more fossil fuels preferentially coal to the extent that the emission-free nature of nuclear energy is not only offset thereby but even overcompensated. Such a conjecture is not supported by the analyses of the databases presented here: the average fossil shares are 50% and 61% in the complete databases DBeu and DBgl and with 34% or 41%, respectively, lower in the nuclear Mod GDPpc × f res 0.94 > 5% The variables are the same as in Table 3. The critical p values are defined in Table 2 databases DBeun and DBgln. In all cases, f res or f nuc , respectively, correlate negatively with f fos with correlation coefficients of typically − 0.65. There is perfect understanding of CO 2 emission by fossil fuels, which allows predictions and there is actually no need for any statistical assessment as carried out in this paper and many others [26, 27 and references therein]. If a statistical analysis is nevertheless of interest, the most obvious independent variables are total (E tot ), nuclear (E nuc ) and renewable (E res ) electricity generation. E tot would allow to include considerations on additional electricity consumption by mobility and heating or, alternatively, on energy savings. E res and E nuc would limit E fos and define the remaining emissions. A corresponding regression analysis using DBgln yields: CO 2 _el (Mill t) 0.083 + 0.91E tot (TWh) -1.73 E nuc -0.64 E res . The same analysis but with DBeun yields: CO 2 _el − 2.87 + 0.76E tot -0.79 E nuc -0.69 E res and with DBw(t): CO 2 _el 3108 + 0.81E tot -1.2 E nuc -1.08 E res . In the example of DBgln, the increase of E tot by 1 TWh at constant E nuc and E res causes a CO 2 increase of 0.91 Mill tons; the increase of E nuc or E RES , respectively, gives rise to corresponding emission decreases. adjR 2 of this relation is 0.99, the p value is below the 1% level for all dependent variables. The specific emission intensity of Germany, calculated on this basis, is 0.473 kg/kWh; the German data in DBeun together with the fuel-specific intensities of Table 7 of Appendix B yield 0.449 kg/kWh; the EU publishes as official figure for Germany 0.441 kg/kWh [19]. These numbers agree quite well.
We have to admit, however, that the regression of the total CO 2 emission with E tot , E res and E nuc as independent variables does not provide any new or deeper insight; specifically, it does not open the door to the discovery of more speculative inner relationships and correlations with cultural and sociological factors as searched for in Ref. [3].

Brief literature search
In the last decade, specifically economists have explored the correlation or even causality between energy consumption and CO 2 emission using statistical techniques. Iwata et al. [20] identified a uni-directional causality relationship from nuclear energy to CO 2 emissions confirming that nuclear power generates electricity emission-free. Apergis et al. [21] showed in 2010 that the relation between emissions and energy consumption has a statistically significant negative association in case of nuclear energy and a positive one in case of renewable energies. In the same year, Menyah and Wolde-Rufael [22] concluded that nuclear energy can help to mitigate CO 2 emissions, whereas renewable energy has not yet reached a level where it can make a significant contribution. The study of Jaforullah and Alan King [23] from 2015 indicated that CO 2 emission levels are negatively related to the use of renewable energy, but are unrelated to nuclear energy consumption. Guidolin and Guseo [24] demonstrated in 2016 that renewables crowd out nuclear power in Germany and have a measurable effect in determining the observed decline of nuclear power consumption. Jin and Kim [25] concluded in their 2018 study "that nuclear energy does not contribute to carbon reduction unlike renewable energy. Thus, the development and expansion of renewable, not nuclear, energy are essential to prevent global warming". Hassan et al. [26] compared the effectiveness of both nuclear and renewable power in reducing emissions for the BRICS countries and concluded that nuclear power is less effective. Refs. [3] and [4] have already been introduced in Sect. 1.
Reference [27] provides an overview over 18 papers dealing with the "nuclear energy and CO 2 emission nexus". These papers do not question the basic CO 2 -free operation of nuclear power rather search for hidden relations, as stated in Ref. [3], "that higher political, institutional or infrastructural attachments or wider cultural attachments to either nuclear power or renewable energy tend to associate with a lower attachment to the other technology". It is indeed the case that the energy transition of the last two decades is not organised technology-open in by far the most countries. Rather strong political and societal orientations pave one way or the other. A typical case is Germany, where strong political interests sacrifice nuclear power and have it replaced by renewable ones.

The selection of GDPpc as independent variable
In the following, we will comment on same peculiarities of the databases used. A general problem of these statistical analyses could be the replacement of the energy/electricity use by GDPpc as proxy. GDP subsumes many facets of economic activities including those which lead to environmental damages. Therefore, its inclusion might allow access to variables, which cannot directly be identified or expressed as data. The relation between energy or electricity on one hand and economic growth, represented by GDP on the other, is a vital field in economic research. A major issue is whether the availability of energy drives GDP, e.g. in a manner comparable to labour and capital. In numerous papers (see references in [27] and [28]), four causality hypotheses are tested-the growth hypothesis, the conservation hypothesis, the feedback hypothesis, and the neutrality hypothesis. The statistical analysis is supposed to attribute the energy-GDP relation to one of these four possibilities. Each of them has largely different consequences and leads to rather different policy advice, which is the main purpose of these studies. Two papers commented the status of understanding the energy-economic growth relation by critically reviewing the literature available at the time. Ozturk [27] came to the conclusion "that the literature produced conflicting results and there is no consensus neither on the existence nor on the direction of causality between energy consumption (electricity consumption) and economic growth". Omri [28] published a more advanced literature survey discriminating between four topics-the roles of energy, electricity, renewable and nuclear electricity and their impact on economic growth. The author concluded: "Overall results from the reviewed studies in this subsection show that the literature on energy consumption-growth nexus produced inconclusive results and there is no consensus neither on the existence nor on the direction of causality among energy con-sumption and economic growth". "Energy" stands here for energy proper, and the other three energy forms, electricity, nuclear and renewable energy. Omri exemplifies the complexity in finding a consistent pattern in the energy-GDP relation by quoting explicitly results from two papers, which study specifically the nexus between nuclear energy and economic growth. Ref [29] reports on the growth hypothesis for Japan, Netherlands and Switzerland, the conservation hypothesis for Canada and Sweden and the feedback hypothesis for France, Spain, UK and USA. The authors of [30] came to contradictory results though they used the same analysis methods: Canada, Germany and UK follow the feedback hypothesis, USA the neutrality hypothesis and Japan the conservation hypothesis. As a clear causality between energy or electricity, respectively, and economic growth is not established in a broader sense, it might be a problem to select GDPpc as proxy for energy consumption. But a meaningful proxy needs a close correlation with the variable it replaces. One might also worry if a secondary aspect like mutual crowding out of renewable and nuclear technologies can be identified by statistical means if this procedure does obviously not allow to clarify unambiguously a first-order causality. Figure 8 shows India in the middle of countries, which justify their placement by low CO 2 pc values. The normalisation to the population awards the merits of clean electricity production also to large countries in spite of fossil fuel use. Figure 10 provides more detail to this circumstance by selecting the low-CO 2 pc emitting countries of DBgl with CO 2 pc < 1 ton/y. The maximal CO 2 pc value in this database is 8.3 tons per person. This selection is plotted in an f res versus f fos plane. Three observations can be made: (1) countries without nuclear power have to lie on the bisecting line; (2) countries with nuclear power deviate from this line because: f fos + f nuc + f res 1; (3) two classes of countries meet the above CO 2 pc criteria:-clean countries with f fos < 0.3 employing often also nuclear power and countries with f fos > 0.6 with larger populations and generally little or no nuclear power. The selection of CO 2 pc as independent variable mixes countries using clean electricity generation with populous ones.

The role of the leading CO 2 emitting countries
The data of DBgl and DBgln fall apart basically into two classes, the five largest CO 2 emitters China, USA, India, Russia and Japan on one side and the rest on the other. The corollary is a spreading of the data which governs some of the statistical results. These five large countries are responsible for 70% (82%) of the CO 2 emissions of all members in database DBgl (DBgln) and, therefore, play a prominent role for any policy advice, the quintessential aim of Ref. [3].
A separate analysis of these five countries yields the following results: The total emission, CO 2 _el, increases linearly with E fos , the electricity generation by fossil fuels. The slope is 0.95 Mill t/TWh; R 2 0.94. These values compare well with the relation of all data of DBgl yielding a slope of 0.91 Mill t/TWh with R 2 0.97. This quality is totally lost after the normalisation to CO 2 pc and f fos . Whereas Japan and China occupy the corners and USA resides in the middle of a CO 2 _el versus E fos plot, USA and India are at the corners and China is in the middle of a CO 2 pc versus f fos plot. Whereas the spread in E fos is large between Japan on one side and China on the other, allowing credible analysis, it is small when E fos is replaced by f fos (0.63-0.77). Nevertheless, a good linear fit is possible with a negative slope of − 33 Mill t with R 2 0.91: the emission decreases with rising f fos . The results of this formal treatment are obviously nonsense. Nevertheless, the p value turns out to be 1%. We have to conclude that a better statistical analysis is not possible in this case. E.g., India and USA show similar f res -values (0.21 vs. 0.19) but large differences in CO 2 pc (0.87 vs. 5.7); India has a low CO 2 pc thanks to her large population and a low f nuc which define the CO 2 pc versus f nuc relation also in a large data sample giving unavoidably rise to a positive slope between CO 2 pc and f nuc . We have to conclude here that 66% of the world CO 2 emissions caused by electricity generation cannot be treated on statistical grounds using common normalisation. As a consequence, also for the less emitting countries, a policy advice on statistical ground does not seem to be feasible. Regarding the five large countries, there is hardly any evidence for the speculation that cultural attachments would favour nuclear power against renewables. Apart from Russia, the other four nuclear countries take positions between 1 and 8 in the Recai list of AY [11]. The Recai index reflects the market attractiveness for investments into renewable energies of 40 countries and is based on economic considerations.

The role of fossil power in the databases
In the following, we try to elucidate the impact of the fossil power fraction on the relations of CO 2 pc with f res and f nuc in more detail. The fossil fraction varies in DBgl between 100% (Saudi Arabia) and 1% (Switzerland) and in DBgln between 92% (Iran) and the value of Switzerland. To explore the role of fossil power in more detail, DBgl was split into four groups: f fos > 2/3; 2/3 ≥ f fos ≥ 1/3; f fos < 1/3; and f fos < 2/3. As DBgln contains a smaller sample of 31 data points, the two groups f fos > 2/3 and f fos < 2/3 were formed. Table 5 shows the regression results for CO 2 pc with the three independent variables GDPpc, f nuc and f res The positive coefficient of CO 2 pc with f nuc of the group with f fos > 2/3 is highlighted in italics. p values indicating significance are in bold. The variables had been z-standardised. The last column gives the correlation coefficient r between f fos and f nuc ( step 3 in the hierarchical analysis). Of interest are the regression coefficients of f nuc and f res -their signs and relative magnitude-and the related p values. For the f fos > 2/3 group, CO 2 pc is found to increase with f nuc in both databases (marked in italic in Table 5). Regression analysis can yield a positive relation and it does not reproduce the correct action of this CO 2 -free technology. The result is formal and has no significance (judged by the 5% p-level). For variables with significance at the 5% level, the p values in Table 5 are marked in bold. With less fossil power, the regression results for both f res and f nuc gain more significance. In these categories, both nuclear and renewable power reduce CO 2 pc. We have to conclude that the actual and expected dependence can be hidden by samples with high fossil power fractions. However, for both databases, DBgl and DBgln, the correlation between f fos and f nuc is negative for all f fos -groups (last column of Table 5). This confirms our previous findings: a hypothetical lack of CO 2 emission reduction when using nuclear power is not indirectly caused by an inherently higher fossil power share.

The role of hydroelectricity
Within renewable energies, hydroelectricity has the largest share with 15% in both databases, DBgl and DBgln. It is larger than the nuclear fraction of 12% (DBgln), or 11% (DBgl), respectively. In DBw(t), the hydro-share is 17%, whereas wind and solar electricity (with photovoltaic power, PV, being the dominant part) contribute with only 2%; in DBgl, the two figures are 15% and 7%. In case of Europe, wind and PV are with 15% at about the level of the hydroelectricity share. Table 6 summarises the results from correlation analysis where f res is first replaced by f hydro , the fraction of hydroelectricity, and then by f W+PV , the fraction of wind and solar power. The results are shown only for DBgl. The first row of Table 6 repeats previous results: CO 2 pc correlates negatively with f res , which itself has no correlation with f nuc whereas renewables replace or crowd out fossil power. The quality factors R 2 and the p value are also listed. In the next row, f res is replaced by f hydro . Rather similar correlation results are obtained. This is not surprising as f hydro represents the dominant share within f res . In the last row, f res is replaced by f W+PV , which accounts for 7% of the total generation.  Table 2 R 2 does not indicate any meaningful correlation between CO 2 pc and f W+PV . In the standard regression analysis with CO 2 pc depending on the three variables GDPpc, f nuc and f res the data variance is described less and less by the selected independent variables when replacing f res by f hydro or f W+PV , respectively. f hydro , however, turns out to be significant like f res ; no significance at the 5% level could be observed for f W+PV. A recommendation to further develop renewable energies, which is based on the present data situation and uses statistical techniques, is foremost a recommendation to expand hydroelectricity. Though wind and solar power are the only technologies, which can be scaled to large power levels, their share is too small at present for their virtues to be resolved by statistical means. But hydroelectricity is exploited in many countries in Europe up to the limit of undue inroads into biodiversity [31] and is therefore no recommendation which can be generalised. The examples of Sweden and Switzerland demonstrate, however, that hydropower goes along well with nuclear power.

Conclusions
We conclude from the analysis presented here that both, nuclear and renewable power allow a reduction of national CO 2 emission levels. The negative correlation between CO 2 pc and both f nuc and f res is the reason why the German energy policy-green electricity replaces CO 2 -free nuclear electricity-was not very effective in recent years to reduce CO 2 emissions.
The analysis of the databases employed in this study did not yield evidence for any further hidden variables, national CO 2 emission might possibly depend on. Specifically, no evidence for "crowding-out" can be detected. This may not be surprising because in the past, countries exploited first their own energy reservoirs and established the related technologies, which fixed the forms of electricity supply over decades. In case of nuclear power, the build-up of nuclear power reactors was nearly complete in 1990. The decisions to build nuclear reactors were taken years before. Within the first ten countries, listed in the latest Recai index [10], nine use nuclear power. Obviously, EY does not expect that the presence of nuclear power gives rise to losses of investments into renewable energies; rather the opposite seems to be the case [10].
It has to be recognised that nuclear energy is as capable as renewable power is in reducing CO 2 emissions. Several European countries may not have the natural conditions to meet the future national electricity demand by wind and PV power alone and because of high population density, it may not be possible to provide the required space for these low-energy density supplies. This is specifically crucial during the higher-demand winter months when PV power basically fails. European countries which protect the climate by employing nuclear power and are proficient in its development and use are to be encouraged to continue along this path to maintain their environmental standards, to continue meeting the electricity demand of their industries by providing secured electric power, and to avoid the high expenses of importing renewable energies in the future in still unknown quantities and forms, from yet unknown suppliers made available there by technologies not yet proven at industrial scales. Chapter 2 of the 2018 ICPP report, Mitigation Pathways Compatible with 1.5°C in the Context of Sustainable Development, summarises many of the related discussions and concludes on page 130: "By mid-century, the majority of primary energy comes from non-fossil fuels (i.e., renewables and nuclear energy) in most 1.5°C pathways [32]".
The environmental benefits of these two technologies have been confirmed in this paper.
Literature values typical for the German power mix [42] and regression results to compare with are listed for the three databases studied here. In DBeu, lignite and hard coal are provided separately. The values in brackets are without statistical significance

Appendix B: databases and data handling
All data used in this paper are related to electricity generation and they are collected from publicly accessible sources. Three sets of databases are put together -one with European data only (DBeu and DBeun), one with global data (DBgl and DBgln) and one with world data (DBw(t)). DBeun and DBgln are subsets restricted to countries employing nuclear power. DBeu (DBeun) lists 26 (15) countries; DBgl (DBgln) lists 62 (31) countries. The countries of DBeu and DBgl are listed in appendix A. The European and the global data are from 2018 and are used in cross-sectional studies. DBw(t) looks at the temporal development of electricity-related data from 1990 to 2018. Each database contains the CO 2 emission per capita in tons per year, CO 2 pc, as response variable. Independent parameters are the nuclear power fraction, f nuc E nuc /E tot and the renewable power fraction f res E res /E tot with E nuc , E res , E tot being the annual nuclear, renewable and total electricity energy. E res is added up from hydropower, wind, PV, biomass, and waste. The fossil fuel share of electricity generation f fos E fos /E tot is added up from coal, gas and oil consumption for electricity production. A direct dependence of CO 2 emission on E fos can be expected. f fos , f res and f nuc add up to one. Following general practice, we also include the gross-domestic-product per capita, GDPpc. The reliability of the European data for DBeu and DBeun is controlled in two steps. First, we compare published CO 2 -emission intensities measured in gCO 2 /kWh el with the calculated emissions based on the shares of coal, gas, and oil in electricity generation. The fuel-specific emission factors, necessary to calculate the specific CO 2 contributions are taken from the literature [42] and are representative for German fossil power generation. The parameters are listed in Table 7 for the four fossil fuel forms. For those cases where coal is quoted without discrimination between lignite and hard coal, we take the average. Figure 11 compares the calculated specific emission intensities with averaged published values [35][36][37]. The horizontal bars indicate the respective maximal and minimal country value in the different data sources. This plot should provide a visual impression of the overall data quality. Data of Estonia, Lithuania, Luxemburg, and Malta have been omitted as they are obvious outliers Fig. 11 For the three databases DBeu (black), DBgl (red), and DBw(t) (blue) calculated CO 2 emission intensities from electricity generation are compared with values taken directly from the data sources [15, [35][36][37][38]. The calculated emission intensities are obtained from the fuel-specific values of Ref. [42]. The black dots of DBeu represent the average values of the data sources indicating inconsistencies in the databases. In case of Lithuania and Luxemburg, one reason could be the high electricity import, falsifying the consistency of the data if ignored. Estonia may be a special case as it uses shale oil for most of its electricity generation.
After this step, the final European database comprises 26 countries, 24 from EU (without the four eliminated EU members) and with Norway and Switzerland. 15 of these countries use nuclear energy.
In a second step of scrutinising the consistency of the data, the three databases were regression analysed (total CO 2 emission by electricity generation versus electricity from coal, gas and oil) yielding the fuel-specific emission intensities. The results are listed in Table 7 for the three databases and can be compared with the standard results provided by Ref. [42] (first line in Table 7). The p values indicate "significance" for all specific CO 2intensities apart from oil and gas in case of DBw(t). One reason is the little use of oil in electricity generation (~5% in the average).
We conclude from Table 7 and the results shown in Fig. 11 that the emission factors-total CO 2 emissions or specific emission intensities-are fairly well reproduced by the countryspecific shares of fossil power and that the data quality allows the statistical analyses as presented here.