Measurements of E_g↓ were made with regularly calibrated thermopile pyranometers at the 23 sites in Israel shown in Figure 1; the number of sites increased from two in the early 1950’s to more than ten in the 1990’s. The mean annual values of E_g↓ for all available sites together with their inter-site variation, as

represented by the standard error, varied between 248 ± 6 W∙m⁻² in the first decade of measurement to 225 ± 4 W∙m⁻² in the last decade. Measurements of E_g↓ were subject to the quality control procedures recommended by the World Meteorological Organization and have been corrected to the current World Radiometric Reference scale [12] .

In addition to mean annual values of E_g↓ three series of mean monthly values normalized to their extra-terrestrial values, i.e. as Clearness Indices CI [13] were analyzed. In the central coastal plain the measurements were made at the Israel Meteorological Service’s Observatory at Lod airport until 1964 and subsequently at its new site at Bet Dagan some 10 km NW. Measurements in the central hill region were made at three sites in Jerusalem less than one km apart. The third group of monthly CI values analyzed consisted of measurements made before 1961 at sites in the central coastal plain, central hill region and northern Negev.

Additional details of the E_g↓ measurements made before 1995 can be found in Stanhill and Ianetz [14] .

Observations at 08, 14 and 20 Israel Standard Time, were analyzed as mean monthly values after conversion from oktas to fraction of sky covered C. Six stations in the Israel Meteorological Service’s climate station network were selected to represent the five major climate regions on the basis of completeness and quality of the observations and the data was subject to the quality control procedures recommended by the World Meteorological Organization. Locations of the stations are shown in Figure 1.

In the absence of land based or satellite observations covering the 60-year period under study, national statistics of monthly values of total fuel consumption in units of TOE, thousand tons of oil equivalent F, were used as a proxy for the anthropogenic aerosols emitted by local fossil fuel combustion. The data is available from the Central Bureau of Statistics at http://www.cbs.gov.il/energy/new.enr.nach.eng.new.huz.html.

After 2000 measurements of aerosol optical depth, AOD were available from the MODIS Terra satellite for a 1˚ pixel centered on Israel (http://giovanni.gsfc.nasa.gov/giovanni/#service=ArAvTs&starttime=2000-03-01100.00:00Z&endtime+2016-04-30T23:59Z&bbox+39.6948.31.5857,35.4858,32.4866&data=MOD008).

Annual mean values of global radiation averaged for all available sites are presented in Figure 2(a) in units of W∙m⁻², of cloud cover as the mean of five representative sites in units of fractions of sky cover in Figure 2(b), and of total national fossil fuel consumption (F) in units of log₁₀ Tons of Oil Equivalent, TOE, in Figure 2(c). For ease of comparison the changes were also shown as normalized anomalies in Figure 2(d). The trends in global radiation (E_g↓)and clouds (C) were significant at P < 0.01 as determined by the non-parametric Mann-Kendall test used to eliminate the effect of auto correlation common to climate series [15] . Parametric analysis by linear regression yielded the following relationships with year of measurement, N.

E g ↓ = − 0.49 ± 0.055 N + 1205.8 , R 2 = 0. 56 , P < 0.00 1   ( 1955   -   2 0 13 )

C = − 0.000803 ± 0.000255 N + 1.895 , R 2 = 0.23 , P < 0.08   ( 1955   -   2013 )

F = 165 ± 23 N − 32150 , R 2 = 0.91 , P < 0.0001   ( 1970   -   2013 )

There was no significant difference between trends in E_g↓ measured at Bet Dagan and in Jerusalem [16] ; trends in C differed between the stations; an increase was observed at the two hill stations until 2000 after which all stations showed a decrease which was statistically significant (P > 0.05) at two of the lowland sites.

Analysis of variation of the multi-linear relationship between E_g↓, C and F over the 1970 to 2013 period for which data for all parameters was available indicated that the relationship of E_g↓ to C and F was highly significant while the interaction between C and F was not. After removing the interaction term the coefficient of determination was 0.25. Replacing F with log₁₀F raised the value of R² to 0.31; justifications for the use of a logarithmic scale for fossil fuel consumption are discussed in Section 4.1.3.

The final relationship was,

E g ↓ = ( − 116 .2 ± 81 .4 ) C − ( 31 .97 ± 15 .1 ) log 10 F + 381 .6 ± 74 .2 , R 2 = 0.31 , P < 0.001

After normalization to the mean annual extra-terrestrial value of solar radiation, 360 W∙m⁻², the relationship for clearness index CI, illustrated in Figure 3(a), is

C I = ( − 0.371 ± 0.26 ) C − ( 0.102 ± 0.048 ) log 10 F + 1.219 ± 0.24 , R 2 = 0.31 , P < 0.001

The multi-linear analyses of monthly values were based on E_g↓ measurements from Bet Dagan as this was the only site with an almost complete series of monthly values for the 1970-2013 period analyzed. The use of data from this site as a proxy for the national mean is justified by the highly significant correlation between the two series (P < 0.01) and the near unity of their slope, 1.004. Values of E_g↓ were converted to CI to remove the major effect of seasonal variation in Sun-Earth geometry. As was the case with the annual values, analysis of variance of the multi-linear relationship indicated that the interaction between cloud cover and fossil fuel consumption was not significant, R² = 0.003, P > 0.23. After eliminating this term stepwise regression indicated that cloud and local fossil fuel consumption together accounted for almost two thirds of the inter-monthly variation in CI (R² = 0.63) with clouds accounting for 0.61 of the variation and fossil fuel consumption only adding another 0.02 to the coefficient of variation. The multi-linear relationship for monthly values, illustrated in Figure 3(b), was

C I = ( − 0.511 ± 0.034 ) C − ( 0.0606 ± 0.023 ) log 10 F + 0.920 ± 0.062 R 2 = 0.63 , P < 0.0001

Under overcast sky conditions CI was highly significantly inversely related to the fossil fuel combust ion (F in units of MTOE) both on logarithmic and linear scales as shown in Figure 5(a) and Figure 5(b). The relationships at Bet Dagan were

C I c l o u d = − 0.1574 log 10 F + 0.8349 ,   R 2 = 0.732

C I c l o u d = − 0.0114 F + 0.3135 , R 2 = 0.697

Under cloudless skies the relationships were not statistically significant:

C I c l e a r = − 0 .2811 log 10 F + 0.8608 , R 2 = 0.019

C I c l e a r = − 0.0017 MTOE + 0.7728 , R 2 = 0.019

Over the 1970-2013 period the relationship CI_cloud = −0.0114F + 0.3135, on a unit area basis (total area 20,770 km²) indicates that the combustion of each unit TOE, by definition equivalent to 41.868 GJ, reduced E_g↓ by an average of 4.1 W∙m⁻².

Under cloudless conditions both the log and linear relationships indicate much smaller effects of fuel combustion which were not statistically significant.

Replacing the subjective synoptic observations of cloud cover at Bet Dagan with measurements of sunshine duration increased the coefficient of determination in the relationship with normalized global radiation to R² = 0.81; similar high coefficients of determination were found at five other sites covering a wide range of climates and aerosol emissions. At Bet Dagan and the two other urban sites the transmission of cloud was found to decrease with time [30] .

Trends in the direct and indirect aerosol effects derived from the intercepts and slopes of the relationships between CI and C shown in Table 1 indicate that the trend in direct aerosol effect was small, −0.003 per decade, and not statistically significant, P > 0.54. For the period of 2000 to 2016 covered by satellite measurements this conclusion is supported by the lack of inter-annual change in values of aerosol optical depth at 550 nm measured by MODIS Terra over the 1˚ pixel centered on Israel. The mean monthly values of AOD shown in Figure 6 indicate that during this century the trend in annual values of AOD was small; the reduction in inter-annual values from 0.32 to 0.30 was dwarfed by the large but irregular intra-annual variation.

By contrast the increase in the indirect aerosol effect over the 60 years was significant. The decrease in cloud transmittance is highlighted by a comparison of the values listed in Table 1 for the 1953-1961 period skies when complete

cloud covered skies transmitted half of the top of atmosphere irradiance; during the later period only a third was transmitted.

Similar results showing major changes in cloud transmission and minor changes in clear skies were reported in an analysis of high frequency direct and diffuse solar radiation measurements at seven USA sites between 1996 and 2011 [31] and in studies showing the major role of clouds in solar dimming in India [32] and in Iran [33] .

The significant relationship between cloud transmission and fossil fuel consumption in Israel during the period under study shown in Figure 5 indicates anthropogenic contamination of clouds, also referred to as the cloud albedo effect [34] was a cause of the changes in cloud transmission documented in this study. Other possible causes include a change in the diurnal or seasonal distribution of cloud cover [35] [36] ; and/or a change in the frequency of different cloud types with their associated radiative properties [37] . Changes in the frequency of the different synoptic situations reaching the Eastern Mediterranean region are known to have occurred during the period covered in this study, they include air masses with very diverse loads of dust and non-anthropogenic aerosols [38] and changes related to Hadley Cell expansion [39] . On a global scale changes in cloud cover were found to be significantly related to changes in solar activity through its effect on the flux of cosmic rays reaching the lower atmosphere [39] [40] suggesting changes in solar emissions could be related to those in cloud cover and global radiation at the Earth’s surface.