**6. Year-to-year variations of seasonal and monthly direct irradiance**

The major contribution to the values of *G/Gclear* came from the variations of the relative direct irradiance *I'/I'clear*. In all seasons and months, overcast days occurred when no direct irradiance was recorded. In late autumn and early winter majority of days were overcast. In December of one of the years under study, sunshine was available only in one day out of 31. In such situations it is impossible to study the probability density distributions of *I'/I'clear* like it was done for the global irradiance *G/Gclear*. The monthly and seasonal values of *I'/I'clear* presented in Table 1 and Table 2 were obtained by dividing the recorded sum of I' by the integrated *I'clear* for the same period.

The sunniest season during the study was spring, when 0.43 of the direct irradiance relative to the assumed clear sky conditions was available on average. Similarly during autumn, darkest period, less than 0.25 was available. For the whole summer half-year, the *I'/I'clear* was 0.41 on average. The range of interannual variations has been the largest in autumnal period

only one exception above 1.02 out of 648. The distribution of the ratio StDevMed/StDevTri exhibits only one case of value below 0.98, but the tail often reaches the range between 1.06

Jan 87.0 0.251 0.484 0.726 50.6 0.038 0.184 0.389 Feb 184.9 0.304 0.554 0.773 117.8 0.108 0.262 0.522 March 416.5 0.350 0.640 0.989 291.1 0.095 0.365 0.756 Apr 626.1 0.390 0.634 0.851 491.7 0.117 0.373 0.625 May 830.4 0.465 0.700 0.899 675.0 0.244 0.451 0.765 June 904.9 0.528 0.693 0.852 748.6 0.222 0.435 0.630 July 878.7 0.484 0.687 0.889 732.9 0.199 0.424 0.696 Aug 698.8 0.428 0.662 0.878 566.7 0.153 0.405 0.739 Sept 458.4 0.384 0.593 0.774 366.7 0.114 0.323 0.597 Oct 263.0 0.271 0.447 0.760 188.7 0.070 0.248 0.519 Nov 113.4 0.200 0.345 0.646 73.2 0.020 0.130 0.355 Dec 58.5 0.208 0.442 0.705 36.2 0.028 0.144 0.307

Table 2. The monthly values of assumed normal *Gclear* in physical units and recorded minimal, mean and maximal values of the trimean of monthly relative global *G/Gclear*. Monthly assumed normal *I'clear* and recorded minimal, mean and maximal values of *I'/I'clear*

**6. Year-to-year variations of seasonal and monthly direct irradiance** 

The major contribution to the values of *G/Gclear* came from the variations of the relative direct irradiance *I'/I'clear*. In all seasons and months, overcast days occurred when no direct irradiance was recorded. In late autumn and early winter majority of days were overcast. In December of one of the years under study, sunshine was available only in one day out of 31. In such situations it is impossible to study the probability density distributions of *I'/I'clear* like it was done for the global irradiance *G/Gclear*. The monthly and seasonal values of *I'/I'clear* presented in Table 1 and Table 2 were obtained by dividing the recorded sum of I' by the

The sunniest season during the study was spring, when 0.43 of the direct irradiance relative to the assumed clear sky conditions was available on average. Similarly during autumn, darkest period, less than 0.25 was available. For the whole summer half-year, the *I'/I'clear* was 0.41 on average. The range of interannual variations has been the largest in autumnal period

MJ m-2

Min Mean Max Min Mean Max

*I'/I'clear*

*G/Gclear* trimean *I'clear* 

and 1.10.

Month *Gclear* 

in 1955-2010

integrated *I'clear* for the same period.

MJ m-2

when the largest value exceeds about four times the smallest one. In the winter period this ratio was close to three, and in spring and summer it was close to two. The monthly *I'/I'clear* varied from its overall maximum 0.765, encountered in one May to overall minimum 0.02 encountered in one November. The typical monthly values have been between 0.40 and 0.45 in the brightest months, May to August, and between 0.135 and 0.185 in the darkest ones, November to January. The range of interannual variations of monthly *I'/I'clear* was the smallest in June as it was for *G/Gclear*.


Table 3. Monthly ratios Mean/Tri of G/Gclear (first 3 columns) and their linear correlation with kurtosis and skewness of the distribution of daily values G/Gclear (columns 4 and 5); linear correlation of kurtosis and skewness (column 6) and percent of positively skewed distributions (column 7)

Sunshine duration was recorded in more sites than direct irradiance, and the records often covered longer time intervals. Due to this advantage, sunshine duration has been used as a proxy for reconstruction of global irradiance (Ångström, 1924; Zekai, 1998; 2001; Cancillo et al., 2005) and also direct irradiance (Power, 2001). Direct irradiance is a more appropriate measure of potential sunshine effects than sunshine duration because sunshine episodes prefer certain solar elevation ranges. In May to September frequent convective clouds reduce available sunshine during noon hours when the solar elevation is high and the monthly relative direct irradiance is usually about 75-80 % of relative sunshine duration at the study site.
