# Trends from 30-Year Observations of Downward Solar Irradiance in Thessaloniki, Greece
## 3 Results  
### Long-Term SDR Trends  
We calculated the linear trends of SDR from the departures of the mean daily values from the daily climatology and for the three sky conditions. These are presented in Table 1, which also contains the 2\(\sigma\) standard error, the Pearson's correlation coefficient R, and the trend in absolute units. In Figure 1, we present only the time series under all-sky conditions; the plots for clear-sky and cloud-sky conditions, are shown in Appendix A (Figures A1 and A2). In the studied period, there is no significant break or change in the variability pattern of the time series. The linear trends in all three datasets are positive and around 0.4%/y for all-sky and cloudy-sky conditions, whereas for clear-skies the trend is much smaller (-0.1%/y). The linear trends were calculated taking into account the autocorrelation of the time series, and all three are statistically significant at least at the 95% confidence level, as they are larger than the corresponding 2\(\sigma\) errors, despite the small values of R, which is due to the large variability of the daily values. The clear-sky trend is very small, suggesting a small effect from aerosols and water vapor, which are the dominant factors of the SDR variability [12; 13; 28]. In contrast, the large positive trend of SDR under cloudy skies can be attributed to reduction in cloud cover and/or cloud optical depth. Lack of continuous observations of cloud optical thickness that could support these findings does not allow drawing firm conclusions. However, there are indications that the total cloud cover as inferred from the ERA5 analysis for the grid point of Thessaloniki is decreasing over the period of study. From the difference between all-sky and clear-sky SDR trends, expressed in W/m\({}^{2}\)/y using the long-term mean of the respective datasets, the radiative effect of clouds is estimated to 0.96 W/m\({}^{2}\)/y. This estimate is similar to the cloud radiative forcing of 1.22 W/m\({}^{2}\)/y reported for Granada, Spain [29]. The all-sky trend is similar to the one reported in [PERSON] et al. [16] from a ten-year shorter dataset, suggesting that the tendency of SDR in Thessaloniki is systematic. Other studies for the European region reported a change in the SDR trend around 1980 from negative to positive with comparable magnitude [3; 5; 30], well before the start of our records. However, the trends reported here for the three datasets are in accordance with the widely accepted solar radiation brightening over Europe. For the period of our observations, the trend in the TSI is negligible (\(-0.00022\%/y\)), and thus we cannot attribute any significant effect on the SDR trend to solar variability. Although the year-to-year variability of the anomalies (Figures 1, A1 and A2 in Appendix A) shows a rather homogeneous behavior, plots of the cumulative sums (CUSUM) [31] of the anomalies can reveal different structures in the records of all three sky conditions. For time series with a uniform trend, we would expect the CUSUMs of the anomalies to have a symmetric 'V' shape centered around the middle of the series. This would indicate that the anomalies are evenly distributed around the climatological mean, and, for a positive uniform trend, the first half is below and the second half above the climatological mean. In our case, there is a more complex evolution of the anomalies. For all skies (Figure 2a), we observe three rather distinct periods: (a) a downward part between the start of the datasets and about 2000, denoting that all anomalies are negative, thus below the climatology; (b) a relatively steady part lasting for almost 20 years, suggesting little variability in SDR anomalies; and (c) a steep upward part to the present, indicating anomalies above the climatology. The CUSUMs for cloudy skies (Figure 2c) show a similar behavior with some short-term differences that do not change the overall pattern. For clear skies (Figure 2b), a monotonic downward tendency is evident until 2004, suggesting that the anomalies are all negative.