Trends from 30-Year Observations of Downward Solar Irradiance in Thessaloniki, Greece

Abstract

The shortwave downward solar irradiance (SDR) is an important factor that drives climate processes and energy production and can affect all living organisms. Observations of SDR at different locations around the world with different environmental characteristics have been used to investigate its long-term variability and trends at different time scales. Periods of positive trends are referred to as brightening periods and of negative trends as dimming periods. In this study we have used 30 years of pyranometer data in Thessaloniki, Greece, to investigate the variability of SDR under three types of sky conditions (clear-, cloudy- and all-sky). The clear-sky data were identified by applying a cloud screening algorithm. We have found a positive trend of $0.38\%/\mathrm{year}$ for all-sky, ∼0.1%/year for clear-sky, and $0.41\%/\mathrm{year}$ for cloudy conditions. The consistency of these trends, their seasonal variability, and the effect of the solar zenith angle have also been investigated. Under all three sky categories, the SDR trend is stronger in winter, with $0.7$, $0.4$, and $0.76\%/\mathrm{year}$, respectively, for all-, clear-, and cloudy-sky conditions. The next larger seasonal trends are in autumn—$0.42$ and $0.19\%/\mathrm{year}$, for all and cloudy skies, respectively. The rest of the seasonal trends are significant smaller, close to zero, with a negative values in summer, for clear and cloudy skies. The SDR trend is increasing with increasing solar zenith angle, except under cloudy skies, where the trend is highly variable and close to zero. Finally, we discuss shorter-term variations in SDR anomalies by examining the patterns of the cumulative sums of monthly anomalies from the climatological mean, both before and after removing the long-term trend.

1. Introduction

The shortwave downward solar irradiance (SDR) at Earth’s surface plays a significant role on its climate. Changes in the SDR can be related to changes in Earth’s energy budget, the mechanisms of climate change, and water and carbon cycles [1]. It can also affect solar and agricultural production and all living organisms. Studies of SDR variability have identified some distinct SDR trends in different regions of the world in different time periods. The term ‘brightening’ is generally used to describe periods of positive SDR trend, and ‘dimming’ for periods of negative trend [1]. There are many cases in the long-term records of irradiance showing a systematic change in the magnitude of the trend, occurring roughly in the last decades of the 20th century. At multiple stations in China, a dimming period was reported until about 2000, followed by a brightening period [2]. A similar pattern was identified, with a breaking point around 1980, for stations in Central Europe [3] and Brazil [4]. On global scale, an artificial intelligence aided spatial analysis on the continental level with data from multiple stations reached similar conclusions for these regions and for the global trend [5].

There is a consensus among researchers that the major factor affecting the variability of SDR attenuation is the interactions of solar radiation with atmospheric aerosols and clouds. Those interactions, among other factors, have been analyzed with models [6,7], showing the existence of feedback mechanisms between the two. Similar findings have been shown from the analysis of observations at other locations [8,9,10,11] [and references therein]. In the Mediterranean region, aerosols have been recognized as an important factor affecting the penetration of solar radiation at the surface [12,13,14,15]. These studies investigated the long-term trend in aerosol optical depth, which has been found to decrease in the last three decades, the transport and composition of aerosols, and their radiative effects.

Due to the significant spatial and temporal variability of the trends and the contributing factors, there is a constant need to monitor and investigate SDR at different sites in order to estimate the degree of variability and its relation to the local conditions. In this study, we examine the trends of SDR using ground-based measurements at Thessaloniki, Greece, for the period from 1993 to 2023. We re-evaluated and extended the dataset used by Bais et al. [16], we applied a different algorithm for the identification of clear-/cloud-sky instances [17,18], and we derived the SDR trends for the period of study under different sky conditions (all-sky, clear-sky, and cloudy-sky). Finally, we investigated the dependence of the trends on solar zenith angle and season.

2. Data and Methodology

The SDR data were measured with a Kipp & Zonen CM-21 pyranometer operating continuously at the Laboratory of Atmospheric Physics of the Aristotle University of Thessaloniki (${40}^{\circ }{38}^{\prime }$N, ${22}^{\circ }{57}^{\prime }$E, $80$m a.s.l.). Here, we used data for the period from 13 April 1993 to 13 April 2023. The monitoring site was located near the city center, thus we expect that measurements were affected by the urban environment, mainly by aerosols. During the study period, the pyranometer was independently calibrated three times at the Meteorologisches Observatorium Lindenberg, DWD, verifying that the stability of the instrument’s sensitivity was better than $0.7\%$ relative to the initial calibration by the manufacturer. Along with SDR, the direct beam radiation (DNI) was also measured with a collocated Kipp & Zonen CHP-1 pyrheliometer since 1 April 2016. The DNI data were used as auxiliary data to support the selection of appropriate thresholds in the clear-sky identification algorithm (CSid), which is discussed in Section 2.1. It is noted that the limited dataset of DNI was not used for the identification of clear-sky cases in the entire SDR series to avoid any selection bias due to the unequal length of the two datasets. There are four distinct steps in the creation of the dataset analyzed here: (a) the acquisition of radiation measurements from the sensors, (b) the data quality check, (c) the identification of “clear sky” conditions from the SDR data, and (d) the aggregation of data and trend analysis.

For the acquisition of radiometric data, the signal of the pyranometer was sampled at a rate of $1\mathrm{Hz}$. The mean and the standard deviation of these samples were calculated and recorded every minute. The measurements were corrected for the zero offset (“dark signal” in volts), which was calculated by averaging all measurements recorded for a period of $3\mathrm{h}$, before (morning) or after (evening) the Sun reaches an elevation angle of $-{10}^{\circ }$. The signal was converted to irradiance using a ramped value of the instrument’s sensitivity between subsequent calibrations.

A manual screening was performed to remove inconsistent and erroneous recordings that can occur stochastically or systematically during the continuous operation of the instruments. The manual screening was aided by a radiation data quality assurance procedure, adjusted for the site, which was based on the methods of Long and Shi [19,20]. Thus, problematic recordings have been excluded from further processing. Although it is impossible to detect all false data, the large number of available data, and the aggregation scheme we used, ensures the quality of the radiation measurements used in this study.

Due to the significant measurement uncertainty when the Sun is near the horizon, we have excluded all measurements with solar zenith angle (SZA) greater than ${85}^{\circ }$. Moreover, due to obstructions around the site (hills and buildings) that block the direct irradiance, we excluded data with azimuth angle in the range ${58}^{\circ }$–${120}^{\circ }$ and with SZA greater than ${78}^{\circ }$. To make the measurements comparable throughout the dataset, we adjusted all one-minute data to the mean Sun–Earth distance. Subsequently, we adjusted all measurements to the total solar irradiance (TSI) at $1\mathrm{au}$ in order to compensate for the Sun’s intensity variability using a time series of satellite TSI observations. The TSI data we used are part of the ‘NOAA Climate Data Record of Total Solar Irradiance’ dataset [21]. The initial daily values of this dataset were interpolated to match the time step of our measurements.

In order to estimate the effect of the sky conditions on the long-term variability of SDR, we created three datasets by characterizing each one-minute measurement with a corresponding sky-condition flag (i.e., all-sky, clear-sky, and cloudy-sky). To identify the clear cases, we used the method proposed by Reno and Hansen [17], which requires the definition of some site specific parameters. These parameters were determined by an iterative process, as the original authors proposed, and are discussed in the next section.

We note that all methods have some subjectivity in the definition of clear or cloudy sky cases. As a result, the details of the definition are site specific, and they rely on a combination of thresholds and comparisons with ideal radiation models and statistical analysis of different signal metrics. The CSid algorithm was calibrated with the main focus to identify the presence of clouds. Despite the fine-tuning of the procedure, in a few marginal cases, false positive or false negative results were identified by manual inspection. However, due to their small number, they did not affect the final results of the study. For completeness, we provide below a brief overview of the CSid algorithm, along with the site-specific thresholds.

2.1. The Clear Sky Identification Algorithm

To calculate the reference clear-sky ${\mathrm{SDR}}_{\mathrm{CSref}}$, we used the ${\mathrm{SDR}}_{\mathrm{Haurwitz}}$ derived by the radiation model of Haurwitz [22] (Equation (1)), adjusted for our site:

$${\mathrm{SDR}}_{\mathrm{Haurwitz}}=1098\times cos\left(\theta \right)\times exp\left(\frac{-0.059}{cos\left(\theta \right)}\right)$$

(1)

where $\theta$ is the SZA.

The adjustment was made with a factor a (Equation (3)), which was estimated through an iterative optimization process, as described by Long and Ackerman [23] and Reno and Hansen [17]. The target of the optimization was the minimization of a function $f\left(a\right)$ (Equation (2)) and was accomplished with the algorithmic function ‘optimise’, which is an implementation based on the work of Brent [24], from the library ‘stats’ of the R programming language [25].

$$f\left(a\right)=\frac{1}{n}\sum _{i=1}^n{({\mathrm{SDR}}_{\mathrm{CSid},i}-a\times {\mathrm{SDR}}_{\mathrm{testCSref},i})}^2$$

(2)

where n is the total number of daylight data, ${\mathrm{SDR}}_{\mathrm{CSid},i}$ are the data identified as clear-sky by CSid, a is a site-specific adjustment factor, and ${\mathrm{SDR}}_{\mathrm{testCSref},i}$ is the SDR derived by any of the tested clear-sky radiation models.

The optimization and the selection of the clear-sky reference model was performed on SDR observations for the period 2016–2021. During the optimization, eight simple clear-sky radiation models were tested (namely, Daneshyar–Paltridge–Proctor, Kasten–Czeplak, Haurwitz, Berger–Duffie, Adnot–Bourges–Campana–Gicquel, Robledo–Soler, Kasten, and Ineichen–Perez) with a wide range of factors. These models are described in more detail by Reno et al. [18] and are evaluated by Reno and Hansen [17]. We found that Haurwitz’s model, adjusted with the factor $a=0.965$, yields one of the lowest root mean squared errors (RMSE), and the procedure manages to successfully characterize the majority of the data. Thus, our clear sky reference is derived by Equation (3):

$${\mathrm{SDR}}_{\mathrm{CSref}}=a\times {\mathrm{SDR}}_{\mathrm{Haurwitz}}=0.965\times 1098\times cos\left(\theta \right)\times exp\left(\frac{-0.057}{cos\left(\theta \right)}\right)$$

(3)

The criteria that were used to identify whether a measurement was taken under clear-sky conditions are presented below. A data point is flagged as ‘clear-sky’ if all criteria are satisfied; otherwise, it is considered as ‘cloud-sky’. Each criterion was applied for a running window of 11 consecutive one-minute measurements, and the characterization was assigned to the central datum of the window. Each parameter was calculated from the observations in comparison to the reference clear-sky model. The allowable range of variation is defined by the model-derived value of the parameter multiplied by a factor plus an offset. The factors and the offsets were determined empirically by manually inspecting each filter’s performance on selected days and adjusting them accordingly during an iterative process. The criteria are listed below, together with the range of values within which the respective parameter should fall in order to raise the clear-sky flag:

(a)

Mean of the measured ${\overline{\mathrm{SDR}}}_i$ (Equation (4)):

$$0.91\times {\overline{\mathrm{SDR}}}_{\mathrm{CSref},i}-20{\mathrm{Wm}}^{-2}<{\overline{\mathrm{SDR}}}_i<1.095\times {\overline{\mathrm{SDR}}}_{\mathrm{CSref},i}+30{\mathrm{Wm}}^{-2}$$

(4)

(b)

Maximum measured value $M_i$ (Equation (5)):

$$1\times M_{\mathrm{CSref},i}-75{\mathrm{Wm}}^{-2}<M_i<1\times M_{\mathrm{CSref},i}+75{\mathrm{Wm}}^{-2}$$

(5)

(c)

Length $L_i$ of the sequential line segments, connecting the points of the 11 SDR values (Equation (6)):

$$L_i=\sum _{i=1}^{n-1}\sqrt{{\left({\mathrm{SDR}}_{i+1}-{\mathrm{SDR}}_i\right)}^2+{\left(t_{i+1}-t_i\right)}^2}$$

(6)

$$1\times L_{\mathrm{CSref},i}-5<L_i<1.3\times L_{\mathrm{CSref},i}+13$$

(7)

where $t_i$ is the time stamp of each SDR measurement.

(d)

Standard deviation ${\sigma }_i$ of the slope ($s_i$) between the 11 sequential points, normalized by the mean ${\overline{\mathrm{SDR}}}_i$ (Equation (8)):

$$\begin{array}{c}{\sigma }_i=\frac{\sqrt{\frac{1}{n-1}{\sum }_{i=1}^{n-1}{\left(s_i-\overline{s}\right)}^2}}{{\overline{\mathrm{SDR}}}_i}\end{array}$$

(8)

$$\begin{array}{c}{s}_i=\frac{{\mathrm{SDR}}_{i+1}-{\mathrm{SDR}}_i}{t_{i+1}-t_i},\overline{s}=\frac{1}{n-1}\sum _{i=1}^{n-1}{s}_i,\forall i\in \left\{1,2,\dots ,n-1\right\}\end{array}$$

(9)

For this criterion, ${\sigma }_i$ should be below a certain threshold (Equation (10)):

$${\sigma }_i<1.1\times {10}^{-4}$$

(10)

(e)

Maximum difference $X_i$ between the change in measured irradiance and the change in clear sky irradiance over each measurement interval:

$$\begin{array}{c}{X}_i=max\left\{\left|x_i-x_{\mathrm{CSref},i}\right|\right\}\end{array}$$

(11)

$$\begin{array}{c}{x}_i={\mathrm{SDR}}_{i+1}-{\mathrm{SDR}}_i\forall i\in \left\{1,2,\dots ,n-1\right\}\end{array}$$

(12)

$$\begin{array}{c}{x}_{\mathrm{CSref},i}={\mathrm{SDR}}_{\mathrm{CSref},i+1}-{\mathrm{SDR}}_{\mathrm{CSref},i}\forall i\in \left\{1,2,\dots ,n-1\right\}\end{array}$$

(13)

For this criterion, $X_i$ should be below a certain threshold (Equation (14)):

$$X_i<7.5{\mathrm{Wm}}^{-2}$$

(14)

In the final dataset, $26\%$ of the days were identified as under clear-sky conditions and $48\%$ as under cloud-sky conditions. The remaining $26\%$ of the data correspond to mixed cases and were not analyzed as a separate group.

2.2. Aggregation of Data and Statistical Approach

In order to investigate the SDR trends that are the main focus of the study, we implemented an aggregation scheme to the one-minute data to derive series in coarser time scales. To preserve the representativeness of the data, we used the following criteria: (a) we excluded all days with less than 50% of the expected daytime measurements, (b) daily means for the clear-sky and cloudy-sky datasets were calculated only for days with more than 60% of the expected daytime measurements identified as clear or cloudy, respectively, and (c) monthly means were computed from daily means. For the all-skies dataset, monthly means were computed only when at least 20 days were available. Seasonal means were derived by averaging the monthly mean values in each season (winter: December–February, spring: March–May, etc.). The daily and monthly climatological means were derived by averaging the data for each day of the year and calendar month, respectively. The daily and monthly datasets were deseasonalized by subtracting the corresponding climatological annual cycle (daily or monthly) from the actual data. Finally, to estimate the SZA effect on the SDR trends, the one-minute data were aggregated in $1^{\circ }$ SZA bins, separately for the morning and afternoon hours.

The linear trends were calculated using a first-order autoregressive model with lag of 1 day using the ‘maximum likelihood’ fitting method [26,27] by implementing the function ‘arima’ from the library ‘stats’ of the R programming language [25]. The trends were reported together with the $2\sigma$ errors.

3. Results

3.1. 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. Trends in SDR daily means for different sky conditions for the period 1993–2023.

Sky Conditions	Trend [%/year]	Trend S.E. (2σ)	Pearson Correl.	Trend [W/m2/year]	Days
All skies	0.380	0.120	0.091	1.460	10,251
Clear skies	0.097	0.033	0.140	0.501	2684
Cloudy skies	0.410	0.180	0.081	1.180	4937

, 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 (Figure A1 and Figure 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 Bais 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 (Figure 1, Figure A1 and Figure 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. After 2004, the anomalies turn positive at a fast rate for about five years and at a slower rate thereafter.

In order to unveil further the features of the variability of the three datasets, Figure 3 presents another set of CUSUM plots using anomalies after the long-term linear trend is removed. With this approach, periods when the CUSUMs diverge from zero can be interpreted as a systematic variation of SDR from the climatological mean. When the CUSUM is increasing, the anomalies values are above the climatology, and vice versa. Overall, for all- and cloudy-sky conditions (Figure 3a,c), we observe periods with anomalies diverging from the climatological values, each lasting for several years. These fluctuations are probably within the natural variability, and no distinct changes are identified. The pattern in both datasets is similar, suggesting prevalence in cloudy skies over Thessaloniki. For clear skies (Figure 3b), the distinct change in 2004 is now clearer. The most likely reason for this change is the monotonic reduction of aerosols in Thessaloniki. In that year, there was a change in the rate of decrease in aerosol optical depth, as illustrated in Figure 7 of Siomos et al. [32]. This abrupt change in CUSUMs lasted until about 2010, when the anomalies become again variable.

3.2. Effects of the Solar Zenith Angle on SDR

The solar zenith angle is a major factor affecting the SDR, as increases in SZA leads to enhancement of the radiation path in the atmosphere, especially in urban environments with human activities emitting aerosols [33]. In order to estimate the effect of SZA on the SDR trends, we grouped the data in bins of $1^{\circ }$ SZA and calculated the overall trend for each bin separately for the daily periods before noon and after noon (Figure 4). Although there are seasonal dependencies of the minimum SZA (see Appendix A, Figure A3), these dependencies are not discussed further.

For all-sky conditions, the brightening effect of SDR (positive trend) increases with SZAs (Figure 4a), ranging from about $0.1\%/$y to about $0.7\%/$y for the statistically significant trends. The trends in the morning and afternoon hours are more or less consistent with small differences at small SZAs, which can be attributed to effects on clear sky SDR from systematic diurnal patterns of aerosols during the warm period of the year, consistent with the results reported for China by Wang et al. [33]. Note that SZAs less than ${25}^{\circ }$ can only occur during the warm period of the year around noon when clear skies are more frequent. The increasing trend with SZA is likely caused by the increased attenuation of SDR with SZA. The effect is larger when aerosol and/or cloud layers are optically thicker; therefore, decreases in aerosol and clouds through the study period will result in larger positive trends of SDR at larger SZAs.

Under clear skies (Figure 4b), the trends are smaller and less variable, ranging between $0.1$ and $0.15\%/$y up to ${77}^{\circ }$ SZA. At higher SZAs and in the afternoon hours, there is a sharp increase in the trend up to $0.3\%/$y, which may have been caused by the long path length of radiation through the atmosphere as discussed above for the all-sky conditions. The small differences in the trend between morning and afternoon between ${35}^{\circ }$ and ${60}^{\circ }$ SZA is likely a result of less attenuation of SDR in the morning hours due to lesser amounts of aerosols and a shallower boundary layer.

For cloudy-sky conditions (Figure 4c), we cannot discern any significant dependence of the SDR trend with SZA, as the variability of irradiance is dominated by the cloud effects leading to insignificant trends. Statistically significant trends appear only in the afternoon and for SZAs larger than ${60}^{\circ }$. The sharp increase of the trend at SZAs larger than ∼75${}^{\circ }$, observed also for clear skies, is probably associated with stronger attenuation by clouds under oblique incidence angles, which also result in smaller variability.

3.3. Long-Term SDR Trends by Season

Similarly to the long term trends from daily means of SDR discussed above, we have calculated the trend for the three sky conditions and for each season of the year using the corresponding mean monthly anomalies (Figure 5 and

Table 2. SDR linear trends of monthly anomalies for each season of the year and related statistical parameters.

Sky Condition	Season	Trend [%/year]	Trend S.E. (2σ)	Pearson Correl.	Trend p-Value
All skies	Winter	0.70	0.43	0.54	0.003
	Spring	0.11	0.24	0.17	0.371
	Summer	0.11	0.15	0.25	0.175
	Autumn	0.42	0.30	0.47	0.009
Clear skies	Winter	0.40	0.20	0.60	0.001
	Spring	0.06	0.17	0.13	0.497
	Summer	−0.05	0.06	−0.30	0.106
	Autumn	0.05	0.12	0.17	0.366
Clear skies	Winter	0.76	0.40	0.59	0.001
	Spring	0.06	0.23	0.10	0.593
	Summer	−0.08	0.27	−0.11	0.560
	Autumn	0.19	0.43	0.16	0.384

). Table 2 also contains the $2\sigma$ standard error, the Pearson’s correlation coefficient R, and the corresponding p-value. The winter linear trends generally exhibit the largest R values, ranging between $0.54$ and $0.60\%/$y. For all-sky conditions, the trend in SDR in winter is the largest ($0.7\%/$y), followed by the trend in autumn ($0.42\%/$y, a value close to the long-term trend), both statistically significant at the $95\%$ confidence level. In spring and summer, the trends are much smaller and of lesser statistical significance. These seasonal differences indicate a possible relation of the trends in SDR to trends in clouds during winter and autumn. For clear skies, the trend in winter is $0.4\%/$y and is associated with the decreasing trend in aerosol optical depth [32]. Moreover, it is almost half of that for all skies, which is another indication of a decreasing trend in cloud optical thickness. In other seasons, the clear-sky trend is very small (below $0.1\%/$y). Finally, for cloudy skies, the winter trend is the largest ($0.76\%/$y) and greater than for all skies, followed by a much smaller trend in autumn ($0.19\%/$y).

The trends under clear- and cloudy-sky conditions are in the same direction, and it would be expected that their sum is similar to the all-sky trend. This does not happen, especially for winter, likely due to the way the monthly means for clear and cloudy skies were calculated. Daily means were calculated only when at least $60\%$ of the clear- or cloudy-sky data were available (see Section 2.2).

4. Conclusions

We have analyzed a 30-year dataset of SRD measurements in Thessaloniki, Greece (1993–2023), aiming to identify the long-term variability of solar irradiance under different sky conditions. Under all-sky conditions, there is a positive trend in SDR of $0.38\%/$y (brightening). A previous study [16] for the period 1993–2011 also reported a positive trend of $0.33\%/$y. The slight increase in this trend indicates that the brightening of SDR continues and is likely caused by continuing decreases in aerosol optical depth and the optical thickness of clouds over the area. A smaller trend has been found under clear-sky conditions ($0.097\%/$y), which supports the notion that part of the brightening is caused by decreasing aerosols. Siomos et al. [32] showed that aerosol optical depth over Thessaloniki was decreasing constantly, at least up until 2018. The attenuation of SDR by aerosols over Europe has been proposed as major factor by Wild et al. [3]. Unfortunately, for this study, aerosol data for the entire period were not available in order to quantify their effect on SDR. The brightening effect on SDR under cloudy-sky conditions ($0.41\%/$y) suggests that cloud optical thickness is also decreasing during this period. As long-term data of cloud optical thickness are also not available for the region, we cannot draw quantitative conclusions.

The observed brightening on SDR over Thessaloniki is dependent on SZA (larger SZAs lead to stronger brightening). The trend is also dependent on season, with winter showing the strongest statistically significant trend of $0.7$ and $0.76\%/$y for all- and cloudy-skies, respectively, in contrast to spring and summer. The trends for autumn are also significant but smaller ($0.42$ and $0.19\%/$y for all- and cloudy-skies, respectively). The trend for clear skies is largest in winter ($0.4\%/$y) and negligible in spring, summer, and autumn.

Using the CUSUMs of the monthly departures for all and cloudy skies, we observed a 20-year period starting around 2000 where the CUSUMs remain relatively stable, with a steep decline before and a steep increase after. The rather smooth course of the CUSUMs suggests that no important change in the SDR pattern has occurred in the entire record.

Continued observations with a collocated pyrheliometer, which started in 2016, will allow us to further investigate the variability of solar radiation at ground level in Thessaloniki. Also, additional data of cloudiness, aerosols, atmospheric water vapor, etc., will allow better attribution and quantification of the effects of these factors on SRD.