## 2 Data and Methods
### Methodology
#### 2.2.3 Evaluation of SSR Data, Radiative Effects, and Trends  
The SSR data produced by the radiative transfer system described above are evaluated against ground-based observations from three stations in Greece, and CM SAF SARAH-2.1 and CERES EBAF edition 4.1 satellite-based observations for the 16 selected locations in Greece. Then the radiative effect of aerosols, tropospheric NO\({}_{2}\), and liquid and ice clouds is calculated by running the system five times, with the following conditions: (1) with all the parameters, (2) without aerosols, (3) without tropospheric NO\({}_{2}\), (4) without liquid clouds and (5) without ice clouds. The radiative effect of each parameter i (REi) is defined as the difference between the SSR from the simulation with all the parameters and the SSR from the simulation without i (SSR\({}_{\text{without-i}}\)) as shown in Equation (1).  
\[\text{REi}=\text{SSR}-\text{SSR}_{\text{without-i}} \tag{1}\]  
The trends of the radiative effects of the aerosols, tropospheric NO\({}_{2}\) and clouds, and the related parameters are examined for the period 2005-2019 using the well-established method of [PERSON] et al. [89] as described in detail in [PERSON] et al. [27]. The monthly timeseries are fitted by using a model with a linear trend and a Fourier-based seasonal component for the annual cycle (Equation (2)).  
\[\text{Y}_{\text{t}}=\text{A}+\text{B}\text{X}_{\text{t}}+\sum\
olimits_{n=1}^ {6}[\text{a}_{\text{n}}\sin(\frac{2\pi}{\text{T}}\text{n}\text{X}_{\text{t}}) +\text{b}_{\text{n}}\cos(\frac{2\pi}{\text{T}}\text{n}\text{X}_{\text{t}})]+ \text{N}_{\text{t}} \tag{2}\]  
Y\({}_{\text{t}}\) is the monthly mean of month t, X\({}_{\text{t}}\) is the period of time (in fractional years) after January 2005 (t/12), A is the monthly mean for January 2005 and B is the annual trend. The seasonal component contains the amplitudes a\({}_{\text{n}}\) and b\({}_{\text{n}}\), T is the period (one year) and N\({}_{\text{t}}\) is the remainder. The remainder represents the difference between the modeled and the measured value and is given by the following formula: N\({}_{\text{t}}\) = \(\varphi\)N\({}_{\text{t}-1}+\epsilon_{\text{t}}\). \(\varphi\) is the autocorrelation in the remainder and \(\epsilon_{\text{t}}\) the white noise. The precision of the trend \(\sigma_{\text{B}}\) is given as a function of \(\varphi\), the length m of the dataset in years, and the variance \(\sigma_{\text{N}}\) of the remainder for small autocorrelations (Equation (3)).  
\[\sigma_{\text{B}}\approx\left[\frac{\sigma_{\text{N}}}{\text{m}^{3/2}}\sqrt{ \frac{1+\varphi}{1-\varphi}}\right] \tag{3}\]  
The trend \(\omega\) is considered statistically significant at the 95% confidence level if \(|\omega/\sigma_{\text{B}}|\) is greater than 2. Only trends for timeseries with at least 8 months per year are presented here following previous studies [90; 91]. Specifically for the radiative effect, which takes negative values, the trends refer to its magnitude (absolute values of the radiative effect) rather than its algebraic values, for easier interpretation of the results (e.g., decreasing AODs over the years would lead to a negative trend of the radiative effect magnitude).