## 2 Materials and Methods
### Data Processing  
In Table 2 the different variables that have been monitored in both the experimental setup and the weather station are displayed. Since there were data gaps during most of the time series for wind speed, the data for this variable were obtained from a weather station at the Airport of Almeria (36.85\({}^{\circ}\) N, 2.38\({}^{\circ}\) W), whose identification number at the World Meteorological Organisation (WMO) is 08487. These sensors provided a value for each measure every minute from 2 February 2024 to 31 May 2024 with two periods during which some data were missing. The first period extended from 31 July 2023 to 21 September 2023, and the second from 11 February 2024 to 23 March 2024. The night data were eliminated using the zenith angle that drops below 90\({}^{\circ}\) during the day. Since soiling data are best measured at central times of the day and to remove some erroneous data caused by shadowing, all data points corresponding to a zenith angle over 75\({}^{\circ}\) in the morning and over 65\({}^{\circ}\) in the afternoon were excluded. This filtering process resulted in a dataset of 176,518 one-minute data instances. To calculate soiling Loss (SL) as a percentage, Equation (1) was used [22]. Calibration was performed to ensure that any difference between the measurements of the two panels was attributable solely to soiling. \[SL[\%]=100\cdot\frac{\frac{I_{\text{sc,maintained panel,ref}}}{I_{\text{sc, maintained panel,ref}}}-\frac{I_{\text{sc,maintanceance-free panel}}}{I_{\text{sc,maintance-free panel,ref}}}}{I_{\text{sc,maintained panel,ref}}} \tag{1}\]  
In addition, a computed variable called days without rain or days since last rain (DSLR) was calculated. This variable measures how many days have passed since it rained enough to clean solar panels and reduce soiling losses. The chosen threshold for rain accumulation to trigger cleaning is crucial: too low a threshold may result in incomplete cleaning, while too high a threshold might delay resetting the variable. [PERSON] and [PERSON] [19] used a 1 mm threshold in their simple model and observed that when the threshold is lower than that, e.g., 0.5 mm, the model experiences more frequent cleaning events. In an experiment in \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Maximum Power (\(P_{\text{max}}\)) & 222 W \\ Efficiency (\(\eta\)) & 13.63\% \\ Short-circuit Current (\(I_{\text{SC}}\)) & 8.17 A \\ Open-circuit Voltage (\(V_{\text{OC}}\)) & 36.42 V \\ \hline \end{tabular}
\end{table} 
Table 1: Electrical characteristics of the Atersa A222P photovoltaic panel. \begin{table}
\begin{tabular}{l l l l} \hline
**Measure** & **Sensor** & **Unit** & \(\Delta\)**Measure** \\ \hline Short Circuit Current & KAINOS Shunt KL\_0.5 15 A/150 mV & A & \(\pm 1\times 10^{-2}\) A \\ Ambient Temperature & Biral SWS-250 & \({}^{\circ}\)C & \(\pm 5\%\) \\ PM\_2.5 & Aerquolal AQ51 & \(\text{\mu g}/\text{m}^{3}\) & \(\pm 1\times 10^{-1}\)\(\text{\mu g}/\text{m}^{3}\) \\ PM\_10 & Aerquol AQ51 & \(\text{\mu g}/\text{m}^{3}\) & \(\pm 1\times 10^{-1}\)\(\text{\mu g}/\text{m}^{3}\) \\ Relative Humidity & Vaisala HMP60 & \% & \(\pm 3\%\) \\ Wind speed & WMO-Station ID 08487 & km/h & \(\pm 0.1\) km/h \\ Precipitation & Biral SWS-250 & mm & \(\pm 3\times 10^{-4}\) mm \\ \hline \end{tabular}
\end{table} 
Table 2: Variables monitored by sensors in the CIESOL station. Jaen, Spain, [23] different cleaning thresholds (CTs) were tested in some existing models, and the best results were obtained for a CT of 0.3 mm/day. The CT that adjusted best to the soiling loss measured in Almeria, Spain, in this experiment was 0.1 mm/day, as seen in Figure 2, which shows how three different CTs affect the computed variable DSLR and how these different DSLR computations fit the soiling losses calculated earlier. As can be seen in Figure 2, the measured soiling values vary throughout the year.