## 3 Results
### Comparison with Existing Literature  
This study aims to assess whether machine learning models trained on data from a specific site can reliably estimate soiling losses when applied to a different geographical location. To this end, our results are compared with previously published models, particularly those presented by [PERSON] et al. in _Characterizing soiling losses for photovoltaic systems in dry climates: A case study in Cyprus_ (26). Their work characterizes soiling losses using both physical and machine learning models evaluated with experimental data from Nicosia, Cyprus. In that study, physical models developed at different locations in Cyprus were tested, offering a relevant benchmark for our models trained with Madrid (CIEMAT) data. On the other hand, the machine learning models were trained and tested using a two-year dataset from Cyprus, including meteorological variables, particulate concentration, and soiling losses. The data were split 50:50 for training and testing and will be used for compari  
Figure 26: Measured vs. estimated values of SL for the ANN CIEMAT model. Figure 25: Measured and estimated values of SL for the ANN CIEMAT model. son with the models developed in this paper trained and tested with data from Almeida (CIESOL). The physical models used in the reference study include the following:  
* **Kimber Model**[32]: this model estimates soiling losses based on daily soiling rate, rainfall threshold for cleaning, and a post-rain grace period. * **You Model**[33]: this models efficiency loss as a function of dust deposition density, based on PM concentration and number of dry days. * **Coello and Boyle Model**[19]: this model incorporates PM concentration, deposition velocity, rainfall, and the tilt angle of the PV panel. In addition, three gradient boosting algorithms were used for machine learning: _XGBoost_, _LightGBM_, and _CatBoost_, as described and utilised in this paper. Table 9 presents the comparative results using normalized metrics: normalized mean bias error (nMBE), normalized root mean square error (nRMSE), and the coefficient of determination (\(R^{2}\)). The Kimber model achieved the best nMBE (\(-0.55\%\)), while the LightGBM model evaluated on the CIESOL dataset had the best performance for nRMSE (\(22.3\%\)) and \(R^{2}\) (\(0.86\)). Two categories of models are considered:  
* **Locally Evaluated Models:** Models evaluated on data from the same location at which they were developed. This includes the CIESOL models and the boosting models from Cyprus. Among these, the best-performing model is LightGBM trained on CIESOL data (nMBE = \(1.65\%\), nRMSE = \(22.30\%\), \(R^{2}\) = \(0.86\)). * **Extrapolated Models:** Models evaluated on data from locations different from where they were trained. This group includes machine learning models tested on CIEMAT data and the physical models (Kimber, You, and Coello) applied in Cyprus. The Kimber model stands out in this group (nMBE = \(-0.55\%\), \(R^{2}\) = \(0.56\)), while the Coello model achieved the best nRMSE (\(55.57\%\)). Machine learning models transferred to the CIEMAT dataset experienced performance degradation, with nRMSE values ranging from \(66.12\%\) to \(76.32\%\) and nMBE from \(2.27\%\) to \(19.56\%\). These results, however, remain comparable to the physical model metrics. Models trained and evaluated on CIESOL data showed strong predictive performance, surpassing the machine learning models developed for Cyprus. However, when applied to new geographical contexts (CIEMAT), their accuracy decreased considerably. Nevertheless, their normalized error metrics are still comparable to those of the physical models tested in Cyprus, suggesting a promising yet limited generalization capability of machine learning approaches for soiling loss estimation.