# Extension of PAR Models under Local All-Sky Conditions to Different Climatic Zones
## 5 Conclusions  
A set of MLR and ANN models were obtained to model _PAR_ from a set of meteorological indices in Burgos. It was determined that the most influential variable when modelling _PAR_, both when analysing all-sky types and for each particular type (clear, partial, and, overcast skies) was _RaGH_. For clear and partial skies, _cosZ_ also had a very strong influence, while this same MI also had a strong relationship with _PAR_ for all-sky types and for overcast skies. The MI \(k_{t}\) had a strong relationship with _PAR_ for all-sky types, while the relationship was moderate for clear, partial, and overcast skies. [PERSON]'s clearness index, \(\varepsilon\), showed a moderate relationship with _PAR_ for all-skies and clear skies, and \(\Delta\) was the MI with a moderate relationship for overcast skies. Four _PAR_ estimation models were obtained with MLR models that yielded an \(R^{2}>0.97\), reaching an \(R^{2}>0.99\) in the cases of all-skies types and clear skies; the mean square errors were lower than 8%, although this error was 3.27% for clear skies. The statistical coefficients of the ANN model were also very well adjusted because the \(R^{2}\) value was in all cases  
Figure 4: \(nRMSE\) (MLR) values (%) for all sky type categories at the SURFRAD stations. Figure 5: \(nRMSE\) (ANN) values (%) for all sky type categories at the SURFRAD stations. greater than 0.97 and the \(nRMSE\) was also less than 8%. In this case, the model fitted clear skies better than any other, obtaining an \(R^{2}>0.99\) and an \(nRMSE\) of 3.01%. These models obtained in Burgos were directly applied to seven SURFRAD stations in the USA to verify their utility, obtaining a very good fit for all of them for all sky conditions, with both MLR and ANN models, as the \(R^{2}\) values were greater than 0.98 and the mean square errors were less than 11%. It is worth noting that clear skies were the sky type condition where the \(nRMSE\)s were the lowest, between 3 and 5%. Models for overcast sky conditions presented worse results, mainly due to the variability of the phenomena of absorption and dispersion of solar radiation that can appear under cloudy sky conditions and that cannot be characterized by a single parameter such as \(k_{t}\). It was also noteworthy that the models showed a worse fit at Desert Rock station under all sky conditions, each with an \(nRMSE\) at around 9-10% for partial and overcast skies. There were no significant differences when the data were studied by climatic zones, which in all cases showed a good fit with an \(R^{2}\) higher than 0.98, a lower \(nRSME\) in continental zones (Dfa and Dfb), and higher errors in semi-arid and desert zones (Bsk and Bwh). Both the MLR and ANN models that were used to estimate \(PAR\) on the basis of experimental data collected at Burgos may be used in other locations independently of the climatology, insofar as they yielded very good statistical coefficients across the seven meteorological stations representative of very different climates within the United States. They also fitted well for different climates, although in the case of a hot arid climate, the models presented the largest quadratic errors for each type of sky. Conceptualization, M.D.-M. and C.A.-T.; methodology, A.G.-R. and S.G.-R.; software, D.G.-L.; validation, D.G.-L., [PERSON]-R., M.D.-M.; formal analysis, A.G.-R. and [PERSON]-R.; investigation, [PERSON]-R. and S.G.-R.; original draft preparation, M.D.-M.; writing--review and editing, C.A.-T.; visualization, A.G.-R. and S.G.-R.; supervision, M.D.-M. and C.A.-T.; project administration, M.D.-M.; funding acquisition, C.A.-T. All authors have read and agreed to the published version of the manuscript. This research was funded by the Spanish Ministry of Science and Innovation, grant number RTI2018-098900-B-I00, and Consejeria de Empleo e Industria, Junta de Castilla y Leon, grant number INVESTUN/19/BU-0004. Not applicable. We would like to thank the SURFRAD network for placing complete and quality weather data in the public domain.