# Extension of PAR Models under Local All-Sky Conditions to Different Climatic Zones
## 1 Introduction
This methodology is based on a clustering process applied to the _k\({}_{t}\)_, _PAR_, calculated by dividing the _PAR_ at the Earth's surface by the part of the spectrum corresponding to the _PAR_ band at the top of the atmosphere (39.8% of the total). In recent years, machine learning techniques have been used to develop algorithms for estimating PAR. The most decisive variable for _PAR_ estimation was _RaGH_ when comparing MLR and ANN models, regardless of climate [15]. Even when ANN models were run, their results clearly worsened without _RaGH_. In this sense, [PERSON] [20] used the _sunshine fraction_ (_nN_), \(T\), _RaGH_, _G0_, and _RH_ as input variables for the ANN models. They found that sunshine duration plays an important role in obtaining acceptable model predictions and that the model that best predicted _PAR_ values combined sunshine duration and _RaGH_. [PERSON] et al. [10] presented a model using _PAR_ data collected at radiometric stations using a neural network. They estimated _PAR_ with _RaGH_ as the only measured variable. A second ANN model based on sunshine duration measurements was shown to be an acceptable alternative for calculating _PAR_. In contrast, [PERSON] et al. [21] developed an ANN model for estimating hourly _PAR_ data using seven atmospheric parameters (cosine of solar zenith angle, cloud index, precipitable water content, and aerosol optical depth) as the input collected from satellite data. They concluded that _PAR_ estimation with an ANN model presented a good fit with a root mean square difference of 10.2%. [PERSON] et al. [2] tested eight artificial intelligence models, among which the BackPropagation neural network model yielded the highest accuracy. [PERSON] et al. [22] proposed three improved ANN models: MLP, Generalized Regression Neural Network (GRNN), and Radial Basis Neural Network (RBNN) for _PAR_ estimation, from long-term hourly observations of _RaGH_ and meteorological variables (air temperature, relative humidity, dew point temperature, water vapour pressure, air pressure). They found that different meteorological parameters influenced _PAR_ estimation in accordance with each particular (agricultural land, soil, forest, bay, prairie, desert, and lake) ecosystem. [PERSON] et al. [23] studied the relationship between hourly _PAR_ and _RaGH_ from data collected over three years at the Bondville, IL, and Sioux Falls, SD, ground weather stations (United States). From these data, they determined the temporal variability of the _PAR_ fraction and its dependence on different sky conditions (defined by the clearness index (\(k_{t}\))). Furthermore, the results in terms of the normalized Root Mean Square Error (_nRMSE_), the (\(R^{2}\)) coefficient of determination, the Mean Percentage Error (_MPE_), and Relative Standard Error (_RSE_) from the ANN-based models were compared with the same results from four existing conventional regression models. The authors found that the ANN model could accurately predict hourly _PAR_, especially under cloudy and clear sky conditions. In general, as the literature review has highlighted, research on the modelling of different components of solar radiation has focused on obtaining models at specific locations, which can rarely be applied directly to other locations and usually requires local recalibration to achieve adequate results. In this study, our aim is to extend locally obtained models for _PAR_ estimations as a function of the sky type to other locations. The sky conditions were determined from the clearness index (\(k_{t}\)). Three different _PAR_ models, one for each sky type (clear, overcast, and partial), were developed from experimental data collected over ten-minute intervals at Burgos, Spain. The meteorological indices had previously been selected as the model inputs. Multi-Linear Regression (MLR) and ANN were the two modelling procedures. Both models were applied to experimental _PAR_ data from all seven ground stations that form the SURFRAD network, corresponding to various Koppen-Geiger climate classification types [24].