# Extension of PAR Models under Local All-Sky Conditions to Different Climatic Zones
## 1 Introduction  
Photosynthetically Active Radiation (_PAR_) is a key factor for photosynthesis, vegetation growth, and climate change. The importance of its measurement and modelling is widely recognized [1; 2; 3], as PAR has a major influence on plant canopy growth, agricultural yields, and other environmental variables. Measurement of the _PAR_ band is needed for sky-modelling of biomass growth and forestry production [4; 5; 6] and in natural greenhouse illumination [7]. Moreover, _PAR_ affects the relationship between atmospheric systems and plants, so much so that its availability is a regulatory factor in the natural carbon cycle and in CO\({}_{2}\), water, and energy exchanges within the atmosphere [8]. Within the solar radiation spectrum, _PAR_ is the portion with a wavelength between 400 and 700 nm [9]. Unfortunately, _PAR_ sensors are not commonly found at ground meteorological stations [10]. It is therefore usually measured on the basis of other meteorological parameters and variables. The relationship between two different variables and _PAR_ has been analyzed in different works, obtaining mathematical models of greater or lesser accuracy. Many of these models described in the literature for modelling _PAR_ are based on linear regressions of global horizontal radiation [3; 11; 12], optical air mass [1], and the clearness index [13]. Other authors modelled _PAR_ by simultaneously taking several variables into account: solar radiation, solar zenith angle, columnar perceptible water vapour, and aerosol optical depth [14]. [PERSON] et al. [13] estimated _PAR_ with the clearness index, day length, and zenith angle. [PERSON] et al. [15] used Global Horizontal Irradiance (_RaGH_), Global extraterrestrial irradiance (\(G_{0}\)), atmospheric Temperature (\(T\)), and Relative Humidity (_RH_) as input variables for their models. These relationships have been analysed in most studies as a function of sky conditions [16] to estimate _PAR_ for clear skies where the most importantvariable is the solar zenith angle. The brightness index indicates whether the model is used in the presence of clouds. In several studies, _PAR_ has been treated as a variable that depends on the location where it is measured or estimated [17]. As regards measurement temporality, the ratio of _PAR_ and insolation in both tropical and arctic regions has been observed to remain fairly constant on different days and over longer time scales, regardless of cloud cover, atmospheric composition, surface type, season, and day length [18]. [PERSON] et al. [15] modeled _PAR_ in oceanic and Mediterranean climates, testing 22 (11 multi-linear regression and 11 artificial neural network) models, using _RaGH_, _G0_, \(T\), and _RH_ as their input variables. They concluded that areas with different climatic conditions needed different models. The Mediterranean climatic models showed better fits, and the models for oceanic climates needed some corrections depending on their geographical location, as the higher humidity of an oceanic climate, due to higher levels of atmospheric water vapour, means more radiation in the infrared spectrum, increasing the _PAR_ to _G0_ ratio. Although the combination of using geostationary and polar-orbiting satellites is an optimal solution for estimating _PAR_, a network of _PAR_ sensors is necessary for better validation [18]. [PERSON] et al. proposed a _PAR_ estimation model for India at six latitudes between 9\({}^{\circ}\) to 34\({}^{\circ}\), based on hourly and monthly averages of daily global radiation and a power regression model that accounted for different solar angles, cloud cover, and climatic conditions, which they linked to _RaGH_[3]. Several researchers have used data from different satellites, supplied from CM-SAF, to develop their _PAR_ models, although field data had to be used for validation in each study [12; 15]--a need that [PERSON] et al. [19] considered when presenting methodology to determine optimal locations for _PAR_ measurement stations.