# A New Index Assessing the Viability of PAR Application Projects Used to Validate PAR Models
###### Abstract  
Photosynthetically active radiation (_PAR_) is a useful variable to estimate the growth of biomass or microalgae. However, it is not always feasible to access _PAR_ measurements; in this work, two sets of nine hourly _PAR_ models were developed. These models were estimated for mainland Spain from satellite data, using multilinear regressions and artificial neural networks. The variables utilized were combinations of global horizontal irradiance, clearness index, solar zenith angle cosine, relative humidity, and air temperature. The study territory was divided into regions with similar features regarding _PAR_ through clustering of the _PAR_ clearness index (\(k_{\text{PAR}}\)). This methodology allowed _PAR_ modeling for the two main climatic regions in mainland Spain (Oceanic and Mediterranean). MODIS 3 h data were employed to train the models, and _PAR_ data registered in seven stations across Spain were used for validation. Usual validation indices assess the extent to which the models reproduce the observed data. However, none of those indices considers the exceedance probabilities, which allow the assessment of the viability of projects based on the data to be modeled. In this work, a new validation index based on these probabilities is presented. Hence, its use, along with the other indices, provides a double and thus more complete validation. photosynthetically active radiation (_PAR_); Exceedance Probability Index (EPI); global horizontal irradiance (_GHI_); MODIS +
Footnote †: journal: Applied Meteorology  
APM Proceedings Used to Validate PAR Models  
optimize photosynthesis is a key concern for researchers and technicians who seek to improve agricultural productivity. For instance, _PAR_ is among the main variables to bear in mind when assessing the growth of biomass [1; 2; 3] or microalgae [4; 5; 6; 7]. Many greenhouses use artificial lamps to replicate solar light, and there is an interesting field of research exploring the best lamp spectrum for different crops [8; 9]. _PAR_ is also of interest for gross primary production (GPP) [10], terrestrial net primary production (NPP) [11], and _PAR_ use efficiency [12]. _PAR_ optical properties are also a factor to bear in mind when choosing a cover for a greenhouse [13; 14]. _PAR_ is commonly defined as the band of solar spectrum located between 400 and 700 nm [15; 16] because this portion of the solar spectrum is used by plants to convert light energy into biomass through photosynthesis. However, acquiring _PAR_ measurements is not always possible, since stations that provide _PAR_ data are scarce or do not cover the desired extension of the field. Thus, an interesting option when _PAR_ measurements are not available is to use _PAR_ models. It is possible to sort these models of the bibliography depending on the nature of the data or the mathematical tool used to develop each model. Likewise, there are examples of satellite-derived models proposed in [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. Another approach is using [PERSON]'s bands [29] to obtain _PAR_ estimates [30; 31]. On the other hand, data collected on the Earth's surface, such as global horizontal irradiance (_GHI_), air temperature (\(T\)), relative humidity (_RH_), sky clearness, skylight brightness parameter, and clearness index (\(k_{t}\)), can also develop _PAR_ models [32; 33; 34; 35; 36; 37; 38]. It is also possible to train artificial neural networks (ANNs) to produce _PAR_ estimates [39; 40; 41]. Different statistics are usually employed to validate the models' performance, such as the mean bias error (MBE), the root mean square error (RMSE), the determination coefficient (R\({}^{2}\)), or the slope and the intercept of the linear regression between observed and modeled values. These statistics compare each observed value against the corresponding modeled value, so they assess the extent to which the models adequately reproduce the observed data.