Identification de Modèles de Rayonnement Solaire en Zone Tropicale par Critères d’Information

Identification de Modèles de Rayonnement Solaire en Zone Tropicale par Critères d’Information

Laurent Linguet Yannis Pousset  Christian Olivier 

Laboratoire UMR Espace-DEV, Université de la Guyane IRD, 275 route de Montabo, BP 165, 97323 Cayenne cedex, Guyane française

Laboratoire SIC, Université de Poitiers Département SIC (Signal, Images et Communication) Institut XLIM, 86962 Futuroscope Cedex, France

31 December 2014
| Citation



The aim of this article is to improve the knowledge of the solar radiation in the tropics through the analysis of irradiance measurements at ground. For this, we identify probability distributions introduced in some synthetic solar radiation models, using information criteria. Validation is conducted through different tests and measures between real data distributions and synthesized data distribution. 

Extended Abstract 

The aim of this article is to improve the knowledge of the solar radiation in the tropical areas, through the analysis of irradiance measurements. For that, we dispose of solar radiation time series. They are obtained from measured data at ground or transmitted by satellite. These data or samples are obviously incomplete, no totally representative, and subject to perturbation. 

All these constraints lead to introduce statistical models generating the time series of data. Among several models proposed in literature, we choose the TAG model (for Time dependent Autoregressive Gaussian) of Aguiar and CollaresPereira in 1992, and the model with high temporal resolution given by Polo and al. in 2011. These model generating sequences present random terms with probability density function which are a priori chosen. 

The originality of this paper consists in reconsidering the nature of these probability laws. We dispose of a great number of data. So, to select the best probability law we use a statistical tool based on Information Criteria, also referred as penalized log-likelihood criteria. We retain BIC and Φβ criteria for their strong consistence. 

Among retained probability law candidates, the BIC and Φβ criteria agree to give the same law for the TAG and the Polo models, and this, whatever the different sky conditions. These conclusions differ in part of the literature. 

Then we compare the two probability density functions between solar radiation measured and solar radiation generated from previously elected probability laws. An exact concordance is observed for the TAG model and for the Polo model, except for partially cloud cover case. For this case, the very close values of criteria and the similarity of Nakagami and Beta cumulative functions could explain this discordance. 


L’objet de cet article est d’améliorer la connaissance du rayonnement solaire en zone tropicale à travers l’analyse des données de mesures d’irradiance au sol. Pour cela nous identifions, à l’aide de critères d’information, les distributions de probabilité introduites dans quelques modèles de génération de rayonnement solaire synthétique. Puis, nous validons les résultats à partir de différentes mesures et différents tests entre distributions issues des données réelles et celles synthétisées. 


criteria, synthetic solar radiation model, model selection.


critères d’information, modèles de rayonnement solaire synthétique, sélection de modèle. 

1. Introduction
2. Rappel de Quelques Concepts Statistiques et Physiques
3. Identification des Lois
4. Validations des Modèles
5. Conclusion

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