Stochastic model to describe atmospheric attenuation from yearly global solar irradiation

- A new stochastic model to describe atmospheric attenuation has been developed.
- The whole of atmospheric attenuation elements can be thought as a population.
- The population of attenuators is inversely related to the clearness index.
- The clearness index is the variable of the stochastic process considered.
- The stochastic model has been applied in the different climate zones considered.

A new stochastic model to describe atmospheric attenuation from yearly global solar irradiation has been developed and implemented. The proposed model takes into account the consideration that the whole of all attenuating elements can be thought of as a population where the higher the number of individuals the lesser the clearness index. Thus, the inverse of the clearness index is considered as the variable of a stochastic process. From the proposed master equation as starting point, the new model is characterized by transition rates (assessed from a growing parameter - G - and a decreasing parameter - D) which depend mainly on the climatological characteristics at each location. In this sense, different regions with an attenuation level calculated from the yearly global irradiation have been established using the Köppen-Geiger climate classification as a first approach.The model parameters G and D have been determined for different regions using the inverse of the clearness index as variable. The probability density function obtained after the application of the stochastic model for each climate zone shows how the index mode increases from the zones with lower levels of attenuation to those with higher levels of attenuation. This result confirms the proposed null hypothesis related to the use of the inverse of the clearness index as an attenuation population indicator.The fit between the empirical data and the data provided for the model is good enough according to a Kolmogorov-Smirnov test with a significance level of 0.05. Nevertheless, it is necessary to slightly modify the climate zones of Köppen-Geiger initial classification for a better explanation of the atmospheric attenuation. This climate zones modification can be considered as an additional result.