Markov processes and Zipf's law in daily solar irradiation at earth's surface

• Daily solar irradiation (global and direct) is represented by a Markov process.
• Frequency vs. Rank relationships in solar irradiation are studied.
• Persistence is the most probable observation in sequences of 2 consecutive days.

Sequences of two consecutive days of solar irradiation (global horizontal and direct normal) have been studied here by different approaches. The frequency vs. rank relationships have been analyzed as an attempt to explore whether the Zifp's law is fulfilled, yielding to a partial fulfillment and observing that a good logarithmic fit can be applied to the data in the whole range. In addition, the pdfs of increments in two consecutive daily irradiation values are also studied, showing a relationship between persistence and the coefficients of the logarithmic fit. Finally, it has been shown that a Markov process can represent properly sequences of two consecutive daily irradiation values, for both global horizontal and direct normal components. Thus, synthetic series can be generated by Markov chains for characterizing daily global and direct irradiation.