A Markov-chain probability distribution mixture approach to the clear-sky index

This paper presents a Markov-chain probability distribution mixture approach to the clear-sky index (CSI). The main assumption is that the temporal variability of the state of clear and the state of cloudy can be described by a two-state Markov-chain, and the variability within each state can be approximated by a probability distribution, unique for each state. Measurables such as the mean clear-sky index, fraction of bright sunshine, expected duration of clearness and expected duration of cloudiness events are shown to be related to the parameters of the method. Additionally, the Ångström equation, which relates mean normalized solar irradiance to the fraction of bright sunshine, is shown to arise as the expectation of the method. In order to numerically verify the method, a simulation model is constructed based on data sets for two different climatic regions: Norrköping, Sweden and Oahu, Hawaii, USA. Results from the simulation model based on training data shows good agreement with testing data, and when comparing the results to existing models in the literature it is comparable to the state of the art. It is shown that the simulation model generates a non-trivial, generally non-zero, autocorrelation function. Finally, challenges with the method and open problems are discussed.