Synthetic generation of standard sky types series using Markov Transition Matrices

Abstract

The paper describes a methodology for creating synthetic time series of the fifteen standard sky types considered by the Commission International d'Eclairage (CIE). Since the measurements of sky luminance and accordingly CIE sky types are limited to a small number of locations, it is important to develop models to generate the time series of these parameters. The method is applied to two different locations [Pamplona (Spain) and Arcavacata di Rende (Italy)] where experimental luminance data are available. Firstly, the standard sky types corresponding to the observed luminance values are determined every 10 min and from these, Markov's Transition Matrices (MTM) are obtained corresponding to the four seasons. Secondly, it is statistically verified that the process follows a Markov's chain of first order and that it is stationary. Thirdly, obtained MTMs are used as a basis for generating the synthetic series of types of sky. Finally, experimental and synthetic time series are compared for the two locations, exhibiting good fitting results. As a conclusion, it is verified that first order MTM method can be used to generate time series of occurrence of CIE standard sky types, for the two locations. To clarify the general applicability, it should be applied to different locations having different climates and in addition with longer data sets.