Simplex analogy of equilibrium structure in Shiraz monthly rainfall with an emphasis on chaotic-fractal functions

Analysis and prediction of complex systems and nonlinear changes in climate parameters, especially rainfall using chaos, fractal and fuzzy theory are considered appropriate solutions for recognizing equilibrium trend and dynamic analysis in parameters of climate change. Therefore, in the present study, the dynamic fluctuations in rainfall climatic parameters were analyzed according to the rainfall months in Shiraz synoptic stations in a period of 58 years (1956-2013). The examination was conducted within a fractal approach. Having implemented the Mathematical Reference Parameter related to the rainfalls per month through applying trigonometric fractal structure on the data obtained, the results were analyzed to compare with classical geometry fractal. Findings revealed that monthly precipitation trend in seven months along with the rainfall in January, February, March, April, May, November and December of fractal structure did not follow the structure of geometry fractal. In other words, the logic of the structure rainfall parameters in seven months with rainfall moves from equilibrium to in equilibrium. Findings, in addition, suggested that if we want to fully get access to the dynamics of fluctuations of these parameters in the months with rainfall, it would be appropriate to apply the logics of fuzzy and chaos for the future studies.