Detection of Daily Precipitation Structure in Shiraz Synoptic Station

Introduction
Recently, issues raised by changes in precipitation, especially problems brought about by floods and droughts, along with the environmental effects of diminished rainfall, have underscored the importance of precipitation studies at different temporal and spatial scales. Due to the pervasive impact of precipitation parameter in various urban, industrial and agricultural fields with respect to water supply, the identification of fluctuations, changes and precipitation structure is of particular importance, especially in arid and semi-arid regions. The similarity feature in climatic variables allows the use of fractal geometry and analysis of temporal and spatial changes. Accordingly, the use of fractal geometry in predicting the behavior of many natural processes, including precipitation in different regions, has a special place. The goal of this study is to investigate the structure of different time periods of precipitation in Shiraz synoptic stations to explore changes and determine the spatial position of precipitation in the stability and instability period.
 
 Methodology
In this study, daily precipitation data was received over a period of 58 years (1956-2013) from the Meteorological Organization of Fars Province to investigate the structure governing precipitation parameter. Then, statistical deficiencies were corrected by restructuring using difference ratio and linear regression. The methodology and algebraic logic of calculations in this study are such that in the first step, research parameters are arranged from minimum to maximum in an ascending order. Then, based on the triangular threshold coordinates(2Π), the minimum and maximum were extracted based on linear structures of the desired criteria and algebraic mathematical reference was conducted using Relation (1).
Relation (1)  F (x) =   
Then, in order to apply the fractal structure by applying the criterion for mathematical reference using Relation (2), the real structure of the desired meteorological parameters was obtained.
Relation (2) Y = m² × sin (1/m)                     
Finally, by overlapping the output charts of the actual structures and the classical structure of the fractal (Figure 2) in the algebraic ranges of -0.4 to +0.4, the algebraic process of each climatic parameter was evaluated separately.
 Results and discussion
In this study, based on the results, in addition to the daily analysis of the governing structure of precipitation over a 58-year period (1956-2012), which covered 21185 days, the governing structure along with the analysis of equilibrium dynamics of structures and its functions in three time periods (three 20-year periods) of different daily precipitation were also examined separately.
The first period began in January 1, 1956 and lasted for 7065 days. The relevant calculations were performed on the data derived from the first period, which based on the findings of this study, precipitation in Shiraz''s synoptic stations do not follow the fractal logic in the first period by applying fractal algebraic structures,
Also, in the second period, similar to the first one, the precipitation structure does not comply with a particular fractal logic. In other words, the logic governing precipitation parameter during the first and second periods changes from equilibrium to non-equilibrium. However, unlike the previous two periods, the fractal logic is followed in the third period.
 Conclusion
The self-similarity feature in climatic variables allows the use of fractal dimension and analysis of temporal and spatial changes. Accordingly, the use of fractal geometry in predicting the behavior of many natural processes, including precipitation in different regions, has a special place. The goal of this study was to investigate the structure of different periods of precipitation in Shiraz synoptic station to identify changes and determine the spatial position of precipitation structure in the period of stability and instability. The behavior of meteorological parameters in various parts of the world is a function that never follows uniform algebraic structure. Therefore, the analysis of complex systems and changes in nonlinear climate parameters using chaotic, fractal and fuzzy concepts offers a suitable way to understand the equilibrium state and dynamic analyses of climate fractal changes. The results indicate the dynamic transition of this time period from non-equilibrium to equilibrium. Therefore, according to the three time periods, the equilibrium dynamics of the daily precipitation structure approaches fractal structure.