Evaluation of the Time Occurrence Extreme Rainfall and Runoff Using Circular Statistics (Case study: Gavkhoni wetland)

Background and Objectives
Regarding water supply, water resource management is very important. Rainfall and floods are among the climate variables that play an important role in water management and agriculture. The inconsistency between the occurrence of the maximum rainfall and the flooding is one of the noteworthy manifestations of changes in land use. Knowing the reasons for the inconsistency between the time interval of rains and extreme floods can potentially be used to advance agricultural programs, water resources management, flood prevention, groundwater feeding, natural resources management, land use, industry and national economy should be important. Any extreme rainfall causes a flood at any subsequent time. In the case of annual analysis of the occurrence of extreme rainfall and floods, valuable information can be obtained from the state of land use or water resources.
Methodology
Today, various statistical methods along with efficient software are used to check rainfall and flood data. In the meantime, we can mention the method of directional statistics in MATLAB environment with coding, which has attracted the attention of many experts and researchers. In fact, circular statistics is a branch of statistics that is dedicated to the development of statistics and supports special data such as directional data. Therefore, for the statistical analysis of extreme data or any data that has a time frequency, the use of directional statistics, which is also called circular statistics, is applicable. In this study, Circular statistics have been used to investigate the range of time of occurrence and distribution of threshold data regarding rainfall and runoff from 21 rain gauge stations and 17 hydrometric stations in the Gavkhoni wetland.
 Findings
The average index of seasonality (dispersion) of time occurrence in most stations is above 0.6 or (60%) and their variance is less than 0.4. Due to the fact that the rainfall in the region is recorded in the stations, the occurrence values of the maximum rainfall during different years have been almost without manipulation or any human factors (influenced by human factors). Therefore, the time of occurrence of maximum rainfall was mostly in the area of 0 to -π/2, and the highest value of was from -81.80⁰ to -19.65⁰ for Lange and Isfahan stations, respectively. The average seasonality index (dispersion) of time occurrence was calculated from 0.27 at Diziche station to 0.87 at Ghale Shahrokh station. The input in some hydrometric stations has undergone changes in different years, or it may have been blocked or deviated before entering some stations. So the time of maximum runoff in those stations will not coincide with the time of rainfall. Therefore, the occurrence time of extreme floods is mostly scattered, and the highest value of is calculated from 161.25⁰ to -43.63⁰ for Diziche and Heydari stations, respectively. In Gavkhoni wetland basin, 9 out of 17 stations are not affected by the dam and 8 other stations are affected by the dam (hydrometric stations immediately after the reservoir or diversion dam).
The Rayleigh test rejects the null hypothesis (non-uniformity of flood occurrence in the perimeter of the circle) in all the stations, except for Diziche station. For this reason, it is not possible to calculate the upper and lower confidence band at Diziche station.
Conclusion
The last hydrometric station for draining the runoff to the Gavkhoni lagoon is the Varzane station, which has an average seasonality index and the time of the maximum flood output on the 2nd day of the new year. In general, it is affected by the changes of land use in the catchment area. In almost three seasons, spring, autumn and winter, it has output and runoff extreme data, so it shows that the water resources stored upstream of Varzaneh station are consumed and the remaining sewage is discharged from the station with a very low flow rat and it is transferred to Gavakhuni wetland. Therefore, the reason for the dryness of the wetland is being deprived of the natural source of Zayandeh River and it can be concluded that with directional statistics and histogram curves of rainfall and runoff extreme data, land use changes can be detected compared to rainfall and runoff and from the average seasonality index. And another use of indicates that the water intake valves for agricultural and industrial uses should be closed so that the runoff is transferred to the wetland.