Evaluating the trend and behavior rain the Shahrood city using the model statistically and spectral analysis

Abstract
    Time series in climate studies are reviewed, including the differently has features and behavior of the Trends, oscillation, Rise and fall and mutation. Each time series may contain a number of hidden features and behaviors that are not derived from simple statistical methods and modeling. In this context, the spectral analysis technique a useful tool in the detection of latent and apparent fluctuations in a time series. This technique is to transform the time series behavior of the fluctuations of time (of time) to the next frequency Cycles or fluctuations in series with simple statistical functions such as autocorrelation and moving average, and so can not reveal. In this paper to detect the precipitation behavior the Shahrood city is used the average annual precipitation is 60 years old (2012- 1953), based on the statistical distribution, Identifying trends, the modeling trend and finally identify the cycles using Harmonic Analysis and spectrum analysis And with the aid of software Matlab, Minitab and SPSS. To Identifying more precisely the behavior of the average annual rainfall is divided into two periods of 30 years and after the calculation of each period was compared. So after the initial identification of precipitation, rainfall time series from the time domain to the frequency domain became. The variance of each frequency (or harmonic frequency is Hrjft sine and cosine), and the proportion of variance in each cycle of the total variance, respectively. In the next step the journalist and the return period for each cycle was calculated and random variations variables (noise) were extracted for each of the courses selected. The results show that the rainfall distribution is not normal Shahrood and the Weibull distribution is the best distribution to fit the rain Shahrood. Output direction the value trends non-parametric and parametric methods vary So that the nonlinear nonparametric Spearman Kendall and linear positive trend and its value in mm, respectively 0.176 and 0.140 But the the method of parametric linear negative trend with an annual rate of -0.0352-mm. Also result of the modeling trends by using non-parametric method represents a decrease in annual precipitation amounts to -0.685 to be mm. The value of linear and exponential modeling approach is positive. Spectral analysis of two cycles at a frequency of 95% confidence level at frequencies 0.03 and 0.17 return period of approximately 15 and 3 years old to 60-year mean annual precipitation (2012- 1953), A cycle is of 95% in frequency by a factor of 0.05 year return period 7.5  rainfall for the average 30 year period (1982, 1953) and a cycle rate of 99% a year return period for the average at the frequency 0.47 Due to the 30-year period (2012- 1983). Also negative autocorrelation noise indicating is blue in all three periods, That means zero line joining the first cycle to the last cycle of continuous upward through it.