Multifractal analysis of daily precipitation of selected stations in the west - southwest of Iran

Document Type : Research


Geography Sciences Department, Lorestan University, Khorramabad ,Iran



The region in this study, which is included large parts of the western-southwestern of Iran, has a special topographic and climatic diversity. As this region is exposed with geomorphological features such as mountains and plains. In this regard, western and southwestern precipitation systems, entering the region, make different interactions with these meso-scale phenomenon (Jahanbakhsh et al., 2020) that such a process has caused the scale behavior and more complex the dynamic structure of the precipitation signal in the region. Therefore, on the other hand to cover the whole region and on the other hand in order to have long-term daily rainfall statistics, were elected six synotic stations including Khorramabad, Kermanshah, Sanandaj, Dezful, Ahvaz and Abadan stations that have long-term statistics with 1961-2018 as Representatives of this region. Also, in order to identify the scale behavior and dynamics of the structure of the time series of rainfall in the west-southwest of Iran, was used the fractal and multifractal detrended fluctuation analysis (DAF2, MF-DFA2).The based on result, it was found that the precipitation of all stations has a scale behavior. In this regard, three different scale regimes for precipitation were identified. Thus, the fitting of the fluctuation function of DFA2 against different scales showed that there are two crossover points that separate the three different precipitation regimes in the fluctuation function of the stations. These two crossover are based on a time scale of 180 (6 months) and 550 days; Therefore, there are three different scale regimes including small-scale (less than 6 months), meso-scale (from 180 to 550 days) and large-scale (more than 550 days) in the precipitation time series of stations. A crossover behaviour in precipitation time series usually represents different precipitation generating mechanisms of different time scales (Lovejoy and Mandelbrot, 1985; Matsoukas et al., 2000; Gan et al., 2007; Tan and Gan, 2017). The scale exponent values in these three regimes showed that large-scale precipitations do not follow a specific spatial pattern and show relatively homogeneous behavior. However, small-scale precipitation has a spatial behavior, in that the precipitation of southwestern stations shows more instability and short-term memory than western stations. The results of MF-DFA2 also showed that these two crossover points are present in all fluctuations, so that different scale regimes are also shown in small to large fluctuations and are not limited to medium fluctuations. The results of MF-DFA2 show that the generalized Hurst exponent (hq) converges with increasing precipitation time scale, as the difference between small fluctuations and large fluctuations in the small-scale time series is much larger than the large-scale time series; Thus, on a small scale, periods with large fluctuations can be clearly distinguished from periods with small fluctuations. Other multifractal properties, including a decrease in hq with increasing fluctuations momentum (q), increased nonlinearly with the increase of q, indicate the multifractal nature, multiple scale behavior, and nonlinear memory of the precipitation signal of the studied stations (Adresh et al. 2020; Shimizu et al., 2002 ; Bunde et al., 2012; Tan and Gan, 2017).

On the other hand, the comparison of the parameters of the singularity spectrum of the stations shows that all the singularity parameters are similar in the region but have different intensities. In this regard, the singularity spectrum of all stations in the region is asymmetric and has long left tails. Such a tendency in the singularity spectrum indicates the predominant role of large fluctuations in the multifractal structure of the precipitation signal (Da Silva et al., 2020; Telesca, and Lovallo, 2011). Thus, the shape of the singularity spectrum reveals that the precipitation time series in the region has such a multifractal structure that it is sensitive to local fluctuations with large values (Kalamaras et al., 2017). In this regard, the precipitation time series in Khorramabad, Kermanshah and Dezful stations were more complex than other time series and Abadan and Ahvaz stations showed a very unstable and noisy structure. On the other hand, the extreme precipitation of southwestern stations including Abadan, Ahvaz and Dezful are much more unstable than the western stations and show heavy precipitation. In this regard, the structure of Sanandaj station precipitation series, although it is highly sensitive to extreme precipitation, but the intensity of its instability precipitation is lower than the limit precipitation of southwestern stations such as Dezful, which are less sensitive to Sanandaj. Its scale exponent is equal to 0.67 with the scale exponent of Khorramabad and Kermanshah stations. In general, such results indicate complexities time series s of precipitation that have very strong local fluctuations


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