# Chaotic Features of Decomposed Time Series from Tidal River Water Level
###### Abstract
(2012) used five nonlinear dynamic methods using the runoff time series observed at the Sohutluhan hydrological station in Turkey, and suggested the existence of low-dimensional chaos [11]. Meanwhile, [PERSON] et al. (2015a) analyzed the chaotic behavior of hydro-meteorological processes in the Great Salt Lake and Bear River Basin, USA, by applying wavelet transform and correlation dimension to the precipitation, air temperature, discharge, and storage volume. They found out that the chaotic characteristic of the storage volume which is output is likely a byproduct of the chaotic behavior of the reservoir system itself, rather than that of the input data. In addition, [PERSON] et al. (2015b) analyzed the time series characteristics related to the drought length (DL) using nonlinear dynamic techniques, such as BDS statistic and a close returns test (CRT) [19]. The utility and effectiveness of the methods were first demonstrated on synthetic time series and then tested on real hydrologic time series. They suggested that the daily inflow of the Soyang River in South Korea is different from the DL data in the characteristics. The different characteristics of the original real series and their DLs may be due to the noises from many sources and therefore, noise cancellation may be important for obtaining original property of the time series. On the other hand, [PERSON] et al. (2019) extracted the dominant quasi-periodic components through the wavelet analysis of the flow rate at the Lees Ferry station in the Colorado River and quantified the trajectory branching in the phase space over time using local Lyapunov exponents [20]. As a result, the flow rate of the Colorado River was revealed to be highly predictable. Previous studies have mostly used the runoff data of the rivers inland that are influenced by the rainfall-runoff process. However, tidal rivers are influenced by many other factors, such as tidal level, wave height, river water level, and rainfall, which make their properties nonlinear. Tidal rivers are typically affected by backwater, a zone of spatially decelerating flow that is transitional between the stream flow of upstream and the tidal flow of downstream in the river, and it has a complex characteristic. Since water level and runoff of tidal rivers vary with the influence of the tide, the backwater effect during high tides can cause more flooding damages [2]. For example, in 2016, the damages by the typhoon 'Chaba' in Ulsan city area of South Korea were aggravated by the tide. During the typhoon 'Jebi' in 2018, the maximum tide level has been observed, and the effect of tidal currents did not drain the runoff into the river, causing great damage to the KansaiAirport in Japan [21]. In order to reduce flood damage by tide effect, many studies have been analyzing tides and waves. [PERSON] and [PERSON] (2010) predicted storm surges using a nonlinear chaos model and showed that the chaotic characteristics were caused by the tidal level and tidal wave's complex effects [2]. In addition, [PERSON] and [PERSON] (2016) identified the chaotic characteristics of a coastal area's dynamic system using significant wave height, wave period, and wave direction [6]. They suggested that the wind direction has a low correlation dimension of 4 or less, while the significant wave height and the mean wave period have a high correlation dimension of 5 to 8 in their chaotic characteristics. However, these studies conducted chaos characterization only for storm surges or single hydrological factors, implying a limitation in applying the method to tidal rivers affected by various hydrological components. As mentioned above, many studies have been analyzed to characterize the nonlinear characteristics of rainfall and runoff. Understanding the dynamics of the rainfall and runoff process is one of the most important problems in hydrology for the management of water resources.