Chaotic Study and Reconstruction of the Dynamic Phase Space of Evaporation Using Chaos Theory (Case Study: Semnan Synoptic Station)

Investigating the behavior of water surface evaporation is one of the basic issues in design, operation, and studies related to water engineering. Therefore, the application of new methods such as chaos theory in hydrology and water resources has recently been considered due to its innovation and capabilities. Since the fluctuations of evaporation from free water surfaces are dynamic and non-linear in nature, the aim of this study was to investigate the possibility of chaotic behavior in evaporation from the free water surface in the Semnan synoptic station on daily and monthly time scales in 1995-2018 using the concepts of chaos theory. The daily, monthly, and annual evaporation rates of this synoptic station were calculated to be 68.8, 200, and 2600 mm, respectively. To reconstruct the state space, two parameters of delay time and embedding dimension are needed. The mean of mutual information and false nearest neighborhood has been used to estimate these two parameters. The first step to study a process with chaos theory is to investigate the chaotic nature of the correlation dimension method as one of the most common methods. First, the embedded dimension was calculated by the nearest neighborhood method equal to 3.  To calculate the delay time, cross-evaporation diagrams were drawn at Semnan station at different time scales. According to this method, the first local minimum in the diagram is considered the latency, which was obtained for evaporation at daily and monthly scales of 30 and 3, respectively. Unlike complicated and conventional computational methods, these results are obtained by observation and in the least amount of time, as follows: monthly data are more chaotic than daily data. The enclosed dimension and the slope of the correlation dimension diagram were obtained at 8.8 and 9.8, respectively, after calculating the latency and reconstruction of the state space.