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Showing 3 results for Correlation Dimension
Investigating the Chaotic Nature of Flow the Upstream and Downstream of Zayandehrud-Dam Reservoir Using Chaotic Systems’ Criteria
M. Boustani, F. Mousavi, H. Karami, S. Farzin,
Volume 23, Issue 4 (12-2019)
Abstract
River discharge is among the influential factors on the operation of water resources systems and the design of hydraulic structures, such as dams; so the study of it is of great importance. Several effective factors on this non-linear phenomenon have caused the discharge to be assumed as being accidental. According to the basics the chaos theory, the seemingly random and chaotic systems have regular patterns that are predictable. In this research, by using methods of phase space mapping, correlation dimension, largest Lyapunov exponent and Fourier spectrum power, a period covering 43 years of Zayandehrud River discharge (1971-2013) was evaluated and analyzed based on the chaos theory. According to the results, the non-integer value of the correlation dimension for Eskandari and Ghale Shahrokh stations (3.34 and 3.6) showed that there was a chaotic behavior in the upstream of Zayandehrud-Dam Reservoir. On the other hand, in the Tanzimi-Dam station, the correlation dimension curve was ascending with respect to the embedding dimension, showing that the studied time-series in the downstream of Zayandehrud-Dam Reservoir was random. The slope of the Lyapunov exponent curve for Eskandari, Ghale Shahrokh and Tanzimi-Dam stations was 0.0104, 0.017 and 0.0192, respectively, and the prediction horizon in the chaotic stations was 96 and 59 days. The non-periodical feature of time series was studied by using the Fourier spectrum power. The wide bandwidth, besides other indices, showed that river discharge in the upstream stations of Zayandehrud Reservoir was chaotic.

Investigating the Land Use Changes in the Upstream of the Zayandehrood Dam (A Study Case: The Toff-sefid Watershed, Chaharmaha and Bakhtiari Provin
L. Cheraghpoor, M. Pajoohesh, A. Davoodyan, A. Bozorgmehr,
Volume 23, Issue 4 (12-2019)
Abstract
River discharge is among the influential factors on the operation of water resources systems and the design of hydraulic structures, such as dams; so the study of it is of great importance. Several effective factors on this non-linear phenomenon have caused the discharge to be assumed as being accidental. According to the basics the chaos theory, the seemingly random and chaotic systems have regular patterns that are predictable. In this research, by using methods of phase space mapping, correlation dimension, largest Liapunov exponent and Fourier spectrum power, a period covering 43 years of Zayandehrud River discharge (1971-2013) was evaluated and analyzed based on the chaos theory. According to the results, the non-integer value of the correlation dimension for Eskandari and Ghale Shahrokh stations (3.34 and 3.6) showed that there was a chaotic behavior in the upstream of Zayandehrud-Dam Reservoir. On the other hand, in the Tanzimi-Dam station, the correlation dimension curve was ascending with respect to the embedding dimension, showing that the studied time-series in the downstream of Zayandehrud-Dam Reservoir was random. The slope of the Lyapunov exponent curve for Eskandari, Ghale Shahrokh and Tanzimi-Dam stations was 0.0104, 0.017 and 0.0192, respectively, and the prediction horizon in the chaotic stations was 96 and 59 days. The non-periodical feature of time series was studied by using the Fourier spectrum power. The wide bandwidth, besides other indices, showed that river discharge in the upstream stations of Zayandehrud Reservoir was chaotic.

Chaotic Study and Reconstruction of the Dynamic Phase Space of Evaporation Using Chaos Theory (Case Study: Semnan Synoptic Station)
F. Hooshmandzade, M.r. Yazdani, F. Mousavi,
Volume 26, Issue 1 (5-2022)
Abstract
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.

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