Civil and Project journal

Historical Analysis of Chaos in Rainfall Models and a New Approach Using Conjugate Mapping (Case Study: Runoff Collection Network Baghbadaran)

https://doi.org/10.22034/cpj.2025.506175.1345
Volume 7, Issue 2 - Serial Number 72
May 2025
Pages 11-25
Civil and Project journal

Document Type : Research Article

Authors

Mehran Iranpour mobareke 1
Ali Fazlizade 2

1 1-Assistant Professor, Civil Engineering, Islamic Azad Branch of Lenjan, Esfahan, Iran 2-Aghigh Non-Profit Higher Education Institute Shahrab sazahIrsaConsulting Engineers Company-

2 MSC Student, Civil Engineering, Aghigh of Shahinshahr Institute, Esfahan, Iran

Abstract
Investigating the behavior of rainfall 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 rainfall process has a dynamic and non-linear nature, it is very important to identify the rainfall process from a chaotic point of view. For this purpose, conventional methods such as Lyapunov exponential, correlation dimension, phase space reconstruction, delay time determination, embedding dimension estimation, Fourier power spectrum, Hurst coefficient, autoregressive moving average have been used. Although these methods are developed and show good results in identifying chaotic systems, but more parameters are needed to identify chaos. In addition, the concepts of these parameters are difficult, and therefore they often have interval values, there is an error in decision-making. For these reasons, the conjugate mapping method is suggested to identify the rainfall process. To use this method, first, the average, standard deviation, and coefficient of variation are obtained from the statistical data of the 56-year rainfall period (1344-1400) of the Kilishadrokh synoptic station in the study area. Then a mapping whose process is chaotic and whose correlation dimension is higher than 4.236 is candidate. After that, the quadratic mapping is selected due to the nonlinearity of the studied system, and the coefficients of this mapping are obtained by determining the standard deviation, the coefficient of variation, and also the definition of the conjugate mapping. then by using the theory of conjugate mappings, the chaotic behavior of the process is investigated. The simple calculations and simple concepts of this method, are those the advantages of this method. Details of this method are discussed as follow.

Keywords

Mapping
Conjugate
Chaos
Embedding
phase
Delay Time
Subjects
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  • Receive Date 12 January 2025
  • Revise Date 24 February 2025
  • Accept Date 28 February 2025
  • First Publish Date 28 February 2025
  • Publish Date 21 April 2025

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