Analysis of Monthly Rainfall in India Using Wavelets

Kumar, Sumeet (2014) Analysis of Monthly Rainfall in India Using Wavelets. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Sumeet Kumar) Sumeet_Kumar_09MS047.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

This thesis is related to the time series analysis of Indian rainfall data. Through the process of analyzing monthly rainfall time series data, we used di�erent types of tools and techniques. D4 wavelet was used to �lter the signal at an appropriate level. We used level 1 decomposition for all types of time series data. We used the �ltered signal to analyze its periodic behavior using Morlet wavelet. We saw that rain- fall in all the zones was periodic after 10 months and approximately after 380 months. With the help of Phase plot, we determined that for approximately 30 months, rainfall in di�erent zones were in phase. Then they went out of phase for next 20 months. Again they showed in phase behavior for next 30 months. This cycle of in phase and out of phase behavior was shown for the whole 60 years. Correlation among di�erent regions of India was analyzed using correlation matrix and results from RMT. Corre- lation matrix showed that apart from southern and north - eastern states, all regions were highly correlated. We used RMT to testify our result and hence we found out that there were three eigenvalues which were present outside random noise domain. Compo- nents of eigenvector corresponding to the highest eigenvalue were shoot up whereas only few components were shoot up for second highest eigenvalue. These components were contributed by zone2, zone3 and zone6. Our time series signal showed the power law behavior. We determined the Hurst exponent using WMFF. For all the zones, value of Hurst exponent was less than 0.5. This means that our time series data show anti-persistent behavior.

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