Dispersion Analysis of Monthly Rainfall and Temperature Time Series, 1901–2015

India is a country with different climates throughout the year, which can be broadly classified into four seasons: Winter, Hot Weather Summer, Rainy Southwestern monsoon, and post- monsoon/Northeast Monsoon. The months for the seasons are January-February, March-May, June- September and October-December. The climate in India is affected by the seasonal winds which are: Northeast and southwest monsoon. Over the years the arrival of monsoon and the expected rainfall has been varying due to changing rainfall pattern and average rise in the temperature across the globe. India is a country where about dollar 2 trillion share as the economy is shared by agriculture. India is primarily an agrarian economy. The aim of the study is to study the time series of rainfall from 1901 to 2015 for studying the shift in monsoon and it could be clearly seen that in the month of June the value of Hurst exponent is 0.6537 which is the least among all the other months. The maximum temperature is showing anti-persistent (AP) behaviour in the month of March and December and other months are also near to anti-persistent behaviour. The studies show that over years that temperature is rising continuously. A study says that annual mean surface temperature is rising to 0.630C per 100 years during the past 115 years that is 1901–2015 whether as the number of depressions and cyclonic storms has decreased from 1951 to 2015. It is clearly observed that the rainfall is less in the month of June hence showing that the monsoons are getting shifted since long time. The result of fractal calculation shows that there is persistent (P) behaviour in the time series and hence indicates that there is reduction in the accuracy for the forecasting of rainfall in the same.