Rescaled range analysis and conditional probability-based probe into the intrinsic pattern of rainfall over North Mountainous India

In work reported here, we have explored rainfall over North Mountainous India for pre-monsoon (MAM), Indian summer monsoon (JJAS), post-monsoon (OND) and annual. The dependence of JJAS on MAM and OND on JJAS has been explored through conditional probabilities utilizing frequency distribution. An autocorrelation structure has shown that a low lag-1 autocorrelation coefficient characterizes all the time series. We have implemented rescaled range analysis. Through Hurst's exponent and fractal dimension, we have observed that the MAM time series of rainfall over North Mountainous India has a smooth trend and low volatility. We have further observed that for MAM and JJAS, we have , and D is closer to 1 than to 2. However, we have further observed that for OND and annual rainfall over North Mountainous India and . Therefore, these two time series have been characterized by high volatility and randomness.

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