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

Abstract

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. HIGHLIGHTS We have explored rainfall over the Himalayan region of India for different seasons.; The seasonal dependence is explored through conditional probabilities.; An autocorrelation structure is explored for low persistence.; The MAM time series of rainfall over the Himalayan region has a smooth trend and low volatility.; We have observed that for MAM and JJAS, we have , and D is closer to 1 than to 2.;

Keywords

• autocorrelation
• conditional probability
• hurst exponent
• rainfall
• rescaled range analysis