Bayesian Modeling of Long-Term Dynamics in Indian Temperature Extremes

TL;DR

This paper introduces two advanced Bayesian models, CTRW and BSAR, to analyze long-term temperature extremes in India, providing insights into climate change impacts and complex temperature dynamics over more than a century.

Contribution

It presents a novel application of the CTRW model coupled with Bayesian spectral analysis to better understand temperature extremes and their long-term trends in India.

Findings

CTRW captures complex temperature dynamics including memory effects.

BSAR effectively models non-linear temperature variations.

Comparison reveals strengths and limitations of each approach.

Abstract

Annual maximum temperature data provides crucial insights into the impacts of climate change, especially for regions like India, where temperature variations have significant implications for agriculture, health, and infrastructure. In this study, we propose the Coupled Continuous Time Random Walk (CTRW) model to analyze annual maximum temperature data in India from 1901 to 2017 and compare its performance with the Bayesian Spectral Analysis Regression (BSAR) model. The CTRW model extends the standard framework by coupling temperature changes (jumps) and waiting times, capturing complex dynamics such as memory effects and non-Markovian behavior. The BSAR model, in contrast, combines a linear trend component with a non-linear isotonic function, modeled using a Gaussian Process (GP) prior, to account for smooth and flexible non-linear variations in temperature. By applying both models to the temperature data, we evaluate their ability to capture long-term trends and seasonal fluctuations, offering valuable insights into the effects of climate change on temperature dynamics in India. The comparison highlights the strengths and limitations of each approach in modeling temperature extremes and provides a robust framework for understanding climate variability.