Applications of Markov chains in climate change modelling: A comprehensive review of advances, challenges, and future directions

Markov chains have emerged as powerful tools for modelling complex climate systems and their evolution over time. This comprehensive review examines the state-of-the-art applications of Markov chain methods in climate change modelling, highlighting recent advances, ongoing challenges, and promising future directions. We survey how Markov chains are being utilized to capture stochastic processes in climate dynamics, model extreme weather events, and project long-term climate trends. Key areas of progress include the development of nonhomogeneous and higher-order Markov models to better represent nonstationary climate processes, the integration of Markov chains with machine learning techniques for improved predictive power, and the application of hidden Markov models to uncover latent climate states. The challenges discussed include parameter estimation in high-dimensional systems, the ability to handle nonlinear climate dynamics, and the ability to quantify uncertainty in Markov-based projections. In the future, we identify emerging research directions such as the use of quantum Markov chains for modelling quantum effects in climate systems, the development of adaptive Markov models for real-time climate forecasting, and the application of Markov decision processes to climate adaptation strategies. This review synthesizes current knowledge and provides a roadmap for future research, emphasizing the critical role of Markov chain methods in advancing our understanding and prediction of climate change.