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Nonlinear phenomena in complex multiscale turbulent dynamic systems are ubiquitous in geoscience. Effective modeling methods and efficient computational analysis in these geophysical processes remain a significant challenge in contemporary science, with substantial social implications for pressing issues in many geophysical, ocean, and atmospheric fields. Modeling, analyzing, and forecasting these complex systems is especially challenging due to the intermittent energy transfer between unresolved subscales induced by nonlinear effects and the occurrence of extreme events. Therefore, it is of practical importance to develop novel models, design new numerical algorithms, and implement model-based and machine-learning techniques to advance efficient forecasts and enhance our understanding of nature. This session aims to integrate novel applied math tools with geophysical systems. The main themes will include, but not be limited to, local- and global-scale dynamical modeling, stochastic and statistical reduced-order models, machine learning theory and algorithms, understanding intermittency, predicting rare and extreme events, analyzing observational data, data-driven techniques, multiscale analysis, optimal design, hybrid methods, data assimilation, and uncertainty quantification. Studies focusing on modeling and predicting specific phenomena such as ENSO, Monsoon, MJO, atmospheric rivers, hurricanes, and sea ice also belong to the main themes. In addition, applications such as case studies and the development of new datasets, software, and open-source codes are also welcome.