Nonlinear phenomena in multiscale turbulent systems are ubiquitous in the geosciences, as well as many other scientific disciplines dealing with complex systems. New mathematical theories and computational tools are needed that incorporate several key aspects: i) to better model crucial but poorly represented processes, such as intermittent extreme events; ii) to quantify uncertainty in intermediate bursting structures and long-range forecasts.

The aim of this special session is to demonstrate how applied mathematics can contribute new concepts and shed light into complex nonlinear processes in geophysical systems by blending together rigorous mathematical theory, asymptotic/qualitative prediction models, and efficient numerical algorithms.

This session will cover several key research directions, including recent advances in:

Mathematical models for statistical prediction, uncertainty quantification, and sensitivity analysis;

Mathematical models for the analysis and prediction of extreme events;

Multiscale algorithms for filtering/state estimation for nonlinear geophysical systems;

Data-driven and machine learning strategies to model unresolved nonlinear processes.