Weather Simulation has been recently gaining traction among researchers due to Climate Change mitigation becoming increasingly important. Spectral Deferred Correction (SDC) has shown high potential for the field, especially in the age of parallel computing. Recently, a new family of SDC methods has been discovered: Exponential Time Differencing SDC, or ETDSDC. This branch of SDC methods utilises operator splitting in a Lawson fashion for a slow mode, and uses exponential basis interpolation, allowing for higher fast mode resolution. This novel approach to time integration showed promising stability properties and low function evaluations to order ratio when proposed back in 2015, yet hasn't been applied to Weather Simulation problems or compared with state-of-the-art methodologies in the field.

This work aims to address this gap by investigating ETDSDC benefits within Ocean and Atmospheric Modelling. We implement ETDSDC based on SWEET academic HPC solver and assess its performance on classical problems within the domain, including Dahlquist's test equation, and Shallow Water Equations on a rotating sphere. Additionally, we outline the stability benefits and implementation challenges of ETDSDC, as well as provide a comprehensive comparison with traditional approaches such as Lawson methods.