Project: Statistical inference for Ocean and Climate Models based on Stochastic Partial differential equations
Supervisors: Randolf Altmeyer (Imperial) & Almut Veraart (Imperial)
Project Description:
The aim of this project is to develop statistical theory for ocean and climate models. Such models evolve in time and space and are often best described by stochastic partial differential equations (SPDEs). As such, they depend on specific effects and parameters that need to be determined from observational data. Examples are viscosity parameters in fluid dynamics, nonlinear flows in transport equations, or stochastic forcing terms due to wind stress.
While SPDEs are well-established in probability theory and numerical analysis, there are only few results on their statistical properties and how to validate models on data. The project will develop new estimation methods for parameters and provide uncertainty quantification for downstream tasks. For this, we will explore ideas at the intersections of different mathematical areas, such as statistics, probability theory, PDEs and computational mathematics. The results will be applied to real and simulated data.
