# Fenwick Cooper

# Fenwick Cooper

Postdoctoral Research Assistant

My main research goal is to unite the theoretical, computational and statistical approaches to modelling the long time scale dynamics of geophysical and turbulent fluids. Applications include long-range weather forecasting and prediction of climate change. With the continual large increases in data and computational power, new approaches that I am interested in exploiting, such as fluctuation-dissipation theory, are finally becoming practical and will lead to a leap in our understanding of geophysical flows.

**Sub-grid turbulence modelling**

One of the fundamental challenges in classical physics is to find a practical theory for the statistics and effects of turbulent flow. For example, the impact of turbulent flow below the grid scales of a computational ocean or atmosphere model can drastically alter the model’s climatology. I have developed a stochastic method of modelling sub-grid turbulence such that the climatological mean and variance of a low resolution turbulent flow are the same as a high resolution truth. This has been successfully tested in an idealised primitive equation ocean model and fluctuation-dissipation theory is applied to ensure that the low resolution model responds to forcing in the same way as the truth. An exciting application of this method is to dramatically improve the accuracy of state-of-the-art oceanic and atmospheric climate models.

**Fluctuation-dissipation**

The prediction of the response of the climate system to an external forcing or to a change in some parameter of the system is a problem that can potentially be addressed using the fluctuation-dissipation theorem (FDT). I have developed a version of the FDT that is applicable in practice. The key new developments are that there is no practical limit upon the dimensionality of the system considered, there is no need for the system to be Gaussian and the governing equations are not required, (instead we require a sufficiently large data set). I am currently working on extending application of the FDT from idealised systems to real geophysical data sets, such as the ERA interim reanalysis, with the aim of making predictions regarding the dynamical atmosphere.

**Turbulence closure**

The statistics of turbulent dynamical systems, subject to stochastic regularisation, obey the Fokker-Plank equation. Unfortunately attempts to solve this equation are severely hampered by the so-called curse of dimensionality. I am working on a technique for solving the Fokker- Plank equation in high dimensional spaces provided the dynamical system considered has certain properties. For application to a fluid, this method of solution is still computationally expensive. However, there is the tantalising prospect of being able to reduce the cost by taking advantage of conservation laws. Ultimately, this approach has the potential to dramatically reduce the computational effort required to find the statistics of any turbulent system.