Dr Tim Payne

Areas of expertise

• Data Assimilation, especially four dimensional variational data assimilation (4D-Var)
• Several areas in mathematics relevant to numerical weather prediction

Current activities

In recent years Tim has been engaged in improving the incremental 4D-Var scheme used to assimilate data into the Met Office numerical weather prediction models.

His current activities and interests include:

The longer-term  development and viability of 4D-Var, in particular the role and formulation of the linear model for covariance evolution;

Nonlinearity in data assimilation;

Alternative strategies for the data assimilation - forecast cycle in which the data assimilation updates are more frequent than at present, while retaining the benefits of longer assimilation windows.

Career background

Tim has researched and developed data assimilation methods for atmospheric models since joining the Met Office in 1997. He has BA, MSc and PhD degrees in mathematics and immediately prior to joining the Met Office was engaged in post-doctoral research funded by the SERC.

Since joining the office Tim has been involved in the development of 3D-Var (operational 1999) and then 4D-Var (operational 2004) data assimilation schemes.

4D-Var finds the atmospheric state (or "analysis") which "best fits" both the prior information (or "background", a short forecast from a previous analysis) and recent observations. It does this by minimising a cost function which penalises the departure of the analysis from the background, and the departures of the forecast from the analysis to the observations distributed in time. To make the problem manageable the latter is done using a linear "perturbation forecast" (PF) model which is approximately tangent-linear to the full model.

The minimisation problem which must be solved every analysis time is very large (currently of order 100 million variables), which for the timely delivery of forecasts must be solved very efficiently. Tim has been heavily involved in devising and refining algorithms which do this.

He has shown practically and theoretically how the PF model can and should account for nonlinearity, and developed and implemented parts of the PF Model.

In addition to the work on minimisation algorithms and the Perturbation Forecast Model mentioned above, he has also worked more widely on topics in numerical weather prediction. These areas include: the stability of the semi-implicit semi-Lagrangian discretisation of the fully compressible equations; Krylov subspace techniques for the solution of the Helmholtz equation occurring in semi-implicit models; the use of alternative control variables in Var, and the development of a singular vector capability to generate the fastest growing perturbations in the PF Model.