Tim works on four dimensional variational data assimilation (4D-Var).
Recently Tim has been engaged in improving the incremental 4D-Var scheme used to assimilate data into the Met Office numerical weather prediction models.
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.
In the early days of 4D-Var the PF model represented the dynamics but almost none of the physical parametrizations of the full atmospheric model. The physics poses a particular problem as it tends to be rapidly evolving in space and may even be represented in the full model by switches, so even if a direct linearisation exists it may be of little value. Tim has been developing ideas to overcome this problem, and developed a PF Model parametrization for boundary layer processes.
The minimisation problem which must be solved every analysis time is very large (currently of order 10 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.
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. 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 discretization 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.