Developing the Met Office's core operational data assimilation system.
4D-Var calculates a forecast model trajectory that best fits the available observations to within the observational error over a period of time. The observational error includes allowance for the finite resolution of the model. Since the model cannot represent the atmosphere exactly, a trajectory cannot be fitted to observations for a period longer than 12 hours without making corrections to it. The expectation is that the best forecast will be achieved by constructing a best fit over a long time interval while making the smallest possible corrections, and then extrapolating forward in time. This exploits the maximum amount of observed information given that only limited observations are available in any one six hour period.
Fitting a model trajectory to observations is very computationally demanding. The only feasible method is to assume that an accurate background forecast is available and that an adequate fit to observations can be made by adding small increments to it. The problem can then be written as minimising a cost function which measures the departure of the corrected forecast from the observations and from the background forecast, weighted by the errors in each.
The iteration strategy is to approximate the evolution of increments to the forecast model, which is nonlinear, by a linear perturbation forecast model. It is then possible to minimise the cost function as a function of the initial increments. Optimising this procedure requires careful preconditioning, and interleaving of nonlinear iterations with linear iterations. The nonlinearity comes both from the forecast model itself and from the nonlinear relation between many observed quantities, such as satellite radiances, and model variables.
4D-Var is used at many operational centres as well as the Met Office. However, future computers will have an increasingly parallel architecture, and ensemble methods, which can fully exploit this, will become more attractive. It is therefore necessary to establish the full potential of 4D-Var in order to see whether it will remain the preferred operational method in the future.