In numerical weather prediction, parameterisations are used to simulate missing physics in the model. These can
be due to a lack of scientific understanding or a lack of computing power available to address all the known
physical processes. Parameterisations are sources of large uncertainty in a model as parameter values used
in these parameterisations cannot be measured directly and hence are often not well known; and the
parameterisations themselves are also approximations of the processes present in the true atmosphere. Whilst
there are many efficient and effective methods for combined state/parameter estimation in data assimilation
(DA), such as state augmentation, these are not effective at estimating the structure of parameterisations.
A new method of parameterisation estimation is proposed that uses sequential DA methods to estimate errors
in the numerical models at each space-time point for each model equation. These errors are then fitted to
pre-determined functional forms of missing physics or parameterisations that are based upon prior information.
We applied the method to a one-dimensional advection model with additive model error, and it is shown that
the method can accurately estimate parameterisations, with consistent error estimates. Furthermore, it is shown
how the method depends on the quality of the DA results. The results indicate that this new method is a powerful
tool in systematic model improvement
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