# Matthew Lang, University of Reading

## Parameterisation estimation using ensemble data assimilation

##### Coauthors

Peter Jan van Leeuwen and Phil Browne#### Abstract:

Data assimilation is routinely used for forecasting and reanalysis, but is still not used optimally for systematic model improvement. Comparing forecasts to observations is not optimal as the mismatch is due not only to missing physics in the model equations but also to the nonlinear propagation of errors in the state from the previous assimilation time. Ideally one would compare the model forecast over one time step with observations, but the observational density in space and time is typically not good enough to do this.

A possible solution is to compare a one-time-step model forecast with another much more accurate model of higher resolution. The higher-resolution model will not be perfect, but experience has shown that its systematic errors tend to be much smaller than those in the original model. A problem is that it is possible to start both models from a similar state, but the two models quickly diverge, and again the difference between the two is a combination of one-step model errors and the nonlinear propagation of previous one-step model errors.

To solve this problem we propose to assimilate a high-resolution model into the model that we want to improve. Because we have access to complete model fields we can assimilate all model variables at every grid point at every time step. We then compare at each time step a pure one-step model forecast with the assimilated result at the next time step. Part of this difference will be due to processes that cannot be resolved or parameterised at the courser resolution, and will show up as random at that resolution, but part will be systematic. These systematic space-time-variable fields contain the missing physics we are after. This idea can be used in NWP, climate, and other geophyscial models. Examples using ensemble data assimilation techniques are presented.