Linearized Physics for Data Assimilation at ECMWF - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 249

physics package must be as cheap as possible. To reduce computational cost, it
is therefore often necessary to simplify the set of linearized parameterizations by
retaining only physical processes that dominate in the full forecast model. Linearity
considerations can also influence this choice: if a given process is known to be
highly non-linear (e.g. thresholds, switches), this process should be discarded from
the linearized code since this might otherwise lead to instabilities during TL and AD
integrations. However, some of those instabilities can be overcome through adequate
modifications of the code. At the same time, though simplified, parametrization
schemes used in the linearized model must remain realistic enough to keep the
description of atmospheric processes physically sound.

11.3.1 Simplification

For important practical applications (incremental approach of 4D-Var - Courtier
et al. 1994 , adjoint based sensitivities, initial perturbations of EPS), the linearized
version of the forecast model is run at a lower resolution than the non-linear model.
In this case, since the dynamics is already simplified through the reduction in
horizontal resolution, the linearized physics does not necessarily need to be exactly
tangent to the full physics. In principle, physical parameterizations can already
behave differently between non-linear and tangent-linear models due to the change
in resolution. Consequently, some freedom exists in the development of a simplified
physics package, as long as the parameterizations can represent general feedbacks of
physical phenomena present in the atmosphere. Simplified approaches can allow the
progressive inclusion of physical processes in the tangent-linear and adjoint models.
This strategy has been used, for instance, in the operational 4D-Var systems of
ECMWF ( Mahfouf 1999 ; Mahfouf and Rabier 2000 ; Rabier et al. 2000 ; Janiskova
et al. 2002 ; Janiskova 2003 ; Tompkins and Janiskova 2004 ; Lopez and Moreau
2005 )andatMeteo-France ( Janiskova et al. 1999 ; Geleyn et al. 2001 ).

11.3.2 Regularization

As already mentioned, physical processes are often characterized by thresholds.
These can be:

- Discontinuities of some functions themselves describing the physical processes

or some on/off processes (for instance produced by saturation, changes between
liquid and solid phase);

- Some discontinuities in the derivative of a continuous function (i.e. the derivative

can go towards infinity at some points);

- Some strong non-linearities (such as those created by the transition from unstable

to stable regimes in the planetary boundary layer).