Linearized Physics for Data Assimilation at ECMWF - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 277

diagnose short-range forecast sensitivities to observations. Furthermore, employing
linearized moist physics parameterizations in the 4D-Var minimizations has per-
mitted the assimilation of the ever-increasing number of satellite and ground-based
observations that are sensitive to clouds and/or precipitation.
However, the development of efficient and well-behaved TL and AD codes is
made difficult by many obstacles and is therefore time consuming and often tedious,
if not sometimes rather frustrating. In particular, a substantial amount of work is
required to simplify and regularize the code or, in other words, to eliminate or
smooth out the discontinuities and non-linearities that often characterize physical
processes. The behaviour of the linearized physics package also needs to be
constantly and thoroughly monitored in a wide range of potential applications
(e.g. data assimilation, singular vectors computations, sensitivity experiments). In
particular, every time one of the physical parameterizations is modified in the
non-linear forecast model (which in practice occurs at every new model release),
it is necessary to verify that the tangent-linear approximation is not degraded.
If it is, appropriate updates have to be made to the TL and AD code so as to
avoid a likely degradation of the 4D-Var operational performance. Eventually, a
delicate compromise must constantly be achieved between linearity, computational
efficiency and realism, to ensure that the best analysis and (above all) forecast
performance are obtained.
With the continual trend towards higher and higher resolutions (both in the hor-
izontal and the vertical), maintaining a well-behaved linearized physics package is
bound to become more and more challenging. Currently, the minimizations involved
in ECMWF's 4D-Var are still run at a relatively coarse resolution of roughly 80 km,
even though trajectories and final analyses are computed at 16 km resolution. When
minimization resolution is increased, the ability to represent smaller-scale and often
noisier processes (such as convection) is likely to make it more difficult to fulfil the
TL hypothesis. However it should be mentioned that preliminary TL approximation
tests were recently performed with a global resolution of 25 km and over 12 h, with
no sign of a degradation. One of the major uncertainty for the future is whether it will
remain possible to make linearized physics to work when the resolution of the non-
linear forecast model reaches a few kilometres, while the resolution remains well
above 10 km in the 4D-Var minimizations. At this stage, the paradox of explicitly
resolving convection in the trajectory but still needing to parameterize it in the
minimization could be very challenging, and the current 4D-Var approach might
need to be modified so as not to include the smaller scales in the entire analysis
process (e.g. through trajectory smoothing).
There should nonetheless be some even greater concern about the growing
complexity of the physical parameterizations used in the non-linear forecast model.
Over the years, the increasing level of detail added to the representation of physical
processes has been synonymous for enhanced and more numerous sources of
non-linearity, which by construction cannot be included in the linearized physics
package. There is a risk that if nothing is done to keep this trend under control, it will
become impossible to make the linearized physics follow its non-linear counterpart
closely enough, in which case 4D-Var as we know it may not be sustainable.