Geoscience Reference
In-Depth Information
“downward” approach, both relying on the prioritization of the various processes
represented in the full NL code used in standard forecasts. With the upward
technique, the simplified code is obtained by keeping only the most relevant
processes found in the full NL version. In the downward approach, the simplified
code is built by ignoring the least significant processes from the full NL code.
Ideally, both approaches should converge to more or less similar simplified codes,
which should be computationally cheaper than the full NL code, and contain fewer
discontinuities but are still able to provide realistic forecasts. Once the simplified
code has been written, it is thus necessary to tune and validate it in traditional
forecasts over periods at least equal to the maximum length of the expected
applications. At ECMWF for instance, this period corresponds to 12 h for 4D-Var
DA or to 24 h for singular vector computations involved in the ensemble prediction
system. It is particularly crucial to ensure that the new simplified NL code does not
depart too much from its full NL counterpart over this period of time. Verification in
much longer integrations (up to climate timescales), although not essential, is also
recommended to make sure that the new simplified scheme is stable and behaves
reasonably well.
11.4.2
Linearization Techniques
Once the NL version of the simplified scheme is deemed adequate, efforts are
devoted to the development of the TL code, first, and then of the AD code. In
practice, linearization can be achieved using either a manual line-by-line approach
or an automatic coding software (e.g. Giering and Kaminski 1998 ; Araya-Polo
and Hascoet 2004 ). However attractive automatic coding may sound, the manual
technique is usually more suitable as soon as one has to deal with the large amounts
of complex code used in modern NWP systems. Until now, in our own experience,
the code produced through automatic differentiation and adjoining often turned
out to be computationally very expensive (no optimization) and sometimes not
bug-free. This is the reason why so far only manual line-by-line TL and AD
coding has been applied to derive and update ECMWF's full set of linearized
physical parameterizations. In the future this strategy might be revisited if automatic
softwares become more efficient and reliable.
11.4.3
Tangent-Linear Version
An estimation of sensitivity of model output with respect to input required by
many studies can be efficiently done by using the adjoint. For atmospheric models
evolving in time, this backward integration requires to have the tangent linear model
acting forward in time. To build the TL model, the linearization is performed with
respect to the local tangent of the model trajectory.
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