As it was discussed in the last ALADIN Newsletter, a number of experiments made with the ARPEGE 4d-var system, to diagnose the problem of the appearance of large positive humidity increments over some subtropical land areas, were performed. They didn't reveal any interesting result. They were, for most of them, rerun because of a dirty error in the 4d-var chain scripts used. But again without any new result. For remember these experiments were carried out to study:
The overestimated precipitations (linked to this large positive humidity analysis increments) observed on Sahara region, are also present over the USA in June/July period, and on other subtropical hot regions. It has been shown that these large short-range forecast errors exist in ARPEGE but not in other models as the ECMWF or UKMO ones.
Thanks to François Bouttier, sensitivity experiments, executed with no specific humidity in the cost function, revealed the presence of a non-zero gradient with respect to the specific humidity parameter. So it turns out that there is something annoying in the TL/AD formulation of the dynamics. The specific humidity increments are caused by the linearization of three terms in the dynamics :
Cp = q Cpv
+ (1-q) Cpd
R = q Rv + (1-q) R d
d(RT) = T dR + R dT
This three terms are coded respectively in GPRCP, GPRCP and
CPG. d(.) indicates the Lagrangian derivative. Indices v and d
stand for "dry" and "vapour" respectively.
Experiments done by F. Bouttier revealed also that more than 90% of the
humidity increments are caused by the adjoint of the third above equation.
This fact happens, for example, in Sahara region because, apparently, there is
a combination of high temperatures and large horizontal gradients of (RT)
on the model surfaces. One must keep in mind that this is not due to incorrect
adjoint formulation, it is a feature of the dynamics equations. It seems that
a solution of the problem could be the introduction of some extra terms into
the TL/AD models, to prevent large local derivatives. The problem is probably
not limited to the humidity field.
As a first confirmation of this investigation, an experiment consisting in forcing Rv by Rd along the 4d-var minimisation, is performed.
d(RT) = (Rv - Rd)
T dq + ...
d(grad q) = (Rv - Rd)
T d(gradT)
As it can be seen on the figures below, the problem disappears completely. But putting : Rv = Rd
is not the solution of the problem, it is just a mean to
confirm the importance of local derivatives in the TL/AD part. More
investigations need still be done to find a scientific reasonable cure.
From figures, one can notice that, when compared to 3d-var, the experiment
with Rv forced to Rd
is the better one, indicating that the formulations of the TL/AD of dynamics
still need some tuning to work correctly.
Figure 1 : Convective precipitations (00+24H) over Sahara area, for the period between 01/06/2000 and 10/06/2000. Right column : operational charts. Left column : 3d-var reference charts. Middle column : results when forcing Rv to Rd in 4d-var.
Figure 2 : Zonal means of specific humidity (right), relative humidity (middle) and temperature (left). From top to bottom : operational 4d-var against 3d-var, adiabatic 4d-var against 3d-var, unique truncation incremental 4d-var against 3d-var, experiment Rv =Rd against 3d-var.
Figure 3 : Same as figure 2, but for zonal means averaged on standard levels over a 10-days assimilation experiment.
See :"Ways to address the issue of compensating errors in physical parameterizations" by Jean-Marcel Piriou in the proceedings of the 10th ALADIN workshop and the ALADIN & ALATNET reports for Toulouse in this Newsletter.
Last news in Newsletter 19.
Last news in Newsletter 19.
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