Proceedings - C-SRNWP Project

2.1 Pseudo prognostic turbulent kinetic energy scheme (pTKE)
The aim of this scheme is to simply use the old well tuned scheme, which is a Louis type one,
and add the missing features of the full TKE scheme (advection of TKE, shear, buoyancy
terms and dissipation) in a simplest possible way. The reasoning is that the stationary solution
of a full TKE scheme should be close to the values obtained by diagnosing this value from
local vertical gradients of wind and potential temperature and we are looking for a prognostic
equation of which stationary solution would yield exactly those diagnosed values.
The idea is to replace the full TKE equation with a simplified (pseudo) one (1), where the
diagnosed values of the coefficients are used to compute E ~ (TKE), K
E
( TKE self-diffusion
coefficient) and τ
ε
(relaxation time scale of the dissipation process for TKE). The three terms
on right hand side are: advection, TKE self-diffusion and the last term is a simple way of
describing the balance between shear and buoyancy production and destruction on one hand
and dissipation on the other.
∂E
∂t
=
1 ∂E
1 ~
Adv( E)
+ ρK
E
+ ( E − E)
ρ ∂z
τ ε
(1)
After obtaining the new TKE values, the new K coefficients are obtained by simply inverting
the process.
The scheme was tested in ALADIN model and it gives neutral or slightly improved scores for
the winds at the top of the PBL. The results of testing of the scheme with GABLS II
experiment are shown on figure 5. The pTKE is much better in simulating the evolution of
PBL height compared to the operational scheme (full TKE considered as reference). The
constant difference between the pTKE and the full scheme is due to the value of asymptotic
mixing length parameter and can be reduced with better tuning.
Figure 5: GABLS II experiment - comparison of PBL height computed with full TKE, pseudo TKE and
operational (diagnostic) scheme.
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