Proceedings - C-SRNWP Project

2.2 Mixing length parameterisation in ALARO -0 (preliminary results)
The way of the mixing length formulation appears to be very important in current ALARO–0
model that uses the first order closure pseudo-TKE parameterisation of turbulent fluxes
(Geleyn et al., 2006, Redelsperger et al., 2001). Classical first order closure turbulence
schemes in ARPEGE/ALADIN were using constant profiles of mixing length based on
observational studies and on the knowledge of the typical variation of eddy viscosity in the
atmosphere (e.g. O` Brien, 1970). A new empirical formulation was introduced in 2005 by J.-
F. Geleyn and J. Cedilnik (Cedilnik, 2005, hereafter GC05) which made the mixing length
profile dependent on the height of the planetary boundary layer (PBL). The formula for the
mixing length for momentum/enthalpy l yields:
m / θ
κ ( z + z0 / θ
)
( z + z ) ⎛ 1
l
m / θ
=
, (2)
κ
0 / θ
+ ε
m / θ
⎞
1+
⎜
⎟
λm
/ θ ⎝ β
m / θ
+ ε
m / θ ⎠
where κ is the Von Kármán constant, z
0
is the roughness length and
function prescribed as:
ε
m / θ
−α
m / θ
( z + z )
0 / θ
+
hPBL
β
m / θ
ε m / θ
is an exponential
= e
(3)
Parameter hPBL
is the diagnostic height of the PBL (Ayotte et al., 1996).The profile of l
m / θ
can be further modified via parameters λ m / θ
, α m / θ
, β m / θ
. Minor modifications of this
formulation were tested in 2006 in order to have a faster decrease of the mixing length over
h
PBL
and a dependency of the asymptotic mixing length λ m / θ
on the height of the PBL.
The pTKE parameterisation using the formulas (2) and (3) for mixing length was tested in
single column model on second GABLS experiment (see e.g. Cuxart et al., 2006). It provided
satisfactory results for stably stratified PBL (e.g. further improvement of the PBL height
diagnostics). However, the GC05 type of mixing length and its modification do not match
well situations with large mechanical production of turbulent kinetic energy above PBL that
occur in the region of strong jet stream (figure 6, left). The mixing length parameterisation
dependent on TKE and integral buoyancy calculation seemed to be better for this purpose
(Bougeault and Lacarrère, 1989, hereafter BL89). Nevertheless, direct application of the
BL89 type of mixing length in the pTKE turbulence scheme has a consequence of TKE
overestimation and further, rather negative impact on certain meteorological parameters (too
strong surface wind and wind gusts). Hence, a combination of the empirical GC05 and BL89
formulation was tested to achieve a reasonable compromise. The resulting formula yields:
l
( l −l
)
= l + k
(4)
m / θ 0 m / θ m / θ BL89
0m
/ θ
Here l0 m /
denotes a first-guess for the mixing length represented by the GC05
θ
parameterisation (2) and (3), l
BL89
is the BL89 formulation, which gives information about the
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