Proceedings - C-SRNWP Project

A simple parameterization for detrainment in shallow
cumulus.
Wim de Rooy and Pier Siebesma
Royal Netherlands Meteorological Institute, The Netherlands
Recently there has been a regained
interest in the parameterization for
entrainment in cumulus convection.
Unfortunately little attention has been paid
to the parameterization of the detrainment
process although this counterpart of the
cloud mixing process is, as this study
shows, even more important for obtaining
realistic mass flux profiles in cumulus
convection.
A new simple but flexible
parameterization for the detrainment
process in shallow convection is presented.
From ensemble considerations and
confirmed by LES results it is shown that
the magnitude of the fractional detrainment
for shallow convection is decreasing with
increasing depth of the cloud layer. A
simple detrainment formulation is
presented that takes this dependency into
account by considering the mass flux
profile in a non-dimensionalized way. The
only free parameter in this detrainment
formulation is the percentage of the mass
flux at cloud base that is still present halfway
the cloud layer (called m * ). This free
parameter turns out to depend on the
environmental conditions as well as
updraft properties and can be expressed
with a parameter coming from the
buoyancy sorting concept, χ
c
, the fraction
of environmental air necessary to make the
updraft air just neutrally buoyant and
averaged over the lowest half of the cloud
layer. LES results show a distinct relation
___________________
* Corresponding author address: Wim
de Rooy, KNMI, P.O. Box 201, 3730
AE, De Bilt, The Netherlands. E-mail:
rooyde@knmi.nl
between m * and χ
c
which can be used to
close our parameterization.
z [m]
2500
2250
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1750
1500
1250
1000
750
500
250
0
initial profile (0:00 UTC)
LES (24:00 UTC)
fixed ε and δ (24:00 UTC)
new δ (24:00 UTC)
4 5 6 7 8 9 10 11 12 13 14 15 16 17
q t
[gr kg -1 ]
Fig. 2. Total specific humidity profiles
after 24 hrs of simulation during the RICO
case for the LES model (black squares)
and the SCM using fixed ε and δ (blue
squares) or the new detrainment
parameterization (red triangles). The black
solid line represents the initial profile.
Results of the new parameterization in
a Hirlam single column model (SCM) for a
wide range of shallow cumulus convection
cases (BOMEX, ARM and RICO)
illustrate the strength of this new
detrainment parameterization. As an
example, we show in Fig. 2 the total
specific humidity profile of the
independent RICO case after 24 hours of
simulation. Presented are the results for an
LES model, a SCM with fixed fractional
entrainment (ε) and detrainment (δ)
coefficients as known from literature, and
finally a SCM with the new detrainment
parameterization. The new
parameterization gives an almost perfect
match with the LES humidity profile.
There is also a large improvement on the
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