114
Air Pollution and Turbulence: Modeling and Applications
model (Lafore et al. 1998), taking advantage of the eddy-diffusivity turbulence
closure scheme based on the TKE budget equation of Cuxart et al. (2000) (CBR
hereafter). The MesoNH model has a convection scheme based on the Kain and
Fritsch (1993) bulk MF convection parameterization for deep and shallow convection (Bechtold et al. 2001).
The shallow cumulus representation is an extension of the dry EDMF scheme,
when an ascending parcel condensates. Therefore, the updraft model may also be
used as a trigger function for the initiation of deep convective clouds.
The updraft originates at the surface layer and ascends entraining environmental air, up to the level where its vertical velocity vanishes. During the ascent, the
occurrence of oversaturation is checked, in which case condensation takes place in
the entraining rising plume. The condensation test used is based on the algorithm
proposed by Davies and Jones (1983). Cloud base height is in that case defi ned as the
height of the lifting condensation level, while cloud-top height is defi ned as the level
above the lifting condensation level at which the vertical velocity vanishes according to Equation 4.55. The cloud model aims to represent an ensemble of convective
shallow cumulus clouds.
The EDMF scheme proposed by Soares et al. (2004) showed some improvements in the description of the dry BL when compared with the version presented in
Section 4.4.4 (EDMF-EMP). The main modifi cations in the EDMF formulation for
the dry BL are related to the parcel initialization and the MF coeffi cient.
Once it is aimed to describe both the dry and shallow BLs, the rising parcel is
designed to determine the updraft liquid water potential temperature, total specifi c
humidity and vertical velocity, and BL height. In order to initialize the parcel, it is
necessary to estimate its excess virtual potential temperature, which is a function
of the surface layer variability. Soares et al. (2002), in close agreement with Troen
and Mahrt (1986), showed that the excess scales very well with the ratio between the
surface heat fl ux and e 1/2 , for any level k in the surface layer:
1/2
(
)
( )
( )
,
( )
v s
vu k
v k
k
w
z
z
e z
θ
′ ′
θ
=θ
+β
(4.83)
where the value of the coeffi cient β was adjusted to 0.3. Similar equations apply to
other properties such as θ lu and q tu . This initialization requires the solution of the
TKE prognostic equation and is rather insensitive to the initialization level k.
If Equation 4.55 is a reasonable approximation to the ensemble vertical velocity,
it may be directly used to compute M from its defi nition, once a u has been determined. It was proposed that a u = 0.1, in agreement with the diagnosed value of the
average horizontal area containing buoyant updrafts (Lenschow and Stephens 1980,
van Ulden and Siebesma 1997). This way the parameterization is able to represent
the overshooting process. Instead of considering z i as the level where the buoyancy is zero, the vertical velocity equation is used to determine the level where w u
vanishes.
Compared to the updraft model presented before, this latter model has
some advantages: (1) it is less sensitive to the initialization level, z k , or to model
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
model (Lafore et al. 1998), taking advantage of the eddy-diffusivity turbulence
closure scheme based on the TKE budget equation of Cuxart et al. (2000) (CBR
hereafter). The MesoNH model has a convection scheme based on the Kain and
Fritsch (1993) bulk MF convection parameterization for deep and shallow convection (Bechtold et al. 2001).
The shallow cumulus representation is an extension of the dry EDMF scheme,
when an ascending parcel condensates. Therefore, the updraft model may also be
used as a trigger function for the initiation of deep convective clouds.
The updraft originates at the surface layer and ascends entraining environmental air, up to the level where its vertical velocity vanishes. During the ascent, the
occurrence of oversaturation is checked, in which case condensation takes place in
the entraining rising plume. The condensation test used is based on the algorithm
proposed by Davies and Jones (1983). Cloud base height is in that case defi ned as the
height of the lifting condensation level, while cloud-top height is defi ned as the level
above the lifting condensation level at which the vertical velocity vanishes according to Equation 4.55. The cloud model aims to represent an ensemble of convective
shallow cumulus clouds.
The EDMF scheme proposed by Soares et al. (2004) showed some improvements in the description of the dry BL when compared with the version presented in
Section 4.4.4 (EDMF-EMP). The main modifi cations in the EDMF formulation for
the dry BL are related to the parcel initialization and the MF coeffi cient.
Once it is aimed to describe both the dry and shallow BLs, the rising parcel is
designed to determine the updraft liquid water potential temperature, total specifi c
humidity and vertical velocity, and BL height. In order to initialize the parcel, it is
necessary to estimate its excess virtual potential temperature, which is a function
of the surface layer variability. Soares et al. (2002), in close agreement with Troen
and Mahrt (1986), showed that the excess scales very well with the ratio between the
surface heat fl ux and e 1/2 , for any level k in the surface layer:
1/2
(
)
( )
( )
,
( )
v s
vu k
v k
k
w
z
z
e z
θ
′ ′
θ
=θ
+β
(4.83)
where the value of the coeffi cient β was adjusted to 0.3. Similar equations apply to
other properties such as θ lu and q tu . This initialization requires the solution of the
TKE prognostic equation and is rather insensitive to the initialization level k.
If Equation 4.55 is a reasonable approximation to the ensemble vertical velocity,
it may be directly used to compute M from its defi nition, once a u has been determined. It was proposed that a u = 0.1, in agreement with the diagnosed value of the
average horizontal area containing buoyant updrafts (Lenschow and Stephens 1980,
van Ulden and Siebesma 1997). This way the parameterization is able to represent
the overshooting process. Instead of considering z i as the level where the buoyancy is zero, the vertical velocity equation is used to determine the level where w u
vanishes.
Compared to the updraft model presented before, this latter model has
some advantages: (1) it is less sensitive to the initialization level, z k , or to model
© 2010 by Taylor and Francis Group, LLC