Parameterization of Convective Boundary Layer Turbulence and Clouds
91
The source of this process is the surface buoyancy fl ux (
)
v s
w θ
′ ′ . The process
of top-entrainment also contributes, in general, for the dilution of clouds, once it
mixes dry and warm air into the BL (Randall 1984). It is not possible to represent
this process explicitly in large-scale and mesoscale models, where it needs to be
parameterized. The K-diffusion schemes, in general, underestimate the effect of topentrainment (Ayotte et al. 1996), and there is not yet a scheme that represents well
this process for different types of BL. Additionally, the representation of this process
depends highly on the resolution of the model.
4.4 EDDY DIFFUSIVITY/MASS-FLUX PARAMETERIZATION
IN THE CBL
In GCMs, the sub-grid turbulent mixing is parameterized using different schemes.
When cloud formation exists in the CLC, these models use, in general, an alternative parameterization for the vertical transport in the cloud layer: the MF approach,
whereas the sub-cloud layer is parameterized by K-diffusion. This discontinuity
seems to contribute for weak results in shallow cumulus simulations (Lenderink
et al. 2004). Some MF parameterizations have been applied to the dry BL (Wang and
Albrecht 1990; Randall et al. 1992), pointing out that the MF schemes are adjusted
for the parameterization of the turbulent mixing due to thermals. These facts associated with the discontinuity in the treatment of the different scales of turbulent
mixing suggest the development of a unifying scheme, for the representation of the
turbulent mixing of heat and moisture in the BL with and without clouds.
This section introduces the eddy diffusivity/mass-fl ux (EDMF) parameterization. This parameterization resulted from an original idea of Siebesma and Teixeira
(2000) and was developed by Soares et al. (2004) and Siebesma et al. (2007). These
different developments aimed at the implementation of EDMF in different scale
models, from GCMs to LAMs. The EDMF scheme includes both a turbulent diffusion approach and a MF contribution. This combination is based on the division of
the CBL turbulent mixing between the mixing done by thermals and the mixing due
to smaller eddies. The nonlocal transport associated with thermals, structurally nonsymmetrical, is represented by a MF term. The local mixing due to smaller eddies
is described by the diffusion contribution. As mentioned above, the need of nonlocal
contribution is found to be crucial in the description of the CBL evolution.
4.4.1 THE EDDY DIFFUSIVITY/MASS-FLUX SCHEME
The EDMF scheme is based on the decomposition of mixing scales, responsible for
the subgrid turbulent transport (Figure 4.5).
Considering an horizontal slab of the CBL divided into an area with strong thermals, with a fi xed fractional area a u , and a complementary environment, the turbulent fl ux of a moist conserved variable φ can be decomposed into three terms:
(1
)
(
) (
),
u
e
u
u
u
u
e
u
e
w
a w
a w
a w w
φ =
φ + −
φ +
−
φ − φ
′ ′
′ ′
′
(4.49)
© 2010 by Taylor and Francis Group, LLC
91
The source of this process is the surface buoyancy fl ux (
)
v s
w θ
′ ′ . The process
of top-entrainment also contributes, in general, for the dilution of clouds, once it
mixes dry and warm air into the BL (Randall 1984). It is not possible to represent
this process explicitly in large-scale and mesoscale models, where it needs to be
parameterized. The K-diffusion schemes, in general, underestimate the effect of topentrainment (Ayotte et al. 1996), and there is not yet a scheme that represents well
this process for different types of BL. Additionally, the representation of this process
depends highly on the resolution of the model.
4.4 EDDY DIFFUSIVITY/MASS-FLUX PARAMETERIZATION
IN THE CBL
In GCMs, the sub-grid turbulent mixing is parameterized using different schemes.
When cloud formation exists in the CLC, these models use, in general, an alternative parameterization for the vertical transport in the cloud layer: the MF approach,
whereas the sub-cloud layer is parameterized by K-diffusion. This discontinuity
seems to contribute for weak results in shallow cumulus simulations (Lenderink
et al. 2004). Some MF parameterizations have been applied to the dry BL (Wang and
Albrecht 1990; Randall et al. 1992), pointing out that the MF schemes are adjusted
for the parameterization of the turbulent mixing due to thermals. These facts associated with the discontinuity in the treatment of the different scales of turbulent
mixing suggest the development of a unifying scheme, for the representation of the
turbulent mixing of heat and moisture in the BL with and without clouds.
This section introduces the eddy diffusivity/mass-fl ux (EDMF) parameterization. This parameterization resulted from an original idea of Siebesma and Teixeira
(2000) and was developed by Soares et al. (2004) and Siebesma et al. (2007). These
different developments aimed at the implementation of EDMF in different scale
models, from GCMs to LAMs. The EDMF scheme includes both a turbulent diffusion approach and a MF contribution. This combination is based on the division of
the CBL turbulent mixing between the mixing done by thermals and the mixing due
to smaller eddies. The nonlocal transport associated with thermals, structurally nonsymmetrical, is represented by a MF term. The local mixing due to smaller eddies
is described by the diffusion contribution. As mentioned above, the need of nonlocal
contribution is found to be crucial in the description of the CBL evolution.
4.4.1 THE EDDY DIFFUSIVITY/MASS-FLUX SCHEME
The EDMF scheme is based on the decomposition of mixing scales, responsible for
the subgrid turbulent transport (Figure 4.5).
Considering an horizontal slab of the CBL divided into an area with strong thermals, with a fi xed fractional area a u , and a complementary environment, the turbulent fl ux of a moist conserved variable φ can be decomposed into three terms:
(1
)
(
) (
),
u
e
u
u
u
u
e
u
e
w
a w
a w
a w w
φ =
φ + −
φ +
−
φ − φ
′ ′
′ ′
′
(4.49)
© 2010 by Taylor and Francis Group, LLC