84
Air Pollution and Turbulence: Modeling and Applications
results from the association of all the vertical transport in two distinct areas of
this PDF: the saturated area of uprising motion, with positive buoyancy, a c and
the remaining area, 1 − a c . Thus, the horizontal domain is divided accordingly,
and considers the average properties of each one of these areas, resulting in two
peaks in the distribution function, whose intensity is equal to each one of the areas
(Ooyama 1971; Betts 1973; Yanai et al. 1973). This simplifi cation neglects some
of the smaller-scale variability (Wang and Stevens 2000) since it is based on the
average properties of these two sub-domains. This simplifi cation is known in literature as “top-hat” since properties of the horizontal domain have only two possible values.
The MF schemes have been used with great success in the representation of cumulus convection (Betts 1973; Arakawa and Schubert 1974; Tiedtke 1989). That has
led to its implementation in many numerical weather prediction models and to the
development of different methodologies. The results of several numerical and observational studies have contributed to that development (e.g., Randall et al. 1992). The
MF approach was extensively analyzed using LES simulations, for different types of
BL: with stratus (Schumann and Moeng 1991a), stratocumulus (Randall et al. 1992),
and shallow cumulus (Siebesma and Cuijpers 1995; Siebesma and Holstlag 1996;
Brown et al. 2002; Siebesma et al. 2004).
Recently, this type of parameterization was also applied to the clear sky BL
(Businger and Oncley 1990; Wang and Albrecht 1990; Randall et al. 1992; Wyngaard
and Moeng 1992), since observations of this type of BL also point out to the prominent role played by (dry) updrafts in the vertical transport of properties (Lenschow
and Stephens 1980; Lenschow et al. 1980; Nicholls 1989). Beyond the vast number
of applications of this type of approaches, it is important to mention that the MF
1 – a c
pdf
q
q c
q zb
q sat
q
a c
FIGURE 4.4 The PDF of a shallow cumulus BL. q sat is the saturation-specifi c humidity
and q zb is the specifi c humidity at the level where buoyancy is zero in saturated conditions. a c
corresponds to the horizontal area with saturated air and positive buoyancy of the PDF, 1 − a c
corresponds to the remaining area. The height of the two picks is equal to those areas. To
represent this PDF by the two picks corresponds to the MF approach.
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
results from the association of all the vertical transport in two distinct areas of
this PDF: the saturated area of uprising motion, with positive buoyancy, a c and
the remaining area, 1 − a c . Thus, the horizontal domain is divided accordingly,
and considers the average properties of each one of these areas, resulting in two
peaks in the distribution function, whose intensity is equal to each one of the areas
(Ooyama 1971; Betts 1973; Yanai et al. 1973). This simplifi cation neglects some
of the smaller-scale variability (Wang and Stevens 2000) since it is based on the
average properties of these two sub-domains. This simplifi cation is known in literature as “top-hat” since properties of the horizontal domain have only two possible values.
The MF schemes have been used with great success in the representation of cumulus convection (Betts 1973; Arakawa and Schubert 1974; Tiedtke 1989). That has
led to its implementation in many numerical weather prediction models and to the
development of different methodologies. The results of several numerical and observational studies have contributed to that development (e.g., Randall et al. 1992). The
MF approach was extensively analyzed using LES simulations, for different types of
BL: with stratus (Schumann and Moeng 1991a), stratocumulus (Randall et al. 1992),
and shallow cumulus (Siebesma and Cuijpers 1995; Siebesma and Holstlag 1996;
Brown et al. 2002; Siebesma et al. 2004).
Recently, this type of parameterization was also applied to the clear sky BL
(Businger and Oncley 1990; Wang and Albrecht 1990; Randall et al. 1992; Wyngaard
and Moeng 1992), since observations of this type of BL also point out to the prominent role played by (dry) updrafts in the vertical transport of properties (Lenschow
and Stephens 1980; Lenschow et al. 1980; Nicholls 1989). Beyond the vast number
of applications of this type of approaches, it is important to mention that the MF
1 – a c
q
q c
q zb
q sat
q
a c
FIGURE 4.4 The PDF of a shallow cumulus BL. q sat is the saturation-specifi c humidity
and q zb is the specifi c humidity at the level where buoyancy is zero in saturated conditions. a c
corresponds to the horizontal area with saturated air and positive buoyancy of the PDF, 1 − a c
corresponds to the remaining area. The height of the two picks is equal to those areas. To
represent this PDF by the two picks corresponds to the MF approach.
© 2010 by Taylor and Francis Group, LLC