VERTICAL TURBULENCE CALCULATED BY THE INTERFACE
In
the CBL, the vertical velocity variance or turbulence (
2wT
) is profiled using an
expression that
contains a mechanical and convective portion and is similar to one
introduced earlier by Panofsky et al. (1977) and included in other
dispersion models (e.g., Berkowicz at al., 1986, Hanna and Paine,
1989, Weil, 1988). It is
The
above expression effectively interpolates between a mechanical or
neutral stability limit (wT
~ wc ~u* )
and a strongly convective limit (wT
~ wc ~w* ).
The
convective portion (2wT
) of
the total variance is calculated as follows: 2
Wc
where the expression for z
0.1
zic is the free convection
limit (Panofsky et al, 1977), for 0.1zi < z zic
is
the mixed-layer value (Hicks,1985) and for z > zic is a
parameterization to connect
the mixed layer 2wc
to the assumed near-zero value
well above the CBL. The profile of convective vertical
turbulence described in eq. (36) is also presented pictorially
in Figure 5.
Figure 5: Convective
portion of the vertical turbulence in the CBL.
In
an earlier AERMOD formulation for mechanical (or shear induced)
turbulence, values at the top of the mechanically mixed layer, i.e., v
{zim } and w {zim
}, were based on their
values at the surface.
Peer review comments suggested that since the surface is generally
decoupled from higher layers, a formulation based either on
measurements above zim or an assumed parameterized turbulent
intensity at zim coupled with wind speed estimates would be more
appropriate.
Therefore,
the mechanical turbulence portion of 2wT
is assumed to consist of a
contribution from 2 wT the
boundary layer and from a “residual layer” above the boundary
layer (z>zi ). This is done to: I 1) satisfy the assumed
decoupling between the turbulence aloft (z>zi ) and at the
surface in the I
CBL shear layer, and
2) maintain a continuous variation of 2wt
with z near z=zi .
The mechanical
turbulence is parameterized by:
The expression used to calculate _ is wml
where
the wml =1.3u at
z=0 is consistent with Panofsky et al. (1977).
For
z > zi wmr
is set
equal to wmx
, the maximum value of the
mechanical turbulence in the residual layer. wmx is calculated
as the average of all measured values above zi . If
measurements are
not available, then wmx
is taken as the default value
of 0.02u{zi}. The 0.02 is an assumed turbulence intensity iz
( = w
/ u)
for the very stable conditions presumed to exist above zi
.
This value
of turbulence intensity is similar to that assumed in Gifford (1975).
Within the mixed layer, i.e. z<zi , the residual turbulence is reduced from its value at zi to zero at the surface. Therefore, for all z the residual turbulence takes the form
Figure
6 presents the profile of
the mechanical portion of the vertical turbulence in the CBL. The
effect of combining the residual and boundary layer mechanical
turbulence (eq. (37)) can be seen in this figure. For the
purposes of computing wmr
in Figure 6 we set L=.1zi and zo =.0001Zi
Figure 6: Mechanical
portion of the vertical turbulence in the CBL
In
the SBL the vertical turbulence contains only a mechanical portion
and it is given by eq. (37) and eq. (38). The use of
the same wm
expressions for the SBL and CBL
is done to ensure 2 wm continuity
of turbulence in the limit of neutral stability, i.e., as z 
0 or | L | 
. That is, the turbulence should be the same as neutral
stability is approached either from unstable or stable conditions. Figure
7 is similar to Figure 6 except for a notably increase in
the value of wmr.
Values for wmr are based on
the magnitude of the wind speed at zi . Therefore the
differences in the
two figures stem from setting zo =.0001Zi in the CBL and zo
=.001Zi in the SBL
Figure 7: Profile of
vertical turbulence in the SBL
4 AERMOD’s Meteorological Interface
4.1
General Profiling Equations
4.1.1
WIND SPEED PROFILING IN THE INTERFACE
4.1.2
WIND DIRECTION PROFILES IN INTERFACE
4.1.3
PROFILES OF THE POTENTIAL TEMPERATURE GRADIENT IN THE
INTERFACE
4.1.4
POTENTIAL TEMPERATURE PROFILING IN THE INTERFACE
4.1.5
VERTICAL TURBULENCE CALCULATED BY THE INTERFACE
4.1.6
LATERAL TURBULENCE CALCULATED BY THE INTERFACE
4.2
Vertical Inhomogeneity in the Boundary Layer as Treated by the INTERFACE
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