MECHANICAL MIXING HEIGHT (zim ) IN THE CBL
In the early morning when the convective mixed layer is small, the full depth of the PBL may be controlled by mechanical turbulence. AERMET estimates the height of the PBL during convective conditions as the maximum of the estimated (or measured if available) convective boundary layer height (zic) and the estimated (or measured if available) mechanical mixing height (zim ). AERMET uses this procedure to insure that in the early morning, when zic is very small but considerable mechanical mixing may exist, the height of the PBL is not underestimated. When measurements of the mechanical mixed layer are not available, the mechanical boundary layer height is calculated by assuming that it approaches its equilibrium height given by Zilitinkevich (1972):
Although eq. (11) was designed for application in the SBL, it is used in the CBL only for the short transitional period at the beginning of the day when mechanical turbulence dominates. The procedure, used by AERMET, guarantees the use of the convective mixing height once adequate convection has been established even though the mechanical mixing height is calculated during all convective conditions. Since AERMET used eq. (11) to estimate the height of the mixed layer in the SBL, discontinuities in zi from night to day are avoided.
Venkatram (1980) has shown that, in mid-latitudes, eq.
(11) can be empirically epresented as where zie is in (m) and u* is in (m/s). zie calculated from Eq. (12)) is the unsmoothed mechanical mixed layer height. When measurements of the mechanical mixed layer height are available they are used in lieu of zie .
We smooth the equilibrium height, whether measured or calculated from eq. (12), in order to avoid sudden and unrealistic drops in zim during hours that experience a large decrease in wind speed. This smoothing is accomplished by controlling the time evolution of zie .
The time evolution of the mechanical mixed layer height, zim , is taken to be
where
is the time scale at which
the mechanical mixed layer height approaches its equilibrium value
given by eq. (12). Notice that when zim < zie, the
mechanical mixed layer height increases to catch up with its
current equilibrium value; conversely, when zim > zie
, the
mechanical mixed layer height decreases
towards its equilibrium value.
It
is reasonable to assume that the time scale, , that governs the
evolution of the stable boundary layer is governed by the boundary layer height and the
surface friction velocity,
so
that where ß is an
empirical constant, which, we have tentatively assigned the value of
2. As an example, with u*
of order 0.2ms–1 , and zim of order 500 m, the time scale is
of the order of 1250 seconds.
Because the friction velocity, u* , changes with time, we integrate eq. (13) numerically as follows:
where
the average time scale, 
, is given by:
In
eq. (15) zim {t} is the smoothed value at time t (previous
hour) and zie {t +
t
} is the current hour’s unsmoothed
value. Therefore eq. (15) produces a smoothed value for use in
for the current hour.
3 Meteorological Preprocessor (AERMET)
3.1
Derived Parameters in the CBL
3.1.1
SENSIBLE HEAT FLUX (H) IN THE CBL
3.1.2
FRICTION VELOCITY (u ) & MONIN OBUKHOV LENGTH (L)
IN
THE CBL 15 *
3.1.3
CONVECTIVE MIXING HEIGHT (z )
3.1.4
CONVECTIVE VELOCITY SCALE (w )
3.1.5
MECHANICAL MIXING HEIGHT (z ) IN THE CBL
3.2
Derived Parameters in the SBL
3.2.1
FRICTION VELOCITY (u ) IN THE SBL
3.2.2
SENSIBLE HEAT FLUX (H) IN THE SBL
3.2.3
MONIN OBUKHOV LENGTH (L) IN THE SBL
3.2.4
MECHANICAL MIXING HEIGHT (z ) IN THE SBL
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