Geoscience Reference
In-Depth Information
Typical Values of ε x
10
3
(m
2
sec
-3
)
Type
Typical estimate
Reference
Simmons and
Hoskins, (1978)
D
N
0.2
Model
6 (Over major
mountains)
D
GW
Model
Shutts (2005)
Radar and aircraft
observations
Meischner et al
(2001)
D
C
1-10
1000 (within the
surface layer)
2 (in shallow sloping
frontal layers);
3 (close to the ground
before surface front
passes);
20 (jet stream level;
clear air turbulence)
30 (jet stream level;
clear air turbulence)
Piper and Lundquist
(2004)
Chapman and
Browning (2001);
Chapman and
Browning (2001);
Kennedy and
Shapiro (1975, 1980)
Gage et al (1980)
Hot-wire
anemometer at 3m
Radar observations
Aircraft observations
Radar observations
D
F
Lidar observations at
several hundred
metres
Lidar observations
Up to 4 (urban areas)
0.2 - 6.2 (urban areas)
Davies et al (2004);
Davis et al (2008)
D
B
(Urban areas)
Table 5. Energy dissipation rates, ε (m
2
sec
-3
) (from Collier and Davies, 2009)
Generally the vertical velocity in the turbulent boundary layer is very small, and difficult to
measure. It is clear that significant temporal averaging is necessary. Kropfli (1984) suggested
averaging over 20 minutes for VAD radar data, whereas Davies et al. (2005) averaged lidar
data over 10 to about 50 minutes. However, the errors in the wind velocity, particularly
those in w were thought by Sathe et al. (2011) to prelude the use of Doppler lidar with the
VAD technique from measuring boundary layer turbulence precisely. This conclusion is not
necessarily appropriate when two lidars are used as demonstrated by Davies et al. (2005)
and Pearson et al. (2009).
In order to investigate the detailed structure of the turbulent motion above the Urban
Canopy Layer (UCL), Davies et al. (2004) compared Doppler lidar-measured turbulent
structure functions with those derived using the Von Karman model of isotopic turbulence
in the inertial sub-range. Making allowance for the spatial averaging of the lidar pulse
volume, the correspondence is comforting (Fig. 4). Hence, estimates of the integral length-
scale, the dominant spatial scale of the turbulence above the UCL, can be made from the fit
of the model to the observations, giving a range from 250-400 m. In addition, measurements
were made of the velocity covariance power spectra, and the corresponding eddy
dissipation rates are shown in Fig. 5. The slope of the spectra within the inertial sublayer is
usually −5
/
3, although this depends upon the presence of inversion layers and the strength
of the turbulence. The fact that the spectrum falls off faster than −5
/
3 may indicate that the
turbulence approaches isotropy locally in the inertial range (Lumley, 1965). However, in the
