Geoscience Reference
In-Depth Information
This is greatly simplified if this operation is performed in cylindrical coordinates with axis
chosen to be in the line connecting the two radars 1 and 2, referred to as the baseline. The
mean Doppler velocity is corrected for the reflectivity-weighted mean terminal velocity of
the scatterers w
t
. Hence the estimate of the radial component of air motion is:
v v'
wsin
1,2
1,2
t
e1,2
where v
1,2
' are the mean Doppler target velocities measured by radars 1,2 at data points and
w
t
is positive. To estimate w
t
an empirical expression such as that given by Atlas et al. (1973)
can be used. The estimated radial velocities v
1,2
of the air can be interpolated to uniformly
spaced grid points in planes at an angle α to the horizontal surface containing the baseline.
The wind component w
α
normal to the plane is obtained by solving the continuity equation
in cylindrical coordinates:
1/r ∂/∂r (rρw
r
) + 1/r ∂/∂x (ρw
α
) + ∂/∂s (ρw
s
) = 0
with the boundary condition w = 0 at the ground. Generally this approach covers a smaller
area compared to the full dual-Doppler coverage and may contain residual errors.
An improved albeit similar approach has been developed by Bousquet and Chong (1998) for
three dimensional wind retrieval from multiple airborne Doppler radars, called the Multiple
Doppler Synthesis and Continuity Adjustment Technique (MUSCAT). It was extended for
application over both flat or complex terrain by Chong and Cosma (2000), and for ground-
based radar systems by Chong and Bousquet (2001). An alternative computationally
inexpensive plane-to-plane solution known as the Multiple Analytical Doppler (MANDOP)
system has been described by Tabary and Scialom (2001).
In 2003 two mobile Doppler lidars were sited at either end of a disused runway
approximately 1.6 km apart at RAF Northolt in West London (Collier et al., 2005). The aim
was to investigate the optimal lidar configuration to measure wind flow turbulence
characteristics. Three dual-lidar configurations are shown in Figure 2. Figures 2a and 2c
show data taken with the two lidars where the beams cross at a point, which is in the
vertical plane defined by the line joining the two lidar positions. With each lidar system the
radial velocities along the beams were measured every five seconds. The two radar
computer clocks were first synchronised, and then for the different configurations, the time
series of data were taken. Table 4 gives statistics derived from operating the lidar systems as
in configuration 2c. The data were taken for a period of 700 seconds, and for different
heights over a period of approximately 50 minutes. The errors in the vertical velocities from
this dual-Doppler lidar deployment were analysed by Davies et al. (2005). It was found that
the spread in vertical velocities due to the combined effects from instrumental errors of the
two lidars can in some cases act to cancel each other out, although on other occasions this
was not the case. We discuss the implications of this in the next section.
Drechsel et al. (2009) applied the MUSCAT processing system to dual-Doppler lidar data
collected during the Terrain - induced Experiment (T-REX) in the spring of 2006. The flow
pattern derived from 19 three dimensional wind fields revealed differences of wind speed
and direction of less than 1.1 m sec
-1
and 3 degrees on average compared to radiosonde and
wind profiler data. The average vertical motion from MUSCAT was -0.24 m sec
-1
compared
to -0.52 m sec
-1
from wind profiler data and -0.32 m sec
-1
from radiosonde data.
