Data Assimilation ofWeather Radar and LIDAR for Convection Forecasting and Windshear Alerting in Aviation Applications - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 533

Fig. 22.12 The geographical setup in the vicinity of the Hong Kong International Airport (HKIA)
with height contours in 100 m. The locations of the meteorological equipment considered in the
present study are also shown

ŒW 3 .x/ 2 @

2

C W 4 .x/ 2 @

2

J 3 C J 4 C J 5 D X
i;j

u
@x

C @

v
@y

v
@x

@

u
@y

C W 5 .x/ 4 . r 2 u Cr 2 v / 2 : (22.11)

Here m is the grid size in the retrieval domain.

The last term in ( 22.8 ) is the conservation constraint. In Qiu et al. ( 2006 ), the con-
servation of precipitation content based on Radar reflectivity is used. In the present
paper, conservation of the observed radial velocity is employed because the
LIDAR's backscattered power data appear to have beam-to-beam variability arising
from the fluctuations of the output power. The conservation equation is given by:

x D y D 100

"

2 #

@

J 6 D X
i;j

X

v obs
r
@t

v obs
r
@x

v obs
r
@y

C u @ C v @

W 6 (22.12)

n

where is the time index. It is involved in the time derivative of the observed radial

velocity. In the current scanning strategy of the LIDAR, the PPI scans are performed
every 2 min or so. Three consecutive scans are used in the 2D wind retrieval in this
paper. Equation ( 22.12 ) is the approximate form of the conservation of momentum

n