Data Assimilation ofWeather Radar and LIDAR for Convection Forecasting and Windshear Alerting in Aviation Applications - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 536

Fig. 22.14 Ridge of updraft identified to the east of the airport, during the episode of spring
tropical cyclone. ( a ), ( b ), and ( c ) are the LOS velocity output from LIDAR. It is not apparent
that a ridge structure is present. ( e ), ( f ), and ( g ) are the backward-time FDFTLE. A long ridge of
FDFTLE maxima is seen persistent over time, trailing Lin Fa Shan. The different times, from left
to right for each pair of plots, are 14:36 UTC, 14:39 UTC and 14:41 UTC. ( d ) Hovmoller diagram
of the LOS velocity at 5 km range between 14:00-16:00 UTC. The coverage is shown as the arc
of black dots in ( a ). ( h ) Hovmoller diagram of the backward-time FDFTLE between 14:00-16:00
UTC. The FDFTLE maxima (on the persistent ridge) is connected by the black curve . This curve
is also plotted in ( d ). It is seen that the ridge correspond to a rather strong change in LOS velocity

(Fig. 22.14 d) and the backward-time FDFTLE (Fig. 22.14 h) at 5 km range between
45 ı and

105 ı azimuth and 14:00-16:00 UTC to study the relation between LCS and
LOS velocity for this specific updraft. Since the updraft structure is transversal to
the arc 5 km from LIDAR, we locate its time evolution in terms of the change in
azimuthal angles where the ridge appears. We plot the evolution of the azimuthal
angle in black in both Hovmoller diagrams. It is seen that this curve corresponds to
a sharp transition of LOS velocity at 5 km range from the LIDAR. Above the curve,
the flow is to the right of the ridge, and move faster towards the LIDAR. Below the
curve, the flow is to the left of the ridge and move slower. As such, the converging
flow gives rise to the persistent ridge in our analyses.

22.4.3 Retrieval of 3-Dimensional Winds from LIDAR

Using 4DVAR

The use of 4DVAR analysis in retrieving the three wind components and thermody-
namic fields from LIDAR radial velocity data has been investigated by researchers in
recent years. Fundamentals of the 4DVAR include a forward large-eddy-simulation
(LES) and a backward adjoint integration. The adjoint formulation is particularly
complicated due to the required estimation of the gradients of the cost function
with respect to all control variables. Two major approaches in constructing 4DVAR
have been developed by Chai et al. ( 2004 )and Newsom and Banta ( 2004 ). The