Doppler radar analysis techniques - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 425

Appendix

Doppler radar analysis techniques

Dual- (or multiple) Doppler analysis is possible when two or more Doppler radars
scan the same volume at the same time from two different viewing angles. The
equations relating the Doppler velocities—V r i , where i refers to the first (1),
second (2), , nth (n) radar—to the three wind components (u, v ,andw) in, for

example, Cartesian coordinates are, as originally formulated by Larry Armijo in
the late 1960s, are as follows ( Figure A.1 ):

...

V r 1 ¼ 1 = R 1 ½ xu þ y vþ z ð w þ W t Þ ð A : 1 Þ

V r 2 ¼ 1 = R 2 ½ð x x 2 Þ u þ y vþ z ð w þ W t Þ ð A : 2 Þ

.

V r n ¼ 1 = R n ½ð x x n Þ u þð y y n Þvþ z ð w þ W t Þ ð A : 3 Þ

where the first radar is at the origin, the second is at (x 2 ; 0), and the nth is at

(x n ; y n ); R n is the range of the nth radar from the target volume; and W t is the

terminal fall speed of scatterers in the volume. It is assumed that targets move
along with the wind, but also have a component of terminal fall velocity. In the
case of sharply curved flow and relatively massive hydrometeors or other targets,
the centrifugal force may also make targets deviate from air motion.
Much attention must be given to how one interpolates radar data to grids not
native to the data collection mode (most data from fixed radars are collected in
tilted planes in cylindrical coordinates), such as Cartesian coordinates (e.g., as
above). Gaussian weighting (or interpolating) functions are commonly used,
though in some instances others may be more appropriate (e.g., polynomial func-
tions and functions whose radii of influence are dependent upon direction).
Specifying the proper spatial filter (e.g, via parameters in the Gaussian weighting
function) is necessary to extract the maximum detail from the data, given the