radsynth −− construct Cartesian velocity components from radar Doppler velocities
radsynth [-xw] minradars suffix1 suffix2 ...
Radsynth expects a Candis file on the standard input containing the merged radcart output for two or more Doppler radars. This file is transmitted to the standard output with a number of fields added. These fields are the easterly, northerly, and upward components of particle velocity, u, v, and w (in meters per second), geometric error fields, eu, ev, and ew, the time after midnight in kiloseconds, time, and conventional time and date variables, year, mon, day, hour, min, and sec. All new fields are added to the variable slice.
The command line arguments have the following meanings. Minradars is the minimum number of radars producing good data at a point that is required before a synthesis is attempted at that point. If a synthesis is not attempted at a point, all new fields at that point are given bad data values. The suffixes are those used in the invocation of cdfmerge that produces the input file. The number of these suffixes indicates the number of radars, and this must be greater than or equal to minradars.
Markedly different behavior results from setting minradars to two or to some greater value. (Two is the smallest legal value.) For minradars = 2, a dual Doppler synthesis is attempted, even if more than two radars are available. The vertical air velocity is constructed by integrating the continuity equation upward from the surface, where w = 0 is assumed. The vertical partical velocity, wp, is computed from w using the Joss-Waldvogel relationship for particle terminal velocity, wt = 2.6*Z^0.107, where Z is the radar reflectivity in linear units. If the -w flag is specified, the vertical particle velocity is used in constructing the horizontal winds in the dual Doppler case. Otherwise, particles are assumed to fall with their terminal fall speed relative to the ground in the synthesis of the horizontal winds.
If minradars is three or greater, a triple Doppler synthesis is attempted, in which u, v, and wp are all directly calculated from radial velocity components. The vertical air velocity, w, is again computed by integrating the continuity equation upward from the surface.
If the -x flag is set, radial velocities and reflectivities are extrapolated from the second level down to the first level if first level values are bad. This is helpful when the curvature of the earth or ground clutter keeps the radars from obtaining a good low level measurement.
Radsynth allows there to be more than two radars for dual Doppler synthesis, and more than three radars for triple Doppler synthesis. The calculation is performed using a least squares analysis which yields the exact answer when the solution isn’t overconstrained. When the solution is overconstrained, all radar radial velocities are given equal weight in the triple Doppler case. In the dual Doppler case, radial velocities are weighted by the square of the distance of the radar from the synthesis point. This has the effect of giving radars with lower elevation angles higher weights.
Radsynth also computes RMS errors for each derived Cartesian velocity component, assuming that radar radial velocity components all have unit RMS error. These errors are contained in the fields eu, ev, and ew for the u, v, and wp velocity components respectively. The purpose of this computation is to isolate the contribution of reconstruction geometry to the overall error. For dual Doppler synthesis, eu and ev don’t contain contributions to the error from uncertainties in the assumed values of w.
Radsynth assumes certain names for the radar input fields. These are put in defines near the beginning of the program, so that they can be easily changed.
Suppose that the output of four Doppler radars was put through the radcart program, producing four files cart.dr1, cart.dr2, cart.dr3, and cart.dr4. The Cartesian grids defined by radcart should be identical for all the radars. The first step in doing a triple Doppler synthesis is to invoke cdfmerge, so as to combine these files into a single file:
kestrel%cdfmerge cart.dr1 .1 cart.dr2 .2 cart.dr3 .3 cart.dr4 .4 > merge
The respective field names from each input file have been given the suffixes ".1", ".2", etc. To then do triple Doppler synthesis on these data, requiring a minimum of 3 good radial velocities at each point, invoke radsynth as follows:
kestrel%radsynth 3 .1 .2 .3 .4 < merge > synth
Setting the first argument to 4 would force a minimum of 4 radial velocities at each point for the determination of u, v, and w. Setting it to 2 would force a dual Doppler reconstruction, i. e., a minimum of two good radial velocities would be required, and only u and v would be computed. Either w would be assumed zero for this calculation, or if the w field existed in the input, the values presented there would be used.