The three PRF (PRF1, PRF2 and PRF3) that are used are very low and very close to each other: 379, 325 and 303 Hz. The associated individual Nyquist velocities, VN1, VN2 and VN3 range between 4 and 5 m/s. The ratios VN2/VN1 and VN3/VN1 are respectively equal to 6/7 and 4/5. The resulting extended Nyquist velocity is equal to 60 m/s.
The three radial velocities (V1, V2 and V3) corresponding to the three PRF are computed using the Pulse-Pair technique. The combined radial velocity (V123) is then obtained classically by dealiasing the long PRT radial velocity (V3) with the two others (V1 and V2) being used as references. Possible (multiple) aliasing is taken into account in the comparison. The dual-PRT velocities are also computed : V12, V13 and V23.
One month of data (August 2004) representing more than 10000 PPIs of clear-air, convective and stratiform rain, has been analyzed and histograms of errors have been computed. The reference velocity that is required in order to compute the velocity errors is generated internally by applying a 5x5 km² median filter to the clutter-corrected, dealiased combined velocity. The radial velocity field is assumed to be uniform in the 5x5 km² window. All radial velocities (V1, V2, V3, V123, V12, V13 and V23) are then compared against that reference velocity. All histograms are symmetrical and show a well defined peak centered on zero. The error distributions of V12, V13, V23 and V123 have secondary peaks that correspond to dealiasing failures. Overall, the dealiasing success rate for V123 is beyond 95%.
A Zrnic's simulation of Is and Qs time series is then used to reproduce the observed error distributions (including the secondary peaks). The principle of the simulation is to generate a uniform time series with a very short PRT and then to re-sample it at three (staggered) PRT that are used operationally. The length of the time series is entirely dictated by the dwell time of the antenna over each radar pixel. The mean velocity that is used in the Is and Qs simulations follows the climatology around the radar. The width of the Doppler spectrum is tuned to match simulated histograms with observed ones.
Finally, the choice of the three PRT of the staggered scheme is revisited using the climatological value of the Doppler spectrum width computed in the previous step. The principle of that final step is again to generate uniform Is and Qs time series at a very short PRT and resample it in many different ways according to different PRT ratios ((VN2/VN1;VN3/VN1)=(4/5,6/7), (VN2/VN1;VN3/VN1)=(3/5,4/5), (VN2/VN1;VN3/VN1)=(3/5,4/7)...). All possible couples of ratios are then classified in terms of 1) resulting extended Nyquist velocity and 2) dealiasing success rate.