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velocity field (too strong), especially at upper levels (Fig. 10). The addition of random noise
to the upward integration method exacerbated these errors (data not shown).
These experiments reveal 1) that the variational approach provides more realistic estimates
of vertical velocity than the upward integration method, and 2) that observational noise
does not propagate upward when the variational method is used. These results have been
obtained using a volume scan with 30 PPIs (experiment EL30). This choice of volume scan is
currently unrealistic because it would take more than 10 minutes using typical current
antenna rotation speeds (a few rotations per minute). For operational use, volume scans
with 15-20 PPIs are realistic given the need for rapid updates (less than 400 seconds). Two
further experiments are performed to mimic volume scan data with 20 PPIs (experiment
name: EL20) and 17 PPIs (experiment name: EL17). The analysis method is the same for the
EL20 and EL17 experiments as for the EL30 experiment. In EL20, the highest elevation angle
is 18.9° (Fig. 2). A beam at this elevation angle reaches 14 km ASL 40 km away from radar.
This is sufficient to ensure a valid upper boundary condition (w = 0) in this case, because the
storm top is located at 12 km ASL. In EL17, however, the highest elevation angle is 15.7°
(Fig. 2). This beam does not reach 12 km ASL within the detection range of the radar.
Fig. 10. As in Fig. 8 but using an upward integration scheme.
Figure 11 is the same as Fig. 8 but for EL20 rather than EL30. Vertical velocities retrieved by
EL20 are similar to those retrieved by EL30 (Fig. 8) below 8 km ASL; however, the
downdraft associated with gravity wave dynamics is not retrieved by EL20 because the
pseudo-radar configuration does not observe that location. The maximum updraft was 20 m
s -1 , a 1 m s -1 underestimate of the EL30 retrieval. As with EL30 (Fig. 8), a spurious updraft
and downdraft are retrieved near 8-12 km ASL to the west of the strong updraft (Fig. 11).
The area of this spurious downdraft is larger in EL20 than in EL30. This implies that EL20 is
not capable of fully observing the storm top, so that erroneous upper boundary conditions
induced the spurious downdraft.
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