My approach was guided by the recognition of limitations arising from (i) problems associated with the in situ probe data, (ii) the unknown relationship between spectra measured along the flight line and at other regions sampled by the radar and (iii) the possible influence of air velocities on the actual flux of precipitation at specific locations in or below the cloud.
No direct measurements of drizzle rates, in terms of mass flux, are available for DYCOMS, so this conversion from Z to R cannot be subjected to independent evaluation. A rough estimate of the accuracy of drizzle rates so derived is a factor of 2. Improvements in the estimated accuracy (for better or worse) may come later from comparisons with data from other projects, and from further analyses, possibly involving use of the measured Doppler velocities, which are reflectivity-weighted fall velocities, plus air velocities.
In situ data for hydrometeor size distributions are available for flights rf02, 03, 04, 07, 08, and 09. Analyses to date were done only for these flights. This may be complemented later with data from the Fast-FSSP. The basis for this set of analyses was 1-Hz data archived as C130 variables CS100_LPI, C260X_RWO and C2DC_RWI2.
The following summarizes a set of results I derived using procedures
to be detailed later. Other results for Z-R are being generated by
Margreet van Zanten at UCLA, by Qing Yang at UW, and possibly by others
as well.
These results are shown in Fig. 1 (below).
Numerical definitions of the equations are shown in the table below
with a designating
the pre-factor, b the exponent, c
the correlation coefficient, and rmin
and rmax define the range of values
for the data of given flight.
rf02
26 legs: a = 2.58 b = 1.32 c = 0.96
rmin = 0.0002 rmax = 6.3367
rf03
29 legs: a = 23.56 b = 1.70 c = 0.98 rmin = 0.0003
rmax = 0.7160
rf04
11 legs: a = 18.57 b = 1.68 c = 1.00 rmin = 0.0005
rmax = 1.1810
rf07
24 legs: a = 18.49 b = 1.67 c = 0.98 rmin = 0.0051
rmax = 3.9131
rf08
25 legs: a = 13.95 b = 1.77 c = 0.96 rmin = 0.0002
rmax = 1.6294
rf09
27 legs: a = 3.21 b = 1.38 c = 0.97
rmin = 0.0002 rmax = 0.1246
The number of legs in this table refers to the
number of flight segments, each roughly 5-min in duration, for which independent
Z-R equations were fit. No stratification of these legs by location,
altitude, etc. is involved at this point.
The leg by leg data are also available in tabular
form via this link.
Some of the flights show possible groupings of legs with discernible differences in Z-R. This is the case for rf02 and rf07, the two heavy drizzle cases. Other stratifications may also emerge as the results are further scrutinized.
Clearly, more can be done, but there is also a clear limit to how much
is worth investing in this effort. With that in mind, I will be glad
to receive all sorts of inputs on the issue, specially good insights regarding
patterns in droplet and drizzle size distributions which might show some
orgnization of the Z-R relationships too.