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5 Apr 2001
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Polarisation algorithms to correct for attenuation at Cband
ChunLei Liu and Anthony J. Illingworth
The problem
 Attenuation is a severe problem at Cband
 Cband used operationally in Europe and Japan
 Gatebygate correction of Z is notoriously unstable
 Attenuation is not uniquely related to differential phase shift
Simulations by Bringi et al (1990) suggested attuation is
related to differential phase shift, but they did not consider Values
of median diameter D_{0} above 2.5mm
(Z_{DR}>3dB). Most attenuation events have higher
Z_{DR} (Smyth and Illingworth, QJ, 1998 p2398).
Nonpolarisation technique solution
 UK Met. Office currently use empirical 2way correction at
Cband (Gunn and East 1954):
A = 0.0044 R^{1.17} dB/km
at 18°C
(1)
 It is based on exponential drop spectra with the drop shape of
sphere. Gatebygate correction can blow up, so the correction is
capped at 3 dB.
 New rain sizespectrum analysis: raindrop spectra are best
represented by normalised gamma functions
(2)
where D_{0} is the diameter that splits the volume of water in
two equal parts. Fitting to spectra by forcing the third, fourth and
sixth moments to equal the appropriately weighted integral of the
gamma function show that N_{L} is close to 8000
m^{3}mm^{1} (MarshallPalmer value) and mu is about
five. this leads to a relationship of the form:
A_{v} = 0.00258 R^{1.23} dB/km at
0°C
(3a)
A_{v} = 0.00124 R^{1.31} dB/km at 20°C
(3b)
 This is about 50% of the value predicted by Equation 1 (Gunn and
East); e.g. for 100mm/hr, the Gunn and East formula predicts 1 dB/km
wherease the new gamma functions predict 0.5 dB/km.
Predicted Cband attenuation
for horizontal and vertical polarisation at 0°C and 20°C
for a normalised gamma function with mu=5 and N_{L} = 8000
m^{3}mm^{1}.
Conclusion: recommend (3b) used operationally in the UK,
not (1)
Polarisation technique solution
 At Sband, simulations by Bringi et al (1990), in which
D_{0} was limited to 2.5 mm, suggested the attenuation could
be derived from differential phase shift (K_{DP}). This leads to
Total attenuation A_{h} = 0.016
K_{DP} dB/°
Differential attenuation A_{h}A_{v} = 0.00367
K_{DP} dB/°
 but D_{0} = 2.5 mm is a Z_{DR} of only 3 dB; most attenuation events have higher Z_{DR} values (i.e. large raindrops)
 If we extend simulations up to D_{0} = 3.5 mm we find
the unique relationship breaks down and we can't derive attenuation
from differential phase shift (K_{DP}).
 Observations of differential attenuation and differential phase
shift confirm there is no simple relationship between the two. A plot
of observed negative Z_{DR} against total differential phase
suggests
 Attenuation higher than Bringi et al.
 Highest values of all when Z_{DR} > 5 dB (bold points)
 Ryzhkov and Zrnic (1994) also found differential attenuation
higher than Bringi et al. and invoked half melted ice cores, but
this can be explained simply by highZ_{DR} rain.
Example of negative
Z_{DR} at Sband behind intense rain cells (high Z and
Z_{DR}). Gauge 5 was recording a rain rate of 267
mm/hr.
Observed values of total
differential phase shift, phi_{DP}.
Total differential attenuation, A_{h}A_{v}, observed
behind intense echoes with the sband chilbolton radar. Bold points
correspond to rays with Z_{DR} above 5 dB
Simple solution at Cband
 At Cband, it turns out that differential attenuation is
linearly related to total attenuation. so we can estimate total
attenuation from the negative Z_{DR} behind the heavy rain.
Predicted variation of
A_{h} versus A_{h}A_{v} at Cband for
N_{L} = 8000 m^{3}mm^{1} at 0°C and 20°C
for mu = 0 and 5. The dashed line is for N_{L} = 40000
m^{3}mm^{1}.
 The problem with using K_{DP} to correct for attenuation
is that K_{DP} depends on the real part of the forward scatter
amplitude, and attenuation to the imaginary part; these have different
behaviour with size and temperature.
 However, differential and total attenuation both depend on the
imaginary part of the scatter amplitude, so
Recommend use of negative ZDR behind heavy rain to
estimate total attenuation. Would work for UKMO Cband radars if
radars had dual polarisation.
