Optimum values for C
1
and C
2
vary from site to site, but some guidance can be obtained
using numerical simulations. The results shown below were obtained when the algorithms
were applied to realistic weather time series having a spectrum width = 0.1 (Nyquist), SNR =
+10 dB, and an intermittent additive interference signal that was 16 dB stronger than the
weather. The interference arrived in isolated single pulses with a probability of 2%.
The algorithm performance is summarized in the first 3 columns of the following table, for
which C
1
and C
2
have the common value shown. The fourth column also uses Algorithm #3,
but with the value of C
1
raised by 2 dB. The Missed rate is
defined as the percentage of
interference points that manage to get through the
filtering process without being removed.
The False (false alarm) rate is the percentage of non- interference points that are
incorrectly modified when they should have been left alone.
Table 45 Algorithm Results for +16 dB Interference
C1,C2 Alg.1 Missed/
False
Alg.2 Missed/
False
Alg.3 Missed/
False
Alg.3, C1+=2 dB
Missed/False
6.0dB 17.8% 10.91% 17.8% 4.06% 17.8% 3.48% 10.3% 4.15%
8.0dB 10.5% 6.57% 10.5% 2.42% 10.4% 1.71% 6.1% 1.92%
9.0dB 8.5% 5.09% 8.5% 1.81% 8.3% 1.16% 5.4% 1.28%
10.0dB 7.3% 4.01% 7.3% 1.42% 7.5% 0.79% 5.4% 0.85%
11.0dB 8.9% 3.14% 8.9% 1.06% 8.3% 0.51% 6.5% 0.54%
12.0dB 11.6% 2.53% 11.6% 0.85% 11.3% 0.33% 9.9% 0.35%
13.0dB 17.0% 2.07% 17.0% 0.67% 16.3% 0.22% 15.3% 0.23%
14.0dB 23.5% 1.70% 23.5% 0.54% 22.4% 0.14% 21.6% 0.15%
16.0dB 39.2% 1.21% 39.2% 0.35% 39.6% 0.06% 38.9% 0.06%
20.0dB 67.3% 0.65% 67.3% 0.14% 72.5% 0.01% 72.4% 0.01%
A false alarm in actual precipitation echo aects the values of moments calculated at the
gate of the false alarm. For example, the measured power and estimates of
reflectivity,
subsequently, become slightly lower. The following table maps the rates of false alarms to
mean relative changes of reflectivity (in dB).
Table 46 Impact of False Alarms on
Reflectivity Estimates
Alg.1 False Bias
(dB)
Alg.2 False Bias
(dB)
Alg.3 False Bias
(dB)
Alg.3, +2 dB False
Bias (dB)
10.91%
. .
4.06%
. .
3.48%
. .
4.15%
. .
6.57%
. .
2.42%
. .
1.71%
1.92%
. .
5.09%
. .
1.81%
. .
1.16%
. .
1.28%
. .
4.01%
. .
1.42%
. .
0.79%
. .
0.85%
. .
Chapter 7 – Processing Algorithms
179