348
Eugene E. Clothiaux, Thomas P. Ackerman, David M. Babb
a pseudorandom generator. We added one signal power sample to each noise power sample and
plotted the results as samples 101 to 200 in Figure 13.16Al. Since the signal power levels are
small compared to the noise power levels, i.e., look for the second solid line in Figure 13.16Al,
it looks as though nothing has changed from the first 100 samples. The top dashed line in the
figure has a power level of 2.4 x 10- 9 m W, which we obtained by adding the standard deviation
of the first 100 noise power samples to the mean obtained from these same samples. We use
this power level to differentiate signal plus noise from noise: everything above the dashed line
is considered as signal plus noise, whereas everything below the dashed line is classified as pure
noise. Applying this criterion to the series in Figure 13.16Al leads to poor results since many
of the first 100 power samples are classified as signal plus noise and almost all of the last 100
power samples are identified as noise. To detect the power associated with the signal we must
reduce the standard deviation of both the noise and signal plus noise samples; to accomplish
this we must average samples.
To this end we generated 10 000 noise power samples as before. We averaged the noise samples
in blocks of 100 before plotting them in Figure 13.16Bl. We then generated 10 000 noise power
samples, 10 000 signal power samples, added a distinct signal power sample to each noise sample
and averaged the summed samples in blocks of 100 to produce samples 101 to 200 in Figure
13.16Bl. In Figure 13.16B2 we magnify the y-axis to show that we still get poor separation of
the signal plus noise from the noise if we use the same criterion as in Figure 13.16Al.
Finally, we averaged blocks of 40 000 noise samples and signal plus noise samples to produce
Figure 13.16Cl. Notice that the standard deviations of both the noise and signal plus noise
samples are much reduced compared either to Figure 13.16Al or Figure 13.16Bl. More importantly, the magnified plot in Figure 13.16C2 demonstrates that the criterion for separating
noise from signal plus noise performs much better on this data; the number of signal plus noise
samples that are identified as noise are greatly reduced from before. Therefore, by averaging
more samples the average of the noise samples converges to the actual mean radar noise power
and the standard deviation goes to zero. Furthermore, the signal plus noise samples converge
on the mean noise power plus the mean sigal power also with a vanishing standard deviation.
If enough averaging is performed on the samples, the standard deviations become sufficiently
small that the atmospheric return process is unmasked. We use this standard technique to
separate signal plus noise from pure noise when processing the Penn State radar data and we
use a simple filter on the results in an attempt to remove the type of misclassifications that are
illustrated in Figure 13.16C2 (Clothiaux et a!., 1995). Once we have obtained an estimate of
the signal power by subtracting the noise power from the signal plus noise power, we can use the
radar equation (13.26) to solve for the reflectivity 7J(ro), which is one of the radar observables.
13.7 The Doppler Moments
From the I and Q voltages we obtained an estimate of the quantity 7J(ro) which provides
information about cloud drop locations. 7J(ro) also provides information about the particle size
distribution, but only through the integral of the backscatter cross section across all particles
in the radar resolution volume. We are now at the point where we take the I and Q voltages
and manipulate them in order to retrieve information about the motion of the scatterers in the
resolution volume. As we illustrate, the power density spectra enables us to better estimate
the particles sizes in the resolution volume.
The two techniques that we use are the fast fourier transform (FFT) and the pulse pair autocovariance algorithm. We apply these algorithms to the simulated I and Q time series in Section
13.5 and we then interpret the results in the context of the particle size distribution (Figure
Eugene E. Clothiaux, Thomas P. Ackerman, David M. Babb
a pseudorandom generator. We added one signal power sample to each noise power sample and
plotted the results as samples 101 to 200 in Figure 13.16Al. Since the signal power levels are
small compared to the noise power levels, i.e., look for the second solid line in Figure 13.16Al,
it looks as though nothing has changed from the first 100 samples. The top dashed line in the
figure has a power level of 2.4 x 10- 9 m W, which we obtained by adding the standard deviation
of the first 100 noise power samples to the mean obtained from these same samples. We use
this power level to differentiate signal plus noise from noise: everything above the dashed line
is considered as signal plus noise, whereas everything below the dashed line is classified as pure
noise. Applying this criterion to the series in Figure 13.16Al leads to poor results since many
of the first 100 power samples are classified as signal plus noise and almost all of the last 100
power samples are identified as noise. To detect the power associated with the signal we must
reduce the standard deviation of both the noise and signal plus noise samples; to accomplish
this we must average samples.
To this end we generated 10 000 noise power samples as before. We averaged the noise samples
in blocks of 100 before plotting them in Figure 13.16Bl. We then generated 10 000 noise power
samples, 10 000 signal power samples, added a distinct signal power sample to each noise sample
and averaged the summed samples in blocks of 100 to produce samples 101 to 200 in Figure
13.16Bl. In Figure 13.16B2 we magnify the y-axis to show that we still get poor separation of
the signal plus noise from the noise if we use the same criterion as in Figure 13.16Al.
Finally, we averaged blocks of 40 000 noise samples and signal plus noise samples to produce
Figure 13.16Cl. Notice that the standard deviations of both the noise and signal plus noise
samples are much reduced compared either to Figure 13.16Al or Figure 13.16Bl. More importantly, the magnified plot in Figure 13.16C2 demonstrates that the criterion for separating
noise from signal plus noise performs much better on this data; the number of signal plus noise
samples that are identified as noise are greatly reduced from before. Therefore, by averaging
more samples the average of the noise samples converges to the actual mean radar noise power
and the standard deviation goes to zero. Furthermore, the signal plus noise samples converge
on the mean noise power plus the mean sigal power also with a vanishing standard deviation.
If enough averaging is performed on the samples, the standard deviations become sufficiently
small that the atmospheric return process is unmasked. We use this standard technique to
separate signal plus noise from pure noise when processing the Penn State radar data and we
use a simple filter on the results in an attempt to remove the type of misclassifications that are
illustrated in Figure 13.16C2 (Clothiaux et a!., 1995). Once we have obtained an estimate of
the signal power by subtracting the noise power from the signal plus noise power, we can use the
radar equation (13.26) to solve for the reflectivity 7J(ro), which is one of the radar observables.
13.7 The Doppler Moments
From the I and Q voltages we obtained an estimate of the quantity 7J(ro) which provides
information about cloud drop locations. 7J(ro) also provides information about the particle size
distribution, but only through the integral of the backscatter cross section across all particles
in the radar resolution volume. We are now at the point where we take the I and Q voltages
and manipulate them in order to retrieve information about the motion of the scatterers in the
resolution volume. As we illustrate, the power density spectra enables us to better estimate
the particles sizes in the resolution volume.
The two techniques that we use are the fast fourier transform (FFT) and the pulse pair autocovariance algorithm. We apply these algorithms to the simulated I and Q time series in Section
13.5 and we then interpret the results in the context of the particle size distribution (Figure