reverse direction is not complete, with a typical
signal magnitude quanta are represented by a
range of color or gray scale. With 16-shade gray
power "leakage" of about 20 dB. The leakage be-
scale graphics, the maximum signal magnitudes
tween ports 1 and 3 is used as the reference signal
appear black, and intermediate levels appear as
for the mixer. The front-end assembly is mounted
lighter shades of gray. Below a preset magnitude
on a tripod that can be accurately positioned with
an inclinometer to within 1 in the vertical plane.
threshold all is shown as white. The levels can be
set in the DSP software to display the Doppler fre-
Horizontally, the radar is visually aimed upstream
quency clearly. A multicolor spectrographic dis-
into the flow, and alignment is adjusted during the
play provides a 256-shade color gradient that sig-
ice motion by manually panning the antenna until
nificantly improves graphical resolution.
the radar response indicates a velocity maximum.
Data acquisition and display were performed
with a 33-MHz 80386 DOS computer system. A
ERROR ANALYSIS
DSP card acquires 16-bit data and displays the dig-
To assess the capability of Doppler radar to
ital signal of the velocity spectrum in real time.
measure ice velocity we must identify and quanti-
Data were recorded continuously on one track of a
fy the sources of error inherent in the method and
four-track digital audio tape (DAT) recorder for
minimize these errors for minimum total error. It
later playback, processing, and analysis. The DAT
would be useful to combine the individual errors
recorder was also used to record concurrent river
and obtain an upper bound on the total error. We
stage data from a millimeter-wave FMCW radar
take v in eq 2 as the dependent variable, and write
(Yankielun and Ferrick 1993), event timing, and a
the total differential dv as
voice channel for a descriptive narrative.
After completion of a survey, the raw Doppler
data were processed and displayed. Each radar
v
v
v
v
dv =
dβ +
dα +
dλ +
(3)
dfd .
β
α
λ
scan was digitized to provide 1024 time series
fd
samples, transformed into a power spectrum and
processed with a Hanning window to suppress
An upper bound on the total error is obtained as
the effect of spectral sidelobes that could mask
the sum of the absolute values of the terms in eq 3,
lower-level signals. The processed power spec-
when each term represents an individual upper
trum can be displayed in either a single-scan for-
bound. The differentials of the independent vari-
mat or as a continuous series of scans in spectro-
ables will be replaced by finite quantities that we
graphic form (Fig. 4). In a spectrogram, discrete
assume are small enough for eq 3 to provide an
accurate estimate of each component of error.
The vertical angle and horizontal angle must
100
be known precisely to obtain an accurate velocity
75
Monochrome
measurement. The partial derivatives of velocity
Spectrogram
50
in eq 2 with respect to α and β have the same form:
of Multiple Scans
25
v
v
0
= v tan β;
= v tan α .
(4)
0
20
40
60
80
β
α
60
Power Spectrum
When maximum error is being evaluated, the val-
of Single Scan
ues of α and β in eq 4 should be the most probable
70
angle plus the estimate of angular error. The
Black
wavelength of the CW RF source is known and
White
80
should be precise and stable for accurate mea-
surement. Wavelength error is the difference be-
tween the actual and the measured radar source
90
carrier wavelength. The quantized nature of digi-
tal sampling is a source of error in the Doppler fre-
100
quency. The partial derivative of velocity in eq 2
0
20
40
60
80
with respect to wavelength λ and Doppler fre-
Frequency (Hz)
quency fd have the same form:
Figure 4. Power spectra of single and multiple scans
that indicate the relationship between the amplitude
vv
v
v
= ;
= .
(5)
threshold setting and the bandwidth of Doppler fre-
λλ
fd fd
quencies.
4
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