reverse direction is not complete, with a typical

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

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

(3)

β

α

λ

scan was digitized to provide 1024 time series

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

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

wavelength of the CW RF source is known and

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 *f*d have the same form:

= ;

= .

(5)

λλ

4