CRREL REPORT 95-21

A Doppler Radar for

Continuous Remote Measurement

of River Ice Velocity

Michael G. Ferrick, Norbert E. Yankielun

and David F. Nelson November 1995
For conversion of SI units to non-SI units of measurement consult Standard

Practice for Use of the International System of Units (SI), ASTM Standard E380-

93, published by the American Society for Testing and Materials, 1916 Race St.,

Philadelphia, Pa. 19103.

Abstract

River ice velocity measurements are fundamental to analyses of river ice dynamics. Ice velocity measurement with a continuous-wave Doppler radar

system having real-time data acquisition and digital signal processing capability was evaluated during a river breakup and a frazil run on the Connecticut

River. This system can be rapidly deployed, requires minimal operator interaction, will continuously acquire, process, store, and display ice velocity

data and does not depend on visibility conditions. In parallel, video records

of ice motion were obtained at the same location for later manual processing

and comparison with the radar results. We describe the Doppler radar system

and obtain bounding estimates of possible measurement errors. The principal error in Doppler ice velocity measurement is due to the beam width of the

radar antenna, and an analytical method is developed to minimize this error.

Measured ice velocities ranged from 1 to 2.5 m/s during the river breakup

and from 0.5 to 0.65 m/s in the frazil run. Quantitative comparisons between

the radar and video results show fundamental agreement between these

measurement methods, and demonstrate that Doppler radar is an effective,

efficient, and precise tool for obtaining river ice velocities over the full range of

possible ice and velocity conditions.

Cover: Frazil ice run on the Connecticut River, 28 December 1993. Top: From

the Cornish–Windsor Bridge radar site looking upstream. Bottom: From

the left bank video site looking across the river. (Photos by M. Ferrick.)
CRREL Report 95-21

A Doppler Radar for

Continuous Remote Measurement

of River Ice Velocity

Michael G. Ferrick, Norbert E. Yankielun

and David F. Nelson November 1995

Prepared for

OFFICE OF THE CHIEF OF ENGINEERS

Approved for public release; distribution is unlimited.

US Army Corps


of Engineers

Cold Regions Research &


Engineering Laboratory
ii

PREFACE

This report was prepared by Michael G. Ferrick, Research Hydrologist, Snow and Ice

Division; Norbert E. Yankielun, Electronic Engineer, Engineering Resources Branch; and

David F. Nelson, Physical Science Aide, Snow and Ice Division, Research and Engineering Directorate, U.S. Army Cold Regions Research and Engineering Laboratory

(CRREL), Hanover, New Hampshire.

Funding for the study was provided by work unit DT08–74–101, Combat Engineering

System, and DA Project 4A762784AT42, Design, Construction, and Operations Technology

for Cold Regions, Work Unit 001, Task CS, Winter Combat Engineering.

This report was technically reviewed by Steven Arcone and James Lever of CRREL.

The authors wish to thank Nicholas Goodman (data processing), Patricia Weyrick (field

work), William Bates (illustration), Maria Bergstad (editing), and Donna Valliere (final

report preparation).

The contents of this report are not to be used for advertising or promotional purposes.

Citation of brand names does not constitute an official endorsement or approval of the

use of such commercial products.
iii

CONTENTS

Preface ............................................................................................................................... ii

Introduction ...................................................................................................................... 1

System description .......................................................................................................... 1

Error analysis ................................................................................................................... 4

Velocity from a Doppler frequency band and a video record .................................. 5

Ice breakup—March 1993 .......................................................................................... 7

Frazil ice run—December 1993 ................................................................................. 9

Conclusions ...................................................................................................................... 11

Literature cited ................................................................................................................. 11

Abstract ............................................................................................................................. 13

ILLUSTRATIONS

Figure

1. The effect of surface roughness on radar backscatter, and defining terms

and parameters ................................................................................................ 2

2. The 3-dB beam width of a radar antenna ........................................................... 3

3. Fundamental components of the Doppler radar system with an expanded

view of the front-end ...................................................................................... 3

4. Power spectra of single and multiple scans ....................................................... 4

5. Relationship between the velocity ratio and θa for both the near and far

edges of the beam width and a range of β values ...................................... 5

6. Example that quantifies the near- and far-edge velocity ratio with the

boresight velocity ............................................................................................ 6

7. Data band of raw Doppler velocities and peak returns for the ice breakup

event .................................................................................................................. 7

8. Calculated θa as a function of time for the raw and peak radar data records

for the breakup event ...................................................................................... 8

9. Ice breakup boresight velocities and their normalized difference obtained

from the edge traces ........................................................................................ 8

10. Ice velocity data, best polynomial fit, and normalized difference between

the data and polynomial of the video ice breakup record ........................ 9

11. Comparison of ice velocity results for breakup ................................................. 9

12. Video and radar data, best polynomial fits, and normalized difference

between the data and corresponding polynomial for the frazil ice run . 10

13. The part of the radar velocity record for breakup with dispersed ice floes

in the river ........................................................................................................ 10

14. Comparison of ice velocity results for the frazil run......................................... 11

TABLE

Table

1. Doppler system configurations ............................................................................ 7

A Doppler Radar for Continuous Remote Measurement

of River Ice Velocity

MICHAEL G. FERRICK, NORBERT E. YANKIELUN, AND DAVID F. NELSON

River during the March 1993 ice breakup and

again in December 1993 during a frazil ice run

prior to ice cover formation. Ice velocity data

were continuously acquired, processed, displayed, and stored. The system can be transported in a vehicle and rapidly redeployed to permit

data acquisition at a number of locations during a

single event with minimal operator interaction.

Simultaneous ice velocity data were obtained at

the same site with video techniques during both

of these events.

In this paper we describe the Doppler radar

system, analyze the contributions to measurement error inherent in the system, determine error bounds, and develop data processing methods to minimize the error in the velocity measurement. Quantitative comparisons of measured ice

velocity are made between the radar and video

techniques for both the breakup and frazil events.

Methods for enhancing the accuracy of Doppler

radar ice velocity measurement and its ease of

use follow from the analysis.

SYSTEM DESCRIPTION

The primary requirement for a successful

radar measurement is that the target provide sufficient backscatter of the incoming wave. If the

surface area illuminated by the radar were perfectly smooth, the incident energy would be reflected away from the radar antenna. However,

the inherent roughness of frazil, sheet, and rubble ice provides backscatter towards the antenna

(Fig. 1). The fundamental relationship between

transmitted and received power of a radar signal

traveling through free space was described in

Skolnik (1980). Lewis et al. (1987) discussed the

specific problem of radar detection of floating ice

INTRODUCTION

Accurate ice velocity measurement during river

breakup in spring is needed for analysis of river

and ice dynamics and for flood hazard or water

resource assessment. Ice velocity measurements

presented by Ferrick et al. (1993) demonstrated the

spatial and temporal variability of the motion during a dynamic breakup of the Connecticut River.

Similar though generally slower and more gradually variable motion occurs during the freeze-up

of a river. Ferrick et al. (1992) described the acquisition of ice velocity data by locating a length reference on the ice, recording the ice motion on videotape, developing a computer-generated reference

grid that is dubbed over the videotape, and timing

the motion of individual floes through the grid.

The shortcomings of this method are that it is

laborious and it requires visual observation of the

ice, which can be precluded by fog and darkness.

Ice scour of the bed and banks frequently prevents

the use of measurement methods that require

sensor and cable placement in the river. Radar systems have been applied to hydrological investigations, including the measurement and mapping of

ice thickness on rivers and lakes (Arcone and

Delaney 1987, Arcone 1991, Yankielun et al. 1992,

1993) and the continuous monitoring of river stage

(Yankielun and Ferrick 1993). Doppler radar techniques for velocity measurement are well established (Barton 1964, Skolnik 1980) and provide a

remotely mounted, readily installed, continuously

recording alternative for ice velocity measurement

that is not affected by light, fog, or ice motion conditions.

A continuous wave (CW) Doppler radar with

real-time data acquisition and digital signal processing capability was mounted on the Cornish

(N.H.)–Windsor (Vt.) bridge over the Connecticut
2

Radar

Rough Surface

Radar

Smooth Surface

β

θ

Stand Off

3 dB Footprint

Height

above

Target

Radar

Moving Ice

Boresight

Radar

River Flow Direction

α

Figure 1. The effect of surface roughness on radar backscatter, and defining

terms and parameters.

masses on large bodies of water. The backscattered power received Pr (W) is related to system

and target parameters as

 

P PG A

R L r t o =

2 2

3 4 4

λ σ

( ) π , (1)

where Pt = power transmitted (W)

G = antenna gain

λ = radar wavelength (m)

A = area illuminated by the radar (m2)

R = range to the target (m)

σo = normalized cross section of the target

L = system losses.

An ideal reflector returns all incident energy back

to the source, corresponding to a σo of 1. The

radar cross section of a target is defined as the

normalized area of an ideal reflector that would

return the same signal strength as the target. Several factors affect the radar cross section of a

given target, including transmitted wavelength,

target geometry, aspect, and reflectivity. A calibrated radar system is necessary to measure σo

for various target conditions. Moving river ice

presents an inhomogeneous target with complex

and variable geometry, and the radar cross section can vary widely.

An additional requirement for Doppler veloc-
3

0

–5

–10

–15

–20

–25

40° 20° 0° 20° 40°

Relative Gain (dB)

θ

Figure 2. The 3-dB beam width of a radar antenna.

ity measurement is that the frequency shift

obtained must be resolvable by the radar system.

In a CW Doppler system a single-frequency RF

carrier is transmitted toward the target at an oblique angle (Fig. 1). When the target is moving, the

backscattered signal exhibits an apparent shift

from the transmitted carrier frequency—higher if

movement is toward the radar and lower if it is

away from it. A low-level sample of the transmitted carrier frequency fs is used as a reference and

mixed with the backscattered signal received. The

mixing process results in four frequencies: the

reference signal, the backscattered signal, and the

sum and difference of these frequencies. The difference frequency resulting from the mixing is the

Doppler frequency fd proportional to the velocity

of the target. The velocity v (m/s) of a moving target is obtained as (Roddy 1984)

 

v f = λ

α β

d

2cos cos (2)

where λ = wavelength (m) of the RF source

α = horizontal off-stream angle as shown

in Figure 1.

β = vertical look-angle measured downward from the horizontal

The wavelength and frequency of the source are

related as λ = c/fs, where c is the speed of light in

a vacuum (3 × 108 m/s). The power transmitted

by the radar is not localized at the point on the

target surface aligned with the center of the antenna boresight. Instead, it is distributed over an

area on the surface, with the incident power diminishing with distance from the boresight. The

3-dB beam width shown in Figure 1 is defined as

the angular width of the radar beam at the halfpower points, as illustrated in Figure 2.

The Doppler radar implementation used for

these experiments (Fig. 3) includes a radar frontend and a data acquisition and processing computer. The radar front-end system (expanded in

Fig. 3) consists of a standard gain horn antenna

that is connected via a circulator to a single-frequency, continuous-wave microwave source and

a single-ended diode mixer. The circulator is a ferromagnetic device that directionally commutates

power on a sequential port-to-port basis and permits simultaneous noninterfering transmission

and reception of the radar signal using a single

antenna. Ideally, all power entering port 1 is

transmitted to port 2, power entering port 2 is

transmitted to port 3, and power entering port 3 is

transmitted to port 1. Port-to-port isolation in the

Figure 3. Fundamental components of the Doppler

radar system with an expanded view of the front-end.

DAT

Recorder

Doppler

Radar

System Audio

Amplifier

Computer

with

DSP Card

Single

Frequency

Microwave

Source

Circulator

To Audio Frequency

Data Acquisition and

Processing Hardware

Diode

Mixer

ReferenceSignal

Leakage Path

Port 1 Port 3

Port 2

Horn

Antenna
4

reverse direction is not complete, with a typical

power “leakage” of about –20 dB. The leakage between ports 1 and 3 is used as the reference signal

for the mixer. The front-end assembly is mounted

on a tripod that can be accurately positioned with

an inclinometer to within ±1° in the vertical plane.

Horizontally, the radar is visually aimed upstream

into the flow, and alignment is adjusted during the

ice motion by manually panning the antenna until

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 digital signal of the velocity spectrum in real time.

Data were recorded continuously on one track of a

four-track digital audio tape (DAT) recorder for

later playback, processing, and analysis. The DAT

recorder was also used to record concurrent river

stage data from a millimeter-wave FM–CW radar

(Yankielun and Ferrick 1993), event timing, and a

voice channel for a descriptive narrative.

After completion of a survey, the raw Doppler

data were processed and displayed. Each radar

scan was digitized to provide 1024 time series

samples, transformed into a power spectrum and

processed with a Hanning window to suppress

the effect of spectral sidelobes that could mask

lower-level signals. The processed power spectrum can be displayed in either a single-scan format or as a continuous series of scans in spectrographic form (Fig. 4). In a spectrogram, discrete

signal magnitude quanta are represented by a

range of color or gray scale. With 16-shade gray

scale graphics, the maximum signal magnitudes

appear black, and intermediate levels appear as

lighter shades of gray. Below a preset magnitude

threshold all is shown as white. The levels can be

set in the DSP software to display the Doppler frequency clearly. A multicolor spectrographic display provides a 256-shade color gradient that significantly improves graphical resolution.

ERROR ANALYSIS

To assess the capability of Doppler radar to

measure ice velocity we must identify and quantify the sources of error inherent in the method and

minimize these errors for minimum total error. It

would be useful to combine the individual errors

and obtain an upper bound on the total error. We

take v in eq 2 as the dependent variable, and write

the total differential dv as

 

dv v d v d v d v

f

=+ ++ df ∂

∂β β ∂∂α

α

∂

∂λ

λ ∂

∂ d

d. (3)

An upper bound on the total error is obtained as

the sum of the absolute values of the terms in eq 3,

when each term represents an individual upper

bound. The differentials of the independent variables will be replaced by finite quantities that we

assume are small enough for eq 3 to provide an

accurate estimate of each component of error.

The vertical angle and horizontal angle must

be known precisely to obtain an accurate velocity

measurement. The partial derivatives of velocity

in eq 2 with respect to α and β have the same form:

 

∂

∂β β ∂∂α

α

v

v

v = = tan ; tan . v (4)

When maximum error is being evaluated, the values of α and β in eq 4 should be the most probable

angle plus the estimate of angular error. The

wavelength of the CW RF source is known and

should be precise and stable for accurate measurement. Wavelength error is the difference between the actual and the measured radar source

carrier wavelength. The quantized nature of digital sampling is a source of error in the Doppler frequency. The partial derivative of velocity in eq 2

with respect to wavelength λ and Doppler frequency fd have the same form:

 

∂

∂λ λ

∂

∂

vv v

f

v

f = = ; .

d d

(5)

Figure 4. Power spectra of single and multiple scans

that indicate the relationship between the amplitude

threshold setting and the bandwidth of Doppler frequencies.

0 20 40 60 80

Monochrome

Spectrogram

of Multiple Scans

100

75

50

25

0

Scan Number

0 20 40 60 80

Frequency (Hz)

Black

White

Power Spectrum

of Single Scan

–60

–70

–80

–90

–100

Relative Power (dB)
5

We can now rewrite eq 3 as an upper-bound

percentage error in velocity, expressing each of

the differentials as finite errors ∆:

 

∆ ∆ ∆ v ∆ ∆

v

f

f

= + ++ tan tan . ββ αα • • λ

λ

d

d

(6)

Our vertical angle measurement by inclinometer

of 25° was accurate to within ±2°, and the horizontal angle alignment to the maximum velocity

at 0° was accurate to about ±5°. The upper-bound

percentage error contributions of these terms are

then 0.018 and 0.0076, respectively. A source frequency of 5 GHz and an upper bound frequency

error of 100 MHz yield a percentage error in λ of

0.02. The percentage error in fd is

 

∆f

f N

d

d

= 1 (7)

where N is the number of samples acquired and

processed per second for each Doppler frequency

determination. In our system, the sampling frequency N was 1024 Hz, corresponding to a negligible digital sampling error of less than 0.001.

The sum of the absolute values of the upperbound error estimates in eq 6 yields ∆v/v equal

to 0.047.

The beam width of the radar antenna introduces another potential error, in addition to those

given by eq 6. The antenna beam width corresponds to an area on the surface of the ice that is

illuminated by the radar and returns backscatter

to the antenna. Because fd is angle-dependent, a

band of Doppler frequencies represents the backscatter from across the illuminated area. The near

edge of the beam corresponds to the largest vertical angle and the upper-bound error. Following

the approach taken above, we obtain an upperbound estimate of this error by replacing β by β +

θ/2 in eq 2 and taking the partial derivative of

velocity with respect to θ/2:

 

θ ∂

∂ θ β θ θ2 2 22





 



 ( ) = + 



 



 



 



 v

v

/

tan . (8)

When is θ greater than 10°, the beam-width error

given by eq 8 is potentially larger than the sum of

the upper-bound errors in eq 6.

VELOCITY FROM A DOPPLER FREQUENCY

BAND AND A VIDEO RECORD

Systems with large beam width antennas require additional data analysis to obtain an accuθa (°)

0 10 20 30 40 50

0.8

0.4

0.0

1.2

Velocity Ratio

β = 35°

β = 25°

β = 15°

β = 15°

β = 25°

β = 35°

Far Edge

Near Edge

Figure 5. Relationship between the velocity ratio and

θa for both the near and far edges of the beam width

and a range of β values.

rate velocity from the Doppler frequency band at

each selected time throughout the record. If the

actual vertical angle β representing any point in

the frequency band were known, the velocity at

the corresponding time could be obtained from eq

2. However, these angles are not generally known.

The apparent far and near edge returns are the

most readily identifiable locations on the frequency band. The width of this band depends on the

antenna beam width and the threshold setting on

the power spectrum of the backscattered signal.

Our initial step in data reduction is to replace the

frequency scale of the data band by a velocity

scale using eq 2 with the boresight angle as β. The

center of this band is the approximate ice velocity,

and it can be obtained immediately. For more precise work during postprocessing, the apparent far

and near edge velocities v+ and v–, corresponding

to the upper and lower edges of the band, are related to each other and the desired velocity v as

 

vv v =

− 



 





=

+ 



 





+ −

cos

cos

cos

cos

, β

β θ

β

β a a θ

2 2

(9)

where θa is an apparent beam-width angle. The

velocity v corresponding to the antenna boresight

is bounded above by v+ and below by v–. We obtain the difference between the edge velocities as

a percentage of the velocity v from eq 9 as

 

v v

v

+ − − =

− 



 



 − + 



 

 cos cos 

cos .

β θ β θ

β

a a

2 2 (10)

The near and far edge velocity ratios v–/v and v+/

v are plotted in Figure 5 as a function of θa for a

range of boresight angles β. The potential beam-
6

Doppler Velocity

Spectrogram

1.5

1.0

0.5

0

1.15

1.10

1.05

1.00

0.95

0.90

0.85

0.80

0.75

–20 –15 –10 –5 0 5 10 15 20

Apparent Beam Width about Boresight (°)

Velocity (m/s)

Time (min)

Velocity Ratio

Far Edge

Boresight

Near Edge

Far - edge Error

0 10 20

Near - edge

Error

θa

Figure 6. Example that quantifies the near- and far-edge velocity ratio with the boresight

velocity for a specific case, β = 25° and θa = 20°, and relates them to specific locations on the

spectrogram.

width errors increase significantly with θa for all

boresight angles and increase with β for all beam

widths. A sample Doppler velocity spectrogram

is related to the velocity ratio relationship for β =

25° and θa = 20° in Figure 6.

Manipulating the relationship between the

edge velocities in eq 9 we solve for θa as

 

θ

β

a =

+

+ + 







































2

1

1

1 tan –

–

–

tan

. –

v

v

v

v

(11)

If both upper and lower bounding traces are

drawn consistently, θa should vary randomly

within a narrow range. Velocity estimates v1 and

v2 are obtained with the mean θa as

 

v vv v 1

a

+ 2

a

2 2

=

− 



 





=

+ 



 





cos

cos

;

cos

cos

. –

β

β θ

β

β θ

(12)

Finally, the measured Doppler velocity v, representing the bulk ice velocity within the radar

footprint, is taken as the average of v1 and v2.

A reference grid for video ice velocity measurement was established by placing visual targets on the winter ice cover at known spacing.

The video records of the breakup and frazil run

events were obtained by timing ice floes through

this grid. As in previous work, we assume that

the measured data contain a slowly varying component that provides the global variation of ice

velocity with time and a comparatively rapid

variation of small amplitude that represents

measurement error or noise in the data. Separating these components requires the development

of a function that contains most of the information in the data and little of the error or noise.

The video data were fitted with orthogonal polynomials of increasing order until the maximum

differences ceased to diminish and the time series of these differences appeared random. The

polynomial, as a single-valued function of time,

permits quantitative comparison of the radar

and video records.

Prowse and Demuth (1991) emphasized the

importance of a viewing position with large freeboard and accurate vertical angle measurement

to obtain accurate ice velocity measurement with

a related optical method. The water levels during

breakup were much higher than those during

target setup, occupying 30% of the setup freeboard. The resulting change in vertical angle

from the camera to all points on the ice caused

distortion of the original grid by length-scale

changes that depend on position in the cross section of the river. The open water during the frazil

ice run was at a level comparable to that of the

winter ice cover. The data from both events were

obtained along a single streamline in the river,

providing consistent results that can be corrected

for a change in length scale. The velocity data obtained from the original grid vgrid are related to

the actual velocity v as
7

 

v

X

t

X X

t

v v grid

grid = = +

= +

∆

∆

∆

∆ , (13)

where X is the actual length scale, ∆t is the transit

time of a floe over X, and ∆v is a velocity error

corresponding to length-scale error ∆X. The

actual video velocity v can then be obtained as

 

v

X X

t

CX

t = Cv − = = grid grid

grid

∆

∆ ∆ , (14)

where C = 1 indicates no grid distortion, and

increasing grid error is indicated as C departs

from 1.

Ice breakup—March 1993

A 30-minute Doppler radar ice velocity record

and a simultaneous video ice velocity record

were obtained for the Connecticut River at the

Cornish–Windsor bridge on 30 March 1993.

Specifications that characterize the radar system

used are given in Table 1. The radar antenna was

mounted about 6 m above the ice and aimed directly upstream with an angle β of 25° below horizontal. Concurrently, a video camera was

mounted at the top of the left bank and aimed

normal to the direction of the flow. The streamline where video data were obtained passed

through the footprint of the radar. Ice breakup

Table 1. Doppler system configurations.

Event

Breakup Frazil run

Radar band C Ka

Frequency 5 GHz 30 GHz

Wavelength 6 cm 1 cm

Antenna gain 15 dB 27 dB

3 dB antenna beam width 20° 9°

Microwave power 20 dBm 20 dBm

Raw Radar Bounds

0 5 10 15 20 25 30

Peak Data

Raw Data

0

Velocity (m/s)

Peak Radar Bounds

2.5

1.5

1.0

0.5

0

2.0

2.5

1.5

1.0

0.5

2.0

0 5 10 15 20 25 30

Time (min)

V+

V–

V+

V–

Figure 7. Data band of raw Doppler velocities and peak returns for the ice breakup event and

boundaries that were drawn for each of these data sets.

was underway at a river flow of approximately

850 m3/s when measurements began. For most

of this record, the ice was densely packed rubble

that provided strong radar reflections and many

video targets. Toward the end of the sampling

period, the surface ice concentration diminished

and the ice velocity increased.

The ice velocity–time trace obtained from the

Doppler frequency band is presented in Figure 7.

Digital signal processing software identified the

peak return from each radar scan in this record.

These peak detector data, representing the highest magnitude power reflections from within the

footprint illuminated by the radar, are also plotted in Figure 7. Both of these data sets were

processed by first identifying the upper v+ and

lower v– edges of the trace at 20- or 30-s intervals

throughout the record; the results are shown in

Figure 7. The peak returns generally originated
8

Figure 9. Ice breakup boresight velocities and their normalized difference obtained from the

edge traces, with the corresponding mean θa of both the raw and peak radar data records.

0 28 4 8 12 16 20 24

Time (min)

0 28 4 8 12 16 20 24

Time (min)

0.04

0.02

0

–0.02

–0.04

–0.06

0.04

0.02

0

–0.02

–0.04

2.5

2.0

1.5

1.0

0.5

0

2.5

2.0

1.5

1.0

0.5

0

Raw Radar Raw Radar

Peak Radar Peak Radar

v1

v2

Velocity (m/s)

(v1 – v2)/v

v1

v2

distribution. The v1 and v2 results and the difference between these values nondimensionalized

by the corresponding mean velocity are given in

Figure 9. Except for a few points, the absolute

value of this dimensionless difference was less

than 0.04 in both records, corresponding to an

absolute value of the difference between v and

either v1 or v2 of less than 0.02 v. The delineation

of the limits of each radar trace and calculation of

a mean θ has reduced the large potential beamwidth error to the same order as the other minor

errors inherent in Doppler velocity measurement. The peak data are smooth relative to the

raw data, but they are shifted systematically to

lower velocities, following the downward shift

of the far edge of the trace. The resulting mean

velocity of the peak radar record is 1.35 m/s, and

that of the raw radar record is 1.61 m/s.

The velocity data from the video record are

shown with the selected polynomial fit and the

corresponding normalized error in Figure 10.

The mean and median of the normalized error

were very close to zero, with a standard deviation of 0.026. The maximum normalized error of

about 0.06 v is within the measurement error

bound for this method (Ferrick et al. 1992). Comparison of the radar and video velocities reveals

that the video results are consistently low. For

ease of comparison we assume that this systematic difference is due entirely to video grid distortion. We obtain C in eq 14 from the ratio of the

raw radar to video polynomial mean velocity

values as 1.067.

50

0 4 8 12 16 20 24 28

40

30

20

10 Raw Data

Peak Data

Time (min)

θa (°)

0

Figure 8. Calculated θa as a function of time

for the raw and peak radar data records for the

breakup event. These values result from an

equal boresight velocity requirement for the

near and far edge traces.

close to the near edge of the footprint, consistent

with the inverse relationship between backscattered power and range to the fourth power given

in eq 1.

Using eq 11 we calculated θa for both the raw

and peak detector data records; we present the

respective results in Figure 8 as a function of

time. For the raw data record the mean, median,

and mode of θa are approximately equal, with a

mean of 44.6°, a standard deviation of 2.2°, and a

range of 10.0°. The mean, median, and mode of

θa for the peak data record are also approximately equal, with a mean of 26.0°, a standard deviation of 2.1°, and a range of 9.4°. The peak-finding

algorithm significantly reduced the apparent

beam width of the radar without altering the θa
9

2.0

1.6

1.2

0.8

0.4

0

0.04

0

–0.04

–0.08

0 10 20 30

Time (min)

Ice Velocity (m/s) Normalized Difference

Video Data

Time (min)

0 10 20 30

0

2.5

2.0

1.5

1.0

0.5

Velocity (m/s)

Video Data

Peak Data

Raw Data

peak, and raw–peak records, respectively. Given

the various measurement errors, these comparisons suggest fundamental agreement of the

methods. However, additional development of

the peak return data reduction method is needed

because of the significant underprediction of the

mean velocity.

Ice velocities exceeding 5 m/s during breakup

have been reported on some rivers. The maximum Doppler frequency that can be obtained

with a given system is limited by the Nyquist

sampling rate, fd ≤ N/2. With our system, velocities of up to 6 m/s can be obtained with Doppler

frequencies less than 200 Hz, indicating that the

Nyquist rate does not restrict velocity measurement at the high end of the observed range. Unlike optical methods, the large changes in river

stage that can occur during breakup do not affect

Doppler radar velocity measurement.

Frazil ice run—December 1993

Doppler radar ice velocity and simultaneous

video ice velocity records were obtained for the

Connecticut River at the Cornish–Windsor

bridge on 28 December 1993. Frazil pans and

floes were moving downstream during the

measurement period at a river flow of about 170

m3/s, just prior to ice cover formation. Over several hours of data collection, the river flow and

ice velocity conditions were relatively steady,

and we selected a typical 1000-s record for analysis. The video setup and grid were the same as in

the previous event. The radar antenna was

mounted at the same height and location as before, about 11 m above the lower water surface.

To reduce the data processing requirements of

the method, an antenna with a much narrower

beam width was used. With slower ice motion

expected, the wavelength of the radar was decreased to improve the velocity resolution. Using

eq 2, the Doppler frequency shift needed to resolve velocity differences of 0.05 m/s is only 1.5

Hz for a 5-GHz microwave source. The corresponding frequency shift increases to 9 Hz with a

30-GHz millimeter-wave source. A millimeterwave source provides sufficient resolution for ice

velocity measurement at speeds above about 0.1

m/s. The modified radar system specifications

are given in Table 1.

The video velocity data, best fifth-order polynomial fit, and difference between the data and

the polynomial normalized by the polynomial

velocity are given in Figure 12. The mean video

velocity was 0.518 m/s, and the normalized difFigure 11. Comparison of ice velocity results

for breakup after multiplying the video and

peak radar results by a constant that equates

the mean velocity of each record.

Figure 10. Ice velocity data, best polynomial fit,

and normalized difference between the data and

polynomial of the video ice breakup record.

Almost identical correlation coefficients were

obtained for all pairs of the raw radar, peak radar,

and polynomial video velocity records, ranging

between 0.933 and 0.950. The ice velocity–time

traces obtained with each method are superposed

in Figure 11, following multiplication of the peak

return results by 1.191 and the video polynomial

results by 1.067 to correct for the mean offset from

the raw radar results. The root-mean-square

(RMS) difference obtained between any pair of

records was less than 7.7 cm/s, corresponding to

dimensionless RMS velocity differences of 0.033,

0.037, and 0.048 between the video–raw, video–
10

0.6

0.4

0.2

0

0 1000

Velocity (m/s)

0.6

0.4

0.2

0

200 400 600 800 0 1000 200 400 600 800

0.10

0.05

0

–0.05

–0.10

–0.15

0.15

0.10

0.05

0

–0.05

–0.10

–0.15

0.15

Normalized Difference

Time (s) Time (s)

Video Video

Radar Radar

Figure 12. Video and radar data, best polynomial fits, and normalized difference between the

data and corresponding polynomial for the frazil ice run.

record during the period of dispersed ice motion.

Bands of velocity through time from floes producing strong backscatter are clearly visible.

Small underestimates of α and β would cause a

systematically high radar velocity, corresponding

to most of the difference between the Doppler

and video mean velocities. In addition, strong individual reflectors that passed through the radar

footprint at constant speed spent almost 60% of

this time on the high-velocity side of the boresight, potentially introducing a velocity bias.

However, for consistency and ease of comparison

we again assume that the systematic difference

between the radar and video velocities is due to

video grid distortion. The video and radar velocference between the data and the polynomial was

generally less than 0.06. The mean and median

difference are both zero, with an RMS difference

of 0.022 m/s and a maximum difference of 0.065

m/s. The amplitudes of the velocity differences

are within the bounds of experimental error, and

their structure is random. We conclude that the

polynomial adequately describes the video data.

The full width of the Doppler frequency band

was a difference in velocity of 0.05 m/s, or a normalized velocity difference of 0.09. Data representing the midpoint of the band obtained at 10-s

intervals, the best fourth-order polynomial fit to

these data, and the normalized difference between the data and the polynomial are presented

in Figure 12. The mean radar velocity was 0.539

m/s, and the normalized difference was generally less than 0.07. The mean and median differences are both zero, with an RMS difference of

0.023 m/s and a maximum difference of 0.067 m/s.

The amplitudes of the velocity differences are

somewhat larger than would be expected from

experimental error, and their structure appears

periodic. However, the oscillations in this record

are not supported by the video data. The oscillating radar velocities occurred when the open water area in the radar footprint increased and the

number of targets decreased. When a single floe

traverses the footprint there is an apparent

change in velocity from high to low caused by the

relationship between vertical angle and Doppler

frequency. Figure 13 shows part of the breakup

Figure 13. The part of the radar velocity record

for breakup with dispersed ice floes in the river.

Note the movement in time of strong returns from

higher to lower velocity, corresponding to the movement of floes through the antenna footprint.
11

Time (s)

0 1000

Velocity (m/s)

Radar

Video

0

0.6

0.4

0.2

200 400 600 800

ity polynomials are compared in Figure 14 after

the video velocity polynomial is multiplied by

1.041 to correct for the difference in the means.

Discounting the tail of the radar polynomial that

is an end-effect of the final oscillation, the RMS

difference between these curves is 0.014 m/s, or

0.026 when normalized by the mean velocity. Except for the oscillations induced by strong and

sparse reflectors, the Doppler radar and video

data agreement is well within the measurement

errors of the methods. The Doppler radar system

again provided an excellent velocity measurement with minimal processing.

CONCLUSIONS

Doppler ice velocity measurements are made

remotely, can be displayed in real time, and are

not affected by light, fog, or ice motion conditions.

Doppler radar can measure and resolve the velocity of ice moving in a river with precision comparable to or better than analysis-intensive video

techniques, over the complete range of ice and velocity conditions. The maximum error in Doppler

radar measurement of river ice motion is about 5%

of the velocity. Agreement between the mean

Doppler and video velocities was obtained within

7% for the ice breakup case study and 4% for the

frazil run. Video grid distortion during breakup

and sparse radar targets during the frazil run are

likely causes of these systematic differences in velocity. The RMS differences between the meancorrected velocity curves were about 3% for both

cases. A high gain, narrow-beam antenna improved signal-to-noise performance of our Doppler radar system and minimized data processing

requirements. An increase in the source frequency

of the system provided a proportional increase in

the velocity resolution.

Significant cost reduction and miniaturization

can now be realized through application of offthe-shelf 10-GHz and 24-GHz microwave transceiver modules consisting of a horn antenna, circulator, diode mixer, and Gunn oscillator. These

modules only require connections to dc power

and to a data acquisition computer to realize a

Doppler radar system, encouraging long-term or

permanent mounting of sensors at strategic points

on a river to provide early warning and continuous monitoring of ice freeze-up or breakup. A laptop computer equipped with a PCMCIA data acquisition card enhances system portability and reduces power requirements.

LITERATURE CITED

Arcone, S.A. (1991) Dielectric constant and layer

thickness interpretation of helicopter-borne shortpulse radar waveforms reflected from wet and dry

river-ice sheets, IEEE TGARS, 29: 768–777.

Arcone, S.A. and A.J. Delaney (1987) Helicopterborne short-pulse radar profiles of river-ice sheets

in Alaska. Journal of Glaciology, 97: 333–341.

Barton, D.K. (1964) Radar System Analysis. New

York: Prentice-Hall.

Ferrick, M.G., P.B. Weyrick and S.T. Hunnewell

(1992) Analysis of river ice motion near a breaking

front. Canadian Journal of Civil Engineering, 19: 105–

116.

Ferrick, M.G., P.B. Weyrick and D.F. Nelson (1993) A

kinematic model of river ice motion during dynamic breakup. Nordic Hydrology, 24: 111-134.

Lewis, E.O., B.W. Currie and S. Haykin (1987) Detection and Classification of Ice. New York: John Wiley

and Sons.

Prowse, T.D. and M.N. Demuth (1991) Measurement

of freeze-up and break-up ice velocities. In Proceedings of the 48th Eastern Snow Conference, Guelph,

Ontario, 5–7 June, p. 325–331.

Roddy, D. (1984) Microwave Technology. New York:

Prentice-Hall.

Skolnik, M.I. (1980) Introduction to Radar Systems.

New York: McGraw-Hill.

Yankielun, N.E. and M.G. Ferrick (1993) Automatic, continuous river stage measurement with a millimeter-wave FM-CW radar. USA Cold Regions Research and Engineering Laboratory, CRREL Report

93-24.

Yankielun, N.E., S.A. Arcone and R.K. Crane (1992)

Thickness profiling of freshwater ice using a millimeter-wave FM-CW radar. IEEE Transactions on

Geoscience and Remote Sensing, 80: 1094–1100.

Yankielun, N.E., M.G. Ferrick and P.B. Weyrick

(1993) Development of an airborne millimeterwave FM-CW radar for mapping river ice. Canadian

Journal of Civil Engineering, 20: 1057–1064.

Figure 14. Comparison of ice velocity results for the

frazil run after the video results are multiplied by a constant that equates the mean velocity of each record.
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17

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

Doppler radar Radar

River ice Velocity

Ice movement

River ice velocity measurements are fundamental to analyses of river ice dynamics. Ice velocity measurement

with a continuous-wave Doppler radar system having real-time data acquisition and digital signal processing

capability was evaluated during a river breakup and a frazil run on the Connecticut River. This system can be

rapidly deployed, requires minimal operator interaction, will continuously acquire, process, store, and display

ice velocity data and does not depend on visibility conditions. In parallel, video records of ice motion were

obtained at the same location for later manual processing and comparison with the radar results. We describe

the Doppler radar system and obtain bounding estimates of possible measurement errors. The principal error

in Doppler ice velocity measurement is due to the beam width of the radar antenna, and an analytical method

is developed to minimize this error. Measured ice velocities ranged from 1 to 2.5 m/s during the river breakup

and from 0.5 to 0.65 m/s in the frazil run. Quantitative comparisons between the radar and video results show

fundamental agreement between these measurement methods and demonstrate that Doppler radar is an effective, efficient, and precise tool for obtaining river ice velocities over the full range of possible ice and velocity

conditions.

November 1995

A Doppler Radar for Continuous Remote Measurement PR: 4A762784AT42

of River Ice Velocity WU: 001

TA: CS

Michael G. Ferrick, Norbert E. Yankielun and David F. Nelson

U.S. Army Cold Regions Research and Engineering Laboratory

72 Lyme Road CRREL Report 95-21

Hanover, New Hampshire 03755-1290

Office of the Chief of Engineers

Washington, DC 20314-1000

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161.