Document text
GRREL REPORT 92-2Q
AD-A259 368
» » ■ti.i iiii liii
An Airborne Millimeter-Wave
FM-CW Radar for Thickness Profiling
of Freshwater ice
Norbert E. Yankielun
November 1992
i
DTIC
I
JAN 19 19931
^ a I
■iwrvrrni^w
g
»:C
[t]
JT;
Appivrad ior pusilc iclsoM}
DiMittrafloB nnMmlMd
11
1
li"
1
M
If
Abstract
The ability to profile rapidly and accurately the structure of freshwater ice
down to a thickness of a few centimefers over large surfaces of frozen
ponds, lakes and rivers has wide milifary, industrial, commercial and
recreational application, including safety and trafficability surveys. A proto¬
type broadband millimeter wave (26.5 to 40 GHz) Frequency Modulated-
Continuous Wave (FM-CW) radar, employing real-time data acquisition
and Digital Signal Processing (DSP) techniques, has been developed for
confinuously recording fhe fhickness profile of freshwater ice. Thickness
resolution is better than 3 cm ±10%, which improves on short-pulse and
FM-CW radars operating at frequencies less than 10 GHz. These other
radars have a best reported thickness resolution of approximotely 10 cm
with a ±10% accuracy; this is insufficient because c freshwater ice sheet
as thin as 5 cm, floating on wafer, can be safely traversed by an individual
of average weight. System specifications include a 1 5-dBm output RF
(Radio Frequency) power level, a 0.066-second sweep rate and less than
a 50-dB Signal-to-Noise Ratio (SNR). This radar was tested on the ground
and from a helicopter at heights of up to 7 m above ice surfaces at speeds
up to 40 km/hr. Pond and river ice sheets between 3 and 35 cm thick,
with and without fresh snow cover, and with minimal surface roughness
have been profiled. Results have shown direct correlation between rodar
and borehole fhickness measurements. Losses from volume scattering by
imbedded air bubbles did not significantly affect the system's capability to
discern the air/ice and ice/water scattering boundaries.
QUALITY INSPECTED 5
Aooesslon For
HTIS GRAM
DTIC TAB
Unannounced
Justification
By - — - - -
Distribution/
Availability Codea
Ivaii and/or
Special
Cover: Bell Ranger helicopter with prototype radar attached.
For conversion of SI metric units to U.S./British customary units of measure¬
ment consult ASTM Standard E380, Metric Practice Guide, published by the
American Society for Testing and Materiais, 1916 Race St., Philadelphia, Pa.
19103.
CRREL Report 92-20
U.S. Army Corps
of Engineers
Cold Regions Research &
Engineering Laboratory
An Airborne Millimeter-Wave
FM-CW Radar for Thickness Profiling
of Freshwater Ice
Norbert E, Yankielun November 1992
Approved for public release; distribution is uniimited.
PREFACE
This report was prepared by Dr. Norbert E. Yankielun, Thayer School of Engineering, Dartmouth
College, Hanover, New Hampshire. The work, originally done as a Doctor of Engineering thesis, was
performed with support from the U.S. Army Cold Regions Research and Engineering Laboratory. The
U.S. Army Research Office (ARO) funded construction of a working model of the radar after the
research was completed by providing a grant (DAAL03-9 1 -G-0 1 92). Technical and economic details
of this implementation are given in Appendix A.
The author offers much thanks and gratitude to the following people, without whom this project
would not have been a success: Dr. Steven Arcone of CRREL for his continued commitment, patience,
encouragement and shared expertise; Professor Robert Crane for his guidance, assistance with the
ARO grant, and tutelage on spectral analysis and radar; Professor Stuart Trembly for his guidance and
insights; Professor John Walsh for his critical comments and enthusiasm; Alan Delaney of CRREL
forhis assistance with numerous technical and equipment-related issues, field testing and ground truth
collection; Nancy Perron of CRREL for her coldroom assistance with the thin sectioning and micro-
and polarized-light photography of ice core samples; and the author’s family and dear friends for their
generous love, understanding, encouragement and support throughout the frustrations and triumphs
of this endeavor.
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.
CONTENTS
Pag«
P*reface . ii
Nomenclature . vii
Introduction . 1
Problem statement . 1
Previous work . 1
Objective . 2
Procedures . 2
Electromagnetic propagation in ice . 3
Radar range equation . 3
Electromagnetic velocity . 3
Dielectric permittivity of ice, water and snow . 3
Transmission and reflection processes . 6
Attenuation losses . 7
Geometric spreading losses . 7
Refraction and focusing effect . 7
External random noise . 9
Radar technologies . 9
Impulse radar . 9
Synthetic pulse radar . 10
Coded radar . 1 1
FM-CW radar . 12
Selected technology . 13
Specifications . 13
Range and resolution . 14
Signal-to-noise ratio . 1 8
Data acquisition and recording . 22
Antenna parameters . 25
Physical parameters . 28
Summary of specifications . 28
Design and construction . 29
Prototype system configuration . 29
Test platforms . 35
Power requirements . 37
Economic considerations . 37
Results . 38
Skating arena profile . 38
Stationary profiling of thin pond ice . 39
Cart-mounted profiling of overflow pond . 39
Cart-mounted profiling of Post Pond . 40
Profiling of snow-covered pond ice . 41
Truck-mounted profiling of pond ice . 41
Cart-mounted profiling of Connecticut River ice . 43
Airborne profiling of lake ice . 44
Airborne profiling of river ice . 45
iii
Page
Performance analysis . 46
Theoretical measurement accuracy analysis . ‘^6
Radar pulse width analysis . 50
Statistical analysis of radar pulse peak magnitude . 57
System noise analysis . 59
Conclusions and recommendations . 59
Literature cited . 60
Appendix A: Survey details . 63
ILLUSTRATIONS
Figure Page
1 . Ef and e, of freshwater ice as a function of frequency and temperature . 4
2. Cf and Ej of fresh water as a function of frequency and temperature . 4
3. Dielectric constant of freshwater ice with air bubbles . 5
4. Measured ice thickness vs actual ice thickness . 5
5. Reflection and transmission with two interfaces . 6
6. Relative magnitudes of reflections from an air/ice/water multi-layered medium . 7
7. Reflection and transmission with three interfaces . 7
8. Representation of refractive focusing effect . 8
9. Refractive focusing coefficient vs ice thickness for several selected radar ranges . 8
10. Representation of impulse RF burst . 9
1 1 . Representation of a burst of pulses by a synthetic pulse radar . 10
1 2. Time domain display of pulse magnitude on an HP 85 1 OB MMW network analyzer . 10
1 3. Representation of autocorrelation function of complementary codes . 11
14. Representation of an FM-CW linear frequency sweep . 12
15. An FM-CW radar system . 13
16. Typical time series scan for an FM-CW radar . 14
17. Typical Fourier-transformed scan for an FM-CW radar . 14
1 8. Effect of bandwidth on resolution of adjacent pulses . 15
19. Minimum resolution parameters . 15
20. Resolution as a function of maximum radar range . 1 6
2 1 . Pulse-widening effect of windowing . 1 7
22. Parameters defining sweep linearity . 17
23. Computer simulation of radar reflections from a 5-cm slab of freshwater ice floating on
freshwater . 18
24. Example of thickness resolution simulation results . 19
25. Attenuation vs ice thickness for rij = 0.0001 . 20
26. Attenuation vs loss factor for a range of loss factors through a 5-cm-thick sheet of fresh¬
water ice . 20
27. Noise power vs bandwidth . 21
28. Sweep time and sweep rate parameters . 23
29. FM-CW radar difference frequency vs sweep rate for various radar ranges . 24
30. Horizontal displacement per sweep vs sweep rate for a range of typical profiling
ground speeds . 24
3 1 . Geometry of beamwidth vs thickness relationship . 25
32. Antenna beamwidth as a function of ice thickness for reflections from the ice/water
interface and air/ice interface at beam pattern edge . 25
33. Beam geometry of standard gain 9° antenna . 25
34. Footprint diameter for 3-dB antenna beamwidths vs altitude . 26
IV
Page
35. Parameters for determining antenna footprint overlap . 26
36. Dimensions of area illuminated by one scan . 26
37. Geometric elements for calculating percent overlap of antenna footprint on adjacent
scans . 26
38. Percentage of 3-dB antenna beamwidth overlap as a function of ground speed, altitude,
sweep rate and duty cycle . 27
39. Block diagram of the MMW FM-CW radar . 29
40. Radar front end . 30
41 . Amplifier-synchronizer used after mixing . 3 1
42. Record-only mode . 32
43. Playback mode . 32
44. Playback synchronization decoder . 33
45. Typical DSP displays . 34
46. Linear stacked-scan waterfall representation of reflections from an 8-cm-thick granite
slab . 35
47. Radan processed and wiggle-formatted display of reflections from an 8-cm-thick granite
slab . 35
48. Boom-mounted profiling arrangement . 36
49. Pre-prototype mounted on the cart . 36
50. Cart-mounted device profiling pond ice . 36
5 1 . Cart-mounted radar deployed on a bridge . 36
52. Truck-mounted radar . 36
53. Radar mounted on a truck using a tripod . 36
54. Profiling helicopter . 37
55. Segment of skating arena profile . 38
56. Sequence of increasing ice thickness on a frozen outdoor pond . 39
57. Vertical cross section of an overflow pond ice core . 39
58. Indication of surface roughness of overflow pond ice cover . 39
59. Radar and borehole measurements from overflow pond . 40
60. Post Pond survey path . 40
61. Segment of Post Pond profile from survey by cart-mounted radar . 40
62. Horizontal and vertical cross sections of 1 1 January 1991 sample of Post Pond ice core 41
63. Indication of surface roughness of Post pond ice cover . 41
64. Segment of Post Pond profile with snowcover . 42
65. Segment of Post Pond profile without snowcover taken at 10 km/hr . 43
66. Indication of surface roughness of Post Pond ice cover without snowcover . 43
67. Horizontal and vertical cross sections of 23 January 1991 sample of Post Pond ice core 43
68. Radar and borehole measurements from Ledyard Bridge . 44
69. Indication of maximum surface roughness encountered while profiling Connecticut
River ice from Ledyard Bridge . 44
70. Turtle Pond survey site near Concord, New Hampshire . 45
7 1 . Segment of airborne profile of Turtle Pond . 45
72. Pemigewasset River survey site . 45
73. Segment of airborne profile of Pemigewasset River near Franklin, New Hampshire . 45
74. Error attributable to frequency bin resolution as a function of ice thickness . 47
75. T-bar ice thickness measurement tool with offset indicated . 48
76. Radar and borehole thickness measurement from tape 6 . 48
77. Difference between radar and borehole thickness from tape 6 . 48
78. Radar and borehole thickness measurement for tape 1 1 . 49
V
Page
79. Difference between radar and borehole thickness from tape 1 1 . 49
80. Parameters for analysis of a pulse reflected from a metal plate . 50
8 1 . CDF of widths of pulses reflected from a metal plate . 51
82. Pulse width asymmetry (windowed data) . 51
83. CDF of rectangular windowed pulse . 52
84. CDF of Hanning windowed pulse . 52
85. Parameters for analysis of a pulse reflected from an ice sheet . 53
86. CDF of air/ice interface pulse width . 53
87. CDF of ice/water interface pulse width . 53
88. CDF of pulse width difference between first and second interface reflected pulses . 54
89. CDF of pulse width spreading between first and second interface reflections . 54
90. Pulse width asymmetry (interface data) . 55
9 1 . CDF of pulse width asymmetry at -5-dB point . 55
92. CDF of air/ice pulse width asymmetry . 56
93. CDF of ice/water pulse width asymmetry . 56
94. Representation of FM-CW radar waveform components used for statistical analysis . 57
95. CDF of peak magnitudes . 57
96. CDF of peak magnitude differences between air/ice and ice/water interface . 58
97. Summary of ice thickness vs peak magnitude difference . 58
98. Overlay plot of radar system responses to a metal plate and sky, indicating an approxi¬
mate 50-dB SNR . 58
TABLES
Table
1 . Apparent ice thickness for variations in refractive index . 5
2. Computer simulation parameters . 1 8
3. Calculation of SNR from typical system parameters . 21
4. Typical transmitted power levels and related SNR for given system parameters . 22
5. Selection of optimum sweep times . 24
6. FM-CW MMW radar specification summary . 28
7. System power requirements . 37
8. Prototype implementation costs . 37
9. Summary of survey studies . 38
10. Summary of calculated thickness resolution errors for 5- and 10-cm-thick ice . 47
11. Comparison of calculated and measured resolution error . 50
12. Comparison of mean pulse widths at -5- and -10-dB measurement points . 54
1 3. Comparison of mean pulse asymmetry at -5- and -10-dB measurement points . 56
14. Summaiy of pulse peak magnitudes survey data . 59
1 5. Comparison of calculated and prototype system SNR . 59
VI
NOMENCLATURE
Ae
antenna aperture (m“)
wave number in free space (2jt/>.o)
■^illum
area illuminated (m^)
Lx
system losses
^ovlp
area of scan overlap (m^)
L2
random propagation losses
■^sym
percent of pulse width asymmetry
N
total number of samples
all
air-to-ice interface boundary
number of points (bins) in FFT
als
air-to-snow interface boundary
n
complex index of refraction of medium
Bn
noise bandwidth
«a
refractive index of first material at interface
BW
FM-CW swept bandwidth (Hz)
boundary
bw
antenna beam angle/2 (degrees)
«b
refractive index of second material at
interface boundary
c
propagation velocity in free space (m/s)
«i
imaginary part of the complex index of
Difn
percent difference between borehole and
refraction
radar measurements
/Jjce
refractive index of ice
E
complex electric field strength
«0
refractive index of air
Eo
electric field strength
«r
real part of the complex index of refraction
^hi5
trailing edge -5-dB intercept frequency
^snow
refractive index of snow
^hilO
trailing edge -10-dB intercept frequency
'*samp
number of samples per scan
E\i
intermediate frequency
NL
nonlinearity of sweep
E\o5
leading edge -5-dB intercept frequency
Pn
amplifier noise power
^lolO
leading edge -10-dB intercept frequency
Pn
thermal noise power = KT^^j,
E mixer
mixer noise figure
P,
average received power
overall noise figure
Pi
average transmitted power
pulse peak amplitude intercept frequency
r
radius (m)
FrX
difference frequency of air/ice interface
reflection (Hz)
R
range (distance from antenna to ice
surface)
Fa
difference frequency of ice/water interface
Pab
reflection coefficient at interface
reflection (Hz)
boundary ab
FC
focus coefficient
Pmax
maximum radar range in free space
f
frequency
Pres
range resolution per bin (cm/bin)
Aamp
sampling frequency (Hz)
•^Bn
borehole thickness measurement (cm)
/swp
sweep frequency (Hz)
^Rn
radar thickness measurement (cm)
Gr
receiving antenna gain
S
thickness of an ice sheet
Gt
transmitting antenna gain
•^min
minimum measurable thickness of an ice
Gap
spatial gap in coverage between adjacent
sheet
scans (m)
sli
snow-to-ice interface boundary
ilw
ice-to-water interface boundary
SNR,
signal-to-noi.se ratio at system component
j
input
K
Boltzmann’s constant (1.38 x 10“^^ J/K)
SNRo
signal-to-noise ratio at system component
k
wave number
output
vii
T^h transmission coefficient at interface
boundary ab
This one-way travel time to pulse trailing
-5-dB point
Jhiio one-way travel time to pulse trailing
-10-dB point
r|o5 one-way travel time to pulse leading
-5-dB-point
^loio one-way travel time to pulse leading
-10-dB point
To receiver temperature (290 K)
Tp one-way travel time to pulse peak
/b propagation time from antenna footprint
beam edge
to propagation time from nadir ice/water
interface point
tree recovery time between sweeps (s)
fswp FM-CW sweep time (s)
V ground speed (m/s)
voli volume fraction of first material (air)
V0I2 volume fraction of second material (ice)
U^A/i air/ice reflection pulse width (ps)
lF[/w ice/water reflection pulse width (ps)
WHann('*) discrete Hanning window function
H'rect(n) discrete rectangular window function
X real random variable
z resistivity of the medium (W m)
a attenuation constant (Np/m)
p phase constant (rad/m)
A/*W percentage of pulse width increase i/w to
a/i interface
At round-trip travel time
8/ maximum deviation of modulation from
linear
Enjix dielectric constant of mix
£(, permittivity of free space (F/m)
El dielectric constant of first material
£2 dielectric constant of second material
X wavelength in medium
Ao wavelength in free space (m)
Px distribution mean
0 antenna beam angle (degrees)
Pi reflection coefficient for first surface
P2 reflection coefficient for second surface
a radar cross-section of target (m*)
Ox standard deviation
6a incident angle
0b refractive angle with respect to vertical
(0 angular frequency (27tf)
V propagation velocity in a ice
V* complex phase velocity
An Airborne Millimeter- Wave FM-CW Radar for
Thickness Profiling of Freshwater Ice
NORBERT E. YANKIELUN
INTRODUCTION
Problem statement
The ability to profile rapidly and accurately the
thickness of freshwater ice down to a few centimeters
over large surfaces of frozen ponds, lakes and rivers has
wide application and utility for ice safety and traffica-
bility studies. Other important applications include
monitoring ice flow on rivers and non-destructive mea¬
surement of ice sheet thickness for laboratory studies. In
addition, the ability to obtain high-resolution profiles of
other dielectrics, including man-made materials, may
prove to have military, commercial and industrial appli¬
cations. However, to date, no geophysical device has
been able to profile continuously thicknesses of less
than 20 cm. The development of an instrument to meas¬
ure ice thickness in the range of 3 cm or more is
addressed by this research effort.
Previous work
The literature contains numerous studies, including
Frankenstein (1966), Nevel and Assur (1968), Stevens
and Tizzard (1969) and Gold (1971), that investigate
and quantify the static and dynamic load-bearing capac¬
ity of floating freshwater ice sheets. Minimum ice thick¬
ness data for stationary and moving personnel and for a
range of vehicle weight classes have been summarized
(CRREL 1986) and indicate that for safe transit by a
solitary individual, 5 cm is the lower thickness limit.
Thus, it is necessary to develop an ability to profile ice
thickness to a resolution better than that lower limit,
which can provide reliable safety survey profiling for
the entire practical range of personnel and vehicular
transit possibilities.
Geophysical profilirg of the ground, sea ice and
freshwater ice for at least the last 25 years has been
successful with only impulse (or short-pulse) and spread
spectrum (e.g.. Frequency Modulated-Continuous Wave
[FM-CW]) radars. Impulse radar employs a sinusoidal
pulse of a few cycles length and nanoseconds (or less)
in duration, which is then amplified and coupled to an
appropriate antenna for transmission. Morey (1974)
describes in detail impulse radar technology; a summa¬
ry of impulse radar technology is presented in Van Etten
(1979); Hickman and Edmonds (1983) include a de¬
scription of impulse radar in a sur'ey of technologies
for sensing ice characteristics; and Arcone (1985) pro¬
vides a general discussion of the techniques for impulse
radar profiling of ice with emphasis on frequencies
below 1 GHz. Wills ( 1 987) and Riek ( 1 988) summarize
the development and application of radar to ice profiling
and other geophysical surveys. In spread spectrum ra¬
dars, the pulsed echo waveforms are synthesized from
a broad frequency spectrum (Eaves and Reedy 1987).
Ice thickness is then determined from the time separa¬
tion between ice surface and bottom echoes, given that
the pulse is short enough in time to prevent the two re¬
flections from overlapping. In both cases, thickness
resolution is directly proportional to the spectral band¬
width of the radar signal.
To date, efforts with impulse radar have not been
able to resolve ice thickness to better than about 10 cm,
primarily because of the inability to generate a pulse of
sufficiently short duration using a field-portable sys¬
tem. Vickers et al. (1974) describe a helicopter-borne
short-pulse radar, having a high resolution and a 2.7-
GHz center frequency, that is capable of airborne pro¬
filing with a minimum resolvable ice thickness of 10
cm. Cooper et al. (1974), Cooper et al. (1976a) and
L-ooperet al. ( 1 976b) discuss measurement of 29- to 60-
cm-thick freshwater ice with an S-band short-pulse
radar from ground-based, helicopter and fixed-wing
platforms, with an average difference between borehole
ground truth and radar measurements of less than 9.8%.
Annan and Davis (1977a) explored the use of VHF
impulse radar for both ice thickness ( 1-2 m) measure¬
ment and freshwater bathymetry, with graphic recorder
and magnetic tape output. Chudobiak et al. (1978) de¬
veloped and applied a nanosecond-impulse X-band
radar to profile ice with and without snow cover to min¬
imum tbi:>,;;> s.ses of 14 cm; output was directly dis¬
played on .m oscilloscope. Arcone ci al. (1986) ob¬
tained ground-based thickness measurements of 40-cm
freshwater ice sheets and brash ice with 700- and 900-
MHz short-pul.se radars, and Arcone and Delaney (1987)
discussed helicopter-borne continuous river ice profil¬
ing at 500 MHz. with a resulting minimum measurable
ice thickness of 1 5 to 20 cm. Later processing of signals
from impulse radar profiling data by Riek (1988) and
Riek et al. (1990) ha.s lowered the resolution of 900-
MHz impulse r.'dar data to the 10-cm range.
Related work with short-pulse rai_ar includes Vick¬
ers and Rose (1972), who reported an error of less than
10% from a ground-based radar having a 2.7-GHz
center frequency and a 1 -ns pulse for measurement of
snowpack stratigraphy; Butt and Gamberg (1979) and
Rossiter et al. > 1980), who applied airborne VHF im¬
pulse radar for sounding sea ice thickness; Daly and
Arcone ( 1 989). who surveyed freshwater ice from a
helicopter using a 500-MHz short-pulse radar, but who
could not deduce thickness directly because bottom
echoes could not be received; and Arcone et al. ( 1 989),
who employed 6- to 7-ns pulse radar from a helicopter
to detect liquid water trapped beneath ice sheets.
The FM-CW technique has not faired any better in
resolving ice thickness below 15 cm, primarily because
of the unavailability of field-portable sweep oscillators
with su . i'.cient bandwidth and power output level. Ch'i-
dobiak et al. (1974) used a ground-based X-band Ft..
CW radar to measure freshwater ice thickness to a
minimum of 15 cm. Similar results were obtained by
Venier and Cross (1975) with an X-band system that
was ground mobile and by Venier et al. (1975) with an
airborne system, where the radar data were recorded on
magnetic tape for later procc.ssing and display. Jakkula
et al. (1980) have applied an FM-CW mobile radar (1-
1.8 GHz) to measure ice and frost thickness on bogs,
providing a real-time display by means of a bank of 32
bandpass filters and a LED matrix, but only to a mini¬
mum theoretical thickness of 10 cm in ice. Their mea¬
surements were made on ice significantly thicker than
the minimum capability.
Several related geophysical applications of FM-CW
radar techniques have been leported. Wittman and
Stoltenberg (1981) developed a 1- to 2-GHz FM-CW
radar as a general remote sensing instrument, but did not
measure ice thickness with it. Gubler and Hiller ( 1984)
and Gubler et al. (1985) employed an 8- to 12.4-GHz
FM-CW radar specifically for snowpack stratigraphy
and avalanche research; hllerbruch and Boyne (1980)
employed an 8- to 1 2-GHz FM-CW radar to study snow
stratigraphy and water equivalence; and an L-band FM-
CW system was used to detect small objects buried as
deep as 80 cm in a wet snowpack by Yamaguchi et al.
(1991). Not.^ of these efforts, however, attempted to
make ice thickness measurements.
Several other techniques also exist that rely on ultra -
; oiile or electrical capacitance scii.ang to determine ice
thickness, but have been deemed unacceptable al.ema-
tives since physical contact or nearness to the ice sheet
is required, as well as a long dw ell time at the point of
measurement. Thus, the majority of the effort to date
ha' been with impulse or FM-CW radars, requiring
playback and processing in the laboratory prior to dis¬
play, at center frequencies of less than 10 GHz and
relatively narrow bandwidths, with resulting minimum
ice thickness resoludon on the order of 10 cm. These
characteristics, representative of the current state of the
art in radar profiling of ice thickness, aie inadequate for
the real-time, continuous, high-resolution ice safety and
trafficability survey application previously described.
Objective
The objective of this research is to develop an air¬
borne-deployable. real-time, high-resolution radar sys¬
tem for continuous, large-scale river and lake survey¬
ing. The key aspect here is to improve the current lower
limit of freshwater ice thickness measurement to clearly
and accurately profile ice that is less than 5 cm thick.
The real-time and continuous aspects are necessary to
minimize delay in interpreting data when dangerous
conditions are encountered.
Procedures
After a survey of available technologies, a prototype
millimeter wave (henceforth, MMW) FM-CW system,
equipped with a Digital Signal Processing (DSP) co¬
processor, was developed to allow continuous record¬
ing of echo .scans for later playback and processing. The
system was then operated from stationary and mobile
ground platforms and flown in a helicopter over natural
river and lake ice sheets with and without snow cover.
Data were processed to reveal surface and bottom re¬
flection profiles, the time separation of which was used
to determine ice thickness. The results were then com¬
pared with ground truth measurements.
2
ELECTROMAGNETIC
PROPAGATION IN ICE
The basis of radar ice thickness profiling is the meas¬
urement of the time delay of a radar pulse propagating
through a sheet of ice. To make this measurement and
interpret the results, the radar range equation and the
theory of wave propagation through a dielectric medi¬
um must be employed.
Radar range equation
The radar range equation is used to determine the
average power received from a target when illumi¬
nated by a radar signal where radar system, propagation
path and target parameters are known. Development of
the radar range equation is well documented (e.g.. Bar¬
ton 1988). Later, in the Speciyica/ion^ section, a detailed
discussion of the geophysical form of the radar range
equation is provided. A parsing of the radar range equa¬
tion, as done by Eves and Reedy ( 1 987), lends clarity to
its derivation.
Power radiated toward the target = Pfii ( 1 )
where P, = average transmitted power and G^ = transmit¬
ting antenna gain.
Power density at the target = {Pp^ I — ^ — j (2)
where R = range (m) (distance from antenna to ice
surface).
Equivalent power reradiated toward the
radar =(P,G,) I — ! — | (a) (3)
UnR^I
where c = radar cross section of target (m^).
Power density of the reflected wave at
the radar =(P,G,) [ — ^ — \ (o) I — ^ — \ (4)
UTtP^/ UnR^I
Power received at the radar
where
(j
A^ = antenna aperture (m^) = — i — (6)
471
where Gf = receiving antenna gain and X = wavelength.
Substituting eq 6 into eq 5, and including incurred
power losses, we formally state the received power as
•y
p — 0Z-1L2 (7)
(47ifp'‘
where L I = system losses
L2 = propagation scattering losses
a = absorption attenuation rate.
Electromagnetic velocity
The fundamental relationship for wave propagation
through a dielectric medium is
v=2s.= (L (8)
At «r
where v = propagation velocity in ice
s = thickness of an ice sheet
A/ = round-trip travel time in ice
c = propagation velocity in free space
/!;. = real part of the complex index of refraction
of ice n.
Thus, the thickness s of an ice sheet can be deter¬
mined from the equation when v and A/ are known. Am¬
biguities in measuring Ar arise from changes in the
shape of the radar waveform as it propagates through di¬
electric media encountered. Beam spreading and reflec¬
tion boundary effects mainly affect signal strength,
while dispersion considerations can cause waveform
distortion. These phenomena depend strongly on n,
which is related to the dielectric permittivity e, dis¬
cussed next.
Dielectric permittivity of ice, water and snow
Reflection, transmission, propagation and disper¬
sion depend on the absolute and relative dielectric
permittivities of all materials involved. The index of re¬
fraction n, or the permittivity e = rr, is found in the
theory of wave propagation in dielectric media, gener¬
ally described in many texts (e.g., Hayt 1967, Seshardi
1971). A geophysical remote sensing perspective is
given by Ulaby et al . ( 1 98 1 ). Following standard expo¬
nential notation, we may describe a scalar plane wave
propagating in the general direction r by
£ = £oe^“('"i") (9)
where E = complex electric field strength
Eg = electric field strength amplitude
j=^
(0 = angular frequency (2nf)
f = frequency
3
t = time
k = complex wave number (2x'A.) in medium
X = wavelength in medium
r = displacement vector.
The complex phase velocity v* of the wave is
= (10)
k
where k = k^n
kg = wave number in free space (2it/A.o)
Xq = wavelength in free space
n = complex index of refraction of medium.
Complex relative dielectric permittivity is defined as
e = e' -jt", where e' is the dielectric constant and e" is
the loss. These terms are related to the real (n^) and
imaginary (mj) parts of the complex index of refraction
n by
(11)
e" = 2n^,
For low loss materials, such as freshwater ice, at the
frequencies of interest n, « n^, so that
e'=/»2. (12)
Measured and theoretical values have been pub¬
lished for e' or , or both, for freshwater ice (e.g., Ray
1972, Vickers 1975, Blue 1980, Matzler and Weg-
muller 1987) and snow (e.g., Cummings 1952, Halli-
kainenetal. 1986,Hallikainenetal. 1987) that cover the
microwave and millimeter wave range. Variations in
the actual value of (for simplicity will hence¬
forth refer to the real part of the ice refractive index)
from the “standard” value of about 1 .77, as indicated in
Cummings (1952) and Ray (1972), are caused by tem¬
perature change, stratigraphic variation, ice matrix po¬
rosity or metamorphosis and will cause erroneous inter¬
pretation of ice thickness. From the water and ice per¬
mittivity algorithm and data presented in Ray (1972)
and illustrated in Figure 1 , it can be seen that both the
real and imaginary components of the permittivity of
solid, cold freshwater ice remain virtually constant
across the AT^-band at temperatures below 0°C.
Liquid water, on the other hand (Fig. 2), exhibits a
significant variation in both real and imaginary compo¬
nents of dielectric constant, which is both temperature
and frequency dependent across the ATg-band (26-40
GHz).
In applying radar to measuring ice thickness, the
variation of water permittivity affects the reflection
Figure I . tr and e, of freshwater ice as a function of fre¬
quency and temperature (after Ray 1972).
Figure 2. and e, of fresh water as a function of fre¬
quency and temperature (after Ray 1972).
coefficient and resultant amplitude of the reflected
signal at the ice/water boundary, but does not otherwise
interfere with the accuracy or resolution of ice thickness
measurement. The significance of the reflection coeffi¬
cient will be discussed later.
The inclusion of air bubbles is another factor that
affects the dielectric constant of freshwater river and
lake ice. Gow and Langston ( 1 977) indicate that typical
cross-sectional diameters of air bubbles in lake or river
ice are less than 1 mm and that the total air volume is
typically less than 5%, although a wide variation can be
expected. At air volumes less than 20%, the dielectric
4
Volume of Air Bubbles in Freshwater Ice Matrix (%)
Figure 3. Dielectric constant of freshwater ice
with air bubbles as a function of percent air by
volume.
Figure 4. Measured ice thickness vs actual ice thickness
based on ±5 and ±10% variation in refractive index.
mixing formula of Landau and Lifshitz (I960) and used
by Nelson et al. (1989) states that
emix4(voli)^+(vol2)'^] (13)
where = dielectric constant of mix
E] = dielectric of first material
£2 = dielectric of second material
vol) = volume fraction of first material (air)
V0I2 = volume fraction ofsecond material (ice).
Figure 3 illustrates the application of this formula to
an air and ice mixture. Here, an error in dielectric con¬
stant of freshwater ice introduced by air bubble inclu¬
sions is less than 5% over the practical range of interest.
This error will translate into an error in interpreting s as
determined by eq 1 . For example, Figure 4 and Table 1
Table 1. Apparent ice thickness for variations in re¬
fractive index.
Percent deviation Calculated Measured thickness {cmi
from 1.77 5 -cm ice 182-cni ice
-10
1.59
2.53
4.50
200.2
-5
1.68
2.82
4.75
191.1
0.0
1.77
3.12
5.00
182.0
5
1.86
3.45
5.25
172.9
10
1.95
3.79
5.50
163.8
indicate the calculated thickness of ice when the actual
value of n varies by ±5 and ±10% from the “standard”
value of n ice = 1 -77. For a practical air volume of 5%,
the error in thickness would be -2.2%.
In Cummings (1952), permittivity measurements at
lOGHz and-1 8°C with snow samples of varying densi¬
ties indicate that snow with density between 0.7 and 0.8
g/cw? provides permittivities between 2.5 and 2.8,
which lie close to the 1 0 and 5% uncertainty limits listed
above. Additional data in Cummings (1952) indicate a
value of 3.15 for Ejce (density = 1 g/cm-’). This would
seem to indicate that, in terms of permittivity, cold
(below 0°C) ice and snow with densities as low as 0.7 g/
cm^ should provide thickness measurements within a
10% thickness error tolerance.
For warming ice, a melting or saturated snow cover,
and candled ice, thickness measurement based on use of
a “standard” value of njce i.s more uncertain. The bulk
dielectric constant of an ice crystal/water matrix is sig¬
nificantly increased above that of cold ice, proving this
method of measurement unreliable. In Arcone et al.
(1986), measurement of Ejce = 4.1 was made for ice
undergoing grain boundary melting; 4. 1 translates to
about a 1 % water content by volume. This higher index
of refraction provides an increased reflection coeffi¬
cient at the air/ice boundary (top surface), thereby sig¬
nificantly attenuating the signal power that is transmit¬
ted through the slab and, consequently , is reflected from
the ice/water boundary (bottom surface). Additionally,
the loss component of the index of refraction increas¬
es from near zero to a significant value as the ice warms
andmelts.This further attenuates the pulse signal through
the warming ice slab.
These considerations limit the range of conditions
over which the radar may be reliably used given a “stan¬
dard” /tjce of 1.77. It appears that the radar can be
designed to indicate ice thickness with an error of less
than ±10% over the specified thickness measurement
range. Accurate thickness measurement of cold ice and
ice/snow configurations with a density of greater than
0.7 g/cm^is possible. Accurate thickness measurement
of warm, wet ice or ice/snow configurations appears
less feasible, but demands further experimental investi¬
gation.
5
Transmission and reflection processes
A mismatch of refractive indices exists at an inter¬
face of two different dielectric materials. This causes a
fraction of incident electromagnetic energy to be re¬
flected back from the interface, while the complemen¬
tary fraction of the energy is transmitted through the
interface. The fraction of the energy reflected back
depends on the reflection coefficient. Assuming that we
considered no losses ascribable to the medium, then
(14)
where R^b is the field strength reflection coefficient at
interface boundary ab and T^b >s the field strength
transmission coefficient at interface boundary ah.
It is the dielectric discontinuity at the air/ice and ice/
water interfaces and respective reflection coefficients
that make the measurement of ice thickness by electro¬
magnetic means possible. Brekhovskikh ( 1 980), Ulaby
et al. (1981) and Arcone (1984) discuss the reflection
coefficient and its relation to electromagnetic and acous¬
tic propagation in multi-layered dielectric media. At an
arbitrary planar dielectric interface boundary ah, the
reflection coefficient is defined as
^ab
where = refractive index offirst material at interface
boundary
«b = refractive index of second material at inter¬
face boundary
0a = incident angle
0b = refractive angle, with respect to vertical.
Figure 5. Reflection and transmission with two inter¬
faces.
tions and transmissions pertinent to thickness measure¬
ment for a two-interface (air/ice, ice/water) dielectric
medium. (While in practice, pertinent incident and
reflected energy would propagate normal to the surface,
the rays have been angled in the figure for illustrative
clarity.)
Here, the power reflected by the air/ice boundary is
attributable solely to the first interface reflection coef¬
ficient Rq I , which, for consistency of notation later, can
be denoted as p).
The power returned to the surface from the second
ice/water interface is ascribable to the product of the
transmission and reflection coefficients Toi, R\2 and
floor
P2 = (7'oi)(/?12)(7'io) (18)
Then, under Snell’s law with a normal incident angle (0a
goes to zero) and the associated normal refractive angle
(0b goes to zero), the reflection coefficient for a normal
incident wave upon an arbitrary dielectric boundary
discontinuity results in
Each dielectric layer of a multi-layered medium
permits multiple reflections and transmissions at in¬
creasingly attenuated levels. In a multiple layered me¬
dium, discerning the primary and subsequent multiple
reflections from each interface can be confusing and
creates a more complex analytical problem than in a
two- or three-interface medium. To determine ice thick¬
ness, it is necessary to consider only the initial reflec¬
tions from each interface.
Figure 5 illustrates the dielectric interface reflec¬
where the subscripts indicate the specific interface
between dielectric layers and the direction of propaga¬
tion. This can be further represented as
P2-(1 -/?0l)(^l2)(l-/?I0)
where nQ,ni and 112 represent the indices of refraction
of each of the layers in the medium.
Figure 6 illustrates the relative magnitude of pi and
6
P3 = f (20)
\(«0 + «l)^/\(«I + nifr ”2 + «3l I
-
P2
-
P1
— L
-1^
Time
(in terms of number of round trips through ice sheet)
Figure 6. Relative magnitudes of reflections from an
air/ ice/water multi-layered medium.
In the case of an air/snow, snow/ice and ice/water
boundary configuration, the lack of a substantial dielec¬
tric contrast between air and cold, low-density snow
prevents strong reflections from this interface (p j ) com¬
pared with the reflections from the subsequent bound¬
aries (p2 and P3).
Attenuation losses
Signal attenuation because of propagation through
lossy resistive media is described in Ulaby et al. ( 1 98 1 )
and can be determined from the refractive index n.
n = nr-jn,
\ A'o / ftoC V tO--Eo
(21)
FIRST INTERFACE
INCIDENT REFLECTION
Figure 7. Reflection and transmission with three inter¬
faces.
P2 for an air/ice/watermulti-layered dielectric medium.
Here also, P3, p4 and pj indicate the relative magnitude
of subsequent returns occurring after multiple internal
reflections in the ice sheet. The relative magnitude of
these multiples rapidly becomes insignificant.
Figure 7 illustrates the dielectric interface reflec¬
tions and transmissions pertinent to thickness measure¬
ment for a three-interface (air/snow, snow/ice and ice/
water) dielectric medium. In the three-interface case,
the power reflected by the first two interfaces can be cal¬
culated in a similar manner to that indicated above, and
the reflected power at the surface from the third inter¬
face follows as
P3 = (7'oi)(7'i2) (R23) (7'2l)(rio)
or
where a = attenuation constant (Np/m)
3 = phase constant (rad/m)
Eo = permittivity of free space (F/m)
= wavelength in free space (m)
z - resistivity of the medium (W m).
The signal attenuation (dB/m) because of resistive
losses is taken as
A = 20 log, 0 (a). (22)
For freshwater ice, e" is so small (Fig. 1) and r
typically > 5000 Qm (Gow and Langston 1977) that
a = 0
and
P == to = 2il .
X
Geometric spreading losses
Geometric spreading contributes to the attenuation
of signal power. As the signal travels to, and is reflected
from, a point target, the power density per square meter
decreases at a rate proportional to the fourth power of
range. A flat reflector, however, gives a decrease pro¬
portional to the second power. This factor is included in
radar range analysis calculations discussed in the Spec¬
ifications section. For now it suffices to say that at a
helicopter altitude of 3-7 m, an ice sheet thickness of
less than 20 cm presents insignificant spreading atten¬
uation of the bottom reflection relative to the surface
reflection.
Refraction and focusing effect
Focusing of the beam caused by refraction at the air/
7
ice interface boundary will give some amplification to
the bottom reflection. Although the rays leave the ice
sheet at the same angle they entered, the beam has been
collimated over the double thickness of the ice sheet.
Figure 8 illustrates the geometrical parameters that are
used with Snell’s Law to calculate the focusing effect
for an airborne antenna above an ice sheet. This effect
is factored into subsequent radar range analysis calcu¬
lations. The radius of the 3-dB beamwidth footprint at
the air/ice interface r-g is calculated as
Tg = tan(hH’) (23)
where bw = antenna beam angle/2 and R = range from
antenna to surface.
From Snell’s Law for refraction, the refracted angle
is calculated as
where = angle of refraction in ice
hq = refractive index of air
/lice “ refractive index of ice.
Accounting for the effect of refraction at the ice/
water interface rj,, we calculated the 3-dB antenna foot¬
print radius as
= + (25)
where s is ice thickness.
Ignoring the effects of refraction at the ice/water
interface we calculated the 3-dB antenna footprint
radius as
Tc = (/? + s) tan(hH'). (26)
Finally, the focus coefficient FC is calculated as
(27)
r2
FC=^-S-
'b
and in terms of decibels FQg as
FCdB=101og{FC)=101og
(28)
Figure 9 illustrates the result of these calculations for
Figure 9. Refractive focusing coefficient vs ice thickness for several
selected radar ranges ( calcuatedfor a 9 ° beamwidth horn antenna).
8
a variety of radar ranges and ice thicknesses. For exam¬
ple, at a range of 5 m above a 30-cm-thick sheet of ice,
the focus coefficient is approximately 1 .05, or convert¬
ed to decibels, FQb = 0.21 dB.
External random noise
Sources of noncoherent reflected energy are classi¬
fied as external random noise and are caused by surface
and volume scattering. Ulaby et al. (1981) present
several analytical models for the scattering process and
discuss the implications of su face and volume scatter¬
ing on the magnitude of the received reflected energy.
Simply, specular (coherent) reflection of an impinging
electromagnetic wave occurs at a dielectric interface
where the two media form a smooth, infinite plane.
Obeying Fresnel reflection laws, a reflection from this
interface would not be visible with a monostatic radar
unless it was positioned at nadir relative to the ice.
Backscatter from a rough-surfaced dielectric interface
would be sent in all directions and may be noncoherent
or partially coherent.
Surface scattering is frequency dependent relative to
the dimensions of the surface geometry (both large and
small-scale surface variations). Both signal strength
and pulse shape are adversely affected by surface scat¬
tering. Generally, specular scattering amplitude de¬
creases while noncoherent scatter intensifies as surface
roughness increases. Jezek et al. (1988) show that for a
given wavelength, the skewness of a Rice-type ampli¬
tude distribution increases with surface roughness. When
the surface is smooth compared to the wavelength, and
backscatter is dominated by the coherent specular re¬
turn, the Probability Distribution Function (PDF) of the
backscatter magnitude is nearly normal. As the surface
roughness increases and incoherent scatter becomes
more significant, the backscatter magnitude PDF skews
toward a Rayleigh distribution. The Rayleigh rough¬
ness criterion describes the maximum surface irregular¬
ity that will not substantially lower the reflection coeffi¬
cient. The criterion states that, if the surface irregular¬
ities result in path-length variations that are significant¬
ly less than one wavelength, the surface can be consid¬
ered as smooth. A smooth surface is defined as having
variations on the order of < V4 (Eaves and Reedy 1 987).
Dielectric inhomogeneities existing within a volume
result in volume scattering of the radar signal propagat¬
ing through the medium. In naturally occurring fresh¬
water ice, the primary contribution to the volume inho¬
mogeneity is from air bubble inclusions. The typical
range of dimension and density of these inclusions are
discussed in the Dielectric Permittivity of Ice, Water
and Snow section. Volume scattering causes a redirec¬
tion of some of the transmitted energy, resulting in an
attenuation of the transmitted wave. The scattering
strength is proportional to the magnitude of the dielec¬
tric discontinuity and the density of the imbedded
scatterers. Additionally, volume scattering is frequency
dependent relative to the dimension and geometry of the
air bubble inclusions and their spacing within the ice
matrix. Both reflected signal strength and pulse shape
are adversely affected by volume scattering.
RADAR TECHNOLOGIES
All radar technologies investigated here ultimately
rely on a pulse with a large bandwidth and narrow time
domain that is capable of distinguishing top and bottom
ice layer surfaces. Trade-offs between resolution, pow¬
er, signal-to-noise ratio and speed of data processing
exist for all systems and each are examined to conclude
which type is best suited for this thin ice profiling
application. Of the several available options, impulse
radar has been in constant use since the early 1 970s and
has demonstrated the least potential for achieving state
of the art signal-to-noise ratio and performance; the
radar inherently sacrifices much to gain a short pulse. It,
therefore, is described first to be used as a basis of com¬
parison with the other available technologies.
Impulse radar
Background information on the theory of impulse
radar is discussed in Chudobiak et al. (1978), Arcone
(1985), Currie and "'mwn (1987) and Wehner (1987).
Briefly, a 1-2 cycle burst of RF (radio frequency)
energy with a narrow pulse envelope (Fig. 10) is gener¬
ated, transmitted and travels toward the target. It is re¬
flected by the target back to the receiver, where it is then
sampled to be converted to the audio range for recording
and processing. The sampling process inherently cre¬
ates random noise. All radars today use very low gain
antennas to achieve narrow pulse widths.
Q>
1 _
\ r\ _
Q.
<
f Time
Figure 10. Representation of impulse RF burst.
Advantages
Low complexity. At microwave and lower frequen¬
cies, impulse radar designs are relatively simple. Sys¬
tems discussed earlier by Vickers and Rose (1972),
Chudobiak et al. (1978), etc., employ simply a pulser
and an oscilloscope. To a significant degree, systems
can be built from commercially available hardware.
Minimal signal processing. Ice thickness can be
9
measured using only a single return of raw data. This
limited signal processing allows the thickness measure¬
ment to be displayed in real time.
Disadvantages
Antenna considerations. Depending on the band¬
width of the radar pulse and the antenna configuration,
there may be undesirable pulse wave shaping at the
antenna. Currently available technology dictates the use
of low-gain antennas (7 dB at most) to limit this pulse
distortion effect. There are no practical, high-gain,
short-pulse radar antennas apparent in the literature.
Significant clutter is evident, even with shielded anten¬
nas. Shielding, while lessening the effects of clutter,
tends to lengthen the radar pulse, decreasing the ability
of the radar to measure accurately thin ice thickness.
Sampling noise floor. Traditionally, impulse radars
use sampling techniques to reconstruct VHF-UHF (very
high frequency-ultra high frequency) signals in the
audio range for later display and recording on magnetic
tape. The sampling process generates about a 40- to 50-
dB noise floor.
Low average power-low performance figure. With
sampling, several thousand pulses at VHF-UHF must
be used to recreate one pulse at audio frequencies. This
is a waste of power and a drain on batteries. With a low
power impulse and low gain antennas, system perfor¬
mance figures rarely exceed approximately 1 10 dB.
State of the art pulse-forming technology. High-
resolution requires a broad bandwidth and, consequent¬
ly, a proportionally narrow impulse must be generated.
Resolving thickness on the order of a few centimeters
requires a pulse width on the order of hundreds of pico¬
seconds. Two approaches are suggested in the litera¬
ture. The first is gallium arsenide circuit component
technology, currently limited to 200-ps pulse widths at
very low output power, as illustrated by Avtek (1989).
The second is electro-optic pulse generation techniques
discussed by Valdmanis and Mourou (1986), Paulus et
al. (1987), Auston and Nuss (1988), Paulter (1988) and
Paulter et al. (1988). While both of these techniques are
capable of generating sub-nanosecond pulses, they ap¬
pear to be highly experimental laboratory implementa¬
tions, not generally available and, therefore, not readily
suited for application in a field-portable instrument.
where
represents one narrowband pulse.
Figure II. Representation of a burst of
pulses by a synthetic pulse radar.
Synthetic pulse radar
Technical discussions of synthetic pulse radar are
given in Ulaby et al. (1981), Wehner (1987) and in
industrial microwave/MMW network analyzer opera¬
tion manuals (e.g., Hewlett-Packard). Conceptually, a
synthetic pulse radar transmits a burst of an integral
number of narrow band pulses, as represented in Figure
1 1 . Each narrow band pulse in a burst series is displaced
by a uniform frequency step to span the full bandwidth
of the radar. The spectrum of a wide band pulse is
Reflection
Figure 12. Time domain display of pulse
magnitude on an HP 851 OB MMW net¬
work analyzer (waveguide-to-horn tran¬
sition, horn-to-air transition and reflec¬
tion from a metal plate at a range of ap¬
proximately 1 .5 m are indicated).
10
formed when phase and amplitude components from
each pulse in a burst series are combined. Each burst is
coupled to an antenna, transmitted, reflected from the
target, and the received phase and amplitude informa¬
tion is stored. An inverse Fourier transform is computed
from the received phase and amplitude spectra, result¬
ing in a time domain representation of the reflected,
synthesized wide band pulse. Figure 12 is atypical time
domain display of a radar reflection from a metal plate
using an HP 85 1 OB (Hewlett-Packard) network analyz¬
er configured as a MMW synthetic pulse radar.
Advantages
Extremely high resolution. When appropriately con¬
figured, setups such as the HP 851 OB are capable of
range resolutions of less than 1 cm. This requires a broad
bandwidth (>13 GHz), a large number of sampled fre¬
quencies in the bandwidth (801 ) and lengthy acquisition
and processing times (=150 s).
Low transmitted power. The spectrum of a large
amplitude radar pulse can be synthesized from the many
lower power frequency components required to form
the pulse.
High signal-to-noise ratio. Synthetic pulse systems,
exemplified by the HP 85 lOB, allow for multiple sam¬
ples at each synthesized frequency. When these sam¬
ples are averaged by the system, a substantial improve¬
ment in Signal-to-Noise Ratio (SNR) ratio can be
obtained, but with a proportional increase in processing
time.
Disadvantages
While this system provides excellent results in the
laboratory, there are some disadvantages for field or air¬
borne deployment. These include the following.
Expensive hardware. The HP 85 lOB configured as
an MMW radar costs approximately $200,000 (1991
dollars), too expensive for common deployment and for
exposure to typical field environments and handling.
Slow data collection, analysis and display time. The
fastest system throughput is 4 seconds per synthetic
pulse. This is too slow for airborne applications with
typical flight ground speeds of 2 to 9 m/s. (The dwell
time required per sample is too great.)
Limited range. At the highest throughput, 4 seconds
per pulse and a pulse bandwidth of 3 GHz, the system ’s
maximum range is only 5 m. This is near the minimum
limit of altitude of typical helicopter survey flights.
Not portable. The HP 85 lOB is intended as a labora¬
tory instrument, not for field or airborne application.
Fully configured, it weighs more than 200 kg, occupies
close to a cubic meter and requires 1 0 A at 1 20 V (rms),
60 Hz, for operation. It is not designed to be portable,
nor is it field-hardened.
Figure 13. Representation of autocorrelation func¬
tion of complementary codes.
Coded radar
Wehner (1987) and Wills (1987) provide technical
discussions of digital phase coded radar and Wills
(1987) developed a working prototype operating at 40
MHz. Briefly, a pair of complementary coded digital
sequences with power-of-two length are consecutively
transmitted. When the autocorrelation functions of both
codes are added together, a perfect autocorrelation re¬
sponse without time sidelobes results (Fig. 13). Coded
radars provide a satisfactory alternative for some geo¬
physical profiling applications. However, there are se¬
rious considerations that eliminate it from possible
MMW implementation.
Advantages
Low noise. High SNRs are attainable, since both in-
phase and quadrature signal components are available
for processing. (Both magnitude and phase can there¬
fore be derived.) When scans are integrated, an SNR im¬
provement proportional to the number of integrated
scans is obtained. In an instrument where only magni¬
tude information is available, the SNR improvement is
proportional to only the square root of the number of
integrated scans.
Improved range ability. Long transmitted pulse se¬
quences produce greater average transmitted power and
perniit longer range capability.
Disadvantages
Complexity. The coded radars are considerably more
complex than either the FM-CW or pulse radars be¬
cause, at least in part, of their code generation and signal
processing hardware and software. For the level of reso¬
lution required by the radar design under consideration,
it does not appear that this level of complexity provides
any increased advantage over simpler apparatus.
Expense. A cost of $53,000.00 (less overhead and
profit) was estimated by Wills ( 1 987) to develop a VHF
digital phase-coded ground-probing radar. We can ex¬
pect that, if feasible, an MMW system of this type, given
the greater cost of the higher frequency hardware re¬
quired, would be prohibitively expensive.
II
Figure 14. Representation of an FM-CW linear frequency sweep.
Hardware limitations. Even if the two former issues
are not thought to limit this application, digital hard¬
ware for generating the necessary coded pulse trains at
gigahertz switching frequencies is currently unavail¬
able.
FM-CW radar
Detailed technical descriptions of FM-CW (Fre¬
quency Modulated-Continuous Wave) radar are given
in Venier et al. (1975), Wittmann and Stoltenberg
(1981) and Currie and Brown ( 1 987). Basically , the out¬
put of a linear sweep oscillator (Fig. 14) is transmitted
toward the target. The received energy, reflected back
from the target, is mixed with a sample of the sweep
oscillator output. The difference frequency is detected.
This difference frequency is proportional to the target
range and can be determined using spectral analysis
techniques. With two primary scattering boundaries, as
in the case of the air/ice and the ice/water interfaces
found on a sheet of ice floating on water, ideally there
will be two distinct frequency components, one from
each of the interfaces. The difference between these two
frequencies is proportional to the distance between the
two interfaces.
Advantages
Simple RF design. In its most fundamental form, an
FM-CW radar consists of very few components: a
sweep oscillator, a power divider, a mixer, a spectrum
analyzer and two antennas. The sweep oscillator serves
as both the transmitter and local oscillator signal source.
General availability of components. The MMW and
low-frequency components required are readily avail¬
able from several major manufacturers. The key com¬
ponent is the MMW sweep oscillator, models of which
now are specified to maintain better than a ±0. 1 % sweep
linearity at 10- to 15-dBm power levels across the entire
/fg-band.
High resolution. By taking advantage of the full K^-
bandwidth of available MMW sweep oscillators, a
theoretical resolution on the order of 1 cm or less is
possible.
High average power. The FM-CW radar continu¬
ously transmits a sweep frequency signal of constant
amplitude.
Disadvantages
Transmitter-receiver isolation. In FM-CW radar the
sweep oscillator is continuously generating an RF out¬
put signal. The transmitting antenna needs to be isolated
from the receiving antenna so that inter-antenna cou¬
pling is minimized. This coupling, at worst, could dam¬
age the receiver elements and, at least, overload the re¬
ceiver front end, inhibiting the detection of the reflected
signal energy. Isolation also aids in minimizing inter¬
antenna reflections, which appear as spurious respons¬
es. These problems can be somewhat alleviated by ad¬
justing the transmitter power to a sufficiently low level
to avoid receiver saturation.
Sweep linearity. For high range resolution, an ex¬
tremely linear sweep oscillator is required. The wider
frequency deviation that is required in a broadbanded
system may be difficult and expensive to make linear.
Homodyne mixing noise. Currie and Brown (1987)
suggest that a balanced mixer and high gain preampli¬
fier may be required to overcome the effects of high
noise associated with the homodyne mixing process,
potentially increasing complexity and cost.
MMW sweeper component cost and suitability. Lab¬
oratory-grade MMW sweep oscillators (such as units
manufactured by Hewlett-Packard, Inc., and Wiltron,
Inc.) can cost as much as $40,000 (1991 dollars) and are
not particularly suited for a portable or field application.
Component-type MMW sweepers (such as YIG-Tuned
Oscillators [YTO] manufactured by Avantek) are more
suitable for integration into portable or field equipment
and are less expensive options at $5,000 (1991 dollars).
Complex signal processing. Since FM-CW radar
signals must be transformed from the time domain to the
frequency domain for analysis and display, either soft¬
ware or hardware Fast Fourier Transforms (FFT) must
be applied to the received radar reflection signal. Con¬
siderable computer real-time overhead (on the order of
several seconds per scan) is required for software FFT
implementation, substantially affecting the rate of radar
scan throughput. Alternatively, a hardware FFT trans¬
forms a typical radar scan in several milliseconds or
less, but requires an expenditure of between $5,000 and
$10,000 (1991 dollars) for hardware and support soft¬
ware.
12
Selected technology
Based on an examination of available radar technol¬
ogies applicable to the airborne profiling of thin, fresh¬
water ice, an FM-CW radar system is the choice for this
research project. The criteria for selection of this tech¬
nology included component availability (preferably
from stock), reliability, robustness, functionality and
cost.
Impulse radar was eliminated as a candidate prima¬
rily because of the general unavailability of a suitably
robust, readily available, field-deployable and reason¬
ably economical wide-band pulse generator. The coded
radar technique was discarded primarily because of the
unavailability of logic components capable of tens of
gigahertz clock rates. Synthetic pulse radar was rejected
primarily because of the long single-scan dwell times
(order of tens of seconds) required over a target for radar
data acquisition.
An FM-CW MMW radar system can be convenient¬
ly and reliably built with readily available and reliable
hardware. With MMW YTOs having a proven history
of reliability in militai7 avionics applications, they
appear to be an appropriate choice for integration in a
field instrument for use in a harsh (winter or Arctic)
environment. These YTOs operate at a wide tempera¬
ture range (-54 to 85°C), operate directly from single
polarity dc power supplies, are hermetically sealed,
have a robust mechanical design and are physically
small. Full /fa-bandwidth units (as well as units for other
full-bandwidth microwave bands) are readily available
at appropriate power levels given typical range and
SNR requirements for less than $5000 (1991 dollars).
The waveguide hardware for an FM-CW radar system
consists of few, simple, robust stock components that
can be easily repaired or replaced in the field. Signals
can be acquired and processed rapidly and continuously
in real-time using readily available state of the art DSP
technology. Imbedded in a field-hardened computer
system, DSP hardware can immediately process and
display profile survey data or store them to disk or tape
for subsequent playback and analysis.
SPECIFICATIONS
FM-CW radars have been used since the early days
of radar (Ridenour 1947) and Figure 15 illustrates their
present day operation. As the figure shows, the output
13
of a linear ramp oscillator (A) is applied to the control
input of the MMW Voltage Controlled Oscillator ( VCO)
(B), causing a linearly swept-frequency RF signal to be
transmitted toward the target (C). At the same time, a
sample of the swept RF oscillator output is coupled to
the receiver (D). The energy received from the target,
delayed by the round-trip propagation time 2/p (E), is
mixed with the current sample of the sweep RF oscilla¬
tor output. The difference frequency is proportional
to the target range and can be determined using spectral
analysis techniques (F). With two reflecting bound¬
aries, as in the case of the air/ice and the ice/water
interfaces, ideally there will be two distinct frequency
components, one from each of the interfaces. The differ¬
ence between these two frequencies is proportional to
the distance between the two interfaces.
The tasks in designing an appropriate FM-CW radar
to measure ice thickness continuously are to achieve the
desired resolution at the necessary range, to ensure that
the signal amplitude is sufficient to produce a clearly
identifiable pulse after the data processing, and to
implement several original processing specifications to
Range and resolution
Figure 16 shows an example of a typical difference
frequency time-series scan for an FM-CW radar. Figure
17 gives the Fourier transformed power spectrum of this
scan, showing the spectral components that correspond
to the direct coupling, first surface, second surface and
multiple return events.
The one-way travel time is calibrated in terms of
frequency according to the relationship
One-way travel time (ns) ^ (29)
2(BW) (n)
where Fri = difference frequency ascribable to the air/
ice interface reflection (Hz)
^swp - FM-CW sweep time (s)
BW - FM-CW swept bandwidth (Hz)
n = index ofrefraction of appropriate medium.
Ice thickness is calibrated from the separation of the
two difference frequencies according to the relationship
Time (ms)
Figure 16. Typical time series scan for an FM-CW radar.
Frequency
(kHz) doooo----
Figure 1 7. Typical Fourier-transformed scan for an FM-CW radar.
14
where^r2 = difference frequency attributable to the ice/
water interface reflection (Hz)
= index of refraction of freshwater ice = 1 .77
c = velocity of light in vacuum = 3x10* m/s.
There is thus a trade-off between range and resolu¬
tion as there is a limit on the number of time series sam¬
ples that can be taken (typically 1024) during a given
sweep at a set sample rate; the greater the maximum
radar range, the fewer the samples that can be allocated
to a small frequency segment of interest.
There are several things that one must take into
account when designing a radar that affect its ability to
resolve clearly the top (air/ice) surface and the bottom
(ice/water; surface of an ice sheet, thereby determining
the lower limit of measurable ice thickness : bandw idth,
sampling, windowing, surface and volume scattering,
and surface wetress.
Effect of bandwidth
Figure 18 illustrates the effect of bandwidth on
resolving the radar pulse reflections from two dielectric
interface boundaries. Clearly, the greater the band¬
width, the narrower the pulse shape and the easier it is
to resolve closely spaced adjacent pulse maxima. The
results are independent of the center frequency of the
FM-CW bandwidth (i.e., 23-28 GHz yields the same
resolution as 48-53 GHz).
The following calculation, as suggested by Wehner
(1987), provides a theoretical minimum bandwidth.
The minimum resolvable thickness of a dielectric slab
is related to resolving two radar reflection pulses in the
time domain. Under the assumption that the time do¬
main envelope of each of two pulses is of the sin(Px)/jr
Figure 18. Effect of bandwidth on resolution of adjacent
pulses (ire thickness = 5 cm).
Figure 19. Minimum resolution parameters.
form, the resulting frequency domain representation is
rectangular with a bandwidth BW. The minimum reso¬
lution is defined (Fig. 19) as the delay difference be¬
tween these two pulses resulting in a crossover point
that is -4 dB down from the pulse peaks. Then
BW = ^. (31)
At
The quantity A; is also the ^-dB time domain
maximum pulse width for resolution of top and bottom
surfaces of a slab of given thickness.
With this information, the minimum required fre¬
quency bandwidth can be determined. The minimum
time separation At between the pulse reflection off the
air/ice interface and the reflection off the ice/water
interface is
At = ^•^.'nin.'lice (32)
c
where is the minimum thickness of ice.
For example, givensn,jn=5cmandnjcg= 1.77, then
the pulse separation At = 590 ps.
Consequently, the minimum theoretical bandwidth,
given a -4-dB crossover, required for resolution of the
thickness of 5-cm-thick freshwater ice is 1 .69 GHz. If
the entire /fa-bandwidth (26.5 to 40 GHz) is available,
then the minimum theoretically measurable ice thick¬
ness is calculated to be 0.63 cm.
Effect of sampling and transformation
Thickness resolution is also affected by the
maximum radar range in free space allowed by the
bandwidth, sweep time and sampling rate. /?max deter¬
mined from the relationship
(33)
where /samp tb • sampling frequency (Hz).
For a given maximum radar range and FFT trans¬
form size (or number of discrete power spectrum bins)
the maximum radar range resolution can be deter¬
mined by
o -2(>?mJ(»00)
(%.)(«r)
(34)
15
2.5
a. In air
b. In ice.
Figure 20. Resolution as a function of maximum radar range.
where = range resolution per bin (cm/bin)
iVffi = number of points (bins) in FFT
= refractive index of medium (real part).
Figure 20 illustrates the dependency of distance
resolution in free space and thickness resolution in ice
on maximum range and FFT size for practical parameter
values. For example. Figure 20b shows that a 2048-
point FFT is required for the transform resolution to
approach the minimum theoretical resolution calculat¬
ed for a 1 3 .5-GHz bandwidth at a maximum radar range
of 5 m.
Effect of windowing
The general concept of wi rnlowing is explained by
Oppenheim and Schafer (197.5), Stanley et al. (1984)
and Kay (1988). Briefly, when a finite length segment
of a time series is sampled and Founer transformed, the
abrupt beginning and end points of the sampling pro¬
cess introduce spurious spectral components into the
periodogram. These components appear as sidelobes
that may be of sufficient magnitude to mask low level
spectral components of interest. In this case, the sam¬
pled data are said to be windowed by a discrete rectan¬
gular function w„j.,(/j), defined as
H’reci('»)= 1. 0 <n<N-\ (35)
where n is the sample number and N is total number of
samples.
The masking effect of the sidelobes can be mitigated
by convolving the sampled time series with an appropri¬
ate tapered window function, for example a discrete
Hanning window W HannC'’)- defined as
w
Ham
1 - cos -2iyL
\N- 1
0 <n<N-\.
(36)
16
In the time domain, a non-rectangular window, such as
the Hanning, tapers the leading and trailing ends of the
sampled time series to zero. After Fourier transforma¬
tion the frequency domain periodogram appears smooth¬
er and with sidelobe magnitude reduced to a level as
much as 30 dB less than that realizable with a rectangu¬
lar window. This aids in the location of reflection arti¬
facts that would otherwise be overwhelmed by the rec¬
tangular window sidelobe amplitude, especially when
the SNR is low. There are two negative side-effects,
however, as illustrated in Figure 21 . First, the reflection
amplitude is attenuated. In the example shown, the
attenuation is 3 dB. Second, resolution is significantly
limited by the widening of the pulse-width from the ap¬
plication of windowing. In the example shown, the
-4-dB pulse width of the rectangular-windowed data is
100 ps. When Hanning windowed, the -4-dB pulse
width is broadened to 170 ps.
Effect of sweep linearity
Deviation from a linear relationship between sweep
frequency and sweep time will adversely affect the
accuracy with which radar range and ice thickness can
be measured. Nonlinearity of sweep NL is defined as
NL = M. (37)
BW
where 5/, the maximum deviation of modulation from
linear, can negatively affect range resolution accuracy.
Distortions in the sweep frequency vs sweep time rela¬
tionship cause proportional errors in the apparent radar
range of targets, by making them appear closer or far¬
ther away. A typical nonlinear sweep might appear as in
Figure 22.
It is desirable that range distortion attributable to
nonlinearities of the sweep time/frequency relationship
be significantly less than the minimum range resolution
of the system. Thus, a maximum constraint on nonlin¬
earity can be determined by requiring that NL be much
less than the ratio of the minimum resolvable range
to maximum range R^ax of the system. Given that
c
(BW)
(38)
Figure 22. Parameters defining sweep linearity.
17
Relative Power (dB)
then the constraint on NL is
Table 2. Computer simulation parameters.
-8L« J?ies_ (39)
^max
As an example, for a system with a 1 3.5-GHz swept
bandwidth and amaximum range of 1 0 m, the minimum
range resolution is 1 . 1 1 cm and the nonlinearity must be
much less than 0. 1 1 %.
Bandwidth vs minimum resolvable thickness
Computer simulations were done to determine the
effects of bandwidth on thickness resolution. The plane
wave formulations discussed in the Electromagnetic-
Propagation in Ice section were used to simulate the
reflections of a radar pulse at dielectric interface bound¬
aries. An infinite ice sheet with smooth, parallel surfac¬
es and no distorting effects of noise were assumed for
the model. Figure 23 shows the results of one such
simulation with pertinent artifacts labeled. Here, reflec¬
tions from a 1 3.5-GHz bandwidth radarpulse are shown
to resolve clearly the air/ice and ice/water interfaces of
a 5-cm-thick sheet of ice floating on water. The several
multiple reflections of decreasing magnitude are caused
by a portion of the transmitted pulse energy reflecting
back and forth between the two dielectric interfaces
before returning through the air/ice interface. A Kaiser
window was used in this simulation to decrease the
sidelobe level.
Further simulations were conducted using the para¬
meters shown in Table 2 and the reflection coefficients
of the air/ice and the ice/water interfaces, losses in ice
and focusing effects of ice on antenna beam width. Plane
Figure 23. Computer simulation of radar reflections
from a 5-cm slab of freshwater ice floating on fresh
water (bandwidth = 13.5 GHz, Kaiser window coeffi¬
cient = 6l
Antennas: Standard gain pyramidal horns, 24-dB
gain, 9° beamwidth
Range: 10 m
Ice thicknesses: 5. 10. 50. 100 and 200 cm
Peak transmitted power I W
Transmitted waveform: Hanning-windowed sinchronized pulse
Bandwidth: 1.3,5 and 7 GHz
Wavelength: 1 cm (at radar center frequency in free
space)
System losses; 6 dB
Receiver noise figure: 6 dB _
wave reflection coefficients were used, as the beam-
width and range allows a nearly planar phase front to the
waves. The separation and resolution of the air/ice and
ice/water interface reflections were observed; graphical
examples of outputs are shown in Figure 24.
Based on numerous iterations of the process, em¬
ploying the range of practical and realizable band-
widths, peak power levels, Hanning windowing and ice
thicknesses, it appears that a reasonable minimum band¬
width needed to meet the specifications is 3 GHz. At this
bandwidth ice somewhat thinner than the 5-cm mini¬
mum thickness should be reliably measured using sig¬
nal processing techniques (e.g., Riek 1988, Riek et al.
1990) to determine the location of the two interface re¬
flections. This result compares favorably with the 1 .69-
GHz minimum theoretical bandwidth calculated in the
Ejfect of Bandwidth section where windowing was not
applied. Since Hanning windowing broadens the pulse,
a greater bandwidth is required to maintain a specified
thickness resolution.
Attenuation ofMMW radar signals in ice
The loss component of the refractive index /ij for
freshwater ice in the K^-band, as reported in Ray (1972),
is on the order of 0.00 1 to 0.000 1 . Simulations were per¬
formed to determine the effect of this loss on the reflect¬
ed radar signal over a wide range of ice thickness. Figure
25 graphs the total for the bottom reflected signal for a
specified set of radar parameters. The addition of 1 m of
ice adds only about 1 dB ofloss. Figure 26 indicates the
attenuation over a range of values of n, for a given ice
thickness. These results indicate that these losses, while
measurable, have little overall effect on profiling capa¬
bility.
Signal-to-noise ratio
The Signal-to-Noise Ratio (SNR) is the ratio of the
received power P^ to the noise present in the environ¬
ment and system. Consideration of the SNR is es.sential
when specifying system parameters for satisfactory
radar performance. The system SNR is calculated to de¬
termine the feasibility of the proposed design. This SNR
18
‘ ' *
.....
_.,-J
.....
L...J
3-GHz Bandwidth
....
_ j
...
...
_ J
U..-J
5-cm-Thick Ice
U-.-J
— -I
_ J
r n
U- -1
1 1 1 1 1 1
L_.-L _ L _ i.-_i _ L .
1 — 1
-J. _ 1
r 1
- - - f - J - J - f - 1 - - - -
: 1 1 1 1 1 :
_
_
1
.— .J
1 1
1 _ 1
1 1
1 _ J
1 1
I _ 1
1 1
1 _ J
-V
1
....J
1 — 1
1 _ 1
1 — 1
I _ J
1 — 1
1 _ 1
1 — 1
I _ J
1.. ^.
1.. ..
1
1
1 — 1
1 1
I — 1
1....!
1 — 1
1 1
I — 1
L-.— !
L....
1
1
1
t*
I
j
7-GHz Bandwidth
5-cm-Thick Ice
Ml 1 Jm
mill
H - H- . H-
I
'.'ViTJll
7-GHz Bandwidth
50-cm-Thick Ice
Figure 24. Example of thickness resolution simulation results. For all graphs vertical scale is relative power (dB ) and
horizontal scale is one-way travel time (ns). Solid horizontal line is KTB^ noise power associated with given bandwidth.
9
03
•D
Figure 26. Attenuation vs loss factor (nj) for a range of loss factors
through a 5-cm-thick sheet of freshwater ice.
formulation is representative for a FM-CW system
transformation of a single scan. If multiple pulses are
stacked, a proportional increase in the SNR ratio can be
obtained.
Radar range equation for geophysical application
The geophysical form of the SNR relationship was
developed from Annan and Davis (1977b), Currie and
Brown ( 1 987) and Wills (1987) and represents the SNR
ratio of a radar pulse reflected from the top surface of a
sheet of freshwater ice. Many of the parameters that
affect the SNR were defined in eq 1.
SNR = - - (pj) (40)
{Av.)\lR)hT^^^
20
where p| = reflection coefficient for first surface
k = Boltzmann’s constant (1.38 x 10 J/K)
Bp = noise bandwidth
Tq = receiver temperature (290 K)
Fn = receiver noise figure
and
SNRi^=\0\og^Q{Sm) . (41)
The noise power teini is shown as a function
of noise bandwidth in Figure 27.
The SNR of a radar pulse reflected from the bottom
surface (ice/water interface) of a sheet of freshwater ice
is represented by an extension of the above relationship.
SNR = - - (P2) {FC) {L^ (42)
(4jt)l2F)2*F^„F„
where P2 = reflection coefficient for two-interface
medium
FC = focus coefficient
L2 = medium losses due to scattering (absorp¬
tion losses assumed negligible).
5. Receiver noise bandwidth was assumed to be
100 kHz. This value was selected because it is on the
order of the maximum difference frequency expected at
the output of the MMW mixer and input to the audio
amplifier used before data acquisition.
6. Noise figure F^ is defined as
F
" SNR^
(43)
where SNR^ = signal-to-noise ratio at the input and SNR^
= signal-to-noise ratio at the output (of an amplifier,
mixer or system). A typical single-ended mixer noise
figure F^ixer is given as 10 dB by Brookner (1988). The
intermediate frequency noise figure Fjf is calculated as
(44)
where = amplifier noise power, P^ - thermal noise
power = kTffin and
Fn ~ ^mixer "*■ (45)
The viability of this approach was analyzed using
realizable and specified values for these parameters as
obtained from reference materials (Table 3).
1 . Transmitted power F, was assumed to be between
1 mW (1 dBm) and 100 mW (20 dBm), based on the
range of output power levels available from an HP
8350B MMW sweeper source.
2. Receiver antenna gain was assumed to be 24 dB
from the available standard gain pyramidal horn.
3. Transmitter antenna gain G, was assumed to be 24
dB, identical to the receiver antenna since, typically,
identical horns are used for transmitting and receiving.
4. Average wavelength Xg of the radar system (in
free space) was assumed to be 1 .0 cm (30 GHz).
(for a mixer with unity gain). In decibels
F„(db)=101ogFn (46)
where F^ is overall noise figure.
This figure was calculated to be -50 dB based on the
specifications of an Analog Devices, Inc., AD-524
instrumentation amplifier employed as a high-gain au¬
dio amplifier used after the mixer.
7. System losses Lj resulting from signal attenuation
caused by the mixer and other waveguide and signal
processing components were assumed to be 1 5 dB. The
value chosen was significantly larger than typical val¬
ues for radar systems: 7 and 6 dB seen in Currie and
Figure 27. Noise power vs bandwidth.
Table 3. Calculation of SNR from typical
system parameters.
(Woi5t-case would subtract an additional 30 to
40 dB from above total SNR-see text.)
^t(db)
10dB„
(/>, = 10 mW)
‘^KdB)
24 dBj
(C, = 250)
<7|(dB)
24dBi
(C, = 250)
^n(dB)
-50 dB
^t(dB)
-15 dB
®n(dB)
-50 dB
(B„ = 100 kHz)
2^(dB)
-20 dB
(/? = 5 m)
^^dB)
^dB,„
(X = 0.01 m)
P(dB)
-5.6 dB
(p = 0.28 for air/ice)
(4>r)^*7'o<dB)
182 dB
Total SNR
59.4 dB
21
Brown (1987) and in Brookner (1988) respectively. It
was selected as a worst-case estimate to account for
practical levels of system losses and for any unforeseen
losses that may be present in the design.
8. Range R represents the distance from radar anten¬
na to the ice surface. A value of 5 m was assumed since
it represents the typical measurement range employed
in references cited earlier.
9. Losses L2 represent propagation losses that can be
ascribed to random processes, i.e., surface and volume
scattering. It is expected that surface scattering will be
the dominant factor, and that there will be a sufficiently
strong specular reflection from normally oriented
smooth-surfaced facets for a wide range of surface
roughnesses. While the degree to which medium losses
negatively affect the SNR of the system is currently un¬
known, it is expected that scan-to-scan variations in the
magnitude of L2 may range as much as 30 to 40 dB
(Ulaby and Whitt 1988). Jezek et al. ( 199 1 ) show theo¬
retically significant coherent returns from a surface
characterized by a ratio of rms surface roughness to
wavelength over a range of at least 0.0033 to 0.1667.
Therefore, the system needs only have sufficient abso¬
lute SNR to make top and bottom surface returns appar¬
ent. For example, if the radar system has a 60-dB abso¬
lute SNR, then in the worst-case situation where the
signal returns are scatter-attenuated by as much as 40
dB, they would still be clearly apparent, 20 dB above the
noise floor. Additionally, since the magnitude of the re¬
turns are statistically described by a Gaussian or Ray¬
leigh distribution (Ulaby and Whitt 1988, Jezek et al.
1991), it can be expected that, while not every scan
provides a discernible return, a sufficient percentage of
the scans in a continuous profile will include coherent
reflections significantly above the system noise floor
and provide a reasonably detailed ice profile.
Converting the radar range equation (eq 40) to the
decibel form, we obtain
(dB) = [^t(dB)+^r(dB)+^t(dB)''’^(dB)''‘ P(dB)]
- [(^^)^*^o(dB)+^l(dB)+(2^)wB)
■*'^n(dB)+^n(dB)] •
(47)
Given the SNR formulation and the assumed values
of the parameters, the results in Table 4 have been devel¬
oped.
Other signal and noise-related parameters
Several additional quantities that describe the per¬
formance of a radar can be derived from signal and noise
power. These include noise figure, dynamic range and
performance figure.
Table 4. Typical trans¬
mitted power levels and
related SNR for given
system parameters.
P, P, SNR
(W) (dBm) (dB)
0.001 0 49.4
0.01 10 59.4
0.10 20 69.4
Dynamic range. The dynamic range is the difference
between the smallest detectable signal level (typically
at the noise power /*„ [dB] level) and the largest nonsat¬
urating detectable signal level (as from a close or large
target) that can be viewed or recorded during one scan.
For a 13.5-GHz bandwidth, /*„ = kTB^^ = -103 dBm.
For a typical MMW mixer with a 20-dB gain, approxi¬
mately -20 dBm appears to be the input power level to
cause saturation. This results in a dynamic range of 83
dB.
Performance figure. The performance figure of the
radar system is defined as the difference between the
power at the output of the transmitting antenna (dB) and
the smallest detectable signal level (typically at the
noise power P„ [dB] level).
For a 1 3.5-GHz bandwidth, = “^^3 dBm.
With a 10-mW (10-dBm), average transmitter output
and a 24-dB gain antenna, the effective power at the
output of the antenna is 34 dB. The performance figure
is then 137 dB.
External coherent noise
Extraneous radar returns from man-made and natu¬
ral structures that interfere with interpretation of desired
radar return are classified as sources of external coher¬
ent noise. This is of little concern, given the narrow
beamwidth of the radar antennas and distance from
typical sources such as power lines, bridges, docks and
buildings encountered during airborne profiling sur¬
veys of lakes and rivers. Coherent returns from the heli¬
copter itself are not a problem since the narrow-beam
radar antennas are mounted away from interfering strac-
tures. Additionally, the propagation time for a coherent
reflection directly from the helicopter is significantly
less than the round-trip travel time from antenna to the
surface of the ice. A coherent return caused by multiple
reflections from the ice sheet and aircraft structure
undergoes a greater round-trip travel time and is more
greatly alenuated by geometric spreading than a reflec¬
tion returning directly from the ice sheet.
Data acquisition and recording
There is a direct interaction between data acquisition
22
and recording parameters, and sweep time, sweep rate
and radar range. Here, these effects are defined and
examined. Specifications are determined that provide
an optimal compromise between available technology
and desired system capability
The time required to frequency modulate the sweep¬
er linearly from the lower to upper band limits once is
defined as the sweep time (Fig. 28) The full Afa-band-
width sweep time of the HP 8350B MMW source is
adjustable from 0.01 to 100 seconds. Recovery time
(Fig. 28) is defined as the duration between linear fre¬
quency-modulated sweeps. The sweep rate is the num¬
ber of full band frequency sweeps per unit time. Sweep
rate, recovery time and sweep time are related to the
sweep frequency /swp by
relating these parameters can be rewritten to determine
the resulting maximum difference frequency compo¬
nent. For reliable measurements, it is necessary that the
highest possible radar difference frequency for a given
set of system parameters be within the capabilities of
data acquisition sampling rate and data recorder band¬
width.
For the first surface (air/ice interface), the radar
difference frequency F^\ is determined from
_ _2(/?)(giy)(/ij
For the second surface (ice/water interface), the
difference frequency is determined from
f = _ ! _ = _ 1 _
sweep rate (/swp + 'rec)
^ _2(/?)(fiW)(>g ^ 2(s)(gtF)(<v.,)
(^swp)(^) (^swp) (^)
where = sweep frequency (Hz)
/swp = sweep time (s)
free = recovery time (s).
The sweep duty-cycle is the percent of time of a
sweep cycle that the oscillator is linearly sweeping be¬
tween the upper and lower limits of the frequency band
and is defined as
Duty cycle (%) = .(-Vp) ( iQO) .
(^swp ^rec*
(49)
It shall be shown later that sweep duty-cycle, when re¬
lated to parameters including ground speed, antenna
height and beamwidth, is useful in determining the per¬
centage of antenna beam footprint overlap or the gap in
surface coverage between successive radar scans.
Sweep rate vs FM-CW signal frequency
The radar difference frequency is related to several
system parameters, as discussed earlier. The equation
or
Fa = ^^^^-[R{no) + s{n.cS\- (51)
(/swp)(0
Since F,) < Ff2, the data acquisition system must be
capable of a bandwidth greater than Since the data
acquisition sampling rate and recorder bandwidth are
limited, given available technology, accommodations
must be made by adjusting other system parameters.
Figure 29 illustrates the relationship between sweep
rate and radar difference frequency for various radar
ranges. Maximum bandwidths of available data pro¬
cessing and storage technologies are also shown, bound¬
ing the practical limits of sweep rate and maximum
radar difference frequency. A typical Digital Signal
Processing Analog-to-Digital Converter (DSP ADC)
capable of acquiring, processing and displaying radar
difference frequency data has a maximum sample rate
of 128 kHz. A typical Digital Audio Tape recorder
(DAT) useful for recording and long-term storage of
radar difference frequency data has a maximum sample
rate of 40 kHz. For example, given a maximum radar
Sweep Rate
Figure 28. Sweep time and sweep rate parameters.
23
Maximum Radar Difference Frequency (KHz)
FM-CW Sweep Rate (ms/sweep)
FM-CW Radar Sweep Rale (ms/sweep)
Figure 29. FM-CW radar difference frequency vs sweep Figure 30. Horizontal displacement per sweep vs sweep
rate for various radar ranges (sweep bandwidth = 13.5 rate for a range of typical profiling ground speeds.
GHz).
range of 10 m and the maximum radar difference fre¬
quency of 20 kHz (the maximum bandwidth at the DAT
sample rate of 40 kHz), the fastest sweep rate possible
is approximately 45 ms/sweep. With an analog tape
recorder, having a 5-kHz bandwidth, for example, a
sweep rate of 100 ms/sweep at a range of 5 m would be
an acceptable combination.
Selection of optimal sweep time
Most data acquisition hardware is designed with a
limited selection of sampling frequencies derived using
hardware frequency division techniques from an inter¬
nal, fixed-frequency crystal oscillator clock. Available
DSP hardware is typically capable of performing FFTs
based on power-of-two (e.g., 512, 1024, 2048, etc.)
multiple time samples per scan. To assure that advan¬
tage is taken of the full available radar bandwidth, it is
necessary to completely sample the difference fre¬
quency time series output of the radar over the entire
sweep time. Sampling over less than the entire sweep
time translates into a proportional decrease in the avail¬
able radar bandwidth and, thereby, resolution. Since the
choices for the number of samples per scan and the
sample rate are limited by hardware constraints, the
FM-CW sweep time must be adjusted to fulfill the
following relationship
./samp
where = number of samples per scan and /samp =
sampling frequency (Hz).
Using eq 52, Table 5 documents the sweep times
allowed for the available sampling frequencies for a
MacDSP256KNI DSP ADC board (Spectral Innova¬
tions, Inc.). Here, the sampling frequencies /samp and
the samples per scan /isamp are fixed by the DSP ADC
board hardware and software configuration. For exam¬
ple, for /samp = 15.62 and /Jjamp = 1024, fjwp = 0.66
seconds.
Profiling speed and sweep rate
When the radar is in motion, a certain amount of
ground will be covered during a single scan, the dura¬
tion of which is determined by the sweep rate. Figure 30
indicates the effect of profiling speed upon the depen¬
dency of horizontal antenna displacement on sweep
rate. For example, a helicopter flying at 30 km/hr carry¬
ing a radar system with a sweep time of 66 ms would
undergo a horizontal displacement of approximately 55
cm during each scan. The relationship of ground speed
and sweep rate to the amount of antenna footprint over¬
lap between adjacent scans and the ability of the radar
to discern abrupt changes in the ice thickness or surface
roughness is explained in the Antenna Ground Foot¬
print and Overlap section.
Table 5. Selection of optimuiTi sweep times.
Based on samples per scan and sampling frequency
/samp of a Spectral Innovations MacDSP256KNI DSP
ADC board.
Sweep lime (s)
Samples per scan,
"^samp
Sampling frequency. fsamp(kH-f
3.91 7.81 15.62 31.25
1024
0.262
0.131
0.066
0.033
2048
0.524
0.262
0.131
0.066
4096
1.048
0.524
0.262
0.I3I
24
Antenna parameters
The antenna configuration affects the size of the
radar footprint on the ice sheet, the bandwidth of the
transmitted and received radar signal, the effective radi¬
ated power of the signal, the gain of the received signal,
and the effects of sidelobe interference on the top and
bottom surface returns. Standard gain horn antennas
appear to have sufficient bandwidth for this application.
However, beamwidth and phase error across the aper¬
ture may be a limiting factor on minimum thickness
resolution.
Antenna beamwidth and ice thickness
A relationship exists between antenna beamwidth
and the thickness of the measured ice that may lead to
Figure 31. Geometry of
beamwidth vs thickness re¬
lationship (a specular re¬
flection from point A could
mask the return from the
ice bottom).
Air
Ice
Water
a. Range = 5 cm. b. Range = 10 m.
Figure 32. Antenna beamwidth as a function of ice thickness for reflections from the ice/water interface artd
airlice interface at beam pattern edge to coincide at ranges of 5 and 10 m.
ambiguous or confusing results. The confusion would
result from the propagation delay from an ice surface
specular reflector at the edge of an antenna footprint f),
being comparable to the propagation delay from the
reflection at the ice bottom surface t„ (Fig. 31). Ideally,
the return from the ice/water interface should distinctly
occur after any possible returns from the air/ice inter¬
face, that is
fb < t„. (53)
Figures 32 indicates that, to limit reflection ambiguity,
a narrower beamwidth is preferable. The 9° standard
gain horn antennas satisfy this condition for ice thick¬
ness of as little as 1 cm for radar ranges greater than 5
m. Figure 33 illustrates the beam geometry of the 9°
25
Sweep Frequency Antenna Footprint Diameter (m)
Figure 34. Footprint diameter for3-dB antenna beam-
widths vs altitude.
Figure 35. Parameters for determining
antenna footprint overlap, relating an¬
tenna footprint dimensions to FM-CW
sweep signal.
— '' ^wp - ►!
Figure 36. Dimensions of area Figure 3 7. Geometric elements for calculating percent
illuminated by one scan. overlap of a.itenna footprint on adjacent scans.
26
standard gain horn antenna. Narrower beamwidths are
achieved only with a large increase in cost and physical
dimension (dielectric lens horns or parabolic dishes).
Antenna ground footprint and overlap
Figure 34 illustrates the footprint diameter for sever¬
al antenna 3-dB beamwidths over a range of radar pro¬
filing altitudes. For example, a 9° beamwidth hom at an
altitude of 10 m gives a 3-dB main lobe footprint ap¬
proximately 1 .5 m in diameter. The footprint, when
considered with profiling ground speed and sweep rate,
determines the degree of footprint overlap, and hence,
physical averaging of sequential profiling scans. The
percentage of overlap area between sequential scans is
a function of antenna beamwidth, survey altitude and
sweep duty-cycle in addition to sweep rate and survey
vehicle speed. Figure 35 illustrates the physical rela¬
tionship among these parameters. Here, for a given
ground speed and antenna altitude, the ice surface area
illuminated by the antenna’s 3-dB main lobe pattern is
illustrated in relation to the sweep and recovery times of
the FM-CW MMW oscillator.
The percentage of overlapping area of adjacent scans
as shown in Figure 35 is calculated by determining the
3-dB beamwidth area illuminated during one scan. Fig¬
ure 36 illustrates the parameters necessary for this
calculation. The radius r (in meters) of the footprint de¬
pends upon antenna altitude and antenna beamwidth,
and can be determined from Figure 34 or by the relation¬
ship
r = f? tan
(54)
where R is range to surface of the ice (m) and <t) is
antenna beamwidth (°). Then, the area illuminated
Aiiiun, (m^) during one scan is determined from
(55)
where v = ground speed (m/s) and = sweep time (s).
The area (m^) of scan overlap and the percent of
overlap between adjacent scans can be determined us¬
ing geometrical relationships illustrated in Figure 37a.
The distance h, one half of the distance covered during
the sweep recovery time, is calculated as
h =
2
(56)
where free = recovery time between sweeps (s). Then,
The area of the wedge (shaded area in Fig. 37b)
is calculated as
^wedge = :^("'-^) (59)
3oU
and the area of the triangle 4,^ (shaded area in Fig. 37c)
is calculated as
A,ri = hi.
Thus, area of scan overlap A^vip is
(60)
■'^ovip ~ (61)
and the percentage of area overlapping between scans is
Overlap (%) =
If, however
_j ^ovlp
' ilium
(100).
(62)
2r > v/rgg (63)
then, instead of an overlap, there would be a spatial gap
Gap (in meters), in coverage between adjacent scans
where
Gap = 2r - vfjgg. (64)
Figure 38, generated from these equations, illus¬
trates the percentage of overlapping area of adjacent
radar scans for several radar ranges as a function of
ground speed and other parameters, as specified.
0 = cos '
(57)
1 = r sin(0).
(58)
Figure 38. Percentage of 3-dB antenna beamwidth
overlap as a function of ground speed, altitude, sweep
rate and duty cycle (antenna beamwidth = 9°, sweep
rate = 0.066 s and duty-cycle = 75%).
27
For example, a survey vehicle traveling 5 m above the
ground at 25 km/hr with a 0.066-s sweep rate and a 75%
sweep duty-cycle would have an adjacent scan antenna
footprint area overlap of 65%.
Physical parameters
Physically, the system is constrained by the way it is
to be used. Weight, physical dimension, deployment
mode and operational environment influence the sys¬
tem’s configuration.
Weight
As this radar package is intended to be operated from
on-board a small helicopter (e.g.. Bell Jet Ranger 206B),
it is necessary that the weight be limited. The typical
aircraft used for radar profiling purposes can transport a
pilot, three passengers and limited additional payload.
Therefore, total weight should be no more than the equiv¬
alent of one passenger, approximately 90 kg (200 lb).
Also, the system should be made into modular com¬
ponents that can be easily carried by one or two people.
Dimensions
Because the system must be field-transportable, and
space available on-board the survey helicopter is limited,
it, less power supply and antennas, should occupy a
space of no more than 0.25 m^ (8 ft^). Additionally, mod¬
ules should be dimensioned for convenient shipping in
containers, and for easy transport by personal or com¬
mon carrier to the field site.
Operating power
Both the constraints of field and airborne operation
require that the system use a minimum of electrical
power. Typical aircraft suitable for profiling have an on¬
board 24- to 28- Vdc source capable of delivering 50 to 75
A. The supply of 1 15 V rms at 60 Hz is limited to ap¬
proximately 2 A (if available at all). Therefore, the radar
is designed to require less than the available on-board
power or to use an independent battery to supply part or
all required power.
Antenna attitude
Antenna attitude must be maintained to nadir or near¬
nadir pointing. The degree to which off-nadir look-angle
can be tolerated is a function of antenna beamwidth. In
the case of the 9° beamwidth standard gain antennas used
in the prototype, experience indicates that an off-nadir
look-angle of ±5° has minimal effect.
Operational temperature
The radar has to operate at 0°C or less, given the in¬
tended field environment and the typical temperatures at
which helicopters are used.
Operatioruil humidity
The system should operate in a noncondensing, 5 to
95% relative humidity environment. This is typical for
helicopters.
Operational altitude
The system should work over frozen bodies of water
located at altitudes up to at least 4600 m (15,000 ft)
above sea level, permitting surveys at the majority of
locations of interest on earth. This is within the typical
operational range for helicopters.
Vibration levels
All radar components should be capable of with¬
standing the normal range of vibrations and g-shock
associated with being used in the field and aboard
helicopters. This especially applies to rotating memory
devices, which may be particularly vulnerable.
Summary of specifications
The system specifications, as previously defined, are
summarized in Table 6.
Table 6. FM-CW MMW radar specification summary.
Measurement parameters
Range (height above surface)
3 to 10 m
Measutement speed
>20kinAtr
Ice thickness
> 5 to 1 82 cm
Resolution
>±10%
System parameters
Output power
< 20 dBm (continuous)
Modulation type
FM-CW
Sweep rate
IS scans/s (nominal)
DSP processing time
2 ms (1024 pt. real FFT)
Bandwidth
13.5 GHz (full ATj-band)
Center frequency
33.3 GHz
Receiver SNR
>60 dB
Receiver noise figure
<6dB
Receiver dynamic range
83 dB
Receiver performance figure
137 dB
Receiver noise floor
-103 dB
Antenna beamwidth (3 dB)
9°
Antenna gain
> 24 dB (Tx and Rx. each)
Output modes
DSP video display
Time/frequency domain displays
DAT tape storage
For analysis and archiving
Removable/fixed disk storage
For analysis and archiving
Physical parameters
System weight
<90 kg
System dimensions
<0.25 m^
Antenna dimensions
< 0.03 m3
Antenna attitude
Normal to surface
Minimum operating temperature
<0°C
Humidity range
5 to 95% non-condensing
Altitude (maximum)
4600m
28
DESIGN AND CONSTRUCTION
Prototype system configuration
The prototype system was built to best meet our
specifications, given available hardware and software
resources. It (Fig. 39) consists of a computer (Macin¬
tosh II) containing a data acquisition/Digital Signal Pro¬
cessing (DSP) board (Spectral Innovations, Inc.,
MacDSP256KC), an MMW sweeper (HP 8350B), an
analog tape recorder (HP 3964A), audio amplification
and scan synchronization electronics, a homodyne re¬
ceiver constructed from assorted MMW waveguide
components, and two standard gain (24-dB) pyramidal
horn antennas of 9° beam width. Prior to the availability
of computer and data processing hardware necessary
for the prototype, a pre-prototype was assembled using
components that were currently on hand in laboratory
inventory. This system used an 80286-SX, 16-MHz,
DOS-based computer with a 80287 math coprocessor,
data acquisition board, an HP 8350B MMW sweeper, a
homodyne receiver constructed from assorted MMW
waveguide components, and the two standard gain (24-
dB) horn antennas. Processing time with this configura¬
tion was unacceptably lengthy, requiring approximate¬
ly 5 to 10 seconds per scan. This system was used to
acquire and process ice profiling scan data as described
in the Skating Arena Profile section and Appendix A.
The prototype is made from standard off-the-shelf
hardware, with the exception of the high-gain instru¬
mentation amplifier and synchronizerelectronics, which
were designed specifically for this. The amplifier boosts
the millivolt-level difference frequency voltage from
the receiver to an appropriate level for data acquisition
and processing. Synchronization for framing radar scan
data is taken from the “Positive Z-Blank” signal provid¬
ed by the sweeper and interfaced to a two-channel ana¬
log multiplexer that inserts a start-of-frame pulse into
the data stream prior to the beginning of each radar scan.
Scan data acquisition and processing by the DSP board
are triggered by level and slope transition of this intra¬
data stream pulse. For this series of tests, the system was
powered by electric line or gasoline generator, which¬
ever was more convenient at the test site.
The prototype FM-CW MMW can sweep the full
1 3.5-GHz /fg-band, 26.5 to 40 GHz, at a rate of up to 1 00
scans per second. But, because of analog data recorder
bandwidth limitations (5 kHz), a maximum sweep rate
of 20 scans per second has been employed in measure¬
ments to date. Data acquisition at rates of up to 1 28 kilo-
samples per second are possible with dedicated digital
signal processing hardware that also offers windowing,
1024 (or more) point FFTs, block averaging and water¬
fall or spectrographic display. Sweeper power levels of
up to 15 dBm, with a sweep linearity of better than
0.05%, are attainable. The maximum operating range
has been shown to be on the order of 1 0 m, with an SNR
in excess of 30 dB. Simulations indicate that accurate
measurement of freshwater ice in excess of 200 cm
thick is feasible.
The system is designed to acquire and process data in
real-time or to record only. Data recorded to tape in
either mode can be processed later as they are played
back. The various modes of operation are explained
later.
Mac II
Figure 39. Block diagram of the MMW FM-CW radar (configured for
real-time data acquisition and processing).
29
MMW source
There were i wo ommercial options available for the
MMW source: an HP 8350B series MMW source and
an Avantek (YTO) YIG-tuned oscillator (AVO-26xxx
M/W series). In terms of price, physical dimensions and
performance, the Avantek unit is more desirable. How¬
ever, owing to long lead times (more than 20 weeks) for
the Avantek unit and the immediate in-house availabil¬
ity of an HP 8350B sweeper, the latter was chosen.
Subsequent versions of the system will use the smaller,
less expensive YTO.
The prototype employs an HP 8350B sweep gener¬
ator with an HP 83550B RF plug-in unit and an HP
83554A MMW source module. As configured, this
MMW source is capable of sweeping the full ATa-band
(26.5 to 40 GHz), with a sweep time of 0.0 1 to 1 00 sec¬
onds at a leveled power output of up to 15 dBm, and a
sweep linearity of less than 0.05%. The unit requires
3.25 A at 117 Vac and 60 Hz for operation.
Radar front-end
The radar front-end module (Fig. 40), performing
both the transmitting and receiving functions, consists
of a homodyre mixer fabricated with a waveguide crys¬
tal detector diode (HP R422C), two -20-dB wave-guide
directional couplers (HP R752D), and two like-polar¬
ized, co-located, 26-dB standard gain pyramidal horn
antennas (Scientific Atlanta 12A-26).
The theory of homodyne mixing is described in
detail by King (1978) and applied to FM-CW radar by
Gubler and Hiller (1984). It entails the continuous
mixing of a sample of the MMW sweeper output with
the MMW signal reflected from a target without any
intermediate frequency translations. This front-end de¬
sign provides an adequate SNR for this application and
can be conveniently, economically and robustly imple¬
mented.
The central elements of the front end are two -20-dB
waveguide directional couplers with a connection be¬
tween sampling ports. The through-connection of the
transmit waveguide coupler is attached between the
MMW sweeper source and the transmit antenna. The
through-connection of the receive waveguide coupler is
attached between the receive antenna and a waveguide-
mounted detector diode. A sample of the transmitted
sweep signal and the received signal propagate down
the receive coupler waveguide and are mixed by the
detector diode acting as a single-ended mixer. Single-
ended MMW waveguide mixers typically have an ap¬
proximately 10-dB noise figure, according to Currie
and Brown (1987). Substitution of a low-noise, broad¬
band-balanced MMW mixer in place of the diode detec¬
tor single-ended mixer can result in as much as 3 dB of
SNR improvement. Economics and in-house availabil¬
ity prevailed in the choice of the diode detector.
Antenna parameters
The physical dimensions of the antennas are of prac¬
tical concern for reasons of portability, convenience
and safety of external helicopter mounting. Since this
system is intended for airborne application, wind-load¬
ing ano aerodynamic drag may also be of concern. The
commonly available horn antennas used have a half¬
power beam width of approximately 9° and are specified
for coverage of the complete /f^-band (26.5 to 40 GHz);
they are approximately 1 5 cm tall with an aperture 6 by
7 cm wide and offer a maximum wind loading area of 53
cm^.
Analog processing after mixing
The mixing process produces a number of frequency
products, namely a sum and difference, of the two
MMW signals. The sum product is in the higher milli¬
meter frequency range and is not used. The difference
product, here in the audio frequency range, contains the
frequency information that can be transformed into an
indication of ice thickness. This signal amplitude is on
the order of tens of millivolts, peak, and must be ampli¬
fied to the order of several volts, peak, for data acquisi¬
tion. The circuit and corresponding waveforms in Fig¬
ure 4 1 were specifically designed for this function. The
signal is amplified by a cascaded combination of an
HP 83554A
Figure 40. Radar front end.
30
Figure 42. Record-only mode.
Analog Devices AD-524 adjustable gain instrumenta¬
tion amplifier (switch-selectable gains of 1(X) or 1000)
and an LM-741 op-amp, configured as an inverting
adjustable gain amplifier (vernier gain from 1 to 10).
Gain is manually adjustable to provide reflected
signal level strength, as displayed on the oscilloscope,
within an acceptable amplitude range (±3 V) for data
acquisition. Individual radar scans are frame synchro¬
nized using the HP 8350B MMW sweeper “Positive Z-
Blank,” a TTL (Transistor-Transistor Logic) level sig¬
nal that is logic-high (+5 V) during the frequency sweep
and logic-low (0 V) during retrace. When radar data are
recorded for subsequent processing and analysis, the
TTL level. Positive Z-Blank signal, from the HP 8350B,
is used to synchronously key an NE-555 astable oscilla¬
tor producing bursts of 5-kHz tone. The amplified radar
signal and the tone-burst synchronization signal are re¬
corded on two separate channels of an analog data
recorder. When real-time data are acquired and pro¬
cessed (Fig. 39), the radar signal and the Positive Z-
Blank signal are multiplexed into a single data acquisi¬
tion channel. The system data acquisition-DSP ar¬
rangement uses level and edge triggering to frame-
synchronize the data stream.
A hardware block diagram of the record-only mode
is shown in Figure 42, where system components, as
earlier described, are assembled to collect and store pro¬
file survey data on audio tape forprocessing later. While
there is no provision for instantaneous display of profil¬
ing results, the limited size, weight, complexity and
power consumption facilitates portable and mobile op¬
eration.
In the playback mode, data that have been acquired
and recorded to tape either during real-time or record-
only operation can be played back and input to the com¬
puter for processing. A hardware block diagram of the
playback mode is shown in Figure 43.
A circuit designed specifically for playback and
corresponding waveforms is shown in Figure 44. Here,
the 5-kHz tone bursts recorded to tape in the real-time
or record-only modes are decoded back into the TTL
synchronization pulse train by an NE-567 phase-locked
loop tone decoder. The reconstructed synchronization
signal is interfaced to a 4066 CMOS analog switch con¬
figured as a two-channel analog multiplexer, which in¬
serts a 5-V start-of-frame pulse into the data stream dur¬
ing the sweeper retrace prior to the beginning of each
radar scan. Again, in this configuration, the system data
acquisition-DSP arrangement uses level and edge trig¬
gering to frame-synchronize the data stream.
In both the record and playback modes, a Tektronics
475 dual-trace oscilloscope is employed as a diagnostic
tool to monitor sweep rate, signal amplitude and general
waveform appearance.
Raw data storage
The amplified output of the radar mixer and synchro¬
nization tone burst are recorded on an HP 3964A reel-
to-reel four-channel instmmentation recorder capable
of being powered from an ac or dc source. Manufacturer
specifications for this analog data recorder indicate a
30-dB SNR and a 5-kHz audio bandwidth when record¬
ing at the highest tape rate of 38 cm/s ( 1 5 in./s). Here, a
550-m-long reel of tape provides approximately 15
minutes of recording time. Radar range, playback¬
mode SNR ratio and scan rate can be improved by sub¬
stituting a Digital Audio Tape (DAT) recorder for the
analog recorder used in the prototype. The greater audio
bandwidth of the DAT (20 kHz compared to 5 kHz for
the analog recorder) permits a proportional increase in
scan rate and radar range. With a 70-dB SNR, the DAT
recorder is approximately 10 to 20 dB better than the
radar system noise floor and more than 40 dB better than
the analog tape noise floor, thus permitting an increase
in radar range. Use of the HP 3964A recorder prevailed
because of the urgency of taking data in the winter,
economics and in-house availability.
Figure 43. Playback mode.
32
74LS04
Recorder Out
CH 2 A_0J_|(_
(sync burst in) i
Recorder Out
CHI
(signal inj-t
a. Circuit schematic.
Recorder Out +3
CHI 0
(signal in) -3
— f##
Recorder Out +1
CH2 I
(sync burst in) -1
Sync Out
Signal + Sync +3
Out 0
j WsiJ
+3
Signal Out g
-3
b. Waveforms (waveform period is determined by sweep rate).
Figure 44. Playback synchronization decoder.
Digital signal processing
A wide choice of DSP boards was available, includ¬
ing one Macintosh-based and several DOS-based boards.
All DSP systems considered for this application had
reasonably similar capabilities, specifications, econom¬
ics and software support. Selection was based on the in-
house availability of a Macintosh II computer as well as
for reasons of simplified DSP hardware procurement.
Data are acquired and digital signals processed by a
Spectral Innovations, Inc., MacDSP256KNI coproces¬
sor board, with an AT&T WE DSP32 32-bit floating¬
point, 32 MFLOP (Million FLoating-point OPerations
per second) chip and a piggyback 16-bit 128-kilobyte-
per-second analog-to-digital converter. The MacDSP
256KNI board, under software control, is capable of
vector mathematics for arithmetic, digital filtering, win¬
dowing and other DSP functions. Processed data can be
displayed in several formats, including single trace,
waterfall and spectrogram. Single-trace display (Fig.
45a) is a log-magnitude versus linear-frequency repre¬
sentation of one frequency domain-transformed and
processed radar scan, which is updated with each sub-
d
A O Al ^
d o 6 —
Frequency (kHz)
a. Single-trace (log magnitude presentation).
■q
b. Waterfall (linear magnitude presentation).
c. Spectrogram (log magnitude presentation).
Figure 45. Typical DSP displays.
34
sequent scan. The waterfall representation (Fig. 45b)
displays a continuously scrolled sequence of single
scans.
In a spectrograph display (Fig. 45c), discrete signal
magnitude quanta are represented by a range of color or
gray scale. In monochrome, as illustrated, this results in
signal magnitudes greater than a preset threshold ap¬
pearing as white and those below the threshold as black.
The level can be set in the DSP software to display clear¬
ly both the air/ice and ice/water interfaces. A multi-
colorspectrographic display provides significantly great¬
er graphical resolution than is possible with a mono¬
chromatic display by indicating intermediate levels of
signal intensity by a color gradient. Unfortunately, for
this development and consequently for illustration in
Figure 46. Linear stacked-scan waterfall representa¬
tion of reflections from an 8-cm-tliick granite slab (as
processed by Cricket Graph).
Direct
^Coupling
Front Interlace
Rear Interlace
t
n]
o
W
4-4-
'f-4
4j,
4-4-
W.
—►I 600 ps
' • 8 cm
(one-way travel time)
(measured thickness)
Figure 47. Radan-processed and wiggle-formatted display of reflections from an 8-cm-thick
granite slab.
this document, only monochromatic display output was
available. Ice or snow thickness is then computed as a
function of the distance from peak to peak on the single
scan or waterfall display and as the center-to-center dis¬
tance of the two white bands on the spectrogram. Addi¬
tionally, acquired data can be formatted for stacked-
scan graphical display using the Cricket Graph (Cricket
Software, Inc.) software package (Fig. 46) or for further
processing and display by the Radan (Geophysical Sur¬
vey Systems, Inc.) geophysical radar analysis program
(Fig. 47).
Test platforms
At various stages the radar was tested and operated
using a boom, cart, truck and helicopter over a variety
of ice conditions.
Boom-mounted test platform
Several profiling measurements were made with the
radar antennas deployed on a 4-m long cantilevered arm
positioned over the ice from a shore-mounted tripod
(Fig. 48). This configuration was used for ice too thin to
support safely the system and operator. The boom was
moveable in elevation (from 2 to 3 m) above the ice sur¬
face and in a 180° arc. All electronics, including the
MMW sweep oscillator, were located on the shore. The
MMW sweep signal was coupled to the radar front end
by a 4-m length of WR-28 waveguide and the audio out¬
put from the mixer was returned to the system via a 6-
m length of RG-58/U coaxial cable.
Cart-mounted test platform
The radar was mounted on a manually propelled cart
35
Figure 48. Boom-mounted profiling arrangement.
Figure 50. Cart-mounted device profiling pond ice.
Figure 52. Truck-mounted radar (range is approxi¬
mately I m).
and supplied with electrical power via an extension cord
connected to a ground-fault interrupted 1 17 Vac main.
Short-length profiles (less than 25 m) were made on an
indoor ice sheet grown on a concrete, refrigerated floor,
or on ice, marginally thick enough (about 10 cm) to
safely support the cart and operator and formed on a
shallow (about 0.5 m deep) outdoor pond (Fig. 49).
Figure 49. Pre-prototype mounted on the cart.
Figure 51. Cart-mounted radar deployed on a bridge.
Figure 53. Radar mounted on a truck using a tripod
(range is appro.ximately 2 m).
Where the ice was thicker (about 30 cm) and capable of
supporting heavier loads, longer profile runs were pos¬
sible by powering the radar from a gasoline generator
mounted on the cart (Fig. 50)
A variant of the cart-mounted arrangement was used
for profiling river ice from a bridge deck. In this ar¬
rangement a tripod was used to elevate the antennas
36
above the bridge safety railing and provide sufficient
horizontal displacement to prevent extraneous reflec¬
tions from the bridge structure (Fig. 5 1 ).
Truck-mounted test platform
The radar was mounted on a truck to simulate the
ground speed and radar range that would be encoun¬
tered in the air. With ice sufficiently thick to safely sup¬
port a vehicle (more than 30 cm), the radar was mounted
on the rear of a pickup truck and driven across a frozen
pond at speeds up to 40 km/hr, allowing for high-speed
profiling experiments. A truck was also used for mea¬
surements where the ice was snow-covered and it would
have otherwise been difficult to manually propel the
cart. Radar range was 1 m with the 4-m long antenna
boom mounted across the top of the cargo bed (Fig. 52).
Profiling without extraneous radar reflections from the
vehicle body and without disturbance to the snowcover
was possible by placing the boom-mounted antennas
off to the side and away from the vehicle. With the an¬
tenna boom supported by a tripod bolted to the pickup
bed, the range was increased to approximately 2 m (Fig.
53). Electrical power was supplied by a gasoline pow¬
ered generator.
Figure 54. Profiling helicopter. Waveguide leads out the
rear window to MMW horn antennas visible in inset.
Airborne test platform
The radar setup for airborne deployment was similar
to that used during ground-mounted testing. A 12-V
battery and power inverter were used for a power
source. The two horn antennas were affixed centrally to
the underside of a Bell Jet Ranger 206B helicopter (Fig.
54) and were adjusted to point normally to the ground
during survey flight.
Power requirements
The power requirement for the prototype (Table 7) is
calculated based on the power specifications on the
equipment nameplates.
Table 7. System power requirements
(VA).
HP 8350B MMW sweeper 375
HP 3964A recorder 150
Tektronics 475 oscilloscope 100
Audio amplifier and synchronizer 5
Total power requirement _ 630
The recorder, oscilloscope and audio amplifier and
synchronizer can be powered directly by battery. The
sweeper requires a dc-to-ac inverter for battery opera¬
tion. If the Mac II computer were also to be field-
operated, an additional 500 VA of dc-to-ac inverter
capacity would be required for battery operation.
Economic considerations
Since the majority of hardware used here was ob¬
tained from existing laboratory inventory or borrowed
from other projects, there was little actual expenditure.
The following accounting (Table 8) is provided to indi¬
cate the overall cost should all system components be
purchased new. Costs are approximated to the nearest
$100 in 1991 dollars and are listed by functional sub¬
system. In the case of manufacturer discontinued com¬
ponents (e.g., HP 3964A analog data recorder), a price
of a current-technology DAT (TEAC RD-101) is sub¬
stituted.
Table 8. Prototype implementation costs.
MMW source
HP 8350B sweep oscillator $4,900
HP 83550B RF plug-ln $ 1 6,000
HP 83554A MMW source module $9,000
$29,900
Radar front end
Scientific Atlania standard gain horns (2 ea) $1 ,600
HP R422C crystal detector $800
Miscellaneous WR-28 waveguide $500
HP 752AD directional couplers (2 ea) $2,000
$4,900
Processing aher mixing
Amplifier and synchronizer electronics $500
$500
Bulk data storage
HP 3964 A analog recorder (TEAC RD- 1 0 1 ) $8,600
$8,600
Digital signal processing
Macintosh II computer (8 MB RAM, 140 MB HD ) $5,(XX)
Macintosh monochromatic monitor $S(X)
MacDSP256KNI data acquisition/DSP coprocessor $5,000
Data acquisition/DSP software $2,600
$13,100
Grand Total $57,000
37
Table 9. Summary of survey studies.
Siir\’ey
.siiuIy
Tape
no.
Date
Location
Mode
Speed
(kmihr)
Ice
Range thickness
(m) _ (cm)
Air
temperature
m
tee
surface
conditions
A
NA
2 Nov 90
Thompson Arena Ice
Rink, Dartmouth
College, Hanover, N.H.
Cart
3
1.2
3
0
Very smooth (surface pre¬
pared by rink surfacing
machine).
B
2
26 Dec 90
Overflow pond,
CRREL
Fixed
0
2
5
2
Clear ice. minimal surface
roughness.
C
6
28 Dec 90
Overflow pond,
CRREL
Can
3
1
7-8
-5
Snow cover, shoveled clean
minimal surface roughness.
D
7
8 Jan 91
Post Pond, Lyme,
N.H.
Cart
3
1
20-25
-10
Smooth ice with < 1 cm of
snow cover.
E
9
15 Jan 91
Post Pond, Lyme,
N.H.
Truck
10
1
30
-7
18 cm dry, low-density snow
cover over ice with minimal
surface roughness.
F
10
23 Jan 91
Post Pond, Lyme,
N.H.
Truck
10
2
35^0
-18
<1 cm snow cover with
roughened texture from
refrozen meltwater.
G
lla
25 Jan 91
Connecticut River,
from Ledyard Bridge,
Hanover, N.H.
Cart
3
5-6
25-35
-12
Clear ice. minimal surface
roughness.
H
lib
25 Jan 91
Connecticut River,
from Ledyard Bridge,
Hanover, N.H.
Can
15
5-6
25-35
-12
Surface roughness <1 cm
from refrozen snowplow
ejecta on ice surface.
I
13
26 Feb 91
Turtle Pond.
Concord. N.H.
Helicopter
15
3-5
30
>5
Smooth ice with patches
of <1 cm of wind-packed
snow cover.
J
14
26 Feb 91
Pemigewasset River,
Franklin, N.H.
Helicopter
15
3-5
30
>5
Smooth ice with patches
of si cm of wind-packed
snow cover.
RESULTS
Several survey studies were conducted to examine
the performance of the radar over a variety of ice sheet
and snow cover conditions. Profiling tests were con¬
ducted in the laboratory and field from stationary and
mobile ground platforms, and airborne radar profiling
surveys were made over freshwater pond and river sites.
Survey parameters are summarized in Table 9.
Skating arena profile (survey study A)
On 2 November 1990 thin ice was profiled employ¬
ing the pre-prototype radar mounted on a cart that was
manually propelled over an ice skating arena (Thomp¬
son Arena, Dartmouth College, Hanover, New Hamp¬
shire) where approximately 3 cm of cold, smooth ice
overlaid a concrete floor. The arena presented a viable
alternative to inaccessible natural conditions for testing
performance over thin ice that could be directly mea¬
sured. The results of a survey run of approximately 15
m (Fig. 55) were plotted using DeltaGraph (Deltapoint,
Inc.) and presented in a stacked-scan, linear magnitude
format. Appendix A gives survey details. The lack of a
substantial dielectric contrast between the concrete and
the ice prevented strong bottom returns. Nevertheless.
lir/lce Interlace
One-Way Travel Time from Antenna (ns)
I - 1 - 1 - 1 - 1 - 1
O 1 2 3 4 s
Scale of Ice Thickness (cm)
Figure 55. Segment of skating arena profile (linear
power magnitude; arbitrary vertical scale).
38
CO O (0
it is apparent that the minimum resolution of this system
is far less than the range of thickness encountered. It was
not possible to obtain ground truth since it would have
required drilling into the ice on the rink with the poten¬
tial risk of damage to the refrigeration system. Howev¬
er, rink maintenance personnel reported that the ice
typically ranged in thickness from 2 to 4 cm over the
extent of the slab.
Stationary profiling of thin pond ice
(survey study B)
This experiment examines the capabilities of the
MMW FM-CW radar for profiling thin, naturally oc¬
curring pond ice. Since the ice was too thin to traverse
safely, the radar was mounted on the shore of the pond
and the antennas extended over the ice using a boom.
Figure 56 shows a sequence of several radar returns ex¬
tracted from profiles of a frozen outdoor pond made
over a 3-day period in late December 1990, during
which ice thickness increased from approximately 5 to
10 cm. The pond surface was smooth, with only a light,
dry snow cover less than a centimeter thick. Antenna
Ice Thickness (cm)
Figure 56. Sequence of increas¬
ing ice thickness on a frozen out¬
door pond.
Afl rsn .
Figure 57. Vertical cross section of an ovetflow pond
ice core (from data of 27 December 1990).
Figure 58. Indication of surface roughness of ovetflow
pond ice cover (from data of 27 December 1990).
height was about 2 m. Direct measurement of the ice
thickness by drilling verified the radar thicknesses. It is
apparent from the data that the resolution limit is better
than 3 cm.
Figure 57 is a vertical cross-section of a typical core
sample obtained during this series of profiling surveys.
The core revealed a solid ice cover with air bubble in¬
clusions of less than 0.5 mm, typical of pond ice. An
indication of surface roughness is given in Figure 58.
The surface had a small pitting with height variations on
the order of less than 1 mm. Appendix A gives survey
details.
Cart-mounted profiling of overflow pond
(survey study C)
On 28 December 1990, on a small overflow pond
located on CRREL property was profiled. Here, the ice
ranged in thickness from 5 to 9 cm with no snow cover.
A short (25-m) profile was made using a cart carrying all
components. The lightweight cart permitted the profil¬
ing of naturally occurring pond ice too thin to support a
heavier profiling vehicle. Figure 59 is a DSP spectro-
39
Pond Profile Path (m)
Figure 59. Radar and borehole measurements from overflow pond (not corrected for borehole tape offset error).
Rte. 10
f to Lyme, N.H.
Figure 60. Post Pond survey path.
Air/Ice
Interlace
Ice/Water
Interface
f igure 61 Segment of Post Pond proflle from survey by
cart-mounted radar.
graphic display of the radar ice thickness profile and
graph comparing radar data with borehole measure¬
ments. Here, the comparison plot is not corrected for a
1 .5 cm offset error in the borehole measurement tape.
Further discussion of the tape offset error is given in the
Borehole and Radar Data Error Analysis section. Ap¬
pendix A gives survey details.
Cart-mounted profiling of Post Pond
(survey study D)
On 8 January 1990, as the ice cover thickness had
increased to approximately 30 cm, the cart-mounted
system equipped with a gasoline-powered electrical
generator was taken out on Post Pond, near Lyme, New
Hampshire, to profile of the entire length of the Pond
(Fig. 60). A segment of the data is shown in Figure 61 .
On 1 1 January 1991 several core samples were taken
of Post Pond ice from along the survey path. Figure 62
shows a photograph of a vertical thin-section (in polar¬
ized light) of one of the ice cores, indicating the crystal¬
line structure of the ice and a series of horizontal thin-
sections (non-polarized light) taken at various points
along the core to indicate the dimensions and density of
air bubble inclusions in the ice. The core was solid and
no water inclusions or snow ice layers of low density
were encountered.
40
TOP
Horizontil cross-section
tsksn St spprox. 11 cm
from top of ssmpis
HorIzontsI cross-section
tsken St approx. 18 cm
Scale =
mm div
BOTTOM
Figure 62. Horizontal and vertical cross sections of II
January 1991 sample of Post Pond ice core.
Figure 63. Indication of surface roughness of Post
Pond ice cover (from data of II January 1991 ).
An indication of surface roughness of the pond is
given in Figure 63. The surface roughness is estimated
at 1-2 mm. There was no significant snow cover.
Appendix A gives survey details.
Profiling of snow-covered pond ice
(survey study E)
High-speed profiling is illustrated in Figure 64a,
which shows both snow cover and ice thicknesses on
Post Pond in Lyme, New Hampshire. The data were col¬
lected on 15 January 1991 from a truck-mounted ver¬
sion of the prototype radar traveling at a velocity of 10
km/hr. Interpretable data were also obtained at ground
speeds of up to 40 km/hr (Fig. 64b), with some degrada¬
tion in visual quality caused by the mechanical vibration
of the truck moving over rough terrain coupled to
antenna boom assembly. This subjected the antennas to
substantial vertical displacement, pitch and roll, result¬
ing in intra-scan and scan-to-scan range and signal level
variations. Appendix A gives survey details. The pond
was covered with approximately 18 cm of cold, low-
density snow (0. 1 5 g/cm^). Boreholes revealed solid ice
with no water inclusions and with bubble dimensions
and density similar to that found along the same survey
line during the survey study D, 4 days earlier. In Figure
64 the thickness of the snow cover was calculated in a
similar manner to that of the ice, using a value for the
index of refraction, risnow =1-12, based on the correla¬
tion of measured snow density with the results reported
by Cummings (1952). The radar results agree favorably
with ground truth measurements at the test site.
Truck-mounted profiling of pond ice
(survey study F)
Figure 65 shows a portion of a profile of Post Pond
41
_TOP OF SNOW
(Air/Snow Interface)
, _ TOP OF ICE
(Snow/Ice Interface)
a. Taken at 10 kmihr.
.BOTTOM OF ICE
(Ice/Water Interface)
TOP OF SNOW
(AirSnow Interface)
TOP OF ICE
(Snow/Ice Interface)
b. Taken at 40 kmihr. Deteriorated
spectrogram quality primarily caused
by vibration of sensor boom at high
ground speeds.
. BOTTOM OF ICE
(Ice/Water Interface)
Figure 64. Segment of Post Pond profile with snowcover.
42
Figure 65 . Setiment of Past Pond profile without snaucovcr
taken at 10 km! hr.
F it^ure 66. Indication of. surface rou^^hness of Post Pond
ice cover without snowcover (from data of 23 January
19911.
■re with no snow cover. The data were
collected on 24 January 1991 from a
truck-mounted version of the prototype
radar travel ing at a veloc ity of 1 0 km/hr.
The earlier snow cover had melted and
refrozen, providing an increased sur¬
face roughness and eliminating all but a
subsequent, minimal windblown snow-
cover. The radar results agree favorably
with ground truth measurements at the
test site.
On 23 January 1991 several core
samples were taken of Post Pond ice
from along the survey path. An indica¬
tion of surface roughness is given in
Figure 66. A photograph of a vertical
thin-section (in polarized light) of one
of the ice cores, indicating the crystal¬
line structure of the ice, and a series of
horizontal thin-sections (non-polarized
light) taken at various points along the
core to indicate the dimensions and den¬
sity of air bubble inclusions in the ice, is
presented in Figure 67.
Cart-mounted profiling of
Connecticut River ice
(survey studies G and H)
This experiment was performed to
verify the capability of the radar to pro¬
file ice thickness from typical helicop¬
ter survey altitudes. A survey was made
on 25 January 1 99 1 from Ledyard Bridge
over the Connecticut River in FJanover,
New Hampshire, at an altitude of 5 to 7
TOP
Horizontal cross- sect ion
taken at approx. 22 cm
from top of sample
Horizontal cross-section
taken at approx. 35 ern
from top of sample
Scale =
1 m m d I V
Fiftiire 67. Horizontal and vertical
BOTTOM .sections of 23 January 1991
.sample of Post Pond ice core.
43
Figure 68. Radar and borehole measurements from Ledyard Bridge (not corrected for borehole tape offset error).
m. The system was mounted on a cart with the antennas
suspended over the river by a 4-m-long boom and
manually propelled across the bridge at approximately
3 km/hr.
Figure 68 compares borehole measurements with
the spectrogram of a river ice profile. The plotted radar
thicknesses were determined between the signal peaks
at the center of the returns. The maximum ice surface
roughness was estimated at less than 0.5 cm. Figure 69
indicates the maximum degree of ice surface roughness
encountered. Variations in ice surface roughness ap¬
proached 0.5 cm in the mid-span section of the survey.
Closer to both river banks the ice was smooth with no
measurable surface roughness. Relative surface rough¬
ness can be deduced by observation of the variation in
intensity of the first surface return along the profile path.
The smoother the reflecting surface, the less diffused
the scattering and, consequently, the greater the magni¬
tude of the received reflection above the spectrograph
threshold; thus, the whiter (and broader) trace. The
sloping appearance of the spectrogram is caused by an
elevation differential of the bridge roadbed from the
New Hampshire to the Vermont side.
Data from sections of the ice sheet with minimal
surface roughness (survey study G) and with the rough¬
er surface (survey study H and Fig. 69) were statistically
analyzed and documented in Appendix A.
Figure 69. Indication of maximum surface roughness
encountered while profiling Connecticut River ice from
Ledyard Bridge.
Airborne profiling of lake ice
(survey study I)
An airborne survey was undertaken on 26 February
1991 on Turtle Pond near Concord, New Hampshire
(Fig. 70). For the pond survey shown in Figure 7 1 , the
helicopter was flown at an altitude of approximately 5
m and a ground speed of 1 5 km/hr. Other survey passes
were conducted at altitudes of up to 7 m and ground
speeds up to 40 km/hr with similar results. Boreholes
44
drilled along the survey path indicated an ice thickness
in the range of 25 to 28 cm, which agrees favorably with
the radar data.
Airborne profiling of river ice
(survey study J)
Another airborne survey was done on 26 February
1 99 1 along the Pemigewasset River near Franklin, New
Hampshire (Fig. 72)
For the river profile segment shown in Figure 73, the
helicopter was flown at approximately 2 m above the
surface of the ice at a speed relative to the ground of
approximately 10 km/hr. Other survey passes on the
Pemigewasset River were conducted at altitudes of up
to 7 m and ground speeds up to 40 km/hr with similar
results. The deviations from straight horizontal traces
visible in the spectrogram are ascribable to variations in
helicopter altitude.
Figure 70. Turtle Pond survey site near Concord,
New Hampshire.
' ' 0.5 km ■ '
Figure 71. Segment of airborne profile of Turtle Pond (ground speed = 15 kmihr).
t
Figure 72. Pemigewasset River survey site.
Figure 73. Segment of airborne profile ofPemigewasset Ri ver near
Franklin, New Hampshire (ground speed = 8 kmihr ).
45
Visual inspection of the hom antennas during hover¬
ing revealed small horizontal vibration, but no percep¬
tible vertical vibration. Effects of helicopter vibration,
pitch and roll during profiling runs were not apparent in
the data. Surface melt water conditions were encoun¬
tered and are seen in the spectrogram as segments where
only the top surface reflection is extant due primarily to
the high reflection coefficient of the air/melt water
interface. The surface melt water was not always visu¬
ally observable owing to snow cover, but was consis¬
tently and clearly indicated by the profiling radar.
Ground tmth was unavailable for this profile survey.
PERFORMANCE ANALYSIS
Survey data were analyzed to examine the perfor¬
mance of the radar and to compare it with theoretical
expectations. Pulse shape spreading and asymmetry
were statistically examined. The radar profiling data
were compared with borehole thickness measurements
to determine thickness measurement accuracy and sta¬
tistical techniques were applied to determine if other
physical attributes of the ice (e.g., surface roughness
and dielectric loss) could be derived. A comparison
between calculated and experimentally determined sys¬
tem SNR is presented. Specific details of individual
surveys are included in Appendix A.
that can be set to ±1.0 ms. For typical profiling
experiments, is 0.066 s, resulting in a sweep time
error of approximately ±1.5%.
Sampling synchronization error. An error source
related to t^^^p is sampling synchronization offset error.
Radar data time series sampling is triggered by a change
in level and slope at the transition from imbedded
synchronization signal to sampled time series data (see
the Analog Processing after Mixing section). This syn¬
chronization event is detected within ±1 sample inter¬
val. For a 1 024 point time series scan, that translates into
a 0. 1 % error.
Refractive index error. The Dielectric Permittivity
of the Water and Snow section determined that the max¬
imum variation of dielectric constant E from air bubble
inclusions in cold, natural freshwater ice is approxi¬
mately -5%, resulting in a worst-case variation in the
refractive index of ice of -2.24%.
Frequency bin resolution error. Errors correspond¬
ing to the air/ice and ice/water boundary difference
frequencies, F^^ and Fr2> are primarily attributable to the
FFT frequency bin resolution in relation to maximum
range and range resolution per FFT frequency bin
as indicated in eq 33 and 34 respectively.
Theoretical measurement accuracy analysis
Error factors will be examined and their effect on
system resolution accuracy calculated. Radar profiling
field data are correlated with borehole measurements to
obtain error statistics. A comparison and discussion of
the resolution error values derived from these two exer¬
cises is included.
Radar system resolution error analysis
The factors in eq 30 contain the primary error sources
in radar thickness measurements.
Ice thickness (m) - - ri ) ( swp) —
2{BW) (n^J
Changes in any of the variable terms of the above equa¬
tion will yield a proportional error in the ice thickness
measurement. The error contribution from each term is
pre.sented in terms of percent error in thickness mea¬
surement.
Bandwidth error. The swept bandwidth BW used
with the HP 8350B MMW sweeper was 1 3.5 GHz, with
a specified resolution error of ±20 MHz or ±0. 1 5% of the
swept bandwidth.
Sweep time error. The HP 8350B has a sweep time
By use of the actual system parameters of
BW = 13.5 GHz
/samp = ^ 5,620 samples/s
/jwp = 0.66 s/sweep
N(f^ = 1024
f = 3x10^ m/s
n^ - 1 .00 (for air) or
n^ = 1.77 (for freshwater ice)
the theoretical R^^ - 5.72 m in air and R^^ = 1 . 12 cm
in air or 0.63 cm in ice. Figure 74 indicates the percent
error in thickness resolution as a function of ice thick¬
ness for = 0.63 cm.
Nonlinearity error. The effect of nonlinearities of
the sweep frequency/time relationship must be consid¬
ered. By use of the specified HP8350B sweep nonlin¬
earity of 0.05%, and R^.^ and R^^ calculated above, and
eq 39, then
M- =. 0.0005
BW
46
and
^^ = 0.002
D
^ max
so that the criterion
_5L« Am-
BW /?^ax
is satisfied.
Thus, the error from nonlinearity of the sweep fre¬
quency/time relationship over the given bandwidth is
*4 of that from the minimum range resolution. That is,
resolution error from sweeper nonlinearity is 0.28 cm in
air and 0.16 cm in ice.
Table 10 provides a summary of the error compo¬
nents affecting the resolution accuracy. The most sig¬
nificant source of thickness resolution errorresults from
Figure 74. Error attributable to frequency bin resolu¬
tion as a function of ice thickness for ^ffi- 1024 (per¬
cent error for 5-, 10- and 20-cm-thick ice is indicated).
Table 10. Summary of calculated thickness resolution
errors for 5- and 10-cm-thick ice.
Error
type
Percent error
(Relative to ice thickness)
Bandwidth error
±0.15
Sweep error
±1.5
Sampling synchronization error
±0.10
Refractive index error
-2.24
Frequency bin resolution error
±12.8 t5 cm ice)
(for%= 1024)
±6.4 (10 cm ice)
Nonlinearity error
±3.2 (5 cm ice)
±1.6 (10 cm ice)
frequency bin resolution. Varying system parameters to
obtain smaller values of /^max ‘tnd larger values of /Vff,
may decrease this error, but to not less than the mini¬
mum resolution possible for a given radar system band¬
width. Thus, summing from Table 10, the calculated
worst-case error that could result for 5-cm-thick ice is
15.5%, and for 10-cm-thick ice is 7.5%.
Borehole and radar data error analysis
As a measure of system accuracy, radar and borehole
data are compared and analyzed. T wo profiling surveys
(survey studies C and F) included extensive thickness
measurements taken from boreholes along the survey
line. These measurements were made using a home¬
made depth gauge consisting of a collapsible “T-bar”
linked to a length of measurement tape with ’/4-in.
(0.64-cm) graduations. The T -bar and tape were placed
down each borehole, hooked on the underside of the ice
sheet and thickness measurements were taken at the ice
surface to the nearest '/4 in. Borehole measurements
were taken from a datum point at evenly spaced incre¬
ments along the survey line across the ice sheet. At¬
tempts were made to profile at a constant velocity so that
the resulting survey spectrogram would represent a
linearly scaled horizontal displacement. Radar thick¬
ness measurements were graphically derived from the
survey spectrogram by measuring the distance between
the center of the air/ice and ice/water reflection traces.
The position of each radar thickness measurement was
graphically correlated to an associated borehole using a
datum (e.g., shoreline) and known physical features
(e.g., bridge piers) as points of reference.
Initial comparison of radar and borehole measure¬
ments for both surveys indicated a systematic offset
between borehole and radar measurements. This offset
is on the order of 0.5 in. ( 1 .27 cm ) and is accounted for
by a foreshortened linkage between the measurement
tape and the T-bar. Verification of the precise offset of
the particular tape used for these surveys is impossible
since it was lost in the Arctic. However, consi.stent
offsets were found with other identically constructed T -
bar tapes. Figure 75 illustrates the cause of the offset to
the borehole measurement tape. The average offset
Ojfset^^^ for the data is calculated as
Offset (cm) = - (65)
s ^
where N = number of borehole samples
5Bn = borehole thickness measurement (cm)
Srp = radar thickness measurement (cm).
This yielded an average offset of 1 . 1 3 cm for survey
study C and 1.52 cm for survey studies G and H. Subse-
47
: DiHerence (%) Ice Thickness (cm)
Figure 75. T -bar ice thickness meas¬
urement tool with offset indicated.
15 10 15 20 25
Borehole Number
Figure 76. Radar and borehole thickness
measurement from tape 6. Dotted tine indi¬
cates ±0.64-cm ruler resolution hounds about
borehole measurement.
0,1 0.2 0,3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x): Fraction of Observations with x s Indicated Value
Figure 77. Difference between radar and borehole
thicknessfrom tape 6 (95 and 5% confidence bounds
shown for normal distribution).
48
quent analysis was done with these average offsets sub¬
tracted from the borehole data.
With the offset corrected data, the percent thickness
difference between borehole and radar measurements
Di/n for each borehole-radar data pair was calculated as
Di/„ (%) = ■^Rn (100). (66)
•^Bn
Figure 76 compares survey study C radar profiling
data with a ±0.64-cm error-band region bounding the
offset-corrected borehole measurements. Here, bore¬
holes were drilled every 1 m along the survey path. With
the exception of boreholes 1 , 2 and 3, the majority of the
radar measurements fall within the resolution bounds of
the measurement tape. The error exhibited by the first
three points is possibly caused by variations in the di¬
electric constant or scattering by bottom grass and other
debris imbedded in ice formed over shallow water close
to the shoreline. Figure 77 gives an indication of the
percent difference (relative to the offset-corrected bore¬
hole measurement) Di/n for the data. Excluding the
error data from boreholes 1, 2 and 3, the greatest error
is approximately ±10% about the mean.
Figure 78 compares survey study G and H radar
profiling data with a ±0.64 cm error-band region bound¬
ing the offset-corrected borehole measurements. Here,
boreholes were drilled every 3 m along the survey path.
Figure 79 gives an indication of the percent difference
Di/n for the data. With only one exception, the error
range is less than ±10%. The error for boreholes 29 and
30 is again potentially caused by shoreline effects, as
Figure 78. Radar and borehole thickness meas- 34
urementfor tape 11. Dotted line indicates ±0.64-cm
ruler resolution bounds about borehole measurement.
/■ )
m'A m'M
B
■: »••••♦ :
4 \
♦ ; '• ;
it
1 '4 ■ ■,«
B
\v
.4 \ .♦ x:
/
f V
* 4 \ A •
4
>
/ \/ \l
• '* Vi
t
B
u n
u 1?
\\ / *
jj'
'•■.i /
p!
2 \ %£
i
^ M
C ® 'i
■ Radar Measurement
i"
Borehole Measurement
0 0
5 ■
0)
±0.64 cm (±V4 in.)
E S
Q cO
15
Borehole Number
Figure 79. Difference between radar and borehole
thickness from tape 11 (95 and 5% confidence
bounds shown for normal distribution).
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
F(x): Fraction of Observations with x < Indicated Value
Table 11. Comparison of calculated and
measured resolution error.
Nominal Calculated Measured
Survey thickness error error
study (cm) (%) (%)
C 5 ±15.5 S±10
G&H 25 ±2.7 S±10
discussed earlier. Error in registration of borehole data
with radar thickness may be attributable to nonlineari¬
ties in the horizontal displacement on the spectrogram
because of varying velocity of the profile vehicle.
Error analysis summary
The radar system resolution error calculations of the
Radar System Resolution Error Analysis section com¬
pare favorably with resolution errors encountered in the
radar profiling and borehole thickness measurement
data described in the previous section. Table 1 1 summa¬
rizes the calculated and measured error for the nominal
ice thicknesses measured.
Radar pulse width analysis
Radar reflection data obtained from a flat metal plate
and from natural pond ice were statistically analyzed to
look for pulse distortion, which would compromise
thickness resolution, and to serve as a baseline for fur¬
ther pulse width and shape analysis. Pulse symmetry
can be distorted by the frequency-dependent effects of
radar hardware elements, including waveguide, anten¬
nas, mixer and analog recorder bandwidth, along with
pulse-spreading effects of surface and volume scatter¬
ing.
Radar reflections from a metal plate
An indication of the limit of realizable thickness
resolution can be obtained by measuring the time width
of a received radar pulse reflected from a flat metal
plate, a situation in which there should be minimal dis¬
tortion or spreading of the pulse shape results. A 1 - x 1 -
m rectangular metal plate oriented on a center line nor¬
mal to the antennas at a range of 2 m was employed. For
the 9° beamwidth antennas used, the 3-dB footprint
diameter is approximately 30 cm.
Pulse width measurements were taken at points 5 and
1 0 dB below the peak of the reflected pulse. The -5-dB
below-peak measurement point was selected because it
could be conveniently and repeatedly located, given the
nature of the DSP hardware and software, and was with¬
in only 1 dB of the below-peak point described in the
Effect of Bandwidth section (-4 dB) for defining mini¬
mum bandwidth resolution. The -10-dB below-peak
point was also selected for DSP hardware and software
Figure 80. Parameters for analysis of a pulse reflected
from a metal plate.
considerations because it was far enough down the skirt
of the pulse to give an indication of pulse width spread¬
ing, yet substantially above a level that would be influ¬
enced by the effects of side lobes or the noise floor.
Figure 80 illustrates the parameters used in width and
symmetry analysis of a radar pulse reflected from a flat
sheet of metal. The parameters are
FloiO = leading edge -10-dB intercept frequency
^lo5 = leading edge -5-dB intercept frequency
Fp = pulse peak amplitude intercept frequency
F|,i5 = trailing edge -5-dB intercept frequency
F|,jio = trailing edge -10-dB intercept frequency.
As is normally done in the radar DSP, each scan of
the radar reflection data was converted to 1024 digital
samples, then zero-padded to 2048 points, windowed
appropriately and transformed into a power spectrum.
Scans were then individually displayed so that the val¬
ues of F|(,io, F|o5, Fp, Fj,i5 and F^j iq could be located on
the pulse of interest using a curve-tracking cursor, inte¬
gral to the DSP hardware and software. Statistical anal¬
ysis was performed on data extracted from 50 scans.
The frequencies F,o,o, Fi^j, Fp, Fhij and F^no are
directly related to corresponding one-way travel times
from the antennas, F,(,,o, r,o5, Fp, This and Thno by eq
29. Differences between these one-way travel times
provide pulse width and pulse symmetry information
where
^hi5“^lo5 = “5 -dB pulse width (ps)
^hilO- ^lolO = -10-dB pulse width (ps)
^hi5-^p = -5 -dB trailing half pulse width (ps)
FhiiQ- Fp = -10-dB trailing half pulse width (ps)
Fp - Fi(,5 = -5-dB leading half pulse width (ps)
Fp- Fioio = -10-dB leading half pulse width (ps).
50
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x): Fraction of Observations with x < Indicated Value F(x); Fraction of Observations with x < Indicated Value
a. Rectangular windowed. h. Hanning windowed.
Figure 81. CDF of widths of pulses reflected from a metal plate (95 and 5% confidence hounds shown for normal
distribution).
Figure 8 1 shows Cumulative Distribution Function
(CDF) plots illustrating the -5- and - 1 0-dB pulse width
data for rectangular and Hanning windowed pulses.
Both sets of data appear to conform consistently to a
normal distribution, lying within the normal distribu¬
tion 5 and 95% confidence bounds (dotted lines either
side of the data points). The normal (Gaussian) Prob¬
ability Distribution Function (PDF) pix) is defined as
p(x) = —^exp
1
2
— OO < JC < OO
(67)
where x = real random variable
Px = mean
<Tx = standard deviation.
Using eq 3 1 and the mean values for the -5-dB pulse
widths of the rectangular and Hanning windowed puls¬
es from Figure 81, we can compute a lower bound on
realizable ice thickness resolution of 0.50 cm forrectan-
gular windowing and 0.67 cm for Hanning windowing.
The extent of scattering, resulting in a widening of the
reflected radar pulse, may have a significant limiting
effect on the minimum achievable resolution. Figure 82
illustrates the leading-to-trailing half pulse width asym¬
metry for rectangular and Hanning windowed pulses.
The symmetry of leading and trailing half-pulse widths
is described by the diagonal line on the graphs. When
rectangularly windowed, the pulse exhibits an asymme¬
try with a broader trailing half-pulse width; Hanning
windowing further broadens the entire pulse and in¬
creases the tendency toward symmetry of the leading
and trailing pulse halves.
0 10 20 30 40 so 60 70 0 10 20 30 40 50 60 TO
Leading Half Pulse Width (ps) Leading Half Pulse Width (ps)
a. Rectangular windowed. b. Hanning windowed.
Figure 82. Pulse width asymmetry (diagonal line represents locus of perfect symmetry).
51
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x): Fraction of Observations with x < indicated Value F(x): Fraction of Observations with x < Indicated Value
a. -5-dB asymmetry. b. -10-dB asymmetry.
Figure 83. CDF of rectangular windowed pulse (%) (95 and 5% confidence bounds shown for normal distribution).
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x): Fraction of Observations with x £ Indicated Value F(x): Fraction of Observations with x £ Indicated Value
a. -5-dB asymmetry. b. -10-dB asymmetry.
Figure 84. CDF of Hanning windowed pulse (Wo) (95 and 5Wc confidence bounds shown for normal distribution).
The percent of asymme**;' 4^^ ^ ><■ He.fmed for the-5-
dB measurement point as
^ sym ( 100) (68)
V^hi5 - ^los'
and for the -10-dB measurement point as
'^sym(%) ~ ^P^ ~ ^^P ~ ( 100) ■ (69)
^ (4il0-7’lolo)
CDFs indicating the statistics of percent asymmetry of
the examined radar pulses are illustrated in Figures 83
and 84. The figures show that statistically the rectangu¬
lar windowed reflections from the metal sheet have an
8-9% half pulse width asymmetry, with the trailing half
pulse roll-off less steep. This suggests a low-pass fre¬
quency dependence, attributable to either the radar
components, including the antennas and waveguide, or
to physical deformations of the thin metal reflector
sheet as it lay on the ice surface.
Radar reflections from an ice sheet
The methodology of the previous section was ap¬
plied to obtain the effects of scattering on pulse width
spreading and pulse symmetry for the air/ice and ice/
water interface reflections from a sheet of natural pond
ice. Figure 85 illustrates the pertinent components of the
reflection pulses from both the air/ice and ice/water in¬
terfaces used in the analysis. The particular data ana¬
lyzed (survey study F) were of pond ice nominally 40
cm thick, with minimal surface roughness (see Appen¬
dix A for details).
Figure 86 shows CDFs of the air/ice interface reflect¬
ed pulse widths at the -5- and - 1 0-dB points, while Fig¬
ure 87 shows CDFs of the ice/water interface reflected
pulse widths at the -5- and -10-dB points. Table 12
52
O.t 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x): Fraction of Observations with x 6 Indicated Value F(x): Fraction ol Observations with x s Indicated Value
a. At -5-dB point. b. At -10-dB point.
Figure 87. CDF of ice! water interface pulse width (95 and 5% confidence bounds shown for normal distribution).
53
Table 12. Comparison of mean pulse widths at -5- and
-10-dB measurement points.
Reflecting
boundary
Window
type
Mean pulse width (ps)
-5-dB point 10-dB point
Metal plate
Rectangular
58.91
81.94
Metal plate
Hanning
78.61
109.66
Air/ice interface
Hanning
98.58
150.80
Ice/water interface
Hanning
130.30
161.00
compares the -5- and -10-dB pulse widths of reflec¬
tions from a metal plate with the air/ice and ice/water
interfaces. The pulse widens significantly when it is
scattered by surface roughness at the air/ice interface.
Additionally, the pulse widens when it is reflected from
the ice/water interface because of two scattering events
at the air/ice interface (in and out), the effects of volume
Pulse width spreading can also be characterized in
terms of the pulse width difference between the ice/
water and air/ice interfaces AW (ps) at the -5-dB and
-10-dB measurement points by the relation
AW=W,/w-W^/, (70)
where Wi/w is the ice/water reflection pulse width (ps)
and W;^I is air/ice reflection pulse width (ps). Figure 88
gives the CDFs of the pulse width differences, relative
to the air/ice interface pulse width, measured at the -5-
and -10-dB points.
The percentage of pulse width increase exhibited by
the pulse reflected from the ice/water interface com¬
pared with that from the air/ice interface APW is char¬
acterized by
scattering, and scattering ascribable to roughness at the
ice/water interface.
APW(%) = (.Alii (100).
W,J
(71)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 t.O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x): Fraction of Observations with x s Indicated Value F(x): Fraction of Observations with x s Indicated Value
a. At -5-dB point. h. At -10-dB point.
Figure 88. CDF of pulse width difference between first and second interface reflected pulses (95 and 5% confidence
bounds shown for normal distribution).
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x): Fraction of Observations with x s Indicated Value F(x): Fraction of Observations with x < Indicated Value
a. At -5-dB point. b. At -10-dB point.
Figure 89. CDF of pulse width spreading (% ) between first and second interface reflections (95 and 5% confidence
bounds shown for normal distribution).
54
Figure 89 gives the CDFs of the percentage pulse width
differences, relative to the air/ice interface pulse width,
measured at the -5-dB and -10-dB points. The figures
show that at the -5-dB measurement point the ice/water
reflection return is, on average, 30 ps or 26% wider
relative to the associated air/ice interface return reflec¬
tion. It is believed that this is caused by volume scatter¬
ing in the ice as well as by “surface” scattering at the ice/
water boundary.
The pulse asymmetry may lead to a degree of ambi¬
guity or measurement error when measuring ice thick¬
ness based on the location of interface boundary reflec¬
tion pulse peaks. Here, pulse asymmetry is examined to
determine the extent of this ambiguity. Pulse width
symmetry between the leading and trailing half pulse
widths was measured for the air/ice and ice/water re¬
flection pulses at the -5- and -10-dB points by methods
earlier discussed. Figure 90 illustrates the asymmetry
between the leading and trailing -5- and -10-dB half¬
pulse widths for the reflected pulse from the air/ice and
ice/water interfaces. CDFs of the difference between
the leading and trailing half pulse widths at the -5-dB
measurement point for reflections from both the air/ice
and ice/water interfaces are shown in Figure 91. Here,
the mean pulse width asymmetry is 3.42 ps for the pulse
reflected from the air/ice interface and 1 1 .7 1 ps for the
pulse reflected from the ice/water interface. The worst-
case -5-dB pulse asymmetry spread is approximately
±50 ps. If ambiguity in pulse peak location is assumed
to be half of the mean asymmetry of the ice/water inter¬
face, approximately 6 ps, then the associated thickness
measurement error in ice would be approximately 0.10
a. Airlice interface.
b. Icelwater interface.
Figure 90. Pulse width asymmetry (diagonal line represents locus of perfect symmetry; sample size = 50).
F(x); Fraction of Observations with x s Indicated Value F(x): Fraction of Observations with x < Indicated Value
a. Airlice interface. b. Icelwater interface.
Figure 91. CDF of pulse width asymmetry (ps) at -5'dB point (95 and 5% confidence bounds shown for normal
distribution).
55
100
50H
&•
o
E
E
M
<
O
.gi^mQQ ..
'dtoo
OH
..-aaiiixpogtiiiiooii'
□, — -
-30 Hen
Mean - -3.49
Std. Dev. - 27.94
•100-
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x): Fraction of Observations with x 6 Indicated Value
F(x): Fraction of Observations with x < Indicated Value
a. At -5-dB point.
b. At -lO-dB point.
Figure 92. CDF of air! ice pulse width asymmetry (%)(95 and 5% confidence bounds shown for normal distribution ).
F<x): Fraction of Observations with x £ Indicated Value F(x): Fraction of Observations with x £ Indicated Value
a. At -5-dB point. b. At -10-dB point.
Figure 93. CDF of icelwater pulse width asymmetry (%)(95 and 5% confidence bounds shown for normal distribution).
cm, significantly below the calculated thickness resolu¬
tion of the system Even with half of the worst-case
spread, 23 ps, the associated thickness measurement
error would be 0.42 cm, still less than the minimum
resolution.
Percent asymmetry i4syn, is described for the air/ice
interface reflected pulse by the CDFs of Figure 92 and
for the ice/water interface reflected pulse by the CDFs
of Figure 93. Table 13 compares the mean pulse asym¬
metry for the metal plate, air/ice and ice/water reflection
Table 13. Comparison of mean pulse asymmetry
at -5- and -10-dB measurement points.
Reflecting
boundary
Window
type
Mean pulse asymmetry (%}
-5dB -10 dB
Metal plate
Rectangular
-8.27
-9.94
Metal plate
Hanning
-1.86
-1.26
Air/ice
Hanning
-3.49
-3.47
Ice/water
Hanning
-12.00
-3.69
boundary data. A negative percent asymmetry indicates
that the trailing half pulse width is wider than the
leading half pulse. The asymmetry is less apparent for
the Hanning windowed pulses at the -10-dB measure¬
ment point because of the widening of the leading and
trailing pulse halves relative to their difference in width.
Table 1 3 shows only a slight difference in the -5-dB-
point asymmetry between Hanning windowed pulses
reflected from a metal plate or from the air/ice bound¬
ary. However, an order of magnitude greater mean
asymmetry is apparent when comparison is made to the
pulse reflected from the ice/water interface. Given the
slight increase in asymmetry because of reflection from
the air/ice boundary, it appears that the asymmetry of
the pulse reflected from the ice/water boundary is pri¬
marily attributable to frequency-dependent volume scat¬
tering by entrapped air bubbles or by the effects of “sur¬
face” scattering at the ice/water boundary itself. Since
the pond was smooth, relative to the Rayleigh smooth¬
ness criteria (Eaves and Reedy 1987), it is believed that
56
volume scattering dominated in this study. Several
features in the ice core (Fig. 67) from this study support
this conclusion, including a granular, saturated refrozen
snow layer and three distinct bands of air bubbles.
Statistical analysis of
radar pulse peak magnitude
The peak magnitude of reflected pulses from the air/
ice boundary, the ice/water boundary and the difference
between the two were examined to see if electromagnet¬
ic properties of ice, such as dielectric loss, could be di¬
rectly determined from the radar data. In all the ice data
scans examined, coherent reflections were observed in
that the pulse shape was similar to those reflected from
a flat metal plate despite the variability (to be discussed)
in pulse width and magnitude. Pulses were neverstacked
(because of altitude fluctuations), so that the coherence
seen in the pulse shapes of the spectrogram are essen¬
tially that of the windowed data.
Figure 94 indicates the attributes of the Fourier trans¬
formed FM-CW radar difference frequency output sig¬
nal used in the analysis. The peak values of the air/ice in¬
terface dBy and the ice/water interface dB2 as well as
their associated spectral frequencies, Fji and Ff2, were
determined for a sequence of radar scans from each data
tape. To obtain these data, survey tapes were digitally
signal processed by converting each scan into 1024
digital samples. Each sampled scan was zero-padded to
2048 points, Hanning windowed and transformed into
a power spectrum. Scans were individually displayed
and the values of dfl], dB2, Ffi and fr2 were located
using a curve-tracking cursor, integral to the DSP hard¬
ware and software. Data collected from 100 such scans
from within a given profiling survey were then statisti¬
cally analyzed.
Figure 94. Representation of FM-CW radar waveform
components used for statistical analysis.
The values of F,i and Ff2 are directly related to radar
range and ice thickness by eq 29 and 30. Radar range
and range-gain normalization were applied to the data
so that direct scan-to-scan comparisons could be made
and CDFs generated.
Figures 95 and 96 compare CDFs of reflection peak
magnitude data from the air/ice and ice/water interfaces
and a CDF of the peak magnitude difference between
the first and second interface. They were generated as
described in the Cart-mounted Profiling of Overflow
Pond section. They represent data from nine selected
ice thickness surveys exhibiting unique ice conditions
(e.g., surface roughness, snow cover or thickness) or
measurement vehicle configurations (e.g., cart, truck or
helicopter), or both. Specific details of each of these sur¬
veys are documented in Appendix A. Here, for conve¬
nience of comparison and clarity, the data have been
normalized to a zero mean and each data set appears
reasonably well-bounded by the 5 and 95% confidence
CD «J
2-1
^ ^ 0
- ,
II
° Survey Study B
A Survey Study C
« •§ -5 -
■ Survey Study D
li
« Survey Study E
• Survey Study F
X ^
♦ Survey Study G
-to -
-15-
■
?
- 1 - 1 - 1 - 1 1 - - 1 1 - »— T 1 - 1
+ Survey Study H
0 Survey Study 1
X Survey Study J
1 I ' l l 1 '
O.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F(x}: Fraction of Observations with x s Indicated Value
a. Air/ice interface.
F(x); Fraction of Observations with x < Indicated Value
h. Icelwater interface.
Figure 95. CDF of peak magnitudes (zero-mean nor¬
malized).
57
20
15^
-'5H
-20 H — ■ — I — ■ — I — ■ — I — ■ — I — ■ — 1 — 1 — I — ■ — I — 1 — I — ■ — I — ■ — r*
0,1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 t .0
F(x): Fraction of Observations with x < Indicated Value
o Survey Study B ♦ Survey Study E + Survey Study H
Survey Study C • Survey Study F ° Survey Study I
* Survey Study D * Survey Study G ** Survey Study J
Figure 96. CDF of peak magnitude differences between
air! ice and ice! water interface (zero-mean normal¬
ized).
a Survey Study B » Survey Study E + Survey Study H
Survey Study C • Survey Study F o Survey Study I
* Survey Study D * Survey Study G ^ Survey Study J
Figure 97. Summary of ice thickness vs peak magnitude
difference.
m
2,
«
3
o
a.
OJ
JE?
V)
oc
-100-H
0
1 - 1 - 1 - r
2 3 4 5
Frequency (kHz)
6
Figure 98. Overlay plot of radar system responses to a metal plate and sky, indicating an
approximate 50-dB SNR.
bands of a log-normal distribution (see Appendix A for
individual survey details). The peak magnitudes’ CDFs
of Figure 95 show a variability on the order of 25 dB,
while for the CDF displayed in Figure 96 there is a
maximum peak variability on the order of 35 dB.
Figure 97 is a compilation of ice thickness vs peak
magnitude differences for data from all analyzed sur¬
veys. There is approximately a 35-dB range of peak
magnitude difference, which does not appear to be a
function of ice thickness nor have a statistically consis¬
tent tendency for the first interface pulse magnitude to
be larger (or smaller) than the second across the entire
range of data. Thus, it appears that e" cannot be reliably
deduced from the data. Surface roughness at both the
air/ice and ice/water interfaces has a significant effect
on the variability of pulse amplitudes, pulse width and
pulse asymmetry. Finally, Table 14 summarizes the
statistics data from all surveys analyzed.
58
Table 14. Summary of pulse peak magnitudes survey data.
Survey
study
Tape
no.
Platform
Speed
(km//ir)
Radar
range
(m)
Ice
r\pe
Ice
tluckne.ss
(cm)
Air
temperature
Ice
surface
conditions
Sample
size
Measurement
(dB)
Mean
(dB)
Std.
dev.
B
2
Suuionary
0
2
Pond
5
2
Clear ice. minima)
100
Air/ice peak
-38.12
1.46
surface roughne.ss
Ice/waier peak
-33.99
1.29
A/1 - I/W
^.12
1.24
C
6
Cart
3
1
Pond
7-8
-5
Snow cover shoveled
100
Air/ice peak
-26.33
3.48
clear, minimal sur-
Ice/water peak
-26.33
3.48
face roughness
A/1 -I/W
^.15
4.08
D
7
Cart
1
i
Pond
20-25
-10
Smooth ice with
100
Air/ice peak
-36.85
3.70
<1 cm of snow cover
Ice/waier peak
-.32.81
2.82
A/l-I/W
^.17
5.44
E
9
Truck
10
1
Pond
30
-7
18 cm dry. low-density
too
Air/snow peak
-.36.42
2.74
snow cover over ice
Snow/icc peak
-30.38
with minimal surface
Ice/water peak
-26.46
2.22
roughness
A/s - S/I
-3.69
3.36
S/I-I/W
-6.29
3.30
F
10
Truck
10
2
Pond
35-40
-18
<1 cm snow cover with
50
Air/ice peak
-22.30
3.09
roughened texture
Ice/water peak
-21.82
4.82
from refrozen meltwater
A/I -I/W
-0.72
6.67
G
11a
Can
3
5-6
River
25-35
-12
Clear ice; minimal
100
Air/ice peak
-21.73
4.60
surface roughness
Ice/water peak
-27.21
4.28
A/I - I/W
5.13
6.05
H
lib
Carl
3
5-6
River
25-35
-12
Surface roughness <1 cm
100
Air/ice peak
-30.62
3.54
from refrozen snowplow
Ice/waler peak
-30.53
3.68
ejecta on ice surface
A/I - I/W
-0.10
5.41
1
13
Helicopter
13
3-5
Pond
30
>5
Smooth ice with patches
100
Air/ice peak
-30.33
3.09
of <1 cm of wind-packed
Ice/water peak
-31.72
.3.31
snow cover
A/I -I/W
1..38
4.48
J
14
Helicopter
15
3-5
River
30
>5
Smooth ice with patches
100
Air/ice peak
-38.93
.3.26
of 51 cm of wind-packed
Ice/water peak
-41.61
4.04
snow cover
A/I-l/W
2.64
4.18
System noise analysis
The SNR performance of the prototype radar system
was determined experimentally and compared with
values calculated by the method described in the Radar
Range Equation for Geophysical Application section.
Radar reflection data from a normally positioned metal
plate of known dimension and at a known range were
compared with radar reflection data obtained by point¬
ing the antennas skyward. The system was configured
identically for both measurements. The flat metal sheet
target at a known distance provides a relative indication
of power returned from a smooth reflecting surface.
Table 15. Comparison of calculat¬
ed and prototype system SNR.
Range
Calculated
Prototype
(m)
SNR
systetti SNf
1.5
65.5
50
3.0
59.4
44 *
6.0
53.5
38 *
Pointing the antenna toward the sky eliminates the
effectsof nearby targets on the radar signal. The remain¬
ing signal components are from the noise and reflec¬
tions internal to the receiver itself and serve as an
indication of the system noise floor. The radar data were
acquired directly by the Macintosh 11 computer and
DSPcoprocessorforprocessing and display, thus avoid¬
ing additional incurred noise from an analog or DAT
magnetic tape recording and playback process. Com¬
paring the two measurements gives an estimate of the
system SNR. Figure 98 indicates about a 50-dB SNR for
the prototype radar system when a 45- x 55-cm alumi¬
num plate (Ip 1 1 = 1 ) was placed 1 50 cm from the antenna
and an output power level of 1 3 dBm was used. Table 1 5
compares prototype system experimental results with
theoretical SNR using eq 47 and shows that the SNR
decreases by 6 dB for each doubling of radar range.
CONCLUSIONS AND RECOMMENDATIONS
Accurate helicopter-bome, high-speed, high-resolu-
tion continuous profiling of freshwater ice and snow
thickness is po.ssible at MMW wavelengths. The mini-
* Values calculated based on -b-dB SNR
change for a doubling of range.
59
mum thickness resolution capability with a 13.5-GHz
bandwidth radar was significantly below the thinnest
measured ice (3 cm). Warming ice, high water content
ice and snow, and surface meltwater inhibit profiling
capability at millimeter wavelengths. Profiling accura¬
cy, compared to borehole measurements, was approxi¬
mately ±10%. Based on an examination of the width and
shape of pulses reflected from metal plates, air/ice and
ice/water boundaries, it appear5 that the pulse spreading
is caused primarily by surface scattering. The degree of
ice surface roughness, and resulting radar scattering
encountered, did not inhibit thickness profiling of cold,
natural, freshwater ice and snow over a range of 5 cm to
40 cm. Volume scattering from air bubbles (typically
less than 1 mm diameter) trapped within natural fresh¬
water ice did not inhibit profiling capability nor notice¬
ably affect thickness measurement accuracy. However,
volume scattering along with “surface” scattering at the
ice/water boundary appear to play a significant role in
increasing the asymmetry between leading and trailing
half pulse widths, which may contribute to thickness
measurement errors for very thin (less
…[truncated]