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Ultra high frequency radio echo sounding of glaciers Narod, B. Barry 1975-01-28

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ULTRA HIGH FREQUENCY RADIO ECHO SOUNDING OF GLACIERS V by B. Barry Narod B.Sc, University of British Columbia, 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOB THE DEGREE OF MASTER OF SCIENCE in the Department of Geophysics and Astronomy We accept this thesis as conforming to the required standard The University of British Columbia April 1975 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Depa rtment The University of British Columbia 20 75 Wesbrook Place Vancouver, Canada V6T 1W5 i ABSTRACT For determining the thickness of ice, radio echo sounding of glaciers is well established as a technigue for rapid gathering of data. However it has become evident that radio echo sounder parameters must be tailored to meet specific requirements in order to achieve best results. In particular rapid sounding of temperate, alpine glaciers and larger polar valley glaciers could be surveyed by a radio echo sounder having a very short pulse, very wide land response and narrow beam antenna. Such requirements can be fulfilled by Ultra High Frequency (300 MHz - 3 GHz) radio echo sounders, improved performance being achieved at the expense of decreased maximum range. This thesis, after considering previous attempts at radio echo sounding of glaciers, with respect to surveying valley and temperate glaciers, proposes and details a UHF radio echo sounder operating at 840 MHz. Conventional performance is predicted, and some new experiments, possible because of the short wavelength, are proposed. Appended to the thesis is a review and discussion of problems associated with the use of thermistors as thermometers in snow or ice. A procedure is described for optimizing the techniques of thermistor selection and use. ii TABLE OF CONTENTS Abstract .......I List Of Tables Iv List Of Figures V Acknowledgements Vi Chapter 1: Introduction 1 1.1 Background1.2 Dielectric Properties Of Ice 4 Chapter 2: System Design 6 2.1 General Description ...6 2.2 Selection Of The Carrier Frequency 7 2.3 System Performance 8 Range 10 2.4 Antenna Design .........12 Chapter 3: Circuit Design 15 3.1 Transmitter Circuit 7 3.2 Receiver/pulse Generator Circuit ., .18 3.3 Display And Recorder ...............21 Chapter 4: System Capabilities ...25 4.1 System Performance ...............................25 4.2 Maximum Range And Besolution 26 4.3 Reflectivity of Layers Hithin A Glacier ....28 4.4 Polarization 29 4.5 Conclusion 34 Bibliography 6 Appendix 45 iii 1 Introduction ....46 2 Thermistor Characteristics , 48 3 Bridges And Bridge Power Supply ......52 4 Transmission Line Effects .....61 5 Evaluation Of Available Systems (dmnus) ............62 Conclusion 64 Bibliography 7 LIST OF TABLES i v 0 Table 2.1: Radar Parameters .7 Table 2.2: System Performance 10 Table 1: Digital Multimeters ......63 Table 2: Digital Multimeter Errors ....64 LIST OF FIGURES Figure 2.1 .. 13 Figure 3.1: Radar Interconnection Diagram .16 Figure 3.2: Transmitter Block Diagram . .....17 Figure 3.3: Receiver Block Diagram 19 Figure 3.4: Intensity Modulation Recording Block Diagram .23 Figure 3.5: Digitizer Block Diagram ....24 Figure 1: Generalized Bridge .............................47 Figure 2: Bridge Configurations ......54 Figure 3: Digital Multimeter Errors ...6vi ACKNOWLEDGEMENTS I wish to thank my supervisor, Dr. Garry Clarke, for his patience and guidance during the course of this work. I would also like to thank Dr. Clarke, Dr. R, B. Russell, the Department of Geophysics and Astronomy, and the Department of Physics for financial support I received while I was completing this thesis. I am very grateful to Dr. Ron Goodman of Calgary for his invaluable assistance and advice while development of the radio echo sounder progressed. I wish to acknowledge the services of the University's Computing Center, which supported this typescript; and the numerous manufacturers who participated in the development of the radio echo sounder. I thank the Department of Geophysics and Astronomy for providing laboratory facilities for this project. I thank all of my friends among the faculty, staff and students of the Department, especially Mr. Peter Michelow, for all their contributions to this project. Finally, and especially, I wish to thank the National Research Council of Canada which financed the development of both the UHF radio echo sounder and the thermistor resistance bridge. The radio echo sounder was financed by grant A3479 from the National Research Council to Dr. Clarke. The resistance bridge was financed by grant A4327 from the vii National Research Council cf Canada also to Dr. Clarke. 1 CHAPTER 1: INTRODUCTION 1.1 BACKGROUND Radio echo sounding of ice was "successful" as early as 1946 when aircraft pilots using pulsed radar altimeters ever Antarctic ice reported possible fatal errors in radar interpretation. In 1955 440 MHz pulsed radar altimeters attempted the first intentional vertical transmission through ice on the 800 ft. thick Ross Ice Shelf. A lack of results induced attempts in 1958 to probe 500 ft. thick ice at Wilkes Station. Strong echoes combined with seismic information provided information about the propagation velocity of electromagnetic radiation in ice. Further work in Greenland confirmed the dielectric constant value in ice of 3.2 (von Hippel, 1954). In 1960 tests were made of altimeters operating at 110, 220, 440 and 4300 MHz. These shewed that the lowest frequencies were most suited to sounding of thick ice. A summary was reported by flaite and Schmidt (1962). In 1963, the British Antarctic Survey operated the 35 MHz SPRI Mk I apparatus, the first radar system designed specifically for the use of sounding ice sheets. The SPRI Mk I sounder had a 40 W r.m.s. transmitter pulse power, a -93 dBm receiver sensitivity, a 10 MHz bandwidth and moncpole antennae (Evans, 1963a). Further tests by the Scott Polar 2 Sesearch Institute (SPBI) and the U. S. Army Electronics Laboratory (DSAEL) determined that signal attenuation was reduced at lower freguencies (Evans, 1963b). During the following field season the Ninth Soviet Antarctic Expedition (Bogorodskiy, Rudakov, Tyul'pin, 1965) operated a type-1M4 radar apparatus, with a carrier freguency of 213 MHz, and a pulse power of 80 Kw r.m.s. Strong echoes were obtained from depths up to 900 m. The project terminated with the loss of the apparatus and the driver into a crevasse. The next three years saw expanded use of the SPRI Mk II sounder (500 w pulse power, otherwise same as Mk I) and the SCR 718 radio altimeter (440 MHz), including airborne surveying in Canada, Greenland and Antarctica (Evans, 1966). The SPRI operated a SPRI Mk IV sounder from an aircraft during the 1969-70 field season. Flight lines are in Evans and Smith, (1971). The following year the SPRI operated a modified SPRI Mk IV apparatus (modified to 60 MHz) from an aircraft. Butterfly plan multi-wire dipcle antennae were used to maintain a large bandwidth. A maximum ice thickness cf 4450 m was recorded (Evans, Drewry, Robin, 1972). In 1973 Davis, Halliday and Miller reported a Cambridge expedition attempt to sound the Roslin Gletscher in Stauning Alper, East Greenland, using a modified SCR 718 radio altimeter with a 45° corner reflector antenna. Op to this time all radio sounding had been with systems eguipped" with 3 monopole, dipole or two element Yagi antennae. For frequencies below 300 MHz high gain antennae would be prohibitively large. Sounding in ice sheets, however, could be improved by using higher power transmitters. Returned power that arrived later than the initial bottom bounce did not affect the accuracy of the record. In valley glaciers, wall echoes could obscure or be mistaken for bottom echoes, Davis et al (1973) recognized that in order to achieve consistent results radiated and received power must be restricted to a narrow beam. Using an antenna with 8 dB forward gain they recorded echoes up to 350 m. In 1972, in a continuing project, the Department of Energy Mines and Resources, Canada, made soundings on the Athabasca Glacier, Alberta, Canada, with a UHF apparatus developed by R. Goodman. The unit featured a 620 MHz carrier frequency, 3 Kw pulse power and a very high gain corner reflector antenna. Results were generally negative, but very fine interglacier structure was detected. The following year the unit was operated on the Trapridge and Rusty Glaciers, surging glaciers in the Yukon Territory, Canada, with total success (Clarke 6 Goodman, 1975; Goodman et al, 1975). In 1974, using a transmitter developed by the Stanford Research Institute, Watts, Meier et al (1974) made soundings on the South Cascade Glacier, Washington U.S.A. and the Columbia Glacier, Alaska, U.S.A. The apparatus featured a monopulse signal with 1-5 MHz carrier frequency and 100 ns pulse length. Successful soundings were made up to 1200 m in temperate ice (Meier £ Watts, private coffimunicaticn) . Its chief disadvantage was in its antennae configuration. It was necessary to use butterfly half wave dipoles spread cn the glacier surface. The transmitter and receiver antennae were separated by 50 m. This configuration precludes continuous profiling due to its size and its method of deployment. Radio echo sounding has been established as a practical method for obtaining ice thicknesses, with reasonable reliability. Sounding in large polar ice masses is most satisfactory at low frequencies, the lower limit being determined by antenna size and communication interference. Large temperate ice masses could be sounded with low frequency monopole sounders. However sounding in smaller valley and alpine glaciers, in particular temperate or partially temperate glaciers, could be successfully studied with UflF sounders. These sounders have very narrow antennae beams, very fast risetimes and short pulse lengths. They will be the most practical system for continuous profiling over these glaciers. 1.2 DIELECTRIC PROPERTIES OF ICE 1.2.1 PERMITTIVITY Pure ice has a relatively high static permittivity (approximately 100) (Evans, 1965) and a long relaxation time 5 (0.1 ms) due to its polar molecules. At radio frequencies of the order of 1 MHz the effects of the relaxation spectrum, and its corresponding effect with temperature cn the relative permittivity have virtually vanished. Numerous programs have detemined that above 1 MHz the relative permittivity cf ice is 3.2±0.2 (Auty S Cole, 1952; Cumming, 1952; von Hippel, 1954). It is virtually independent of temperature, and in temperate ice it is suspected that water content is insufficient to t cause large variations (Evans, 1965). 1.2.2 LOSS TANGENT In 0°C ice below 300 MHz, ftanS is virtually constant, and in spite of the lack of effect on permittivity, power losses are due primarily to the relaxation spectrum. Above 300 MHz infrared absorption becomes evident. At reduced temperatures, the infrared absorption, which is relatively temperature insensitive, is evident at lower frequencies. Residual absorption from the relaxation spectrum decreases with lower temperatures (Evans, 1965). In temperate ice, water content can have .widely varying effects on the loss tangent. This is due in part to the wide relaxation spectrum of water, but probably B.C. conductivity of water and scattering by water inclusions provide the greatest losses (Evans, 1965; Smith S Evans, 1972). 6 CHAPTER 2: SYSTEM DESIGN 2.1 GENERAL DESCRIPTION In designing a radio echo sounder for sounding in valley glaciers one has basically five parameters to work with: carrier frequency, bandwidth, pulse length, antenna pattern and peak transmitter power. Echo risetime at the receiver is determined by transmitter, receiver and antenna bandwidth and by the antenna pattern. Maximum range is determined by the peak transmitter power, the carrier freguency, and the antenna pattern. Resolution is affected by pulse length, system bandwidth and antenna pattern The parameters for a system designed at the University of British Columbia are listed in table 2.1. The carrier frequency is 840 MHz, the bandwidth is 40 MHz, the pulse length is 70 ns, the antenna gain is 19 dE and the peak r.m.s. transmitter power is 4.1 Kw. 7 2.2 SELECTION OF THE CARRIER FREQUENCY The decision to operate at 840 MHz can be divided into two steps. First, the decision to operate within the U.E.F. T.V. band. Secondly, what frequency within the band to use. TRANSMITTER PARAMETERS Operating frequency 840 MHz Bandwidth 35 MHz Pulse length 70 ns Rise time 18 ns Fall time 28 ns Peak power 4.1 Kw (66 dEm) Repetition rate 25 KHz ANTENNA CONFIGURATION 90° dual dipole corner reflector Gain 19dB over isotropic Front/side ratio 60 dB VSWR < 1.5 RECEIVER PARAMETERS Bandwidth 40 MHz Dynamic range 97 dB Minimum sensitivity -82 dEm SYSTEM PERFORMANCE Single antenna > 95 dE Dual antenna 138 dB TABLE 2.1: RADAR PARAMETERS The prime factor in choosing a high frequency is the constraint that the first use of the system will be to sound small icecaps and valley glaciers of the Canadian Arctic and Northwest, where valley wall echoes necessitate a high gain antenna. VHF or lower frequencies cannot be operated with a 8 high gain antenna which would be conveniently small for either aerial or surface use. The useful frequency range is limited to 300 MHz cr higher (Davis, 1973) . Once the decision has been made to operate within the useful UHF range (300MHz - 1GHz) a single freguency must be selected. In sounding -20°C ice at these freguencies ftan 6 increases as the second power of the frequency (Walford, 196 8; Bleaney 8 Bleaney, 1957). This is countered by the antenna gain, in that for a given aperture size gain also goes up as the second power of the freguency, and the effects cancel. The advantage of using a higher freguency lies in the narrower beamwidth available for a given aperture size. The beam will illuminate a smaller area of the glacier bed, hence clearer echoes will be achieved. As the temperature increases the variation of ftanS with frequency decreases so that at 0°C ftan6, or attenuation per unit length is effectively constant (0.057dEm_1: Smith 5 Evans, 1972) hence the advantage of going tc a higher freguency due to having a greater gain for a given aperture is real. The two way gain increases as the fourth power cf the frequency whereas transmission losses decrease only as the second power. The advantage of the narrower beamwidth still applies, especially considering that the beam will illuminate fewer scattering objects whose range is close to the range of the bedrock (Davis, 1973), Davis (1973) also suggests that 9 scattered power may actually tend to decrease with these higher frequencies, although evidence for this is limited. The final decision to use 840 MHz rather than any nearby frequency (either higher or lower) is economic. 840 MHz ± 20MHz lies within a common carrier landbased mobile, and interim UHF TV band for which hardware is more easily available. Due to its dual use, this frequency has been set as a break point in transmitter design; any lower frequency would require a larger, more expensive cavity amplifier (R.L. Sepulveda, Microwave Control Co,, private communication) . 2.2.1 TRANSMITTER DESIGN At the carrier frequency selected it is more stable to employ a crystal frequency generator rather than use an L-C tank to produce the frequency, as is the case with more conventional systems such as the SPRI Mk II. The transmitter derives its frequency from a 120 MHz crystal oscillator, fed into a x7 multiplier. Two stages of amplification and modulation lead the signal to a cavity triode R.F. power amplifier. Here some of the advantages of the crystal generated frequency become apparent. It is much easier to detune the characteristicly high Q of a cavity amplifier, giving the efficient result of having all of the transmitted power within the receiver bandwidth. 10 2.2.2 ANTENNA S TRANSKIT/RECEIVE SWITCH A corner reflector antenna was selected for the prototype configuration. With a two colinear dipole driven element the antenna should have sufficiently high gain and narrow beam width to yield strong echoes with short fading patterns. Concurrently the 90° side lobes should be sufficiently low that valley wall echoes will not obscure bottom echoes when the apparatus is operated at the ice surface. A circulator is used as a passive transmit/receive switch when the system is operated with a single antenna. 2.2.3 RECEIVER AND RECORDER The receiver has a logarithmic intermediate freguency (I.F.) amplifier as its primary component. Initially a photographic X-Y or intensity-modulated recording will be used. In the future it is hoped to be able to record the signals digitally onto magnetic tapes. 2.3 SYSTEM PERFORMANCE 5 RANGE The smaller more efficient cavities available at this freguency yield higher peak power, hence greater system performance. Important parameters are listed in Table 2.2. If we assume dielectric losses B of 0.057dEm_1 and a bedrock reflection coefficient R of -20 dB (Rcbin, Evans, Bailey, 1969; Harrison, 1972) an antenna gain G of 19 dE and a 11 system performance of 138 dB then the maximum range is determined by p , received _ G^X^R .. -0.2Dr T~T 10 (1) P. , 64iTr transmitted Peak power 66 dBm Receiver sensitivity --90 dEm Mixer conversion loss -8 dB Maximum system performance 138 dB Linear system performance 118 dB 1 1 Receiver is linear down to -70 dBm. TABLE 2.2: SYSTEM PERFORMANCE The maximum range r is then 700 m which should be ample for sounding many valley glaciers.. According to Davis (1973) a criterion for successful sounding of temperate glaciers is pr(plan£) =f(f^) >1 (2) r(scattered) m where R is the bedrock reflectivity, assumed to be -20 dE; C is the scattering coefficient, calculated to be 0.01 m~l (based on Davis* (1973) analysis of the DEMB sounder operating at 620 MHz); G is the antenna gain, set at 19 dE and 1 is the pulse length in ice. In our case R.G-l 0.01 80-1 CK 1 ; 0.01/m^ lW ' (3) m 12 hence our system should be successful at sounding temperate glaciers. 2.4 ANTENNA DESIGN There are numerous styles of antennae which can provide large bandwidth and high gain at the freguencies discussed here. Some are capable of very great brcadbanding. The Yagi, paraboloid, helical and broadside array are some. However, in selecting an antenna to sound valley glaciers, forward gain is not the only constraint. Igually important is the 90° side lobe level, or the "front to side" ratio. In a valley, the dip of the valley walls rarely exceeds 450 [Fig* 2.1]. If we model a glacier as filling approximately a parabolcidal valley it follows that over a large range of distances from the valley wall, L, the travel time for the transmitted pulse to reach the valley wall closely matches the time for that pulse to reach the bed, at height H below the ice surface (using a velocity in ice cf 176 m/ sec). Since the surface wave is not noticably attenuated, in a large glacier the valley wall echo may easily obscure or be confused with the bottom echo. For example the paraboloidal reflector antenna has a front to side ratio of 30 dB. With 0.05 dBm-1 attenuation in ice the bottom echo will be the same strength as the wall echo Valley wall dip Usg-a H FIGURE 2.1 14 after only 600 m of two way travel. In temperate ice this maximum range decreases rapidly. Ideally the front to side ratio should not be greater than one half the system performance in order tc have pcwer returned from the walls obscured in system noise. It is possible to achieve a front to side ratio of 60 dB by using a corner reflector. This will reduce system performance to 120 dB when operated in such a valley. aperture synthesis may improve the front to side ratio still further, though this technique is difficult and necessarily very slew. 15 CHAPTER 2k CIRCUIT DESIGH The radio echo sounder consists of five units (not including power supply) connected in the field only during use. They are the transmitter, circulator, antenna, receiver/pulse generator, and display. The assembly is depicted in Figure 3.1. 3.1 TRANSMITTER CIRCUIT The transmitter was built for U.E.C. by Microwave Control Company, Farmingdale, New Jersey, U.S.A. A block diagram for the transmitter is shown in Figure 3.2. The carrier freguency is generated by a crystal oscillator operating at a 120 MHz harmonic. The signal is then amplified by two NPN transistors, both operating class A (2N3866). Two more stages of amplification buffer the 120 MHz carrier. The 120 MHz signal is fed to parallel x6 and x7 multipliers which yield 720 MHz signals for the local oscillator, and 840 MHz for the broadcast carrier. The 720 MHz signal passes through a bandpass filter to the local oscillator output jack. The 840 MHz carrier then drives two stages of tuned common base amplifiers. The first stage is gated by the modulator pulse which has been amplified from a TTL pulse provided by the external pulse generator. The second stage provides a maximum B. F. power of 20 watts. CIRCULATOR TRANSMITTER SMA SMA LOCAL OSCILLATOR TRIGGER PULSE SMA SMA RECEIVER N N BNC VIDEO BNC ANTENNA BNC DISPLAY TRIGGER BNC VERTICAL SCAN BNC DISPLAY BNC FIGURE 3.1: RADAR INTERCONNECTION DIAGRAM vVWV SM SOLID STATE AMPLIFIER TRIODE AMPLIFIER TIMES 7 MULTIPLIER LOCAL OSCILLATOR OUT PULSE AMPLIFIER TIMES 6 120 MHz AMPLIFIER MULTIPLIER / 720 MHz ' BANDPASS 120 MHz OSCILLATOR TRIODE AMPLIFIER R.F. OUT ISOLATOR SMA TRIGGER IN POWER SUPPLY / 26v REGULATOR e -o 30v IN FIGURE 3.2 RADAR TRANSMITTER BLOCK DIAGRAM h-1 18 The 20 watt R. F. power then passes through a 30 watt isolator to a triode amplifier/modulatcr, which is also gated by an amplified pulse from the external pulse generator. The high power modulated R. F, signal is then fed finally tc a broad band triode power amplifier which delivers 4.1 kilowatts peak R. F. power through an isolator to the R. F. output jack. i Power for the transmitter is drawn from a 28 v - 30 v supply which is dropped and regulated to 26 v. All voltages used (up to 4 Kv) are derived from this 26 v regulated supply. A digital timing circuit disables the high voltages for 1.5 minutes after turnon to allow for warmup. Internal sensing circuits provide for immediate shutdown should any subcircuit overload, for any reason. The shutdown circuit throws a circuit breaker which may be reset by applying a potential to a pin on a test jack provided. 3.2 RECEIVER/PULSE GENERATOR CIRCUIT The receiver/pulse generator was designed and assembled at the University of British Columbia, Department of Geophysics. Figure 3.3 is a block diagram for the receiver/pulse generator. The received R. F. signal passes through a diode switch which is enabled during the transmit pulse when the system is DIODE SWITCH MIXER R.F. IN LOG I.F. AMPLIFIER VIDEO AMPLIFIER ATTENUATOR SMA LOCAL OSCILLATOR IN PULSE GENERATOR 100 KHz MULTIVIBRATOR SYNCRONOUS DIVIDE BY 4 Ai DIODE SWITCH PULSE FORMER TRANSMITTER! TRIG. DELAY TRANSMIT PULSE FORMER FIGURE 3.3 6 C RADAR RECEIVER BLOCK DIAGRAM D 6 BNC VIDEO OUT TRANSMIT TRIGGER 3" SMA BNC -4 DISPLAY TRIGGER i-1 20 operated in the single antenna mode. The diode switch is enabled by an amplified pulse derived from the pulse generator. The R. F. signal is then mixed down tc the 120 MHz intermediate freguency, using the 720 MHz local oscillator provided in the transmitter. The local oscillator provides 22 dBm of R. F. power to the mixer. This is attenuated to 10 dBm, The mixer is a Mini Circuits Laboratory model MA-1 with a conversion loss of 8 dB, The I, F. signal is then amplified through a logarithmic I. F, amplifier. The amplifier is an EHG model ICLT12040. It has a center frequency at 120 MHz, a 3 dB bandwidth of 40,1 MHz. It has a dynamic range of 97 dE and is linearly logarithmic (±1 dB) for 70 dB of its range. Its risetime is less than 20 ns; its noise figure is 10 dE. Its output voltage range is from 0,017 v at -90 dBm to 2,670 v at +7 dBm. The detected video signal passes through one final stage of gain which adjusts amplitude and bias for display purposes. The pulse generator provides trigger pulses to the transmitter, diode switch and oscilloscope display. It is capable of only a single repetition rate and pulse length. The repetition rate is determined by a 100 KHz TTL multivibrator. The 100 KHz clock pulse then passes through a divide-by-four TTL counter which provides the 25 KEz trigger pulse rate. The counter provides two bits cf control information for a proposed digitizer. The 25 KHz pulse then 21 drives two monostable TTL flipflops. One monostable pulse is amplified and enables the diode switch. The second mcnostable pulse provides a time delay between the diode switch enable pulse and a third monostable TTL flipflop. The third monostable vibrator is adjusted to have a pulse length of 70ns. This pulse provides the modulating signal to the transmitter and the trigger for the oscilloscope display. The length of the diode switch enable pulse is adjusted so that the switch and the transmitter disable simultaneously. 3.3 DISPLAY AND RECORDER The initial display oscilloscope is a Tektronics model 475 oscilliscope with a Polaroid film pack. When operated using intensity modulation a ramp generator scans the vertical axis on the oscilloscope, which exposes one frame. The ramp generator consists of a variable clock pulse which drives a nine bit counter, which drives a digital to analog converter. Intensity and modulation amplitude are controlled by the video amplifier. A block diagram appears in Figure 3.4. In addition it is hoped eventually to be able to digitize and record the complete radar record. The proposed digitizer will be capable of 1024 channels with 10 ns channel separation.the digitizer will sample 128 pulses at one time 22 delay and average them. The time delay will then be incremented by 10 ns and the process will continue. The analog circuitry is based on a sample and hold amplifier with 175 MHz bandwidth designed by H. Baldis and J. Aa2am-Zangeneih. The output will be eight bit parallel. A block diagram appears in Figure 3.5. + 6v O EXAR 2240M clock start eight bit counter J i stop -4A/V -AAAr vertical scan FIGURE 3.4: INTENSITY MODULATION RECORDING BLOCK DIAGRAM (vertical scan) NJ CO DATA OUT OUTPUT FLAG data OUTPUT BUFFER data 15 BIT REGISTER clock clear A o 100 KHz IN clock] 15 BIT ADDER X data 8 BIT A/D CONVERTER X 1 BNC / VIDEO IN T 10 ns SAMPLE & HOLD ENABLE DECODER B C 10 BIT SAMPLE & HOLD ZERO DETECT TRIGGER 100 MHz OSCILLATOR 10 BIT ECL TIME DELAY COUNTER T 10 BIT ECL CHANNEL SELECT COUNTER -O D 7 BIT. COUNTER 1 FIGURE 3.5 RADAR DIGITIZER BLOCK DIAGRAM 4>-25 CHAPTER 4: SYSTEM CAPABILITIES 4.1 SYSTEM PERFORMANCE The maximum range of any radar system is a function of four parameters: antenna gain, frequency, medium attenuation and system performance. The latter is defined as the maximum r.m.s. transmitted power divided by the receiver sensitivity, thus system performance is a function of the transmitter and receiver parameters, but it is also possibly determined by antenna characteristics. It is possible that there is sufficient transmitter leakage power, which may be available to the receiver, and could obscure otherwise usable echoes. In the present case this is a real consideration when a single antenna is used. If the ON/OFF transmitter ratio is only 100 dE and the circulator isolation is 25 dB, then system performance could be limited to their sum, 125 dB. Further, if the antenna is mismatched so that it has a reflection coefficient greater than -25 dB, then the system performance would be degraded still further. Any attempt to improve system performance by improving receiver sensitivity would be wasted. This problem can be avoided by employing two antennae as with the SPRI Mk II sounder (Evans 8 Smith, 1969). It is relatively easy to produce antennae pairs with the required 26 isolation, particularly if high gain antennae are used. Another, possibly less expensive method is available for increasing isolation. Passive or active diode switches operated between the transmitter and circulator can increase the ON/OFF ratio by at least 40 dB. The only reguirement cn the switch is the ability to conduct the maximum transmitter power, with minimum loss. Switching speed is net critical as the switch need only be off for maximum range echoes, usually several microseconds after the transmitter pulse. 4.2 MAXIMUM RANGE AND RESOLUTION In radio echo sounding in ice the bedrock has generally been modeled as a specular plane reflector with a reflection coefficient of -20 dB. This figure has been considered conservative (Davis, 1973). Deviations on this model have also been considered (Harrison, 1974). If the plane model is assumed then the maximum range is determined by P O ; received G^R . -0.2Dr ... F , " 64^10 (1) transmitted where the left expression eguals the inverse system performance, G is the free space antenna gain, A is the free space wavelength, R is the bedrock reflectivity, D is the loss in dBm-1, and r is the range. In cold ice, if the attenuation of the signal is 0.057 dBm-1, then the maximum range is 700 m, with the 27 described apparatus, as stated in Chapter 2. In temperate ice the maximum range is only 210 tn for a total attenuation of 0.2 dBm-*. If total attenuation is 0.15 dBm-1 (Ragle et al, 1964), then the maximum range is 280 m. Improved gain due to refraction at the ice surface may improve the system performance by about 2 dB increasing the maximum range to 290 m in the last case. If precision is defined as the time for echo power to rise 3 dB above local average power, then it follows that precision is a constant fraction of range. In the present case, precision is 18ns-88m/ys _ zoUm of range in temperate ice. In cold ice the precision is 0.25% of range. (Note: these figures are based upon the assumption that the plane reflector is sufficiently specular, that for the high gain antenna, the plane is effectively identical to a spherical reflector centered at the antenna with radius equal to the real range. The validity of the assumption is solely a function of the antenna gain and beamwidth. If fading patterns resulting from too broad a beam degrade the echo risetime, a deconvolution of the echo, if possible, using the transmitted pulse as a source function, will return this accuracy). 28 4.3 REFLECTIVITY OF LAYERS WITHIN A GLACIER Harrison (1973) has shown that the reflection coefficient R, for random variations in permittivity vary with the pulse length in radians L, as R - i^r) L2e"2Li (5) where layer thickness is greater than the pulse length. ^E' is a step change of the relative permittivity e with depth. Harrison has concluded that it is necessary to restrict oneself to the case where the layer thickness is much less than the pulse length. In this case TT2L 2 . 2 R - -ft {^fr} (6) m for single reflectors, and 7T3p L . 2 -k 2L 2 _ _ m m fAS i e m m . for multiple reflectors where 1^ is the layer thickness or spacing, ^m is the wavelength in ice, Pm is the pulse length in ice and km is the wave number in ice. Harrison has also shown that there is a maximum reflectivity at lm= 1/^2 where •m A 2 -h &mav = T7" Pmk {—^} (8) max lb mm e In the present case, this reduces to AF2 R = 0.119 {-^T} (9) max e 29 at L =2.5 cm. To obtain a power reflection m -70 dB in this case would require that Ae = 10~3 e It is clear that UHF radio echo sounders can be to small variations in e over centimeter ranges. 4.4 POLARIZATION 4.4.1 OPTICAL ACTIVITY Optical activity is usually described as the tendency of transparent matter to rotate the E-vector of plane polarized electromagnetic radiation. The E-vectcr of any radiation traversing optically active matter will rotate either clockwise or counterclockwise when viewed from the radiation source. With a radio echo sounder, plane polarized radiation enters a glacier at normal incidence. Any rotation due to optical activity in the ice during the first transit (to the bottom) should equal the rotation due to the return traverse. Since the rotation sense does not change, the total rotation should cancel. Hence radio echo sounding cannot detect optical activity. coefficient of (10) very sensitive 4.4.2 DOUBLE REFRACTION Double refraction (also known as birefringence) is 30 defined as a difference in refractive index for radiation with E-vectors normal and parallel to a well defined crystal axis (Jenkins & White, 1957). At visible wavelengths the ordinary and extraordinary indices of refraction in ice differ by 0.3%. In the ideal situation, with crystals having their optical axes parallel and horizontal, a 90° phase shift of the ordinary and extraordinary rays at 840 HHz could occur in only 16 meters of two way transit (it is necessary to assume that the ratio of refractive indices is constant with frequency above the relaxation spectrum). However this is excessively optimistic for two reasons. First, there is a tendency for the optical axes of ice crystals in glaciers to align vertically (Paterson, 1969). Secondly, and predominantly, nonuniforrcity in axis orientation causes double refraction to cancel. Consider an orthonormal base vector set, say vertical, in the direction of glacier flow, and horizontal and normal to glacier flow. By direction cosines the glacier can be divided into three equivalent thicknesses of ice with pure crystal axis orientations. The component with vertical axes does not exhibit double refraction and can be ignored. The equivalent thickness of ice available for affecting double refraction is equal to the difference of the other two components. Hence it is necessary to have a very strong prefered horizontal orientation to make double refraction visible. Sounding at frequencies of about 60 HHz, double refraction would require 31 at least 120 m of ice to produce a 90° phase shift. Jiracek (1965) reported that at South Pole Station, using a 30 MHz system, a bottom echo could not be received Kith antennae broadside and parallel. Maximum receiver power occurred when the antennae were perpendicular and horizontal. Jiracek interpreted this as a 90° rotation from the original transmitted pulse. "On the Skelton Glacier, bottom echo amplitude was practically independent of receiving antenna orientation in the horizontal plane." Jiracek interpreted this as a transformation of liner polarized radiation into near circular polarization by double refraction. 4.4.3 DETECTING DC0BL1 REFRACTION The orthonormal basis with one axis vertical, which maximizes the effective double refracting thickness defines the privileged directions in its two horizontal axes. These are the directions in which all of the transmitted power is either in the ordinary ray or the extraordinary ray. In these directions double refraction is not visible. Bowever upon arrival at the bedrock the ideal reflector model fails by returning only a component fraction of polarized power instead of maintaining all polarization. The remaining reflected power is returned unpolarized. A receiver antenna based cn dipoles, when rotated cannot distinguish between eliptically polarized radiation and combined linear and unpolarized 32 radiation. All that is possible is a determination of the major axis of returned power. If this differs from the transmitted axis, then double refraction has been detected. By rotating the transmitter antenna and repeating the procedure two transmitter antenna orientations should appear where no double refraction is evident, i.e. the major receiver power axis coincides with the transmitter pcwer axis. At these positions an estimate for bedrock depolarization can be made. Once this is known it may be possible tc estimate the amount of double refraction and hence draw a conclusion about the ice fabric. 4.4.4 FARADAI EFFECT In many substances when plane-polarized radiation traverses in a direction parallel to an applied magnetic field, the plane of vibration is rotated. The amount of rotation Qis proportional to the field strength fi, and tc the distance traversed L. i.e. 0 = VLH where V, the Verdet constant is determined by the substance and the wavelength. For water M equals 0.0131 minutes Oersted-1cm-1 at the Sodium D lines. In the infrared V is the order of 10~3 minutes Oersted_lcm-* (Jiracek, 1967). When radiation is reflected back through the medium the field direction is effectively reversed, and the rotation due 33 to the second traverse adds to the rotation due tc the first traverse. This is unlike natural optical activity which cancels exactly. If Faraday rotation in ice due to the lccal magnetic field is detectable, it can be distinguished from double refraction by observing the average angular variation of receiver maximum from transmitter orientation, averaged over all transmitter directions. Jiracek (1965) has considered the magnitude of the Faraday effect at the South Pole. He determined that rotation in the infra-red would be only 5°. Since the Verdet constant decreases with frequency (Jiracek, 1965) the effect should be negligibly small, even in the very thickest ice. 4.4.5 PHOTO-ELASTICITY A transparent isotropic medium becomes optically anisotropic when subjected to mechanical stress. The privileged directions are along the directions of the principal stresses. Since photo-elasticity is optically identical to double refraction, the two effects cannot be distinguished. It is unlikely that any information regarding the ice fabric can be determined a posteriori from information gathered by studying the effects of alpine or small valley glaciers upon polarized radio echo sounder radiation. All that may be possible is the detection of one or more of these 34 effects, 4.4.6 DIGITAL RECORDS A proposed digitizer having 8 bit resolution and 10 ns channel separation will be used to record the received envelope as provided by the output of the video amplifier. 10 ns channel separation yields a Nyguist frequency of 50 HHz so that no receiver power will alias into a lower frequency. By deconvolving fading patterns using the transmitter pulse as a source function, and averaging over several records greater rangy accuracy should result and intermediate reflectors in the ice should become visible. Gross bottom roughness may be estimated by observing the spread in time of returned power from the bottom echo. Of particular interest would be the detection of fine interglacier structure near the bedrock. 4.5 CONCLUSION This thesis has presented a basis for the design of a UHF radio echo sounder for the purpose of studying glaciers in mountainous terrain, Specific design parameters have been presented for a radio echo sounder to be built at the University of British Columbia. These parameters have been discussed and according to normal radio altimetry practices and engineering principles practical limits cf the technique 35 have been proposed. The design has followed as a basis a radio echo sounder built and operated by the Department of Energy, Mines and Resources, Ottawa, Canada, and Environment Canada, operating at 620 MHz. He suggest that UHF radio echo sounding will provide a highly mobile method of sounding the alpine and valley glaciers which have previously evaded successful study. 36 BIBLIOGRAPHY - Auty, R. P., and Cole, R. H. 1952. Dielectric properties of ice and solid D20. The Journal of Chemical Phjsics, Vol. 20, No, 8, p. 1309-1314. Bailey, J. T., Evans, S, and Robin, G. de Q. 1964. Radio echo sounding of polar ice sheets. Nature, Vol. 204, No. 4967, p. 420-421. Baldis, H. A,, and Aazam-Zanganeh, J, 1973, High speed single event sampler. Reviews of Scientific Instruments, Vol. 44, No. 6, p. 712-714. Beckmann, P., and Spizzichinc, A. 1963. The scattering of electromagnetic waves from rough surfaces. Oxford^ Pergamon Press. Berry, M. V, 1972, On deducing the form of surfaces from their diffracted echoes. Journal cf Phvsics A: General Phvsics, Vol. 5, p. 272-29TT Berry, M• V. 1974. Theory of radio echoes from glacier beds. ££££§®ili2SS of the Symposium on Remote Sensing in Glacioloav^ Cambridge^ September J974, in press. Bleaney, B. I., and Bleaney, B. 1957. Electricity and magnetism. Oxford^ Clarendon Press. Bogorodskiy, V. V., and Fedorov, B, A. 1968, Radar sounding of glaciers, Soviet Antarctic lx£§dition Information Bulletin, Vol,~67~io.~ 657~p. ~511-518~in~AGU~English translation. Bogorodskiy, V. V., and Fedorov, B. A. 1970. Radar probing of Severnaya Zemlya Glaciers. i£JSnicheski^ i Antarkticheskiv MS£llSO-IssledovatelJ[ski^ Jnstitutx Tr u dy, (Translated by Israel Program for Scientific Translations. Jerusalem, 1971, p. 1-11). 37 Bogorodskiy, V. V., Rudakov, V. N. , and Tyul'pin, V. A. 1965. Electromagnetic probing of the Antarctic Ice Sheet. Soviet Physics - Technical Physics, Vol. 10, No. 6, p. 886-888. Bogorodskiy, V. V., and Trepov, G. V. 1968. Radar measurements of the thickness of mountain glaciers. (Translated from Zhurnal Tekhnicheskcj Fiziki, Vol. 38, No. 8.) Soviet Physics - Technical Physics, Vol. 13, No. 8, 1969, pT 1135-367 Calkin, P. E. 1971, Radio-echo sounding records from southern Victoria land. Antarctic Journal, Vol. 7, p. 208-209. Clarke, G. K. C, and Goodman, R. (In press) Radio echo sounding and ice temperature measurements in a surge type glacier. Journal of Glacioloqj. Clough, J. W. 1973. Radio echo sounding: brine percolation layer. Journal of Glaciology, Vol. 12, No. 64, p. 141-143. Clough, J. W., and Bentley, C. R. 1968. Measurements of electromagnetic wave velocity in the East Antarctic Ice Sheet. IASH Publication 86, p. 115-128. Collin, R. E. 1966. Foundations for microwave engineering. New York*. McGraw - Hill. Cook, J. C. 1960. Proposed monocycle-pulse very-high-frequency radar for air-borne ice and snow measurement. Transactions of the American Institute cf Electrical Engineer, PtT iT VolT ~797 p. 588-5 94. Cumming, W. A. 1952. The dielectric properties of ice and snow at 3.2 centimeters. Journal of Allied Physics, Vol. 23, No. 7, p. 768-773. 38 Davis, J. L. 1973. The problem of depth sounding temperate glaciers. Unpublished, M.Sc Thesis, University of Cambridge. Davis, J. L., Halliday, J. S., and Miller, K. J. 1972. Radio echo sounding of a valley glacier in last Greenland. Journal of Glaciologj, Vol. 12, No, 64, p. 87-91. Evans, S. 1963a. Radio techniques for the measurement of ice thickness. Polar Record, Vol. 11, No. 73, p. 406-4 10. Evans, S. 1963b. International co-operative field experiments in glacier sounding. Polar Record, Vol. 11, No. 75, p. 725-726. Evans, S. 1963c. Radio techniques for the measurement of ice thickness. Polar Record, Vol. 11, No. 75, p. 795. Evans, S. 1965. Dielectric properties of ice and snow - a review. Journal of Glaciolocjj, Vo. 5, No. 42, p. 773-786. Evans, S. 1966. Progress report on radio echo sounding. Polar Record, Vol. 13, No. 85, p. 413-420. Evans, S. 1969. Glacier sounding in the polar regions: a symposium. Geographical Journal, Vol. 135, Pt. 4, p. 547-563. Evans, S., Drewry, D. J., and Robin, G. de C. 1972. Radio echo sounding in Antarctica. Polar Record, Vol. 16, No. 101, p. 207-212. Evans, S., and Robin, G. de Q. 1966. Glacier depth-sounding from the'air. Nature, Vol, 210, No. 5039, p. 883-885. 39 Evans, S., and Smith, B. M, E. 1969. A radio echo equipment for sounding in polar ice sheets. Journal of Scientific Instruments ^Journal of Phjjsics E}_, Series 2, Vol. 2, p. 131-1367 Evans, S., and Smith, B. M, E. 1971. Badio echo exploration of the Antarctic Ice Sheet. Polar Record, Vcl. 15, Nc, 96, p. 336-338. Fitzgerald, W. J., and Earen, J. G. 1974. The dielectric properties of Antarctic ice. PloceedJ.ngs cf the Sjmjgosium on Remote Sensing in Glaciolog^^ Camhridgex September J974, in press. Glen, J. W., and Paren, J. G. 1974. The electrical properties of snow and ice. Proceedings of the Sjm^osium on Remote Sensing in Glaciolocj2x Cambridge^ September J974, in press. Goodman, R. H. 1970. Radio-echo sounding on temperate glaciers: a Canadian view. (Gudmandsen, P. ed.) Eioceedin^s of the International Meeting on ladioglacjJBlogv^^^ Lyngby7 Technical University of Denmark, Laboratory of Electromagnetic Theory, p. 135-146. Goodman, R., et al. 1975. Radio soundings on Trapridge Glacier, Yukon Territory, Canada, by R. Goodman, G. K. C. Clarke, G. T. Jarvis, S. G. Collins, and R, Metcalfe. Journal of Glaciolog_y, in press. Gudmandsen, P. ed. 1970. Proceedings of the international meeting on radioglaciology, Lyngby, May 1970. Laboratory, of Electromagnetic Theory the Technical University of Denmark7 L^ngb^, R 86, 170 p. Gudmandsen, P. 1972. Radio echo sounding of pclar ice. laboratory of Electromagnetic Theory the Technical ^ilversitv of Denmarkt jLyngbv, D 170, 27 p. 40 Gudmandsen, P. 1973. Radioglaciology soundings at proposed drill sites. Laboratory of Electromagnetic Theoryx the Technical University of Denmark^ Iyngjbl» E 185, 20 pT Harrison, C. H. 1970. Reconstruction of subglacial relief from radio echo sounding record. Geophysics, Vol. 35, No. 6, p. 1099-1115. Harrison, C. H. 1971. Radio echo sounding: focusing effects in wavy strata. Geophysical Journal of the Royal Astronomical Society,~Vol7 247 p7 383-40 0. Harrison, C. H. 1972. Radio propagation effects in glaciers. Ph.D. thesis, Cambridge University. Harrison, C. H. 1973. Radio echo sounding of horizontal layers in ice. Journal of Glaciology, Vol. 12, No. 66, p. 383-397. Hattersley-Smith, G., Fuzesy, A., and Evans, S. 1969. Glacier depths in northern Ellesmere Island: airborn radio-echo soundings in 1966. Ottawa,. Defence Research Bcardx JOperation Hazen 3 6p,~23 p. Jasik, H. ed. 1931. Antenna engineering handbook. New Ycrkx McGraw - Hill. Jenkins, A., and White, H. E. 1957. Fundamentals cf optics. New Yorkx McGraw - Hill. Jiracek, G. R. 1965. Radio sounding of Antarctica ice. M.Sc. thesis, University of Wisconsin. Jiracek, G. R. 1967. Radio sounding of Antarctic ice. Research Report Series Number 67-Jx The University of Wisconsin geophysical and Polar Research Center,.~ 41 Jiracek, G. R.f and Bentley, C. R. 1965. Dielectric properties of ice at 30 Mc/sec. Journal cf Glaciclogy, Vol. 6, No. 44, p. 319. Kraus, J. D. 1940. The corner-reflector antenna. Proceedings of the Institute of Radio Engineers, Vol. 28, p. "513-519.~ Kraus, J. D. 19 50. Antennas, New Ygrkx McGraw - Hill. Linlor, W. I. 1974. Electromagnetic reflection from multilayered models. P£2£Si^iH3s of the Symposium cn Remote Sensing in Glacioloay~Cambridgex September J974, in press. ~~ ~ Longhurst, R. S, 1957, Geometrical and physical optics. London^ Longmans^ Green and Co. Nye, J. F., Kyte, R. G., and Threlfall, D. C. 1972. Proposal for measuring the movement cf a large ice sheet by observing radio echos. Journal of Glaciolocjy, Vol. 11, No. 63, p. 319-325. Oswald, G. K. A. 1974. Investigation of sub-ice bedrock characteristics. Proceedings of the Symposium on Remote Sensing in Glaciologyx Cambridqex September .1974, in press. Page, D. F., and Ramseier, R, 0. 1974. Application cf active radar techniques to the study cf ice and snow. 2^ the Symposium on Remote Sensing in SiSSiSlSSIjt Cambridgex September 1974, in press. Paren, J. G. 1970, Dielectric properties of ice, Ph.D. thesis, Darwin College, Cambridge. Paterson, W. S. B. 1969, The Physics of Glaciers. Oxfordx Pergamon Press. 42 Binker, J. N. 1964. Radio echo sounding and strain rate measurement in the ice sheet of North-west Greenland; 1964. Polar Record, Vol. 12, No. 79, p. 403-405. Ragle, R. H., and others. 1964. Ice cere studies cf Ward Hunt Ice Shelf, by R. H. Ragle, R. G. Blair and L. E. Persson. Journal of glaciolocjj. Vol. 5, No. 37, p. 39-59. Robin, G. de Q,, Evans, S., Drewry, C. J., Harrison, C. E., and Petrie, D. L. 1970. Radio echo sounding cf the Antarctic Ice Sheet. Antarctic Journal, Vol. 6, p. 229-232. Robin, G. de Q., Swithinbank, C. W. M., and Smith, B. M. E. 1968. Radio echo exploration of the Antarctic Ice Sheet. IASH Publication 86, p. 97-115. Rossiter, J. R., and others, 1973. Radio interferometry depth sounding: part II - experimental results, by J. R. Rossiter, G. A. LaTorraca, A. A. Annan, C. W, Strangway and G. Simmons. Geophysics, Vol. 38, No. 3, p. 581-599. Smith, B. H, E. 1971. Radio echo studies of glaciers. Ph.D. thesis, Cambridge University. Smith B. M. E., and Evans, S. 1972. Radio echo sounding: absorption and scattering by water inclusions and ice lenses. Journal of Glacioloay, Vol. 11, No. 61, p. 133-146. Strangway, D. W., Simmons, G., LaTorraca, G., Watts, R., Bannister, L., Baker, R., Redman, J. C., and Rossiter, J. R. 1974. Radio-frequency interferometry - a new technigue for studying glaciers. Journal of Glacioloc], Vol. 13, No. 67, p. 123-132. 43 Swithinbank, C. 1968. Radio echo sounding cf Antarctic glaciers from light aircraft. IASH Publication 79, p. 405-414. Swithinbank, C. W. M. 1972. Field work. Radio Echo Sounding by the British Antarctic Survey. Polar Record, Vol. 16, No. 102, p. 411-412. Von Hippel, A. 1954. Dielectric materials and applications. New Yorkx Technology Press and Wiley, p. 12, p. 301. Waite, A. H. Jr. 1966. International experiments in glacier sounding, 196 3 and 1964. Canadian Journal of Earth Sciences, Vol. 3, No. 6, paper 17, p. 887-892. Waite, A. H. , and Schmidt, S. J. 1962. Gross errors in height indication from pulsed radar altimeters operation over thick ice or snow. Proceedings cf the Institiute of Radio Engineers, Vol. 50,~No.~ 6~ p. 1515-1520. Walford, M. E. R. 1964. Radio echo sounding through an ice shelf. Nature.* Vol. 204, No. 4956, p. 317-319. Walford, M. E. R. 1965. Radio echo sounding cf polar ice masses. Ph.D. thesis, Cambridge University. Walford, M. E. R. 1968. Field measurements of dielectric absorption in Antarctic ice and snow at very high freguencies. Journal of Glaciology, Vol. 7, No. 49, p. 89-94. . Walford, M. E. R. 1972. Glacier movement measured with a radio echo technique. Nature, Vol. 239, p. 93-95. Watts, B. D., England, A. W., Meier, M. F., and Vickers, R. S. 1974. Radio echo sounding of temperate glaciers at freguencies of 1 to 5 MHz. Proceedings of the Symposium on Remote Sensing in Glaciology^ Cambridge^ September J974, in press. 44 Weber, J. R., and Andrieux, P. 1970. Radar sounding of the Penny Icecap, Baffin Island. Journal of G la cj. elegy, Vol. 9, No. 55, p. 49-54, 45 APPENDIX Some considerations on the selection and use of thermistors for the purpose of making absolute temperature measurements in snow or ice. 46 1 INTRODUCTION In general, thermistors, when used as temperature measuring devices, are used singly or in pairs in some impedance net, that net being driven by some power supply, and also having an output, which is monitored by a detector. Frequently the thermistor is placed at the end of a transmission line (Fig. 1). Errors in precision and accuracy enter from numerous sources: from the thermistor itself, from the power supply or its configuration, from the the detector, impedance net or transmission line. The measurement of temperature can only be as good as the precision standard against which the thermistor was calibrated. If it has been assumed that the thermistor characteristic will fit a theoretical curve, then the accuracy can be no better than the quality of that fit. Of necessity one must assume that a given thermistor will be stable over the long term, although it is known that this is not necessarily the case; environmental factors such as stress or moisture may affect a thermistor's behaviour, and over a period of time a thermistor»s stucture may change. Preaging can reduce these effects, however they cannot be eliminated. If a thermistor is recoverable fcr recalibration after its period of use, it may be possible to monitor some cf these effects. POWER SUPPLY V V INTERFACE CB RIDGE) DETECTOR TRANSMISSION LINE FIGURE 1: GENERALIZED BRIDGE 48 It is the intent of this paper tc examine instrumental parameters, and to discuss how they may be used or determined, in order to optimize the precision with which the resistance cf a given thermistor in a fixed situation, can be determined. These parameters include: thermistor self-heating, nominal thermistor resistance, transmission line resistance and reactance, impedance net or bridge configuration, type cf bridge power supply, and guality of the detector. This examination applies equally to both calibration systems and field situations since both conditions can be completely described. 2 THERMISTOR CHARACTERISTICS 2.1 THERMISTOR SEIF-HEATIUG If we assume that a thermistor has spherical symmetry, and that the ambient temperature of the surrounding ice (or snow) is constant at T, then the steady state solution of the heat equation shows that the temperature of ice close to the thermistor can be no greater than T + 4,k? r <D xce where P is the power dissipated in the thermistor, K±ce is the thermal conductivity of ice (assumed tc be constant with T) and r is the radius from the center of the thermistor. Let 49 AT. = -7—7^ (2) ice 4frk. r ice and let AT+T be the temperature as indicated by the resistance cf the thermistor. It follows that AT > AT. I . = . , P (3) ice ' mm 47rk. r . ice min where rmln is the radius of the ice closest tc the thermistor; in effect the radius of the thermistor. Owing to the failure of our spherical approximation in (1) and tc the great variety in structure and shape of thermistors, it shall be assumed here that the relation in (3) is an eguality, where rm-£n must now be a typical radius. Manufacturers of thermistors generally provide figures for their thermistors that indicate the ability of the device to dissipate power into the surrounding medium. This •Dissipation Constant1 which shall be called Ec, is specifically defined as the amount of power reguired to raise the temperature of the thermistor 1°C above the ambient temperature. More conveniently from (3), in ice D = 4TTk. r . (5) c ice mm 50 Equation (4) clearly depends on the environment of the thermistor. Manufacturer's figures are usually given for the thermistor in still air. In ice Dc is at least a factor of three greater [Fenwal D-1; Eg. (5)], and although increases in It will improve the measurement precision, a factor cf three in Dc results in no more than 1.5dB improvement in precision. Hence for the examples used here, since Dc is generally difficult to measure or calculate, manufacturers' figures will be used. 2.2 THERMISTOR SELF-HEATING WITH WATER LAYER If the temperature of the ice is sufficiently close to the melting point that before reaching steady state the temperature of the thermistor reaches the melting point a layer of water will form arround the thermistor. Since the thermal conductivity of water is much smaller than that of ice, the thermistor will tend to self-heat greatly. This effect has been demonstrated in attempts tc measure the thermal conductivity of ice by using a thermal drill cable as a line heater, and attempting tc observe the logarithmic rise cf temperature with time. If too much power is supplied to the cable a water layer forms before the lcgarithmic approximation becomes valid. In another case, in temperate ice, the ice cannct conduct power away from the thermistor. The only available sink is in 51 the ice melt, hence steady state will never be approached. However after sufficient time the ice/water boundary should be sufficiently distant and large, that it may be modelled as stationary. In this case D = 4 TT k r . (6) c water mm v ' also if too much power is available, induced water currents may cause fluctuations in the thermistor temperature. Any system which must consider this case should be designed so that this effect is too small to be measurable. 2.3 THERMISTOR RESISTIVITY GRADIENT Thermistors have negative thermal coefficients of resistivity, which shall be called Bp. For most thermistors RT - -0.05°C-1 (7) and this figure will be used in all of the examples in this paper. 2.4 TIME CONSTANTS The 'time constant' of a thermistor, as defined by some manufacturers is the time required for a thermistor tc change its temperature 63% of the amount of temperature change of a value impressed upon it in a step change [Fenwal EMC-5]. For 52 a given thermistor this may vary from fractions cf seconds to minutes [Fenwal D-1] as a function of environment. For steady state temperature measurements a more useful time constant would be the time reguired for a thermistor tc reach 63% of #T above T, from the initiation cf power, but because of the effects of environment on Dc and hence AT, and also consideration of the fact that the twc constants as defined here are probably closely related, the latter time constant is almost certainly indeterminable, especially when the thermistor would be deployed in a bore hole in ice. The best that should be said about a thermistor being used to measure a steady state temperature is that the temperature it measures is between T and T+AT, both as defined before. It is necessary then that the allowable error due to self-heating must be the full value of T, and that in most cases this will not be reduced. 3 BRIDGES AND BRIDGE POWER SUPPLY. 3.1 POWER SUPPLY TYPES In this paper only two kinds of power supply will be considered. They are first a D.C. supply, and secondly an A.C. supply of angular freguency u . Further in this paper they will be shown to be both optimal when compared tc pulsed 53 supplies. 3.2 BRIDGE TYPES The simplest type of resistance measuring device consists of a current source driving the unknown resistance. A voltmeter then measures the voltage drop accross the resistance (Fig. 2A), A measure of the signal available is dV/dR. In this case Si-* <« Thermal noise voltage is proportional tc provided we assume that the thermistor is an ideal Johnson ncise generator. Signal to noise ratio is thus proportional to i//R. All analog ohmmeters and digital chmmeters work in this fashion. The difficulties involved in taking this approach is that with analog meters, they rarely have enough dynamic range cr precision to be useful, and with digital meters long term linearity and short term thermal stability are generally not good enough so that overall accuracy approaches the resolving capability of the instrument. This is particulary the case when different instruments are used for calibration and field measurements. Null detectors have the advantage that they do not require the dynamic range or linearity of the •chmmeter* type cf instrument. However, they may still be thermally 54 FIGURE 2: BRIDGE CONFIGURATIONS 55 sensitive, ana they cannot be used for 'instant* measurements. This is a problem if continuous measurements in time ever a large temperature range are reguired. For making single measurements of steady state temperatures, null detectors are well suited. Figures 2B and 2C show two possible configurations. The chief difficulty in implementing a system generalized by the type in Figure 2E lies in providing an accurate low impedance voltage reference vB/2 exactly half of the primary bridge supply (In all cases vB refers to the B.M.S. Voltage). Figure 2C represents a Sheatstcne bridge with the four arms equal. In Figure 2B v dV = _B dR 4R and noise voltage is times smaller than in case A. Signal to noise voltage ratio is then proportional tc VB /8T3" If power dissipated in the thermistor is the same in both cases V 2 i2R = 7J- (10) and signal to noise ratios may be compared. It follows that S/U voltage ratio for case A is ^2 times greater than for case B, and is two times greater than for case C (Fig. 2C). 56 Difficulties in constructing relatively noiseless current and voltage sources would likely counter the advantages cf case A or B over case C. For this reason, and for ease in calculations, case C will continue to be used. 3.3 BRIDGE AND DETECTOR RESOLUTION Let AT* be the desired temperature resolution. Then M = AT*RT (11) where AR is the necessary resolution in terms of resistance. From (9) and (11) I?- = —*— (12) AV AT*RT where Av is the required voltage resolution cf the detector. Johnson noise power from the bridge is ideally Pn = Y= 4kTB (13) where Vn is noise voltage, k is Boltzmann's constant, T is in degrees Kelvin, and B is the bandwidth of the detector. A convenient measure of the quality of the detector may be defined as S = ^ = noise figure (14) n V n where AV now represents the detector's best resolving ability Recall from (10) that 57 V P = -2— 4R From (10), (12), (13), and (14) s 2 PR„ AT* = (16^ X15) T But from (4) P = ATD (16) c A minimum of the sum of AT and AT* occurs at AT* AM -TT- = AT (17) It follows that AT = (^4^(18) c T AT* = (32XT)1/3 (19) c T AT + AT* = (108Sn2kTB)l/3 (2Q) D K m c T Equations (18), (19) and (20) are useful for determining the optimum resolution of any system as the parameters approach the ideal. More realistically it would be convenient to have an expression for the optimum in terms of the detector resolution Ay. From (13), (14), (18), (19) and (20) 58 AT = ( AV2 1/3 (21) RBCRT AT* = ( 8AV2 1/3 (22) AT + AT* = ( (23) From (21), (22) and (23) detector parameters and power levels may be optimized, and overall accuracies known. Consider for example a thermistor with Dc = Imwoc-1 which shall be operated at 10K^. Suppose our detector has an input noise voltage of ivv. Then Here signal power has been assumed to be egual to noise power, Generally it would be desirable to have signal tc noise ratios cf at least 10dB. Then 3.4 D.C. BRIDGES If a D.C bridge is used with a good detector [eg. ANALOG DEVICES chopper amp. Model 261K] it would have input noise on AT + AT* = 0.001°C AT + AT* - 0.0023°C 59 the order of 1vv P-P with a bandwidth to 10Ez. Since a reasonable response time is desirable, a bandwidth cf 5 Hz is minimal. Input noise voltage drift of 0.1VV°C-1 would boost effective input voltage noise to about 3.5W. This would boost a usable Av to 12PV, and in our example AT + AT* = 0.0054°C This may be considered a practical limiting accuracy for a thermistor with Dc = 1 mwoc-1 and B = 10Kfi, when driven by a D.C. system. Other difficulties involved in using a D.C. system arise from thermal voltage offsets, and from the proximity of 50 Hz or 60 Hz sources. The first may be helped by selecting a chopper stabilized detector or similar detector designed for thermal immunity. The second, which may be large enough to obscure measurements in spite of a sharp roll off should be helped by using good shielding and grounding (the most likely mechanism would be that the transmission line, acting like an antenna, would provide sufficient common mode signal to overload the detector input). 3.5 ft, C. EBIDGES It is possible to get amplifiers which operate at audio frequencies, that have considerably less input noise voltage per unit bandwidth than D.C. amplifiers. Detectors, either phase-locked, or simple, are easily designed. Bandwidths may 60 be limited to less than 100 Bz, which will keep input noise voltage well below the best available D.C. detectors. For systems where extremely high precision is necessary, the designer may consider using an a.C. voltage source tc feed his bridge. However, new design problems accompany the choice of an A.C. source. The operating frequency should be kept as low as possible. The reason is twofold: first, since a lew bandwidth is desirable, a low center frequency would minimize the need for a large Q; second and predominant, the effects of stray reactance in the bridge, and particularly in the transmission line to the thermistor would be minimized. Belcw 100 Hz flicker noise predominates and all the difficulties cf D.C. bridges ensue. 3.6 OPTIMUM BRIDGE SUPPLIES It is possible to use a pulsed power supply or seme ether form of intermittent supply. However in no case can one improve on either a pure D.C. or pure sine wave source if one considers the signal to noise ratio. This can be shown as follows.Since all measurements must be of finite duration we can assume that the power supply pattern repeats regularly. Consider its Fourier decomposition. The maximum signal to noise ratio occurs when all the signal power is confined to the minimum bandwidth; i.e. in one component. Any attempt cf 61 spreading the signal power among more than one component necessarily increases the required bandwidth of the detector and thus increases noise. Hence a single component, sine wave or pure D.C. is optimal. 4 TRANSMISSION LINE EFFECTS 4.1 TRANSMISSION LINE RESISTANCE Presumably it is possible tc determine the resistance of the transmission line being used, or at least get an estimate well within the required accuracy. This may then be corrected for when determining the actual thermistor resistance. If a three or four wire transmission line is used, the problem can be eliminated entirely. 4.2 TRANSMISSION LINE REACTANCE In an A.C. bridge, it is desirable to know what the maximum transmission line capacitance C is which will still permit a null of amplitude v. If C is sufficiently small, then its effect is to phase shift the current, amplitude changes being second order. The constraint on C is a)RC < ^ (24) B If the detector is phase-locked then 62 ^observed —//R j ioC actual (25) To a first approximation AR = R - R = f(coRC)2 (26) actual observed 2 ' provided the transmission line is short (this error will usually be sufficiently small that an estimate of C will yield a correction AR of sufficient accuracy). 5 EVALUATION OF AVAILABLE SYSTEMS (DMM.S) On the basis of (16) and the relation cf AT* tc P (from (13) (14) and (15)) AT* = (27) Rt7PR~ It is possible to evaluate and compare measurement systems for a given R and Dc. The following digital multimeters have been evaluated as thermistor measurement systems with respect to thermistor selfheating, displayed precision, guaranteed accuracy, each when used with a FENHAL GB34P2 thermistor - 10K < R < 15K, D c= Imwoc-i. 63 FLUKE MODEL 8 100A FLUKE MODEL 8000A DANAMETER 2000 DATA PRECISION 245 SYSTRON DONNER 7205 SYSTRCN DONNER 7050 SYSTRON DONNER 7005 TABLE 1: DIGITAL MULTIMETERS Table Two lists pertinent data. CONCLUSION Present technology can easily yield a device for measuring thermistor resistances within 0.01°C, however the value of achieving this resolution of absolute temperature measurements can be guestioned. In deep boreholes, where the thermistor resistances are used to infer both absolute temperatures and temperature gradients, the thermistors are not recoverable and long term stability limits the accuracy possibly tc only 0.4°c (Muller S Stolton, 1953) although 0.08<>c is more common [Fenwal- TI-1] and0.02<>C is possible (Beck, 1956). 64 Ar Errors in Temperature Measurement vs..Power to a FENWAL GB34P2 Thermistor, for Seven Digital Voltmeters The diagonal line represents thermistor self-heating. The thick error bars represent the meter resolution. The thin error bars represent the meter accuracy. The numbers in circles indicate the points plotted from Table 2. FIGURE 3: DIGITAL "MULTIMETER ERRORS 65 UNIT RANGE POWER AT AT* (1) AT* (2) FLUKE 8100A 12Kfi 120yW 0.12°C 0.002OC 0.02OC CD 120 Kfi 13yW 0.013«c 0.02«C 0.2°C DATA PRECISION 245 20Ktt 1, 3mW 1.3«c 0.002«C 0. 1°C DANAMETER 2000 ® 20Kfi 140yW 0.14°C 0.02OC 0. 04 OC FLUKE 8000A 20Kfi 120yW 0.120C 0.02°C 0.06OC ® SYSTRON DONNE R 7050 150Kfi 1. 2yW 0.001°C 0. 2°C 0.28°C SYSTRON DONNER 7205 130Kfi 1.2yW 0.001«C 0.002OC 0.01°C 13KR 120yW 0.12°C 0.0002«C 0.001°C SYSTRON DONNER 7005 ® 130Kfi 30yW 0.03°C 0.02«C 0.04OC 13Kfi 3mW 30C 0.002°C 0.004OC TABLE 2: DIGITAL HULTIKETER ERRORS Data lines followed by numbers in circles are graphed for comparison in Figure 3, AT*(1) is the resolution determined by the number of available digits. AT* (2) is the effective guaranteed accuracy of the meter. In shallow experiments such as snow pack studies, or permafrost detection, fine temperature resolution is not required since in one case the temperature variations are gross and nonlinear, and in the latter the experimenter generally wishes only to detect subfreezing temperatures, not to estimate them. The greatest value in achieving fine resolution of thermistor resistances lies first in thermistor calibrations (it is possible to achieve 0.03$ accuracy easily and rapidly) and in experiments where temperature transients are measured. Thermistor measurement technique is an important consideration in any temperature measurement system where 66 optimum accuracy is required. Errors due to thermistor stability, reference temperatures, and measurement are comparable in magnitude. As the quality of thermistors and thermometers improve, so should the techniques of thermistor use. 67 BIBLIOGRAPHY Baxandall, P. J. 1968. Noise in transistor circuits, part 1. Wi£§lgss World, November 1968, p. 388-92. Baxandall, P. J, 1968. Noise in transistor circuits, part 2. Wireless World, December 1968, p. 454-59. Beck, A. 1956. The stability of thermistors. Journal of Scientific Instruments, Vol. 33, p. 16-18. Beck, A. E. 1963. Lightweight borehole temperature measuring eguipment for resistance thermometers, Journal cf Scientific Instruments, Vols . 40, p. 452-47" Bosson, G., Gutmann, F., and Simmons, 1. M. 1950. A relationship between resistance and temperature of thermistors. Journal of Applied Physics, Vcl. 32, No. 2, p. 1267-68. " Carslaw, H. S., and Jaeger, J. C. 1959. Conduction cf heat in solids, second edition. Oxford Clarendon Press. Clarke, G. K. C, and Goodman, R. (In press) Radio echo sounding and ice temperature measurements in a surge type glacier. Journal of Glaciology. Classen, D. F., and Clarke, G. K. C. 1972. Thermal drilling and ice temperature measurements in the Rusty Glacier (in Bushnell, V. C. and Ragle, R. E. Ed. Icefield Ranges Research Project. Scientific Results. Vol. 3. New York, American Geographical Society; Montreal Arctic Institute of North America, p. 103-16). Doucet, Y., and Guignard, J. P. 1952. Essai d'interpretation de la loi~donnant la resistance des "thermistors" en fonction de la temperature. Academie des Sciences-Ccmptes Rendus, Vol. 234, No. 19, p7 1856-58." 68 Garfinkel, C. I. 1974. How to match readouts to temperature transducers. Electronics, vol. 47, Ho.. 24, p. 117-123. Greenhill, E. B., and Whitehead, J. R. 1949. An apparatus for measuring small temperature changes in liguids. Journal of Scientific Instruments, Vol. 2 6, p. 92-95. Harrison, W. D. 1972, Temperature of a temperate glacier. Journal of Glaciology, Vol. 11, So. 61, p. 15-29. Jarvis, G. T. (unpublished) Thermal studies related to surging glaciers. (M.Sc. Thesis, U.B.C. 1973). Jarvis, G. T., and Clarke, G. K. C. (unpublished) The thermal regime of Trapridge Glacier and its relevance to glacier surging. Jessop, A. M. 1964. A lead-compensated thermistor probe. Journal of Scientific Instruments, Vol. 41, p. 503-504. Jessop, A. M., and Judge, A. S, 1974. Temperature measurement in boreholes for the mining industry. division of Seismology^ Earth Physics Branchx Department of Energy^ Mines and Resources^ Ottawa^ Canada. letzter, S., and Webster, ft. 1970. Noise in amplifiers. IJEJ Spectrum, August 1970, p. 67-75. ~ Lliboutry, L. 1971. Permeability, brine content, and temperature of temperate ice. Journal of Glaciolcgy, Vol. 10, No. 58, p. 15-29. Misener, A. D., and Thompson, L. G. D. 1952. The pressure coefficient of resistance of thermistors. Canadian Journal of Technology, Vol. 30, p. 89-94. Muller, R. H., and Stolton, H. J. 1953. Use of thermistors in precise measurements of small temperature differences. Analytical Chemistry, Vol. 25, No. 7, p. 110 3-06. 69 Paterson, S. B. 1972. Temperature distribution in the upper layers of the ablation area of Athabasca Glacier, Alberta, Canada. Journal of Glaciology, Vol. 11, He. 61, p. 31-41. Staley, R. C. 1952. Performance characteristics of Sanbcrn rod thermistors. American Meteorological Society Bulletin, Vol. 32, No. 2, p7~ 67-727" Stuart, J. R. 1973. An approach to audio amplifier design, part 1. Wireless World, August 1973, p. 387-91, Stuart, J, R, 1973, An approach to audio amplifier design, part 2. Wireless World, September 1973, p. 439-46. Stuart, J. R. 1973. An approach to audio amplifier design, part 3. Wireless World, October 1973, p. 491-94. Technical Note: Thermistor Manual. FENWAL ELECTRON ICS, INC., EMC-5. Technical Note: [Thermistor] Stability and Reliability Characteristics. FENWAL ELECTRONICS, INC., TC-1. Technical Note: Considerations in the testing cf thermistors. FENWAL ELECTRONICS, INC., TD-2, EM-34/ Revision 2. 

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