Combined Radar-Acoustic Sounding System

J. M. Marshall, A. M. Peterson, and A. A. Barnes, Jr.

Acoustic pulses at 85 Hz (4 m) directed vertically into the lower atmosphere have been tracked by a

36.8-MHz (8-m) pulse doppler radar. Signal-to-noise power ratios in excess of 10 dB were obtained to a

height of 1.5 km in the initial tests under conditions of calm winds. This technique has the potential

of providing temperature soundings of the lower atmosphere for pollution studies and short-range

terminal weather forecasts.

Introduction

In a recent article in Applied Optics, Derr and Little'

compared remote sensing techniques capable of prob-

ing the lower few kilometers of the atmosphere. This

report concerns a remote sounding method not coveredin the above report that is capable of monitoring the

temperature profile of the lower atmosphere on a con-

tinual basis under conditions of small atmosphericturbulence. This method is a combination of radar

and acoustics to provide a vertical temperature sound-ing system and has been given the acronym RASS.Briefly, a sound packet directed vertically into the

atmosphere is tracked by a doppler radar, and the speedof the acoustic packet provides the in situ air tempera-ture.

Atmospheric pollution becomes critical under condi-tions of light winds when a temperature inversion trapsthe pollutants in the lower part of the atmosphere.Along with the winds and the flux of pollutants, theheight and strength of the temperature inversion are

the determining factors in the severity of the pollutionproblem. Hence an essential ingredient for effectivepollution control during periods of strong inversions is amethod of actually monitoring the inversion and thetemperature profile in real time. The RASS appearsto be capable of providing such profiles every few

seconds while emitting only minor amounts of acousticand rf noise.

The system also has potential applications in the

area of short range forecasting. Monitoring of the

temperature profile would lead to more accurate pre-

dictions of the onset and dissipation of fog and lowstratus.

J. M. Marshall is now with ESL, Inc., Sunnyvale, California

94086; A. M. Peterson is with Stanford University, Stanford,

California 94305; and A. A. Barnes, Jr., is with AFCRL, Bed-

ford, Massachusetts 01730.Received 10 February 1971.

Background

Prior publications concerning this technique2 -7

detailed the theoretical aspects of the problems, but theinitial attempts at application were terminated be-cause of the failure to obtain usable signals beyond 30m from the source. Upon reviewing these papers, it

was apparent that failure of the technique was not dueto inherent vagarities of the atmosphere but rather toan unfortunate selection of equipment parameterscausing an unfavorable interaction with the atmosphere.In particular, the acoustic wavelengths had been takento be very short and, because considerable power was

utilized, caused the acoustic waves to change into shockwaves, which then dissipated the energy very rapidly.This suggested that longer wavelengths be employedand that an array of acoustic sources be used to providea large amount of energy. An array would direct moreof the energy vertically and spread the energy densityin the near field so as to avoid the formation of shockwaves. Both the absorption of sound in air and sys-

tem sensitivity limitations can be shown to prevent allbut short range measurements at the high frequenciesemployed in the previous experiments. 8

TheoryAn acoustic wave traveling through the atmosphere

may be viewed as a local condensation of the air followedby a rarefaction. These density variations cause achange in the dielectric constant of air that reflects orscatters a small part of the electromagnetic energy.When the acoustic source and the radar are collocated,and under the ideal conditions that the wavefronts ofboth the acoustic and radar waves are spherical withtheir center at the source point, the radar energy back-scattered from the acoustic wave will come to a focusat the radar set. This is in contrast to the l/R 2 one-way spreading loss associated with scattering from

naturally occurring dielectric fluctuations of the atmo-sphere such as is associated with clear air turbulence.The amount of rf energy returned to the radar from

108 APPLIED OPTICS / Vol. 1t, No. 1 / January 1972

m 0 -ZsI-z

W

It _

3- -10

>

0U

0

W -20-

i -IJJ

o .. 30-La.

X~ -40--

Fig. 1. Reflectionpulse lengths of 10

Xe a X

coefficient vs wavelength ratio for acousticand 100 wavelengths (e, radar wavelength;X., acoustic wavelength).

naturally occurring dielectric fluctuations is so smallthat it can be detected only by the most powerful andmost sensitive radars.

In addition to focusing the scattered energy, RASSderives an advantage from the spatial coherence of thepartially reflecting surfaces created by the acousticwavecrests. The electric fields scattered from eachwavecrest will add in phase at the receiving antenna ifthe wavecrests are spaced one half the electromagneticwavelength, Xe. This is achieved by emitting a pulse ofsinusoidal acoustic waves with wavelength Xa adjustedso that Xa = (/ 2)Xe. Under these conditions thepower of the returned signal increases as the square ofthe number of interacting acoustic and rf waves.From Fig. 1 it can be seen that a tenfold increase in thenumber of interacting waves produces a 20-dB gain inpower when =e/Xa 2. It can also be seen that thematch in wavelengths must be more accurate whenlarge numbers of waves are involved. Wind, turbulence,and inhomogeneities of the atmosphere, such as tem-perature gradients, will impose limitations on the per-formance of such a system, since the reflected rf energyis sensitive to the spatial properties of the acousticwaveshape.

Under the assumption of ideal focusing from sinus-oidal acoustic waves, the expression for the receivedpower, P, is given by

P = 1.38 X 0 -"6PtPag7n {sin[(ka - 2k(nX/2)] }2r ~~R2 tJ (k. - 2k)(nx\a/2)

where P = radiated power for the radar (W); Pa=acoustic source radiated power (W); n = number ofwavelengths in acoustic pulse; g = acoustic sourcegain (ratio); R = distance from source to acousticpulse (m); ka = 27r/Xa (m-l); k = 27r/Xe (m-l).

The 1/R 2 loss in the above equation is due to the de-pendence of the reflection coefficient on the intensity ofthe spherically diverging acoustic wave.

This equation assumes that the radar and acousticbeamwidths are the same. This was not the case forthe experimental system, as the acoustic beamwidthwas much narrower than the radar beamwidth. Thesignal-to-noise power ratio is approximately 20 log(2R/Q-A) 20 dB less than that given by the aboveequation.' R and QA are the solid angles of the radarand acoustic beams, respectively.

The temperature profile is obtained from the dopplershift vs height information. Under the assumptionthat the vertical wind velocity is zero, the verticalvelocity of the acoustic pulse is a function of ambientair temperature; and if we measure the velocity by thedoppler shift, the temperature, in degrees Kelvin, isgiven by

(fdXe)2

where

fd = doppler frequency (Hz);Xe = radar wavelength (m);

q = (RIM)' = 20.05;R = gas constant;

-y = ratio of specific heatsfor air (-1.4);

M = mean molecular weightof the constituents ofthe medium.

From the above equation, it can be shown that tomeasure the temperature to within 0.5 K the dopplerfrequency must be resolved to 0.1%. When the acous-tic and radar wavelengths are properly matched, thedoppler frequency is equal to the acoustic frequency,thus the percent accuracy required of the frequencymeasurement is independent of other system param-eters. This doppler resolution requires a short-term (10 sec) radar frequency stability of one partin 109.

Since vertical wind velocities of 1-2 msec-' are ob-served in clear air under stable inversion conditions(gravity waves) and in convective situations, it mayprove necessary to make directional sightings withspatially separated terminals. Air temperature andwind velocities can be unambiguously determined by di-rectional sightings taken from four separate terminals. 2

The velocity of sound increases in moist air. Thetotal contribution of the atmospheric water vapor to thephase velocity of sound is typically less than 1 msec-'.Acoustic soundings' could be performed simultaneouslyto determine humidity profiles.

Equipment

A radar operating at 36.8 MVJHz was being assembled 9

to obtain returns from ionized meteor trails in the 80-110-km altitude region. This pulse doppler radar wasmade available for the experiment, thereby preselectingthe wavelengths to be utilized. Table I lists the pa-rameters of the radar and the antennas used in theRASS experiment as well as the pertinent acousticsource equipment parameters.

January 1972 / Vol. 11, No. 1 / APPLIED OPTICS 109

Acoustic source:Frequency (wavelength)Radiated acoustic powerPulse lengthPlanar array

GainBeamwidth

Radar:Frequency (wavelength)Radiated power (average)PRFPulse lengthYagi antennas

GainBeamwidth

Receiver noise bandwidthReceiver losses

-85 Hz (4 m)6.5 W100 wavelengths (variable)3 X 3 elements of 38.1-cm

loudspeakers-6.4 (ratio) (8.0 dB)e16.80

36.8 MHz (8.15 m)320 W40 kHz2 ltsec

10 dB4505 Hz3 dB

With the radar wavelength of Xe = S.15 m, the acous-tic wavelength X0\ should be taken as Xa = Xe/2 = 4.07m to obtain maximum return. A 3 X 3 planar arrayof loudspeakers was used, first, to provide a largeamount of radiated acoustic power, second, to avoid theproblem of shock waves being formed, and, third, todirect the major part of the energy into the vertical.Figure 2 shows the calculated intensity pattern of the 3X 3 acoustic array.

Since the acoustic wavelength will change with heightas the temperature changes, the transmitted acousticfrequency was manipulated so as to obtain the maximumradar return at a particular range. From Fig. 1 itcan be seen that for a large number of interacting wavesthis could give the in situ acoustic wavelength accu-rately enough to deduce the in situ temperature. Twofundamental disadvantages of this matching techniqueare, first, the loss in range resolution and, second, theloss of detailed information due to averaging over alarger depth of the atmosphere. Figure 3 is a plot ofthe calculated signal-to-noise power ratio as a functionof the acoustic wavetrain length and altitude. Thenoise power was calculated from the well-known rela-tion N = kTB; k = Boltzmann's constant, B = re-ceiver bandwidth. The equivalent system noise tem-perature was measured to be -11,000 K.

Details of the radar are given in a report by Nowak,9

and application of this equipment to the RASS isdelineated in the report by 1\MIarshall.8 The equipmentwas located on the Stanford University campus,and the initial soundings were taken in the summerof 1969.

Results

Figure 4 shows a typical sounding taken 20 July 1969with the range gate set at approximately 1 km. Thebottom trace is a reference channel for the acoustictone bursts. Each burst was 100 wavelengths long,

and the bursts were spaced approximately 17 see apart.Each of the pulses produced a clear signal that waswell out of the noise. It took approximately 3 seefor the burst to reach 1 km and about 2 see to travelthrough the range gate. Measurements could not bemade below about 600 m since the rf preamp saturatedduring the radar pulse and did not recover for about4 usec. This deficiency could be easily corrected,but this was not done, since the purpose of this experi-ment was to test the feasibility of such a soundingsystem.

The system operated best on calm days, and detect-able signal returns could not be obtained when windspeeds exceeded 7-10 msec-'. Occasional returns wereobtained ith surface winds in the 7-10-msec-range, but it remains to be proved that the effectsof wind and temperature can be separated. On theother hand, as pointed out in the Introduction, it isunder the conditions of low wind speeds associatedwith stable conditions that these temperature profileswould be most important.

On calm days it was found that the length of theacoustic wavetrain over which coherent reflectionsoccurred was about 200 m (50 wavelengths). Thiswas determined in two ways; the peak amplitude

o~~~~~~~~o

I X 0~~~~~~~~~~~~~900Fig. 2. Calculated intensity pattern of the acoustic array.

30 - NO ABSORPTION OF SOUNDLSO _ ESTIMATED MAXIMUM

MOLECULAR ABSORPTION-n-NUMBER OF WAVELENGTHS

25

0

I~ 20

0

0

I-

42

5-

0.1 0.2 0.4 0.6 0.8 1.0 2 4 6 8 10ALTITUDE (hm)

Fig. 3. Calculated signal-to-noise power ratio as a function ofaltitude for the experimental RASS terminal.

110 APPLIED OPTICS / Vol. 11, No. 1 / January 1972

Table I. Experimental RASS Parameters

RANGE GATE RADAR ECHOINTERNAL

IkmAL~~~___.... Si-e- kS -x :- <L . .1 T.____ __ _ _ _ _ __RECORDER MARK IIn CHiART NO RA292g 32 BDRUSH INS7-7 ~ ~ ~ ~ ~ i ____II;

AUU II. I TONE BURSTS _ _.

REFERENCE _ ---- -_CHANNEL

t171 I1717171 17\ -I Vk -

I i 1

t I i l

TIME (Isec/div)

Fig. 4. A typical sounding taken 20 July 1969 about 1 km in altitude. The acoustic frequency is 84.5 Hz.

(lid not increase after the number of wavelengthsexceeded 50, and, second, the rise time of reflectedsignals as the acoustic pulse entered the range gate gavean effective coherence depth of about 50 wavelengths.During periods of better reception on calm days themeasured signal-to-noise power ratio was about 12dB at 1 km, which is i good agreement with a cal-culated 14 dB for 50 wavelengths at 1 km. The2-dB difference is attributed to the effects of small-scale turbulence and atmospheric inhomogeneitiesthat affect the acoustic wave shape.

An attempt was made to match the frequencies formaximum response. With fifty waves interactingit can be seen from Fig. 1 that the main peak of theresponse curve would be fairly sharp, and indeed thesharp sensitivity of the doppler returns to the acousticfrequency of the tone burst was clearly evident in therecords. Since the acoustic frequencies in these testswere not determined more accurately than one half acycle, any derived temperature could be in error byas much as 3 K. Even though this experiment did notallow a precise temperature measurement, the sharp-ness of the match indicates that a sensitive system canbe built. However, we feel that for an operationalsystem, it probably would be better to determine thetemperature using just the doppler information ratherthan trying to determine the optimum acoustic fre-quency.

The top of the temperature inversion on 19 July 1969was just above 1 km according to the Oakland rawin-sonde sounding taken at 0500 PDT approximately30 km to the north. RASS records taken at 0800PDT show a sudden decrease of amplitude with heightthat we attribute to turbulence in the region just abovethe inversion. Thus the rate of signal strength decreasemay be taken as a measure of the atmospheric tur-bulence and could be used as an operational tool todetect low-level turbulence -and to monitor the forma-tion and dissipation of the nighttime low-level jet.

Conclusions

The experimental system has shown that on calmdays, when winds are 3 msec-' or less, radar signalsscattered from the acoustic wavetrain could be detectedto 1.5 km in altitude. Based on the results of theexperimental system, the RASS system conceptappears to be workable, but considerable work remainsbefore an operational system can be developed. Inparticular, it remains to make precise doppler fre-quency measurements and to compare the derivedtemperature profile with rawinsonde data taken simul-taneously. Because many of the functional elementsof the system were nonoptimal, the full potential of aRASS terminal has yet to be determined.

Experimental evidence with the 4-m acoustic wave-length indicates that a major effect of small-scaleturbulence and atmospheric inhomogeneities is tolimit the length of the acoustic wavetrain over whichcoherent scattering can take place. Another majoreffect of turbulence and inhomogeneities is to roughenthe acoustic wavefronts. For the experimental system,wavefront roughening prepared to cause an additional2-dB loss in signal strength at 1 km. It is possiblethat losses due to small-scale turbulence and inhomo-geneities can be minimized by employing narrowbeam acoustic sources.

The signal-to-noise power ratios calculated usingthe maximum effective depth of scatter agree to within3-dB of those measured during calm conditions.

It was also observed that signal strength decreasedrapidly above suspected temperature inversions. Sinceturbulence usually exists above temperature inversions,this decrease may indicate that the height and intensityparameters of such turbulence may be obtained fromthe RASS. On the other hand the presence of tur-bulence above the inversion will tend to limit thealtitude to which satisfactory operation can be reliablyachieved.

January 1972 / Vol. 11, No. 1 / APPLIED OPTICS 111

r1p I'll- 1. r -r=7I""-- - - -___ 7T,7 7' 77"r-77 1.

- - -

i , . , .. . , .. .. i; t . t t 2 t t t t I' z r _

A God lNTlPII

- ----- - ___ __ ---f M _I . ' 111 i ' ; 1 -I I

I � i -� I ; - � � � 1 � � 1 1 , " � I� I � � .. -1 I I I t I � � I I � 7A - '

Dispersion of the wavetrain due to temperaturegradients did not appear to cause significant degrada-tion of performance and hence should not cause diffi-

culty to systems operating over the first few kilometers.It was observed that the experimental system ceased

to provide usable signals when wind speeds exceeded7-10 msec-1. Hence RASS terminals most likelywill be restricted to use during periods of light surfacewinds. Since it is during such periods of light winds

that fog and pollution problems become acute, we

believe that the RASS, by providing vertical tempera-ture profiles every few seconds, has the potential of animportant meteorological instrument.

By utilizing a slightly higher frequency and a more

accurate doppler determination, a RASS terminalshould be capable of a 35-70-m height definition andabout 0.5-K temperature accuracy. Rawinsondes are

capable of 10-m definition and 0.05-K temperatureaccuracy; but the advantage of the RASS, operatingunder conditions of low wind speeds with acousticprobes spaced every few seconds, is that it can contin-

ually monitor the temperature profile and temperatureinversions of the lower atmosphere.

This work was performed under AFCRI, contractAF19(628)-6152.

References

1. V. E. Derr and C. G. Little, Appl. Opt. 9, 1976 (1970).

2. P. L. Smith, Jr., Remote Measurement of Wind Velocity by

the Electromagnetic Acoustic Probe, 1 (Midwest ResearchInstitute, Kansas City, 1961).

3. R. W. Fetter, Remote Measurement of Wind Velocity by the

Electromagnetic Acoustic Probe, 2 (Midwest Research Institute,Kansas City, 1961).

4. R. W. Fetter, P. L. Smith, Jr., and B. L. Jones, Investigationof Techniques for Remote Measurement of Atmospheric Wind

Fields (Midwest Research Institute, Kansas City, 1962).5. C. II. Allen and S. D. Weiner, Bolt Beranek and Newman

Report 1056 (AFCRL-63-596, 1963).

6. A. Tonning, Appl. Sci. Res., Sec. B 6 (1957).

7. F. R. Brassfield, II. C. Stultz, and E. T. Fago, Jr., An Electro-

magnetic Acoustic (EMAC) Probe for Remote Measurement of

Wind Velocity (Midwest Research Institute, Kansas City,1968).

8. J. M. Marshall, Report SU-SEL-70-050 (AFCRL-70-0438),Radioscience Laboratory, Stanford Electronics Laboratories(Stanford University, 1970).

9. R. Nowak, E. M. North, and M. S. Frankel, Report SU,SEL-70-021 (AFCRL-70-0365), Radioscience Laboratory,Stanford Electronics Laboratories (Stanford University,1970).

L. A. Jones-OSA Charter Member, OSA President 1930-31, Ives

Medallist 1943-in the Kodak Sensitometry Laboratory in 1922.

112 APPLIED OPTICS / Vol. 11, No. 1 / January 1972