Atmospheric Temperature Measurement Using Raman Backscatter

R. G. Strauch, V. E. Derr, and R. E. Cupp

A ground-based method of measuring atmospheric vertical temperature profiles using Raman backscatterfrom N2 is discussed. Experimental measurement of temperature fluctuations at tower heights is de-scribed.

Introduction

Atmospheric probing with laser radar (lidar) isbecoming an increasingly useful tool for gathering datathat enables the meteorologist to better understandatmospheric processes. The potentials of lidar havebeen discussed' and experiments have been conductedusing Mie scattering to study aerosols,2 fluorescentscattering to study the sodium layer,' and Ramanscattering to study vertical water vapor profiles up toseveral kilometers.45 The potential of Raman lidarin pollutant detection has been studied theoreticallyand experimentally.6 The relatively weak Ramansignals present considerable experimental difficulty,and only limited success has been reported for pollu-tion detection in the atmosphere.7 In this paper, wediscuss the measurement of the vertical temperatureprofile using Raman backscatter from nitrogen andreport the results of experiments that indicate thefeasibility of the method.

The most widely used method of obtaining a remotemeasurement of the vertical temperature profile witha ground-based instrument utilizes the absorption lineof oxygen near 60 GHz to vary the transmission dis-tance for received energy in a radiometer. The radiom-eter temperature measurements require an integralinversion to determine an atmospheric temperatureprofile. A radar-type determination offers improvedresolution and simplicity of data analysis, and allowsthe measurement of temperature fluctuations at knownaltitudes of specific interest as well as a determinationof a long-term average profile. In addition to water

The authors are with the Environmental Research Labora-tories, National Oceanic and Atmospheric Administration, Boul-der, Colorado 80302.

Received 3 May 1971.

vapor profile measurement and pollution detection,temperature information can be obtained directlyfrom the Raman signal intensity.

The concept of using molecular density measure-ments to derive temperature profiles is not new. Elt-erman, 89 using searchlights, has measured tempera-ture profiles from 10 km to 67.6 km by assuming that thescattering from above 10 km is due only to molecularscattering. Accurate temperature and pressure mea-urements were made at the lowest altitude that thescattering could be assumed to be Rayleigh. Belowabout 10 km the scattering is from molecules and aero-sols and very accurate measurements of particulatescattering would have to be made to separate out themolecular scattering component. Methods of separat-ing the scattering components have not been per-fected. Aerosol density measurements rely on usingan assumed Rayleigh density. Raman backscattercan be used to measure molecular density because theRaman component of backscatter is shifted in wave-length from aerosol or Rayleigh scattering. Therelatively weak Raman backscatter can be used fordensity measurements in the lower atmosphere tocomplement density measurements made by Ray-leigh scattering from the higher clean air.

A lidar backscatter measurement is a measurementof the product of the volume backscatter and the two-way extinction. In the case of on-frequency lidar,both the volume backscatter and the extinction arethe sum of molecular and aerosol terms, whereas thevolume backscatter for the Raman component in-volves only the molecular density. The total extinctionmust be measured for the Raman determination ofdensity. For example, suppose that a 3400-A lidarmeasurement of the backscatter at 1-km altitude isbeing made. Suppose that the total extinction fromaerosol scattering is the same as that from Rayleighscattering and assume that the total extinction can bemeasured to within 5%. Then the Raman backscat-ter can be used to determine a molecular density towithin 1.4%, whereas the on-frequency backscatterwould not give a useful density measurement.

December 1971 / Vol. 10, No. 12 / APPLIED OPTICS 2665

Theory

The use of the ideal gas law in the form

P(h)= p(h)T(h)R/M, (1)

where h is the altitude, P is the pressure, p is the density,R is the universal gas constant, and M is the molecularweight leads to

AP(h)/P(h) = [Ap(h)/p(h)] + [AT(h)/T(h)].

For a fixed altitude h, where the pressure can usuallybe taken as constant for the duration of a measurement,

Ap(h)/p(h) = -AT(h)/T(h).

The signal received by a lidar system measuringRaman backscatter from nitrogen would indicate, forconstant pressure (altitude),

ASN,(h)/SN,(h) = - AT(h)/T(h),

where SN(h) is the backscattered Raman signal andis proportional to PN,(h). Thus, at any altitude wherethe partial pressure of nitrogen is approximatelyconstant, the Raman backscatter gives a direct indica-tion of temperature fluctuations. The results ofexperiments demonstrating this capability of Ramanlidar will be discussed later.

The measurement of a temperature profile usingnitrogen density measurements is not as direct as themeasurement of temperature fluctuations.' Fromthe ideal gas law and the hydrostatic relationship, itfollows that

T(h) = PNa(h)/[pNo(h)R/M]

rhPN(ho) - g| pN(z)dz pN2(h)R/M, (2)

where PN,(ho) is the partial pressure of N2 for a ref-erence altitude. The integral in the numerator indi-cates that in order to measure temperature at anyaltitude, using density measurements, the density mustbe measured as a function of altitude from ho to h.The lidar measures pN2(h), using the lidar equation'

rhN, = (N0,JaN2PN,*LA-qthq/h 2) exp J -(Bt + B,)dz, (3)

where the number of received signal photons countedper transmitted lidar pulse is N., Nt is the number oflaser photons per pulse, q, is the transmitter efficiency,UN2 is the Raman scattering cross section for N2 for thetransmitted wavelength, pN,* is the number densityof N2 at height h, L is the length of the atmosphericcolumn obscrved by the gated lidar receiver, A, is thereceiver aperture, n, is the receiver optical efficiency,77q is the detector quantum efficiency, B, is the atmo-spheric extinction coefficient for the transmitted wave-length, and B, is the extinction coefficient for theRaman wavelength. B and B, are the Rayleigh ex-tinction coefficients (neglecting aerosol attenuation)and are proportional to pN,, so the measurement ofpN2 (h) as well as PN2(h) requires the evaluation of

fh

f PN2(Z)dZ.

There are two ways to approach the evaluationof the integral; an a priori statistical model of theatmosphere can be used or the integration can beperformed using the lidar measurements.

Consider first the statistical approach. An apriori statistical model based on the statistics ofradiosonde measurements at a nearby station can beused to approximate PN2(h) in Eq. (2) and the extinc-tion term in Eq. (3). The statistical model has theimportant constraint that accurate measurements ofPN,(ho) and T(ho) can be made. The statisticalmodel can also be constrained by time of day, date,and ground measurements of meteorological data ofimmediately preceding days at the local site and sur-rounding sites. One of the approaches to performingthe temperature inversion for microwave radiometerdata utilizes this approach for the pressure term.10If the pressure and density measurement errors ofPN,(h) and pN,(h) are independent, then

(VarT)I/T = [(VarPN 2 /PN,2) + (arpN 2 /N 2 )2)-

The bar denotes the mean value of an ensemble of mea-surements and VarX = X2 - 2. The measurementerrors are not completely independent in this case, sincepN2(h) also depends on the statistical model to obtain theRayleigh attenuation. However, the optical thicknessfor wavelengths and altitudes of interest here is lessthan 1, so that covariance terms can be neglected.

As an example of the statistical approach, considerthe model using only the constraint of pressure atground level, P(o). Westwater' 0 has analyzed theyearly data from radiosondes taken near sunrise andsunset at Denver, Colorado. The results are shownin Table I. The unconstrained variances Var [P]are about 30 (mbar) 2 for all altitudes, but the con-strained variances Var [PIP(o)] [variance of P,given P(o)] are much less at low altitude because ofthe strong correlation between P(h) and P(o) for theyearly average data. Additional constraints, par-ticularly T(o), will further reduce the variances andmake the statistical approach applicable to widerranges of meteorological conditions. If the pressureis found from the statistical model with uncertainty[Var[PP(o)]f}l/P as in Table I, and the uncertaintyin the lidar measurement (VarpN,)1/pN, is numeri-

Table I. Atmospheric PressureMeasurements at Denver, Colo.

P Var[P] Var[PP(ho)]h (km) (mbar) (mbar)2 (mbar)2 {Var[PP(ho) I /P

0.00 = ho 837 35.2 0 00.35 802 31.7 0.85 1.14 X 10-30.648 773 30.1 2.27 1.94 X 10-31.013 739 28.9 4.55 2.88 X 10-35.040 437 39.8 28.62 1.22 X 10-2

10.000 210 20.9 19.28 2.08 X 10-2

2666 APPLIED OPTICS / Vol. 10, No. 12 / December 1971

Table II. Signal Intensity Required forTemperature Measurement

Observationtime

(Var. T)ii S (photon requiredh (km) T counts) (see)

o 0 0 00.35 1.61 X 10-' 7.69 X 101 20.20.648 2.74 X 10-3 2.66 X 10' 25.61.013 4.07 X 10-' 1. 21 X 105 30.85.040 1.72 X 10-2 6.72 X 1J3 95.0

10.000 2.94 X 10-2 2.31 X 10' 317

(VarT)1/T= {2Var[PJP(o )] /p2}

Table III. Lidar Characteristics

iVt, photon transmitted per pulse = 1.7 X 1015, transmitter efficiency = 80%

0N,, cross section for N2 = 1.86 X 10-"3 m2/sraL, range resolution = 50 mA, receiver aperture = 0.36 m2vq ., receiver optical efficiency = 25%77a detector quantum efficiency = 25%PRF, pulse repetition rate = 100 sec'Xt, transmitter wavelength = 3371 i

a Calculated by D. A. Leonard Aveo-Everett (private commu-nication).

cally the same, then the temperature uncertainty isthat shown in Table II. Also listed in Table II arethe number of photon counts required to obtain thisaccuracy for a lidar system where the Poisson statisticsof the signal determine the lidar signal-to-noise ratio.The fourth column in Table II lists the observationtime required for a lidar system having the charac-teristics listed in Table III. (The attenuation termwas calculated for a standard atmosphere.) TableII indicates that present lidar systems can maketemperature profile measurements using an a prioristatistical model of the atmosphere to obtain pressureprofiles and using the lidar to measure pN2(h). Apressure model with sufficient constraints will makethe temperature uncertainty depend only on the lidarmeasurement of PN2 for a wide range of conditions.

The second approach to making a temperature pro-file measurement utilizes the measured density fromho to h to find the pressure and the Rayleigh extinction.In this case, the inaccuracy of the temperature mea-surement depends on the inaccuracy of pN,(h). Thetemperature uncertainty is given by

(VarT/T2) = (VarpN,/N22) + (VarPN2/PN2 )

- [2Cov(PN21PN2)/PN2fiN2I-

Since PN2 is found from PN2 through the hydro-static relationship, VarPN2 is the variance of thespatial average of gPN,. The covariance term dependson the correlation between the density measurement ath and the spatial average of the density measurementsfrom ho to h. If the lidar contains no systematic

errors, the covariance term becomes negligible (ex-cept for the low altitudes where the density measure-ment will be most accurate), because the lidar systemmust have sufficient bandwidth (i.e., spatial resolu-tion) to make the measurement of PN,(Z) independentof the measurement of PN,(Z + Az). The varianceof the spatial average of PN, from ho to h is the varianceof a sum of independent measurements, and if the lidarcontains no systematic errors, this variance will bemuch less than the variance of pN,(h). Hence, themain contribution to the temperature uncertainty at hwill be the uncertainty in the measurement of pN,(h)

for lidar systems with no systematic error. The ap-plicability of this method depends on the developmentof a Raman lidar system free of systematic error.

Lidar measurement of temperature profiles pre-sents a major practical problem not found in watervapor profile measurements. Effects of aerosol at-tenuation, laser beam misalignment, 1/h2 corrections,etc. can be accounted for in water vapor measurementsby measuring the mixing ratio instead of the watervapor density. A nitrogen profile measurement, how-ever, would require a careful calibration of the lasersystem and a measurement of attenuation. An ab-solute measurement of pN,(h) is not necessary for theprofile measurement of temperature if the minimumaltitude of the lidar system is ho where p(ho) or T(ho)can be measured with meteorological instruments.

Experimental Results

An experiment was devised to check the feasibilityof using Raman backscatter to observe temperaturefluctuations using a high pulse repetition rate laser.A lidar system with parameters similar to those inTable III was used. The range was reduced to towerheight (30.5 m) so that temperature could be preciselymonitored and compared with the Raman backscatter.The length of the backscatter volume was 5 m andwas determined by the geometry of the transmittingand receiving beams. Thermistors were placed nearthe center and near both ends of the 5-m observationlength. The laser beam passed vertically approxi-mately 2 m from the thermistors. A pressure indi-cator located at ground level continuously monitoredtotal pressure. The atmospheric pressure changeduring any observation time was less than 0.2 mbar sothat AP/PN, is negligible compared to (AT/T) fortemperature changes of 10 C or greater. Since (AT/T)- 0.35% per 'C, the stability of the laser outputpower becomes important for monitoring fluctuationsof atmospheric N2 density. (For profile measurementswhere the backscatter from each range increment ismeasured for each laser pulse, the laser power stabilityis not as important.) During these experiments theS/N ratio was sufficient to allow observations ofRaman signal fluctuations of 0.35% with a 3-sec timeconstant, but the long-term record contained randomfluctuations of approximately 1%. These changeswere traced to laser power variations, temperatureeffects on the transmission of optical filters, andmechanical instability.

December 1971 / Vol. 10, No. 12 / APPLIED OPTICS 2667

19 JANUARY 197106

°C -TEMPERATURE12

RELATIVE INTENSITY (S)

130

850 i- 20Osec8:06 PM

S

8:22PM

perature is shown; the other two thermistors indicatedthe same temperature. In Figs. 1-3, data points wereread every 20 sec and a plot of relative Raman back-scatter () vs T is shown with the data. The the-oretical curve () (T) = constant is shown for reference.This curve is approximately a straight line over therange of values measured in these experiments.Fluctuations other than temperature are recorded onthe Raman channel, but temperature changes areclearly recorded by the Raman lidar. In Fig. 3,compensation for the change in laser power was madein the S-T graph. Figure 4 shows a 23-min segmentof data during which T changes by approximately 2degrees. Data points were read every 4 sec and across-correlation of the S-T data was performed. Nocorrections were made to the raw data. The peak

T ( K)

Fig. 1. Raman backscatter intensity vs temperature.

27 JANUARY 1971

- TEMPERATURE

RELATIVE INTENSITY

8:32 PM

662

658

654

S

650

646

279 280

Fig. 2. Raman backscatter intensity vs temperature.

19 JANUARY 1971

TEMPERATURE

8408 RELATIVE INTENSITY

660

680840 - RELATIVE INTENSITY

- (LASER POWER)860 __ -

Fig. 3. Raman backscatter intensity vs temperature.

The total extinction due to Rayleigh scatteringof the transmitted and backscattered laser energy isabout 0.7%, and fluctuations of the Rayleigh ex-tinction will be negligible. Fluctuations of the totalaerosol extinction were also shown to be negligibleby monitoring the laser power output with a 10-mtransmission path.

The Raman backscatter signal was recorded using afast sample and hold gate to measure a voltage levelproportional to the number of backscattered photonsreceived from the 5-m interaction region after eachpulse. The steplike signal was filtered and recordedon a zero-suppressed strip chart.

Figures 1-4 show the examples of data in whichtemperature changes of several degrees were recordedby the thermistors. Only the center thermistor tem-

19 JANUARY 1971

_ TEMPERATUREIC 12

RELATIVE INTENSITY385 -

405 2

8.04 PM 8271.

Rr)

-128 -64 0

r(sec)64 128

Fig. 4. Cross-correlation of Raman backscatter intensity andtemperature.

2668 APPLIED OPTICS / Vol. 10, No. 12 / December 1971

154

728 (S)(T= Const.

722 . .

716 -

710282.4 2848 281.2

IC

780

S 800

0g P 8:25 PM

815

809

803

S (S)=Const.

_ I .I\

797

791

275 216 217 278T( K)

8:46 PM

- .: 0(SXT)Const. -

I I I I282 283 284 285

T 0 K)286 287

CROSS - I ICORRELATION of

06 -904-927PMDATA SEGMENT

04 -

12-

0 1 1

1s

t

PM

correlation, at zero time lag, was 0.76 and the correla-tion decreases to 0.2 with about 1-min time lag.Laser power variations and mechanical instabilityalso contribute to short-term signal fluctuations. Thenoise on the signal channel and uncertainty in chartreading contribute approximately three divisionsof uncertainty to the relative Raman signal level(S) in Figs. 1-3. The rms deviation of the Raman sig-nal from the theoretical curve is 4.14, 3.58, and 2.28divisions for Figs. 1-3. The other major factor thatprevents perfect correlation of the data is that theRaman signal is a volume measurement and the therm-istor is essentially a point measurement. Thetemperature variations move with the wind and anabrupt change in T can be recorded by the pointsensor, whereas the volume sensor will record thetotal abrupt change only when it fills the entire volume.

ConclusionThe correlation between the Raman scattering of

nitrogen and the temperature measured by thermistorsshows that lidar can measure temperature fluctuations.Detailed study of temperature fluctuations can bemade with the narrow pulse and high pulse repetitionrate of available lasers. Temperature profiles in theclear atmosphere can be measured with acceptableaccuracy if the lidar is calibrated. Available laserequipment can be utilized for studying the temperature

structure of the atmosphere to several kilometersaltitude. Pressure information can be obtained if thelidar system is free of systematic error. Data pro-cessing equipment capable of measuring the backscatterfrom each range increment for each laser pulse isneeded for efficiency of operation and to eliminatepractical problems encountered in field operation.

References1. V. E. Derr and C. G. Little, Appl. Opt. 9, 1976 (1970).2. E. W. Barrett and 0. Ben-Dov, J. Appl. Meteorol. 6, 500

(1967).3. M. R. Bowman, A. J. Gibson, and M. C. W. Sanford, Nature

221,456 (1969).4. J. Cooney, J. Appl. Meteorol. 9, 182 (1970).5. S. H. Melfi, J. D. Lawrence, and M. P. McCormick, Appl.

Phys. Lett. 15, 295 (1970).6. T. Kobayasi and H. Inaba, Nature 224, 170 (1969).7. T. Kobayasi and H. Inaba, Appl. Phys. Lett. 17, 139 (1970).8. L. Elterman, J. Geophys. Res. 58, 519 (1953).9. L. Elterman, J. Geophys. Res. 59, 351 (1954).

10. E. R. Westwater, Ph.D. Thesis, University of Colorado(1970).

C. L. Sanders of the National Research Council of Canada, editor ofthe feature in this issue on photometry.

December 1971 /Vol. 10, No. 12 / APPLIED OPTICS 2669