Remote Atmospheric Sensing with an Airborne Laser Absorption Spectrometer R. T. Menzies and M. T. Chahine A laser absorption spectrometer, using an ir laser transmitter and a heterodyne radiometer, can be used from an aircraft or spacecraft to measure altitude profiles of air pollutants and other atmospheric constitu- ents. The technique involves measurement of differential absorption at several wavelengths, using the dif- fusely reflecting earth's surface to provide a return signal. The pressure broadening of absorption lines al- lows one to discriminate between high and low altitude absorbers. Application of the technique to mea- surements of ozone, nitric oxide, and water vapor are presented. C 2 and CO lasers are considered as transmitters. The discussion includes altitude resolution limitations, atmospheric temperature depen- dence, and frequency stability requirements of the instrument. Introduction The laser absorption spectrometer that we discuss here is a double-ended system that does not need a cooperative remote reflector. It can operate using a diffusely reflecting surface or a conglomerate of scat- terers at the opposite end of the atmospheric path to be monitored. The instrument consists of an ir con- tinuous output laser (or several lasers) that can be tuned to several selected frequencies and a hetero- dyne receiver that is sensitive to the laser radiation that returns after having been transmitted and scat- tered back. The capabilities of laser differential absorption systems can be significantly enhanced by using heter- odyne detection. The heterodyne radiometer is sev- eral orders of magnitude more sensitive to the re- turning ir laser radiation than are direct photodetec- tors. Even when using a diffusely reflecting surface to provide a return signal, operation can be successful over a several kilometer path with a laser transmit- ting a few milliwatts. The laser absorption spectrometer can be used not only to provide data on the average concentration of an air pollutant or its total burden over a specific re- gion, but also to provide some information about a pollutant's concentration at various altitudes. The idea of using an airborne, downward looking LAS (Laser Absorption Spectrometer) to measure the total burden of several air pollutants has been briefly The authors are with Jet Propulsion Laboratory, California In- stitute of Technology, Pasadena, California 91103. Received 1 April 1974. discussed elsewhere. 1 The possibility of using an LAS with limited frequency tuning ability to obtain altitude profiles of various pollutants was the topic of a NASA patent application written in 1972.2 This possibility has also been discussed recently by Seals and Bair.3 Atmospheric constituents that are ir ab- sorbers have absorption lines that can be described near line center by the Lorentz shape, k(v) = (Sr){oU/[(v - VO) + Uz2]}, (1) where k (v) is the absorption coefficient at frequency v, S is the line strength, a-is the line half-width, and vo is the line center frequency. The Lorentz shape is valid when pressure broadening is larger than Dop- pler broadening. This condition is satisfied for at- mospheric constituents throughout the troposphere and part of the stratosphere. The parameter a de- pends on background pressure and temperature. The line strength S is also dependent on background temperature. Ignoring temperature dependence for the moment, we can write a as a = cOP, (2) where P is the background pressure in atmospheres. Most of the pressure broadening is due to the major atmospheric constituents, such as nitrogen and oxy- gen, which are uniformly mixed throughout the at- mospheric regions that we are considering. If the LAS uses a laser source that spectrally overlaps an absorption line and if the laser can be tuned over a spectral interval equivalent to ao, altitude profiles can be obtained. For a given density of an absorbing constituent, the absorption at line center increases as the background pressure decreases. Thus a mea- surement of total absorption at frequency vo will be 2840 APPLIED OPTICS / Vol. 13, No. 12 / December 1974
Transcript
Remote Atmospheric Sensing with an Airborne LaserAbsorption Spectrometer
R. T. Menzies and M. T. Chahine
A laser absorption spectrometer, using an ir laser transmitter and a heterodyne radiometer, can be usedfrom an aircraft or spacecraft to measure altitude profiles of air pollutants and other atmospheric constitu-ents. The technique involves measurement of differential absorption at several wavelengths, using the dif-fusely reflecting earth's surface to provide a return signal. The pressure broadening of absorption lines al-lows one to discriminate between high and low altitude absorbers. Application of the technique to mea-surements of ozone, nitric oxide, and water vapor are presented. C 2 and CO lasers are considered astransmitters. The discussion includes altitude resolution limitations, atmospheric temperature depen-dence, and frequency stability requirements of the instrument.
Introduction
The laser absorption spectrometer that we discusshere is a double-ended system that does not need acooperative remote reflector. It can operate using adiffusely reflecting surface or a conglomerate of scat-terers at the opposite end of the atmospheric path tobe monitored. The instrument consists of an ir con-tinuous output laser (or several lasers) that can betuned to several selected frequencies and a hetero-dyne receiver that is sensitive to the laser radiationthat returns after having been transmitted and scat-tered back.
The capabilities of laser differential absorptionsystems can be significantly enhanced by using heter-odyne detection. The heterodyne radiometer is sev-eral orders of magnitude more sensitive to the re-turning ir laser radiation than are direct photodetec-tors. Even when using a diffusely reflecting surfaceto provide a return signal, operation can be successfulover a several kilometer path with a laser transmit-ting a few milliwatts.
The laser absorption spectrometer can be used notonly to provide data on the average concentration ofan air pollutant or its total burden over a specific re-gion, but also to provide some information about apollutant's concentration at various altitudes. Theidea of using an airborne, downward looking LAS(Laser Absorption Spectrometer) to measure thetotal burden of several air pollutants has been briefly
The authors are with Jet Propulsion Laboratory, California In-stitute of Technology, Pasadena, California 91103.
Received 1 April 1974.
discussed elsewhere.1 The possibility of using anLAS with limited frequency tuning ability to obtainaltitude profiles of various pollutants was the topic ofa NASA patent application written in 1972.2 Thispossibility has also been discussed recently by Sealsand Bair.3 Atmospheric constituents that are ir ab-sorbers have absorption lines that can be describednear line center by the Lorentz shape,
k(v) = (Sr){oU/[(v - VO) + Uz2]}, (1)
where k (v) is the absorption coefficient at frequencyv, S is the line strength, a-is the line half-width, andvo is the line center frequency. The Lorentz shape isvalid when pressure broadening is larger than Dop-pler broadening. This condition is satisfied for at-mospheric constituents throughout the troposphereand part of the stratosphere. The parameter a de-pends on background pressure and temperature.The line strength S is also dependent on backgroundtemperature. Ignoring temperature dependence forthe moment, we can write a as
a = cOP, (2)
where P is the background pressure in atmospheres.Most of the pressure broadening is due to the majoratmospheric constituents, such as nitrogen and oxy-gen, which are uniformly mixed throughout the at-mospheric regions that we are considering. If theLAS uses a laser source that spectrally overlaps anabsorption line and if the laser can be tuned over aspectral interval equivalent to ao, altitude profilescan be obtained. For a given density of an absorbingconstituent, the absorption at line center increases asthe background pressure decreases. Thus a mea-surement of total absorption at frequency vo will be
strongly influenced by the upper altitude molecules.At a frequency v such that v - vo = ao, the total ab-sorption will be strongly influenced by the lower alti-tude molecules. Measurements of total absorptionat several frequencies will then provide informationabout concentrations at various altitudes in additionto a value for total burden.
One salient characteristic of the LAS is the highsensitivity to low altitude pollutants, such as pollu-tants beneath an inversion layer in an urban environ-ment. This is in contrast to all passive radiometricinstruments that sense upwelling thermal radiation.Since low altitude pollutants are at very nearly thesame temperature as the earth's surface, they arenearly invisible to these passive instruments.
Signal-to-Noise and Coherence Considerations
The laser in the LAS would normally function bothas a transmitter and a local oscillator. It must have acontinuous, single-mode output to serve as a local os-cillator, and it must have adequate power and fre-quency stability for the absorption measurements tobe made accurately. The laser must be tunable overlimited frequency regions (about 1 GHz in the vicini-ty of an absorption line center) in order to provide al-titude profile information.
To determine the necessary transmitter power andpoint out the advantages of heterodyne detection, wecompare the received laser power of an LAS using thescattering off the earth's surface with the noise-equivalent power of the heterodyne radiometer. Ifwe assume an average earth surface reflectivity r, thepower collected by the receiver, assuming its collect-ing mirror has an area A and its altitude is H, is
Pr = rPW(A/27TH2 ), (3)
where Pt is the transmitter laser power. (We assumethat the earth's surface is a depolarizing Lambertiandiffuse reflector.) The sensitivity of the heterodyneradiometer, in terms of noise equivalent power(N.E.P.), is
N.E.P. = (2hu/,q)(BIF/ T)1/ (4)
where h v is the energy of each quantum of the laserradiation, is the mixer quantum efficiency, BIF isthe IF bandwidth, and r is the postdetection integra-tion time.
Let us consider an example of a typical laser ab-sorption spectrometer in flight operation. If thelaser radiation wavelength is near 10 gm and the het-erodyne detection system has a mixer quantum effi-ciency -q = 50%, an IF bandwidth B IF = 106 Hz, andan integration time = 1 sec, the N.E.P. = 7.6 X10-17 W. Note that this value is several orders ofmagnitude lower than background limited ir photo-detectors operating near 10-gm wavelength. Theheterodyne radiometer discriminates against back-ground radiation very effectively because of its ex-tremely narrow spectral filtering property. If H =20 km and r = 0.02, a 1-W transmitter and a collect-ing lens of 10-cm diam would provide a received
power of 8 X 10-14 W. Thus a SNR of 1000 can beachieved in this example if the atmospheric absorp-tion is small. The spectral resolution of this LAS isequivalent to the IF bandwidth, which is 3.3 X 10-5.cm1
One might wonder how effective a coherent receiv-er really is in responding to laser radiation that hasbeen scattered off a rough surface and passes through.a turbulent atmosphere. We can think of the scat-tering process in terms of a collection of point sourcesthat are radiating independently with lifetimes dic-tated by the length of time they are illuminated.From the theorem of van Cittert and Zernicke, onecan deduce that the field radiated from an extendedsource of this type will be spatially coherent over anyreceiver aperture that cannot resolve the dimensionsof the source.4 This concept was recognized byGould et al. in their heterodyne experiments.5 Aslong as the spot size of the laser transmitter on theground is equal to or smaller than the field of view ofthe heterodyne receiver at the ground, these condi-tions are satisfied. Atmospheric turbulence willcause a time variation of the phase of each radiatingpoint source, which will broaden the spectral width ofits radiation in addition to its finite lifetime and theoriginal laser spectral width. This effect of turbu-lence is analogous to atomic radiators that are per-turbed by collisions, the result being a broadening oftheir emission lines. The lifetime and turbulence ef-fects together should produce no more than a few ki-lohertz of spectral broadening when spot sizes on theground are at least a few meters in diameter. Theturbulence will also cause the phase fronts to deviatefrom those of a plane wave as the radiation passesthrough the atmosphere and arrives at the receiver.Fried6 has calculated maximum effective aperture di-ameters for coherent receivers when the radiation ispassing vertically through the entire atmosphere.His results indicate that at 5-gm wavelength, a 0.3-maperture diameter is about the maximum diameterfor which the coherent receiver will not suffer degra-dation due to normal daytime turbulence. The tur-bulence degradation is less at 10-gm wavelength.
It is also important to consider the field of viewtradeoffs in an instrument that uses heterodyne de-tection. The heterodyne radiometer acts as an an-tenna, obeying the restriction that its effective aper-ture, integrated over all possible arrival directions,equals X2, where X is the signal wavelength. 7 Be-cause of this, one cannot have both a wide field ofview and large collecting optics without sacrificingheterodyne conversion gain. In Fig. 1 we illustrate alaser source that is split into a local oscillator compo-nent and a transmitted signal component. The pho-tomixer is illuminated by the local oscillator beamand the return signal beam. Let's assume that thetwo lenses each have a focal length f and that thetransmitted signal and local oscillator beam diame-ters are each DLO. The diameter of the transmittedsignal beam determines the spot diameter on theground,
Fig. 1. Elements involved in photomixing. The return signal hasbeen frequency shifted from the transmitted signal by external
means, such as a Doppler shift provided by the remote scatterer.
dg 2H/DLo. (5)
The diameter of the collecting aperture D can bevaried by using an adjustable iris in front of the col-lecting lens, as shown. If DLO = D, the two spotsizes on the photomixer are equal, and the hetero-dyne mixing efficiency or conversion gain is maxim-ized. In this case, the field of view at the ground isalso equivalent to dgs. In the previous example of anairborne LAS with DLO = D = 10 cm, if the altitudeof the instrument were 20 km, dgs would equal 4 m.This ground spot diameter is quite small, and itwould be reduced further if the aircraft were at alower altitude. A larger ground spot size would helpin reducing the magnitude and frequency of surfacealbedo fluctuations, which would probably mean agreater accuracy in determining differential absorp-tion quantities.
One method of filtering out albedo fluctuations isto transmit simultaneously two closely spaced laserfrequencies whose beams coincide at the ground andsynchronously detect the return signals, using achopping frequency that is much larger than themaximum albedo fluctuation frequency. One laserfrequency would interact strongly with an atmo-spheric constituent of interest, while the other laserfrequency would interact with the constituent to alesser degree. The instrument would measure thedifferential absorption. The frequencies would beclose enough so that no differential absorption orscattering due to ground materials or aerosols wouldexist, due to the relatively broad spectral characteris-tics of solids and liquids. Effects of other atmo-spheric constituents must obviously be carefully ex-plored ahead of time in order to obtain accurate re-sults. Experimental high resolution spectral data onmany atmospheric constituents is incomplete, andpresent spectral tables are sometimes not accurateenough when applied to laser transmission. Watervapor absorption in the 6.3-gm 2 band is one exam-ple where laser transmission measurements do notentirely agree with predictions based on spectral ta-bles.8 9
When flying an LAS at low altitudes, it might benecessary to run at a reduced receiver efficiency, orwith the collecting lens area stopped down, in orderto keep the amplitude and frequency of albedo fluc-
tuations at a reasonable level. If we adjust the opticsto reduce the size of the laser source beam, keepingDC in Fig. 1 fixed, the ground spot size and the fieldof view increase together. (Note that this is true aslong as the local oscillator intensity falls entirely onthe mixer and as long as the focused return signalwavefronts from the edges of the field of view are nottilted from parallelism with the local oscillator wave-fronts by more than X/d, where d is the diameter offocused return signal spot on the mixer.) The angu-lar field of view 0 in this case (DC > DLO) is given bythe ratio of the local oscillator spot diameter on themixer to the collecting lens focal ength f or
o = (2xf/DLO) (1/f) = 2X/DLO. (6)
Now the collection efficiency is proportional to D,2/H2, which has not changed, but the heterodyne con-version gain is reduced by the factor DLO2/D,2, theratio of the return signal and local oscillator spotsizes on the mixer. The entire local oscillator inten-sity is contributing to the mixer dc current and relat-ed gr or shot noise, but only a portion of it is beingmixed with the return signal from a given direction.Increasing the ground spot size correspondingly re-duces the resulting total efficiency (the product ofcollection efficiency and heterodyne conversion effi-ciency) of the radiometer.
Of the candidate ir lasers under consideration foruse in the LAS, the CO2 and CO gas lasers are mostappropriate. They are capable of single mode, singleline operation with power outputs of 1 W or more.Frequency stability of a few kilohertz over millisec-ond time durations has been demonstrated. Thismeans the spectral width of the beat frequenciesfrom the photomixer, due to laser stability, can easilybe much less than the 1-MHz IF bandwidth that weconsidered in the example. The biggest drawback ofthese gas lasers is limited tunability. They are dis-cretely tunable over large wavelength intervals andcontinuously tunable over much smaller regionsabout each emission line. Several spectral coinci-dences between CO2 and CO laser emission lines andpollutant absorption lines have been reported.' 0'1 'Normal low pressure molecular gas lasers cannot befrequency tuned the necessary amount about an at-mospheric absorption line for the determination ofaltitude profiles, unless an external frequency shifteris used. However, gas waveguide lasers, which oper-ate at much higher pressures, can be tuned over a fre-quency range of more than 1 GHz,'2 which is ade-quate to obtain profiles in several cases.
Altitude Resolution
The determination of concentration vs altitudeprofiles with the LAS rests upon the ability to tunethe operating frequency from near an absorption linecenter to a point on the wing of the line. Total ab-sorption over the vertical path would be measured ata few selected frequencies in this region, and fromthese data and known information about the absorp-
tion line, an altitude profile of the absorber can beplotted. Since the method depends on the fact thatthe pressure broadened absorption line widths differat altitudes, it is applicable only in the region of theatmosphere where pressure broadening predominatesover Doppler broadening. The altitude at whichDoppler broadening becomes comparable to pressurebroadening depends on the constituent of interest.For ozone it is 30-35 km, and for nitric oxide it is justover 20 km.
When the LAS is operating, the return signal in-tensity at frequency vi can be expressed as
Ir(vj) = I, exp[-2K(v,)], (7)
where Io is the transmitted intensity multiplied bysurface albedo, optical collection efficiency, etc., andK (pi) is the total absorption coefficient due to a par-ticular atmospheric constituent at frequency vi:
K(vi) = I W(h)kjip(h), T(h)]dh. (8)
Here W(h) is the density of the species of interest, his the altitude, and ki is the absorption coefficient atvi for a given ambient pressure p and temperature T.The altitude of the LAS is hm. (We will considerhere the simple case of only one constituent withoutany interference or blending due to other constitu-ents.) Equation (8) is a linear integral equation andcan be reduced to a system of linear equations. Inour analysis, we express Eq. (8) in a slightly differentform:
K(vi) f ki[p, T(p)]q(p)dp, (9)g ,s
where mg is the gravitational force on a mass m, Psand p are the atmospheric pressures at the surfaceand at the instrument, respectively, and q(p) is themass mixing ratio of the constituent of interest. Theunits we use for ki are cm-1/g cm- 3 .
We are interested in the inverse solution to Eq. (9).The quantities K (vi) are measured by the LAS. Theabsorption coefficient at Pi is due to one or more Lo-rentzian absorption lines whose center frequenciesare known [see Eq. (1)], and both the dependence ofthe line strength S and line width a on altitude arealso assumed to be known beforehand for each line.This means the dependence of S and a on both Tand p must be known, and the temperature profile ofthe atmosphere must be known. The dependence ofa on T for temperature ranges encountered in the0-30-km altitude region is slight, and for most cases aline should be chosen whose line strength S dependsonly slightly on temperature. This means the energyof the lower level of the absorption line should not bemuch larger than kT. Later in the paper we will dis-cuss effects of temperature profile errors on the con-centration profile determination of constituents.
Assuming the necessary information about linestrengths and widths is known beforehand, the accu-racy and altitude resolution of inverse solutions to
Eq. (9) depend on the shapes of the weighting func-tions ki[p,T(p)]. Information about the mixingratio at a certain altitude must be obtained from aweighting function that peaks near that altitude andhopefully peaks sharply. The more sharply peakedthe weighting functions, the better is the altitude res-olution. The weighting functions ki[p,T(p)] in Eq.(9) are in general not sharply peaked functions,meaning that the altitude resolution obtainable withthe LAS is limited. This limitation is physical, notinstrumental, although the profile determination canalways be improved somewhat if the signal to noise isincreased. If the weighting functions used in the in-verse solution overlap substantially, they cannot beexpected to behave as an independent set of basisfunctions. Therefore, the linear set of equationsbased on Eq. (9) will not be well conditioned. In thiscase small errors in the absorption measurements willproduce substantial errors in the altitude profile de-termination. A set of weighting functions should bechosen whose overlap is acceptable, and this limitsthe number that can be used. The number of mean-ingful data points in the profile solution cannot ex-ceed the number of weighting functions used, andthis limits the altitude resolution.
In Fig. 2 are shown several normalized weightingfunctions that can be used for nitric oxide altitudeprofile determination. The sounding frequency cor-responding to each weighting function is also listed.The temperature profile used in the determination ofthese functions is shown in Fig. 3. The nitric oxideabsorption line that is being probed here is the R (6 -1/2)1/2 line centered at 1900.076 cm-'. This line is alambda doublet, with the lambda splitting being
a
II--
0.4 0.6 0.8k.(p, T (k. )max
20
50
100 's
C,)
CXCxa-
200
500
Fig. 2. Normalized weighting functions for nitric oxide absorp-tion at various altitudes. The sounding frequencies that produce
Fig. 3. The temperature profile used to compute the measuredvalues of total absorption. In most cases this was also used in theconcentration profile reconstruction; however, other temperatureprofiles were sometimes used in the reconstruction process (see
Temperature Effects Section).
0.011 cm1 .1 3 The total line strength at T = 295 Kis 3.46 cm- 2 atm-1,1 4 or 2.79 X 103 cm- 3/g cm- 3 .The line width at 1 atm and 295 K is assumed to be0.035 cm-1,15 and the energy of the lower level is E"= 82 cm- 1 .1 6 This nitric oxide absorption line isclosely matched to a CO laser line, the 9-8 band, P (9)at 1900.050 cm-1.7 Note that the laser must betuned a maximum of 720 MHz from its line center tocover the frequency range indicated in Fig. 2.
There is some reason to believe that the value forthe nitric oxide line width quoted in Ref. 15 shouldbe larger, possibly around 0.05 cm-1.18 The airbroadened NO line widths should be carefully mea-sured using high resolution laser techniques in orderto establish an accurate value. If the pressure broad-ening is around 50% larger, the normalized weightingfunctions in Fig. 2 will change shape, but not dramat-ically. The contributions from higher altitudes willbe slightly larger for each function. It is demon-strated in the next section that this will decrease theaccuracy of the determined profiles at high altitudeswhen the nitric oxide concentrations are high nearthe ground.
Nitric Oxide Altitude Profile Determination
The five sounding frequencies listed in Fig. 2 wereused to compute an inverse solution to Eq. (9), givenan actual nitric oxide concentration vs altitude pro-file and temperature profile with which the valuesK (i) were calculated. [We will denote these actual
values of total absorption by Ka(v ] The tempera-ture profile that was used is the one shown in Fig. 3.The temperature dependence of the line strength inEq. (1) is
S = S(TO/T)nexp{1.439E[(T- T)/TTO]}, (10)
whereT is the temperature of the absorbing gas;To is the reference temperature (298 K here);So is the line strength at To in cm-1/g cm2;E" is the lower energy level of the transition incm-1; andn is the exponent that results from the tempera-ture dependence of the rotational partition func-tion and depends on the absorbing gas.
The temperature dependence of the Lorentz linewidth is
a(T) = (To)(To/T)m, (11)
where the value of m, according to simple kinetictheory, is 0.5,19 but in reality depends somewhat onthe absorbing gas. For nitric oxide we use the valuesn = 1.0, m = 0.5.
Equation (9) was solved by iteration, using thebasic technique developed to solve the radiativetransfer equation for temperature profile informa-tion.20 The steps are as follows:
(1) Select a set of pressure levels pi so that eachsounding frequency vi is used to monitor the concen-tration at one pressure level. The pressure levelsshould lie near the maxima of the weighting func-tions ki(p,T).
(2) Make an initial guess q(p) and use, e.g., lin-ear interpolation to complete the profile at interven-ing pressures.
(3) Compute the values for K(vi), using the trape-zoidal rule approximation of Eq. (9).
(4) Compare the actual K (vi) and computed K (vi)for each frequency and compute the percentage re-siduals R = (102) [Ka (vi) - Kc (vi)]/Ka (vi)} and anrms residual summed over all vi.
(5) Calculate a new profile q (p) based on therelation
[q'(pi)J/[q(Pi)] = [Ka(v,)]1[K,(v,)]
and use linear interpolation to complete q (p) at in-tervening pressures.
(6) Repeat the sequence (3)-(5), each time com-puting new values q(pj) with j being the iterationnumber.
The rate of convergence is determined by the re-siduals, which are calculated after each iteration.Using this method, one can determine the rate andaccuracy of convergence for each pressure level.This information is then used to judge the efficacy ofeach weighting function.
The degree of accuracy and vertical resolution ofthe recovered composition profile depends on theproperties of the corresponding weighting functions,or kernels, ki(p,T), and the shapes of these kernels
priori information about the expected solution, suchas the shape of the concentration profile.
Figure 4 through 6 illustrate how nitric oxide pro-files can be reconstructed based on the soundingfrequencies of Fig. 2 and the iterative method. Fig-ure 4 illustrates two profile cases, both over relativelyunpolluted areas. We have assumed a single initialguess and in each case are shown the resulting datapoints after twenty iterations. The residuals de-crease quickly during the first five iterations, andfurther convergence is slow. One can see that in thecase of profile 2, the calculated values were not ableto reproduce the major change in slope at the upperaltitude. The two upper altitude data points aremore like average values instead. Figure 5 illustratestwo profile cases over polluted areas, such as typicalurban areas. The same initial guess was used. Theground concentration is much different from the ini-tial guess and the iteration process overcorrected inthis case. The slight overcorrection at ground levelaffected the fit at the upper altitudes, where concen-trations are small and the sensitivity is lower. At theend of twenty iterations, the upper altitude residualswere around 5%, while the lower altitude residualswere much lower. Figure 6 illustrates the same twoprofile cases over polluted urban areas. A differentinitial guess was used, and the resulting data pointsclose in on the actual profiles quite well except at the50-mbar level. When low altitude concentrations arevery high, the resulting solutions are less accurate atthe upper altitude because the lower altitude nitricoxide contributes substantially to the total absorp-tion at each sounding.frequency. For this reason, wealso found that initial guesses that were within a fac-tor of 4 of the actual concentrations at ground levelproduced much better solutions at the higher alti-tudes. The two initial guesses used in Figs. 4 and 6
depend not only on the pollutant molecule but alsoon the particular'absorption line of a pollutant. Theline strength and its temperature dependence are im-portant considerations when choosing a region aboutan absorption line for monitoring. As stated pre-viously, the best kernels are those that produce a setof curves that are narrow and only slightly overlap-ping. In cases where the weighting functions arestrongly overlapping, one might require the use of a
Fig. 7. Water vapor profiles used in the evaluation of the refer-ence frequency technique for determining water vapor
interference.
are nearly the same at upper altitudes but come rea-sonably close to the actual profiles at ground level.In practice this limitation should not be a handicap,since a single reading of total absorption at the lowaltitude sounding frequency can be used to guess ini-tially the surface nitric oxide concentration within afactor of 4. Other modifications of the reconstruc-tion technique are being investigated with the hopeof improving the high altitude fits.
Water Vapor Effects on Nitric Oxide Measurements
Several important atmospheric constituents ab-sorb in the spectral neighborhood of the nitric oxidefundamental band. The strong 2 band of watervapor, the 3v2 overtone vibration of C0 2, and the v, +P2 combination band of N20 are all in this wave-length region. The wavelengths chosen to monitornitric. oxide must avoid strong lines in these interfer-ing bands. For vertical sounding through the tropo-sphere, the water vapor interference is the most se-vere. Some information about water vapor contentmust be known in order to make successfully the ni-tric oxide measurements. Is total water burdenbelow the LAS enough information or is an accuratewater profile necessary? If total burden is enough,how accurate must that information be in order tomeasure nitric oxide with a reasonable accuracy?We have attempted to answer these questions bystudying water absorption at several frequencies, in-cluding those listed in Fig. 2.
The results of water vapor transmission studies in-dicate that total water burden below the LAS is suffi-cient data for one to be able to separate adequatelythe contributions to absorption due to water vaporand nitric oxide. We computed water vapor trans-mission at four frequency regions, each being centtered at a CO laser line frequency and extending to+1GHz from the line center. Two of these frequencyregions overlap nitric oxide absorption lines. Theyare near the CO 9-8, P(9) line at 1900.049 cm-1 andthe CO 7-6, P(15) line at 1927.299 cm-1. Radiation
at the other two frequency regions is not absorbed bynitric oxide. These are near the 7-6, P (14) line at1931.409 cm-l and the 6-5, P(19) line at 1936.001cm-'. (These frequencies were calculated using theconstants in Ref. 18.) All four of these frequency re-gions fall between strong water lines, in regions ofrelatively high water transmission, where absorptionline wings contribute to the absorption. Thus thesefrequencies are primarily absorbed by low altitudewater, and accurate water profiles cannot be obtainedby sounding at these frequencies alone. Three dif-ferent water vapor profiles, pictured in Fig. 7, wereconsidered in these computations. For each profile,the total absorption at the sounding frequencies wascalculated, using the tables of Benedict and Calfee.21Then we attempted to reproduce the total absorptionnumbers at each sounding frequency in a given re-gion using a profile with a uniform mixing ratio q.The quantity q would hopefully satisfy the relation
= {lJ K[p, T( P)]q(P)dP}/{f K[p, T(p)]dp} (12)
at each frequency v. The results were favorable.The total absorption residuals at each frequencywithin a region were never more than 0.15% when theoptimum q was computed. The optimum q was notthe same for each frequency region. The largest de-viation involved the 9-8, P (9) region; the optimum qfor this region was consistently 3% lower than the op-timum q for the 7-6, P (14) region. Since these differ-ences were consistently the same with each of thethree water profiles of Fig. 7, a simple correctioncould remove the discrepancy. Thus a relative trans-mission measurement at single frequencies near the7-6, P(14) and 6-5, P(19) CO laser lines could pro-vide a value for q, and this value of q (multiplied bythe small correction factor just mentioned) could beused to determine the amount of water vapor absorp-tion at either of the other two frequency regions.Then the contribution to absorption due to nitricoxide could be determined. In warm, high humidityenvironments, the low altitude water vapor absorp-tion coefficient in these frequency regions amounts toaround 2 km-1.8 The low altitude nitric oxide ab-sorption coefficient near 1900.076 cm-' is 0.3 km-'when the concentration is 0.1 part per million. If thewater vapor absorption is known with 1% accuracy atthe nitric oxide sounding frequencies, the low alti-tude nitric oxide measurements are accurate to about10 parts per billion.
The LAS can provide adequate information aboutwater vapor absorption if another sounding frequen-cy is added. In some cases it would be preferable touse the water vapor information provided by a pas-sive instrument. If the LAS operates from a low or-biting spacecraft, valuable time and/or power can besaved if another instrument on the spacecraft pro-vides the water vapor data. In this case, an accuratemeasurement of total water burden or a water profilethat is accurate at low altitudes is sufficient.
frequencies are near the P (24) line of the CO2 laser,oscillating in the 0001 - (100, 0200)ii band. Thisline frequency is 1043.163 cm-'. The next twosounding frequencies are near the P (20) line at1046.854 cm-', and the last one is near the P (22) lineat 1045.022 cm-1. (These CO2 laser frequencies arefrom Ref. 23.) Again the maximum frequency dis-placement from laser line center to sounding fre-quency is about 750 MHz.
Figures 9 and 10 illustrate how ozone profiles canbe reconstructed, using the above sounding frequen-cies and the iteration technique. In Fig. 9 we showthe results when the initial guess is a uniform mixingratio of ozone. The tremendous disparity between
3
2
Fig. 8. Normalized weighting functions for ozone. See text forthe sounding frequencies that produce these functions.
Ozone Altitude Profile Determination
The V3 band of ozone, around the 9.5-gim region,was studied using the AFCRL line parameter compi-lation2 2 in order to find useful sounding frequenciesthat were near CO2 laser line frequencies. [Theozone line strengths obey Eq. (10) when n = 1.5, andwe assume m = 0.5 in Eq. (11).] The region near the(7, 1, 6) - (7, 1, 7) line at 1043.188 cm-' providesgood upper altitude weighting functions, because thisis a medium strength line that is fairly well separatedfrom other lines of comparable or larger line strength.[The energy level quantum number designation is (J,Ka, Kj. ] The line strength of this line is So = 12.28cm-2/g cm-3, ao(T = 295 K) is 0.110 cm-', and E" is26 cm-. In order to obtain good lower altitudeweighting functions, one should use soundingfrequencies that are as far removed from strong linesas possible,, but at which the absorption coefficient ina 1-atm pressure background is appreciable. Theseconditions can be met because of the multitude ofclosely spaced, weak absorption lines in the Y3 band.
Ozone profiles were determined up to a 30-km alti-tude, the point where Doppler broadening becomescomparable to pressure broadening. The sevensounding frequencies that were chosen for determin-ing the ozone profiles are as follows: (1) 1043.188cm- 1 ; (2) 1043.186 cm-'; (3) 1043.184 cm-'; (4)1043.180 cm- 1 ; (5) 1046.875 cm-l; (6) 1046.870 cm-I;(7) 1045.039 cm-'. The normalized weighting func-tions obtained with these sounding frequencies areshown in Fig. 8. These curves for ozone are similarin shape to the nitric oxide normalized weightingfunctions shown in Fig. 2. The first four sounding
the initial guess and the actual profile at lower alti-tudes cannot be overcome, and the result aftertwenty iterations is an average value for the lower 10km and a good fit for the higher altitudes. This re-sult is expected because the lower altitude weightingfunctions overlap somewhat as seen in Fig. 8. In Fig.10 we present fits to two different ozone profiles. Asingle initial guess is used for both profile reconstruc-tions. One profile corresponds to what might be ex-pected over an urban area, with high concentrationsnear the ground. The profile reconstruction is quitegood at all altitudes. The fit to the other profile isalso good at the upper altitudes and near the ground,but there is not enough altitude resolution to followthe inflection in the 8-16-km region. The weightingfunctions used for this altitude region are quite broadand overlap extensively.
We conclude that with the LAS technique it is pos-sible to gain information about ground level concen-trations even when looking through a large part ofthe stratospheric ozone band. These profile deter-minations should be carried further by including theozone above 30 km with Voight line shapes to simu-late looking downward from spacecraft altitudes.We do not expect the profile determinations to losemuch accuracy when this is done.
Effect of Errors in Absorption Measurements
The iterative technique of profile reconstruction ishelpful when information concerning measurementserrors is desired. The percentage residual,
R = (102){[Ka(i) - Kc(Vi)1/Ka(l)}, (13)
is computed for each sounding frequency vi aftereach iteration. When the percentage residuals aftera number of iterations fall below a value that is ac-cepted as the accuracy with which absorption mea-surements can be made, the iterations can be termi-nated. The reconstructed profile at that iteration isthen accepted as the best that can be done given theinstrumental limitations. In the nitric oxide andozone cases, the residuals reached a level of severaltenths of a percent after twenty iterations when aneffective set of sounding frequencies was used. Thiswas taken as the termination point in our computa-tions. We can estimate that the profile reconstruc-tions shown in this paper would not deteriorate if anabsorption measurement accuracy of 1% is achievedat each channel. We plan to make further computa-tions that include a random noise term in the totalmeasured absorption at each sounding channel. Theresults of these computations will produce more de-finitive answers to the question of how much variousabsorption measurement errors deteriorate profile re-constructions.
Temperature Effects
The differential absorption technique of obtainingconcentration vs altitude profiles is quite insensitiveto the temperature profile if absorption lines are cho-sen that have a small value of E", the energy of the
lower level. This reduces the exponential depen-dence of line strength on temperature. In addition,when a line has a value of E ", dependence of linethat is comparable to or larger than kT, the weight-ing function corresponding to a sounding frequencyat line center will fall off at high altitudes, which isnot desired. If E" is small compared with kT, theline strength dependence on temperature, accordingto Eq. (10), is predominantly due to the rotationalpartition function factor (TO/T)n. This factor caus-es the sounding frequency at line center to becomerelatively more sensitive to upper altitude molecules.
The temperature dependence of the line width,given in Eq. (11) with m normally equal to 0.5, causesthe line width to increase with altitude when thetemperature is decreasing. However, this effect isvery small compared with the opposite pressure ef-fect. The temperature profile normally reaches aminimum around the 15-km region, where the tem-perature factor in Eq. (11) might reach a value of 1.2at the most. On the other hand, the pressure at thataltitude is around 100 mbars, causing the line widthto be reduced by a factor of 10.
We have studied the effect of uncertainties in theknowledge of the temperature profile on the concen-tration profile reconstructions, and we have foundthe resulting errors to be quite small. Temperatureprofiles that are obtained by using flight radiometersdesigned for that purpose are generally accurate towithin 5 at a given altitude. Thus it is advanta-geous to use a technique that does not depend criti-cally on knowlege ofthe temperature profile to with-in a few degrees. We modified the iteration tech-nique described earlier so that the computations ofKC (vi), using the trapezoidal rule approximation ofEq. (9), were made with a temperature profile guesswhich was different from the actual profile. Severalguesses were used, all differing from the actual tem-perature profile in Fig. 3 by 3-6° at any given alti-tude. In all cases, both nitric oxide and ozone profilereconstructions based on these guesses differeed fromthe original profile reconstructions by no more than5% at any altitutde. The average deviation wasabout 3% for nitric oxide profiles and 2% for ozoneprofiles. Thus temperature profile uncertainties ofthis magnitude do not cause major problems.
Although we have not explicitly demonstrated theLAS capabilities in isothermal atmospheric regions(e.g., near the tropopause), the active absorptiontechnique should be able to obtain information inthese regions as well as elsewhere. This contrastswith the foible of passive radiometers in this area; allpassive instruments that detect upwelling thermalradiance do not see isothermal regions, and constitu-ents in these regions do not contribute to the instru-ment measurements.
Frequency Stability Requirements
The sounding frequencies corresponding to the ni-tric oxide weighting functions in Fig. 2 differ from
each other by a few thousandths of a wavenumber.In frequency units, 0.001 cm-1 equals 30 MHz. Thusin some cases a laser frequency instability of theorder of 30 MHz would noticeably alter the soundingcharacteristics and smear out the altitude resolutioncapability. No quantitative studies of the effects offrequency instabilities on each sounding channelhave been conducted. However, it seems reasonableto set a limit of about 10 MHz on the frequency ex-cursions of a given sounding channel in order to avoiddeterioration. This restriction is more important forthe sounding channels near the center of the absorp-tion line.
Conclusions
The airborne laser absorption spectrometer hasmany capabilities that other remote sensing instru-ments lack. Passive radiometers that operate in adownward looking mode detect predominantly scat-tered sunlight in the spectral region below 3 gm or 4,m and upwelling thermal radiation at longer wave-lengths. The instruments that detect scattered sun-light can measure the total burden of a constituentand are sensitive to the presence of trace constitu-ents. However, they cannot be used to determine al-titude profiles, and they operate only in daytime.The instruments that detect upwelling thermal ra-diation can be used to determine altitude profiles,but the profile reconstruction technique is relativelycomplex and depends critically on the temperatureprofile.24 The necessary number of sounding chan-nels is large because the weighting functions dependon the altitude profile itself, in addition to the tem-perature profile. The sensitivity to low altitude con-centrations is poor, but the sensitivity to upper alti-tude concentrations is good, especially if the instru-ment has high spectral resolution. The LAS can bequite sensitive to constituent concentrations at anyaltitude and is capable of producing altitude profilesup to the lower stratosphere at the least. It is rela-tively insensitive to the temperature profile, and onlya few sounding channels are necessary. This is fortu-nate, since the price of adding a large number ofsounding channels to a laser instrument is high interms of power requirements and instrument com-plexity. The LAS can be useful both in low flyingaircraft, monitoring local areas, and in low orbitingspacecraft, for regional and global monitoring. Insome respects the LAS complements the differentialabsorption lidar technique based on Mie scattering,25
which appears to be promising for mapping pollutantconcentrations near the ground over shorter rangeswith a high range resolution.
The sounding frequencies that we used for deter-mining nitric oxide and ozone profiles are not neces-sarily optimum; there is plenty of room for improve-ment. The nitric oxide R (6 - 1/2)1/2 line is verystrong, and consequently the total absorption nearline center is very large if nitric oxide concentrationsare large. A weaker NO line with a low E ", which isin a region of high water vapor transmission, might
be a better candidate. The ozone spectrum is com-plicated, and further study might produce a betterset of sounding frequencies, especially for the alti-tude region from 5 km to 15 km. Rare isotope CO2and CO lasers offer a multitude of lines that we didnot consider in this work. They will make availablemany more frequency regions that can be used in at-mospheric sounding.
This paper presents one phase of research carriedout at the Jet Propulsion Laboratory, California In-stitute of Technology, under contract NAS 7-100,sponsored by the National Aeronautics and SpaceAdministration.
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