Aerosol backscattering profiles at X = 10.6 ptm

M. J. Post, F. F. Hall, R. A. Richter, and T. R. Lawrence

A systematic program of observing atmospheric backscatter ( profiles from 4 to 16-km above sea level is de-scribed. Initial monthly averages indicating a lognormal distribution are presented. Cirrus prevalence,volcanic layers in the stratosphere, diurnal effects, convection, calibration, and absorption effects are dis-cussed as well.

1. Introduction

NOAA's pulsed CO2 Doppler lidarl has begun along-term measurement program at the Table Moun-tain field site north of Boulder, Colo. We are deter-mining the average backscattering profile of the atmo-sphere and its statistical variability for this location.Our motivation is to test the validity of various modelsfor 10.6-um backscattering2 which are crucial to theperformance (and feasibility) of a global wind moni-toring system such as Windsat.3

II. Procedure

Data are recorded daily, weather permitting, with thelidar pointed vertically. Doppler information of thereturn signal is not used, but only the backscatteredirradiance vs range (or altitude) is recorded and pro-cessed for this study. Typically, 500 pulses of 60-120-mJ energy of 3-6-psec duration are transmitted fora data run covering 50 sec in time. Experience hasshown that at the altitudes and range resolutions(0.3-1.0 km) considered, fluctuation of the mean valueof aerosol backscattering is <10% in 50 sec. This isconsistent with earlier boundary layer studies 4 showingthat atmospheric aerosol backscatter structure func-tions nearly follow Kolmogorov variability. Incoherentaveraging of pulses is essential in the reduction of dataas indicated by Fig. 1 because of large fluctuationswithin the return from a single pulse induced by Ray-leigh phasor statistics.5

Our system has been repeatedly calibrated as de-scribed in Ref. 1 and thus far has performed within 7 L1 dB of a theoretically perfect lidar. To determine /values from observed SNR vs range we use the equa-tion

SNR = KnPTAjA2A3A 4 A5a2 7rCT (1)8hvBR 2

where K = unexplained loss term,7 = detector quantum efficiency (as specified

by the manufacturer),PT = peak pulse power (W),

The authors are with NOAA Environmental Research Laboratories,Wave Propagation Laboratory, Boulder, Colorado 80303.

Received 29 March 1982.

Al = round-trip optical loss factor,A2 = CO2 gaseous absorption loss factor

(range dependent),A3 = H20 gaseous absorption loss factor

(range dependent),A4 = laser beam truncation loss factor,A5 = shot noise loss factor,

a = exp(-2) Gaussian beam power radius atprimary (m),

c = speed of light (m sec'),-r = pulse duration (sec),/ = backscatter coefficient (m-1 sr-'),h = Planck's constant (Jsec),v = frequency of laser (Hz),

B = bandwidth (Hz), andR = range (m),

and solve for /3.Much care was taken in investigating the effects of

the gaseous absorption (A2,A3) and truncation terms(A4) on the: / profiles, and those effects were found tobe large (and nearly equal) but tenable. Figure 2 showsthe magnitude of the two effects on the observed data.For gaseous absorption we use the mid-latitude summermodel previously developed by WPL2 and cross-checked on its validity with the WPL dual-channel ra-diometer,6 which determines total water vapor content,integrated vertically. Errors caused by assuming themodel profile when the actual profile differed werefound to be <1 dB. Truncation effects were verified inseparate experiments involving hard targets at variousranges. They quantify heterodyne mixing degradationscaused by using a finite portion of the infinitely wideGaussian transmitted beam. A trade off in how muchof the beam to use must be made involving overfillingthe primary (losing power) and underfilling, it (largediffraction-limited focal volume). We truncate at 0.93of the exp(-2) power.

Daily profiles such as that shown in Fig. 2 are plottedusing 0.3-km vertical resolution, the approximate rangeresolution of the lidar. For statistical purposes, how-ever, backscattering is averaged over 1-km increments,with each increment centered on even altitude intervalsin kilometers above sea level (ASL).

The minimum detectable /3 level shown in Fig. 2 isdetermined by comparing the relative uncertainties insystem noise power (N) and signal plus noise power (S

2442 APPLIED OPTICS Vol. 21, No. 13 / 1 July 1982

20

a

0

.0

EZ

0a.

spheric ~~~~~~~~ ~ ~~1 Pulse

Time (s)

Fig. 1. Incoherent averaging of coherent lidar returns from atmo-spheric aerosols to reduce both Rayleigh phasor noise and systemnoise (14 May 1981, Boulder, Colo.). We typically average 500 pulsesbefore processing for f. Vertical scale is one-tenth of the systemdynamic range. Cirrus thickness was determined to be 105 ± 15 m

by deconvoluting the lidar pulse shape from the observed return.

-j

CD

.

10 11 10-10 10-9

,G (m-1

sr-1

)

10-8 10-7

Fig. 2. Backscatter coefficient profile for a single 500-pulse (50-sec)data run showing the effects of including truncation and absorption(solid line, corrected data) and ignoring it (dashed line, uncorrecteddata). Also depicted as a dotted line is the minimum detectable j3

level for 500 pulse averaging.

15

10

5

01xl i 3 4 5 6 7 8 lxlOS

Backscatter Coefficient, , ' sr')Fig. 3. Histogram of backscattering coefficients for sixty-eight500-pulse data runs late spring and summer 1981 at Boulder, Colo.

Range gate is 1 km centered at 7-km ASL.

+ N) after incoherent averaging. The mean noise levelN has an uncertainty oN determined numerically froman average noise profile (telescope blocked). For verylow signals (S + N) N and N = OlS+N = . Whileprocessing for /3 we choose a noise window containingl points and a resolution in : representing 1,3 points.The uncertainty in mean power levels when averagingover points is reduced by 1-112. Thus to detect signal(S) above noise, where each is averaged over 1 and 1,Z,points, respectively, S = (S + N) _ (N) > (l/2 +1~1/2). We define a quality factor Q = S/ > 1d1/2 +w1/2, and require that the observed data meet this re-

quirement before they are accepted for inclusion in a/profile.

111. Monthly Averaged Profiles

While analyzing the /3 data it became obvious that theday-to-day / values at higher altitudes were distributedin a lognormal fashion; that is, skewed strongly towardlower values of / as shown in Fig. 3. By weighting eachday's value equally the resultant linearly averaged orarithmetic mean value is unrealistically high, primarilybecause of a few extremely high / values. But by firsttaking the logarithm of /, averaging the logarithms, andthen taking the inverse logarithm of this average, a morerepresentative geometric mean value is obtained some6 dB lower than the linearly averaged case.

We must stress that the linearly averaged / value isnot wrong, but one must then apply the proper lognor-mal fluctuations onto this mean value when doing sys-tems studies.7 If such fluctuations are not incorporatedinto the study, a more representative /3 value is thelog-averaged /.8 This property is exemplified in Fig.4, where the spread of the /3 data even at a relatively low(well-mixed) altitude of 4-km ASL is clearly logarithmicin character. At a higher altitude of 7 km the data fita lognormal distribution even better.

Physically, in the free atmosphere many of theaerosols have been convected upward out of the

1 July 1982 / Vol. 21, No. 13 / APPLIED OPTICS 2443

geometric

mean

arithmetic

mean

-T 41r,

1.4 -7

S

-a

E

E

air-0_1

1.2 7

lx 7 E can -8

- c0.8 E

0.6 0 -9

0.4 E

0.2 Q:w -100

o -j1 2 5 10 20 40 60 80 90 95 99 | 1 1 | I I I I i I I I I I I

Cumulative Probability () 1 2 5 10 20 40 60 80 9095 99Cumulative Probability (%)

Fig. 4. Cumulative probability of 13 for May-July 1981 at Boulder, Colo. The top data set (a) of seventy-five independent measurementsfor 4- km ASL indicates an approximate lognormal distribution, comparing logy (left ordinate) with 13 (right ordinate) distributions. The

lower data set (b) for 7-km ASL is a very good fit to a lognormal distribution.

16

14

-jC)

'D

1 2

1 0

I I I

Average ProftilesFor June 1981X = 10.6um

| \ Arithmetic Mean

N

-Geometric Mean

4L

Cirrus

I I I

1-11 10-10 10 9 10-8 10-7

/3 (m-1

sr-1

)

Fig. 5. Average profiles for Boulder, Colo., June 1981, includingand excluding data containing cirrus returns. Both linear-averaging(arithmetic mean) and log-averaging (geometric mean) are indicated.Compare with model profiles of Fig. 6. At each level standard de-

viations are approximately equal to the mean value.

boundary layer by convective plumes. While aerosolsources may be additive (Gaussian) at the surface, theconvective plumes are multiplicative in nature, 9 therebyorganizing the aerosols into a lognormal spatial distri-bution at higher altitudes but more weakly at lower al-titudes. This result should not be surprising since theheight and horizontal dimensions of cumulus clouds areknown to follow lognormal distributions,' 0 and manyof the aerosols in the midtroposphere may have passedthrough short-lived convective clouds.

Figure 5 shows two linearly averaged profiles for themonth of June 1981-one including backscatter fromeasily visible cirrus and one excluding it. In additionthe log-averaged profile, which is identical for bothcases, is shown for comparison. Note how the geo-metrically averaged profile separates from the otherswith increasing altitude. For the month over sixtyprofiles were recorded at various times of day and invarious weather conditions. Any profile showing thepresence of cumulus clouds was not used in the averages,nor was more than one profile per day included, and itwas chosen at random. (Choosing a different set ofrandom profiles does not affect the averages signifi-cantly.) Standard deviations of the /3 values at eachaltitude are not shown, but typically they are similar inmagnitude to the value of the data except for cirrus,where fluctuations are much higher." Figure 6 showsmodel profiles2 used by WPL in lidar system analysesfor comparison.

Several features of these linearly averaged profiles areworthy of note. Enhanced at cirrus altitudes is moreprevalent in our data (-50% of the time) than we ob-serve visually (30% of the time). Even the profileexcluding cirrus shows enhanced backscatter, perhapsthin or diffuse cirrus, in the upper levels, although thisfeature disappears with log-averaging. Calculationspredict (and our observations of volcanic dust beyondthe cirrus support) the hypothesis that attenuation bythin cirrus at X = 10.6 Mim is not significant, althoughbackscatter is greatly enhanced. This is an importantconsideration for Windsat, meaning that a satellite-lidarmeasurement of winds in the upper atmosphere wherecirrus occurs but where backscattering is otherwiserelatively low may be possible on many occasions. Asan aside, the level of cirrus on any particular day did notnecessarily correlate well with Denver radiosonde de-termination of the tropopause. Many times in earlysummer cirrus appears in our profiles above the radio-sonde tropopause, the lowest level at which the tem-perature lapse rate decreases to 2K km-' or less.1 2 On

2444 APPLIED OPTICS / Vol. 21, No. 13 / 1 July 1982

I . .

- 7

16

14

:- 12-J

-=10

41

deModel

I I I

- WPL \ I

- I

. I- I

I WPL- Midiatitu

S ummer-I

-I

- WPL XSubarctic \

- Winter Model \

I-10-11 10-10 10-9 10-8 10-

7

(m1 sr'1 )

Fig. 6. Model profiles used by WPL in its Windsat studies. Themid-latitude summer model fits the average June profile excluding

cirrus rather well.

18

Stratospheric StratosphericDust Dust

14-

ThunderstormAnvil Cloud

~12-

10

5

- ~~~~~~~~iing} ondensation6 Level

4 - 11:17 MDT 19:56 MDT

1o-1r 10 to i0-9

lo-, lo-, 10-li io-10 lo-, lo-, lo-,

13 (mt

sr-) )3 (m-1

sr-')

Fig. 7. Profiles taken on 13 June 1981 at Boulder before (11:17MDT) and after (19:56 MDT) strong convection showing the precloudformation lifting condensation level, injection of particulates into themidtroposphere, and the anvil blowoff from a cumulonimbus cloud.

these occasions, such as on 20 June 1981, air trajectoryanalyses show that these cirrus clouds are probably oftropical origin, having passed through a tropopausebreak.

The slightly enhanced backscatter at 6-km altitudeprobably represents the increased size and scatteringefficiency of aerosols at the lifting condensation level.Here the high relative humidity allows water coatingand growth of natural aerosols.13 Similar monthlyaverages will be computed each month for a one-yearcycle or as continuously as possible.

I I I

IV. Case StudiesThree case studies are worthy of note-one involving

strong convection, another diurnal variationsthroughout a day, and the third volcanic dust layers inthe stratosphere.

Two : profiles are shown in Fig. 7-the first in themorning before strong convection and the second for thesame air mass but in the evening after strong convectionhad occurred. The latter was taken in the clear airbetween towering cumulonimbus. Apparently aerosolsare carried aloft by the cumulus and are deposited in theupper atmosphere in the region of the tops of thun-derstorms, where they recirculate downward in thedowndraft regions between cells. We reach this con-clusion because of the enhanced upper-level returnsobserved in the second profiles, and because we ob-served both visually and with the lidar, a thunderstormanvil cloud near the center of the enhanced region.

A stacked set of profiles made once per hour fortwenty-one consecutive hours is shown in Fig. 8. Cu-mulus buildup near the end of the period prevented thecompletion of a full 24-h cycle. The diurnal changes in/ are generally as expected. The boundary layer growsboth in altitude and in backscatter value as mixingcarries particles aloft during the daytime hours. Themiddle tropospheric backscattering also increases andreaches higher levels as well, but the mechanism fordoing so is not obvious. No cumulus buildup was ob-served during this time, but dry convection over theRocky Mountains to the west certainly occurred. A clueto another mechanism may lie in the sudden enhance-ment and weakening of backscatter in the midtropo-sphere at sunrise and sunset, respectively. Perhapsphotochemical formation of particulates is occurring.We plan to do similar 24-h sequences during the nextyear to better characterize diurnal trends.

Figure 9 shows strong scattering layers in thestratosphere which may be related to the 13.5-15-kmhigh ash plume from the 28 April Kurile Islands(U.S.S.R.) volcanic eruption of Alaid.14 Satellite ob-servations indicated that the plume did drift ESE to40°, the latitude of Boulder. Our observations weremade during daylight hours in contrast to normalnighttime stratospheric observations for ruby lidars.These layers persisted for nearly two weeks over Boul-der before dissipating. We also occasionally observethe Junge layer at 18-22-km ASL.

More recent (fall, 1981) spot checks of /3 both inBoulder and at Edwards Air Force Base, Calif., showsignificantly lower mean values in the 6-15-km altituderegion than those reported here (spring and summer,1981). Future analysis will quantify these dropoutswhere /3 < 10-'0 m-1 sr-' is measured.

The authors wish to acknowledge the help in systemdevelopment, data taking, and data processing affordedby R. M. Hardesty, D. V. Jensen, and D. K. Churchill,and the advice in data analysis by R. J. Keeler.

1 July 1982 / Vol. 21, No. 13 / APPLIED OPTICS 2445

Fig. 8. The 21-h stacked backscatter profiles for22, 23 June 1981. Diurnal effects are discussed in

the text.

1o-01 1010 10-9 10-8 10-7

( 1 s 1)

E

-J

0

V)

0 500 1000 1500Relative Power (linear)

2000

Fig. 9. Raw data (signal power vs altitude) for the strongest observedvolcanic debris return. Aerosols are present to 10-km ASL, and debrisis observed through a tenuous cirrus layer. Power scale is one-tenth

of the system dynamic range.

References1. M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, and

F. F. Hall, Jr., Proc. Soc. Photo-Opt. Instrum. Eng. 300, 60(1982).

2. M. J. Post, Appl. Opt. 18, 2645 (1979).3. R. M. Huffaker, Ed., "Feasibility Study of Satellite-Borne Lidar

Global Wind Monitoring System," NOAA Tech. Memo. ERLWPL-37 (U.S. Government Printing Office, Washington, D.C.,1978).

4. M. J. Post, Opt. Lett. 2, 166 (1978).5. R. M. Hardesty, R. J. Keeler, M. J. Post, and R. A. Richter, Appl.

Opt. 20, 3763 (1981).6. F. 0. Guiraud, J. Howard, and D. C. Hogg, IEEE Trans. Geosci.

Electron GE-17, 129 (1979).7. R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T.

Priestly, and J. A. Korrell, "Feasibility Study of Satellite-BorneLidar Wind Monitoring System, Part II," NOAA Tech. Memo.ERL WPL-63 (U.S. GPO, Washington, D.C., 1980).

8. R. Langley, Practical Statistics (Dover, New York, 1971), Chap.4.

9. J. Aitchison, and J. A. C. Brown, The Lognormal Distribution(Cambridge U.P., London, 1957).

10. R. E. Lopez, Mon. Weather Rev. 105, 865 (1977).11. F. F. Hall, Jr., M. J. Post, R. A. Richter, and G. M. Lerfald, "A

LOWTRAN V Subroutine for Cirrus Cloud Transmittance fromUltraviolet to Infrared," NOAA Tech. Memo. ERL WPL- (U.S.Government Printing Office, Washington, D.C., 1982).

12. R. A. Craig, The Upper Atmosphere Meteorology and Physics(Academic, New York, 1965), pp. 23-33.

13. G. Hanel, Tellus 20, 371 (1968).14. EOS Trans. Am. Geophys. Univ., 62, (19) 494 (1981).

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