# Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

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Ground-based measurements of atmospheric backscatter andabsorption using coherent CO2 lidar

Jeffry Rothermel and William D. Jones

A slant path method is used to derive vertical profiles of atmospheric absorption and backscatter coefficientsfrom eleven months of coherent pulsed CO2 Doppler lidar measurements in Huntsville, Ala. Good agreementis found between lidar- and radiosonde-derived absorption profiles. A strong seasonal variation of backscat-ter and absorption is evident throughout the lower troposphere as well as variations on a wide range of finertemporal and spatial scales. Typical summer and winter backscatter values in the boundary layer fall in the10-7-10-8- and 10-$-10- 9 -m-1 sr-1 range, respectively. Measurements beyond the lower troposphere arehampered by modest pulse energy and lidar beam absorption; however, backscatter values as small as 4 X10-11 m- 1 sr-' occasionally are observed at midtropospheric levels during the winter months when absorptionis minimal. A monomodal lognormal backscatter distribution is found within the lower boundary layer; athigher levels, evidence is found of a bimodal lognormal distribution.

1. IntroductionInterest is rapidly growing in the measurement of

atmospheric aerosol backscatter coefficients at CO2laser wavelengths. Initially, measurements of thiskind were used in radiative energy exchange models toassess the possible role of atmospheric aerosols as anagent for climatic change.1 Ground-based and, in par-ticular, mobile lidar measurements have also beenused to study the processes of aerosol origin, transport,and removal. More recently, major CO2 aerosol back-scatter measurement programs have been initiated inresponse to a proposed concept to measure tropo-spheric winds on a global scale using a satellite-borneCO2 lidar.2 One preliminary study3 has indicated thatthe input of global wind measurements into an atmo-spheric general circulation model would result in im-proved forecasts of global weather by providing betterspatial and temporal resolution over areas of the globewhich are not sampled adequately by the present ra-winsonde network. The accuracy of the lidar-derivedwinds and the design criteria for the lidar system are

Both authors are with NASA Marshall Space Flight Center,Huntsville, Alabama 35812; J. Rothermel is in the Systems Dynam-ics Laboratory, Atmospheric Sciences Division, and W. D. Jones is inthe Information & Electronics Systems Laboratory, Guidance, Con-trol, & Optical Systems Division.

Received 29 April 1985.

critically dependent on knowledge of the spatial andtemporal distribution of global tropospheric backscat-ter.2

Knowledge of global backscatter at CO2 wavelengthsis incomplete, because existing CO2 aerosol backscat-ter data sets have been obtained on a rather limited,although rapidly expanding, spatial and temporal ba-sis. The data base includes airborne measurementswith focused cw CO2 lidars by Schwiesow et al. 4 in thelower troposphere near Boulder, Colo., during winter1978 and by Vaughan and Woodfield5 up to a 13-kmaltitude over Northern Europe and the U.K. duringmore than three years of operation over different sea-sons as well as in Colorado during the summer 1982Joint Airport Weather Studies (JAWS) experiment.5Menzies et al. have described an ongoing measurementprogram at the Jet Propulsion Laboratory in Pasade-na, Calif., using a ground-based coherent CO2 pulsedlidar at 9.25 and 10.6 m.6 The most extensive CO2backscatter data set at a fixed location includes over600 vertical profiles obtained by the Wave Propaga-tion Laboratory, NOAA at Boulder, Colo., betweenMay 1981 and May 1984.7

A key portion of the existing data base has beenprovided by measurements from workers at NASAMarshall Space Flight Center (MSFC). The MSFCdata include airborne measurements with a focused10.6-,gm cw CO2 system over California and the centralU.S.A. during several weeks in summer 19818 and overCalifornia, Montana, and the Caribbean during springand summer 1982. Intercomparisons between theMSFC airborne cw system, the MSFC airborne pulsed10.6-um CO2 Doppler lidar system (DLS), and the

1 November 1985 / Vol. 24, No. 21 / APPLIED OPTICS 3487

NOAA ground-based lidar have shown generally goodagreement. The DLS was also used in a ground-basedmode during the 1982 JAWS experiment. Analysis isin progress on new airborne MSFC measurements us-ing the DLS and cw systems over California and theeastern U.S.A. during summer and fall 1984.

After JAWS, the DLS was returned to MSFC atHuntsville, Ala., where it was operated in the ground-based mode from Apr. 1983 through Feb. 1984. Cali-brated measurements of backscattered intensity,winds, and turbulence intensity were made until thesystem was removed in preparation for the 1984 air-borne measurement program. This paper reports re-sults of calculations of backscatter coefficient and ab-sorption profiles in the troposphere using a slant pathmethod. Section II gives a brief site description. Sec-tion III describes the method of solution and datasampling procedure. Section IV presents and dis-cusses vertical profiles, time series, and cumulativeprobability distributions of backscatter at selectedvertical levels. A brief summary is given in Sec. V.

II. Site DescriptionThe DLS was located in a small field in the west-

central part of the U.S. Army Redstone Arsenal, whichlies on the western boundary of Huntsville, Ala. Thecity and county have populations of -150,000 and200,000, respectively. The Arsenal, with 190-m eleva-tion, is surrounded on three sides by the foothills of theAppalachian Mountains with maximum altitude of550 m in the city limits and is located 480 km north ofthe Gulf of Mexico in the Tennessee River Valley.Land use is primarily agricultural. Typically, the lo-cal weather is determined by alternating air masseswith origins either in the Gulf of Mexico (maritimetropical) or Canada (continental polar) with occasionalintrusions from maritime polar source regions. Janu-ary and July mean monthly temperatures, which rep-resent the extremes, are 4 and 260C, respectively. Av-erage annual precipitation is 1415 mm with negligiblesnowfall.

Ill. Method of SolutionA number of techniques exist to separate the back-

scatter coefficient from the effect of extinction (trans-mission loss) due to scattering and absorption of thelidar beam by the intervening atmosphere on a two-way trip to a measuring volume and back. In the firstset of methods, extinction is determined by direct cal-culation of molecular absorption or molecular and par-ticulate scattering, either from climatological averagesor standard models for a given season, latitude, or airmass type,9 or from nearby rawinsonde measurementsof atmospheric thermodynamic structure. Both ap-proaches have drawbacks. The climatological meth-ods depend on averages that may not be valid on aparticular day, and the rawinsonde method presentsoperational difficulties and additional data reduction.

In a second set of methods, the lidar system itself isused to determine both backscatter and absorption.The Klett method" uses backscatter and intensity

I

:3E-.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

*CONSTANT ( ) a WITHIN r!- EACH LAYER "I'

I,,i . , '

= ~~~~~~~~~~,

LIDA R

sented as a stack of plane-parallel layers. The thick-ness of each layer is taken equal to the range resolutionof the lidar cr2, where c is the speed of light (3 X 108 msec'1) and T is the pulse duration (seconds). Withineach layer the extinction a and the backscatter 3(71-)coefficients are taken to be constant within the maxi-mum range (30 km) of the lidar. Consider the caseshown in Fig. 1 where the lidar probes the atmosphereat an arbitrary elevation angle 0. The lidar equationfor the SNR due to backscatter from the layer at heightz is

- 7E Xb /3(T) CT lo-02cIZ adz, (1)N hb 2 +R 2 2 Jwhere q = system efficiency;

E = pulse energy (J);hv = photon energy (J);X = wavelength (m);b = Rayleigh distance (m);

R = slant range (m) = z csc0;0(01 = atmospheric backscatter coefficient (m-' sr-'),

anda = atmospheric extinction coefficient (dB m-).

Converting Eq. (1) to decibel units and rearrangingterms,

10 log10 (N) = C + B - 10 1oglo(b2 + R2) -2 cscOT2 , (2)where C = 10 loglo [(nEXbcr)/2hv)], system constant;

B = 10 logiofl(r); andT = Jo adz, one-way vertical transmission to

height z.Equations (1) and (2) show that the backscattered

intensity of the lidar signal is affected by the charac-teristics of the lidar, range, elevation angle, and atmo-spheric extinction and backscatter coefficients.Without a priori information or assumptions aboutthe vertical distribution of either backscatter or ex-tinction, it is not possible to determine both the back-scatter and extinction profiles from a single lidarsounding of the atmosphere. However, informationfrom lidar shots at different elevation angles can becombined to determine T. To illustrate the simplestcase, let SNRV and SNRS be the signal-to-noise ratiosobtained, respectively, from a vertical sounding of alayer with its center at height z and from a sounding ofthe same layer along a slant path at elevation angle 0(see Fig. 1). Using Eq. (2),

SNR = C + B - 10 logl0(b2 + 2) - 2Tz, (3)SNR = C + B - 10 logl0(b2 + 2 csc2) - 2 cscOTz. (4)

Subtracting Eq. (4) from Eq. (3), assuming horizontalhomogeneity, and solving for T yields

SNR - SNR + 10 log1 0 ( b2 + 22(escO - \b2 + ) w e c (

The third term in the numerator of Eq. (5), where b=

7rD2/4X, corrects for diffraction loss; D is the diameter(30 cm) of the coaxial transmit/receive optics. Typi-cally, the diffraction loss term was 2 orders of magni-tude smaller than the difference (SNRV - SNRS.) Tobe strictly valid, this diffraction correction should con-tain additional terms to correct for such factors astruncation, telescope aberrations, and local phasefront distortions. As suggested by Post,15 the ap-proach described by Rye16 could be used to determinethe correction. This method requires knowledge ofthe telescope aberration and any misalignment be-tween laser transmitter and telescope. Alternatively,the diffraction loss at various ranges could be mea-sured experimentally using a large disk target as de-scribed by Hardesty et al.'7 This approach was notpossible at the MSFC DLS site due to the lack of asuitable test range and low contrast when visuallysighting through the lidar telescope. Thus the ap-proach was to model the transmitted beam as an un-truncated Gaussian, where all the factors stated aboveare accounted for by the system efficiency wq containedin the term C in Eq. (4).

Following the method of Hamilton, Eq. (4) wassolved by linear regression. Graphically, T and Bcorrespond to the slope and ordinate-intercept, re-spectively, of the best-fit line. The least-squares algo-rithm was modified to calculate the standard errors forboth the slope and intercept. The standard error isrepresented in the vertical profiles of Sect. IV as thelength of an error bar. The standard error of theestimates was reduced significantly by assigning thecenter of a bin falling within a layer to the height of themiddle of the layer rather than to the actual height.Results of the slant path method were also improvedby rejecting data from elevations above -67 and occa-sional data from within or above cloud layers.

Measurement sets were collected by scanning thelidar through a vertical plane at a rate of 0.5-1.0 sect1,thus one scan through a vertical plane took 1.5-3.0min. Approximately 3-5 min elapsed between thecompletion of one scan and the initiation of another.Determination of backscatter and absorption at two ormore cardinal compass points, closely spaced in time,allowed qualitative assessment of the degree of hori-zontal inhomogeneity. Highest confidence would begiven only to those groups of profiles with good agree-ment at different azimuth angles. Frequently, datawere taken using pulse durations (lengths) of 2 and 8gsec (320- and 1280-m range resolution, respectively).The former permitted finer vertical resolution, whilethe latter frequently permitted observation at longerranges and higher altitudes due to higher pulse energyand higher average output power. The signal-to-noiseratio was improved by averaging 50-200 shots depend-ing on the pulse duration. Since sufficient signal wastypically received only within the first 15 km, the meanand standard deviations for noise were calculatedbased on the average value of noise intensity over tenouter range gates, corresponding typically to a range of20-30 km. This method produced values which variedby only a few percent among data sets. Return signals

1 November 1985 / Vol. 24, No. 21 / APPLIED OPTICS 3489

were not analyzed if less than three standard devi-ations above the noise floor.

A detailed description of the ground-based DLS isgiven by Rothermel et al.1 8 Briefly, the transmitter isarranged in a master oscillator power amplifier(MOPA) configuration; the receiver employs a hetero-dyne arrangement. A pulse rate of 110 pps was used,the energy per pulse typically being 15-20 mJ. Thelidar system is contained within a trailer, the beambeing directed through the roof and to a hemisphericscanner. The intensity, velocity, and spectral width ofthe received signal are obtained from a polypulse pairestimation technique.' 9

IV. Results and Discussion

A. Absorption Profile ComparisonInitial attention focused on corroborating the slant

path method of calculating absorption profiles. On 27May 1983 a radiosonde was released in the vicinity ofthe lidar while scans were being made at 1301 CDT.Lidar pulse duration was 8 gsec. Radiosonde mea-surements of pressure, temperature, and humiditywere used to derive an absorption profile.10 Figure 2compares total one-way vertical absorption (transmis-sion loss) profiles (decibels) based on the slant pathmethod and the radiosonde measurements. Goodagreement is noted to a 7-km height. Included forcomparison are profiles based on Air Force Geophysi-cal Laboratory (AFGL) models of midlatitude summerand winter pressure, temperature, and humidity. Amaximum round-trip error of -2 dB would result fromcorrecting the corresponding backscatter profile (seeFig. 3) using either one of these standard models. Thisfinding is consistent with that of Post, who compared anumber of Denver, Colo., radiosonde absorption pro-files with those based on AFGL models, the extremeerror being 2.7 dB.7 It is conceivable that the AFGLextreme absorption profiles are unrepresentative ofHuntsville extremes, the latter being more widely sep-arated. The backscatter values in Fig. 3 have a maxi-mum of 10-8 m-1 sr-' near the surface, decrease steadi-ly until 3.2-km altitude, and stay relatively constant at10-9 m'1 sr-' above that altitude.

B. Vertical ProfilesRepresentative summer and winter profiles (Figs. 4

and 5, respectively) illustrate the observed extremes inthe annual variation. Variations on a wide range offiner spatial and temporal scales are evident from theensemble of vertical profiles. When the lidar wasoperated on consecut...

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