ground-based measurements of atmospheric backscatter and absorption using coherent co_2 lidar

10
Ground-based measurements of atmospheric backscatter and absorption using coherent CO 2 lidar Jeffry Rothermel and William D. Jones A slant path method is used to derive vertical profiles of atmospheric absorption and backscatter coefficients from eleven months of coherent pulsed CO 2 Doppler lidar measurements in Huntsville, Ala. Good agreement is 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 finer temporal and spatial scales. Typical summer and winter backscatter values in the boundary layer fall in the 10-7-10-8- and 10-$-10- 9 -m-1 sr- 1 range, respectively. Measurements beyond the lower troposphere are hampered by modest pulse energy and lidar beam absorption; however, backscatter values as small as 4 X 10-11 m- 1 sr-' occasionally are observed at midtropospheric levels during the winter months when absorption is minimal. A monomodal lognormal backscatter distribution is found within the lower boundary layer; at higher levels, evidence is found of a bimodal lognormal distribution. 1. Introduction Interest is rapidly growing in the measurement of atmospheric aerosol backscatter coefficients at CO 2 laser wavelengths. Initially, measurements of this kind were used in radiative energy exchange models to assess the possible role of atmospheric aerosols as an agent for climatic change. 1 Ground-based and, in par- ticular, mobile lidar measurements have also been used to study the processes of aerosol origin, transport, and removal. More recently, major CO 2 aerosol back- scatter measurement programs have been initiated in response to a proposed concept to measure tropo- spheric winds on a global scale using a satellite-borne CO 2 lidar. 2 One preliminary study 3 has indicated that the input of global wind measurements into an atmo- spheric general circulation model would result in im- proved forecasts of global weather by providing better spatial and temporal resolution over areas of the globe which are not sampled adequately by the present ra- winsonde network. The accuracy of the lidar-derived winds 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 in the Information & Electronics Systems Laboratory, Guidance,Con- trol, & Optical Systems Division. Received 29 April 1985. critically dependent on knowledge of the spatial and temporal distribution of global tropospheric backscat- ter. 2 Knowledgeof global backscatter at CO 2 wavelengths is incomplete, because existing CO 2 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 measurements with focused cw CO 2 lidars by Schwiesow et al. 4 in the lower troposphere near Boulder, Colo., during winter 1978 and by Vaughan and Woodfield 5 up to a 13-km altitude over Northern Europe and the U.K. during more than three years of operation over different sea- sons as well as in Colorado during the summer 1982 Joint Airport Weather Studies (JAWS) experiment. 5 Menzies et al. have described an ongoing measurement program at the Jet Propulsion Laboratory in Pasade- na, Calif., using a ground-based coherent CO 2 pulsed lidar at 9.25 and 10.6 m. 6 The most extensive CO 2 backscatter data set at a fixed location includes over 600 vertical profiles obtained by the Wave Propaga- tion Laboratory, NOAA at Boulder, Colo., between May 1981 and May 1984.7 A key portion of the existing data base has been provided by measurements from workers at NASA Marshall Space Flight Center (MSFC). The MSFC data include airborne measurements with a focused 10.6-,gm cwCO 2 system over California and the central U.S.A. during several weeks in summer 19818 and over California, Montana, and the Caribbean during spring and summer 1982. Intercomparisons between the MSFC airborne cw system, the MSFC airborne pulsed 10.6-um CO 2 Doppler lidar system (DLS), and the 1 November 1985 / Vol. 24, No. 21 / APPLIED OPTICS 3487

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Page 1: Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

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. Introduction

Interest is rapidly growing in the measurement ofatmospheric 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

Page 2: Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

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 Description

The 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 Solution

A 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

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Fig. 1. Schematic representation of atmospheric vertical planeprobed by ground-based lidar. Within each layer, absorption and

backscatter coefficients are assumed constant.

measurements along a single line of sight to derivebackscatter range profiles using an iterative technique.This method assumes an analytical relationship be-tween aerosol backscatter and extinction and a prioriknowledge of the backscatter value at a given rangegate. This method has been generalized to treat thecombined effects of aerosol and molecular scatteringextinction. The Hamilton method12 uses backscattermeasurements at several elevation angles to derive asingle vertical backscatter profile. Hamilton assumesthe atmosphere to be horizontally homogeneous inbackscatter and extinction at a given height and deter-mines the extinction and true backscatter (i.e., correct-ed for absorption) from a least-squares regression ofrange-corrected SNR as a function of normalized slantpath length. In principle, observations at two eleva-tion angles are sufficient for a direct solution. Howev-er, horizontal backscatter inhomogeneity, combinedwith noisy return signals, can lead to significant errors.In a modification of Hamilton's method, Spinhirne etal.13 considered the atmosphere to be divided intolayers, in each of which it was assumed that (1) theparticulate extinction-to-backscatter cross-section ra-tio is constant, and (2) the effective vertical transmis-sion is constant for all slant paths through the layer.Backscatter and extinction profiles were determinedby using regression analysis with respect to elevationangle for integration of the angle-dependent lidarequation within a given layer. Russell and Living-ston14 used a similar approach. All the above mea-surements were made at the 0.69-gim (ruby) wave-length. The slant path method of Hamilton wasdetermined to be most appropriate for the presentstudy because, at 10.6 ,gm, particulate backscatteringdominates over molecular scattering, while molecularabsorption dominates over particulate absorption.Since the feasibility of this approach for coherent CO2Doppler lidar measurements has not been demonstrat-ed previously, the slant path analytical method and thedata sampling procedure used in this study are docu-mented below.

Figure 1 is a schematic representation of the lidaroperated from the ground. The atmosphere is repre-

3488 APPLIED OPTICS / Vol. 24, No. 21 / 1 November 1985

Page 3: Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

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 J

where 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); and

T = 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 + 2

2(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

Page 4: Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

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 Comparison

Initial attention focused on corroborating the slantpath 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 Profiles

Representative summer and winter profiles (Figs. 4and 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 consecutive days within the same air mass(e.g., no frontal passage), similar vertical profiles ofbackscatter and absorption were found. In generalhowever, the validity of the horizontal homogeneityassumption varied daily within air masses that were intransition.

Figure 4 shows profiles measured on 19 Aug. 1983using 2- and 8-gisec pulse durations. Differences be-tween 2- and 8-gtsec profiles are comparable to differ-ences among individual 8-gsec profiles. However, the

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TRANSMISSION LOSS (dB)

Fig. 2. Comparison between absorption profiles calculated usingslant path method (bars) and calculations of gaseous absorptionbased on measurements of humidity using radiosonde. Included forreference are profiles based on AFGL models of midlatitude summer

and winter pressure, temperature, and humidity.

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Backscatter (/m/sr)Fig. 3. Backscatter profile corresponding to Fig. 2 based on lidarmeasurements and using slant path method. Profile is corrected forabsorption obtained from the same method. The slanted line de-notes lidar system sensitivity for vertically directed shots in the ideal

case of no atmospheric attenuation.

8-gsec profiles are consistently higher. Radar andaircraft observations in clear-air convection (see Sec.IV.D) suggest that there occurred a bias to highervalues by pockets of high backscatter within the longer8-gsec pulse scattering volume. Profiles from obser-vations taken on 18 Aug. (not shown) are nearly identi-cal to those shown in Fig. 4. The high relatively uni-form backscatter and absorption cross sections,suggestive of a deep planetary boundary layer, were

3490 APPLIED OPTICS / Vol. 24, No. 21 / 1 November 1985

AZ 180

Page 5: Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

-19-83

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Fig. 4. Vertical profiles of transmission loss (left) and backscattermeasured using two pulse durations on 19 Aug. 1983 in Huntsville,Ala. Slanted lines denote sensitivity. Strong attenuation is typical

during summer months.

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Fig. 5. Same as Fig. 4 except for 9 Feb. 1984. Weak absorption istypical during winter months. Note secondary backscatter maxi-

mum in 2-Asec profiles not resolved in 8-,usec profiles.

typical of the summer profiles. For several days, en-compassing 19 Aug.'s meteorological conditions inHuntsville were characterized by daytime high tem-peratures of 35-37 0C, light southerly winds, and highhumidities associated with a stagnant high pressurearea over the southeastern U.S.A. During this periodthe Huntsville-Madison County Jetplex, located 10km west of the lidar site, reported visibilities as low as 4km. Visible extinction was so strong that it was possi-ble to view the sun with the unaided eye at least 2 hprior to sunset.

Interestingly, the backscatter profiles in Fig. 4 ter-minate 1-2 orders of magnitude above the system sen-sitivity limit. The strong attenuation (-I dB km-)suggests that the beam is almost completely absorbedon a two-way trip to levels higher than 4 and 6 km,respectively, for 2-,gsec pulse durations. Thus thebackscatter values above 4 km may have been higherthan the system sensitivity limit for 2-,gsec pulses. Ingeneral during the summer and fall months, this type

of strong attenuation limited usable returns to withinthe planetary boundary layer, especially for 2-gusecdata; however, returns from higher levels were ob-tained occasionally at 8-gsec pulse duration.

The largest backscatter values were found in Au-gust. On 19 Aug. a maximum value of 1 X 10-7 m'1sr-1 was found at 3.2-km altitude. On the same day avalue of 2 X 10-8 m'1 sr-' was found at a maximumaltitude of 5.8 km.

Figure 5 shows 2- and 8-gtsec profiles for 9 Feb. 1984.The weak absorption at all levels was typical of thewinter months. The agreement among profiles indi-cates good horizontal homogeneity on this day. Thebackscatter profiles suggest the existence of a muchshallower boundary layer than was evident in Fig. 4.The 2-gsec profiles show a secondary backscatter max-imum at -2 km, which is not apparent in the coarseresolution 8-,gsec profiles. This secondary peak maycorrespond to a haze layer remaining from the diurnalcycle of growth and decay of the boundary layer on the

1 November 1985 / Vol. 24, No. 21 / APPLIED OPTICS 3491

2 microsec B microsec

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Page 6: Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

previous day. Profiles for 8 Feb. show slightly higherbackscatter and absorption values for a given levelwith no evidence of a secondary backscatter maximumnear 2 km.

The smallest backscatter values were found in Janu-ary and February. In January a minimum value of 4 X10-1 m'1 sr-' was found at a maximum altitude of 4.5km. In February a minimum of 7 X 10-1 m-' sr-' wasobserved at a maximum altitude of 5.8 km.

Comparisons with backscatter profiles obtained byother workers at CO2 wavelengths must be treatedwith caution because of the strong backscatter depen-dence on geographic location, elevation, season, cur-rent meteorological conditions, air mass history, con-centrations of anthropogenic aerosols, as well aspossible wavelength dependence. Even so, profilesover Colorado during winter 1978 ranged from 8 X 10-9M sr-1 near the surface to 10-1 m'1 sr-' at 5200-maltitude,4 in good agreement with the present study.A direct comparison with the NOAA/WPL data seriesis not possible because nearly all the MSFC data wereobtained below NOAA's minimum altitude. Airbornemeasurements over California during summer and fall1981 yielded boundary layer values of 10-7-10-8 m'1sr'1,8 comparable to the summer and fall data reportedhere. Wintertime boundary layer values reported byMenzies et al.

6 during winter 1983 in southern Califor-nia exceed those of the present study by -1 order ofmagnitude. The measured summer and winterboundary layer backscatter values are typically small-er than model values presented by Post9 by a factor of 4similar to that reported by Schwiesow et al.

4

C. Time Series

Backscatter time series were examined for eachstandard level at which calculations were made. Aseasonal trend is evident at levels that are typicallywithin or near the top of the planetary boundary layerwhere returns were sufficient. Figure 6 is representa-tive of seasonal variations in backscatter with (an ap-parent) maximum in July-August and minimum inJanuary-February. A corresponding time series ofabsorption (not shown) would be in phase with thedistribution in Fig. 6. The solid and dashed linesdenote the geometric mean and one geometric stan-dard deviation, respectively. An annual geometricmean of 10-8 m-1 sr-' is representative of the bound-ary layer. However, this value may be biased by oper-ation for <12 months and by aperiodic sampling due tolimiting factors such as unfavorable weather condi-tions (e.g., extremely high humidity, rain, snow) andequipment repairs. The annual geometric mean de-creases by a factor of 4 from the surface to -2 km. Ingeneral, annual extremes within the boundary layervary over -2 orders of magnitude with values of10-7-10-8 and 10-8-10-9 m-1 sr-' characteristic ofsummer and winter months, respectively. The rangein daily values for 8-,gsec pulse duration is typicallysomewhat larger than for the shorter pulse duration.At a given height, the distribution of a time series at 8gsec encompasses that for 2 gsec.

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Fig. 6. Time series of backscatter observations at 800-m heightusing 2-usec pulse duration. Variation is typical of other levelswithin the planetary boundary layer; observations at 8 ,sec are

comparable at similar heights.

Seasonal trends, similar to those reported here, areevident in the seasonally averaged profiles reported byPost.7 Aerosol size distribution measurements madeover Nebraska in 1966 also show strong seasonal varia-tion.20 Maximum and minimum number concentra-tions occurred in summer and winter, respectively, theformer probably being due to enhanced biological ac-tivity. In the lower troposphere the size distributionsin summer tended toward greater uniformity: howev-er, considerable variability occurred on the scale ofweeks at all altitudes.

D. Backscatter Frequency Distribution

At nearly all vertical levels the frequency distribu-tion is skewed toward lower backscatter values and isapparently lognormally distributed. To evaluate andquantify this behavior in the present study, cumula-tive probability distributions were generated as a func-tion of height. For days when multiple backscatterestimates were obtained for a given height, a singlevalue was derived in the following manner. First, thegeometric mean value was determined from the back-scatter estimates for each level as well as a standarderror associated with each estimate. Second, a set ofnormalized weighting factors was computed, eachweight being inversely proportional to the correspond-ing standard error. Finally, a weighted geometricmean value was obtained. As a check of the validity ofthis method, cumulative distributions were also con-structed by replacing the weighted geometric meanwith a randomly selected value from each day on whichmultiple scans were made. No significant differencewas found between cumulative distributions obtainedusing both methods. Because of the small size of thedata base, results summarizing the entire measure-ment period are presented.

Distributions obtained by using 2 (8)-,gsec pulse du-ration have been determined at 320 (1280)-m intervalsfrom levels of 160-2080 m (640-1920 in), beyond whichinsufficient data existed (see Sec. IV.B). If the datadropouts at the higher altitudes resulted in a samplingbias so that the missing values are smaller than thesmallest measured value at a given level (a censored

3492 APPLIED OPTICS / Vol. 24, No. 21 / 1 November 1985

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Page 7: Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

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-7.(a

m

0)J

-9.

-d .

Height 2060 mApr 63 - Feb 64

2 Microsec16 Samples

2 5 0 20 40 60 60 90 95 999Probability (%)

Height 2060 Apr 63 - Feb 64

2 Microsec16 Samples

1 2 5 10 20 40 60 60 90 95 999Probability (%)

Fig. 7. Cumulative probability distribution at 2080 m assuming (A)no sampling bias exists and (B) values of missing backscatter data

are smaller than the smallest measured value.

-6.

-7.CU

4J

mI

0)0IJ

-9. I

-10.

-6.

-7.Cu4

m

I

-9 .

-10.

Height 160 Apr 83 - Feb 84

2 Microsec23 Samples

2 5 10 20 40 60 80 90 95 9899Probability %)

Height 160 mApr 83 - Feb 84

2 Microsec23 Samples

1 2 5 0 20 40 60 80 90 95 9899Probability (%)

Fig. 8. Same as Fig. 7 except for 160 m. Lognormal behavior inboth (A) and (B) indicates no sampling bias existed at this level.

-7.lognormal distribution2 1), the probability distributionmust be adjusted to compensate for their absence. Toillustrate, Fig. 7(A) shows the probability distributionat the 2080-m level assuming no data are missing (orequivalently that the missing data are not biased); Fig.7(B) shows the adjusted distribution using the samedata but assuming the missing backscatter values arebiased, that is, smaller than the smallest measuredvalue. The straight line denotes a linear least-squaresfit. A better fit to lognormality is found after adjust-ment. Data dropouts also occurred at the lowest alti-tude (160 m), because the presence of obstructions atvarious points along the slant path at different azi-muths occasionally precluded a reliable calculation of3(7r). However, Fig. 8 shows that in this case no major

sampling bias occurred, because the distributions withand without compensation for the missing data areboth lognormally distributed with similar parameters.

As a check of the degree of lognormality, the chi-square statistic was computed for all levels. Overall,the 2-gsec distributions through the 2080-m level de-part insignificantly from lognormality at an averageconfidence level of 76%. At 160 and 480 m, confidencelevels of 90 and 97% are found, respectively. In con-

-6.I(a

m

0)0I

-10.1

-Ii .

Height 480 Apr 83 - Feb 84

2

2 Microsec3± Samples

-U]

E

-1

. 3w

Cu4JI

CC03

5 0 20 40 60 s0 90 95 999Probability (%)

Fig. 9. Cumulative probability distribution at 480 m. The data setindicates a lognormal distribution comparing log () (left ordinate)

with 3 (right ordinate).

trast, values of 27 and 11% are found for the samelevels, respectively, when testing for a normal distribu-tion; the average confidence level overall is 21%. Fig-ure 9 is representative of the statistical validity of thelognormal description for boundary layer backscatterdistributions. Evidence of lognormality in the bound-ary layer probably indicates that the convective

1 November 1985 / Vol. 24, No. 21 / APPLIED OPTICS 3493

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I I I I I I I I I I I

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C I I I I I I I I I I I I

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growth and organization in the subcloud region havetransported aerosols through the boundary layer andinto the free troposphere. There is considerable ob-servation evidence, using radar22 and instrumentedaircraft,2 3 of convective organization of small-scaleconvective elements into larger structures within theoptically clear boundary layer. The 8-gisec probabilitydistributions also tend more toward a lognormal distri-bution at an average confidence level of 75%. Thishigh average value may be somewhat fortuitous forseveral reasons. Observations at 8 gsec, as opposed to2 gsec, were gathered on - 38% fewer days. Further-more, the 8-gusec data set is biased toward the Septem-ber-October and January-February time periodswhen the frequency of observations was highest. Fi-nally, greater variation in f(lr) at 8 gsec is evident fromweek to week as well as from one quadrant to anotheron a given day. This feature may be due to -a largerpulse scattering volume within which the aerosol dis-tribution can be expected to be more inhomogenous.

The tendency for backscatter to be lognormally dis-tributed also has been noted in the NOAA data base7

,24

at heights of 4 km and beyond. The reason for theexistence of the lognormal distribution is still subjectto speculation. It has been postulated2 4 that the inter-action and nonlinear growth of convective plumes andthermals, which transport aerosols out of the planetaryboundary layer from Gaussianlike sources near thesurface, organize the aerosols into a spatial distribu-tion that becomes more skewed toward smaller valueswith height. This view is consistent with findings thatthe dimensions of cumulus clouds are lognormally dis-tributed25 ; such clouds may be responsible for aerosoltransport into the middle troposphere over short timescales.

Consistent departures from lognormality are evi-dent in the 2-gtsec distributions only at the 1120-, 1440-,and 1760-m levels (see Fig. 10). The chi-square statis-tic indicates that the distributions are more lognormalthan normal, the differences between confidence levelsranging from 10 to 53%. However, in contrast to obvi-ous monomodal distributions evident at other levels(e.g., Fig. 8), these levels suggest the existence of abimodal distribution. Apparently, the secondarymode is not resolved because of modest pulse energyand beam absorption. The dominant observed modeoccurs near 10-8 m-1 sr-'. This mode, with no com-pensation made for missing data, also appears to belognormal.

The abrupt falloff in the tail of the distributions near10-9 in Fig. 10 may correspond to the intermodal gap.The seasonal profiles suggest that the resolved modecorresponds to aerosols within the planetary boundarylayer. The intermodal gap corresponds to measure-ments made at the top of the boundary layer or some-what above, suggesting that the missing secondarymode corresponds to aerosols in the middle tropo-sphere. No evidence of bimodality is seen in the 8-,gsec probability distributions for the same levels,probably for reasons cited in the preceding paragraph.The published data from NOAA/WPL, which are aver-

-6.

-7.(04.)mIf - .

- .0.

-10o.

-6.

-7.(a

m0)M-

-2.

-±0.

Height 1760 mApr 83 - Feb 64

2 Microsec16 Samples

Probability (%)

Height 440 mApr 3 - Feb 84

2 Microsec23 Samples

1 2 5 ±0 20 40 60 60 90 95Probability (%)

Height 1120 m

-6.

-7.

m0)03I-8.

-9.

-10.

9699

2 Microsec

1 2 5 10 20 40 60 80 90 95 9899Probability (%)

Fig. 10 Cumulative probability distributions at 1120, 1440, and1760 m suggesting bimodal backscatter distribution. Dominantmode falls around log(f) =-8.0 corresponding to 10-8 m- 1 sr 1 .The possible intermodal gap occurs around 10-9 m- 1 sr-1 . Thesecondary mode is not detected due to weak transmitted pulse

energy and beam attenuation.

3494 APPLIED OPTICS / Vol. 24, No. 21 / 1 November 1985

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Page 9: Ground-based measurements of atmospheric backscatter and absorption using coherent CO_2 lidar

aged over complete seasons, give no clear indication ofa bimodal distribution. Instead an excellent fit tolognormality is found for the selected data.

Several studies provide examples of a bimodal dis-tribution exhibited by one or more aerosol properties.Daily aerosol measurements at three stations in theNorthern Tropical Atlantic during the summer of 1974exhibited a bimodal distribution of mass concentra-tion with one mode decidedly dominant.26

V. Summary

A slant path method has been applied to measure-ments of backscattered intensity to calculate verticalprofiles of volumetric backscatter and absorption.The advantage of the method is that both quantitiescan be determined using the lidar system alone. Tothe authors' knowledge, this study represents the firstapplication of the slant path method to coherent CO2Doppler lidar measurements. Since the validity ofthis method depends on the degree of horizontal homo-geneity, vertical scans were often made at more thanone azimuth angle to evaluate the horizontal homoge-neity assumption. The validity of the assumptionvaried with highest confidence placed in profiles show-ing closest agreement.

Good agreement was found between lidar- and ra-diosonde-derived profiles of absorption. Errors of theorder of 2 dB in the calculation of backscatter couldhave occurred if a climatological profile of absorptionhad been assumed. Variations on a wide range ofspatial and temporal scales were evident. Use of 2-gsec pulse duration provided finer vertical resolution,whereas 8-Asec pulse duration allowed observations athigher altitudes. Observations were generally con-fined to the planetary boundary layer (1-3 km) due tomodest pulse energy and beam attenuation. Back-scatter was at a maximum (10-7-10-8 m-1 sr-') andminimum (10-8-10-9 m-1 sr-') during the summer andwinter months, respectively. Absorption varied inphase with backscatter. A minimum backscatter of 4X 10-1, m-1 sr-1 was observed in the middle tropo-sphere in winter when absorption was weakest.

Observations at nearly all vertical levels showedbackscatter to be lognormally distributed. Excellentfit to lognormality was noted in the lower boundarylayer, which should not necessarily be surprising inlight of radar and aircraft studies showing evidence ofconvective organization in the cloud-free boundarylayer. Consistent variations evident in the cumulativeprobability distributions near the top of the boundarylayer could be explained by the presence of two aerosolpopulations or modes. The first is apparently associ-ated with boundary layer aerosols; this mode was ob-served most frequently. The second mode was notresolved; however, its existence is suggested by thepresence of an apparent intermodal gap. The domi-nant mode and intermodal gap occurred at values of10-8 and 10-9 m-1 sr-', respectively.

The MSFC Doppler lidar system has been moved toa permanent structure since being returned from thefall 1984 flight series of experiments. After a program

of refurbishment and realignment has been completed,it will be possible to resume measurements, thus add-ing to the data base described here.

The authors are indebted to David Bowdle, Univer-sities Space Research Association, Charles DiMarzio,Raytheon Corp., and Daniel Fitzjarrald and JamesBilbro, Marshall Space Flight Center, for their contri-butions throughout the course of this study. Ac-knowledgment is also deserved by Steven Johnson,Marshall Space Flight Center, and Edward Gorzynski,Raytheon Corp., who conducted the actual operationof the lidar system. This research was partially sup-ported by the Universities Space Research Associationunder contract NAS8-34010. Jeffry Rothermel is aUniversities Space Research Association visiting sci-entist.

This paper is based on one presented at the TopicalMeeting on Optical Remote Sensing of the Atmo-sphere, Incline Village, Nev., 15-18 Jan. 1985.

References

1. B. M. Herman and S. R. Browning, "The Effect of Aerosols onthe Earth-Atmosphere Albedo," J. Atmos. Sci. 32, 1430 (1975).

2. R. M. Huffaker, T. R. Lawrence, M. J. Post, J. T. Priestley, F. F.Hall, Jr., R. A. Richter, and R. J. Keeler, "Feasibility Studies fora Global Wind Measuring Satellite System (Windsat) Analysisof Simulated Performance," Appl. Opt. 23, 2523 (1984).

3. M. Halem, "GCM Simulation Studies on the Relative Impor-tance of Wind Observing Systems for Numerical Weather Pre-diction," in Technical Digest, Second Topical Meeting on Co-herent Laser Radar: Technology and Applications (OpticalSociety of America, Washington, D.C., 1983), paper TuAl.

4. R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F.Pueschel, and P. C. Sinclair, "Aerosol Backscatter CoefficientProfiles Measured at 10.6 jm," J. Appl. Meteorol. 20,184 (1981).

5. J. M. Vaughan and A. A. Woodfield, "Backscatter Measure-ments in the Atmosphere with a 10-jum Airborne Velocimeter,"in Technical Digest, Topical Meeting on Optical Remote Sens-ing of the Atmosphere (Optical Society of America, Washing-ton, D.C., 1985), paper WC21.

6. R. T. Menzies, M. J. Kavaya, P. H. Flamant, and D. A. Haner,"Atmospheric Aerosol Backscatter Measurements with a Tun-able CO 2 Lidar," Appl. Opt. 23, 2510 (1984).

7. M. J. Post, "Aerosol Backscattering Profiles at CO2 Wave-lengths: the NOAA Data Base," Appl. Opt. 23, 2507 (1984).

8. W. D. Jones, "Airborne and Ground-Based Measurement ofAtmospheric Aerosol Backscatter at CO2 Laser Wavelengths,"in Technical Digest, Second Topical Meeting on Coherent La-ser Radar: Technology and Applications (Optical Society ofAmerica, Washington, D.C., 1983), paper ThB5.

9. M. J. Post, "Effects of the Earth's Atmosphere on a SpaceborneIR Doppler Wind-Sensing System," Appl. Opt. 18, 2645 (1979).

10. R. A. McClatchey et al. "AFCRL Atmospheric Absorption LineParameters Compilation," AFCRL-TR-73-0096 (1973).

11. J. D. Klett, "Stable Analytical Inversion Solution for ProcessingLidar Returns," Appl. Opt. 20, 211 (1981).

12. P. M. Hamilton, "Lidar Measurement of Backscatter and Atten-uation of Atmospheric Aerosol," Atmos. Environ. 3, 221 (1969).

13. J. D. Spinhirne, J. A. Reagan, and B. M. Herman, "VerticalDistribution of Aerosol Extinction Cross Section and Inferenceof Aerosol Imaginary Index in the Troposphere by Lidar Techni-que," J. Appl. Meteorol. 19, 426 (1980).

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14. P. B. Russell and J. M. Livingston, "Slant-Lidar Aerosol Extinc-tion Measurements and their Relation to Measured and Calcu-lated Albedo Changes," J. Climate Appl. Meteorol. 23, 1204(1984).

15. M. J. Post, NOAA Environmental Research Laboratories; pri-vate communication (1984).

16. B. J. Rye, "Primary Aberration Contribution to IncoherentBackscatter Heterodyne Lidar Returns," Appl. Opt. 21, 839(1982).

17. R. M. Hardesty, R. J. Keeler, M. J. Post, and R. A. Richter,"Characteristics of Coherent Lidar Returns from CalibrationTargets and Aerosols," Appl. Opt. 20, 3763 (1981).

18. J. Rothermel, C. Kessinger, and D. L. Davis, "Dual DopplerLidar Measurement of Winds in the JAWS Experiment," J.Atmos. Oceanic Technol. 2, 138 (1985).

19. R. W. Lee and K. A. Lee, "A Poly-pulse-pair Signal Processor forCoherent Doppler Lidar," in Technical Digest, Topical Meetingon Coherent Laser Radar for Atmospheric Sensing (OpticalSociety of America, Washington, D.C., 1980), paper WA2.

20. I. H. Blifford, Jr., and L. D. Ringer, "The Size and NumberDistribution of Aerosols in the Continental Troposphere," J.Atmos. Sci. 26, 716 (1969).

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

22. K. R. Hardy and H. Ottersten, "Radar Investigations of Convec-tive Patterns in the Clear Atmosphere," J. Atmos. Sci. 26, 666(1969).

23. D. R. Grant, "Some Aspects of Convection as Measured fromAircraft," Q. J. R. Meteorol. Soc. 91, 268 (1965).

24. M. J. Post, F. F. Hall, Jr., R. A. Richter, and T. R. Lawrence,"Aerosol Backscattering Profiles at X = 10.6 jm," Appl. Opt. 21,2442 (1982).

25. R. E. Lopez, "The Lognormal Distribution and Cumulus CloudPopulations," Mon. Weather Rev. 105, 865 (1977).

26. D. L. Savoie and J. M. Prospero, "Aerosol Concentration Statis-tics for the Northern Tropical Atlantic," J. Geophys. Res. 82,5954 (1977).

Meetings Calendar continued from page 34631985

9-13 10th Ann. Int. Conf. on Infrared & Millimeter Waves,Lake Buena Vista, Fla. K. Button, MIT Natl. Mag-net Lab., Bldg. NW14, Cambridge, Mass. 02139

10-12 Advanced Geological Remote Sensing: Shortwave In-frared, Thermal Infrared, & Microwave Techniquescourse, Wash., D.C. Cont. Eng. Ed. Program, Geo.Wash. U., Wash., D.C. 20052

10-12 Fiber Optic Communications course, Tempe Ctr. forProf. Dev., Coll. of Eng. & Applied Sciences, AZ StateU., Tempe, AZ 85287

11 D25-2 Colorimeter Service course, Reston Hunterlab.,11495 Sunset Hills Rd., Reston, VA 22090

1986

? 3rd Int. Conf. on Metal-Organic Vapor Phase Epitaxy,Pasadena N. Bottka, Naval Res. Lab., ElectronicMaterial Tech. Branch, Wash., D.C. 20375

January

6-8 Fiber Optics Workshop & Lab., Lake Buena Vista V.Amico, Central Florida U., Coll. of Extended Studies,Orlando, FL

6-17 Optical Science & Engineering course, TucsonSlater, P.O. Box 18667, Tucson, AZ 85731

P.

19-24 Optoelectronic & Laser Applications in Science & Engi-neering Symp., Los Angeles SPIE, P.O. Box 10, Bel-lingham, Wash. 98227

22-23 Regional Color & Appearance course, PhiladelphiaHunterlab., 11495 Sunset Hills Rd., Reston, VA22090

29-31 33rd Ann. Conf. Western Spectroscopy Assoc., PacificGrove D. Saperstein, IBM, E42/13, 5600 Cottle Rd.,San Jose, CA 95193

December

2-6 Fall Mtg. of the Materials Research Soc., Boston J.Ballance, Materials Res. Soc., 9800 McKnight Rd.,Suite 327, Pittsburgh, Pa. 15237

February

2-7 Int. Conf. on Picture Archiving & Communication Sys-tems for Medical Applications, Newport BeachSPIE, P.O. Box 10, Bellingham, Wash. 98227

2-6 Int. Conf. on Lasers, Las Vegas Lasers '85, P.O. Box245, Mclean, Va. 22101

2-6 Fundamentals & Applications of Lasers course, Albu-querque Laser Inst. of Amer., 5151 Monroe St., Ste.118W, Toledo, Ohio 43623

2-6 Optical Interference Coating Tech. course, Los AngelesUCLA Ext., Eng. Sciences, P.O. Box 24901, Los Ange-les, CA 90024

3-6 4th Int. Conf. on Biostereometrics, Cannes SPIE, P.O.Box 10, Bellingham, Wash. 98227

2-7 Medicine XIV: Medical Image Production, Processing,& Display, Newport Beach SPIE, P.O. Box 10, Bel-lingham, Wash. 98227

5 D25-9 Colorimeter Service course, Reston Hunterlab.,11495 Sunset Hills Rd., Reston, VA 22090

5-6 Regional Color & Appearance course, Seattle Hunter-lab., 11495 Sunset Hills Rd., Reston, VA 22090

9-15 Astronomical Instrumentation Conf., Tucson SPIE,P.O. Box 10, Bellingham, Wash. 98227

9-15 Instrumentation in Astronomy VI Conf., Tucson SPIE,P.O. Box 10, Bellingham, Wash. 98227

4-5 Regional Color & Appearance course, Los AngelesHunterlab., 11495 Sunset Hills Rd., Reston, VA22090

3496 APPLIED OPTICS / Vol. 24, No. 21 / 1 November 1985

continued on page 3518