Cirrus cloud transmittance and backscatter in the infraredmeasured with a CO2 lidar

Freeman F. Hall, Jr., Richard E. Cupp, and Seth W. Troxel

Two independent methods of measuring the transmittance of cirrus clouds are compared. Both used a CO2pulsed Doppler lidar at a wavelength of 10.59 um. The first method used backscatter from the calibrationtarget El Chichon stratospheric cloud that was present over Boulder in 1982 and 1983. The second methodused conical lidar scans at different zenith angles when uniform cirrus decks were present. Extinctioncoefficients measured from both methods average 0.1 km-' for tenuous cirrus 1.0 km thick to 0.78 km-' forcirrus several kilometers thick. There is a wide standard deviation in extinction values. Extinction-to-backscatter ratios S vary from <1000 sr for tenuous clouds to 2600 sr for dense clouds. Mie scattering and ex-tinction calculations for spherical ice particles of 10-50 gm in radius lead to ratios S > 2000 sr, so long as the iceabsorption is entered into the calculations. The backscattering ratio for ice cylinders is 1 order of magnitudelower than for spheres. Backscatter in the IR may, therefore, be reasonably well modeled by some combina-tion of spheres and cylinders. Cloud thickness statistics from lidar returns show that cirrus decks average-500 m thick. Clouds thinner than 300 m were often overlooked by the unaided surface-based observer.These preliminary results are in rather close agreement with the LOWTRAN 6 cirrus cloud model predictions.

1. Introduction

The continuing interest in the optical properties ofcirrus clouds has a long history. Cirrus-imposed limitson visibility for air-to-air refueling led Stone' to write acomprehensive and still useful Air Weather Servicereport on the topic. Satellite IR observation problemsproduced by cirrus were treated by Wark et al. 2 andZdunkowski et al. 3 Even tenuous or subvisual cirruswere shown to have significant IR radiance and extinc-tion at large zenith angles.4 The importance of highclouds in earth heat budget and radiative transferstudies has been documented by Cox 5 and Stephensand Webster. 6 A transmittance code for cirrus was,therefore, added to the latest version of LOWTRAN.7

In this paper, two new methods for measuring the IRproperties of cirrus using a CO2 Doppler lidar are pre-sented together with backscatter and extinction coeffi-cients.

II. Methods of Measurement

There are several advantages in using a calibrated,ground-based, pulsed, IR, Doppler lidar to measure

When this work was done all authors were with NOAA WavePropagation Laboratory, Boulder, Colorado 80303; F. F. Hall, Jr., isnow with Harrier Consultants, Boulder Colorado 80302, and S. W.Troxel is now with MIT Lincoln Laboratory, Bedford, Massachu-setts 01730.

Received 27 July 1987.

the 8-13-Am thermal window optical properties of cir-rus. Calibration allows the absolute magnitude of thebackscatter coefficient to be determined. With ourlidar, day-to-day absolute calibration using a sandpa-per target repeats to within 10%; relative accuraciesfrom one range gate to the next are estimated to bewithin 1%. Aerosol atmospheric transmittance losseswere accounted for by using the computer code LOW-TRAN, and molecular absorption parameters camefrom the HITRAN8 database. A pulsed lidar allowsrange gating of the backscattered radiance for spatialresolution along the probing beam as determined bythe pulse length. A CO2 laser operating in the thermalwindow does not require spectral extrapolation intothis region to obtain the thermal IR properties, aswould be required for visible or near-IR lidars usingruby or neodymium-doped sources. With a Dopplerlidar it is possible to measure wind speed, direction,and shear in the cloud. Finally, scanning the lidarbeam allows probing a large spatial extent of the cloudin a short time.

An appreciation for the range of cirrus IR backscat-ter coefficient values can be gained by studying Fig. 1.This is a compilation from the NOAA database forcirrus properties, uncorrected for transmittance losswithin the cirrus, acquired using pulsed CO2 lidarsover the past six years. Data for many cases of thinclouds with the same thickness are plotted using thesame data point, so although over 120 different cloudswere probed, there are fewer than 100 data points.About half of the cirrus measured had thicknesses of

2510 APPLIED OPTICS / Vol. 27, No. 12 / 15 June 1988

FIRE 28OCT86 1350 UT FILE 24 RECORD I - 35516I

E

sJ

ID

t

°b-10 ID-9 lo-8 10-7 10-6

Backscatter Coef ., , (I/m x I/sr)

Fig. 1. Scattergram of over 120 cirrus cloud 10.6-gm backscattermeasurements, uncorrected for extinction within the cirrus. Thesloping line is the least-squares best fit. Backscatter coefficientunits are m-1 sr-'. Day-to-day absolute calibration uncertainties

are -10%.

500 m or less. Note that for a given cloud thickness,the backscatter can vary by 3 orders of magnitude. Asshown below, this implies that the IR extinction coeffi-cient can also vary widely, even for clouds of compara-ble thickness.

As we processed the data, our BETA computer pro-gram9 gave us several standard plots that helped tomonitor cirrus conditions. Figure 2 is the plot of back-scatter vs height, where the lidar calibrations and at-mospheric extinction conditions are accounted for,and only the cirrus attenuation affects the accuracywith which in the cirrus is known. The horizontaldimension of the data points in the figure is indicativeof the absolute accuracy of the measurement. In Fig. 2the rather thick cirrus layer between 6.5 and 11.6 kmcontributes significant attenuation of backscatterfrom the top of the cloud, and it is necessary to invertthe lidar equation to correct for this attenuation. Thisplot illustrates a common characteristic of most cirruslayers: The backscatter (here averaged over 6 min) isgreatest near the middle of the layer with the gradualdecreases near the top and base often showing sporadicchanges. The lower altitude returns are from aerosols,which also can show much day-to-day variation.

Standard lidar equation inversion methods10 canbecome quite complex for cirrus because the cloudproperties can vary so rapidly from one range gate tothe next. The two thin cirrus layers at 10 and 11 km inFig. 3 certainly have greater backscatter coefficientsthan the uncorrected abscissa values shown because ofattenuation in the complexly layered, lower cirrusfrom 6.2 to 8.3 km. Even then, note that the highestand thinnest layer at 11 km shows greater backscatterthan the thicker layer at 10 km. Such are the variabili-ties of cirrus, even over short-range increments, thatindicate the desirability of new methods of lidar equa-tion inversion.

Two new experimental methods were used to deter-mine extinction coefficients during this investigation:(1) measuring attenuation by the clouds of a remotestratospheric target of known backscatter and (2)

12

10

8

6

4

2 . . -10- I 1-10 10-9 10-8 10-7 10-6

Backscotter Coef. . . (I/m x I/sr)

Fig. 2. 10.6-gm backscatter uncorrected for cirrus extinction vsheight for a thick cirrus layer between 6.5 and 11.6 km. The lower-altitude return is from aerosols. Although absolute uncertainties incalibration are -10% (about the radius of the data circles), the

relative uncertainties from one range gate to the next are <1%.

FIRE IIOCT86 1147 UT FILE 2 RECORD I - 100016r I

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Fig. 3. 10.6-,gm backscatter uncorrected for cirrus extinction ver-sus height for a thick cirrus layer between 6.2 and 8.3 km and twohigher thinner layers. Lidar pulse energy was 0.95 J, and 1000

pulses were averaged.

probing at stepped zenith angles and analyzing Lang-ley plots of the data.

A. Stratospheric Target Extinction

In late 1982 and early 1983 the stratospheric aerosolcloud from the El Chichon (EC) eruption was consis-tently over Boulder. In the absence of cirrus clouds,the measured backscatter coefficients of EC were be-tween : = 2 X 10-9 and 9 X 10-9 m- 1 sr-', and thesevalues varied only slowly over periods of several hours.We recorded many files of lidar data when tropospher-ic cirrus of different thicknesses and densities ob-scured the stratospheric EC target. Periods when thecirrus properties were relatively constant with timewere identified by examining plots of the integratedbackscattered radiance vs time, another standardproduct of our BETA program. An example is shown inFig. 4. During the period from 24 to 37 s the cirrus(which contributed most of the signal in the plot) weretenuous but showing constant backscatter. Similarly,from 60 to 68 s, a thicker patch of cirrus drifted throughthe vertically directed lidar beam.

If we plot the apparent backscatter of the EC targetfor a number of differing cirrus conditions character-

15 June 1988 / Vol. 27, No. 12 / APPLIED OPTICS 2511

4CIRRUS CLOUD 10.6 pjm ACKSCATTER

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Fig. 4. Lidar integrated backscattered radiance (in arbitrary units)vs time as a cirrus deck of varying thickness advected through thevertical beam. A decreased signal signifies a thinner cirrus cloud.This diagram illustrates the difficulty in assigning absolute errorbars to the reduced data; although a 20-s run with 200 lidar pulsesproduces a 10% probable error for a constant scatterer, the cloud can

show real changes in a 20-s interval.

ized by the different integrated (actually discretelysummed by range gate) backscatter cases from thecirrus, we get the graph shown in Fig. 5. The straight-line least-squares best fit has a regression coefficient of0.96, and the intercept with the y axis at 19.6 (XE-8)represents the unattenuated EC backscatter, whichwas integrated over the range gates between 15- and22-km altitude. The straight-line plot can be under-stood, at least for thin clouds, when we consider thatthe backscatter measured from EC PEC is related to theunattenuated (y-axis intercept) value ILEC and a, theextinction over a given range gate of length 1, by

AEC =EC exp [ 2 J a(l)dl] EC exp ( 21 ai (1)

cEC (21ai) X (2)

where only the first-order terms in the series expansionfor the exponential are retained. Since a << 1, thehigher-order terms can be neglected when is not toolarge and still retain accuracy comparable to the mea-surement precision.

We define the extinction-to-backscatter ratio S ofthe cirrus as

S = a/13, (3)

where a is the cirrus extinction coefficient, and fl is thecirrus backscatter coefficient. (Note that with extinc-tion coefficient dimensions of km-' and backscattercoefficient dimensions km"' sr-', S has dimensions ofsr.) From Fig. 5 we can determine the averaged ex-tinction coefficient through the entire cirrus cloud (thesolid circles represent actual data points as the cirruschanged thickness and density over time) and thencorrect A3 as measured for this extinction. For thecirrus of 17 Dec. 1982 at Boulder, CO, the extinction-to-backscatter ratio for the most tenuous clouds (that

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Fig. 5. Cirrus attenuation of El Chichon backscatter for integratedcirrus beta values,

rt f| Ildl,

from base b to top t of cirrus layer. Estimated error bars areconsistent with the data circles as before.

were then 1 km thick) was 1100 sr; for the more denseclouds, S = 2600 sr. These ratios were determined byusing Eq. (3) after first correcting : for the lidar cloudtransmittance loss in irradiating the ice crystals andfor the cloud transmittance loss for the backscatteredradiance. Multiplying these values by the averagedbetas gives an extinction coefficient of -0.05 km-' forthe most tenuous clouds and 0.78 km-' for the denseclouds that were 3.5 km thick. However, a more typi-cal value for a 1.0-km thick section of cloud on this daywas a f3 of about twice this most tenuous value, or a =0.1 km". These extinction values would have beenpredicted to be 0.14 km-' for the thin clouds and 0.49km-' for the thick clouds if the LOWTRAN 6 model of

a = 0.14L km-' (L is cloud thickness in km) (4)

had been used. Thus the LOWTRAN model is in theright range, perhaps predicting too much extinctionfor (these particular) thin clouds and too little for thethick clouds. Still, the model is well within the stan-dard deviation that one might expect for something asvariable as cirrus clouds. During the EC measure-ments, the lidar was pointed vertically (zenith angle0.00). There can be enhanced backscatter with thisgeometry because of specular reflection from ice crys-tals falling with a preferred horizontal orientation."Such reflections would cause a greater value and,therefore, a lower scattering ratio than might be mea-sured if the clouds were probed from off zenith angles.We investigated this effect using the next-describedprobing method.

B. Stepped Zenith Angle Scans and Langley Plots

The IR Doppler lidar was transported to Oshkosh,WI in Oct. 1986 to participate in the first intensivecirrus measurement phase of the First InternationalSatellite Cloud Climatology Project Regional Experi-

2512 APPLIED OPTICS / Vol. 27, No. 12 / 15 June 1988

ment (FIRE). We devised a scan pattern calledstepped zenith angle for the particular purpose of pro-viding a new method to measure cirrus extinction coef-ficients. While operating the lidar at 5 pulses/s or 5Hz, we scanned 3600 in azimuth, starting at a zenithangle of 700 (200 elevation), and stepping the lidarbeam upward 100 at the end of each complete circleuntil a zenith angle of 30° was scanned. (The 700 scanwas seldom useful for data reduction unless the cirruswere extremely uniform in both height and thickness.)An entire stepped zenith angle scan was completed in-20 min. Such scans avoid the possibility of en-hanced backscatter from specular reflection on hori-zontally oriented ice crystals.

The tape-recorded data were analyzed by runningthe BETA program separately for each zenith angle.The backscatter coefficients (betas) obtained, uncor-rected for cirrus attenuation, were then plotted asshown in Fig. 6, where the abscissa is the secant of thezenith angle A, and : (scaled logarithmically) forms theordinate. This is similar to a technique used in thepast for measuring the atmospheric absorption affect-ing the determination of the solar constant, the so-called Smithsonian long method or Langley method. 12

For sect = 1.0, the best straight line fit predicts the f3that would be obtained looking vertically and by ex-trapolating for sect = 0.0, the : corrected for attenua-tion in the clQud is predicted. This method is similarto the aerosol extinction-to-backscatter lidar methodemployed by Spinhirne et al.13 except that our scans inazimuth provided improved layer averages, and wecomputed separate S values for each layer. The meth-od we used is entirely graphical; the intersection of thebest-fit line with the y axis determined the correctedvalue of /3. Since we avoided values of s much largerthan 600 this simple (unweighted) best fit is appropri-ate; the larger fluctuations in extinction to be expectedfor large air (cloud) mass were not a problem. 14

Since the measured beta values are plotted for eachdata set for the same altitude within the cloud, it ispossible to range resolve : with the resolution providedby the lidar pulse length (300 m in our case). Thiscontrasts with the stratospheric target method whereonly extinction averaged through the entire cloudcould be measured. Note, however, that the Langleymethod requires horizontal homogeneity within thecloud for consistent results. This requirement limitsthe applicability near a cirrus cloud base where typi-cally localized fall streaks descend from the cloud. Asubjective judgment was used to decide when the cir-rus conditions were uniform enough in azimuth for theLangley plots: The regression coefficient of the datapoints for a constant altitude had to exceed 0.8. Thiscorresponds to a 5% level of significance that there is nocorrelation of the measurements with zenith angle forthe five data points.15 We have seen some regressionsthat exceed 0.97 for such plots, but this is rare. Notethat, even for strong attenuation and, therefore, strongscatter per unit volume of the cloud, we are not influ-enced by additional signals produced by multiple scat-tering from the cloud particles. This is because with

L

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Langley Plot, FIRE, 280ct86. 1310 UT

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Fig. 6. Langley plot for determining cirrus extinction layer by layerfrom the base of the cloud. The slopes of the lines become morenegative for increasing depths into the cloud, indicating higherscattering ratios. The backscatter values are also greater with in-creasing distance into the cloud, where the ice loading and particleconcentrations are greater. Different symbols are used to helpidentify each range-resolved height gate within the cloud: 0, 1.5

km; X, 2.3 km; etc.

L

-ccc

1 0-

10-

10-

Langley Plot. FIRE, 31Oct86, 1608 UT

0 1 2Secant Zenith Angle

3

Fig. 7. Langley plot as in Fig. 6 but for a complex multiple-layercirrus. The more gradually sloping line for 2.1 km above the cloudbase was in a low-particle density region between the two principalcirrus decks, where aircraft collection showed a number of small (10-

am radius) round ice crystals.

our coherent lidar the field of view (FOV) is diffrac-tion-limited at 40 grad or several orders of magnitudeless than the FOV of typical incoherent (direct detec-tion) lidars. The multiple-scattering corrections, asapplied by Carnuth and Reiter16 in their lidar cloudinvestigations using a 10-mrad FOV, amounted to farless than 1% of the returned signal in our case and were,therefore, neglected.

So far we have analyzed only a few cirrus cases usingLangley plots. For a 2-4-km thick cirrostratus layeron 28 Oct. (Fig. 6) and for a cirrostratus-to-cirrus fibra-tus layer 2-3 km thick on 31 Oct., represented in Fig. 7,we found the averaged results listed in Table I. Asstated earlier, the estimated absolute error for anysingle measurement is -10%, and this error estimateapplies equally to /, to S, and to a.

On at least two occasions on 21 Oct. we had thincirrus overhead in 300-600 m thick decks that werecontinuous, at least on the mesoscale. These clouds

15 June 1988 / Vol. 27, No. 12 / APPLIED OPTICS 2513

-6 ' \ 1,6 60 above cloud base

6 ,

I

l

I

I

I

Table I. Summary of Langley Plot-Derived Cirrus IR Optical Properties;Probable Errors for P, S. and a are -10%

Altitude ,3(m-1 sr-) S(sr) a(km-1)

1 km above base 1.0 X 10-7 1000-2000 0.15Midcloud 3.0 X 10-7 1500-2500 0.6Near cloud top 9.0 X 10-8 500-1000 0.07

were not visible to a trained meteorologist in a bluezenith sky with surface visibilities of at least 25. km.We attempted Langley plots for these clouds, but thethin cloud layer was not uniform enough to producebelievable results. (Regression coefficients for theplots were 0.5 and less.) We did obtain accurate betavalues for these clouds and found an average value of = 1.04 X 10-8 in one 300-m range gate and = 7.5 X10-9 in the next higher gate. If we assume an S = 1000for these subvisual clouds, the calculated extinctioncoefficient would average a = 0.01 km 1 . This value isonly 10% of the measured extinction found for a com-parably thin cirrus overcast using the EC method, butthis difference is not too surprising when the particlenumber density and equivalent ice water content arefound to vary by an order of magnitude or more forsuch thin cirrus clouds.'7

At least once each hour during FIRE we recordedfiles of data with the lidar directed at the zenith, fol-lowed immediately by a file 150 from the zenith. Onthe average, we found the zenith data exceeded the 150data by a factor of 20. This is similar to the enhance-ment by a factor of 33 reported by Platt et al.11 whoused a ruby lidar. On some occasions the backscatterat 150 actually exceeded the zenith value, but at othertimes it was weaker by a factor of 100 or more. Therewas no difference in visual appearance of the cirrus forthese different backscatter results. Since our coher-ent detection scheme responds only to backscatteredradiation of the same polarization as our local oscilla-tor laser, any depolarization by backscatter from theirregular ice crystals goes unrecorded with our lidar.We have recorded depolarization of 50% by cirrus inearlier experiments' 8 when the lidar was equippedwith an additional quarterwave plate in a second de-tector path. This additional detector for cross-polar-ized return was not available during FIRE. Had webeen able to measure depolarized backscatter as well,the total backscatter coefficient would have been larg-er. This would lead to extinction-to-backscatter ra-tios smaller by as much as a factor of 2 than the in-plane values reported here.

Ill. Discussion of Results

We now compare the El Chichon attenuation andthe Langley plot results. The EC technique yieldedextinction-to-backscatter ratios 1100 < S < 2600 sr;the lower values were found to apply to thin tenuousclouds, and the higher values were found to apply todense clouds several kilometers thick. The Langleyplots gave S values as low as 500 near the tops of cirruslayers 2 km thick and values as high as 2500 in thecenter of dense clouds several kilometers thick. It is

interesting to note that the lower values of S 500were near a cloud top [at least, the top of one main layerat about 9144 m (30,000 ft) ASL] where the NCARKingAir found a number of ice spheres of 5-2 5 -Amradius.' 9 These probably were particles that were eva-porating and had lost their sharp crystalline edges. Inthe center of the cloud, columnar crystals and rosettesof columns with dimensions of 100-200 Am or greaterwere found.

We will comment shortly on the calculated S valuesthat should be found if spherical or cylindrical parti-cles exist in the cirrus. Here we simply observe thatthe EC and Langley methods are producing compara-ble values for IR extinction in cirrus. The superiorheight resolution of the Langley method is a distinctadvantage so long as uniform layers of cirrus arescanned. We need more experience with this tech-nique, and the resulting better statistics of the resultsbefore a more critical comparison of the two methodscan be done. We have not analyzed enough cases todetermine if we find a correlation between extinctionand cloud temperature as found by Platt et al.2 0

We now compare our experimental results with acalculation of the extinction-to-backscatter ratiosbased on Mie scattering theory. We used FORTRANprograms developed by Bohren and Huffman.21 Us-ing the values for the complex index of refraction forice at 10.59 Am, m = (n - ik) = (1.1089-iO.1222),22 wecalculated for the smaller ice spheres at cloud top anextinction-to-backscatter ratio 700 < S < 2200. If weassume that the rosettes found by Heymsfield could beapproximated by spheres of 50-100-Am radius, we ob-tained 2200 < S < 2600. For ice cylinders 35 gm inradius, S = 205, 1 order of magnitude less than acomparable sphere. A combination of cylinders andspheres would give the actually observed S values.Had we ignored the absorption in ice in our calcula-tions, much larger values of backscatter would havebeen predicted, leading to smaller values for S, theextinction-to-backscatter ratio. This is because thewhispering modes, characterized by those highest-or-der Hankel functions necessary to provide a convergedsolution in Mie scattering, lead to greatly enhancedbackscatter from the outer regions of the spheres orcylinders being investigated for nonabsorbing media.23

For large size parameters these modes may contribute90% of the backscatter. But for ice at 10.59 gm, theabsorption is strong enough to attenuate these modesrather completely. Of course, whispering modes prob-ably would not occur in irregularly shaped particlessuch as cirrus ice crystals, even if there were no absorp-tion. It is probably for this reason that absorbingspheres in which these modes are attenuated do seemto model satisfactorily the observed extinction-to-backscatter ratios.

Some appreciation for the statistical variations inlidar backscatter that we observed during FIRE can begained by studying Table II. The two left columns listthe altitudes of the lidar returns; the next six columnsare 1-min averages of uncorrected for attenuation inthe cirrus. Other columns are as labeled. The cloud

2514 APPLIED OPTICS / Vol. 27, No. 12 / 15 June 1988

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base is at -7.9 km, and the top of the principallayer is at -10.8 km, although there is a diffuseconnection to an upper layer at -13 km. Nearthe center of the main deck the minute-by-min-ute standard deviation in is only 15% of themean value, but near cloud top the standard devi-ation is about equal to the mean. We were ableto measure the fall velocities of the ice crystals(combined with clear-air vertical velocities)through the thicker part of the cloud and also thewinds using our Doppler processor. These dataemphasize that even in the same cloud deck, theIR optical properties of the clouds vary signifi-cantly on spatial scales of -1.8 km.

IV. Conclusions

We have developed two new experimentalmethods to determine the IR extinction coeffi-cients in cirrus clouds using a pulsed Dopplerlidar. The coefficients a so determined varyfrom 0.1 to 0.78 km'. In general, the lowerextinction values are associated with tenuousclouds and the higher values with dense cloudsthat are several kilometers thick. These experi-mentally measured extinction coefficients agreerather well with the coefficients of the LOWTRAN6 model, except that the LOWTRAN model maypredict too high a coefficient for thin cirrus.

The IR backscatter coefficients for cirrusvary over an even greater range, from 2 X 10-10M"1 sr"1 for thin tenuous clouds to >9 X 10-7 M- 1

sr-' for dense thick clouds. The extinction-to-backscatter ratio, S = o//3, may be as low as 500 srfor tenuous clouds to as high as 2000 sr or greaterfor dense clouds. Calculations of S using Mietheory for a combination of ice spheres and right-circular cylinders can reproduce these S valuesfor particle sizes equal to those actually found inthe cirrus by aircraft probes.

These results are based on a limited evaluationof a much more extensive data set that exists atNOAA. A more complete evaluation of thesedata will probably expand the range of and pro-vide improved statistics on the backscatter andextinction coefficients reported here. Compar-ing the lidar-determined coefficients with clouddata gathered by NCAR aircraft during FIREmay provide better insight into assigning the ap-propriate coefficients to particular cirrus cloudspecies.

continued on page 2516

15 June 1988 / Vol. 27, No. 12 / APPLIED OPTICS 2515

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To obtain better understanding of the radiativetransfer properties of cirrus, side-by-side probing us-ing both visual and IR lidars equipped with dual polar-ization receivers is recommended. This would showthe relative importance of scattering from the interiorof the ice crystals (absorbed in the infrared) to surfacediffraction and reflection. It should also be noted thatthe extinction coefficients determined in this paper areapplicable for narrow field-of-view instruments butare probably not appropriate for radiative transfercalculations. Since scattering is so highly concentrat-ed in the forward direction, the effective extinction forhemispheric fields of view is only about half of thevalues derived here. For very thick cirrus, where mul-tiple scattering tends to broaden the resultant scatter-ing diagram, the extinction values reported here be-come more appropriate.

Developing and operating an instrument as complexas our Doppler lidar required the help of our entireteam, especially Madison Post, R. Michael Hardesty,Janis Holler, Rhidian Lawrence, and Ronald Richter.Thomas Baltzer, Susan Carlson, Katherine Jaeger,and Bonnie Weber wrote much of the computer cod-ing. Thanks are also due to Applied Optics refereeswho pointed out ambiguities with suggestions for im-provements.

References

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2. D. W. Wark, G. Yamamoto, and J. H. Lienesch, "Methods ofEstimating Infrared Flux and Surface Temperatures from Me-teorological Satellites," J. Atmos. Sci. 18, 369 (1961).

3. W. D. Zdunkowski, D. Henderson, and J. V. Hales, "The Influ-ence of Haze on Infrared Measurements Detected by SpaceVehicles," Tellus 17, 147 (1965).

4. F. F. Hall, Jr., "The Effect of Cirrus Clouds on 8-13-,um InfraredSky Radiance," Appl. Opt. 7, 891 (1968).

5. S. K. Cox, "Observations of Cloud Infrared Effective Emissivi-ty," J. Atmos. Sci. 33, 287 (1976).

6. G. L. Stephens and P. J. Webster, "Clouds and Climate: Sensi-tivity of Simple Systems," J. Atmos. Sci. 38, 235 (1981).

7. F. F. Hall, Jr., M. J. Post, R. A. Richter, G. M. Lerfald, and V. E.

Derr, "Cirrus Cloud Model," in Atmospheric Transmittance!Radiance: Computer Code LOWTRAN 6, F. X. Kneizys et al.,Eds., AFGL-TR-83-0187, Air Force Geophysics Laboratory,Hanscom AFB, MA (1983), pp. 58-67.

8. L. S. Rothman et al., "AFGL Atmospheric Absorption LineParameters Compilation: 1982 Edition," Appl. Opt. 22, 2247(1983).

9. M. J. Post, J. F. Morrow, and D. B. Jensen, "BETA: A Programfor Calculating and Achieving Backscattering Profiles Takenwith the NOAA Coherent Lidar System," NOAA Tech. Memo.ERL WPL-113, Boulder, CO (1983).

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

11. C. M. R. Platt, N. L. Abshire, and G. T. McNice, "Some Micro-physical Properties of an Ice Cloud from Lidar Observation ofHorizontally' Oriented Crystals," J. Appl. Meteorol. 17, 1220(1978).

12. J. C. Johnson, Physical Meteorology (Wiley, New York, 1954).13. J. D. Spinhirne, J. A. Reagan, and B. M. Herman, "Vertical

Distribution of Aerosol Extinction Cross Section and Inferenceof Aerosol Imaginary Index in the Troposphere by Lidar Techni-que," J. Appl. Meteorol. 19, 426 (1980).

14. B. M. Herman, M. A. Box, J. A. Reagan, and C. M. Moore,"Alternate Approach to the Analysis of Solar Photometer Da-ta," Appl. Opt. 20, 2925 (1981).

15. E. L. Crow, F. A. Davis, and M. W. Maxfield, Statistics Manual(Dover, New York, 1960).

16. W. Carnuth and R. Reiter, "Cloud Extinction Profile Measure-ments by Lidar Using Klett's Inversion Method," Appl. Opt. 25,2899 (1986).

17. I. D. Cohen, "Cirrus Particle Distribution Study, Part 8,"AFGL-TR-81-0316, Meteorology Division, Air Force Geophys-ics Laboratory, Hanscom AFB, MA (1981), 110 pp.

18. A. Gross, M. J. Post, and F. F. Hall, Jr., "Depolarization, Back-scatter, and Attenuation of CO2 Lidar by Cirrus Clouds," Appl.Opt. 23, 2518 (1984).

19. A. J. Heymsfield, NCAR, Boulder, CO; private communication(1987).

20. C. M. R. Platt, J. C. Scott, and A. C. Dilley, "Remote Sounding ofHigh Clouds. Part VI: Optical Properties of Midlatitude andTropical Cirrus," J. Atmos.'Sci. 44, 729 (1987).

21. C. F. Bohren and D. R. Huffman, Absorption and Scattering ofLight by Small Particles (Wiley, New York, 1983).

22. S. G. Warren, "Optical Constants of Ice from the Ultraviolet tothe Microwave," Appl. Opt. 23, 1206 (1984).

23. J. V. Dave, "Scattering of Visible Light by Large Water Spher-es," Appl. Opt. 8,155 (1969).

2516 APPLIED OPTICS / Vol. 27, No. 12 / 15 June 1988