Simplified ultraviolet and visible wavelengthatmospheric propagation model

Edward M. Patterson and James B. Gillespie

We have developed a program to model atmospheric propagation and lidar return at visible and UVwavelengths. This model combines a transmission code suitable for use in the visible and UV regions with abackscatter code for Mie and fluorescence lidar return calculations and a sky background radiance code into amodular menu-driven user friendly FORTRAN program for an IBM PC or PC compatible system. Thispropagation model includes attenuation due to molecular scattering, molecular absorption, and particulateattenuation. The wavelength dependence of our aerosol attenuation is parametrized in terms of the visualrange to provide an approximate match for UV and visible horizontal attenuation data. This aerosol model iscompared with the AFGL standard aerosol models and experimental data on atmospheric attenuation as afunction of the visual range.

1. Introduction

Electrooptical sensor systems design requiresknowledge of the effects of the atmosphere on thereceived signal and on the signal levels to be expectedfrom actively sensed atmospheric targets. Althoughinterest has traditionally been focused on IR and long-er wavelength systems, the availability of improvedsources and detectors and the desire to utilize theincreased resolution available with shorter wavelengthsystems has led to renewed interest in short wave-length optical systems extending into the solar blindregion below 310 nm.

There has been a need for a simple code for deter-mining these parameters in the visible and UV regions.To meet this need, we developed a program to modelatmospheric propagation and lidar return at visibleand UV wavelengths. This model is unique in that itcombines a transmission code suitable for use in thevisible and UV regions with a backscatter code for Mieand fluorescence lidar return calculations and a skybackground radiance code into a modular menu-driv-en user friendly FORTRAN program for an IBM PC orPC compatible system.

Edward Patterson is with Georgia Institute of Technology, Schoolof Geophysical Sciences, Atlanta, Georgia 30332; and James Gilles-pie is with U.S. Army Atmospheric Sciences Laboratory, WhiteSands Missile Range, New Mexico 88002-5501.

Received 8 September 1988.

This propagation model differs from the LOWTRAN61 or similar models in that it is designed for use atvisible and UV wavelengths only, so that the bandmodels and emission calculations that are needed at IRwavelengths are not included. Molecular oxygen ab-sorption is included, a feature not available on PCversions of LOWTRAN; SO2 and nitrogen oxides ab-sorption are also included. In addition, the wave-length dependence of the aerosol attenuation is pa-rametrized in terms of the visual range in our modelrather than having a wavelength dependence that isindependent of the visual range. This different aero-sol parametrization was chosen, in part, because ofdata showing differences between the LOWTRAN re-sults and short wavelength experimental data (e.g.,Baum and Dunkelman2 ). The background radiancealso is parameterized in terms of a zenith angle depen-dence rather than being calculated on the basis ofsingle scattering theory.

In this paper, we describe this computer program,discuss the scientific basis for the model, and compareits results with LOWTRAN calculations and experimen-tal data.

II. Description of the Model

The transmission model determines the path trans-mission between 185 and 700 nm due to aerosol attenu-ation, molecular scattering, and molecular absorption.The model is designed to be used over relatively shortranges in the troposphere, consequently a plane-paral-lel geometry only is assumed. The model does notinclude effects due to density gradients or to atmo-spheric turbulence. The attenuation is in all casesassumed to be given by the Beer-Lambert attenuation

1 February 1989 / Vol. 28, No. 3/ APPLIED OPTICS 425

law T = exp(-o-x) with a- the attenuation coefficientand x the path length. The model does not include aband absorption model because of the interest in UVand visible absorption in which electronic absorptionis important. No IR water bands are included in themodel, and so the long wavelength limit for the modelis -700 nm.

This model is primarily designed for use in the lowertroposphere. Concentrations of attenuating compo-nents are determined for altitudes of 11 km or less.Since no spherical geometry is included, the model ismost appropriate for relatively short ranges.

The attenuation due to molecular scattering is cal-culated by the molecular scattering formula,

() [9.26 exp(+18) - 1.07 exp(+9)(1/X2)j *I o) (1)

based on a fit to data of Penndorf3 that was used inLOWTRAN 5 with a modification to take account ofdifferences in the LOWTRAN formula and more recentresults in the Handbook of Geophysics and SpaceEnvironment. 4 N is the number density of air mole-cules, which is calculated from pressure and tempera-ture data; No is the number density under standardconditions. The correction term C, C = 0.987, is themodification to the Penndorf formula to bring thecalculated Rayleigh scattering into agreement with thestandard molecular scattering given by the Handbookof Geophysics and the Space Environment. 4

Molecular absorption in this model is calculated forthe two major absorbing species, oxygen (02) andozone, and for the minor absorbing species, sulfur di-oxide, nitrogen dioxide, nitrous oxide, and water va-por. The choice of these species for inclusion into themodel was made on the basis of expected concentra-tions of trace species from the 1976 U.S. StandardAtmosphere5 and molecular absorption coefficientsdiscussed in Ackerman6 and Calvert and Pitts.7 It isexpected that in normal conditions the molecular ab-sorption will be almost entirely determined by theoxygen and ozone absorption. The other absorptioncoefficients are included because of the possibility thathigh concentrations of these other gaseous constitu-ents could be present in some circumstances leading tosignificant absorption.

Plots of the absorption cross sections for ozone andoxygen used in UVTRAN are shown in Figs. 1 (03) and 2(02)- Our model resolution is 2.5 nm for the oxygendata and for the ozone Hartley-Huggins bands. TheChappuis band data for ozone have resolutions of 5-10nm. These are relatively low resolution data, but in-terpolation should not cause significant deviationsfrom actual values except in the case of the oxygenSchumann-Runge bands between 185 and 200 nm.For these bands the modeled values are approximateaverages over the adjacent bands. In this case theassumption was made that any measurements in thisregion will be a relatively wide band so that the averag-ing is appropriate.

The aerosol attenuation was parametrized in termsof the visibility according to the equation8

0

01

I

5I

r.

._

0 o

ela,h PJC) o0

ren-1 -

I

I

150 200 220Wavelength (nm)

240 2B0

Fig. 1. Molecular oxygen absorption cross sections in cm2.

eaI

0

.-0 . IC

04

C) O

M -,

I

00.

05 I

M la

11

0I

To

100 200 300 400 500 ooWavelength (nm)

700 800

Fig. 2. Ozone absorption cross sections in cm2 .

aaer () = 3.912 _ a. (550)J * (2)

with X is the wavelength of the light, aext(X) is thedesired particle extinction, ams(550) is the Rayleighextinction at 550 nm, V is the observed visibility, and qis the Angstrom exponent describing the wavelengthdependence of the attenuation; q is defined in terms ofthe visual range V by the relation

q = 0.585v' 3 (3)

426 APPLIED OPTICS / Vol. 28, No. 3 / 1 February 1989

l W w

- - - - s S

_ . , . ,

I

E ocz

0-. _

41I

. 0

0

Z:._

V I _ O2-

Il

100 200 300 400 500 600 700Wavelength (nm)

Fig. 3. Model aerosol attenuation coefficients as a function ofwavelength for different values of visibility V. The dotted linecorresponds to V = 50 km, the solid line to V = 10 km, the dashed and

dotted line to V = 2 km, and the dashed line to a V of 0.5 km.

which is based on an empirical fit to short wavelengthtransmission data.9' 10 This relationship is an exten-sion of the Koschmeider relation between visibilityand atmospheric extinction at 0.55 ,um, V = 3.912/a-ext.1 0 For V in kilometers the -ext is in km- 1.

Because the visibility depends on the total atmo-spheric extinction coefficient, the molecular attenua-tion at 550 nm has been subtracted from the totalatmospheric attenuation coefficient to determine theparticle extinction. The separation is made so thatwavelength scaling and particulate attenuation varia-tion with height can be made in terms of aerosol effectsonly.

A plot of the calculated wavelength dependent aero-sol attenuation for different visibilities is shown in Fig.3. In this figure, the dotted line corresponds to a V of50 km, the solid line to a V of 10 km, the dashed anddotted line to a V of 2 km, and the dashed line to a V of0.5 km. The calculated decrease in the wavelengthdependence of the particle attenuation with decreas-ing visibility is consistent with the idea that the greatlyreduced visibilities are associated with larger particlesthan are the background cases of high visibility.

A plot of the total attenuation coefficient as a func-tion of wavelength and attenuation coefficients due toaerosol attenuation, molecular scattering, and molecu-lar absorption is shown in Fig. 4. The total attenua-tion coefficient is given by the solid line, the aerosolattenuation by the dotted line, the molecular scatter-ing attenuation by the dashed and dotted line, theozone and oxygen attenuations by the long and shortdashed lines. The calculations were made for stan-dard conditions at sea level for an assumed visibility of

0

-4

I

00-

0

U) q

- 0

I

-.

U ') .O~

<;II

100 200 30D 400 800Wevelength (nm)

600 700

Fig. 4. Attenuation calculations for standard conditions at sea levelfor an assumed visibility of 10 km. The total attenuation coefficientis given by the solid line, the aerosol attenuation by the dotted line,the molecular scattering attenuation by the dashed and dotted line,the ozone and oxygen attenuations by the long and short dashed

lines, respectively.

10 km; the relative importance of the individual com-ponents can be readily seen in the figure.

The background radiance values can be calculatedfor three cases: daytime clear sky illumination, day-time cloudy illumination, and nighttime illumination.The values are parametrized in terms of a zenith angledependence relative to assumed horizon radiance lev-els; both sky and terrain backgrounds are consideredfor different zenith angles; sky for zenith angles of lessthan or equal to 900 and terrain for zenith angles of>90°. The horizon brightness levels were inferredfrom various data sources including Ref. 11 and refer-ences therein.

Ill. Comparisons with LOWTRAN and Experimental Data

A comparison of our model and the LOWTRAN 6calculations for standard conditions is shown in TableI. The calculations were made for wavelengths of 300,

Table 1. Transmission for UVTRAN and LOWTRAN for Standard Conditionsa

300 nm 550 nm 700 nmT T X

Wavelength UVT LOW UVT LOW UVT LOW

Tms 0.239 0.233 0.892 0.890 0.956 0.957T03 0.773 0.768 0.998 0.998 0.999 0.999Taer 0.013 0.064 0.206 0.206 0.347 0.307Toth 0.986b 0.997c 0.954dTtot 0.0024 0.0115 0.182 0.183 0.331 0.280

a p = 1013.25 mbar, T = 288.15 K, 03 = 25.2 ppbv, Vis = 23 km,range = 10 km.

b Due to SO2.c Due to NO2 absorption.

d Due to water vapor.

1 February 1989 / Vol. 28, No. 3/ APPLIED OPTICS 427

- I~~~~~~~~~

* '4~~I

* I

I' 1j*K.

E

lI.

550, and 700 nm for the atmospheric conditions listedin the table. The visibility was specified to be 10 km,and the wavelength dependence of the aerosol attenua-tion is given by Eq. (4) for UVTRAN and by the ruralaerosol model for a relative humidity of 70% for LOW-TRAN. 1 In this table, Tins represents the transmittancedue to molecular scattering, ro3 represents the trans-mittance due to ozone, Taer represents the transmit-tance due to aerosol particles, roth represents the trans-mittance due to any other gaseous species, and rtotrepresents the total resulting transmittance.

The Rayleigh scattering attenuation is slightly lessthan the comparable LOWTRAN attenuation as dis-cussed above, leading to slightly higher transmittancein our model. Similarly, there are no significant dif-ferences in the ozone absorption in the different mod-els. The calculated aerosol attenuation values are sig-nificantly different at 300 and at 700 nm in the twomodels, with the greater differences at 300 nm. Theagreement in the aerosol attenuation at 550 nm is dueto the fact that the attenuation at this wavelength isdetermined by the assumed visual range in each model.

The differences in the aerosol attenuation in the twomodels indicate that the variation of attenuation withwavelength is less in the AFGL rural aerosol modelthan in UVTRAN. For the cases shown above, q is 1.7for UVTRAN compared with q = 0.9 for LOWTRAN.While the experimental data on the wavelength depen-dence of the atmospheric attenuation is limited, datado suggest a larger value of q between 300 and 550 nmthan predicted by the AFGL models except in condi-tions of greatly reduced visibility. Middleton. 0 re-ported that the average value of q was 1.6 in good toexcellent seeing conditions and 1.3 in average seeingconditions. Junge12 used a value of q = 1.3 to describethe average atmospheric conditions. The experimen-tal data of Wolff which were used by Loehle9 to derive

Table II. Comparison of Observed and Calculated AttenuationCoefficients at 300 nm for Different Visibilities

Visual aaer aaer aaerrange (UVTRAN) (LOWTRAN) (B&D-emp)(km) (km-') (km-') (km-')

100 0.137 0.047 0.21340 0.284 0.150 0.34020 0.476 0.320 0.55310 0.809 0.662 0.9785 1.41 1.34 1.83

Table 111. Comparison of Observed and Calculated AttenuationCoefficients at 350 nm for Different Visibilities

Visual aaer Caer aaerrange (UVTRAN) (LOWTRAN) (B&D-emp)(km) (km-1) (km-') (km-)

100 0.092 0.042 0.09740 0.212 0.134 0.19820 0.376 0.288 0.36610 0.691 0.594 0.7025 1.21 1.20 1.38

the empirical relationship in Eq. (3) do predict a q of<1 but are for relatively low visibility conditions.

A more detailed set of wavelength dependent atten-uation data is that of Baum and Dunkelman2 whomeasured attenuation coefficients between 250 and550 nm in Pasedena for a range of visibilities. Theydeveloped an empirical relationship between visibilityand wavelength dependent atmospheric attenuation.Comparisons of aerosol attenuation calculated by uv-TRAN and LOWTRAN with the attenuation calculatedfrom the empirical relation of Baum and Dunkelmanfor different visual ranges are shown in Tables II andIII for 300 nm (Table II) and for 350 nm (Table III). Itis only for visual ranges of <5 km that the q for uv-TRAN is less than the q for the AFGL rural aerosolmodel. The UVTRAN and Baum and Dunkelman val-ues are closer at 350 nm than at 300 nm, suggesting thathigher than standard ozone concentrations during theBaum and Dunkelman measurements may be affect-ing the 300-nm comparison.

These comparisons indicate that the value of q isrelated to the visibility and that the parametrizationfor q that we have used in UVTRAN is adequate, al-though certainly not exact. The discussion by Wood-man13 indicates that the wavelength parametrizationsof Eqs. (2) and (3) should be adequate throughout thevisible region. Although Eq. (3) was derived on thebasis of low visibility data only, these comparisons alsosuggest that the model should be adequate for visibili-ties of 50 km and less. Our UVTRAN expression ap-pears to represent better average aerosol transmit-tances at UV and visible wavelengths than the AFGLmodel. We would note, of course, that the primary useand most extensive testing of LOWTRAN have been atIR wavelengths rather than the shorter wavelengthsdiscussed here. The question of the wavelength de-pendence of the transmittance at UV and visible wave-lengths is a question that should be addressed withadditional measurements.

IV. Discussion

We have described a simplified model of atmospher-ic propagation for use at UV and visible wavelengths.The focus has been on the transmittance portion of thecode because of a desire to describe the physical basisof the model. Gaseous absorption does not differ sig-nificantly from that in LOWTRAN 6; likewise our calcu-lated Rayleigh scattering is only slightly less than thatof LOWTRAN, with the difference due to our match ofmore recent values of Rayleigh attenuation coeffi-cients. The major difference in the UVTRAN andLOWTRAN results is due to the different aerosol pa-rameterizations in the two models. The UVTRANmodel is more directly based on empirical transmissiondata; it offers a simpler, yet more accurate parameter-ization of aerosol attenuation at visible and UV wave-lengths than the LOWTRAN parametrization.

This overview of the UVTRAN model is necessarilybrief; a more complete description of the model andthe capabilities of the model for lidar return calcula-tions is available as a technical report.1 4 The model is

428 APPLIED OPTICS / Vol. 28, No. 3 / 1 February 1989

available to qualified users through J. B. Gillespie atthe U.S. Army Atmospheric Sciences Laboratory.

Edward Patterson also works in the GTRI/Electro-magnetics Laboratory.

References1. F. X. Kneizys et al., "Atmospheric Transmittance/Radiance

Computer Code LOWTRAN 6," Technical Report AFGL-TR-83-0187 (NTIS, Springfield, VA, 1983).

2. W. A. Baum and L. Dunkelman, "Horizontal Attenuation ofUltraviolet Light by the Lower Atmosphere," J. Opt. Soc. Am.45, 166 (1955).

3. R. Penndorf, "Tables of the Refractive Index for Standard Airand the Rayleigh Scattering Coefficient for the Spectral Regionbetween 0.2 and 20 ,m and Their Application to AtmosphericOptics," J. Opt. Soc. Am. 47, 176 (1957).

4. A. S. Jursa, Scientific Ed., Handbook of Geophysics and theSpace Environment, (Air Force Geophysics Laboratory, AirForce Systems Command, United States Air Force, 1985).

5. U.S. Standard Atmosphere (National Oceanic and AtmosphericAdministration, National Aeronautics and Space Administra-tion, and the U.S. Air Force, 1976).

6. M. Ackerman, "Ultraviolet Solar Radiation Related to Meso-spheric Processes," in Mesospheric Models and Related Ex-periments, G. Fiocco, Ed (Reidel, Dordrecht, 1971), pp. 149-159.

7. J. Calvert and D. Pitts, Photochemistry (Wiley, New York,1966).

8. P. W. Kruse, L. D. McGlauchin, and R. B. McQuistan, Elementsof Infrared Technology (Wiley, New York, 1963).

9. F. Loehle, "Uber die Lichtzerstreuung im Nebel," Phys. Z. 45,199 (1944).

10.- W. E. K. Middleton, Vision Through the Atmosphere (U. To-ronto Press, Toronto, 1952).

11. W. L. Wolfe and G. J. Zissis, Eds., Infrared Handbook (InfraredInformation and Analysis Center of the Environmental Re-search Institute of Michigan, 1978).

12. C. Junge, Air Chemistry and Radioactivity (Academic, NewYork, 1963).

13. D. P. Woodman, "Limitations on Using Atmospheric Models forLaser Transmission Estimates," Appl. Opt. 13, 2193 (1974).

14. E. M. Patterson, "Ultra-Violet Atmospheric Propagation Mo-del," Final Report on Project DAAL03-86-D-001 Delivery Order0578 (1988). Available from U.S. Army Atmospheric SciencesLaboratory.

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1 February 1989 / Vol. 28, No. 3 / APPLIED OPTICS 429