Definitions of atmospheric radiance and transmittances in remote sensing

REMOTE SENSING OF ENVIRONMENT 13:89-92 (1983)

89

SHORT COMMUNICATION Definitions of Atmospheric Radiance and Transmittances in Remote Sensing

P. Y. DESCHAMPS, M. HERMAN, and D. TANRE Laboratoire d'Optique Atmosph~rique (CNRS), Universit~ des Sciences et Techniques de Lille, 59655 ViUeneuve D'Ascq Cedex, France

Some confusion sometimes arises about atmospheric radiance and transmittances in the remote sensing literature. We propose an appropriate terminology for use in problems of remote sensing of ground-reflected solar radiation through a turbid atmosphere.

The effect of atmospheric scattering upon remotely sensed solar radiation reflected by the ground surface is frequently given in literature as L ' = Lp + Le -T/c°s°,

(1)

where L is the (monochromatic) radiance reflected by the surface at ground level; L', the radiance measured at the top of the atmosphere; ~, the optical thickness of the atmosphere; ~ the zenith viewing angle; and Lp is the so-called path radiance. Equation (1) is valid only in some restricted circumstances and has at times been inappropriately used in the assessment of atmospheric effects, Equation (1) is valid only if it is understood that (i) the pixel size, or the IFOV (instantaneous field of view), must be small relative to the scale of the scattering effect, and (if) the path radiance includes not only atmospheric scattering (Fig. la), but also radiation scattered from the background surface of the pixel (Fig. lb) Landsat-type data have a small pixel size relative to the horizontal scale of the scattering effect--typically 1 km (Tanr~ ©Elsevier Science Publishing Co., Inc., 1983 52 Vanderbilt Ave., New York, NY 10017

et al., 1981). Equation (1) can be used here if the interaction between the background of the pixel and the atmosphere is not neglected. To avoid confusion, it would be better to use the following equation: L ' = L~ + L b + L e - T/cosO

(2)

where L a is called the atmospheric radiance, and L b the background radiance. It therefore is suggested that these two terms replace the term path radiance, which resulted in past misunderstanding. Atmospheric radiance (Fig. la) is defined as the photons scattered by the atmosphere alone. It is a specific property of the scattering atmosphere and would be observed or could be computed over a black uniform surface. Background radiance (Fig. lb) is defined as the photons reflected by the background surface of a given pixel of small size and then scattered by the atmosphere towards the sensor--it thus depends upon both surface and atmospheric properties. When background surface reflectance is uniform and diffuse, one may separate 00344257/83/010089-04503.00

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P.Y. DESCHAMPS ET AL.

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Schematic of the definitions of: (a) the atmospheric radiance; 09) the background radiance; and (c) the useful radiance from the pixel target. F I G U R E 1.

atmospheric scattering and surface properties in the expression of the backgrotmd radiance

Lb=

(3)

Eta(8)

so that

L'=L,,+Et~(8)+Le

,/cosO

(4)

where/~ is the radiance reflected by the background at ground level, and t~(O) is an appropriate transmission factor, here called the diffuse transmittance, which is a specific property of the scattering atmosphere. Equation (4)may also be applied to a nonuniform landscape consisting of parcels of small size. If / ] = L, which implies a uniform surface of large size, Eq. (4) may also be written

L'=L~+LT(O)

(5)

where

T(8)=e

~/~°~°+ts(O)

(6)

is an appropriate transmission factor of

the scattering atmosphere, here called

total transmittance. It also is proposed that transmittance terminology be clarified. Direct (or beam) transmittance, e -~/~°s°, accounts for attenuation of the direct path from the surface to the sensor. Diffuse transmittance, t~(8), should correspond to the probability that photons, arriving diffusely--i.e., at all incidence angles-at the bottom of the atmosphere, be scattered by the atmosphere and escape at the top of the atmosphere at the viewing angle 0. Total transmittance should be defined as the probability that photons, arriving diffusely at the bottom of the atmosphere, escape at the top of the atmosphere at viewing angle 0, having been scattered or not. These three transmittances which are without dimensions, vary from 0 to 1, and depend only on the scattering properties of the atmosphere and the viewing angle. Values of direct and total transmittances are compared in Table 1 for a nadir viewing, and at wavelengths from 450 to 950 nm. They have been computed for three different scattering atmospheres. (R) is molecular scattering only, and corresponds to the best achievable atmospheric conditions; (V23) and

ATMOSPHERIC RADIANCES AND TRANSMITTANCE

91

TABLE 1 Direct and Total Transmittances for the Three Scattering Model Atmospheresa WAVELENGTH

DIRECT TBANSMITrANCE

TOTAL TRANSMITTANCE

(nm)

(R)

OPTICAL THICKNESS

(V23)

(V5)

(R)

V(23)

(V5)

(R)

(V23)

(V5)

450 550 650 750 850 950

0.216 0.095 0.048 0.027 0.016 0.010

0.496 0.330 0.249 0.202 0.171 0.149

1.146 0.875 0.716 0.609 0.531 0.472

0.806 0.909 0.953 0.973 0.984 0.900

0.609 0.719 0.779 0.817 0.842 0.861

0.317 0.416 0.488 0.543 0.587 0.624

0.902 0.955 0.976 0.987 0.992 0.995

0.878 0.931 0.955 0.968 0.975 0.980

0.814 0.871 0.900 0.919 0.931 0.941

a(R), (V2,3), and (V5), defined in the text, at nearly nadir viewing angle (0 = 2.84°).

(V5) have aerosol contents defined in McClatchey et al. (1971) which would give ground visibilities of 23 and 5 km, and correspond to mean and limit conditions for the observation of the earth surface in the visible. If the optical thicknesses for molecular and aerosol scatterings, yR and yA, are known the following approximations can be used rather accurarely (Tanr6 et al., 1979):

atmosphere, E0, and a solar zenith angle, 8o, the direct solar irradiance on the ground surface is given by

EocoSOoe-~/°~°°

(9)

and the total irradiance by

EocosOoT(Oo)/(1-ps)

(10)

where p is the ground albedo ( p =

T( O) = ( l + bY/#o) -1 by = 0.50y R +0.16y A

(7) (8)

with b = ½ ( 1 - g ) , where g is the phase function asymmetry factor and where Arccos #0 is the solar zenith angle, Total transmittance is much closer to one than is direct transmittance because of the large forward aerosol scattering peak. The difference between total and direct transmittances corresponds to diffuse transmittance, which is the relative weight of the background radiance and can never be neglected. Note that total, direct, and diffuse transmittances may also be used to express the solar irradiance incident at ground level, and the direct and diffuse components of that irradiance. For a solar irradiance outside the

IIL /Eoc°St~o f°r a diffuse surface)' and s is the spherical albedo of the scattering atmosphere (s -- 2by/(1 + 2by). It must be remembered that the above definitions and equations apply to scattering by the atmosphere. Direct transmittance through an absorbing gas, ig(0), must be evaluated separately. The radiante at the top of the atmosphere may in most cases be expressed as L " = igL'

(11)

which implies that the gaseous absorption takes place above the atmospheric scattering. In situ measurements of direct transmittance made by viewing the sun disk (Herman et al., 1981) do not allow determination of the optical thickness due to scattering, unless obtained in spectral regions free from gaseous absorption. One

92

must be careful when using computer codes, such as the LOWran_~ 5 code (Kneizys et al., 1980), because they do not distinguish between scattering and absorption in the calculation of direct transmittances. Incorrect use of Eq. (1) has at times caused the background radiance to be neglected and, as a result, the underestimation of the radiance at the top of the atmosphere.

We wish to thank J. P. Durepaire and G. Saint for their helpful comments. We are also grateful to L. F. Martin for his aid in the translation. We acknowledge support from the Centre National d'Etudes Spatiales, (CNES) and from the European Space Agency (ESA). References Herman, B. M. Box, M. A., Reagan, J. A., and Evans, C. M. (1981), Alternate approach to

P.Y. DESCHAMPS ET AL.

the analysis of solar photometer data, Appl. Opt. 20:2925-2928. Kneizys, F. X., Shettle, E. P., Gallery, W. O., Chetwynd, J. H., Abreu, L. W., Selbry, J . E . A . , Fenn, R. W., and McClatchey, R.A. (1980), Atmospheric transmittance/ radiance: computer code LOWTRAN 5, AFGL-TR-80-0067, Air Force Geophysics Laboratory, Hanscom AFB, Mass. McClatchey, R. A., Fenn, R. W., Selbry, J . E . A . , Voltz, F. E., and Caring, J. S. (1971), Optical properties of the atmosphere, AFCRL 71-0279, Air Force Geophysics Laboratory, Hanscom AFB, Mass. Tanr6, D. Herman, H., Deschamps, P. Y. and de Leffe, A. (1979), Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties, Appl. Opt. 18:3587-3594. Tanr6, D. Herman, M., and Deschamps, P. Y. (1981), Influence of the background contribution upon space measurements of ground reflectances, Appl. Opt. 20:3676-3684. Received 18 lanuary 1982; revised 14 luly 1982,