Ground-Based Determination of Atmospheric Radiance for Correction of ERTS-1 Data Keith Peacock

Bendix Aerospace Systems Division, Ann Arbor, Michi­gan 48107. Received 11 September 1974. Sponsored by Donald S. Lowe, Environmental Research Institute of Michigan. The purpose of this communication is to describe a tech­

nique for estimating the atmospheric radiance, LA, ob­served by a downward looking sensor such as ERTS using ground-based measurements. The technique overcomes the geometrical limitations of the method described by Gordon et al., 1 provides good results without recourse to atmospheric modeling or complex mathematical tech­niques, and can be used by the individual Earth Resources investigator. The method used by Gordon et al. 1 requires the space and ground data to be collected at approximately the same time (or the same sun angle), and ground mea­surements must be made of sunlight scattered by the atmo­sphere through the same angle as the sunlight scattered to the spacecraft. This is not usually possible. The geome­try of the situation is shown in Fig. 1.

Incident sunlight is scattered by the atmosphere through an angle ø ' to the vertically looking sensor. The technique of Gordon et al. 1 uses a radiometric measurement of the sky radiance L m e a s (ø) scattered at angle ø, such that ø is identical to ø'. Then, assuming the scattering is symmetri­cal, L A and L m e a s (ø) will differ only because of the greater mass of atmosphere observed by the ground sensor. The correction for this air mass is obtained by application of the equation,

in which t is the atmospheric transmission for one air mass and mo is the air mass in the direction of observation. This equation is similar to Eq. (8) of Gordon et al., 1 and its validity has been demonstrated for measurements taken in a short time period by Rogers and Peacock.2

However, it Z < 45° it is easy to see that ß > 90°, an im­possible situation for measurement of L m e a s (ø). During the summer months, this is frequently the condition at the time of the ERTS passage; and the technique cannot be used. It becomes necessary to make the sky radiance mea­surements at a time when Z > 45° and to correct for the greater attenuation of the incident sunlight. A correction factor, TERTS/TZ, must be applied to Eq. (1) to derive LA, if the time of ERTS overpass of the test site and the sky radiance observations are significantly different. An ap­proach for determining this correction factor is as follows.

Sunlight entering the atmosphere at an angle, Z, as shown in Fig. 1, is scattered at altitude h in the direction of the observer. The energy available for scattering depends on the atmospheric extinction coefficient, τh∞, measured from outside the atmosphere to altitude h. The attenua­tion is given by exp(—τh∞ X m), in which m is the air mass. The energy scattered is a function of the scattering coefficient, αh, at altitude h. Thus, the energy scattered in the direction of the observer from altitude h is propor­tional to

The average attenuation for all altitudes before the energy is scattered to the observer is given by

Fig. 1. Sky radiance measurement geometry.

Fig. 2. Sky radiance measurements.

Fig. 3. Path radiance viewed by ERTS band 4 (0.5-0.6 µm).

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in which N defines each atmospheric altitude used in the summation. Use of the value αh in the equation expresses the importance of each altitude h in contributing energy at the observer location. A normalizing factor is included in the denominator. Values of τh∞ and ah have been tabu­lated.3 To adjust Th∞ from a standard atmosphere to the actual atmospheric conditions at the observer's location, T/ioo is multiplied by exp(—Th∞)/t, in which t is the mea­sured atmospheric transmission and τo∞ is the extinction coefficient for a beam traversing one atmospheric air mass of a standard atmosphere. This is also given by Valley.3

Variations in T are small, so the error in using a corrected standard rather than a real atmosphere is small.

Thus, a complete formula that gives the sky radiance, LA, at the time of the ERTS overpass from L m e a s made at another solar zenith angle and air mass is

in which ø, the scattering angle to the observer, equals the scattering angle to ERTS and T E R T S and Tz are given by Eq. (3) for the zenith angles at the time of the .ERTS pas­sage and the time of the L m e a s readings. The assumption must be made that t is the same for the sky radiance mea­surements as at the time of the ERTS data collection.

The validity of this equation is demonstrated in Figs. 2 and 3. Figure 2 shows ground-based sky radiance mea­surements as a function of the scattering angle for a range of solar air masses. Each of the curves was obtained by pointing a radiometer at the sun and then sweeping it in azimuth and in elevation, taking sky radiance readings at 10-deg intervals. Alongside each curve, the solar air mass at the time of the observations is given. The curve defined by the open squares, which falls steeply, is for a range of solar air masses and was produced by recording the zenith sky radiance over a period of several hours. Application of Eq. (4) to these data in Fig. 2, assuming T E R T S = 1, gives the results shown in Fig. 3. Except for about ±5% of scat­ter, all the points now follow the same line. By selecting L A from the curve at the scattering angle that exists at the time of ERTS overflight, and multiplying this value by T E R T S , the desired value of L A at the time of ERTS overf­light is determined.

Typical values of L A for a solar zenith angle of 48° are, for bands 4, 5, 6, and 7 of ERTS 0.268, 0.127, 0.081, 0.103 mW/cm2 sr, respectively. These values correspond to ground reflectivities of 11.2%, 5%, 3%, and 1% in bands 4, 5, 6, and 7. These relatively high values demonstrate the im­portance of making atmospheric corrections if ERTS data are to be used for quantitative analysis.

This work was supported by NASA Contract NAS5-21863.

References 1. J. I. Gordon, J. L. Harris, Sr., and S. Q. Duntley, Appl. Opt. 12,

1317 (1973). 2. R. Rogers and K. Peacock, Symposium on Significant Results

Obtained from the Earth Resources Technology Satellite-1. March 1973, Vol. 1, Section B, p. 1115, NASA SP-327.

3. S. L. Valley, Ed. Handbook of Geophysics and Space Environ­ments (McGraw-Hill, New York, 1965).

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