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Fig. 7. Limitations of the lambertian assumption for atmospheric correction [use of (1) instead of (8)] for a gentle atmosphere. In that case, correction using directional information (- - - -) is conducted by fitting the results of the correction using (1) (+) with the Hapke BRDF model and reinjecting the BRDF to compute coupling terms of (9a)—(9e).

Figure 7 Limitations of the lambertian assumption for atmospheric correction [use of (1) instead of (8)] for a gentle atmosphere. In that case, correction using directional information (- - - -) is conducted by fitting the results of the correction using (1) (+) with the Hapke BRDF model and reinjecting the BRDF to compute coupling terms of (9a)—(9e).

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and aerosol. As it can be observed on Fig. 4(a) and (b), there is a dependence of the function F'(r) on the view direction for view zenith angle larger than 30°. In order to account for this effect, we choose to fit the environment function at the desired view angle solely as a function of the environment function computed for a nadir view as it is suggested by Fig. 4(a) and (b). The results presented on Fig. 4(a) and (b) [symbols] show that a simple polynomial function of nadir view environment function whose coefficients depend on the logarithm of the cosine of view angle is adequate. For molecules, the F function is fitted by the simple expression
and aerosol. As it can be observed on Fig. 4(a) and (b), there is a dependence of the function F'(r) on the view direction for view zenith angle larger than 30°. In order to account for this effect, we choose to fit the environment function at the desired view angle solely as a function of the environment function computed for a nadir view as it is suggested by Fig. 4(a) and (b). The results presented on Fig. 4(a) and (b) [symbols] show that a simple polynomial function of nadir view environment function whose coefficients depend on the logarithm of the cosine of view angle is adequate. For molecules, the F function is fitted by the simple expression
Fig. 5. (a) Isolines of the pixel background contribution to the signal at the top of the atmosphere for a pure molecular case. The energy source is 10° W and each pixel is considered to have a lambertian reflectance of 1. The contribution of background is the number of Watt coming from each cel (201 x 201 cells). The plain line are for nadir viewing, the broken line are for a view angle of 70°. (b) Same as (a) but for a atmosphere composec exclusively of aerosol particles (Continental model).
Fig. 5. (a) Isolines of the pixel background contribution to the signal at the top of the atmosphere for a pure molecular case. The energy source is 10° W and each pixel is considered to have a lambertian reflectance of 1. The contribution of background is the number of Watt coming from each cel (201 x 201 cells). The plain line are for nadir viewing, the broken line are for a view angle of 70°. (b) Same as (a) but for a atmosphere composec exclusively of aerosol particles (Continental model).
2) BRDF: In 6S, the coupling between the BRDF (Bidirec- tional Reflectance Distribution Function) and the downward radiance at the surface level is taken into account according to the scheme presented in Tanre et al. [12]. The contribution of the target to the signal at the top of the atmosphere is decomposed as the sum of four terms: a) the photons directly transmitted from the sun to the target and directly reflected back to the sensor; b) the photons scattered by the atmosphere then reflected by the target and directly transmitted to the sensor; c) the photons directly transmitted to the target but scattered by the atmosphere on their way to the sensor; and finally d) the photons having at least two interactions with the atmosphere and one with the target. One can compute exactly each contributions a)—d) according to the following set of (9a)-(9d) as already shown in Tanre et al. [12] by defining In 6S, the first three contributions are computed exactly using the downward radiation field given by the SOS method for several directions, which allows us to perform the integrations in (9b) and (9c). The contribution which involves at least two interaction between the atmosphere and the BRDF (9d) is approximated by taking equal to the hemispherical albedo of the target
2) BRDF: In 6S, the coupling between the BRDF (Bidirec- tional Reflectance Distribution Function) and the downward radiance at the surface level is taken into account according to the scheme presented in Tanre et al. [12]. The contribution of the target to the signal at the top of the atmosphere is decomposed as the sum of four terms: a) the photons directly transmitted from the sun to the target and directly reflected back to the sensor; b) the photons scattered by the atmosphere then reflected by the target and directly transmitted to the sensor; c) the photons directly transmitted to the target but scattered by the atmosphere on their way to the sensor; and finally d) the photons having at least two interactions with the atmosphere and one with the target. One can compute exactly each contributions a)—d) according to the following set of (9a)-(9d) as already shown in Tanre et al. [12] by defining In 6S, the first three contributions are computed exactly using the downward radiation field given by the SOS method for several directions, which allows us to perform the integrations in (9b) and (9c). The contribution which involves at least two interaction between the atmosphere and the BRDF (9d) is approximated by taking equal to the hemispherical albedo of the target
Fig. 6. Comparison of the sum of the coupling terms atmosphere-BRDF: PTOA — (pR+A +€°7™ps) computed by 6S with the same quantity computed by the SOS code for different atmospheric conditions (clear, average, turbid). The ground BRDF is from Kimes measurements over a plowed field fitted with Hapke BRDF model.
Fig. 6. Comparison of the sum of the coupling terms atmosphere-BRDF: PTOA — (pR+A +€°7™ps) computed by 6S with the same quantity computed by the SOS code for different atmospheric conditions (clear, average, turbid). The ground BRDF is from Kimes measurements over a plowed field fitted with Hapke BRDF model.
Fig. 9. Influence of the altitude of the target on the molecular optical thickness. A simple valid approximation is to consider that the molecular optical depth is proportional to the barometric pressure as shown.
Fig. 9. Influence of the altitude of the target on the molecular optical thickness. A simple valid approximation is to consider that the molecular optical depth is proportional to the barometric pressure as shown.
Fig. 8. (a)-(b): Influence of the altitude of the target on the gaseous transmission function computed in the case of AVHRR channel 1(a) and 2(b). The atmospheric profile is the tropical atmosphere and the view and sun zenith angles are equal to 30°.
Fig. 8. (a)-(b): Influence of the altitude of the target on the gaseous transmission function computed in the case of AVHRR channel 1(a) and 2(b). The atmospheric profile is the tropical atmosphere and the view and sun zenith angles are equal to 30°.
Fig. 10. Influence of the altitude of target on the molecular intrinsic reflectance, the simulation shows for a typical observation geometry in the backscattering direction (sun zenith = 30°, view zenith = 30°, relative azimuth = 0°). The color code gives the absolute difference in unit of reflectance between the altitude dependent computation and the computation assuming the target is at sea level. The elevation is given by the ETOPOS model. D. Airborne Sensor Simulation vapor content for the portion of the atmosphere located unde: the plane.
Fig. 10. Influence of the altitude of target on the molecular intrinsic reflectance, the simulation shows for a typical observation geometry in the backscattering direction (sun zenith = 30°, view zenith = 30°, relative azimuth = 0°). The color code gives the absolute difference in unit of reflectance between the altitude dependent computation and the computation assuming the target is at sea level. The elevation is given by the ETOPOS model. D. Airborne Sensor Simulation vapor content for the portion of the atmosphere located unde: the plane.
Fig. 11. Variation of the gaseous transmission (Tg) as a function of the observer altitude, z, (airborne case), for AVHRR channel 1(a) and 2(b) spectral responses. The sun zenith angle is 30° and the view zenith angle is 30°, Tropical atmosphere was used.
Fig. 11. Variation of the gaseous transmission (Tg) as a function of the observer altitude, z, (airborne case), for AVHRR channel 1(a) and 2(b) spectral responses. The sun zenith angle is 30° and the view zenith angle is 30°, Tropical atmosphere was used.
Fig. 12. (a) Variation of the molecular environment function, (FR) for different altitude of the sensor. (b) Variation of the aerosol environment function, (F'4) for different altitude of the sensor.
Fig. 12. (a) Variation of the molecular environment function, (FR) for different altitude of the sensor. (b) Variation of the aerosol environment function, (F'4) for different altitude of the sensor.
Fig. 14. Example of ASAS atmospherically corrected vegetation spectrum using the 6S code. The intrinsic atmospheric reflectance in the visible and the gaseous absorption feature by water vapor and oxygen in the near infrared are clearly noticeable before correction.
Fig. 14. Example of ASAS atmospherically corrected vegetation spectrum using the 6S code. The intrinsic atmospheric reflectance in the visible and the gaseous absorption feature by water vapor and oxygen in the near infrared are clearly noticeable before correction.
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