114.

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Page 20

(1.16)

An alternative way to approximate Equation (1.16) is given by:

(1.17)

where the term JD denotes the Julian day (e.g. in the case of 5th February, JD=36).

The introduction of the factor d into Equation (1.15) is justified by the following observations. Since at perihelion the magnitude of solar irradiance is greater than that at aphelion, if a sensor obtains the same radiance L_app at perihelion and aphelion, respectively, the apparent reflectance ρ* at perihelion should be less than that at aphelion. Thus, if the Sun-to-Earth distance is smaller than the average Sun-to-Earth distance, one should use a lower (<1) weighting factor d, and as the Earth is approaching aphelion, a higher value of d should be used.

The final step, that of converting apparent reflectance to ground target reflectance, uses Equation (1.12). We already know the apparent reflectance ρ* from Equation (1.15), while other parameters such as the spherical albedo, S, and the coefficients A and B can be obtained by running either the 5S or the 6S model. An example is given in Table 1.1, which shows part of the output generated by the 5S model. The spherical albedo S and

Table 1.1 Results from the 5S model used for atmospheric correction

	Downward	Upward	Total
Global gas transmission	0.961	0.965	0.932=Tg(θs, θv)
Water transmission	0.988	0.989	0.980
Ozone transmission	0.975	0.978	0.954
CO2 transmission	1.000	1.000	1.000
O2 transmission	0.999	0.999	0.998
NO2 transmission	1.000	1.000	1.000
CH4 transmission	1.000	1.000	1.000
CO transmission	1.000	1.000	1.000
Rayleigh scattering transmission	0.967	0.971	0.939
Aerosol scattering transmission	0.953	0.962	0.917
Total scattering transmission	0.922	0.934	0.861=T(θs)T(θv)
	Rayleigh	Aerosols	Total
Spherical albedo	0.048	0.087	0.123=S
Optical depth total	0.054	0.362	0.416
Optical depth plane	0.054	0.362	0.416
Atmospheric reflectance	0.019	0.017	0.037
			ρa(θs,θv,φ)
Phase function	0.993	0.099	0.215
Single scattering albedo	1.000	0.990	0.992

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