Correction for atmospheric scattering and solar elevation

We have already noted that about 90% of the upward radiance measured by a photometer in a satellite, or in a very high altitude (~20 km) aircraft, above the ocean originates by scattering of the solar beam by air molecules and by aerosol particles (dust, water droplets, salt etc.) within the atmosphere - this is known as the path radiance. To arrive at a value of the water-leaving radiance, Lw(d,f), from the measured radiance, the path radiance must be removed, and furthermore the attenuation of the emergent flux during its passage through the turbid atmosphere to the sensor must be allowed for.

Since it is the ratio of the emergent flux to the incident downward flux, rather than the absolute value of emergent flux alone, which is directly related to the optical properties of the aquatic medium, it is desirable to have an estimate of the downward irradiance at the surface of the water: this will be determined by solar elevation and by attenuation of the solar beam through the atmosphere, and so both of these will have to be taken into account.

As we have seen, there are several spaceborne ocean colour scanners now aloft, in addition to various airborne scanners. The detailed procedure for atmospheric correction is not only somewhat technical, but varies from one scanner to another. Here we shall confine our attention to the underlying principles, and to illustrate these we shall use the procedure developed by Gordon and Wang (1994), for SeaWiFS.

The total radiance, Lt(1), measured at wavelength 1 by the sensor at the top of the atmosphere is the sum of a series of different radiance values originating in various different physical processes, in accordance with


• Lr(1) is the radiance due to multiple Rayleigh scattering by air molecules in the absence of aerosols

• La(1) is the radiance due to multiple scattering by aerosols in the absence of air

• Lra(1) is the radiance generated by multiple scattering of photons between the aerosol particles and air molecules306

• Lg(1) is the radiance due to sunglint, i.e. photons that have undergone specular reflection from the direct solar beam at the wind-roughened ocean surface

• tLw is the water-leaving radiance attenuated by the atmospheric transmittance factor t during its passage from the surface to the satellite.

The atmospheric transmission factor is for diffuse rather than direct transmittance because when the sensor is viewing a given element of area, some of the flux is coming from neighbouring elements, and is given approximately by t(0v, 1) = exp

cos 6v

where tr(1) is the optical thickness due to Rayleigh (molecular) scattering, tOz(1) is the optical thickness of the ozone layer and 0v is the zenith angle of the line between the sensor and any given pixel.

Since it is ultimately the reflectance of the ocean, in the form of Rrs or rrs, rather than the absolute value of water-leaving radiance, which contains information about water composition it is now normal practice to -express the above relationships entirely in terms of reflectance, p. This is defined as

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