1.12 Radiative Transfer Equation

Radiative transfer is defined as the process of transmission of the electro-magnetic radiation through the atmosphere, and the influence of the atmosphere. The atmospheric effect is classified into multiplicative effects and additive effects as shown in Table 1.12.1.

The multiplicative effect comes from the extinction by which incident energy from the earth to a sensor will reduce due to the influence of absorption and scattering. The additive effect comes from the emission produced by thermal radiation from the atmosphere and atmospheric scattering, which is incident energy on a sensor from sources other than the object being measured.

Figure 1.12.1 shows a schematic model for the absorption of the electro-magnetic radiation between an object and a sensor, while Figure 1.12.2 shows a schematic model for the extinction. Absorption will occur at specific wavelengths (see 1.11) when the electro- magnetic energy converts to thermal energy. On the other hand, scattering is remarkable in the shorter wavelength region when energy conversion does not occur but only the direction of the path changes.

As shown in Figures 1.12.3 and 1.12.4, additional energy by emission and scattering of the atmosphere is incident upon a sensor. The thermal radiation of the atmosphere which is characterized by Plank's law (see 1.7), is uniform in all directions. The emission and scattering of the atmosphere incident on the sensor, is indirectly input from other energy sources of scattering than those on the path between a sensor and an object.

The scattering depends on the size of particles and the direction of incident light and scattering.

Thermal radiation is dominant in the thermal infrared region, while scattering is dominant in the shorter wavelength region.

Generally, as extinction and emission occur at the same time,both effects should be considered together in the radiative transfer equation as indicated in the formula in Table 1.12.2.


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