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order to ensure that pixel values are comparable from one image to the next. A more radical view is taken by Smith and Milton (1999), who emphasise that ‘…to collect remotely sensed data of lasting quantitative value then data must be calibrated to physical units such as reflectance’.

The value recorded for each pixel in a remotely sensed image is a function of the sensor-detected radiance. Owing to the atmospheric interaction, this apparent radiance is the combination of the contribution of the target object and the atmospheric effect. Their relationship can be approximated as:

(1.2)

Here, L_app denotes the apparent radiance received by the sensor, L_p is the path radiance, ρ is the target reflectance (%), T is the atmospheric transmittance (%), and E is the incident solar irradiance. Radiance is expressed in units of Wm⁻² sr⁻¹ μm⁻¹, and irradiance is expressed in the units of Wm⁻² μm⁻¹. As these two terms are not expressed in equivalent units, solar irradiance is converted into equivalent solar radiance by introducing the term π into the denominator. This conversion is based on the assumption that the target behaves as a Lambertian reflector (as described in Figure 1.4) (Mackay et al., 1994).

In Equation (1.2), only the first term ρ contains information about the target. The atmosphere contributes the second term, the path radiance L_p, which varies inversely in magnitude with wavelength. In the case of multispectral images, the magnitude of the L_p term in the visible bands will be higher than that in the near- or mid-IR bands.

1.3.1 Dark object subtraction

Two kinds of methods are used for atmospheric effect correction. The first kind consist of the dark object subtraction techniques (Chavez, 1988), which involve subtraction of a constant value (offset) from all pixels in a given spectral band. These methods are based on the assumption that some pixels in the image should have a reflectance of zero, and that the values recorded for these ‘zero’ pixels result from atmospheric scattering. Thus, these pixel values represent the effects of atmospheric scattering. For example, the reflectance of deep clear water in the near-IR waveband is near zero. Dark object subtraction methods assume that non-zero pixel values over deep, clear, water areas in the near-IR band are contributed by the path radiance L_p, and that the path radiance is spatially constant (meaning that a single value of path radiance is subtracted from all pixel values in the image). In the case of the visible bands, one may use shadow areas due to topography as dark objects. In effect, one is using the histo

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