125.

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relevant parameters for deriving A and B are displayed in bold type. For a detailed description of 5S and 6S usage, the reader is referred to Tanré et al. (1986, 1990). Once ground reflectance is retrieved, one may use Equation (1.15) to retrieve radiance followed by using either Equation (1.13) or Equation (1.14) to convert the radiance back to a corrected pixel value.

1.4 Correction for topographic effects

Normally, the surface being measured by the remote sensor is assumed to be flat with a Lambertian reflectance behaviour. Under this assumption, the magnitude of the radiance detected by the sensor is affected only by variations in the solar zenith angle, the wavelength, and the atmospheric interaction. The atmospheric correction model introduced in Section 1.3 is also based on such ideal assumptions, which may be invalid in the case of rugged terrain because the solar incidence angle will vary with topographic variation and will further contribute to differences in the level of radiance detected by the sensor. This is known as topographic effect. More specifically, the topographic effect can be defined as the variation in radiance exhibited by inclined surfaces compared with radiance from a horizontal surface as a function of orientation of the surface relative to the radiation source. Moreover, if we assume non-Lambertian reflectance for the surface being measured, the sensor position is another important variable that should be considered.

Calibration for topographic effects is intended to normalise the sensor-detected signal difference caused by the topographic variation. Various techniques (e.g. Smith et al., 1980; Kawata et al., 1988; Civco, 1989; Colby, 1991) have been published. Here, we present two approaches, using band ratioing and the Minnaert model presented by Smith et al. (1980).

Band ratioing (Jensen, 1986; Colby, 1991; Mather, 1999a) is the most commonly used method for reducing the topographic effect. Colby (1991) uses a Landsat TM band 5/4 ratio image to study the effectiveness of topographic effect calibration by comparing several sample sites having the same vegetation cover, but with differences in topography. In other words, the same vegetation cover should have a similar spectral response, irrespective of location, thus the differences between sample sites are assumed to be caused by topographic effects. Results showed that the variance of spectral response between sample sites in ratio image was lower than that obtained from original TM band 4 and 5 images. Colby (1991) concludes that band ratioing does partially compensate for topographic effects.

Smith et al. (1980) present two empirical photometric functions for studying the effect of topography on the radiance field. The first such function is based on a Lambertian reflectance assumption, while the second function assumes that reflectance is non-Lambertian. Although this is a

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