102.

[Cover] [Contents] [Index]

Page 19

value to radiance, is sensor-dependent. For instance, in the case of Landsat TM images, the relationship between the pixel values and apparent radiance Lapp is expressed as:

(1.13)

while in case of SPOT HRV data the relationship is:

(1.14)

where Ai and Bi are the calibration gain and offset for band i, respectively. These calibration coefficients can be found either from the literature (e.g. Price, 1988; Olsson, 1995; Gellman et al., 1993; Teillet and Fedosejevs, 1995) or from image header files. Note that header files may contain prelaunch calibrations that may differ significantly from the actual calibrations due to sensor degradation over time. Teillet and Fedosejevs (1995) provide time-varying coefficients for the TM instrument that are calculated as a function of the number of days since the launch of the Landsat-5 satellite.

The second step, conversion from apparent radiance Lapp to apparent reflectance ρ*, is based on the observation that, in case of 100% reflectance, the radiance measured by the sensor is the result of multiplication of equivalent solar radiance (E/π), the cosine of solar zenith angle (cos(θs)), and the Earth-Sun distance multiplicative factor d (Kowalik and Marsh, 1982). The factor d is measured in astronomical units (au) and is described further below. One au is equal to the average Earth to Sun distance. About January 3, at perihelion, the Earth-Sun distance is approximately 0.983 au, and on July 5, at aphelion, the Earth-Sun distance is about 1.0167 au.

If the required coefficients are known, then the variation in sensor-detected apparent radiance Lapp is caused by the difference in reflectance. One then obtains the following relation:

 

or, equivalently,

(1.15)

The value of the solar zenith angle can be retrieved from the image header file. Markham and Barker (1987) and Price (1988) provide tables listing values of solar irradiance E. The distance multiplicative factor d is used to compensate for the variation in solar irradiance E caused by the change in distance between the Sun and the Earth. It is obtained from:

[Cover] [Contents] [Index]


Classification Methods for Remotely Sensed Data
Classification Methods for Remotely Sensed Data, Second Edition
ISBN: 1420090720
EAN: 2147483647
Year: 2001
Pages: 354

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