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Poster Session Q
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Atmospheric and topographic correction of multitemporal Landsat TM imagery
The correction procedures
Conceptually, the reflectance images can be obtained through three sequential linear transformations.
- A Transformation From Digital Numbers (DN) To observed Spectral Radiance Values (Lobs)
This is accomplished by using published radiance calibration constants (Barker 1987), which is usually termed absolute calibration. Spectral radiance and irradiance were used in the study instead of in-band units throughout the computation procedures to facilitate comparison between sensor (Price 1987).
The Lobs can be obtained by
Lobs = DN* (Lmax - Lmin) / 255 +Lmin ----------------(1)
Lmax - Lmin are constants representing the radiance at DN= 0 and DN=255, respectively. These constants may vary with date, ground receiving and processing station. Before this tranformation, a relative compensation calobration between etectors were performed for most scenes.
- A Transformation From Radiance Lobs to Spectral Reflectance R
It is complicated and critical. The assumption of a Lambertian scattering behaviour for most targets would simplify the view angle effect as only differential atmospheric effect. Therefore, the correction of main interest is atmospheric and topographic corrections, illumination and view angle corrections, in addition to sensor calibration. The radiance observed by a sensor in a given band can be expressed as
Lobs = 1 / p (Eo cosi Exp(-t/cosqo) +gEd)R Exp(-t/cosqv ) +Lp --(2)
or in a simplified form
Lobs = 1/ p R Eg Tv +Lp
and the transformed reflectance R for a target can be expressed as
R= p (Lobs- Lp ) / Eg Tv) ..............(3)
The meanings of various factors are defined as follows:
Lobs = radiance observed at the sensor (mWcm-2 Sr-1)
1 / p = The bidirectional reflectance distribution function (BRDF) for a Lambertian surface
Eo= solar irradiance at the top of the atmosphere (m Wcm-2),
Eo was calibrated with published solar exoatmospheric spectral irradiances in TM bands
Eo was calibrated with published solar exoatmospheric spectral irradiances in TM bands
i= solar incidence angle with respect to surface normal
t= atmospheric extinction coefficient (optical thickness)
qo, qv = solar zenith angle and observation zenith angle
g = a geometric factor taking into account of the part of sky radiance not contributing in the illumination of inclined terrain , g= 0.5+0.5coss, s=terrain slope angle
Ed = diffuse sky irradiance on a horizontal surface (m Wcm-2) Ed is modified by atmosphere and topography.
Eg= (Eo cosi Tq+g Ed) = global irradiance on the surface (m Wcm-2)
Tq = exp(-t/cosqo) = atmospheric downward transmittance
Tv = Exp (-t/ cosqv) = atmospheric up eard transmittance
Lp = path radiance from multiple scattering (m Wcm-2 sr-1 )
This reflectance tranformation involves the approximation of some varibles by using different methods according to parameters available . Combining equation (1) and (3) we obtain
R= p / (Eg Tv) *(DN(Lmax - Lmin) / 255 +Lmin -Lp) -----(3a)
- A Transformation of R to an Eight-bit Digital Number (DN')
It may be a linear or non-linear transformation, incorporating appropriate contrast stretch between predefined minimum and maximum reflectance limits Rmax - and Rmin
DN' = 255 F[(R-Rmin) / (Rmax - Rmin)] ................(4)
The linear transformation is convenient if the enhanced reflectance images are to undergo further processing, but for the hard copy products, a non-linear transformation can be applied to TM bands. The square root function increases the contrast of low reflectance portion, and compress the contrast of high reflectance portion (Ahern 1989).
Although each step involves much consideration and techniques, the second step requires more investigation and exploration. The actual scattering properties of natural surfaces differ from the Lambertian assumption to varying extent (Teillet et al. 1982) The diffuse approximation is more likely to be valid for terrain slopes of less than 25 degrees and effective illumination angles of less than 45 degrees (Smith et al. 1980) or further less (Cavayas 1987). In our study, the solar zenith angle exceeded these limits, which may cause a system error of the reflectance values. Since we have no sufficient knowledge about the BRDF for natural targets, such assumption is the only convenient solution at present, espescially for forest canopy complexities which are considered to be Lambertian surface in small solar zenith angle.
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