Multi-Sensor Radiometric Correction: A Case Study from Malaysia
Atmospheric correction
The basic philosophy of atmospheric correction is to obtain information about the atmospheric optical characteristics and to apply this information in a correction scheme (Kaufman, 1989). It is a process of surface reflectance retrieval,
rs,
from the corresponding reflectance at the top of atmosphere, or simply apparent reflectance,
r*. The relationship between the radiance, L, of spectral band
li , and the apparent reflectance can be expressed using equation (3):
| r* (li) = |
L(li)
------------
Ex.d.Cos(q) |
(3) |
Where Es is the exo-atmospheric solar irradiance at the top of the atmosphere
(Wm
-2 sr
-1mm
-1), d is the distance multiplicative factor (unit less) and q is the solar zenith angle (degree). Subsequently, the relationship between apparent reflectance and surface in the present of atmospheric constituents can be expressed as follows:
Where
ra is atmospheric reflectance,
DÆ is the relative azimuth between sun and satellite direction, S is the atmospheric spherical albedo, T(li.qs) and T(li.qv) are the scattering transmittance in the solar and sensor direction respectively and T g(li.qs.qv) is the gaseous absorbing transmittance. A detailed description of this relationship can be found in Tanre et al. (1990).
This study employs a combination of the method proposed by Moran et al. (1992) and Kaufman and Sendra (1998), i.e. using the 6S radiative transfer code and tropical forest cover as the controlled dark dense vegetation (DDV) to derive the aerosol optical thickness and to correct for atmospheric effects on remotely sensed images. The reflectance of tropical forest is in the range of 1-2% in the blue
(0.4-0.5
mm) and red (0.6-0.7
mm) region, and 2-3% in the green
(0.5-0.6
mm) region (Kaufman, 1989). The 6S radiative transfer model was first used to determine the atmospheric optical characteristics at the time of each satellite overpass. The tropical atmospheric model and maritime aerosol model were used to represent the atmospheric condition at the time of satellite overpass. These models are representative of atmospheric conditions in the Malaysia environment (Mispan, 1996). Given the atmospheric optical characteristics of each spectral band, the inverse of the 6S model was used to retrieve the surface reflectance of the DDV. The inversion equations are as follows:
| A1 = |
1
--------------------
Tg(qs, qv)T(qs)( qv) |
(5) |
| B1= - |
ra(qs, qv,Æ)
----------------
T(qs,)( qv) |
(6) |
| Y = A1 r*+ B1 |
(7) |
| rs= |
y
-------------
(1+SY) |
(8) |
where A
1 is the multiplicative coefficient, B
1 is the additive coefficients and Y is the atmospheric correction factor.
Sensor inter-calibration
The different between the central wavelengths and viewing angle of SPOT-HRV and Landsat-5 TM spectral bands are large enough to introduce a supplementary variability in the spectral response of a given target and need to be adjusted. This study adopts a method proposed by Muller (1993) to reduce these effects. Invariant objects available on these two data sets were used to derived correction coefficients. Sample points from each pseudo-invariant object were extracted from atmospherically corrected Landsat and SPOT images, and for each sample the mean and standard deviation were computed. The relationship between off-nadir of SPOT-HVR and Landsat-TM data is as follows:
NSPOT(i,j)= A0 + A1 SPOT(i,j) (9)
Where
A1=s1/s (10)
A0=x0-x.s0/s (11)
X
0 and
s0 are the mean values and the standard deviation of pseudo-invariant objects in the reference image (Landsat TM data) and
x and
s are the mean value and standard deviation of the pseudo-invariant objects in the image to be corrected (SPOT_HRV data).
