GGR 315 Environmental Remote Sensing, 2024
Assignment 4: Radiometric Correction and Remote Sensing Applications
Questions
(100 marks, 10% of the final grade)
1. (15 marks) In ArcGIS, using the customized minimum/maximum linear stretch to enhance the image Toronto_2011. tiff. Provide images before (5 marks) and after (5 marks) customized linear stretch (you can take screenshots). Discuss your understanding of the linear stretch in displaying the surface features (5 marks).
2. (50 marks, 10 for each) Conversion from DN to reflectance.
The reflectance of ground objects at the surface level, ρ, can be derived using the following equation:
where E is solar irradiance on the object and is expressed as E0*cosθs, where θs is the solar zenith angle at the time of image acquisition; T is the transmissivity of the atmosphere; Lp is the path radiance (radiance due to atmosphere); Ltot is the radiance measured by a sensor. Ltot can be converted from the DN (digital number) of each band of a TM image using the equation:
L = A0 + A1*DN. (2)
tot
Image Toronto_2011_band3.tiff and Toronto_2011_band4.tiff have the DN values of bands 3 and 4 of a TM image. Given A0, A1, T, Lp and E are constants for the whole image (see the following table), please convert the DN values of bands 3 and 4 into reflectance using the Raster Calculator in ArcGIS.
|
Band
|
A0
|
A1
|
T
|
E0
(W/(m2.μm))
|
Lp
(W/(m2.μm. sr))
|
θs
(degree)
|
|
3
|
-4.5
|
0.639608
|
0.78
|
1060.0
|
2.0
|
41.4
|
|
4
|
-4.5
|
0.635294
|
0.80
|
714.0
|
1.5
|
41.4
|
This is a process that involves several steps. Please finish these steps one by one. Check your results at each of these steps.
1) Write down the decomposed equations and the final equations for converting DN to reflectance for band 3 and band 4.
Hint: It can be decomposed into 5 steps. In sequence, it includes the calculation of Ltot, atmospheric corrected Ltot, reflected irradiance, solar irradiance on the surface, and reflectance.
2) Reflected irradiance (the numerator in Equation 1) must be positive. Therefore, a conditional statement in the Raster Calculator is required. Please write down the statements / commands (for band 3 and band 4 respectively) used in the Raster Calculator in ArcGIS Pro.
3) Find out the reflectance values for the following 4 pixels (column, row) for band 3 and band 4.
(1931, 827), (931,3821), (3669, 5840), (5196, 3248)
4) What is the value for the incoming radiation for band 3 at each of the pixels?
5) Provide an image of reflectance in band 4 (you can take a screenshot).
3. (15 marks) Explain the physical principles of the histogram adjustment method for atmospheric correction (10 marks) and assess the limitations of the method (5 marks).
4. (10 marks) What is radiometric correction? Why is radiometric correction needed?
5. (10 marks) Resampling is one of procedures in geometric corrections. In the following drawing, the open circles (o) are the pixel centers in the original image, and closed circles (•) represent the pixel centers in a new image to be created after resampling. The digital number of each pixel in the original image is given by the side of each open circle. Calculate the value for the largest closed circle after bilinear interpolation. Note that the locations of all circles should be assumed to be exactly at the closest cross points of the grid.