This document discusses remote sensing applications and seminar. It summarizes key concepts in remote sensing including radiometric resolution, reflectance, calculating surface temperature using Planck's law, and spectral reflectance and absorptance. It also describes a study applying linear spectral unmixing to percentage tree cover mapping using MODIS data, selecting bands for unmixing based on vegetation skewness, and analyzing results to map percent tree cover.

1. REMOTE SENSING
Thursday, 23 November 2017
Presenter:
J.Mwaura
ENC324-2981/2016
RS APPLICATIONS & SEMINAR

2. Black-0
White-255
Pixel
Grey values
DNs

3. • Radiometric resolution
–Sensor’s ability discriminate small differences in
the magnitude of radiation within the ground
area that corresponds to a
–The greater the bit depth (number of data bits
per pixel) of the images that a sensor records,
the

4. Sky
irradiance 𝐼𝑠
Sky
radiance 𝑅 𝑠
Path
radiance 𝑅 𝑝
T.O.A (𝐸 𝑜)
Pixel
irradiance
𝐼 𝑝
Radiant flux (𝜑)
From sun (𝑤𝑎𝑡𝑡𝑠)
Sensor
( 𝐸 𝑚
′
= 𝐸 𝑚 × 𝐺𝑎𝑖𝑛 +
(2) Surface element of reflectance (𝜌)
Incident
irradiance (𝐸𝑖)
Measured Radiance 𝐸 𝑚 = 𝑡(𝐸 𝑝 + 𝐼𝑠 + 𝐼 𝑝 + 𝑅 𝑝 + 𝑅 𝑠)
Outgoing
radiance(𝐸 𝑝)
Atmosphere

5. • Used to identify materials on earth surface
• …
• 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑎𝑛𝑐𝑒 = 𝜌 =
𝐿
𝐸
=
𝑟𝑎𝑑𝑖𝑎𝑛𝑐𝑒
𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑛𝑐𝑒

6. • Convert D𝑁′
𝑠 to radiance using radiometric
calibration.
• Estimate incident irradiance (𝐸𝑖)

7. • Sun-elevation correction: 𝐸𝑖 = 𝐸 𝑇 ∗ 𝐶𝑜𝑠 𝜃
• 𝐸 𝑇 = 𝑖𝑟𝑟𝑎𝑑𝑖𝑎𝑛𝑐𝑒 𝑖𝑓 sun vertical at mean
Earth−Sun distance (𝑊/𝑚2)
• 𝐸𝑖 = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 (𝑊/𝑚2
)
• 𝜃 = 𝑠𝑜𝑙𝑎𝑟 𝑎𝑛𝑔𝑙𝑒 𝑓𝑟𝑜𝑚 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙
• (90 − 𝑠𝑜𝑙𝑎𝑟 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑔𝑙𝑒)

8. • Earth-Sun distance correction: 𝐸𝑖 = 𝐸 𝑇/𝑑2
• 𝑑 = 𝑒𝑎𝑟𝑡ℎ − 𝑠𝑢𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
»(𝑖𝑛 𝑎𝑠𝑡𝑟𝑜𝑛𝑜𝑚𝑖𝑐𝑎𝑙 𝑢𝑛𝑖𝑡𝑠)

9. • Compute reflectance of a surface from image?
1. Outgoing radiance 𝐸 𝑝 = 𝐸 𝑚 − 𝑅 𝑝
2. Convert DN to radiance at sensor
𝐸 𝑜𝑢𝑡𝑝𝑢𝑡 = 𝐺 ∗ 𝐸𝑖𝑛𝑝𝑢𝑡 − 𝐵
𝐷𝑁 =
(𝐸 𝑜𝑢𝑡𝑝𝑢𝑡 + 𝐵)
𝐺
3. Estimate incident irradiance on the surface
𝐸𝑖 = 𝐸 𝑇 ∗ 𝐶𝑜𝑠 𝜃/𝑑2
4. Reflectance 𝜌 =
𝐸 𝑝
𝐸 𝑖

10. • Calculating Temperature using Planck's Black Body
Radiation Law
𝑇 =
𝑘2
ln
𝑘1
𝑅
+ 1
• Calculating Surface Temperature
𝑇𝑠 =
𝑇
1 + λ ∗
𝐵𝑇
𝜌
∗ log 𝜀
– 𝑇𝑏 = 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒, 𝜀 = 𝑙𝑎𝑛𝑑 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑒𝑚𝑖𝑠𝑠𝑖𝑣𝑖𝑡𝑦
– λ = 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ, 𝑘 = 𝑐𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑅 = 𝑟𝑎𝑑𝑖𝑎𝑛𝑐𝑒,
𝜌 = ℎ 𝑝𝑙𝑎𝑛𝑐𝑘′ 𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑐
𝜎 𝑏𝑜𝑙𝑡𝑧𝑚𝑎𝑛𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

11. • 𝐸 𝑝 𝜆 = 𝐸𝑖(𝜆) − 𝐸𝐴(𝜆) + 𝐸 𝑇(𝜆)
– 𝐸𝑖 = Incident energy
– 𝐸 𝑝 = 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦
– 𝐸𝐴 = 𝐴𝑏𝑠𝑜𝑟𝑏𝑒𝑑
– 𝐸 𝑇 = 𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦
• 𝜌(𝜆) =
𝐸 𝑝(𝜆)
𝐸 𝑖(𝜆)
× 100
– 𝜌 𝜆 = 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡
– 𝐴𝑏𝑠𝑜𝑟𝑝𝑡𝑎𝑛𝑐𝑒 = 𝐸 𝑎
𝐸 𝑖
× 100
– 𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑎𝑛𝑐𝑒 = 𝐸𝑡
𝐸 𝑖
× 100

12. • Brightness values for 8-bit system 0-255:
• 𝐷𝑁𝑠𝑡 = 255 × (𝐷𝑁 𝑖𝑛−𝐷𝑁 𝑚𝑖𝑛)
(𝐷𝑁 𝑚𝑎𝑥−𝐷𝑁 𝑚𝑖𝑛)
• 𝐷𝑁𝑠𝑡 = 255 𝑗=0
𝑘
(
𝑛 𝑗
𝑁
)
• 𝐷𝑁𝑠𝑡 = 𝑒𝑛ℎ𝑎𝑛𝑐𝑒𝑑 𝐷𝑁 𝑣𝑎𝑙𝑢𝑒
• 𝑛𝑗 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑖𝑥𝑒𝑙𝑠 ℎ𝑎𝑣𝑖𝑛𝑔 𝐷𝑁 𝑣𝑎𝑙𝑢𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒
𝑗 𝑡ℎ 𝑟𝑎𝑛𝑔𝑒, 𝑖𝑛 𝑡ℎ𝑒 𝑖𝑛𝑝𝑢𝑡 𝑖𝑚𝑎𝑔𝑒
• 𝑘 = 𝑚𝑎𝑥. 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐷𝑁 𝑟𝑎𝑛𝑔𝑒𝑠 𝑖𝑛 𝑖𝑛𝑝𝑢𝑡 𝑖𝑚𝑎𝑔𝑒
• 𝑁 = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑖𝑥𝑒𝑙𝑠 𝑖𝑛 𝑖𝑛𝑝𝑢𝑡 𝑖𝑚𝑎𝑔𝑒

13. Thanks…
>> Part 2

14. Applicability of the Mix–Unmix Classifier in
percentage tree and soil cover mapping
Thursday, 23 November 2017
Author:
T. NGIGI et.al
RS APPLICATIONS & SEMINAR

15. Problem
• The under-determination in linear spectral
unmixing

16. Percentage tree
cover mapping
• Data
–composite MODIS data {bands 1–7}
–excluded band 5
• stripping
–resampled {bands 1,2,3,4 & 6,7} from 500
m to 1 km.
• reduce the volume

17. Selection of band to
unmix
}
MODIS first 7
bands: 500m
MODIS 6 bands:
1km
Skewness
image
Scatter plot
Interactive on-screen
comparison
Vegetation skewness
image
1. Most pure
equatorial
rainforest
skewness
2. Most impure
equatorial
rainforest
skewness range
Skewness
image
Mix-unmix
classification
% tree
mapping
Omit band 5
& resample
Transformations:
PCs, MNFs,
NDVI, Compute
Parameters

18. Analysis
• The redder the skewness
image, the denser the
equatorial forest
• DN ranges of 1–10:
– Most impure forest
• DN ranges of 80–131:
– Most pure forest
• All DNs in range 1–131 in
skewness image were
unmixed, as above classes
by the Mix–Unmix
Classifier

19. That’s it
Thanks…