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REMOTE SENSING
Thursday, 29 November 2017
J.Mwaura
RS APPLICATIONS & SEMINAR
Linear Contrast Stretching
0-255 in an 8-bit system
β€’ 𝐷𝑁𝑠𝑑 = 255 Γ— (𝐷𝑁 π‘–π‘›βˆ’π·π‘ π‘šπ‘–π‘›)
(𝐷𝑁 π‘šπ‘Žπ‘₯βˆ’π·π‘ π‘šπ‘–π‘›)
DN values range from 60-158
β€’ 0-59 and 159-255 are not utilized
Histogram-equalized
Stretching
β€’ Lets stretch values in the range [75-150]
– 𝐷𝑁𝑠𝑑 = 255 𝑗=0
π‘˜
(
𝑛 𝑗
𝑁
)
β€’ 𝐷𝑁𝑠𝑑 = π‘’π‘›β„Žπ‘Žπ‘›π‘π‘’π‘‘ 𝐷𝑁 π‘£π‘Žπ‘™π‘’π‘’
β€’ 𝑛𝑗 = π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝑝𝑖π‘₯𝑒𝑙𝑠 β„Žπ‘Žπ‘£π‘–π‘›π‘” 𝐷𝑁 π‘£π‘Žπ‘™π‘’π‘’ 𝑖𝑛 π‘‘β„Žπ‘’
𝑗 π‘‘β„Ž π‘Ÿπ‘Žπ‘›π‘”π‘’, 𝑖𝑛 π‘‘β„Žπ‘’ 𝑖𝑛𝑝𝑒𝑑 π‘–π‘šπ‘Žπ‘”π‘’
β€’ π‘˜ = π‘šπ‘Žπ‘₯. π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝐷𝑁 π‘Ÿπ‘Žπ‘›π‘”π‘’ 𝑖𝑛 𝑖𝑛𝑝𝑒𝑑 π‘–π‘šπ‘Žπ‘”π‘’
β€’ 𝑁 = 𝑻𝒐𝒕𝒂𝒍 π’π’–π’Žπ’ƒπ’†π’“ π‘œπ‘“ 𝑝𝑖π‘₯𝑒𝑙𝑠 𝑖𝑛 𝑖𝑛𝑝𝑒𝑑 π‘–π‘šπ‘Žπ‘”π‘’
Calculate Slope for
Band and Radiance
Metadata:
β€’ LMAX_BAND6 = 15.303
β€’ LMIN_BAND6 = 1.238
β€’ π‘†π‘™π‘œπ‘π‘’ =
(π‘™π‘šπ‘Žπ‘₯βˆ’π‘™π‘šπ‘–π‘›)
π‘šπ‘Žπ‘₯
β€’ π‘†π‘™π‘œπ‘π‘’ 𝐡6 =
15.303βˆ’1.238
255
β€’ = 0.0551
β€’ π‘…π‘Žπ‘‘π‘–π‘Žπ‘›π‘π‘’ = π‘ π‘™π‘œπ‘π‘’ Γ— 𝐷𝑁 + π‘™π‘šπ‘–π‘›
β€’ 𝑅 𝐡6 = 0.0551 Γ— 𝐷𝑁 𝐡6 βˆ’ 1.238
Β»e.g. DN = 69
β€’ 0.0551 Γ— 69 βˆ’ 1.238 = 2.5639
Calculate Temperature
(at-sensor/TOA)
β€’ Using Planck's Black Body Radiation Law
–𝑇 =
π‘˜2
ln
π‘˜1
𝑅
+1
,
οΆπ‘˜ = π‘π‘Žπ‘™π‘–π‘π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘,
𝑅 = π‘Ÿπ‘Žπ‘‘π‘–π‘Žπ‘›π‘π‘’ π‘“π‘œπ‘Ÿ π‘π‘Žπ‘›π‘‘ = 2.5639
Β»π‘˜1 = 666.09
Β»π‘˜2 = 1282.71
β€’ 𝑇𝐡6 =
1282.71
ln
666.09
2.5639
+1
= 195.54
β€’ Calculating Surface Temperature
𝑇𝑠 =
𝑇𝐡
1 + Ξ» βˆ—
𝑇𝐡
𝜌
βˆ— log πœ€
– 𝑇𝐡 = π‘‘π‘’π‘šπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘Ÿπ‘’, πœ€ = π‘™π‘Žπ‘›π‘‘ π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ π‘’π‘šπ‘–π‘ π‘ π‘–π‘£π‘–π‘‘π‘¦
– Ξ» = π‘€π‘Žπ‘£π‘’π‘™π‘’π‘›π‘”π‘‘β„Ž, 𝜌 = β„Ž π‘π‘™π‘Žπ‘›π‘π‘˜β€² 𝑠 π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ Γ— 𝑐
𝜎 π‘π‘œπ‘™π‘‘π‘§π‘šπ‘Žπ‘›π‘› π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘
β€’ LSE (Ξ΅) can be extracted by using NDVI considering
three different cases
β€’ Bare soil
β€’ Vegetation
β€’ Mixture of bare soil and vegetation
Land Surface
Emissity (LSE)
β€’ For Band 6 of Landsat TM
β€’ πœ€ = 0.004 Γ— 𝑝𝑣 + 0.986
β€’ 𝑝𝑣 is the proportion of vegetation which is
given by
β€’ 𝑝𝑣 = {
π‘π·π‘‰πΌβˆ’π‘π·π‘‰πΌ π‘šπ‘–π‘›
(𝑁𝐷𝑉𝐼 π‘šπ‘Žπ‘₯βˆ’π‘π·π‘‰πΌ π‘šπ‘–π‘›)
}2
Land Surface
Temperature (LST)
β€’ Parameters
»𝑇𝐡6 = 195.54
»𝜌 = 14380
Β»πœ€ = 1.2345
Β»πœ† = 11.5 Β΅m
– 𝑇𝑠 =
195.54
1+ 11.5Γ—
195.54
14380
Γ—log 1.2345
= 192.780
𝑐
Energy Interactions
Irradiance at-TOA?(1)
βˆ’6.70
𝐸 𝑅 = 𝐸 𝑇 Γ— cos ∝
𝑇. πΆπ‘Žπ‘›π‘π‘’π‘Ÿ
πΈπ‘„π‘ˆπ΄π‘‡π‘‚π‘…
𝑇. πΆπ‘Žπ‘π‘Ÿπ‘–π‘π‘œπ‘›
𝑑 = 0.996
π‘†π‘Žπ‘‘π‘’π‘™π‘™π‘–π‘‘π‘’
𝐸 𝑇 =
𝐸𝑑
𝑑2
βˆ’23.30
?
Irradiance at-TOA?(2)
Sky
irradiance
(𝐼𝑠 = 12𝑒𝑛𝑖𝑑𝑠)
Path radiance
(𝑅 𝑝 = 2𝑒𝑛𝑖𝑑𝑠)
Pixel
irradiance
𝐼 𝑝 = 6𝑒𝑛𝑖𝑑𝑠
Sensor
πΊπ‘Žπ‘–π‘› = 0.89,
π‘‘π‘Žπ‘Ÿπ‘˜ π‘π‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘ = βˆ’19
reflectance (𝜌 = 0.62)
Incident
irradiance (𝐸𝑖)
𝐓. 𝐎. 𝐀
Atmosphere
(t = 0.79)
Sky radiance
(𝑅 𝑠 = 14𝑒𝑛𝑖𝑑𝑠)
@𝐬𝐞𝐧𝐬𝐨𝐫
@𝐩𝐒𝐱𝐞π₯
Irradiance at-TOA?(3)
1. 𝐸𝑑 =
258+19
0.89
= 311.24 𝑒𝑛𝑖𝑑𝑠
2. πΈπ‘Ÿ = 311.24 Γ— cos(6.7) = 309.11 𝑒𝑛𝑖𝑑𝑠
 at Sensor Radiance
3. At pixel:
β€’ 𝐼𝑠 = 0.79 Γ— 12 = 9.48𝑒𝑛𝑖𝑑𝑠
β€’ 𝐼 𝑝 = 0.79 Γ— 6 = 4.74 𝑒𝑛𝑖𝑑𝑠
Irradiance at-TOA?(4)
4. Reflected at pixel:
β€’ 𝐼𝑠 = 0.62 Γ— 9.84 = 5.88𝑒𝑛𝑖𝑑𝑠
β€’ 𝐼𝑠 = 0.62 Γ— 4.74 = 2.94𝑒𝑛𝑖𝑑𝑠
5. At TOA (@sensor):
β€’ 𝐼𝑠 = 0.79 Γ— 5.88 = 4.65𝑒𝑛𝑖𝑑𝑠
β€’ 𝐼 𝑝 = 0.79 Γ— 2.94 = 2.32𝑒𝑛𝑖𝑑𝑠
β€’ 𝑅 𝑝 = 0.79 Γ— 2 = 1.58𝑒𝑛𝑖𝑑𝑠
β€’ 𝑅 𝑠 = 0.79 Γ— 14 = 11.06𝑒𝑛𝑖𝑑𝑠
6. Total = 19.61𝑒𝑛𝑖𝑑𝑠
Irradiance at-TOA?(5)
7. Reflected at pixel:
β€’ 0.79 πΈπ‘Ÿ + 19.61 = 309.11𝑒𝑛𝑖𝑑𝑠
β€’ πΈπ‘Ÿ =
309.11βˆ’19.61
0.79
= 366.46𝑒𝑛𝑖𝑑𝑠
8. At TOA (@sun):
β€’ 𝐸𝑖 =
366.46
0.62
= 591.06𝑒𝑛𝑖𝑑𝑠
β€’ 𝐸𝑖@π‘‘π‘œπ‘Ž =
591.06
0.79
= 748.17𝑒𝑛𝑖𝑑𝑠
β€’ 𝐸𝑖@π‘‘π‘œπ‘Ž =
748.17
0.9962 = 754.20𝑒𝑛𝑖𝑑𝑠
That’s it
Thanks…

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Remote Sensing

  • 1. REMOTE SENSING Thursday, 29 November 2017 J.Mwaura RS APPLICATIONS & SEMINAR
  • 2. Linear Contrast Stretching 0-255 in an 8-bit system β€’ 𝐷𝑁𝑠𝑑 = 255 Γ— (𝐷𝑁 π‘–π‘›βˆ’π·π‘ π‘šπ‘–π‘›) (𝐷𝑁 π‘šπ‘Žπ‘₯βˆ’π·π‘ π‘šπ‘–π‘›) DN values range from 60-158 β€’ 0-59 and 159-255 are not utilized
  • 3. Histogram-equalized Stretching β€’ Lets stretch values in the range [75-150] – 𝐷𝑁𝑠𝑑 = 255 𝑗=0 π‘˜ ( 𝑛 𝑗 𝑁 ) β€’ 𝐷𝑁𝑠𝑑 = π‘’π‘›β„Žπ‘Žπ‘›π‘π‘’π‘‘ 𝐷𝑁 π‘£π‘Žπ‘™π‘’π‘’ β€’ 𝑛𝑗 = π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝑝𝑖π‘₯𝑒𝑙𝑠 β„Žπ‘Žπ‘£π‘–π‘›π‘” 𝐷𝑁 π‘£π‘Žπ‘™π‘’π‘’ 𝑖𝑛 π‘‘β„Žπ‘’ 𝑗 π‘‘β„Ž π‘Ÿπ‘Žπ‘›π‘”π‘’, 𝑖𝑛 π‘‘β„Žπ‘’ 𝑖𝑛𝑝𝑒𝑑 π‘–π‘šπ‘Žπ‘”π‘’ β€’ π‘˜ = π‘šπ‘Žπ‘₯. π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝐷𝑁 π‘Ÿπ‘Žπ‘›π‘”π‘’ 𝑖𝑛 𝑖𝑛𝑝𝑒𝑑 π‘–π‘šπ‘Žπ‘”π‘’ β€’ 𝑁 = 𝑻𝒐𝒕𝒂𝒍 π’π’–π’Žπ’ƒπ’†π’“ π‘œπ‘“ 𝑝𝑖π‘₯𝑒𝑙𝑠 𝑖𝑛 𝑖𝑛𝑝𝑒𝑑 π‘–π‘šπ‘Žπ‘”π‘’
  • 4. Calculate Slope for Band and Radiance Metadata: β€’ LMAX_BAND6 = 15.303 β€’ LMIN_BAND6 = 1.238 β€’ π‘†π‘™π‘œπ‘π‘’ = (π‘™π‘šπ‘Žπ‘₯βˆ’π‘™π‘šπ‘–π‘›) π‘šπ‘Žπ‘₯ β€’ π‘†π‘™π‘œπ‘π‘’ 𝐡6 = 15.303βˆ’1.238 255 β€’ = 0.0551 β€’ π‘…π‘Žπ‘‘π‘–π‘Žπ‘›π‘π‘’ = π‘ π‘™π‘œπ‘π‘’ Γ— 𝐷𝑁 + π‘™π‘šπ‘–π‘› β€’ 𝑅 𝐡6 = 0.0551 Γ— 𝐷𝑁 𝐡6 βˆ’ 1.238 Β»e.g. DN = 69 β€’ 0.0551 Γ— 69 βˆ’ 1.238 = 2.5639
  • 5. Calculate Temperature (at-sensor/TOA) β€’ Using Planck's Black Body Radiation Law –𝑇 = π‘˜2 ln π‘˜1 𝑅 +1 , οΆπ‘˜ = π‘π‘Žπ‘™π‘–π‘π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘, 𝑅 = π‘Ÿπ‘Žπ‘‘π‘–π‘Žπ‘›π‘π‘’ π‘“π‘œπ‘Ÿ π‘π‘Žπ‘›π‘‘ = 2.5639 Β»π‘˜1 = 666.09 Β»π‘˜2 = 1282.71 β€’ 𝑇𝐡6 = 1282.71 ln 666.09 2.5639 +1 = 195.54
  • 6. β€’ Calculating Surface Temperature 𝑇𝑠 = 𝑇𝐡 1 + Ξ» βˆ— 𝑇𝐡 𝜌 βˆ— log πœ€ – 𝑇𝐡 = π‘‘π‘’π‘šπ‘π‘’π‘Ÿπ‘Žπ‘‘π‘’π‘Ÿπ‘’, πœ€ = π‘™π‘Žπ‘›π‘‘ π‘ π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ π‘’π‘šπ‘–π‘ π‘ π‘–π‘£π‘–π‘‘π‘¦ – Ξ» = π‘€π‘Žπ‘£π‘’π‘™π‘’π‘›π‘”π‘‘β„Ž, 𝜌 = β„Ž π‘π‘™π‘Žπ‘›π‘π‘˜β€² 𝑠 π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ Γ— 𝑐 𝜎 π‘π‘œπ‘™π‘‘π‘§π‘šπ‘Žπ‘›π‘› π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘ β€’ LSE (Ξ΅) can be extracted by using NDVI considering three different cases β€’ Bare soil β€’ Vegetation β€’ Mixture of bare soil and vegetation
  • 7. Land Surface Emissity (LSE) β€’ For Band 6 of Landsat TM β€’ πœ€ = 0.004 Γ— 𝑝𝑣 + 0.986 β€’ 𝑝𝑣 is the proportion of vegetation which is given by β€’ 𝑝𝑣 = { π‘π·π‘‰πΌβˆ’π‘π·π‘‰πΌ π‘šπ‘–π‘› (𝑁𝐷𝑉𝐼 π‘šπ‘Žπ‘₯βˆ’π‘π·π‘‰πΌ π‘šπ‘–π‘›) }2
  • 8. Land Surface Temperature (LST) β€’ Parameters »𝑇𝐡6 = 195.54 »𝜌 = 14380 Β»πœ€ = 1.2345 Β»πœ† = 11.5 Β΅m – 𝑇𝑠 = 195.54 1+ 11.5Γ— 195.54 14380 Γ—log 1.2345 = 192.780 𝑐
  • 10. Irradiance at-TOA?(1) βˆ’6.70 𝐸 𝑅 = 𝐸 𝑇 Γ— cos ∝ 𝑇. πΆπ‘Žπ‘›π‘π‘’π‘Ÿ πΈπ‘„π‘ˆπ΄π‘‡π‘‚π‘… 𝑇. πΆπ‘Žπ‘π‘Ÿπ‘–π‘π‘œπ‘› 𝑑 = 0.996 π‘†π‘Žπ‘‘π‘’π‘™π‘™π‘–π‘‘π‘’ 𝐸 𝑇 = 𝐸𝑑 𝑑2 βˆ’23.30 ?
  • 11. Irradiance at-TOA?(2) Sky irradiance (𝐼𝑠 = 12𝑒𝑛𝑖𝑑𝑠) Path radiance (𝑅 𝑝 = 2𝑒𝑛𝑖𝑑𝑠) Pixel irradiance 𝐼 𝑝 = 6𝑒𝑛𝑖𝑑𝑠 Sensor πΊπ‘Žπ‘–π‘› = 0.89, π‘‘π‘Žπ‘Ÿπ‘˜ π‘π‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘ = βˆ’19 reflectance (𝜌 = 0.62) Incident irradiance (𝐸𝑖) 𝐓. 𝐎. 𝐀 Atmosphere (t = 0.79) Sky radiance (𝑅 𝑠 = 14𝑒𝑛𝑖𝑑𝑠) @𝐬𝐞𝐧𝐬𝐨𝐫 @𝐩𝐒𝐱𝐞π₯
  • 12. Irradiance at-TOA?(3) 1. 𝐸𝑑 = 258+19 0.89 = 311.24 𝑒𝑛𝑖𝑑𝑠 2. πΈπ‘Ÿ = 311.24 Γ— cos(6.7) = 309.11 𝑒𝑛𝑖𝑑𝑠  at Sensor Radiance 3. At pixel: β€’ 𝐼𝑠 = 0.79 Γ— 12 = 9.48𝑒𝑛𝑖𝑑𝑠 β€’ 𝐼 𝑝 = 0.79 Γ— 6 = 4.74 𝑒𝑛𝑖𝑑𝑠
  • 13. Irradiance at-TOA?(4) 4. Reflected at pixel: β€’ 𝐼𝑠 = 0.62 Γ— 9.84 = 5.88𝑒𝑛𝑖𝑑𝑠 β€’ 𝐼𝑠 = 0.62 Γ— 4.74 = 2.94𝑒𝑛𝑖𝑑𝑠 5. At TOA (@sensor): β€’ 𝐼𝑠 = 0.79 Γ— 5.88 = 4.65𝑒𝑛𝑖𝑑𝑠 β€’ 𝐼 𝑝 = 0.79 Γ— 2.94 = 2.32𝑒𝑛𝑖𝑑𝑠 β€’ 𝑅 𝑝 = 0.79 Γ— 2 = 1.58𝑒𝑛𝑖𝑑𝑠 β€’ 𝑅 𝑠 = 0.79 Γ— 14 = 11.06𝑒𝑛𝑖𝑑𝑠 6. Total = 19.61𝑒𝑛𝑖𝑑𝑠
  • 14. Irradiance at-TOA?(5) 7. Reflected at pixel: β€’ 0.79 πΈπ‘Ÿ + 19.61 = 309.11𝑒𝑛𝑖𝑑𝑠 β€’ πΈπ‘Ÿ = 309.11βˆ’19.61 0.79 = 366.46𝑒𝑛𝑖𝑑𝑠 8. At TOA (@sun): β€’ 𝐸𝑖 = 366.46 0.62 = 591.06𝑒𝑛𝑖𝑑𝑠 β€’ 𝐸𝑖@π‘‘π‘œπ‘Ž = 591.06 0.79 = 748.17𝑒𝑛𝑖𝑑𝑠 β€’ 𝐸𝑖@π‘‘π‘œπ‘Ž = 748.17 0.9962 = 754.20𝑒𝑛𝑖𝑑π‘