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**Study of NDVI, Land Surface Temperature using Landsat (TM) Data**

Mirza Muhammad Waqar Contact: EXT:2257 RG610 Course: Introduction to RS & DIP

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Landsat TM( )

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**Calculating Slope for Band= 3, 4 and 6**

LMAX_BAND1 = LMIN_BAND1 = LMAX_BAND2 = LMIN_BAND2 = LMAX_BAND3 = LMIN_BAND3 = LMAX_BAND4 = LMIN_BAND4 = LMAX_BAND5 = LMIN_BAND5 = LMAX_BAND6 = LMIN_BAND6 = 1.238 LMAX_BAND7 = LMIN_BAND7 = Slope= (LMAX-LMIN)/(Max Gray) Slope(B3)= ( )/(255)= Slope(B4)= ( )/(255)= Slope(B6)= ( )/(255)=

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**Calculating Radiance for Band= 3, 4 and 6**

LMAX_BAND1 = LMIN_BAND1 = LMAX_BAND2 = LMIN_BAND2 = LMAX_BAND3 = LMIN_BAND3 = LMAX_BAND4 = LMIN_BAND4 = LMAX_BAND5 = LMIN_BAND5 = LMAX_BAND6 = LMIN_BAND6 = 1.238 LMAX_BAND7 = LMIN_BAND7 = Radiance= Slope*DN + LMIN R(3)= *B R(4)= *B R(6)= *B

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**Calculating Radiance for Band= 3, 4 and 6**

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**Calculating Brightness Temperature using Planck's Black Body Radiation Law**

TB = K2/Log{(K1/R6)+1)} Where: K1 = Calibration constant 1 ( watt/m2 * ster * µm) K2 = Calibration constant 2 ( K)

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**Calculating Surface Temperature**

Surface Temperature= TB /{1+(λ *BT/ρ*logε)} TB= Brightness Temperature λ = Wavelength of emitted radiance (11.5 µm) ρ = h x c/σ =1.438 x 10-2 mK (σ=Boltzmann constant=1.38 x J/K, h=Planck’s constant=6.626 x Js, c=velocity of light=2.998 x 108 m/s) ε = Land surface emissivity

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**Calculating Land surface emissivity (LSE)- ε**

LSE (ε) can be extracted by using NDVI considering three different cases Bare ground Fully vegetated and Mixture of bare soil and vegetation For Band 6 of Landsat TM ε = 0.004*Pv Pv is the proportion of vegetation which is given by Pv = [(NDVI-NDVImin)/(NDVImax-NDVImin)]2

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Calculating Pv NDVI = [Ref(B4)-Ref (B3)}/{Ref (B4)+Ref(B3)} Pv

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**Pv = [(NDVI-NDVImin)/(NDVImax-NDVImin)]2**

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Calculating ε LSE ε = 0.004*Pv

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Calculating ε Logε

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**Calculating Surface Temperature**

Surface Temperature= TB /{1+(λ *BT/ρ) *logε} λ = Wavelength of emitted radiance (11.5 µm) ρ = h x c/σ =1.438 x 10-2 mK (σ=Boltzmann constant=1.38 x J/K, h=Planck’s constant=6.626 x Js, c=velocity of light=2.998 x 108 m/s)

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**Land Surface Temperature (LST)**

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