This document describes using Landsat TM data to calculate the Normalized Difference Vegetation Index (NDVI), land surface emissivity (LSE), and land surface temperature (LST). It outlines the steps to calculate slope and radiance for bands 3, 4, and 6, then determine brightness temperature. Next, it explains how to derive LSE from NDVI and use this to calculate surface temperature using Planck's law. The goal is to study NDVI and LST for the Landsat image from March 7, 2010.

1. STUDY OF NDVI, LAND SURFACE
TEMPERATURE USING LANDSAT (TM) DATA
Course: Introduction to RS & DIP
Mirza Muhammad Waqar
Contact:
mirza.waqar@ist.edu.pk
+92-21-34650765-79 EXT:2257
RG610

2. Landsat TM(07-03-2010)

3. LMAX_BAND1 = 193.000
LMIN_BAND1 = -1.520
LMAX_BAND2 = 365.000
LMIN_BAND2 = -2.840
LMAX_BAND3 = 264.000
LMIN_BAND3 = -1.170
LMAX_BAND4 = 221.000
LMIN_BAND4 = -1.510
LMAX_BAND5 = 30.200
LMIN_BAND5 = -0.370
LMAX_BAND6 = 15.303
LMIN_BAND6 = 1.238
LMAX_BAND7 = 16.500
LMIN_BAND7 = -0.150
Slope= (LMAX-LMIN)/(Max Gray)
Slope(B6)= (15.303-1.238)/(255)= 0.0551
Slope(B3)= (264+1.170)/(255)= 1.0398
Slope(B4)= (221+1.51)/(255)= 0.8725
Calculating Slope for Band= 3, 4 and 6

4. Radiance= Slope*DN + LMIN
LMAX_BAND1 = 193.000
LMIN_BAND1 = -1.520
LMAX_BAND2 = 365.000
LMIN_BAND2 = -2.840
LMAX_BAND3 = 264.000
LMIN_BAND3 = -1.170
LMAX_BAND4 = 221.000
LMIN_BAND4 = -1.510
LMAX_BAND5 = 30.200
LMIN_BAND5 = -0.370
LMAX_BAND6 = 15.303
LMIN_BAND6 = 1.238
LMAX_BAND7 = 16.500
LMIN_BAND7 = -0.150
R(3)= 1.0398 *B3-1.170
R(4)= 0.8725*B4-1.510
R(6)= 0.0551*B6-1.238
Calculating Radiance for Band= 3, 4 and 6

5. Radiance for Band 6
Calculating Radiance for Band= 3, 4 and 6

6. Calculating Brightness Temperature using
Planck's Black Body Radiation Law
TB = K2/Log{(K1/R6)+1)}
Where:
K1 = Calibration constant 1 (666.09 watt/m2
* ster * µm)
K2 = Calibration constant 2 (1282.71 K)

7. 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 10-23
J/K,
h=Planck’s constant=6.626 x 10-34
Js, c=velocity of light=2.998 x 108
m/s)
ε = Land surface emissivity
Calculating Surface Temperature

8. 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 + 0.986
 Pv is the proportion of vegetation which is given by
 Pv = [(NDVI-NDVImin)/(NDVImax-NDVImin)]2

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

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

11. LSE
ε = 0.004*Pv + 0.986
Calculating ε

12. Logε
Calculating ε

13. 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 10-23
J/K,
h=Planck’s constant=6.626 x 10-34
Js, c=velocity of light=2.998 x 108
m/s)
Calculating Surface Temperature

14. Land Surface Temperature (LST)