One of the common applications of thermal RS is estimation of land surface temperature (LST). LST is the radiative temperature of the earth surface, i.e., land derived from solar radiation. When land interact with incoming solar radiation, the ground is heated, and eventually radiate/emit EMR. LST measures the emission of thermal radiance coming out of the land surface, including the surface of the canopy in a vegetative area. Hence, LST is a mixture of bare soil and vegetation temperatures.

The Landsat 8 Band 10 (10.6-11.2 µm) and 11 (11.5-12.5 µm) covers the thermal spectrum of the EMR. The wavelength peak of earth’s surface radiant exitance is around 10 µm. Hence, the Band 10 is more useful in measuring earth’s surface radiance.

Extraction of LST from Landsat 8 satellite images can be done using the following steps.

Step1: Conversion of Top of Atmosphere Radiance (TOA)

Using the radiance rescaling factor, Thermal Infrared digital numbers can be converted to TOA spectral radiance.

Lλ=ML*Q_cal+Al

Where,
Lλ = TOA spectral radiance ((Watts/(m2*sr* µm))
ML = Radiance multiplicative of band 10
Al = Radiance Add band of band 10
Qcal = Quantized and calibrated standard product pixel values (DN)

Step 2: Conversion of TOA Brightness Temperature (BT)

TOA radiance can be converted to Brightness Temperature (BT) using the thermal constant values in meta data file.

BT = K2/Ln((K1/ Lλ)+1) – 273.15

Where, BT = TOA BT (°C)
Lλ = TOA spectral radiance ((Watts/(m2*sr* µm))
K1 = K1 constant Band (No)
K2 = K2 constant band (No)
Kelvin (K) to Celcius (°C)  =  -273.15

Step 3: Normalized Difference Vegetation Index (NDVI)

The NDVI is standardized vegetation index which calculated using NIR (band 5) and Red (band 4). NDVI is needed for calculating proportionate of vegetation (PV).

NDVI = (NIR-RED) / (NIR+RED)

Where, Red = DN values of Red band
NIR = DN values of NIR band

Step 4: Proportionate of Vegetation (PV)

Proportionate of Vegetation is measured using the minimum and maximum values of the NDVI. The PV value is further needed to calculate Emissivity.

PV = ((NDVI – NDVI_min) / (NDVI_max – NDVI_min))²

Where,
PV = Proportion of vegetation
NDVI = DN values from NDVI image
NDVI_min = Minimum DN values of NDVI image
NDVI _max = Maximum DN value of NDVI image

Step 5: Land surface emissivity (LSE)

Emissivity (E) is essential for measuring LST. 

E = 0.004 * PV +0.986

Where ,
E = Land surface emissivity
PV = proportion of vegetation
0.986 corresponds of a correction value of the equation

Step 6: Land Surface Temperature (LST)

The LST is the radiative temperature which calculated using the BT, wavelength emitted radiance, and LSE.

LST= BT/(1+(λ*BT/c2) * In(E))

Where, BT = brightness temperature (°C)
λ = wavelength of emitted radiance
E = land surface emissivity
c2 = 14388 µm K

c2 = h*c/s = 1.4388*10² mK = 14388 mK
h = Plank’s constant = 6.626*10³⁴ Js
s = Boltzman constant 1.38*10²³ JK
c = velocity of light = 2.998*10⁸ m/s

Note: The values of λ for landsat 8: for band 10 is 10.8, and for band 11 is 12.