LST = BT / 1 + w (BT / p) * Ln (ε) (formula 1)
What is the name of this method?
Additionally, we use the following formula for Landsat 8:
LST = (BT / (1 + (0.00115 * BT / 1.4388) * Ln(ε))) (formula 2)
What are the differences between Formula 1 and Formula 2? If we use separately Formula 1 and Formula 2 to calculate the LST of one Landsat 8 image, will the results be the same?
The equations provided are variations of the radiative transfer equation used for estimating Land Surface Temperature (LST) from satellite imagery, such as that from the Landsat series of satellites. The equation is also known as the Radiative Transfer Equation for Temperature (RTE for T), and it's frequently used in remote sensing applications.
The formula includes variables as follows:
LST represents the land surface temperature,
BT is the at-sensor brightness temperature,
w represents the wavelength of emitted radiance,
p is the constant Planck's constant, and
ε is the emissivity of the surface.
Formula 1 is a general form of the radiative transfer equation for temperature, while Formula 2 is a specialized form specifically tailored for Landsat 8 data.
Comparing Formula 1 and Formula 2, you can see that the terms w(BT/p) and 0.00115BT/1.4388 are similar in their purpose. They are both corrections for the wavelength of emitted radiance, but the actual values used (and their unit) will differ because the second formula is specifically calculated for Landsat 8's thermal bands. The 1.4388 value in Formula 2 represents the Wien's displacement constant in micrometers Kelvin units.
The other difference is that Formula 1 uses a natural logarithm of ε (emissivity), while Formula 2 doesn't include this term. This suggests that Formula 2 assumes a constant emissivity (ε) for Landsat 8, which might not necessarily be the case for all land cover types.
So, if you use Formula 1 and Formula 2 separately to calculate the LST of one Landsat 8 image, the results are likely not to be exactly the same due to the differences in the assumptions made in each formula. The difference in results would be based on how much the assumptions made for each formula match the reality of the particular Landsat image being processed.
In conclusion, the choice of formula should be guided by the specific details of your Landsat image, and your knowledge about the land cover types present, their emissivity, and the specific spectral characteristics of the Landsat platform being used.
Please refer to my article for clarification.
"Data on time series analysis of land surface temperature variation in response to vegetation indices in twelve Wereda of Ethiopia using mono window, split window algorithm and spectral radiance model."
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