3.2.2. LST estimation

Digital numbers (DNs) are used in Landsat sensors to store thermal data (Aik et al., 2020). DNs are converted to radiance using provided equation in the respective sensor's handbook. Landsat 8 have two thermal band, band 10 (10.6 μm–11.19 μm) and band 11 (11.5 μm–12.51 μm). Stray light from far out-of-field has affected Landsat 8, and USGS has recommended not to use band 11 (USGS, 2017). For this reason, the only band 10 TIRS has been used in the present study for LST estimation. There is only one thermal band (band 6) in Landsat 5 used in LST estimation. The underlying model is referred to as the radiative transfer equation (RTE), and it is one of the widely utilized processes for LST retrieval.

DNs are converted to spectral radiance using Eq. (1) for Landsat 5 (USGS, 2019).

Here, L_λ = Spectral radiance at the sensor's aperture; LMAX_λ = Spectral radiance scaled to QCALMAX; LMIN_λ = Spectral radiance scaled to QCALMIN; QCAL = Quantized calibrated pixel value in DN; QCALMAX = Maximum quantized calibrated pixel value; QCALMIN = Minimum quantized calibrated pixel value.

DNs are converted to spectral radiance using Eq. (2) for Landsat 8 (USGS, 2016).

Here L_λ = Spectral radiance at the sensor's aperture; M_L = Radiance multiplicative scaling factor for the band; A_.L. = Radiance additive scaling factor for the band; Q_cal = Pixel value in DN.

The obtained L_λ values are used to calculate the brightness temperature. The given equation is subtracted by 273.15 to achieve results in Celsius

Here T = Brightness temperature in Celsius, K₁ and K₂ = calibration constant L_λ = spectral radiance at the sensor's aperture. The calibration constants K₁ and K₂ are obtained from satellite data metadata are tabulated below in Table 3.

Calibration constants of used thermal bands." Source: Metadata".

Depending on the land cover, spectral emissivity (ε) adjustment needs to be made, which is influenced by several elements such as texture, roughness, and structure (Sharma et al., 2021).

The surface emissivity is an inherent property of land that converts surface heat energy into radiant energy (Sobrino et al., 2004). The present study used NDVI-based emissivity correction using Eq. (4).

Here, P_v is the proportion of vegetation and estimated by Eq. (5)

The ratio of red and near-infrared spectral bands is used to calculate NDVI.

Finally, the LST is calculated using corrected land surface emissivity values using Eq. (7).

Here λ = wavelength of the band; ρ ​=h∗ ​cσ=6.626∗ ​10−34∗2.998∗ ​1081.38∗ ​10−23=14380∗10−2m ​K; Average LST value of each year retrieved using cell statistics tool in ArcGIS 10.8.