| NDVI | $\text{NDVI}=({\rho }_{\text{NIR}}-{\rho }_{\text{red}})/({\rho }_{\text{NIR}}+{\rho }_{\text{red}})$ | 𝜌NIR is near-infrared reflectance, and 𝜌red is red-band reflectance |
| ET | $\lambda \text{ET}={R}_{n}-G-H$ | λET is the instantaneous latent heat flux, Rn24 is the 24-hour cumulative net radiation, G24 is the 24-hour cumulative soil heat flux, Λ is the evaporation ratio, and λ is the latent heat of vaporization of water (J/kg) |
| $\text{Λ}=\frac{\lambda \text{ET}}{{R}_{n}-G}=\frac{\lambda {\text{ET}}_{24}}{{R}_{n24}-{G}_{24}}$ |
| $\lambda =\left[\begin{array}{c}2.051-0.002361\times \left({T}_{s}-273.15\right)\end{array}\right]\times {10}^{6}$ |
| $E{T}_{24}=\frac{{R}_{n24}\times \text{Λ}\times 86400}{\lambda }$ |
| LST | $\text{LST}={T}_{b}/\left[\begin{array}{c}1+(\lambda {T}_{b}/\rho )\mathrm{ln}\epsilon \end{array}\right]-273.5$ | Tb is the sensor-derived temperature, L6/10 represents the radiance for TM band 6 or OLI band 10, λ is the central wavelength of the thermal infrared band, ρ = 1.438×10-2 m∙K, K1 and K2 are sensor calibration parameters, ε denotes surface emissivity, DN is the image pixel’s gray value, and gain and bias refer to the respective waveband’s calibration coefficients. |
| ${T}_{b}={K}_{2}/\mathrm{ln}\left(\frac{{K}_{1}}{{L}_{6/10}}+1\right)$ |
| ${L}_{6/10}=\text{gain}\times \text{DN}+\text{bias}$ |
| NDBSI | $\text{SI}=\frac{({\rho }_{\text{SWIR}1}+{\rho }_{\text{red}})-({\rho }_{\text{blue}}+{\rho }_{\text{NIR}})}{({\rho }_{\text{SWIR}1}+{\rho }_{\text{red}})+({\rho }_{\text{blue}}+{\rho }_{\text{NIR}})}$ | SI is the bare soil index, IBI is the applied building index, ρSWIR1 is the shortwave infrared 1-band reflectance, ρblue is the blue-band reflectance, and ρgreen is the green-band reflectance. |
| $\text{IBI}=\frac{\frac{2{\rho }_{\text{SWIR}1}}{{\rho }_{\text{SWIR}1}+{\rho }_{\text{NIR}}}-\left[\frac{{\rho }_{\text{NIR}}}{{\rho }_{\text{NIR}}+{\rho }_{\text{red}}}+\frac{{\rho }_{\text{green}}}{{\rho }_{\text{green}}+{\rho }_{\text{SWIR}1}}\right]}{\frac{2{\rho }_{\text{SWIR}1}}{{\rho }_{\text{SWIR}1}+{\rho }_{\text{NIR}}}+\left[\frac{{\rho }_{\text{NIR}}}{{\rho }_{\text{NIR}}+{\rho }_{\text{red}}}+\frac{{\rho }_{\text{green}}}{{\rho }_{\text{green}}+{\rho }_{\text{SWIR}1}}\right]}$ |
