*2.5. Mapping of Land Surface Temperature*

According to the United States Geological Survey (USGS), Thermal infrared sensor (TIRS) bands of Landsat 8 have been affected by stray light from far out-of-field since its launch in 2013. A new stray light correction algorithm (SLCA) has been implemented into the USGS ground system since February 2017 and applied to reprocess historical Landsat 8 images. After SLCA implementation, Wang and Lentilucci [33] had a study to compare Landsat 8 TIRS Stray Light Correction with Multi-Sensor Measurements. It was concluded that the maximum difference in a temperature varies from 0.5% to 0.7% only. García-Santos et al. [34] validated the SLCA implementation using in situ LST measurements and three different LST estimation method algorithms (radiative transfer equation (RTE), single-channel algorithms (SCA), and split-window algorithms (SWA)) were applied for 21 scenes of Landsat 8 images. The in situ measured site is composed of different types of land covers, such as buildings, asphalt roads, vegetation regions, and so on. The study concluded that the SWA shows the best result for LST calculation from the Landsat 8 image with the lowest root mean square error (RMSE) (within 1.6–2 K). Therefore, the SWA was selected to calculate the LST for this study.

LST maps were generated by using the thermal infrared bands 10 and 11, which are available in the Landsat 8 TIRS images (1 June 2016 and 4 June 2017). We applied the SWA (Equation (1)) adopted from the literature [35,36] for the generation of the LST maps:

$$\text{LST} = T\_i + c1(T\_i - T\_j) + c2(T\_i - T\_j)^2 + c\_0 + \text{(c3 + c4w)}\left(1 - \varepsilon\right) + \left(c5 + c6w\right)\Delta\varepsilon \tag{1}$$

where *Ti* and *Tj* are the at-sensor brightness temperatures at the thermal infrared bands *i* and *j* (in Kelvins), respectively, *ε* is the mean emissivity, *ε* = 0.5(*ε<sup>i</sup>* + *εj*); Δ*ε* is the emissivity difference, <sup>Δ</sup>*<sup>ε</sup>* <sup>=</sup> *(ε<sup>i</sup>* − *<sup>ε</sup>j); <sup>w</sup>* is the total atmospheric water vapor content (in g·cm<sup>−</sup>2); and *<sup>c</sup>*0 to *<sup>c</sup>*6 are SW coefficients to be determined from simulated data.

*Ti* and *Tj* were calculated on the basis of the following formula (Equation (2)):

$$T = \frac{K\_2}{Ln\left(\frac{K\_1}{L\_\lambda} + 1\right)}\tag{2}$$

where *T* is at-sensor brightness temperatures; *L<sup>λ</sup>* is TOA spectral radiance in W/(m<sup>2</sup> ster μm); *K*<sup>1</sup> and *K*<sup>2</sup> are the pre-launch calibration constants (from metadata file of Landsat 8 image).

The TOA spectral radiance (*Lλ*) (in Equation (2)) was calculated from the radiance rescaling factors provided in the metadata file, applying the following formula (Equation (3)):

$$L\_{\lambda} = M\_L Q\_{\text{cal}} + A\_L \tag{3}$$

where *ML* is the band-specific multiplicative rescaling factor; *AL* is the band-specific additive rescaling factor; *Qcal* are the quantized and calibrated standard product pixel digital numbers (DN).

The land surface emissivity (*ε*) was estimated from the Landsat 8 imagery using the Normalized Difference Vegetation Index (NDVI) threshold method [37]. The total atmospheric water vapor

content coefficient was obtained from NASA's Atmospheric Correction Parameter Calculator (http: //atmcorr.gsfc.nasa.gov/) [38]. At the location of Hanoi (N21.00, E105.83), the total atmospheric water vapor was 5.17 g·cm−<sup>2</sup> for 4 June 2017, and 5.31 g·cm−<sup>2</sup> for 1 June 2016. The coefficients *<sup>c</sup>*0–*c*<sup>6</sup> in Equation (1) were determined from the simulated data provided by Jimenez-Munoz et al. [36]. It was found that the mean error of the LST was less than 1.5 K. The original LST calculated from the Equation (1) is in Kelvin degrees. The LST was converted to Celsius degrees for regression calculation.
