# An IoT System and MODIS Images Enable Smart Environmental Management for Mekong Delta
## 4 Data Processing
### LST Computation  
The daily daytime LST image in the level-3 data processing used in the study can be extracted directly from the MOD11A1 product. However, these LST images usually contain many no-data pixels because the temperature value is estimated using the computational model based on global environmental characteristics and ground measurements by NASA [30]. Therefore, in this study, we apply the algorithm of LST computation from emissive data of two thermal bands developed by [PERSON] in 1984 [31]. The authors exploited the Advanced Very High-Resolution Radiometer (AVHRR) on the NOAA 7 satellite images at two 10.8 and 11.9 \(\upmu\)m bands at 1 km spatial resolution to estimate LST, following Equations (3)-(6). Additionally, the atmospheric correction of radiation from the Earth's surface was found. The algorithm was proposed based on an analysis of AVHRR images on July 1981 and a comparison of the radiative transfer theoretical model, sea surface temperature from satellite data, and ground meteorological measurements. [PERSON]'s algorithm was confirmed by [PERSON] et al. in 1997 [32]. We use AVHRR images corresponding to a flat homogeneous region characterized by the presence of natural grassland with patches of bare soil, and allowing for seasonal changes in surface emissivity due to changes in vegetative cover using NDVI. Then, they developed different algorithms to estimate LST based on exploring atmospheric effects and the land emissivity effect on surface temperature. The algorithms were tested by ground LST measurements. The results indicated that the LST strongly depends on errors in land surface emissivity.  
\[\text{LST(K)}=T_{31}+1.8\times(T_{31}-T_{32})+48\times(1-\epsilon)-75\Delta\epsilon \tag{3}\]  
\[\epsilon=\frac{e_{31}+e_{32}}{2} \tag{4}\]  
\[\Delta\epsilon=e_{31}-e_{32} \tag{5}\]  
\[\text{LST(C)}=LST(\text{K})-273.15 \tag{6}\]  
Here, we use the two MODIS thermal images of bands 31 and 32, corresponding to the two AVHRR thermal images to compute LST (K), following Equations (3)-(6). \(T_{31}\) and \(T_{32}\) (K) are the brightness temperatures obtained from band 31 and 32 images, respectively. \(T_{31}\) and \(T_{32}\) (K) are computed following Equation (2). \(e_{31}\) and \(epsilon_{32}\) are the coefficients of land surface emissivity in band 31, and band 32, respectively. \(epsilon_{31}\) and \(e_{32}\) are estimated from sensor-based measurements and NASA's global computational model. \(\epsilon\) is an average coefficient of bands 31 and 32. \(\Delta\epsilon\) is a difference of land surface emissivity between bands 31 and 32. Moreover, coefficients of land surface emissivity can be calculated from NDVI, using the experimental model proposed by [PERSON] et al. in 1997 [33]. Accordingly, \(\epsilon_{31}\) and \(\Delta\epsilon\) are calculated following Equations (7) and (8), respectively, where NDVI is computed following Equation (1). Figure 6 shows LST (\({}^{\circ}\)C) derived from the data on 9 June 2022.  
\[e_{31}=0.9897+0.029\times ln(NDVI) \tag{7}\]  
\[\Delta\epsilon=0.01019+0.01344\times ln(NDVI) \tag{8}\]