# Monthly Analysis of Wetlands Dynamics Using Remote Sensing Data
## Materials and Methods
### LST Estimation  
The LST has been retrieved using a tool developed in ERDAS Imagine. First, the top of atmospheric (TOA) spectral radiance (\(L\lambda\)) has been calculated using Equation (1). \[L\lambda=M_{L}*Q_{cal}+A_{L}-O_{i} \tag{1}\]  
where \(M_{L}\) represents the band-specific multiplicative rescaling factor, \(Q_{cal}\) is the Band 10 image, \(A_{L}\) is the band-specific additive rescaling factor, and \(O_{i}\) is the correction for _Band_ 10 [30]. After the digital numbers (DNs) have been converted to reflection, the TIRS band data has been converted from spectral radiance to brightness temperature (BT) using the thermal constants provided in the metadata file Equation (2). \(K_{1}\) and \(K_{2}\) are taken from the Landsat 8 metadata file. \[BT=\ \frac{K_{2}}{Ln\left[\left(\frac{K_{1}}{L\lambda}\right)+1\right]}-273.15 \tag{2}\]  
The calculation of \(NDVI\) is needed for further calculation of the proportion of vegetation. The \(NDVI\) equation for Landsat 8 bands is as given in Equation (3), where _Band_ 4 is the Red and _Band_ 5 is the near infra-red band. \[NDVI=\frac{NIR(band5)-R(band4)}{NIR(band5)+R(band4)} \tag{3}\]  
The Proportion of Vegetation represents the fractional vegetation cover and it is calculated based on the \(NDVI\) values (Equation (4)). Thus, NDVI values for vegetation and soil (\(NDVI_{y}\ =\ 0.5\) and \(NDVI_{s}=0.2\)) are suggested to apply in global conditions [31]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Landsat-8**} & \multicolumn{3}{c}{**Sentinel-1**} \\ \hline
**Day** & **Month** & **Year** & **Day** & **Month** & **Year** \\ \hline
01 & 2 & 2017 & 01 & 2 & 2018 \\
17 & 2 & 2017 & 21 & 2 & 2018 \\
05 & 3 & 2017 & 28 & 3 & 2017 \\
24 & 5 & 2017 & 27 & 4 & 2017 \\
25 & 6 & 2017 & 15 & 5 & 2017 \\
11 & 7 & 2017 & 02 & 6 & 2017 \\
27 & 7 & 2017 & 02 & 7 & 2017 \\
12 & 8 & 2017 & 13 & 8 & 2017 \\
13 & 9 & 2017 & 06 & 9 & 2017 \\
31 & 10 & 2017 & 12 & 10 & 2017 \\
16 & 11 & 2017 & 05 & 11 & 2017 \\ / & / & / & 11 & 12 & 2017 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Landsat 8 and Sentinel 1 images used in this study. \[P_{V}=\left(\frac{NDVI-NDVI_{s}}{NDVI_{v}-NDVI_{s}}\right)^{2} \tag{4}\]  
The emissivity can be calculated following Equation (5). \[\varepsilon_{\lambda}=\varepsilon_{v\lambda}P_{v}+\varepsilon_{s\lambda}(1-P_{ v})+C_{\lambda} \tag{5}\]  
where \(\varepsilon_{v}\) and \(\varepsilon_{s}\) are the vegetation and soil emissivities, respectively, and \(C\) represents the surface roughness (\(C\) = 0 for homogenous and flat surfaces) taken as a constant value of 0.005 [32]. The condition can be represented with the following formula and the emissivity constant values are; 0.991 for water, 0.962 for built-up areas, 0.966 for soil, and 0.973 for vegetated areas [24]. \[\varepsilon_{\lambda}\ =\ \left\{ \begin{array}{cc}\varepsilon_{s\lambda},&| NDVI<NDVI_{s}\\ \varepsilon_{v\lambda}P_{v}+\varepsilon_{s\lambda}(1-P_{v})+C,&|NDVI_{s}\leq NDVI \leq NDVI_{v}\\ \varepsilon_{s\lambda}+C,&|NDVI>NDVI_{v}\end{array} \right. \tag{6}\]  
Water class has been assigned, for _NDVI_ values lower than 0, and the emissivity value of 0.991 should be assigned. _NDVI_ values between 0 and 0.2, are considered to be soil, with an emissivity value of 0.996. _NDVI_ values between 0.2 and 0.4 are considered to be mixtures of soil and vegetation cover, and in the case, when the _NDVI_ value is greater than 0.4, it is considered to be covered with vegetation, and the value of 0.973 need to be assigned. The LST or the emissivity-corrected land surface temperature \(T_{s}\) is computed with Equation (7) [33]:  
\[T_{s}=\frac{BT}{\left\{1+\left[\frac{\Delta BT}{\rho}\text{{I}ne}_{\lambda} \right]\right\}} \tag{7}\]  
where \(T_{s}\) is the LST in Celsius, \(\lambda\) is the wavelength of emitted radiance (for which the peak response and the average of the limiting wavelength (\(\lambda\) = 10.895) [34] will be used), and \(\rho\) is a constant calculated with Equation (8).