## 2 Materials and Methods
### Spectral Separability  
An analysis of the multispectral response patterns of the land cover types was used to determine their spectral separability. Spectral separability computes the statistical distance between signatures; therefore, it determines the overall classification accuracy [45]. The transformed divergence (TD) index and Jeffries-Matusita (J-M) distance separability measures were used in this study. Divergence (D) is calculated from the mean and variance-covariance matrices of data representing feature classes [46]:  
\[D_{ij}=\frac{1}{2}tr\Big{[}(\Sigma_{i}-\Sigma_{j})(\Sigma_{j}^{-1}-\Sigma_{i}^ {-1})\Big{]}+\frac{1}{2}tr\Big{[}(\Sigma_{i}^{-1}+\Sigma_{j}^{-1})(\mu_{i}-\mu _{j})(\mu_{i}-\mu_{j})^{T}\Big{]} \tag{1}\]  
The TD is used to lessen the effect of well-separated classes, which may increase the average divergence value and make the divergence measure misleading [46]:  
\[TD_{ij}=c\Big{[}1-e^{\frac{-D_{ij}}{8}}\Big{]} \tag{2}\]  
where \(tr[\cdot]\) is the trace of a matrix, which is the sum total of the diagonal elements of the matrix, and \(\Sigma_{i}\) and \(\Sigma_{j}\) are the variance-covariance matrices of classes \(i\) and \(j\); \(\mu_{i}\) and \(\mu_{j}\) are the corresponding mean vectors; and \(c\) is a constant value defining the range of TD values.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Landsat**} & \multicolumn{3}{c}{**Google Earth**} & \multicolumn{3}{c}{**Topographical**} & \multirow{2}{*}{**Aerial Data**} \\  & & & & & & & & & **Maps** & \\ \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Bands**} & **Landsat** & \multirow{2}{*}{**Sensor**} & **Resolution** & \multirow{2}{*}{**Year**} & **Resolution** & \multirow{2}{*}{**Year**} & **Resolution** & \multirow{2}{*}{**Year**} & **Resolution** \\  & & & **Type** & & **(m)** & & & **(m)** & & **(m)** \\ \hline
1973 & 1–4 & Landsat 1 & MSS & 60 & — & — & 1982 & 10,000 & 1975 & 5 \\
1990 & 1–5, 7 & Landsat 5 & TM & 30 & — & — & 1990 & 1:9500 & 1991 & 5 \\
1995 & 1–5, 7 & Landsat 5 & TM & 30 & — & — & 1996 & 1:7500 & 1996 & 3 \\
2000 & 1–5, 7 & Landsat 7 & ETM+ & 30 & — & — & 2001 & 1:7500 & 2001 & 3 \\
2009 & 1–5, 7 & Landsat 7 & ETM+ & 30 & 2010 & 0.3 & 2010 & 1:7500 & 2010 & 3 \\
2020 & 1–7 & Landsat 8 & OLI & 30 & 2020 & 0.3 & 2020 & 1:2500 & 2017 & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Remote sensing data used to analyze the patterns and dynamics of mangroves in Chwaka Bay and Menai Bay, Zanzibar.  
The J-M distance between distributions of two classes \(\omega_{i}\) and \(\omega_{j}\) has been defined as follows [47]:  
\[JM_{ij}=2\Big{(}1-e^{-B_{ij}}\Big{)} \tag{3}\]  
where \(B_{ij}\) is the Bhattacharyya distance computed as [48]:  
\[B_{ij}=\frac{1}{8}\big{(}\mu_{i}-\mu_{j}\big{)}^{T}\bigg{(}\frac{\Sigma_{i}+ \Sigma_{j}}{2}\bigg{)}^{-1}\big{(}\mu_{i}-\mu_{j}\big{)}+\frac{1}{2}ln\left( \frac{1}{2}\frac{|\Sigma_{i}+\Sigma_{j}|}{\sqrt{|\Sigma_{i}||\Sigma_{j}|}}\right) \tag{4}\]  
where \(\mu_{i}\) and \(\mu_{j}\) are the mean reflectance of species \(i\) and \(j\); \(\Sigma_{i}\) and \(\Sigma_{j}\) correspond to their covariance matrices; and \(|\Sigma_{i}|\) and \(|\Sigma_{j}|\) are the determinants of \(\Sigma_{i}\) and \(\Sigma_{j}\), respectively. \(ln\) is the natural logarithm function, while \(T\) is the transposition function.  
As a general rule, classes are separable if the result is greater than 1.9, fairly separable if it is between 1.7 and 1.9, and not separable if it is below 1.7 [49].