## 3 Method
### Statistical Separability Analysis
#### 3.2.1 Parametric Separability Analysis  
The parametric transformed divergence (TD) separability measure was used. The TD is a commonly used measure that is bounded between values of 0 (no separability) and 2 (completely  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Site Location** & **Unburned to Burned** & **Unburned to Unburned** \\ \hline Australia, Northern Territory, & & \\ near Fish River Block Gorge National Park & 8056 (0.81) & 8612 (0.86) \\ Cambodia, Kratici region, near Snoul & 8072 (0.81) & 8360 (0.84) \\ Canada, Alberta, Fort McMurray & 15,692 (1.57) & 14,124 (1.41) \\ Guinea, Faranah Prefecture, Parc National du Haut Niger & 8616 (0.86) & 8428 (0.84) \\ Colombia, Casanane Department, northern side & 8316 (0.83) & 10,384 (1.04) \\ of the Rio Cravo Sur river & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Number of pairs of unburned (first image acquisition) to burned (second image acquisition) pixel samples and number of pairs of unburned (first image acquisition) to unburned (second image acquisition) pixel samples at 10 m resolution selected at each site. The total summed pixel areas in km\({}^{2}\) are shown in parentheses.  
separable) [52]. It provides a covariance weighted distance between class means to determine whether class signatures are separable as:  
\[\begin{split} TD&=2\left[1-\exp\left(-\frac{D}{8} \right)\right],\\ D&=\frac{1}{2}tr\left[\left(C_{1}-C_{2}\right)\left(C _{1}^{-1}-C_{2}^{-1}\right)\right]+\frac{1}{2}tr\left[\left(C_{1}^{-1}-C_{2}^ {-1}\right)\left(\mu_{1}-\mu_{2}\right)\left(\mu_{1}-\mu_{2}\right)^{T} \right]\end{split} \tag{1}\]  
where \(TD\) is the transformed divergence between class \(1\) and class \(2\), \(C_{1}\) is the covariance matrix of class \(1\), \(\mu_{1}\) is the mean vector of class \(1\), \(tr\) is the matrix trace function, and \(T\) is the matrix transposition function. In this study, class \(1\) was defined by the unburned pixel samples from the first image acquisition and class \(2\) was defined by the corresponding burned samples from the second image acquisition (i.e., unburned-burned pairs). For the control group, classes \(1\) and \(2\) were defined from the unburned pixels from the first and second image acquisitions (i.e., unburned-unburned pairs). The rationale of the TD is to define the separation between two normal distributions (characterized by their mean vectors and covariance matrices), but most metrics used do not follow a Gaussian distribution [53]. In this respect, the TD is only indicative in cases of normality, or when classifiers based on the assumption of normality (e.g., maximum likelihood) are used. Consequently, the Shapiro-Wilk normality test [54] was used to assess if the unburned and burned pixel values were normally distributed. There are several normality tests but the Shapiro-Wilk test is considered to be reliable [55; 56]. The test is best applied with small sample size less than 5000 and with a test null-hypothesis that the sample is drawn from a normally distributed population [57]. As there were typically more than 5000 unburned or burned pixel values at each site (Table 4) the Shapiro-Wilk test _p_-value was computed independently ten times, each time drawing 1000 values at random. This was undertaken for the unburned (first image acquisition) and burned (second image acquisition) pixel samples at each site and for each MSI band (Table 2) and spectral index (Table 3).