# Comparing Sentinel-2 and Landsat 8 for Burn Severity Mapping in Western North America
## 2 Materials and Methods
### Burn Severity Indices  
We evaluated imagery obtained from Landsat and Sentinel for burn severity mapping of each fire using four spectral indices derived from pre- and post-fire imagery. Three indices are based on the normalized burn ratio (_NBR_) [11; 60] and include (a) the differenced normalized burn ratio (_dNBR_) [11] (b) the relativized burn ratio (_RBR_) [61], and (c) the relative delta normalized burn ratio (_RdNBR_) [62]:  
\[NBR=\left(\frac{NIR-SWIR2}{NIR+SWIR2}\right) \tag{1}\]  
\[dNBR=\left(NBR_{prefire}-NBR_{postfire}\right)\times 1000 \tag{2}\]  
\[RBR=\frac{dNBR}{NBR_{prefire}+1.001} \tag{3}\]  
\[RdNBR=\left\{ \begin{array}{ll}\frac{dNBR}{|NBR_{prefire}|^{0.5}},&|NBR_{prefire }|\geq 0.001\\ \frac{dNBR}{0.0010^{3}},&|NBR_{prefire}|<0.001\end{array} \right. \tag{4}\]  
where _NIR_ (Equation (1)) is the near infrared band (Landsat: B5; Sentinel: B8) and _SWIR2_ is the shortwave infrared band 2 (Landsat: B7; Sentinel: B12) (Table 2). In Equation (4), the _NBRpre_ qualifier is necessary so that the equation does not fail when _NBRpre_ equals zero. Due to the resolution differences between the bands of Sentinel (Table 2), we also tested a metric based on the normalized difference vegetation index (_NDVI_) [63], which is often used to assess vegetation change in forests [64; 65; 66]. Unlike NBR, which combines the Sentinel 10 m _NIR_ band with the 20 m _SWIR2_ band, _NDVI_ uses the 10 m _red_ band instead of the _SWIR2_ band, allowing for true 10 m resolution. We tested both the differenced normalized difference vegetation index (_dNDVI_) [55] and a relativized version (_RdNDVI_) \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Band Name**} & \multirow{2}{*}{\begin{tabular}{l} **Index** \\ **Number** \\ \end{tabular} } & \multicolumn{2}{l}{\begin{tabular}{l} **Sentinel-2 MSI** \\ **Wavelength** \\ **(nm)** \\ \end{tabular} } & \multicolumn{2}{l}{\begin{tabular}{l} **Datast 8 OLI** \\ **Resolution (m)** \\ \end{tabular} } & \multicolumn{2}{l}{\
\begin{tabular}{l} **Datast 8 OLI** \\ **Wavelength** \\ **(nm)** \\ \end{tabular} } & \multicolumn{2}{l}{
\begin{tabular}{l} **Spatial** \\ **Resolution (m)** \\ \end{tabular} } \\ \hline Coastal aerosol & B1 & 432–453 & 60 & B1 & 433–453 & 30 \\ Blue & B2 & 459–525 & 10 & B2 & 450–515 & 30 \\ Green & B3 & 541–578 & 10 & B3 & 525–600 & 30 \\ Red & B4 & 649–681 & 10 & B4 & 630–680 & 30 \\ Red edge 1 & B5 & 696–712 & 20 & & & \\ Red edge 2 & B6 & 732–748 & 20 & & & \\ NIR (narrow 1) & B7 & 770–793 & 20 & & & \\ NIR & B8 & 780–886 & 10 & B5 & 845–885 & 30 \\ NIR (narrow 2) & B8A & 853–875 & 20 & & & \\ Water vapor & B9 & 933–955 & 60 & & & \\ SWIR Cirrus & B10 & 1358–1392 & 60 & B9 & 1360–1380 & 30 \\ SWIR 1 & B11 & 1563–1659 & 20 & B6 & 1560–1660 & 30 \\ SWIR 2 & B12 & 2093–2290 & 20 & B7 & 2100–2300 & 30 \\ Panchromatic & & & & B8 & 500–680 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of Sentinel-2 MultiSpectral Instrument (MSI) and Landsat 8 Operational Land Imager (OLI) radiometric and spatial resolutions of spectral bands. similar to the one used in [65], but with \(NDVI_{\textit{prefine}}\) in the denominator squared in the same formulation as RdNBR:  
\[NDVI=\left(\frac{NIR-red}{NIR+red}\right) \tag{5}\]  
\[dNDVI=\left(NDVI_{\textit{prefine}}-NDVI_{\textit{postfire}}\right)\times 1000 \tag{6}\]  
\[RdNDVI=\left\{ \begin{array}{l}\frac{dNDVI}{|NDVI_{\textit{prefine}}|^{0.5}} \left|NDVI_{\textit{prefine}}\right|\geq 0.001\\ \frac{dNDVI}{0.001^{0.5}}\left|NDVI_{\textit{prefine}}\right|<0.001\end{array} \right. \tag{7}\]  
where _NIR_ (Equation (5)) is the near infrared band (Landsat: B5; Sentinel: B8) and _red_ is the red band (Landsat and Sentinel: B4). Because \(dNDVI\) showed weaker correlation to field measures of burn severity than \(RdNDVI\) (i.e., lower \(R^{2}\)), we excluded it from further analysis (Figure S1A). We calculated all indices using the native resolution of each sensor's band.