# Comparing Sentinel-2A and Landsat 7 and 8 Using Surface Reflectance over Australia
## 2 Methods
### Comparison Methods  
The resampled Sentinel-2 pixel values were compared separately with corresponding pixels of Landsat-7 and Landsat-8 from same-day acquisitions. Scatter plots are used to display the corresponding bands. On all plots, the Sentinel-2 version of the variable is shown on the \(x\)-axis, while the Landsat version is shown on the \(y\)-axis. Each scatter plot shows the 1-to-1 line (solid line) representing perfect agreement between the two sensors. In addition, each plot shows a number of statistics which summarize the variation between the two variables. The slope of the Orthogonal Distance Regression (ODR) line is used to capture the proportional relationship between the \(x\) and \(y\) values. This fits a line through the data and intersecting the origin, and this line is plotted as a dashed line on the scatter plots. The slope of this line is a simple summary statistic that shows the average behaviour of the ratio of \(x\) and \(y\) in a robust manner. This is useful because, in general, for the quantities being discussed here, the value of the difference between \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Generic Name** & **Sentinel-2** & **Landsat-7** & **Landsat-8** \\ \hline Blue & 2 (458–522) & 1 (450–520) & 2 (450–510) \\ Green & 3 (543–578) & 2 (520–600) & 3 (530–590) \\ Red & 4 (650–680) & 3 (630–690) & 4 (640–670) \\ Near Infra-Red (NIR) & 8 (758–900) & 4 (770–900) & 5 (850–880) \\ Short Wave Infra-Red 1 (SWIR1) & 11 (1565–1655) & 5 (1550–1750) & 6 (1570–1650) \\ Short Wave Infra-Red 2 (SWIR2) & 12 (2100–2280) & 7 (2090–2350) & 7 (2110–2290) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Corresponding band numbers for each sensor. Nominal spectral window bounds are included in parentheses (in nanometres). and \(y\) is proportional to the \(x\) and \(y\) values themselves. This captures and quantifies the intuitive notion of drawing a line from the origin through the centre of the points on the scatter plot, and seeing how far away that lies from the 1-to-1 line. Orthogonal Distance Regression treats the two variables symmetrically, without assuming that all noise is limited to the independent variable (as is the case with Ordinary Least Squares regression). Perfect agreement between sensors would have a slope value of 1.0. The Pearson correlation coefficient (\(r\)) is also shown on each scatter plot. This is a measure of the linear correlation between the two variables, independent of scaling factors and offsets between them. It is thus a very direct measure of the amount of scatter on the scatter plots. Perfectly correlated variables will have a correlation value of 1.0, while two variables with no linear relationship at all will have a correlation of 0.0. The root mean square error (RMSE) between \(x\) and \(y\) is also shown on each scatter plot. This is a measure of the absolute difference between the values of \(x\) and \(y\). It is affected by a number of different factors, including the amount of scatter, any offset between the two variables, and scaling differences. This is a good measure of the variation between \(x\) and \(y\), but does not distinguish between these different types of variation. To fit prediction models, Ordinary Least Squares regression was used, to create a mapping from Sentinel-2A reflectance to Landsat reflectance. A separate model, of the form shown in Equation (1), was fitted for each band  
\[\rho_{\text{landsat}}=c_{0}+c_{1}\rho_{\text{sen2}}, \tag{1}\]  
where \(\rho\) represents surface reflectance for the given instrument, at a given wavelength, and the parameters \(c_{0}\) and \(c_{1}\) are fitted independently for each band. In addition to comparing the reflectances, comparisons were also performed to show the effect of these reflectance differences when the reflectance values are used to estimate biophysical quantities. A spectral unmixing model of vegetation cover fractions was used to estimate the proportions of green vegetation, non-green vegetation, and bare soil in each pixel.