# Radiometric Comparison within the Sentinel-1 SAR Constellation over a Wide Backscatter Range
## 3 Results
### Sensitivity of Noise Subtraction for Targets with Low SNR  
In order to also derive an accurate radar brightness for targets with low SNR, the noise level has to be considered. Therefore, the noise power is subtracted from observed radar brightness in linear scale, i.e., both values (radar brightness and annotated noise) have to be converted to linear scale before the subtraction step. The noise subtracted backscatter as the result can be converted back to logarithmic scale afterwards. By subtracting the noise in that way, the resulting difference between S-1A and S-1B is reduced from 1.15 dB (without noise subtraction) to 0.65 dB (with noise subtraction) for the given observation area at Lake Constance (see Table 4). For low SNR the noise subtraction is a necessary step for comparing two systems with different noise levels. For low SNR, the image power is only slightly higher than the noise power and the (linear) difference between both values is very small resulting in very low decibel values after reconverting to logarithmic scale. Hence, for areas with low SNR, the resulting noise subtracted backscatter difference between both SAR systems is very sensitive to the derived radar brightness and the estimated noise level. For the given case, the noise level of S-1A is higher than the noise of S-1B or even the measured radar brightness by S-1B. That indicates that S-1A has a higher system noise compared to S-1B (see Table 4). Consequently, S-1B is more sensitive to low backscatter compared to S-1A. Nevertheless, the same target area is observed under the same acquisition geometry and consequently this should result in a nearly equivalent noise subtracted backscatter value. One of the reasons for the remaining difference of 0.65 dB may be a not accurately enough estimated noise level. The following case study evaluates the impact of noise accuracy on the resulting noise subtracted backscatter differences for low SNR from SAR observations of Lake Constance. The measured average image backscatter values of \(-20.12\) dB for S1-A and \(-21.27\) dB for S-1B (see Table 4) are used as fixed parameters - the effect from different noise levels is evaluated and depicted within Figure 9. For a SNR of 0 dB, the measured backscatter values are at noise level, marked by the arrow in the top right corner of the plot. In this case the noise subtracted backscatter is 0 at linear scale for both instruments, i.e., both instruments have different noise levels but are perfectly balanced. The black line marks the balanced case over the noise level range. For each point at the black line, the corresponding noise levels can be assigned to S-1A and S-1B. The noise subtracted image backscatter is well balanced between S-1A and S-1B for these noise pairs. The colored lines within Figure 9 indicate remaining imbalances of 0.5 dB, 1.0 dB, 1.5 dB, or 2.0 dB for the corresponding noise levels. The annotated noise levels extracted from the related SAR products (see Table 4) are marked as a circle within Figure 9. The resulting difference of 0.65 dB between both noise subtracted backscatter values (see Table 4) is also expressed within the figure: the circle is located between green (0.5 dB) and blue line (1.0 dB) but near the green line. The error bars reflect the sensitivity of the \(\beta^{0}\) difference \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **S-1A** & **S1A** & **S-1B** & **S1B** & **S-1A/S-1B [dB]** & **S-1A/S-1B [dB]** \\
**Subswath** & \(\beta^{0}\) [dB] & **Noise** & \(\beta^{0}\) [dB] & **Noise** & **Noise not** & **Noise** \\  & \(\mathbf{(\mu\pm\sigma)}\) & **[dB]** & \(\mathbf{(\mu\pm\sigma)}\) & **[dB]** & **Subtracted** & **Subtracted** \\ \hline IW1-VH & \(-20.12\pm 0.18\) & \(-20.87\) & \(-21.27\pm 0.25\) & \(-22.12\) & \(1.15\) & \(0.65\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean radar brightness and standard deviations (\(\mu\pm\sigma\)) of the low backscatter areas within Lake Constance (\(47.55^{\circ}\)N, \(9.49^{\circ}\)E). between S1A and S1B in terms of noise variation.