# Mapping Atmospheric Exposure of the Intertidal Zone with Sentinel-1 CSAR in Northern Norway
## 2 Materials and Methods
### Methods
#### 2.2.2 Statistical Analysis and Mapping Atmospheric Exposure
As pixels in the intertidal zone are either land (high backscatter) or water (low backscatter), the percentile of the S1 backscatter time series where the pixel changes class corresponds directly to the percentage of time the pixel is water or inversely land. Figure 4: VV and VH backscatter histogram of a median image of a 1 year time series of Sentinel-1 images from a Norwegian coastal area including water and land. Figure 5: VV (**left**) and VH (**right**) backscatter histograms of the second, 50 th, and 98 th percentile backscatter images of a 1 year time series of Sentinel-1 from a Norwegian coastal area. A water line extracted from thresholding a S1 image based on percentile P of the backscatter time series corresponds, therefore, to a percentage of atmospheric exposure time of (100 \(-\) P)%. Backscatter percentile images from long S1 time series and their extracted water lines also correspond, therefore, to the reference tidal levels and inversely to their atmospheric exposure of 95%, 85%, 75%, 50%, 25%, 15%, and 5%, respectively. In addition, we extracted the water line for the second and 98 th backscatter percentiles to detect the near-highest and near-lowest tidal height during the period, respectively. As a first approach and before field data collection, the water line was extracted by thresholding the images at the backscatter histogram's minimum for both polarizations for each percentile image. During our field campaigns, the position of the water line was mapped by handheld GPS or smartphone at several reference levels. The thresholds were then manually refined so that the threshold contour lines in the S1 backscatter percentile images would best fit the GPS tracks, taken at Langnes and Hilleseya. For this best-fit task, the S1 percentile images were subsampled by bilinear interpolation to 1 m resolution. The final land-water thresholds figIVV(perc.) and VPH(perc.) are summarized in Table 2. The S1 maximum noise equivalent sigma zero (NESZ) of \(-\)22 dB defined for the interferometric wide (IW) swath mode [45] limited the lowest of our thresholds. Figure 7 shows the land-water thresholds as a function of percentile level. At low percentiles (second and fifth), the VV threshold is the main parameter to be considered as the observed VH threshold falls below NESZ. At high percentiles (95 th and 98 th), the VH threshold is the main parameter as some noise can be induced from strong winds over the ocean in co-polarized VV SAR images. The VV threshold at high percentiles was, therefore, chosen conservatively to eliminate most ocean noise from wind. Considering the first processing results that, in particular, showed ocean noise at steep incident angles, we also filtered out all S1 data that were acquired at incidence angles below 33.8\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & 2\% & 5\% & 25\% & 50\% & 75\% & 95\% & 98\% \\ \hline \(\gamma^{\circ}\)(VV) & \(-\)18.0 & \(-\)17.3 & \(-\)15.0 & \(-\)14.5 & \(-\)12.7 & \(-\)8.5 & \(-\)6.4 \\ \(\gamma^{\circ}\)(VH) & \(-\)22.0 & \(-\)22.0 & \(-\)22.0 & \(-\)21.7 & \(-\)20.7 & \(-\)19.8 & \(-\)18.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Land–water threshold values for \(\gamma^{\circ}\)(VV) and \(\gamma^{\circ}\)(VH) backscatter for the percentile images at second, fifth, 25 th, 50 th, 75 th, 95 th, and 98 th percentiles. Figure 6: Tidal height percentiles from 2019 tidal gauge measurements at 10 min sampling interval (blue line) and from S1 acquisition times during the 6 month period (June–November 2019) at Hansjordnesbukta (Tidal data ©Kartverket [12]). Each pixel (i,j) in the percentile image (P) was then binary classified by the thresholds \(\mathrm{Y^{\circ}VV(P)}\) and \(\mathrm{Y^{\circ}VH(P)}\) into a land mask and was defined as  
\[\mathrm{P(i,j)}\]  
is land if ( \[\mathrm{Y^{\circ}VV(i,j)>Y^{\circ}VV(P)}\] ) OR ( \[\mathrm{Y^{\circ}VH(i,j)>Y^{\circ}VH(P)}\] ). This was done for the second, fifth, 25 th, 50 th, 75 th, 95 th and 98 th backscatter percentiles images.