# 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  
The overall approach is to use long, dense time series of Sentinel-1 and the fact that the frequency of satellite acquisitions is different than the semidiurnal tidal period, which ensures consistent temporal sampling of the full tidal range. As the period of a tidal phase (2\(\pi\)) is half a moon-day, i.e., 12 h 25.2 min, and Sentinel-1 paths are sun-synchronous and always acquired at the same times of the day, either around 5:20 a.m. for descending paths or 4:10 p.m. for ascending paths in Tromso, every 12 day satellite cycle corresponds to a tidal phase shift of 2 h 20.4 min (\(\sim\)0.38\(\pi\)). The tidal phase shift between an S1A and S1B overpass (6 days) corresponds to 7 h 22.8 min (\(\sim\)1.19\(\pi\)). Inside a 12 day satellite cycle, if both S1A and S1B are operational, each pixel is observed by different satellite paths due to adjacent satellite path coverage overlay (Figure 3). The 10 acquisitions over the tidal gauge in Tromso during the 12 day Sentinel-1 cycle correspond to the tidal phase samples at 0\(\pi\), 0.87\(\pi\), 1.02\(\pi\), 1.03\(\pi\), 1.18\(\pi\), 1.19\(\pi\), 1.68\(\pi\), 1.83\(\pi\), 1.84\(\pi\), and 1.99\(\pi\), which shift by 0.38\(\pi\) for the next 12 day cycle. In the ITZ area, the backscatter signatures vary strongly between low backscatter when covered by water and higher backscatter when land is exposed to the atmosphere. The highest and lowest water lines can, therefore, be extracted from images representing the lowest and highest lowest backscatters of a S1 time series, respectively [27]. The S1 time series were, therefore, statistically analyzed in order to extract backscatter percentile images that each correspond to a specific tidal level. Although the radar backscatter histogram from typical coastal images might be multimodal due to different land covers or wind over ocean, they clearly show distinguishable water and land modes in both polarizations, VV and VH, which are separated by a minimum (Figure 4). Due to speckle noise in single SAR scenes, the separation between water and land can, however, be challenging, and advanced edge detection techniques might be needed [29; 31; 32] to clearly define a water-land separation line. In temporally filtered, e.g., temporally averaged, SAR images where speckle noise has been efficiently filteredout using time series, thresholding is an easy and effective method to detect water lines, either manually or by using automatic thresholding methods [43; 44]. Percentile images between the 5 th and 95 th percentiles of time series decrease the speckle noise enough to apply simple thresholds to detect the water line. Figure 5 shows that the land and water modes in high (98 th) and low (second) percentile images still show clear thresholds but can be more ambiguous for VV and VH polarizations, respectively. As explained later, for low percentiles, the method relies, therefore, more on VV polarization images and, for high percentiles, it relies on VH polarization images. Extracting every fifth percentile from a year-long dataset of tidal gauge height observation every 10 min from Hansjordnesbukta showed a near-linear relationship with tidal height between the fifth and 95 th percentiles (blue line in Figure 6). The second and 98 th percentiles were extracted in addition. The fifth, 15 th, 25 th, 50 th, 75 th, 85 th, and 95 th percentiles of the tidal height observations correspond approximately to the tidal reference levels MLWS, MLW, MLWN, MSL, MHWN, MHW, and MHWS, respectively. Percentiles of tidal heights observed at S1 acquisition times from a 6 month long time series (June to November 2019) over Hansjordnesbukta varied slightly around a linear regression line but could be approximated by this linear relationship. A denser sampling or longer time series brought the curve closer to linearity.