## 3 Methodology
### FFSAR L1A to FFSAR L1B Processing  
The FFSAR processor utilized in this study was developed by isardSAT as part of the ESA S6 Ground Processor Prototype (GPP), employing the back-projection algorithm for radar altimeters detailed by [PERSON] et al. [29]. The along-track resolution (\(\delta R\)) of single-look waveforms processed with this FFSAR method is determined by  
\[\delta R=0.886\frac{cR_{0}}{2f_{c}v_{s}T_{i}} \tag{2}\]  
where \(c\) denotes the speed of light, \(R_{0}\) represents the satellite altitude, \(f_{c}\) is the carrier frequency of the traveling pulse, \(v_{s}\) signifies the orbiting velocity, and \(T_{i}\) denotes the integration time [29]. While most parameters are fixed by satellites' technical specifications, \(T_{i}\) remains variable and is crucial for achieving maximum resolution, contingent upon the illumination time of the targeted location. However, determining the illumination time is complex due to its dependence on topography and orbit characteristics. In this study, we maintained a constant integration time of 2.9 s, resulting in an approximate single-look along-track resolution of about 0.6 m. The reason to maintain such a value is supported by three arguments:  
1. Keeping it close to the maximum value allows us to minimize the along-track dispersion from off-nadir, undesired point-like scatterers, which can be water ponds, metallic roofs, etc. 2. Though we assume a quasi-specular behavior of the target's surface, and thus, according to [PERSON] and [PERSON] [32], there would be no need to integrate more than the along-track distance associated with the Fresnel zone (around 100 m of pulses per waveform), it turns out that a priori we do not know the kind of rugosity of the target; thus, maintaining a high value ensures that no signal is lost. 3. Finally, as the final point of the analysis is to compare the FFSAR algorithm performance against UFSAR, a comparable overall synthetic aperture shall be considered. Figure 2: Methodology used in the retrieval of WL\({}_{a}\)s from operational L1A Sentinel-6 products. The _geoid_ is included in the block of geophysical corrections, although the same value as that of the in situ station is used for validation. The _altitude_ is provided by L1A products. Furthermore, to enhance the resolution, we interpolated the waveforms, which originally had a range sampling of 38 cm [9], using a zero-padding factor of 8. This interpolation allowed for a finer separation of approximately 5 cm between sampled waveform range bins. To preserve waveform integrity, no windowing was applied in either the range or azimuth domain. The along-track sampling of single-look waveforms was configured to 0.65 m. Lastly, to mitigate uncorrelated noise, we averaged the data over 5 m intervals in the along-track direction. This technique, commonly known as multi-looking in the literature, involves combining multiple single looks. Figure 3 illustrates an example of an altimetry radargram captured over the Itoiz Reservoir. The radargram shows the power of the waveforms on the \(y\)-axis and the latitude at which the nadir was located on the \(x\)-axis. Note that a waveform represents the power detected by the satellite during a certain period of time, which is discretized into time bins. These time bins represent the time the echo has traveled, and considering the speed of light, they can be translated into distance. As illustrated in Equation (1), this distance, or range, can be further used to calculate the elevation that each time bin represents. In other words, the power of each time bin can be related to the power of a hypothetical reflecting surface at a certain equivalent nadir elevation. As Figure 3 shows, there is a powerful return at an elevation of approximately 570 m for multiple latitudes. However, we cannot determine if this distance was traveled vertically or at an angle. Note that traditional altimetry was developed for measurements over oceans, where a flat reflecting surface is expected, but over inland terrain, the topography is not flat.