## 1 Introduction
Moreover, they emphasized the importance of reducing errors by selecting the section of the waveform to be retracked based on prior knowledge of the topography, allowing for the disregarding of contaminations. Even if rivers can generally be considered small to medium targets in terms of transect, there is the added difficulty of the river's slope combined with the satellite's drift. As a consequence, the difference in WL\({}_{a}\) measured by two consecutive satellite passes is produced not only by the WL\({}_{t}\) changes in the river but also by the change in elevation produced by the river's slope. In such cases, filtering outliers is particularly delicate, and studies usually include hydrological models [26; 27; 28]. [PERSON] et al. [12] studied six rivers, with widths between a few hundred meters and 3 km, by collecting operational altimetry data from multiple satellites and using a state-space model for filtering WL\({}_{i}\)s. They projected the satellite measurements to the centerlines of the rivers and modeled the continuous and smooth slope of the rivers using cubic splines, thereby achieving errors between 17 and 66 cm with respect to in situ values. Recently, the advent of innovative techniques such as Fully Focused SAR (FFSAR) has paved the way for substantial improvements in inland altimetry [29]. By coherently processing all the pulses within the observation time, the theoretical along-track resolution achieved with FFSAR is around 0.5 m for typical nadir-looking spaceborne radar altimeters with roughly 1 m antennas. This improvement significantly increases the number of independent samples for a fixed transect length compared to UFSAR, allowing for more robust filtering schemes for small to medium inland water targets and increased resolution in shoreline studies. The WL\({}_{i}\) retrieval capabilities with FFSAR-processed data were first assessed by [PERSON] et al. [30]. They processed CS2 data over inland water areas in the Netherlands and concluded that a sub-decimeter error was attainable in transects of a few meters in length. However, the radar altimeters onboard CS2, S3A, and S3B operate using closed-burst pulse transmission. This transmission mode sends bursts of 64 pulses and remains inactive for two-thirds of the time, waiting for the echoes to travel back to the satellite [9]. FFSAR processing is affected by this period of inactivity, leading to information from a certain sample being replicated, with less power, to samples \(\pm\)90 m and \(\pm\)180 m along-track. This may distort the overall FFSAR product, especially when the target is large enough for the replicas to overlap within it. This overlap can potentially lead to signal cancelation in some cases [31]. In contrast, more modern radar altimeters, such as Poseidon-4 (P4) onboard S6, operate with almost continuous pulse transmission, namely open-burst or interleaved mode, and can thus notably minimize the effect from along-track replicas. In fact, P4 is the first ever radar altimeter that implements such a pulse transmission mode and ensures a continuous transmission-reception cycle, also allowing for increases in the number of measurements over a certain target [9]. This fact enables the possibility to evaluate FFSAR performance with almost fully independent samples along the track. It is important to note that under the assumption of small, flat, and specular water targets, which are not surrounded by bright scatterers at different heights, other methodologies exist that are computationally less expensive than FFSAR and achieve similar levels of precision, such as Precise Inland Surface Altimetry (PISA) [32]. The PISA algorithm states that over specular and quasi-specular surfaces it is not worth processing pulses outside the Fresnel zone (approx. 100 m) and, since the range migration variation within this period is neglible, it can be safely skipped.