# Inland Water Level Monitoring from Satellite Observations:
## 3 Review Results
### Waveform Retracking  
Although satellite radar altimetry is an important technique for inland water level monitoring, the issues related to waveform contamination because of its relatively large footprint restrict its use for narrow rivers and small lakes [115]. Therefore, to overcome this problem, the waveforms need to be retracked with appropriate retracking methods. The analysis of a waveform provides valuable information for water level monitoring since it provides the distance between the satellite and the reflecting surface, hereafter range. Except for the range, other physical parameters such as the amplitude of the backscattered signal (Sigma0), and the significant wave height are deduced from the waveform thanks to retracking algorithms that consist of fitting a physical or an empirical model to the waveform. Different retracking algorithms are used on different surfaces since the waveform's shape highly depends on the reflecting surface characteristics, in particular surface roughness [24].  
The water surface orthometric height (WSH) is computed by the following Equation (2):  
\[\text{WSH}=\text{altitude}-\text{range}-\text{corr}-\text{geoid} \tag{2}\]  
Where altitude is the distance between the satellite's center of gravity and the reference ellipsoid (e.g., WGS84), computed by precise orbit determination, the range is the distance between the altimeter's antenna and the reflective surface estimated by the retracking algorithms, augmented by the distance between the altimeter's antenna and the satellite's center of gravity, corr represents the geophysical corrections, and geoid stands for the distance between the reference ellipsoid and the geoid model (e.g., EGM2008). Therefore, the water level is referenced relatively to the geoid model. Also, the geophysical corrections account for the variation of wave pulses because of atmospheric effects and the tides. The corrections are computed as can be seen in Equation (3), in which dry corr and wet corr represent the dry tropospheric and wet tropospheric correction respectively, while the iono corr stands for ionospheric correction.  
\[\text{Corr}=\text{dry corr}+\text{wet corr}+\text{iono corr}+\text{pole tide}+\text{solid earth tide} \tag{3}\]  
The retracker's waveform model fitted the acquired waveform to measure the mean range from the multiple facets within the instrument footprint could be separated into two categories. The model could have either a mathematical form derived from the expected statistics of the physical processes producing the return signal or an empirical form based on getting a robust estimate of the delay in the return signal. In physical waveform retracking, the models are based on the physics of the electromagnetic interaction between the transmitted wave pulse and the scattering surface. On the other hand, empirical models are simple and can be applied to all waveforms. Consequently, some approaches for determining the range of inland water bodies have an inheritance of the physical retrackers, while others are more empirical [48].  
As it can be understood, the quality of water surface height observations obtained from radar satellite altimetry can be improved by waveform retracking. That can be achieved by modifying the initial range derived from the two-way travel time of radar pulses [116]. Therefore, many studies are dedicated to waveform retrackers. In 1986, the Offset Centre of Gravity (OCOG) retracking method was proposed [117], also known as Ice1 or Ice, while nine years later the Threshold retracking algorithm was developed, which turned out to be superior to the 5-6 and 9-8 algorithms [118]. Apart from the different official retrackers of each satellite mission, other novel algorithms have been developed through the years to estimate the range from the altimeter to the water surface. Thus, the novel and improved retracking algorithms included in the publications for monitoring inland water levels are initially presented.