# Inland Water Level Monitoring from Satellite Observations:
## 3 Review Results
### Waveform Retracking
#### 3.2.1 Novel and Improved Retracking Algorithms  
In 2018, a novel and improved empirical algorithm was presented to estimate water surface heights from processing CryoSat-2 InSAR waveforms [64]. The ImpMWaPP algorithm integrates the advantages of the Multiple Waveform Persistent Peak (MWaPP) retracker and the error mixture model [22; 23]. They used in situ gauge data of seven lakes, as well as five existing retrackers for the evaluation of the performance of the proposed ImpMWaPP algorithm. The five existing algorithms used for the evaluation are The Narrow Primary Peak Threshold retracker (NPPTR) with a 50% threshold level (NPPTR [0.5]) [119], NPPTR with an 80% threshold level (NPPTR [0.8]) [119], the Narrow Primary Peak OCOG retracker (NPPOR) [119], the MWaPP retracker [23], and ESAL2 [117]. The root-mean-squared errors (RMSEs), between CryoSat-2 and in-situ data, obtained by the proposed algorithm range between 0.085 m and 0.159 m. Also, ImpMWaPP outperforms the other five algorithms in handling multi-peak waveforms since it obtains the lowest mean RMSE (0.175 m) and the lowest standard deviation (Std) (0.23 m) among all lakes. Therefore, they conclude that the new retracker can effectively process multi-peak waveforms over inland water. It can also extract accurate results independently of ice existence but is more proper for lakes frozen in winter. The next year, a new approach to selecting an optimal peak in a given waveform retracked by the Threshold method was developed [120]. The Threshold algorithm was presented in the study of ice sheet elevation changes. Its implementation is easy, but it is sensitive to surface topography [118]. In this research, data from Sentinel-3A was used to extract water level heights. Instead of the threshold algorithm, the Ocean, OCOG, Ice-sheet, Sea-ice, and Tracker were used for the evaluation of water heights. Also, the results using the new optimized peak selection (optimal and mean-all sub-waveforms) methods show a significant improvement of 50% in RMSEs and 22% in correlations compared to level-2 data relative to in situ gauge measurements. Also, the first meaningful sub-waveform has a contribution of more than 90% in the measurements of precise water heights. Furthermore, a modified retracker was used to determine inland water surface heights from the first altimetric sub-waveform [75]. They used T/P and Jason series missions to retrieve suitable waveforms, as well as in-situ data and other retrackers for the evaluation of the novel method. The retrackers used are Ice, MLE5, MLE4 [121], T, ST, and MST. Jason-2 Sensor Geophysical Data Records (SGDR) provide levels using Ice, MLE3, and MLE4 retrackers. Using the new methodology, the Std of differences between water levels extracted from Jason-2 and in-situ data is 0.06 m compared with Std using Ice Retracker which ranges between 0.08 m and 0.11 m. Also, T/P is less accurate than the combined Jason missions with Std equal to 0.07 m using the new modified retracker. As it is shown, the Ice algorithm is more precise than the oceanic MLE retrackers over inland waters. Moreover, the sub-waveform retracker with threshold 0.1 extract water levels of marginally higher accuracy than the SGDR retrackers. In addition, an automatic multiscale-based peak detection retracker (AMPDR) was presented, suitable for CryoSat-2, Sentinel-3, and Jason-2/-3 missions [67]. The retracker extracts a robust threshold level for each track and using a shortest-path algorithm can obtain the surface water level from the multipeak waveforms. Its implementation is easy and computationally efficient, extracting accurate results. To evaluate the performance of the AMPDR algorithm in-situ gauge data as well as seven existing retrackers were used. The retrackers used for the evaluation are (NPPTR [0.5]), (NPPTR [0.8]), NPPOR, MWaPP, ESA L2/WWMFW, SAMOSA, and ALES+ [23; 117; 119; 122; 123].