## 5 Results and Discussion
### Water Volume Variations  
Figure 13 shows the results of estimating water volume variations (\(\Delta\)V) by applying [PERSON]'s formula in Equation (1), based on altimetry water levels and surface areas estimated by satellite images. Validation of the results was made with the aid of in situ water levels. (Figure 13a) shows a scatter plot of the measured \(\Delta\)V in million cubic meters (MCM) based on altimetry and \(\Delta\)V based on in situ water levels, and presented the water volume variations above the lowest reference water level. A second order polynomial fitting is plotted in the same figure, and a correlation coefficient R\({}^{2}\) = 0.83. An NRMSE value of approximately 12.8% was presented (Figure 13b), and also shows water volume variations over a time period from June 2016 to July 2019. The results are relatively similar to the results of [PERSON] [27], who also applied the [PERSON] method for the period from 2014 to 2015 to estimate water volume variations relative to reference water level for the southern part of AHDL in Egypt. She used available free Landsat and radar altimeter datasets with R\({}^{2}\) = 0.98 and RMSE values that were 13.2% of the mean volume variation. The (\(\Delta\)V versus \(\Delta\)L) relationship in (Figure 14) shows the radar altimetry water levels and the volume variation estimate by [PERSON]'s method (\(\Delta\)V) during the same period of the previous plot. This is called \"Test dataset\". A second order polynomial fitting exhibits a correlation coefficient R\({}^{2}\) = 0.89. Figure 11: Scatter plot of the altimetry level and in situ level with corresponding Sentinel-3 derived water areas on the y-axis. Figure 12: Estimated surface area of the AHDL over the period between 2016 and 2019, surface area estimated by the in-situ level and altimetry level as input of the model, and surface area estimated by unsupervised method in Section 4.2. The (\(\Delta\)V) and (\(\Delta\)A) relationship in (Figure 15a) shows the variation in water area (\(\Delta\)A) estimated in Section 5.2 with volume variation estimated by [PERSON]'s method (\(\Delta\)V) estimated in Section 5.3, and the \"Test dataset\" represented the \(\Delta\)V estimated by the radar altimetry water levels again during the same period. In this case, a 2\({}^{\text{nd}}\) order polynomial fitting exhibits an R\({}^{2}\) = 0.55, the \"Validation dataset\" represented the \(\Delta\)V estimated by the in situ measured levels with NRMSE value 12.8% over the same time period, as shown in (Figure 15b). In addition, the validation of the studies carried out at Lake Mead in USA by [40], Lake IJsselin in the Netherlands, and Lake Tanain in Ethiopia to estimated water volumes of all lakes agreed well with in situ water level R\({}^{2}\) ranged from 0.95 to 0.99, and the RMSE was within 4.6 to 13.1% of the mean volumes of in situ measurements, which is consistent with the estimation results of this study on AHDL. Figure 14: Relation between water level variation in meters and volume variation in MCM of AHDL. Figure 13: The results of estimating water volume variations (\(\Delta\)V) by applying [PERSON]’s formula. (**a**) Relation between estimated \(\Delta\)V by Sentinel-3 altimetry water level and in situ water level in MCM using Heron method. (**b**) Water volume variations estimated by Heron method over a time period with NRMSE value between altimetry water level and in situ water level. The accuracy of \(\Delta\)V affected by the relation between water levels and corresponding surface areas, as when water levels increase, the volume variations estimated from Heron methods will increase. Moreover, the surface area deduced from satellite images will increase especially at boundary regions more than the middle stream of the lake, which may cause unreal water volume variations at the lake [31].