## 4 Results and Validation
### Selected Results
#### 4.2.3. Tharthar, Lake  
Lake Tharthar located in Iraq is an artificial lake created in 1956. It is located 100 km Northwest of Baghdad between the Euphrates and Tigris rivers. The climate in this area is arid and mostly dry. The averaged yearly precipitation is about 130 mm/y [37] which is much less than for Lake Ray Roberts and Poco da Cruz Reservoir. The annual cloud coverage of 27% [38] is also decreasing. Figure 19 shows the estimated surface area time series and area errors of Lake Tharthar. Additionally, the initial surface areas with data gaps and the filled area are shown in order to demonstrate the potential of the new gap-filling approach presented in this paper. The average monthly data gap is about 189.68 km\({}^{2}\) which is about 7% of the AOI. Figure 19 shows the resulting surface area time series (orange) with their errors (blue) of Tharthar Lake which shows seasonal variations and long-term trends. The surface area and water level time series clearly show the drought between 1998 and 2001, wherein also the seasonal variations disappeared. In the study period of 414 months, there are 22 months (5.3%) without any optical images available. In detail, the following monthly data of Landsat-4 (21.7%), Landsat-5 (86.5%), Landsat-7 (91.0%), Landsat-8 (100.0%), Sentinel-2A (100.0%) and Sentinel-2B (100.0%) are available. The processing of final surface areas failed in only 6 months (1.4%). Further 59 monthly data sets (14.2%) have been rejected because of quality deficits which leads to a final surface area time series of 327 months (79.0%). The lower cloud coverage and annual rainfall, leads finally to a more complete time series and a smaller average area error of about 2.72% of the AOI. For Lake Tharthar, only satellite altimetry can be used for validation as no in situ data is available. Therefore, we use the water level time series from satellite altimetry from missions Topex, Jason-1, Jason-2, and Jason-3. The time series contains 835 data points in the period between 1992 and 2018  
Figure 18: Relation between water level and surface area (hypsometry) used for cross-validation at Poco da Cruz Lake. The blue points (10% of all points) are used for the function fitting, the orange points for the validation. The two fitted curves are plotted in red (linear fit) and green (polynom). which are available every 10 days on average. Figure 19 shows the used water level time series from satellite altimetry (blue). Finally, we compute \(R^{2}\) between surface areas and water level. Figure 20 shows the resulting scatter plots of the correlations between surface area and satellite altimetry. \(R^{2}\) between initial surface areas and water levels from satellite is computed showing \(R^{2}\) 0.717 by using 259 months of data. Then, \(R^{2}\) increases up to 0.989 between the final filled surface areas and the water levels from satellite altimetry. After filling the data gaps, the quality improved by about 38%. Figure 19: Water surface area time series (orange) and its errors (blue) of Tharthar Lake. Additionally, the initial surface area with data gaps (gray) and the filled area (green) are shown. Also, the data availability of monthly optical images from Landsat and Sentinel-2 are presented. Finally, the water level time series from DAHITI which is used for validation is shown. Figure 20: Validation of surface area time series for Tharthar Lake using water levels from satellite altimetry. The improvement of our new approach is shown by comparing initial surface areas with data gaps (**left**) and final filled surface areas (**right**). For Tharthar Lake, we also perform a cross-validation shown in Figure 21. At first glance, the dependency between surface areas and water levels seems to be mainly linear but there are also smaller variations caused by the surrounding topography included. The cross-validation for Tharthar Lake yields for the linear fit an RMS of \(20.11\,\mathrm{km}^{2}\) which is 0.81% of the maximum area.