## 4 Results and Validation
### Quality Assessment and Discussion
All study areas are located in different climate zones which are shown in Table 4. The climate zones are defined mainly through precipitation and temperature which finally leads to a different cloud coverage and rainfall. In the data processing, a higher cloud coverage leads to more data gaps which have to be reconstructed. In our study, the annual cloud coverage varies between 22% for Salton Sea and 65% for Poco da Cruz Lake and Forggen Lake. The annual rainfall is not directly connected to cloud coverage as this depends also on the temperature. The annual rainfall varies between 71 mm/y for Salton Sea up to 1749 mm/y for Bankim Lake. are merged on a monthly basis for validation. In this study, water level time series from satellite altimetry are used for 28 study areas crossed by at least one satellite track. The performance of the new gap-filling approach shows improvements of the correlation coefficient \(R^{2}\) between initial and final area time series for all study areas also for satellite altimetry. The correlation coefficient \(R^{2}\) improved by between 0.014 and 0.734 for 28 comparisons with water level time series from satellite altimetry. Overall, the average correlation coefficient \(R^{2}\) increased from 0.611 for initial areas to 0.880 which is an improvement of about 44%. Despite different targets, the performance is similar by using in situ data for validation. The behavior of the correlation coefficient \(R^{2}\) resulting from satellite altimetry is comparable with correlation coefficients \(R^{2}\) using in situ data even though the lengths of the validation time series differ between both data sets. One can conclude that validating surface area time search using in situ or satellite altimetry provides reliable results in both cases. In order to demonstrate the potential of the gap-filling approach one can say that an improvement of about 37-44% can be achieved. In general, the best improvement can be achieved when the initial correlation coefficients \(R^{2}\) with water levels are between 0.4 and 0.6. For those cases, the final correlations have been increased to more than 0.8 or even 0.9 for almost all study areas. In addition to the validation using external data sets, an area error is given for each month. This area error contains a composite of uncertainties from the land-water indexing and the gap-filling step. All pixels which are not clearly identified as water or land within the AOI go into the final error. Moreover, all pixels which are filled in the gap-filling step and have a smaller long-term water probability than the computed threshold plus 5% go also into the error. This usually affects pixels which are located near the lake shore as pixels with a higher water probability are located within the lake or reservoir. This leads to an average area error between 1.31% and 9.68% of the AOI for all 32 study areas. Additionally, comparisons showed that there is no direct dependency between final correlation coefficients \(R^{2}\) and the resulting surface areas. To provide RMS values for validation, we performed a cross-validation for all study areas. This has been already shown in detail for the study areas Ray Roberts, Poco da Cruz and Tharthar. The methodology is described in Section 4.2.1. It is based on a relationship function between water levels and surface areas. Table 6 shows the cross-calibration results for all study areas. Moreover, it provides the number of points used for the regression and the number of points used for the validation of each study area. As can be seen from the table, the relative area errors remain below 8% for all 32 targets. The absolute RMS errors varies between less than 1 km\({}^{2}\) and about 40 km\({}^{2}\). Of course these values not only include the area uncertainties but may also reflect errors coming from the water level measurements or the assumed hypsometry function. When comparing both fittings (linear and polynomial) one can clearly see the influence of this choice. The optimal fitting function depends on the lakes (unknown) bathymetry.