## 4 Results and Validation
### Selected Results  
#### 4.2.1 Ray Roberts, Lake  
Lake Ray Roberts is the first study area which is presented in detail. In Section 3, Lake Ray Roberts was already selected to demonstrate our new approach for estimating surface area time series. The reservoir is located in Texas, United States of America. This reservoir has been created in the Mid 1980s by building a dam retaining the Trinity river. The surface area has been varying strongly up to a maximum of about 123 km\({}^{2}\) over the last few decades. In this area, the climate zone is defined as temperate without dry season and hot summer [36]. The annual cloud coverage is about 45% [38] and precipitation average is about 990 mm/y [37]. Figure 13 shows the resulting surface area time series (orange) and their errors (blue) of Lake Ray Roberts. Also, the initial surface areas including data gaps (gray) are shown in order to demonstrate the impact of this new approach filling the data gaps. For each month, the size of filled areas (green bars) is also given. Additionally, the availability of optical images from Landsat and Sentinel-2 is shown. In the study period between January 1984 and June 2018 theoretically 414 resulting months of surface area are possible. In the case of Lake Ray Roberts, there are 36 months (8.7%) where no optical images from any of the six satellites are available. In detail, the following monthly data of Landsat-4 (0.8%), Landsat-5 (83.6%), Landsat-7 (88.5%), Landsat-8 (98.4%), Sentinel-2A (96.8%) and Sentinel-2B (100.0%) are available. In 20 other months (4.8%), the processing of final surface areas failed. The main reason for this is that the optical images contain too big data gaps over the AOI leading to an invalid indexing or threshold computation. 358 months (86.5%) could be calculated successfully, wherein  
Figure 13: Water surface area time series (orange) and its errors (blue) of Lake Ray Roberts. 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 is presented. Finally, the water level time series from in situ stations and DAHITI which are used for validation are shown. another 68 months (16.4%) have been rejected because of too big indexing errors, cloud coverage, etc. Finally, 290 months (70.0%) of valid surface areas remain in the resulting time series. For the validation of surface area time series external water level data from in situ stations and satellite altimetry are used. In remote areas where no in situ data is available satellite altimetry provides reliable water levels for validation. On the example of Lake Ray Roberts we use both data sets for the validation to show the quality of both independent water level time series. We use the in situ data from the station Pilot Point which is provided by USGS. This time series contains 10,945 daily measurements since January 1988 which are merged on a monthly basis for validating monthly surface areas. The time series from satellite altimetry consists of 252 points and is based on data from Jason-2, Jason-3, and SARAL which have been available since July 2008. The water level time series from satellite altimetry has a lower temporal resolution than in situ data as measurements are only available when the satellite is crossing the water body. Figure 13 shows the used water level time series from the in situ station Pilot Point (red) and satellite altimetry (blue). Visual comparisons between water levels and surface areas show a very good agreement. The dam construction in the 1980s and fluctuations of the water levels (e.g., 1994, 2000, 2014) are clearly visible in both data sets. For a more accurate quality assessment, we compute the squared Spearman correlation coefficient \(R^{2}\) between surface areas and water level. \(R^{2}\) is recommended for monotonic function as the dependency between surface area and water level is. Figure 14 shows the resulting scatter plots of the correlations.