**5. Results, Validation and Discussion**

In this section, the estimated time series of volume variations are presented and validated. This is performed in detail by three examples representing different reservoir sizes with input data of different quality, namely: Ray Roberts Lake, Hubbard Creek Lake and Palestine Lake. Additionally, a general quality assessment will be carried out for all 28 water bodies introduced in Section 2.

### *5.1. Selected Results*

#### 5.1.1. Ray Roberts, Lake

Ray Roberts Lake is a reservoir located in the North of Dallas, Texas. The dam construction started in 1982 and was completed in 1987. In 1989, the reservoir was filled. Since then, the surface area has varied between 70.49 km<sup>2</sup> and 123.22 km<sup>2</sup> [35].

#### Extraction of Input Data

Figure 7 shows the used input data separated into water levels (top) and surface areas (bottom). The water level time series (blue) of Ray Roberts Lake shown the top plot contains 355 data points in the period between 23 July 2008 and 25 February 2020 derived from the satellite altimeter missions of Jason-2 and Jason-3. The water level time series varies between 189.89 m and 195.81 m. The temporal resolution is about 10 days. For validation, the water levels of the gauging station (black) of Pilot Point (ID: 08051100) at Ray Roberts Lake provided by the TWDB/USGS are used. It results in an RMSE of 0.15 m and a correlation coefficient of 0.98 by using 355 contemporaneous points. An offset of −0.11 m between both time series occurs (corrected in the Figure) which can be caused by different vertical datums.

**Figure 7.** Used water level time series from satellite altimetry and surface area time series from optical imagery for Ray Roberts Lake. Additionally, available validation data provided by TWDB and resulting quality assessment are shown.

The surface area time series (green) derived from optical imagery of Ray Roberts Lake is shown in the bottom plot of Figure 7. It contains 543 data points in the period between 10 June 1989 and 25 March 2019 which are derived from the optical imagery satellites Landsat-4/-5/-7/-8 and Sentinel-2A/-2B. The surface areas vary between 70.49 km<sup>2</sup> and 123.22 km<sup>2</sup> . For validation, the surface area time series from TWDB is used. Therefore, water levels from the gauging station and bathymetry were combined. The bathymetry was derived by a survey performed between 11 September 2008 and 15 October 2008 using a multi-frequency, sub-bottom profiling depth sounder [35]. Since the water level at the time of the survey was only 192.79 m, no groud-truth bathymetry information is available above that height, i.e., for surface areas larger than 115.92 km<sup>2</sup> (dashed black line). That's why the TWDB surface area time series is missing above that value. The comparison of both time series results in an RMSE of

1.48 km<sup>2</sup> (about 1%) and a correlation of 0.98 by using 380 points. Additionally, an offset of 3.03 km<sup>2</sup> occurs which may be caused by the DAHITI approach to classify the optical images.

#### Estimation of Hypsometric Curve

For estimating the hypsometric curve of Ray Roberts Lake 262 data points are used, for which the time difference between water level and surface area is smaller than 10 days. In Figure 8, the area of data (orange rectangle) indicates the range of all water levels and surface areas for Ray Roberts Lake. It can be seen that the water levels from satellite altimetry do not cover the full range of surface areas due to the shorter time series. This requires a good estimate of the hypsometric curve in order to extrapolate the uncovered range of surface areas between 70.49 km<sup>2</sup> and 88.36 km<sup>2</sup> . This example already shows occurring small discrepancies for smaller extrapolated values of the hypsometric curve compared to in-situ data which will be discussed in the next processing step.

**Figure 8.** Hypsometry curves of Ray Roberts Lake using modified Strahler approach (blue), linear function (dashed red) and polynomial function (dashed green). Additionally, a hypsometric curve (dashed black) from the TWDB is shown as comparison.

Based on the methodology described in Section 4.2, the hypsometric curve (blue) is estimated following the modified Strahler approach. It shows a correlation coefficient of 0.93 and an RMSE of 0.26 m with respect to the 262 points of input data. For comparison, hypsometric curves based on a linear function (dashed red) and a polynomial of degree two (dashed green) are computed and shown in Figure 8. The resulting correlation coefficient and RMSE decreased slightly for the linear (R<sup>2</sup> : 0.88, RMSE: 0.34 m) and polynomial (R<sup>2</sup> : 0.92, RMSE: 0.28 m) function. The linear hypsometric curve agrees quite well with the used data points below 115 km<sup>2</sup> where the relationship is almost linear. However, the exponential increase of the hypsometric curve above 115 km<sup>2</sup> cannot be captured by a linear function. Otherwise, the polynomial function shows a good agreement for larger areas but has an unrealistic behavior for small areas since the hypsometric curve has to be monotonically increasing. Apparently, both approaches show their disadvantages when the functions are used for the extrapolation of data. So far, this quality assessment can only describe the performance within the range where data is available and not the capability for the extrapolation.

Additionally, the hypsometric curve (dashed black) provided by the TWDB from the survey in autumn 2008 is shown for comparison. Since heights of the TWDB rating curve are referred to

NGVD29, we apply an offset of −0.11 m derived from the validation of the water level time series with in-situ data in order to achieve consistent heights for comparison. However, an offset with respect to the used points still remains. Furthermore, the TWDB rating curve is limited to a water level height of 192.79 m at which the bathymetric survey was carried out. A visual comparison with the other three hypsometric curves coincidentally shows the best agreement with the linear function. The reason is the lack of information for surface areas smaller than about 90 km<sup>2</sup> for the estimation of a precise hypsometric curve.
