**Christian Schwatke \* , Denise Dettmering and Florian Seitz**

Deutsches Geodätisches Forschungsinsitut der Technischen Universität München (DGFI-TUM), Arcisstraße 21, 80333 München, Germany; denise.dettmering@tum.de (D.D.); florian.seitz@tum.de (F.S.)

**\*** Correspondence: christian.schwatke@tum.de; Tel.: +49-89-23031-1109

Received: 2 April 2020; Accepted: 12 May 2020; Published: 18 May 2020

**Abstract:** In this study, a new approach for estimating volume variations of lakes and reservoirs using water levels from satellite altimetry and surface areas from optical imagery is presented. Both input data sets, namely water level time series and surface area time series, are provided by the Database of Hydrological Time Series of Inland Waters (DAHITI), developed and maintained by the Deutsches Geodätisches Forschungsinsitut der Technischen Universität München (DGFI-TUM). The approach is divided into three parts. In the first part, a hypsometry model based on the new modified Strahler approach is computed by combining water levels and surface areas. The hypsometry model describes the dependency between water levels and surface areas of lakes and reservoirs. In the second part, a bathymetry between minimum and maximum surface area is computed. For this purpose, DAHITI land-water masks are stacked using water levels derived from the hypsometry model. Finally, water levels and surface areas are intersected with the bathymetry to estimate a time series of volume variations in relation to the minimum observed surface area. The results are validated with volume time series derived from in-situ water levels in combination with bathymetric surveys. In this study, 28 lakes and reservoirs located in Texas are investigated. The absolute volumes of the investigated lakes and reservoirs vary between 0.062 km<sup>3</sup> and 6.041 km<sup>3</sup> . The correlation coefficients of the resulting volume variation time series with validation data vary between 0.80 and 0.99. Overall, the relative errors with respect to volume variations vary between 2.8% and 14.9% with an average of 8.3% for all 28 investigated lakes and reservoirs. When comparing the resulting RMSE with absolute volumes, the absolute errors vary between 1.5% and 6.4% with an average of 3.1%. This study shows that volume variations can be calculated with a high accuracy which depends essentially on the quality of the used water levels and surface areas. In addition, this study provides a hypsometry model, high-resolution bathymetry and water level time series derived from surface areas based on the hypsometry model. All data sets are publicly available on the Database of Hydrological Time Series of Inland Waters.

**Keywords:** water levels; surface areas; volume variations; hypsometry; bathymetry; lakes; reservoirs; remote sensing; DAHITI; modified strahler approach

#### **1. Introduction**

In the last years, discussions about global climate change have been increasing in the media and society, especially in connection with originators of climate change. Numerous climate studies are based on remote sensing data [1,2]. Since the 1970s, remote sensing has been providing valuable data for monitoring the global water cycle and its changes. Compared to the global water storage, only 0.013% [3] of the Earth's water is stored in lakes and reservoirs which are often affected by the

impact of climate change. Since the 1980s, the number of reported flood events of inland waters has increased by 38% from about 150 to more than 400 in 2008 [4]. Human influences on the terrestrial water such as the construction of dams or agricultural irrigation has also increased in last decades. In the worst case, the resulting water scarcity can lead to political crisis or wars [5]. Therefore, the impact of climate change on the availability of fresh water for human consumption is immense. In future, this will require sustainable water management by the countries [6]. Independent monitoring of inland waters is therefore essential. However, since the 1980s, the number of publicly accessible in-situ measurements has been steadily decreasing which is reflected in the data holding of the Global Runoff Data Center [7]. Especially in remote areas and in developing countries, there is a lack of in-situ measurements. Today, existing data gaps can be often filled by using remote sensing technology which has already provided valuable information about changes on Earth.

Modeling and understanding of the terrestrial water cycle is of great importance for analyses of climate change [8]. Hydrological models have been developed to gain more knowledge. Hydrological models such as the WaterGAP Global Hydrology Model (WHGM) use storage changes of lakes and reservoirs and river discharge to quantify the amount of water on Earth [9]. Data from the Gravity Recovery and Climate Experiment (GRACE), which measures the total water storage, are often used for calibration and data assimilation of hydrological models [10]. However, due to the spatial resolution of about 300 km and the required separation of the signal into surface water, soil moisture, and groundwater [11], GRACE cannot be used to derive volume changes of water bodies directly. GRACE has already been used in several studies to correct leakage errors [12] or to compare them with other geometrical approaches [13,14] to estimate volume changes of lakes.

Satellite altimetry was originally designed to monitor the sea surface and the existing sea level rise since the 1990s. For more than two decades, satellite altimetry has also proven its worth for monitoring water level changes of lakes, reservoirs and rivers [15–19]. Since satellite altimetry measures in nadir direction, only the water body directly crossed by a satellite track can be investigated. To reach water levels with an accuracy between several centimetres and several decimetres, the crossing track requires a track length above water of about a few hundred meters.

Since the 1970s, optical imagery has been used to monitor changes on the Earth's surface, such as flooded regions [20] or wetlands [21]. The Landsat mission with the satellites of Landsat-4/-5/-7/-8 has been providing optical images with constant quality since 1982. The Sentinel-2 mission has been providing high-resolution optical images for monitoring inland waters since 2015. In [22] an automated approach was shown that combines both data sets to extract surface areas of lakes and reservoirs.

The estimation of volume changes requires the most accurate bathymetry and water levels. The generation of both data sets can be done with different approaches which have already been used in different studies. The most precise approach for estimating volume changes is to use ground measurements. For this purpose, water levels from in-situ stations are combined with bathymetry based on ship surveys. This approach is carried out by the Texas Water Development Board (TWDB, https://www.waterdatafortexas.org) for about 120 lakes and reservoirs in Texas. The disadvantages of this method are that the surveys are time-consuming, cost a lot of money and are not easily applicable in remote areas. However, these data sets are very accurate and can therefore be used to validate volume changes based on remote sensing approaches. Up to now, it is not possible to measure the bathymetry of deeper lakes and reservoirs with the help of optical remote sensing images, because the light is attenuated as it enters the water. Even if several studies have successfully shown the potential for estimating bathymetry in shallow waters such as in coastal zones or shallow lakes [23–25], this technique can currently not be used for operational lake volume computation. Other studies estimated the lake bathymetry using the surrounding topographic slopes derived from a digital elevation model (DEM) [26]. Classical approaches for estimating volume changes of lakes and reservoirs are based on the combination of water levels from satellite altimetry and surface areas from optical images. However, the data sources used and the coupling methods applied to estimate volume changes differ considerably, which is shown in the following. Here, water levels from satellite altimetry

(Global Reservoir and Lake Monitor, Hydroweb, ICESat, River Lake Hydrology) are combined with surface areas derived from a few selected Landsat images by applying a polynomial function of degree 2 for the estimation of the hypsometric curve [27]. This approach was applied to three lakes with volumes between 5.5 km<sup>3</sup> and 35.5 km<sup>3</sup> and yielded percentage errors between 4.62% and 13.08%. In another study, water levels from satellite altimetry (Global Reservoir and Lake Monitor, Hydroweb, River Lake Hydrology) and surface areas derived from MODIS are combined with a linear hypsometry model [28]. The approach is applied on 34 globally distributed reservoirs with a volume between 3 km<sup>3</sup> and 165 km<sup>3</sup> . Another approach is to use water levels obtained from IceSAT and corresponding surface images from Landsat and MODIS of Lake Poopó. The resulting contour lines are then interpolated to obtain a partial bathymetry [29]. In another study, the satellite altimetry of Hydroweb is combined with selected images from Landsat and MODIS to estimate a hypsometric model [30]. This involves adjusting polynomial functions of degree 1, 2 or 3, depending on the relationship. Finally, the time series of the volume variations are calculated using a pyramidal approach. This approach showed 24 lakes and reservoirs with a surface area between 350 km<sup>2</sup> and 82,200 km<sup>2</sup> . In a further study, 137 lakes and reservoirs are analyzed by combining water levels from DAHITI and monthly land water masks from the JRC Global Surface Water (GSW) data set based on Landsat data. The volumes are calculated for lakes that have a linear relationship between water level and surface areas. Therefore, volume changes are estimated for consecutive changes of water level and surface area [31].

In this paper, a new approach to calculate time series of volume variations of small lakes and reservoirs (≤6.0 km<sup>3</sup> , <sup>≤</sup>782 km<sup>2</sup> ) is presented. For this purpose, water levels from satellite altimetry and high-resolution surface areas from optical imagery are combined to estimate a hypsometry model. Then, the hypsometry model is used to reconstruct water levels from surface areas to compute a bathymetry above the smallest available surface area. Afterwards, water levels and surface areas are intersected with the bathymetry to calculate a time series of volume variation with respect to the smallest surface area. Finally, all resulting time series of volume variation of 28 selected water bodies are validated with in-situ storage changes. In contrast to existing similar approaches, the quality and number of data sets used in this study differ. Since we are using more data of higher precision, as well as an advanced combination approach, our approach yield better accuracies also for smaller water bodies.

This paper is organized as follows. In Section 2, all the investigated 28 water bodies are introduced. Section 3 describes the data used for processing and validation. Section 4 describes in detail the methodology for combining water levels from satellite altimetry and surface areas from optical images to estimate volume changes. In Section 5, the new approach for estimating volume variations is presented in detail for three selected water bodies, followed by a validation and quality assessment of all water bodies. Finally, a summary and discussion of the results as well as an outlook is given.

#### **2. Water Bodies**

For the demonstration and validation of the new approach, we have selected 28 lakes and reservoirs in Texas, USA, which are shown in Figure 1. All selected study areas are well monitored by the Texas Water Development Board (TWDB). The TWDB provides in-situ water levels, ship survey data, bathymetry data, hypsometric curves, height-area-volume relationships, and detailed reports for each selected water body. This information is essential for a reliable quality assessment of our results.

Table 1 gives an overview of the 28 water bodies and their characteristics. For each water body, the minimum, maximum and variation of water level, surface area and volume are given based on in-situ data.

**Figure 1.** Map of 28 lakes and reservoirs located in Texas.


**Table 1.** List of water bodies and characteristics derived from available in-situ data.

<sup>1</sup> Based on water levels, surface areas and volumes provided by TWDB.

#### **3. Data**

In this study, water levels from satellite altimetry and surface areas from optical imagery are used to calculate time series of volume variations for lakes and reservoirs. For validation and quality assessment, we use water levels from in-situ stations, surface areas derived from bathymetric surveys and volumes resulting from the combination of water levels and bathymetry. Figure 2 gives a detailed overview of the data availability of the input data and validation data used for each of the 28 water bodies.

**Figure 2.** Data availability of the used input data from DAHITI (water level, surface area) and validation data from USGS/TWDB (water level, surface area, volume) for all water bodies.

#### *3.1. In Situ Data*

The availability of in-situ data is essential to assess the quality of our results. We deal with three different types of data sets, but only for one of them, ground truth data is available. Firstly, water levels from satellite altimetry are used which can be easily validated by using in-situ stations. However, surface areas and volume variations cannot be validated in a suitable way without an accurate bathymetry of the investigated lakes or reservoirs. Usually, bathymetry data are obtained by ship

surveys measuring the lake bottom. In combination with in-situ water levels, surface areas and absolute volumes can be derived in a good quality for validation.

The Texas Water Development Board (TWDB, http://www.twdb.texas.gov/) provides water levels, surface areas and volumes for approximately 120 lakes and reservoirs in Texas which will be used to validate this study. The water levels are derived from in-situ stations maintained primarily in cooperation with the United States Geological Survey (USGS). In addition, the TWDB carries out bathymetry surveys which are conducted at irregular intervals. The lake volumes are then calculated using rating curves. However, since the bathymetry surveys refer to the water level on the day of the survey, no directly measured surface areas and volumes are available above that level. These values can only be estimated by extrapolating the calculated rating curve. This fact must be taken into account when validating the resulting volume variations in this study. The surface area time series and volume time series provided in the TWDB can also contain offsets between time periods of the recalculated rating curves. Remaining offsets are corrected to obtain consistent time series for validation. In addition, the TWDB provides reports for each water body containing detailed information on the surveys and the calculated height-area-volume relationships. This is very helpful in this study to understand and analyse inconsistencies in the time series used for validation.

We use the TWDB data holding to validate our results. Water level time series and surface areas time series are used for the quality assessment of the inputs used. In addition, we use the absolute volume time series to validate the resulting time series of volume variations. This is done for 28 investigated lakes and reservoirs in Texas. Figure 2 shows the data availability of water levels (light blue), surface areas (orange) and volumes (light green) provided by USGS/TWDB and used for validation in this study.

#### *3.2. Water Level Time Series from Satellite Altimetry*

In 1992, Topex/Poseidon was launched as the first operational satellite for monitoring sea level. Since then, several altimeter missions have been launched with improved equipment. In the last few decades, satellite altimetry has also been used for hydrological application such as measuring water levels of lakes, reservoirs, rivers and wetlands. Envisat was the first altimeter mission with the potential to derive water level time series of smaller lakes and rivers with sufficient accuracy between a few centimeters and a few decimeters. However, not all inland waters can be investigated, as the altimeter satellites only measure in nadir direction.

DGFI-TUM developed an approach to derive water level time series for lakes, reservoirs, rivers and wetlands. This method is based on a Kalman filtering approach and extended outlier detection [18]. In the first step, all measurements of different altimeter missions are homogenized by using identical geophysical corrections and models. Additionally, a multi-mission cross-calibration is applied to minimize range biases between different altimeter missions [32]. Then, outliers are rejected for each crossing altimeter track by applying different thresholds (e.g., latitude, water level, height error, etc.). Finally, the remaining water levels and their errors are combined in a sequential least square approach to achieve one water level for each day.

Currently, DGFI-TUM's web portal DAHITI makes more than 2600 respective water level time series freely available. In this study, we use 28 DAHITI inland water bodies. The water level time series are based on the altimeter missions Topex/Poseidon, Jason-1/-2/-3, ERS-2, Envisat, SARAL, Sentinel-3A/-3B, ICESat and CryoSat-2. Depending on the location of the water body and the orbit of the altimeter mission, only a subset of missions can be used for processing, resulting in time series with different time spans and numbers of points. Each point contains several altimeter measurements which are combined in the Kalman filtering step of the DAHITI approach. The time sampling also varies between 10 days (Topex/Poseidon, Jason-1/-2/-3) and 369 days (CryoSat-2). For the study targets, the resulting Root Mean Square Errors (RMSE) compared to the in-situ station for the time series used varies between 0.13 m and 0.78 m (average: 0.25 m). In this approach, the used water levels from DAHITI can also be replaced by other data sources of water levels.

#### *3.3. Surface Area Time Series and Land-Water Masks from Optical Satellite Imagery*

In 1972, Landsat-1 was launched as the first satellite in the Landsat series developed by NASA. It was followed by Landsat-2 and Landsat-3 in 1975 and 1978, but Landsat-4 was the first satellite to provide optical images with a spatial resolution of 30 m. It was followed by its successors Landsat-5 (1984), Landsat-6 (1993, launch failed), Landsat-7 (1999) and Landsat-8 (2013). All satellites are equipped with a multi-spectral sensor and a thermal mapper. The European Space Agency (ESA) developed and launched Sentinal-2A and Sentinal-2B in 2015 and 2017, respectively. Sentinal-2A/-2B measures with similar bandwidth as Landsat, but the spatial resolution improved to 10 m and 20 m, respectively.

DGFI-TUM developed an approach for the automated extraction of consistent time-variable water surfaces of lakes and reservoirs based on Landsat and Sentinel-2 [22]. Currently, DAHITI freely provides about 60 surface area time series. The approach is based on a land-water classification using five different water indices. The resulting land-water masks with data gaps caused by clouds, snow or voids are stacked to calculate a long-term water probability mask using all available scenes since 1984. Finally, the long-term water probability is used to fill the remaining data gaps in an iterative approach. The temporal resolution varies between 16 days in the beginning, when only a single Landsat-4 mission is available, and nowadays 2-3 days, when Landsat-7/-8 and Sentinel-2A/-2B take measurements. Consistent and homogeneous surface area time series and corresponding land-water masks (as visible in Figure 3) are used in this study. The advantage of optical imagery over satellite altimetry is the swath measuring technique which has the potential to observe water bodies worldwide. For the test sites, the validation of surface area time series with surface areas derived from in-situ water levels in combination with bathymetry surveys leads to RMSE that vary between 0.13 km<sup>2</sup> and 21.75 km<sup>2</sup> (average: 2.74 km<sup>2</sup> ). In this approach, the used surface areas from DAHITI can also be replaced by other data sources of surface areas.

**Figure 3.** Three selected land-water masks of Ray Roberts Lake from 20 September 2000 (blue, 70.490 km<sup>2</sup> ), 8 September 2013 (orange, 95.750 km<sup>2</sup> ) and 27 December 2018 (green, 114.150 km<sup>2</sup> ).

#### **4. Methodology**

This section describes in detail the new approach to estimate time series of volume variations. A flowchart of the processing steps is shown in Figure 4. First, the input data are extracted from DAHITI, which includes water levels, surface areas, and land-water masks. Based on water levels and surface areas, a hypsometric curve is calculated which describes the relationship between both parameters. The hypsometry curve is then used to reconstruct water levels for all surface areas. Then, the bathymetry is calculated by stacking the land-water masks and associated water levels. Finally, the time series of volume variations is computed by using the calculated bathymetry and the water levels from satellite altimetry and surface areas, respectively. The resulting data sets such as hypsometry, water levels derived from surface areas and hypsometry, bathymetry and time series of volume variations are transferred to the DAHITI web portal.

**Figure 4.** Flowchart of the applied processing steps (blue) and data sets (light red) used for estimating time series of volume variations. Green arrows indicate input data and red arrows indicate output data of the processing steps.
