Constructing Reservoir Area–Volume–Elevation Curve from TanDEM-X DEM Data

Area–volume–elevation (AVE) curves are critical for reservoir operation rules. However, such curves are not publicly available for most global reservoirs. Here, we present a framework to derive reservoir AVE curves from TanDEM-X data, using Lake Mead (~600 km2) as an example. First, the maximum water extent from 1984 to 2018—provided by the global surface water (GSW) dataset—was used as a mask to obtain the TanDEM-X data. Then, the TanDEM-X water indication mask (WAM) was applied to the extracted TanDEM-X data to obtain the visible bathymetry, which represents the topography between the maximum extent (according to GSW) and the water extent from WAM. Last, the AVE curve was generated by integrating the volume values from the top to bottom layers. TanDEM-X also captures the elevation values of the transitional waters, which are defined as the difference between the highest and lowest water levels. The transitional waters were obtained by thresholding amplitude and coherence images, and their elevations were then added to the visible bathymetry to extend the AVE curves with an elevation range extending from 344–369 m to 341–369 m. Validation results against in situ lidar survey values suggest a high-accuracy of elevation–area (E-A) relationships with R2 values of >0.99 and NRMSE values from 2.11% to 2.45%, and elevation–volume (E-V) relationships with R2 values of 1 and NRMSE values from 1.11% to 1.29%. Results also show that TanDEM-X data can capture the interannual variations due to multiple acquisitions, and that the elevation measurements for the lake shore areas are reliable.


I. Introduction
Four billion people are facing water scarcity [1], and freshwater-related risks are increasing significantly with the earth's changing climate [2]. Under these circumstances, reservoirs are playing an increasingly important role in the regulation of freshwater and the mitigation of damages-such as hydropower, water supply, irrigation, and flood control. Additionally, reservoirs are essential constituents of the terrestrial system and are deeply involved in thermodynamic, hydrological, and biogeochemical processes [3]- [6]. As the most important metric capturing the physical features of reservoirs, the area-volume-elevation (AVE) curves have been used as critical inputs in modeling these processes [7], [8] although more and more models will require 3-D bathymetry maps in the future [9]. Moreover, the AVE curve can provide useful information related to the monitoring of reservoir storage variations using satellite optical imageries [10]- [15].
Despite its importance, the AVE curve has been oversimplified in many studies due to the limited availability of necessary data from local to global scales. For example, the floodwater depth estimation tool (FwDET) used water surface elevation values from the existing DEM of Lake Houston and found a considerable underestimation over the reservoir area [16]. Moreover, most of the large-scale hydrological models and earth system models (e.g., Community Land Model [17]) assume the constant water surface area and depth, which may contribute to the uncertainty and inconsistency of regional and global simulations [17], [18]. Recently, Yigzaw et al. [19] published the first global storage-areadepth dataset for over 6800 reservoirs by appropriating the reservoir geometries. However, results can have relatively large uncertainties and errors, especially for the reservoirs with irregular and complicated shapes. Additionally, they only evaluated the storage-depth relationships, while the performance levels of area-depth relationships were undetermined.
The AVE curves are generally obtained from surveying, simulation, and/or remote sensingbased methods. Surveying-based methods (e.g., lidar survey and sedimentation survey) can provide the most accurate curves. However, it is expensive and labor-and time-intensiveespecially for large reservoirs. Simulation-based methods use mathematical equations to derive the AVE curves from the reservoirs' morphological features, but they are highly restricted by the complexity of reservoir geometry [19], [20]. In recent decades, satellite remote sensing has offered the unprecedented alternative of monitoring reservoirs from space. By pairing up the reservoir area and elevation information obtained from satellite observations, the elevation-area (E-A) relationship can be derived and used to calculate the volume values needed to obtain the AVE relationships [10]- [14], [21]. In general, remotesensing-based methods require a number of pairs to generate a robust E-A relationship. For example, Gao et al. [10] combined Moderate Resolution Imaging Spectroradiometer which were then used to estimate the volume variations. More recently, Li et al. [13] developed a method that projects lidar tracks onto the water occurrence image-generated from the water classification results of Landsat scenes from 1982 to 2017-to derive the AVE relationships. Although a minimum of one single lidar track is required (for a given reservoir), this technique still relies on long-term Landsat observations. In addition, the process of associating elevation with area values may introduce additional errors because they are collected by different satellite missions with time gaps. Most recently, Li et al. [14] generated the AVE relationships for 347 reservoirs at a global scale using multisource satellite altimetry and imagery (though it focused on relatively large reservoirs).
In comparison, topographic data can provide both area and elevation information, and has been an excellent data source for deriving AVE curves [15], [22]- [25]. During the last two decades, the availability of global DEM datasets has significantly increased. These include the Shuttle Radar Topography Mission (SRTM) [26], the National Aeronautics and Space Administration's DEM (NASADEM) [27], the Advanced Land Observing Satellite (ALOS) Global Digital Surface Model (AW3D30) [28], the Multierror-Removed Improved-Terrain (MERIT) DEM [29], and the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global DEM (GDEM) [30]. The SRTM DEM is the most complete and commonly used global DEM dataset in hydrology [26]. However, the SRTM data were collected within an 11-day period in February 2000 [26]-when many reservoirs experienced high-fill-which makes it difficult to derive AVE curves for these reservoirs.
In this article, we propose a framework to derive reservoir AVE curves using TanDEM-X [31], [32] data. This framework provides the following advantages over the other aforementioned methods: First, the elevations and their associated area values can be obtained simultaneously from one image, which provides high spatiotemporal consistency; and, second, the TanDEM-X dataset is a composite DEM product based on measurements from multiple acquisitions from 2010 to 2015. This can provide more reliable measurements that are less limited by high-level conditions when compared to DEMs collected with a short acquisition phase (such as the SRTM DEM). Furthermore, we adopted the maximum water extent provided by the global surface water (GSW) dataset (based on the Landsat archives from 1984 to 2018), which can better delineate the maximum boundaries of the reservoirs. Validations against lidar surveyed AVE curves suggest a high-level accuracy for this method.

A. Study Area and Datasets
Lake Mead (36.25°N, 114.39°W)-formed by the Hoover Dam in September 1935-was selected as the study area. Located on the Colorado River, it is the largest reservoir in the United States in terms of storage. However, the reservoir volume has experienced a significant decrease since 2000 due to drought and increased water demand, with annual mean water levels decreasing from 366.84 (2000) to 328.34 m (2016). spatial resolution of 90 m were obtained from the German Aerospace Center (DLR) 1 . The global accuracy of the absolute elevation values is 10 m with a 90% confidence level [35]. In addition to the DEM data, the water indication mask (WAM) [36]-also provided by DLRcan be used to identify the water pixels. Note that, due to the low coherence of the water body in the interferometric data, the water heights are random and may not be meaningful in the TanDEM-X dataset [34]. However, during the TanDEM-X acquisition time, coastal areas (i.e., transitional waters) had multiple states of coverage. Due to the interannual and seasonal water level variations, these pixels were sometimes covered by water while at other times were exposed as land. In the final TanDEM-X DEM product, the elevations observed from all of the acquisitions at a given pixel were weighted to generate a composite value for that pixel. Specifically, the multiple elevations were weighted by Height Error Map (HEM) values in the fusion process, which assures a relatively low (to zero) weight/contribution for the measurements associated with temporary water coverage [34]. Therefore, the elevation values for transitional water pixels are redeemed as reliable.
The maximum water extent of Lake Mead was extracted using the GSW dataset 2 , which is based on the long-term Landsat measurements from 1984 to 2015 [37]. Recently, the GSW dataset was further extended to the year 2018. This represents the maximum extent that water has ever been detected from 1984 to 2018, which can better delineate the water boundaries when compared to those from the HydroLAKES [38] and Global Reservoir and Dam (GRanD) [39] databases-which were mainly derived from various vector datasets and static remote sensing imagery (e.g., SRTM DEM).
The in situ AVE curve of Lake Mead was derived from a lidar survey conducted by the United States Bureau of Reclamation (USBR) in 2009, and was used for validation purposes. The lidar survey with 1-m resolution collected detailed elevation values ranging from 333.76 (1095 ft) to 374.90 m (1230 ft). The associated area and volume for each elevation was obtained from the lookup tables provided by USBR [40].

B. Methods
The flowchart of this framework for deriving the AVE curve is shown in Fig. 1. First, the TanDEM-X data were transformed from WGS84 ellipsoidal heights to EGM96 orthometric heights using the VDatum tool provided by the National Oceanic and Atmospheric Administration (NOAA) 3 . After this, TanDEM-X elevation values for Lake Mead were extracted using the GSW maximum water extent as a mask, and then the elevation imagery was transformed from GCS_WGS_1984 to an equal-area projection (i.e., World_Cylindrical_Equal_Area) with each pixel representing a 90 by 90 m area. In the next step, the WAM layer was overlaid onto the DEM imagery to mask out the water area and obtain valid elevation values, which represent the visible bathymetry of Lake Mead. The visible bathymetry represents the area between the maximum extent (according to the GSW) and the extent of the water mask (from WAM). All elevations with the same value were taken as a band, and the area associated with each band was calculated. Note that the 1  TanDEM-X values were transformed into integers, and therefore, the elevation bands are at 1-m intervals. The band areas were sorted into a descending order, and the bands associated with the most pixels-which represent 90% of the visible bathymetry area-were used to generate the AVE curve. This helps to eliminate the effects of the extreme elevation values, which only account for a small portion of the overall population of elevation values. Starting from the top band, the area value within each band was calculated by integrating the enclosed pixels, generating the E-A relationship. Last, the volume associated with the n th band (V n ) was calculated after the following equation: where V c is the volume at capacity provided by the USBR [40]. A i is the entire water surface area enclosed by the i th band, which corresponds to the elevation E i . Thus, the volume value corresponding to each band was obtained, and the elevation-volume (E-V) relationship was derived. Finally, the AVE curve was generated by combining the E-A and E-V relationships.
As an important by product of the TanDEM-X dataset, WAM reflects the process of water body detection. Because water areas are generally very incoherent, the water heights are random in the TanDEM-X dataset and may not be meaningful [34]. However, the WAM layer can be used for delineating the coastal waters, and the DEM mosaicking approach can take full advantage of the multiple measurements [41]. Therefore, the transitional waters in lake shore areas may provide additional information for AVE generation. The transitional waters are defined by the difference between the highest and lowest water levels, which represent interannual variations. Depending on the water level, these pixels are sometimes covered by water but other times are exposed as land. WAM uses three criteria to detect water: 1) a strict radar brightness threshold of −18 dB for the SAR amplitude (strict AMP Thresh1); 2) a more relaxed radar brightness threshold of −15 dB for the SAR amplitude (relaxed AMP Thresh2); and 3) a threshold of 0.23 for the interferometric coherence (COH Thresh) [36]. Globally, the accuracy for water bodies detected from amplitude and coherence images are up to 71.3% and 71.7%, respectively [36]. The WAM values are coded in a bit mask, with each bit value representing the number of acquisitions with water detected [34]. The WAM values can be used to derive a binary water mask by thresholding the 0-255 WAM byte values. For example, by selecting WAM values from 3 to 7, a water mask using a relaxed AMP-Thresh2 can be obtained. In this case, we first added the pixels from the water mask of the relaxed AMP-Thresh2 to the visible bathymetry, which was then used to derive a new AVE curve. Then, we sequentially included the water mask using different criteria-the strict AMP-Thresh1 (9 ≤ WAM ≤ 31), 1× water with the COH-Thresh (i.e., water was detected once, 33 ≤ WAM ≤ 63), and 2× water with the COH-Thresh (i.e., water was detected twice, 65 ≤ WAM ≤ 95)-and then generated the corresponding AVE curves. It should be noted that we did not use the criteria defined by 3× water with the COH-Thresh (i.e., water was detected three or more times, WAM ≥ 97) because these pixels primarily refer to the permanent waters with extreme height values that are not meaningful.

A. Visible Bathymetry Derived From TanDEM-X Data
The maximum extent of Lake Mead from GSW is 601.67 km 2 , with valid elevation values (i.e., WAM = 1) ranging from 228.66 to 560.35 m, which cover an area of 193.42 km 2 . The extreme high and low elevation values are primarily attributed to two sources. The first comes from the surrounding pixels that represent mountains, which were misclassified as water during the production of the maximum extent layer. The second source is related to the fact that water bodies have very incoherent areas, combined with the fact that measurements of the pixels near these water bodies may be interfered with. However, these extreme values only account for a small portion of the overall data and were excluded from the AVE generation. The elevations ranging from 344 to 369 m-which represent 90% of the visible bathymetry area-were used to generate the AVE curve. This indicates that the water levels during the TanDEM-X acquisition period (2010-2015) were generally less than 344 m due to the historically extended drought since 1999. This is consistent with in situ measured elevation values during this period, which range from 329.37 to 345.70 m. The TanDEM-X data over Lake Mead and its two subregions are shown in Fig. 2. For visualization purposes, the pixels with elevations greater than 369 m were excluded, and the pixels with elevations lower than 344 m (and/or within the WAM area) were assigned a value of 344 m. Overall, the elevations show well-organized patterns and gradients (for example, the shapes of islands were clearly captured). (water was detected at least three times, WAM ≥ 97). Most of these are located in permanent waters with nonmeaningful elevation values.

B. Validation of the AVE Curve Using Lidar Surveys
The E-A and E-V relationships were compared with their counterparts from the lidar survey (see Fig. 5), and the validation results show good agreement (see Fig. 6 and Table I). In addition to the AVE curve from the visible bathymetry (Model 1), we also evaluated the curve's accuracy when including the transitional water pixels with WAM thresholds ( . Moreover, for a given elevation value below 350 m, the relative absolute error of the area decreases from Model 1 to 5 (see Fig. 6). However, the inclusion of transitional waters did not improve the accuracy of the E-A relationship when the elevations were over 355 m (see Fig. 6). This indicates that transitional waters with elevation values larger than 355 m are not very reliable (although we note that these unreliable transitional waters only account for a small portion; Fig. 4).
With regard to the E-V relationships, it is evident that they are in very good agreement with the lidar survey (see Figs. 5 and 6)-with NRMSE values from 1.11% to 1.29% (see Table  I). It is observed that the discrepancies in the E-A relationships have only small effects on the E-V relationships. The relative absolute errors of the volume values increase as the elevation decreases (see Fig. 6). This is because the storage values are integrated from the top and the errors are accumulated at the bottom. Although the transitional waters did not improve the E-V relationship (due to the large vertical bias for elevations over 355 m), all of the E-V cures show good results, with the highest relative absolute error of the volume value being less than 2% (see Fig. 6).

A. Comparison With SRTM DEM
SRTM DEM data have been widely used in hydrologic applications [26], [42]- [44]. The linear vertical absolute height error is less than 16 m with a 90% confidence level [26]. In order to compare with the results from the SRTM, we collected SRTM version 3.0 dataprovided by JPL/NASA with 30-m resolution, which has been void-filled with open source data-using the same extent of Lake Mead as that from GSW, which is from the Google Earth Engine (GEE) platform [45].
The SRTM elevations over Lake Mead range from 206 to 590 m. Similar to the TanDEM-X data, the extreme high and low values in SRTM are primarily attributed to errors (of the maximum extent layer, and vertical measurements over water). The water level detected by SRTM was 372 m, which represents an area of 571.84 km 2 and accounts for 98% of the maximum extent (according to GSW). This suggests that the visible bathymetry that can be used for AVE generation from SRTM DEM represents less than 2% of the total area. More importantly, no elevation gradients or patterns can be found from the SRTM data, and the elevations from 372 to 375 represent 99% of the total area. Therefore, it is not feasible to generate a reliable AVE curve from SRTM DEM for Lake Mead. With regard to the TanDEM-X data, the visible bathymetry accounts for 32% of the total area, which shows clear patterns of gradients.
It is apparent that SRTM provided less bathymetry information compared to TanDEM-X data. This is because Lake Mead was at a relatively high level during the acquisition time of SRTM DEM. According to the elevation gage at Hoover Dam, the in situ value was 369.96 m at the end of February 2000 4 . However, the TanDEM-X data were composited based on multiple acquisitions from December 2010 to January 2015, which captured the low-fill times of the reservoir (with in situ elevations ranging from 329.37 to 345.70 m). According to the Coverage map (COV) layer-a product provided by DLR to indicate the number of valid elevation observations that were available for compositing-the maximum COV value for visible bathymetry of Lake Mead is 10, while the median value is 7 (see Fig. 7). The TanDEM-X product was composited by means of a weighted average (with the height error used as the weight), which takes advantage of multiple observations to reduce the uncertainty and improve the accuracy [41].
It is noteworthy that the WAM of TanDEM-X can capture the interannual variations, which increased the area of visible bathymetry of Lake Mead by up to 13%. However, the primary reason that the TanDEM-X data was more appropriate to derive the AVE curve is that they were collected during a period when Lake Mead was in a low fill state. Additionally, the multiple acquisitions (of TanDEM-X) have a better chance to capture the low fill occurrences. According to Zhao and Gao [46], the area of Lake Mead was 579. 19  resolution version, the elevations of the water bodies are not edited and the values may not be valid.

B. Potential Applications
The derived AVE curve can help to improve various water-resources-related studies and applications. Previous studies have shown that the quality of the E-A relationships has a significant impact on the accuracy of the remotely sensed reservoir storages [48]. We applied the E-A relationships from different studies to the same monthly water area values for Lake Mead derived from Landsat observations between 1984 and 2018 [46] to assess their performances. Validation results show that the remotely sensed water areas are in good agreement with in situ observations [46]. The monthly gauge elevations provided by the USBR 4 were applied to the lidar surveyed E-V curves [40] to obtain in situ storage values.
The storage estimates using different E-A relationships are shown in Fig. 8, with the statistics summarized in  [14] extended this method to ICESat data, which also shows fairly good performance with an RMSE value of 1.21 km 3 . However, the results from MABEL are slightly better due to its higher spatial resolution and vertical accuracy. Overall, the storage estimations using lidar altimeter (i.e., MABEL and ICESat) based E-A relationships outperformed the radar altimetry-based methods. This is due to the fact that lidar instruments can provide more accurate elevation measurements. The E-A relationship derived from TanDEM-X outperformed the abovementioned studies in terms of R 2 (>0.99) and RMSE (0.92 km 3 ). This is attributed to the fact that TanDEM-X can simultaneously provide the elevation and area information, which reduces the uncertainties from pairing up elevation and area values that are from different sources. Moreover, the TanDEM-X product is composited from multiple observations, which improves vertical accuracy and reduces the random elevation error. The storage estimations using the E-A relationships from different WAM thresholds (see Fig. 5) also show good results, with RMSE values ranging from 1.01 to 1.07 km 3 .
Remotely sensed storage variations can provide useful information for many aspects of reservoir management. The storage values are directly related to water availability, which can support the decision-making process in matters related to water supply and flood control. Moreover, a hydrological drought index can be developed based on storage estimates. Recently, Zhao and Gao [49] introduced a framework to monitor hydrological droughts using a reservoir surface area dataset. Reservoir storage should be a better indicator than the surface area in evaluating hydrological droughts.

C. Limitations and Future Directions
Despite the high accuracy of the AVE curve from TanDEM-X data, this method still has some limitations that should be addressed. First, it cannot generate the AVE relationships within the entire elevation range, except in cases when the reservoirs were mostly empty or not yet constructed during the acquisition time of the TanDEM-X data. The full AVE curve can be obtained by extrapolation, which may have large uncertainty. The accuracy and representation of the partial curve derived from the DEM determine the quality of the extrapolated part. Second, it is not applicable to reservoirs with high water levels and small variations during the acquisition period. However, reservoirs are designed for multiple purposes (e.g., water supply, irrigation, and hydropower generation), and are highly impacted by human activities that tend to experience large seasonal and interannual variations. Therefore, TanDEM-X has the potential to be applied to numerous reservoirsespecially those that experienced low levels, and/or large dynamics, during the data acquisition period (2010-2015). Meanwhile, with regard to the reservoirs that remained at high water levels, a sedimentation survey is the most reliable means to obtain the underwater topography. Third, this method was developed over one single reservoir. We specifically used an elevation range, which accounts for 90% of the visible bathymetry area in Lake Mead. However, this threshold value may vary with the reservoir being studied, and further investigation should be conducted to evaluate its representativeness. Li et al. [14] used a Landsat-based method (with a spatial resolution of 30 m) to derive the bathymetry maps and AVE curves for global reservoirs, with the smallest reservoir included being 1.47 km 2 . Due to the 90-m spatial resolution of TanDEM-X data, this method should be applicable to reservoirs with areas larger than 10 km 2 . Additionally, the commercial TanDEM-X product -which has a spatial resolution of 12 m-can observe much smaller reservoirs.
In general, global DEM datasets were collected at various phases and correspond to different water levels for a given reservoir. Therefore, a global dataset of reservoir AVE curves from a single DEM dataset is limited by the visible bathymetry. The most appropriate strategy is to combine all of the available DEM datasets to achieve the maximum coverage of global reservoirs. This could lead to a good complement to the AVE curves derived from the Global Reservoir Bathymetry Dataset (GRBD) [14], which will improve the modeling of reservoirs in land surface and earth system models. Additionally, each DEM dataset can be used to derive the full AVE curve for reservoirs built after the data acquisition period. For example, the SRTM DEM dataset can cover those constructed after February 2000. It has been reported that reservoir construction activities are still ongoing at a high rate in the 21st century (especially in developing countries), with 3700 hydropower dams either planned or under construction [50]. With regard to the recently built reservoirs, their AVE curves can be accurately retrieved from the currently available DEM datasets.

V. Conclusion
In this article, we proposed a framework to derive reservoir AVE curves using TanDEM-X data. With multiple acquisitions collected for each pixel, the composite TanDEM-X product can offer much better reservoir bathymetry coverage than other single acquisition-based DEM datasets (e.g., SRTM). The visible bathymetry from TanDEM-X shows clear patterns and gradients for Lake Mead (see Fig. 2). Based on the visible bathymetry (from 344 to 369 m), we derived the AVE curve for Lake Mead, which agrees well with the lidar survey values. The NRMSE values of the E-A and E-V relationships are 2.19% and 1.11%, respectively. Additionally, benefiting from the interannual variations captured by multiple acquisitions, the transitional waters can also be detected by TanDEM-X DEM. By including the transitional waters, the visible bathymetry can be extended to an elevation range of 341-369 m, with an effective area increase of 13%, and an RMSE value for the E-A relationship reduced by 6.12% (see Fig. 5 and Table I). This suggests that the elevation measurements for transitional waters are reliable in the TanDEM-X dataset. High-quality measurements of these waters can extend the visible bathymetry and improve the quality of the AVE curves derived for reservoirs that experienced large variations during the TanDEM-X data collection phase (2010)(2011)(2012)(2013)(2014)(2015). Moreover, we compared the storage estimations for Lake Mead from 1984 to 2018 using E-A relationships from different studies. Results show that our E-A relationship has the best performance in terms of RMSE (see Fig. 8 and Table II).
It should be noted that Lake Mead has been continuously shrinking since 2000 due to severe droughts and increasing water demand. Changing rainfall patterns and current water use patterns are putting pressure on water resources management at Lake Mead, as the population relying on it for water usage continues to increase. The AVE curve has become an important indicator for supporting spatial decision-making in water resources management activities such as optimizing water harvesting and urban water consumption.
The results indicate that TanDEM-X was able to capture a large amount of visible bathymetry during the acquisition time when Lake Mead experienced low water levels, with observed elevations from 329.37 to 345.70 m. Regarding the SRTM DEM dataset, it was collected in February 2000 when Lake Mead was at a high level (369.96 m)-so only a small domain of visible bathymetry was obtained, which is not adequate for generating the AVE curve. The values contained in global DEM datasets were acquired at different times and are associated with various extents of the visible bathymetry for each reservoir. Thus, a global AVE dataset can be generated by combining all of the available DEM datasets. This dataset will complement the AVE curves derived from the GRBD [14]. The E-A relationships can further extend the coverage of GRBD, and can also update the global reservoir storage-area-depth dataset [19]-which has large uncertainties due to the limitations of mathematical approximation, and the complexities of reservoir geometry. While this method has been specifically examined using Lake Mead, future work will focus on extending this method to global reservoirs to investigate its applicability.
two anonymous reviewers for their constructive suggestions. This work has benefitted from the usage of the Texas Flowchart for deriving the AVE curve from TanDEM-X data.        Table I.  Relative absolute error of area (solid lines) and volume (dashed lines) across the elevation range.  Coverage map (COV) for the visible bathymetry over Lake Mead from December 2010 to January 2015.  Storage estimations of Lake Mead from 1984 to 2018 using different E-A relationships. The E-A relationships were derived from different datasets (e.g., radar altimetry-based elevation measurements and MODIS-based area estimations). The time-series monthly surface area of Lake Mead provided by Zhao and Gao [46] was applied to these E-A relationships to obtain the corresponding storage values.