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Article

Groundwater Storage Variations in the Main Karoo Aquifer Estimated Using GRACE and GPS

1
State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (LIESMARS), Wuhan University, Wuhan 430079, China
2
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
*
Author to whom correspondence should be addressed.
Water 2023, 15(20), 3675; https://doi.org/10.3390/w15203675
Submission received: 13 September 2023 / Revised: 16 October 2023 / Accepted: 18 October 2023 / Published: 20 October 2023

Abstract

:
The Gravity Recovery and Climate Experiment (GRACE) provided valuable insights into variations in Groundwater Storage (GWS). However, the sensitivity of utilizing Global Positioning System (GPS) time series displacement data for detecting changes in GWS remains a subject of ongoing discussion. In order to estimate the spatiotemporal GWS, we selected a vertical displacement from 65 GPS stations located in the Main Karoo Aquifer (MKA). We performed total water storage (TWS) inversion on GPS vertical displacement components; after that, we deducted surface water components based on the Global Land Data Assimilation System (GLDAS) from January 2013 to December 2021. Additionally, for validation, we compared our GWS estimates with the GRACE-derived GWS and observed GWS values derived from the WaterGAP Global Hydrology Model (WGHM) compartments. We discovered that the TWS and GWS trends derived from GPS and GRACE exhibited similar behaviors with trend values overestimated by GRACE and WGHM. Our findings demonstrate relatively typical behavior between GPS and GRACE in the first and second principal component behaviors (PCs) and empirical orthogonal function (EOF) loadings (or spatial patterns). With a contribution of 71.83% to GPS-derived GWS variability and 68.92% to GRACE-derived GWS variability, EOF-1 is a relatively potent factor. For Principal Components PC1 and PC2, the GRACE and GPS PCs have correlation coefficients of 0.75 and 0.84, respectively. Finally, with higher temporal resolution, GPS can perform the same task as GRACE in hydrological applications. In addition, GPS can add important and valuable information to assess regional GWS change.

1. Introduction

Global water crises and water disasters have increased in frequency and severity in the world today as a result of human activity and global warming, underscoring the urgent need for effective management of water resources [1]. As a result, determining the total water storage (TWS) and groundwater storage (GWS), at various scales provide some crucial foundations for determining water availability and developing sustainable water resources [2,3]. In the past, measuring changes in groundwater necessitated in situ point measurements. However, modern advanced hydrological modeling methods and satellite-based remote sensing observations have significantly improved our comprehension of climate dynamics and helped characterize spatiotemporal patterns of GWS.
Groundwater systems are incredibly complex, and directly measuring fluctuations in groundwater storage (GWS) has proven to be a challenging task. While some regions, such as Heretaunga Plains in New Zealand [4] and the Calera aquifer in Zacatecas, Mexico [5], have established well-managed groundwater monitoring networks to gather high-density data reflecting GWS changes, this approach is expensive and impractical for large-scale regional studies. Alternatively, numerical simulations and artificial intelligence (AI) methods offer ways to estimate GWS changes. For instance, in a study by Osman A. et al., 2021 [6], machine learning algorithms were employed to develop an accurate groundwater level prediction model for densely populated areas in Selangor, Malaysia. This model used historical data of rainfall, temperature, and evaporation as inputs and tested the following three machine learning models: Xgboost, Artificial Neural Network, and Support Vector Regression. In another study by Osman A. et al., 2022 [7], the focus was on addressing the challenges of declining groundwater levels (GWL) due to factors like population growth and urbanization. Modeling GWL is recognized as a complex endeavor as it depends on various hydrological and meteorological variables. However, gathering sufficient background information and meteorological data to ensure accurate calculations remains a persistent challenge. Fortunately, the Gravity Recovery and Climate Experiment (GRACE) satellites, launched in 2002, have provided an unprecedented opportunity to monitor large-scale surface mass changes with remarkable accuracy. This technology has opened up new possibilities for quantitatively observing large-scale GWS changes [8,9].
Since 2002, GRACE and its successor GRACE-FO satellites, have been able to measure the changes in TWS on a global scale. This technology gives us the opportunity to measure the change in GWS by integrating GRACE observations with hydrological models, whether using Land Surface Models (LSM) or lobal Hydrological and Water Resources Models (GHWRMs). Barbosa et al., 2022 [10] used GRACE and the Global Land Data Assimilation System (GLDAS) LSM to assess GWS in Niger during the time period from 2002 to 2021. Additionally, Jin and Feng (2013) [11] used GRACE and WGHM (the WaterGAP Global Hydrology Model) and GLDAS to estimate GWS at a large scale. They found that the Annual and semiannual amplitudes of GWS estimated from GRACE–derived TWS minus the WGHM soil-moisture, and GRACE–derived TWS minus GLDAS derived soil-moisture are quite similar. Despite the considerable advantages associated with GRACE missions, their spatial resolution remains confined to a range of 300–500 km because of the specific characteristics of satellite orbits [12]. Regrettably, this limitation hinders the feasibility of conducting high-resolution studies in smaller regions using GRACE data. In contrast, Global Positioning System (GPS) time series displacement data can be employed to detect TWS changes after undergoing certain processing steps. The displacements resulting from variations in TWS, as ascertained through GPS measurements, exhibit consistency with predictions derived from GRACE data, employing Stokes coefficients and an elastic Earth model [13]. It is worth noting that only a limited number of studies have ventured into the utilization of GPS displacements for the estimation of groundwater changes [14]. In addition, none have used GPS data to analyze GWS variations in Africa. In the previous studies, the primary focus was on monitoring land subsidence through GPS measurements and establishing connections with deformations attributed to alterations in groundwater mass [15,16]. Some studies established correlations with groundwater-induced displacements obtained from GRACE data or borehole observations, akin to the investigations as conducted by Tan et al., 2016 [17] in Central Valley, California and Liu et al., 2018 [18] in the North China Plain. Larochelle et al., 2022 [19] investigated the geodetic characteristics of the Ozark Plateaus in central United States. The authors employed GRACE and GPS to analyze the aquifer system’s behavior and response. Lenczuk et al., 2023 [14] studied spatio–temporal patterns of vertical displacements in 9 regions of the world. They used data from 98 GPS stations. They revealed a strong similarity in spatial patterns between GRACE, GPS, and WGHM data, indicating the potential of geodetic methods in studying aquifers.
Densely distributed GPS measurements can be used to resolve fine-scale spatial variations in TWS because point GPS data are incredibly sensitive to local-to-regional-scale mass fluctuations [20]. GRACE, which measures the earth’s gravitational field variations at coarse temporal (monthly) and spatial scales (≈350 km), is considered to perform worse than GPS in terms of producing high-resolution TWS changes. GRACE also has low sensitivity in capturing high-frequency and fine-scale hydrological mass variations [21,22]. Additionally, because of the 2–3-month latency, monthly sampling, and data gaps in the GRACE technology, real-time hydrological monitoring is not optimal. This inevitably hinders scientific applications in operational hydrological monitoring.
Our study combines GPS, GRACE, and GLDAS data to estimate changes in GWS in the Main Karoo Aquifer (MKA) over the period of nine years from January 2013 to December 2021. We selected these particular nine years because they encompass the majority of the GPS observations available during this timeframe. For validation purposes, we utilized data from the WGHM. We also compared the GWS variations estimated from GPS and GRACE using the following two methods: first; principal component analysis (PCA) and the empirical orthogonal function (EOF), second; the effects of the climate factors. The data we used for the analysis and the study area are both described in Section 2. Section 3 explains the calculation process. The methodology section also includes GWS estimation and a flow chart outlining the main parts of the study. Section 4 presents the main findings of our study along with the GPS inversion technique and GWS estimation. The results are discussed in Section 5 along with a comparison of GWS obtained from geodetic missions and an explanation of the relationship between GWS and climate change. We outline the conclusions in the final section.

2. Materials

2.1. Study Area

Essentially, MKA is found in South Africa and Lesotho (Figure 1). Over 560,000 km2 is dominated by the aquifer. It has a multi-layered, hydraulically connected system that is mostly partially enclosed but has some unenclosed areas as well [23]. It is possible to classify the aquifer as a renewable reservoir.
MKA extends from 18.5° E to 31.5° E and −33.5° S to −22.5° S (Figure 1). The climate in the area of study throughout the period of study was as follows: the average temperature (Tm) during the study period was about 16.35 °C, the average precipitation (Pr) rate was 59.37 mm/year, and the average evapotranspiration (ET) rate was 31.24 mm/year (Figure 2).

2.2. GPS Data

GPS offers an impartial method for tracking surface deformation related to the hydrological cycle [24,25]. GPS remotely monitors changes in TWS in near-real time following important hydrological events by detecting instantaneous and continuous water loading signals with lower than centimeter precision and provides useful limits for operational hydrological monitoring [26,27]. The total number of GPS stations in our study area is 83. Out of these 83 GPS stations there were selected only those that have more than five years of observations, therefore 65 GPS stations were chosen as they response to our study conditions. The vertical displacement observations of the 65 GPS stations downloaded from the Nevada Geodetic Laboratory GPS Networks Map website (http://geodesy.unr.edu/; accessed on 20 January 2023), from January 2013 to December 2021 (Figure 3).
Firstly, we used the products offered by the Earth system modeling group at Deutsches GeoForschungsZentrum (ESMGFZ, http://esmdata.gfz-potsdam.de:8080/repository; accessed on 20 January 2023) to remove the non-tidal atmospheric loading (NTAL) and non-tidal oceanic loading (NTOL) effects from the GPS coordinate time series [28,29]. Only vertical GPS motions are used for water loading inversion because of the high sensitivity of the vertical component to hydrological signals and the small contributions of seasonal water changes on horizontal motions [30]. The reprocessed GPS vertical time series are mostly dominated by hydrological signals after the contributions of other factors are subtracted.

2.3. GRACE Data

Here, we evaluated our GPS-based inversion results using three gridded GRACE mascon products from three different centers, namely the Jet Propulsion Laboratory (JPL), Goddard Space Flight Center (GSFC), and the Centre for Space Research (CSR). They were downloaded for the 2013–2021 study period from (https://grace.jpl.nasa.gov/data/get-data/jpl_global_mascons/), (https://earth.gsfc.nasa.gov/geo/data/grace-mascons), and (https://www2.csr.utexas.edu/grace/RL06_mascons.html), respectively (accessed on 21 January 2023). Using a bilinear interpolation, the CSR GRACE Mascon products were up-scaled to 0.5 to match the resolution of the JPL and GSFC based gridded GRACE products [31,32,33]. In this study, the average of these GRACE Datasets was used. Averaged data from these datasets can be used to increase accuracy [34]. We used linear regression analysis to bridge missing separate months and the 11-month gap between GRACE and GRACE-FO.

2.4. Global Land Data Assimilation System (GLDAS)

To produce the best fields of land surface states and fluxes, the GLDAS product uses cutting-edge land surface modeling and data assimilation techniques [35]. As recommended in many previous studies [36,37,38], we selected the GLDAS-2.1 Noah land surface model with monthly observations (0.25° × 0.25° spatial grids) to estimate the GWS water for GRACE and GPS (https://disc.gsfc.nasa.gov/datasets/GLDAS_NOAH025_M_2.1/summary?keywords=GLDAS_NOAH025_M_2.1) (accessed on 21 January 2023). The GRACE- and GPS-derived TWS was subtracted from the sum of the four layers of soil moisture provided by the GLDAS Noah 2.1 at depths of 0–2 m to produce the baseline GWS [39,40]. Additionally, we utilized GLDAS data for the observations of ET [41]. To evaluate the evaporation throughout the basin and how it affects variation in GWS, ET data were used.

2.5. WaterGAP Global Hydrology Model (WGHM)

The updated WGHM 2.2, which was created at the University of Frankfurt and whose water changes are available from January 1901 to December 2019, was used to model groundwater mass changes [42]. There were no additional data available at the time of research, and the WGHM model is not routinely updated. WGHM has been used to offer information on water exchange between ground and surface waters and includes a number of hydrological components. One of the few models that includes groundwater mass fluctuations as a separate element is the WGHM. We used groundwater changes defined on a grid of 0.5° × 0.5° for the period between January 2013 and December 2019.

2.6. Precipitation and Air Temperature

A significant meteorological factor in water circulation, Precipitation (Pr), is closely linked to instances of flooding and drought. To examine its effect on GWS variation, we took into account Pr products from the Global Precipitation Climatology Project (GPCP) [43,44]. The monthly Pr datasets were downloaded from (https://psl.noaa.gov/data/gridded/data.gpcp.html) (accessed on 15 December 2022). In addition, for temperature data, we used GHCN-CAMS data, which combines information from the Global Historical Climate Network (GHCN) and the Climate Anomaly Monitoring System (CAMS), to estimate the surface air temperature (Tm) [45,46]. The global land monthly mean surface air temperature in the GHCN-CAMS dataset has a spatial resolution of 0.5° × 0.5°, with a total covered area of 89.75 S–89.75 N and 0.25 E–359.75 E [47,48]. The GHCN-CAMS dataset can be download from https://psl.noaa.gov/data/gridded/data.ghcncams.html (accessed on 15 December 2022).

3. Methods

3.1. GWS Estimation

GRACE observes TWS being a sum of individual water components stored above and below water surface, as follows:
Δ T W S = Δ G W S + Δ S M + Δ S W S + Δ C W S + Δ S W E
where Δ T W S shows changes in water storage, Δ G W S represents changes in groundwater, Δ S M S represents changes in soil moisture storage, Δ S W S represents changes in surface water, Δ C W S represents changes in the canopy water, and Δ S W E represents changes in snow water equivalent.
The lack of significant gravimetric fluctuation in surface water suggests that the surface water storage component observed in the GRACE TWS data is likely negligible for semi-arid regions like the MKA. Additionally, owing to the region’s warm climate throughout all of Africa, snow is uncommon in this area. Water in the canopy has a very low value and can be disregarded [10]. The following components of TWS can be disregarded to estimate GWS:
Δ G W S = Δ T W S Δ S M
GRACE-derived TWS, calculated using the average of three centers (JPL, CSR, and GSFC). GWS calculations were carried out using GRACE ensuring fairness by subtracting GLDAS-SM from TWS. Spatially resolved monthly outputs from the GLDAS-2.1 Noah model were employed in the estimation, with the top 4 layers used to compute soil moisture (SM) through GLDAS. Viz., 0–10 cm, 10–40 cm, 40–100 cm and 100–200 cm (Equation (3)). The summation of these four layers is the total SMS. All of these layers are accounted for.
S M S t o t a l = S M S 0 10 c m + S M S 10 40 c m + S M S 40 100 c m + S M S 100 200 c m
After this, the soil moisture anomaly is calculated. It is removed from the TWS. Therefore, the groundwater change can be determined.
Alternatively, in order to estimate GPS-derived GWS we used the vertical component of 65 GPS stations and followed this order:
(1)
We used the TSAnalyzer software to eliminate outliers and offsets from the raw GPS time series (https://github.com/wudingcheng/TSAnalyzer/, accessed on 20 January 2023).
(2)
To ascertain vertical crustal deformation tied to seasonal TWS fluctuations, non-tidal atmospheric loading (NTAL) and non-tidal ocean loading (NTOL) influences were averaged into daily results and removed using the product repository by Deutsches GeoForschungsZentrum (GFZ) (http://esmdata.gfz-potsdam.de:8080/repository, accessed on 20 January 2023) [49].
(3)
The preceding two steps prepared the GPS data for inversion through a circular disk and the Green function, converting it into TWS according to the mass loading inversion method illustrated in the next section.
(4)
After obtaining the GPS-derived TWS, the soil moisture anomaly was also calculated from GLDAS-2.1 Noah model as was done with the GRACE data (Equation (3)). Then the GPS-derived GWS can be estimated by removing soil moisture anomaly from the GPS-derived TWS (Equation (2)).

3.2. Mass Loading Inversion Method

The solid Earth deforms as a result of the external mass transformation of the ocean, atmosphere, and terrestrial fluid systems. The elastic Earth’s mass loading theory emphasizes the constitutive relationship between crustal deformation and spatially dispersed loading sources. It is possible to calculate the elastic response of the Earth’s crust to any given surface load distribution by spatially using an appropriate Green’s function with a surface mass loading field. The Green’s functions describe the deformation of the Earth under the influence of a unit surface point mass through the three-dimensional load Love numbers for a spherical nonrotating elastic layered Earth model [50,51]. High-spatial resolution distributed surface mass loads can be resolved thanks to the very sensitive relationship between vertical elastic deformation and the distance from the center of the loading source. An accurate indication of TWS can be obtained by inverting the vertical elastic deformation [52]. In this study, we utilized seasonal vertical displacements obtained from GPS data to perform an inversion for TWS variations across a grid of 0.25° × 0.25°. A scheme that considers the area of each grid cell was applied, taking into account the latitude-dependent variation in the radius of circular disks. The study area spans from 21° to 31° E longitude and from −33.5° to −25.5° S latitude. Additionally, a 3.0° extension was included on all sides of the study area to minimize artificial effects near the edges. A surface load field and load Green’s functions can be convolved to simulate TWS, which can excite elastic displacements of the earth’s crust, as follows:
u = G x
where u is the GPS-measured vertical displacements at scattered stations, x is the gridded mass loads expressed as TWS, G is the Green’s function matrix calculated using load Love numbers (LLNs) of a specified earth model, e.g., preliminary reference earth model (PREM) [53]. Our inversion model was built using the center of figure (CF) frame in order to be consistent with the geocentric reference frame of GPS data. Underdetermined EWH parameters inevitably lead to ill-posed problems, as with other geophysical inversions, and the following term is typically minimized using a regularization technique, such as the Tikhonov regularization [21,26]:
( G x u ) 2 + α 2 L x 2 = min
where L is the Laplacian smoothing matrix, α is the smoothing factor controlling the relative weight between model roughness and data misfit, and one method to determine it is cross-validation [54].
Here, using a technique from Jiang et al., 2022 [14], we inverted the vertical component of the GPS time series to TWS. The above-mentioned authors developed the GNSS2TWS, an open-source MATLAB tool (http://geodesy.noaa.gov/gps-toolbox, accessed on 16 December 2022) for estimating daily TWS changes. In order to achieve the time-varying inversion of vertical position time series in a densely instrumented GPS network, this software uses the PCA dimensionality-reduction technology. The steps that Jiang et al., 2022 [14] used to design their inversion model are shown in Figure 4. Firstly, several so-called Principal Components are derived from the displacement data. Secondly, for a corresponding principal TWS component, each principal component is individually inverted. Thirdly, a linear combination of the above-derived TWS models produces the final water estimates. In contrast to epoch-by-epoch estimates, which would perform inversions frequently, the model only performs the inversion a few times.

3.3. Principle Component Analysis (PCA)

GRACE-derived GWS and GPS-derived GWS results underwent PCA to facilitate a comparison of the GWS outcomes. For very high dimensional data, PCA is an unsupervised linear dimensionality reduction and data visualization technique. It is very computationally intensive because adding insights from high dimensional data is very difficult. This technique’s primary goal is to reduce the dimensionality of highly correlated data by converting the initial set of vectors into a new set known as Principal Components [55]. For dimensionality reduction and feature extraction in GRACE and GPS time series analyses, the PCA method is frequently used [56,57,58]. The GWS datasets used in this study were analyzed using the PCA method to summarize spatiotemporal variations in GWS. The Principal Components (PCs) of a given dataset are mathematically determined by the eigenvalues and eigenvectors of a covariance matrix. This technique assisted in identifying empirical orthogonal functions (EOFs) and Principal Components (i.e., temporal variations) (i.e., spatial maps). In order to decompose variations GWS, the following equation was used:
Z ( s , t ) = k = 1 M c k ( t ) . u k ( s )
where the ( s , t ) vector denotes the space-time location at time ( t ) and spatial position ( S ) , M is the number of modes in orthogonal space-time random fields, i.e., c k ( t ) u k ( s ) . The modes are formulated as an optimal set of orthogonal spatial functions u k ( s ) . In the period of time that the eigenvector describes, the standardized score is a portion of the overall variation proportional to the overall covariance (EOF). The standard deviation of the corresponding Principal Components was used to normalize the EOFs. For instance, the EOF/PC pairs are known as PCA modes while the EOF represents the spatial distribution GWS. In order to identify the predominant patterns of GWS in the MKA, PCA was used in our study to statistically decompose GRACE into PCs (temporal) and EOFs (spatial).
The process steps of our study are outlined in the flowchart presented in Figure 5. From top to bottom, GPS time series were downloaded at the beginning, and after outliers and offsets were removed; non-tidal ocean and atmospheric effects were also taken into account. Finally, the GPS time series were inverted to produce TWS. We download GRACE data from three centers on the same level, and then we estimated GWS by deducting TWS (from GRACE and GPS) from SM. Then, we compared them using PCA and the effect of the climate.

4. Results

4.1. GPS Inversion and Model Resolution Test

Figure 6 illustrates the temporal functions and spatial weights linked to these two Principal Components (PCs) attained via VBPCA. The initial principal component (PC1) (depicted in Figure 6a) accounts for approximately 99.68% of the filtered data’s variance and underscores the primary spatiotemporal characteristic of the annual water cycle in the Main Karoo Aquifer (MKA). This component showcases surface subsidence during the fall and winter periods due to heightened water loads, and ground uplift during spring and summer as water dissipates and soil moisture evaporates.
PC1 displays a positive spatial response in approximately 98% of GPS stations, and the seasonal shift in water storage attains its maximum in the northeastern and southern parts of MKA, diminishing toward the southeast and southwest regions (as shown in Figure 6c). On the other hand, the second PC (PC2) (depicted in Figure 6b) accounts for only 0.32% of the reconstructed data’s variance, significantly less than the contribution of PC1. All GPS stations linked to PC2 demonstrate a positive spatial response (depicted in Figure 6d). Notably, the second PC unveils a discernible interannual alteration, possibly linked to prolonged hydrological extreme events such as droughts and floods.
The resolution of our inversion results significantly relies on the extent of spatial coverage provided by continuous GPS stations. To assess the sensitivity and reliability of our inversion approach, we conducted a synthetic test, utilizing forward vertical surface displacements derived from synthetic TWS data to recover the original TWS thickness (shown in Figure 7). The outcomes indicate that our inversion model successfully recovers approximately 65% to 75% of the input water thickness in regions with dense GPS stations (e.g., northeast, east, southwest, and south of the aquifer). However, the recovery rate is less than 50% in the western and northwestern areas of the aquifer (as depicted in Figure 6c,d and Figure 7b). Therefore, introducing additional continuous GPS stations in the northwest of MKA is recommended to enhance spatial resolution in future studies. On average, the distance between GPS sites in MKA is approximately 93 km, which allows us to capture the primary hydrological features using the VBPCA-based inversion and achieve higher spatial resolution in depicting water changes compared to the data obtained from GRACE and GLDAS water products.
Previous analysis has revealed the TWS inversion and its spatial resolution in the MKA region. Therefore, our study delves into an investigation of the annual oscillations in water storage trends inferred from GPS vertical positions and compares them with water products derived from GRACE Mascon solutions. Figure 8a illustrates the trend in TWS as determined by the three GRACE mascon solutions, observed over the period between 2013 and 2021. On the other hand, Figure 8b displays the TWS trend based on GPS vertical observations. By comparing these two datasets, we aimed to gain insights into the concurrence and disparities between the GPS-derived water storage oscillations and those obtained from the GRACE Mascon solutions during the specified time frame. The study found that the spatial distribution of TWS derived from the three GRACE mascon solutions and GPS observations exhibited consistent variations. The TWS trends obtained from GPS and GRACE were −0.04 ± 0.003 mm/year and −0.30 ± 0.03 mm/year, respectively. These trends indicate a gradual decrease in water storage over time, with GPS showing a smaller rate of change compared to GRACE. Because of variations in signal sensitivity, with GRACE capturing large-scale long-wave signals and GPS focusing on regional short-wave signals, disparities arise between the TWS spatial distribution derived from GPS and GRACE (Figure 8). Nonetheless, basin-scale averaged linear trend of TWS from both GPS (−0.04 ± 0.003 mm/year) and GRACE (−0.30 ± 0.03 mm/year) affirm the consistent deficit of water storage in the MKA.

4.2. Groundwater Storage (GWS)

The MKA’s drought is shown using the Global Precipitation Climatology Centre’s drought index (GPCC DI), which uses a 1.0° grid resolution and an average monthly period. According to Pietzsch and Bissolli, 2011 [50], GPCC DI is a combination of the Standardized Precipitation Index and the Standardized Precipitation Evapotranspiration Index (SPEI). The average monthly drought index from 2013 to 2021 is shown in Figure 9 (9 years). The drought and wet categories are shown in Figure 9 for all of Africa. Figure 9 indicates that there is a mild drought in the south-east region and a mild wet climate throughout almost the entire aquifer [59]. This mild drought indicates that there is a possibility of GWS recharge and the aquifer does not lie in a region that is completely dry.
Because of the limited availability of groundwater observations in situ data from Africa, we utilized data from the WaterGAP Global Hydrology Model (WGHM) as an alternative for comparison with GRACE and GPS data. The results of GWS based on GRACE, GPS, and WGHM are illustrated in Figure 10. The WGHM data covers observations up to December 2019. In Figure 10d, we present the time series of GWS derived from GPS, GRACE, and WGHM, while Figure 10a–c displays the GWS trends derived from GRACE, GPS, and WGHM, respectively.
As shown in Figure 10 and Table 1, comparing the GWS trends for the time period from January 2013 to December 2019, the trend obtained from WGHM is approximately 1.98 ± 0.08 mm/year, whereas the GRACE-derived trend is approximately 1.52 ± 0.11 mm/year, and the GPS-derived trend is approximately 2.37 ± 0.09 mm/year (Table 1). On average, the GWS trend derived from GPS over this period is 2.59 ± 0.12 mm/year, while the GWS trend using GRACE shows 1.41 ± 0.08 mm/year from January 2013 to December 2021 (Table 1). GRACE, GPS, and WGHM results demonstrate spatial domain similarity with strong signals using GRACE’s behavior in GWS. The results show a positive trend throughout the entire aquifer, with the exception of the middle part, as determined by GPS, WGHM, and GRACE-derived GWS.
These findings suggest a dynamic and complex groundwater storage system with varying rates of change over time and across different regions. Nevertheless, all three datasets—GRACE, GPS, and WGHM—reveal spatial similarities in GWS behavior, particularly highlighting the strong signals captured by GRACE in monitoring groundwater storage. In summary, our results point to an overall positive trend in GWS across the entire aquifer, with some exceptions in the middle part, consistently identified by GPS, WGHM, and GRACE-derived GWS analyses.

5. Discussion

5.1. Comparison between GPS and GRACE-Derived GWS

5.1.1. EOF Modes

We used PCA to thoroughly compare the GPS and GRACE-derived GWS over the MKA for a 9-year period (i.e., 2013–2021). The PCA and EOF in MKA are shown in Figure 11. EOF loadings (or spatial patterns) are relatively strong in the first principal component, accounting for 71.83% of the cumulative variability in GPS-derived GWS and 68.92% in GRACE-derived GWS, and are primarily localized over the left part of the aquifer, while the negative EOF localized in the right part (at ≈26° lon) (Figure 11c,d and Table 2).
However, in the second EOF (EOF-2), they are more concentrated in the middle of the aquifer (between about 24° and 29° long), are relatively strong, and account for 28.17% of the cumulative variability in GPS-derived GWS and 31.08% of the GWS derived from GRACE. The only difference between them in the southern region is that GPS has a much stronger positive sign than GRACE (Figure 11e,f; and Table 2). The EOF-1 and EOF-2 both demonstrate consistency between GRACE and GPS, thereby approving GPS’s replacement of GRACE in the hydrology application with high accuracy.
Furthermore, the time series generated through PCA (Figure 11a,b) illustrate a high degree of consistency between GPS and GRACE-derived GWS data. To quantify this consistency, we employed Pearson’s correlation coefficient, which yielded remarkable agreement between the two datasets. Specifically, PC-1 exhibited a correlation coefficient of 0.74, while PC-2 demonstrated an even higher correlation coefficient of 0.84.
These results collectively underscore the robustness of GPS as a viable alternative to GRACE for hydrological applications, as it demonstrates high accuracy and consistency in capturing GWS variability over the MKA. This finding holds significant implications for the field of hydrology, particularly in regions where GRACE data may not be available or as a means to cross-validate the information obtained through different observation methods.

5.1.2. Climate

In our study, we conducted an analysis of the interplay between climate factors and Groundwater Storage (GWS) estimated through GPS and GRACE data. We examined the behavior of these three key climate factors: monthly mean precipitation (Pr), evapotranspiration (ET), and temperature (Tm), in relation to the GWS fluctuations over time in the MKA. Our findings, as depicted in Figure 12, offer valuable insights into these dynamics.
The temporal patterns displayed in Figure 12 reveal intriguing relationships. Specifically, during the months of December and the initial three months of each year, when the temperatures (Tm) are relatively high, it becomes apparent that the amount of evapotranspiration (ET) roughly equals the amount of precipitation (Pr). This balance between ET and Pr suggests that, during these periods, the basin experiences a state of equilibrium where the water input from precipitation is effectively offset by the loss through evapotranspiration. Notably, our study demonstrates the advantage of temporal resolution, particularly when comparing GPS-derived GWS and GRACE-derived GWS data. GPS-derived GWS exhibits a more rapid response to changes in climate conditions compared to GRACE-derived GWS. This heightened temporal sensitivity of GPS data enables it to capture GWS variations with greater precision and agility.
Importantly, both GWS estimates, whether derived from GPS or GRACE, align consistently with the fluctuations in the three climate factors (Pr, ET, and Tm) at a monthly resolution. This alignment reinforces the reliability of GWS data and its responsiveness to climatic variations. Furthermore, in the middle of the year, when temperatures are relatively low and precipitation is abundant, we observe that the groundwater system is replenished by precipitation (Pr). This observation highlights the critical role of seasonal variations in climate factors in influencing groundwater dynamics. Our analysis underscores the intricate interplay between climate factors and groundwater storage in the MKA. It highlights the potential of GPS-derived GWS data to provide high-temporal-resolution insights and reaffirms the sensitivity of GWS to climatic fluctuations, which is particularly crucial for understanding water resource management in this region.
Because daily GPS observations can capture instantaneous changes in climate, GPS is necessary when researching precise hydrological applications.

5.1.3. Groundwater Storage and ENSO

In this research, we examined the impact of El Niño and La Niña on Groundwater Storage (GWS) in the Main Karoo Aquifer. Figure 13 portrays a graph illustrating GWS alongside a bar chart representing the ENSO index spanning from January 2013 to December 2021.
The graph demonstrates notable regions with strong coherence, closely aligning with El Niño events (2015–2016) and La Niña occurrences (2016–2018 and 2020–2022). A recent investigation by Kolusu et al., 2019 [51] emphasizes the significance of factoring El Niño events into strategies for groundwater management, particularly in regions with water scarcity like East and Southern Africa. Their study established a robust correlation between El Niño-driven climate anomalies and their repercussions on groundwater resources, revealing that El Niño leads to drought conditions while La Niña induces flooding, aligning with previous findings by Siam and Eltahir, 2017 [52] who highlighted the importance of considering El Niño impacts in groundwater management for the Nile basin. As groundwater recharge primarily occurs through rainfall infiltration and interactions with surface water, El Niño (La Niña) years are likely to lead to reduced (increased) groundwater storage. In our study, the ENSO bar chart mirrors the fluctuations observed in the GWS time series, as indicated in the paired windows in Figure 13. This correspondence implies a direct influence of GWS fluctuations on the Main Karoo Aquifer’s groundwater storage.

6. Conclusions

In this study, we estimated the GWS in the MKA using GPS time series data and triple GRACE mascon data (CSR, JPL, GSFC). We performed a number of operations on the GPS stations in order to convert them to TWS. Firstly, we removed outliers and offsets. Next, we eliminated the non-tidal ocean effect and non-tidal effect. Finally, we estimated TWS by performing an inversion on the GPS time series data. We combined the soil moisture data from GLDAS with the TWS data from GRACE and GPS to better understand the nature of the groundwater variations between January 2013 and December 2021 (9 years). Strong GRACE signals produced the same behavior for GPS and GRACE-derived GWS and TWS. Positive trends are seen by both GPS and GRACE. While GPS-derived GWS trend is 2.59 ± 0.12 mm/year, GRACE GWS trend is 1.41 ± 0.08 mm/year. The results seen from GRACE, GPS, and WGHM demonstrate a spatial domain similarity, with strong signals resembling the behavior of GRACE’s GWS. Additionally, for both GPS and GRACE-derived GWS, we estimated PCA and EOF. They appear to be quite close. The first and second EOF modes display relatively typical behavior between GRACE and GPS. With a contribution of 71.83% to GPS-derived GWS variability and 68.92% to GRACE-derived GWS variability, EOF-1 is a relatively potent factor. For EOF-2, it was 28.17% and 31.08%. The same GRACE work can be performed by GPS with higher temporal resolution by using GPS inversion (daily vs. monthly as with GRACE). In addition, we calculated climate factors that affect MKA groundwater (Pr, Tm, and ET). Because daily GPS observations can capture an instantaneous change in climate, we strongly advise using GPS for research into precise hydrological applications. The lack of routine distribution of GPS stations and continuous publication of their data is a drawback of using GPS in hydrological applications. To help us better understand the hydrological applications, we also advise increasing the number of GPS stations and offering continuous observations.

Author Contributions

Conceptualization, H.A.M.; Methodology, H.A.M.; Software, H.A.M., J.J. and Q.W.; Formal analysis, H.A.M.; Investigation, H.A.M.; Data curation, H.A.M.; Writing—original draft, H.A.M.; Writing—review & editing, W.S. and J.J.; Visualization, J.J.; Supervision, W.S.; Project administration, W.S.; Funding acquisition, W.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by National Natural Science Foundations of China (No. 41721003, 42030105, 41874023), and Fundamental Research Funds for the Central Universities. In addition, the Open Fund of Wuhan, Gravitation and Solid Earth Tides, National Observation and Research Station (WHYWZ202202).

Data Availability Statement

The GRACE data used in this study are publicly available from the NASA Earth Observing System Data and Information System (EOSDIS) Distributed Active Archive Center (DAAC) at the Jet Propulsion Laboratory (JPL) (https://grace.jpl.nasa.gov/, accessed on 20 January 2023). The data used in this study are from the GARCE and GRACE-FO missions. Details on the data processing and quality control can be found on the JPL GARCE and GRACE-FO websites. In addition, GPS data presented in this study can be accessed from the Nevada Geodetic Laboratory at (http://geodesy.unr.edu/magnet.php, accessed on 20 January 2023).

Acknowledgments

The authors would like to thank the Supercomputing Center of Wuhan University for providing the supercomputing system in numerical calculations.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Area of study. Figure includes Main Karoo Aquifer by a black line in south of Africa. The Aquifer extends from 18.5° E to 31.5° E and −33.5° S to −22.5° S. We employed a digital elevation model (DEM) obtained from the Shuttle Radar Topography Mission (SRTM), which had a spatial resolution of approximately 90 m. This figure was adjusted using the Global Mapper v.23 and Surfer software v.13 (authors).
Figure 1. Area of study. Figure includes Main Karoo Aquifer by a black line in south of Africa. The Aquifer extends from 18.5° E to 31.5° E and −33.5° S to −22.5° S. We employed a digital elevation model (DEM) obtained from the Shuttle Radar Topography Mission (SRTM), which had a spatial resolution of approximately 90 m. This figure was adjusted using the Global Mapper v.23 and Surfer software v.13 (authors).
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Figure 2. The climate factors’ average values. The average precipitation (Pr) rate (a), average temperature (Tm) rate (b), and average evapotranspiration (ET) rate (c), from January 2013 to December 2021 (authors calculations).
Figure 2. The climate factors’ average values. The average precipitation (Pr) rate (a), average temperature (Tm) rate (b), and average evapotranspiration (ET) rate (c), from January 2013 to December 2021 (authors calculations).
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Figure 3. GPS stations. The red triangles represent GPS stations with less than five years’ worth of observations, while the blue triangles represent those with more than five years’ worth of data. The red comprises 18 stations, while the blue totals 65. We consider all available stations in and out of our borders (authors).
Figure 3. GPS stations. The red triangles represent GPS stations with less than five years’ worth of observations, while the blue triangles represent those with more than five years’ worth of data. The red comprises 18 stations, while the blue totals 65. We consider all available stations in and out of our borders (authors).
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Figure 4. A representation of the inversion technique as described in [20]. The left-hand track is used in conventional inversion to directly invert displacement data into a TWS model.
Figure 4. A representation of the inversion technique as described in [20]. The left-hand track is used in conventional inversion to directly invert displacement data into a TWS model.
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Figure 5. The flowchart visually outlines the methodology implemented for this study (authors).
Figure 5. The flowchart visually outlines the methodology implemented for this study (authors).
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Figure 6. Temporal and spatial pattern PCs of vertical GPS component. (a) first PC; (b) second PC; (c) first spatial PC (EOF); (d) second spatial PC (EOF) (authors calculations).
Figure 6. Temporal and spatial pattern PCs of vertical GPS component. (a) first PC; (b) second PC; (c) first spatial PC (EOF); (d) second spatial PC (EOF) (authors calculations).
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Figure 7. A synthetic experiment to assess the inversion of GPS-derived TWS. (a) Represents the input water heights used to estimate the forward vertical displacements at various GPS stations. (b) Displays the results of the inversion process using the forward vertical displacements. The spatial distribution of GPS stations is represented by green circles (authors calculations).
Figure 7. A synthetic experiment to assess the inversion of GPS-derived TWS. (a) Represents the input water heights used to estimate the forward vertical displacements at various GPS stations. (b) Displays the results of the inversion process using the forward vertical displacements. The spatial distribution of GPS stations is represented by green circles (authors calculations).
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Figure 8. The GRACE and GPS-derived TWS trend. (a) Using the average of the three processing centers (CSR, JPL, and GSFC), recent GRACE-derived TWS, and (b) GPS-derived TWS after inversion technique on the GPS time series (authors calculations).
Figure 8. The GRACE and GPS-derived TWS trend. (a) Using the average of the three processing centers (CSR, JPL, and GSFC), recent GRACE-derived TWS, and (b) GPS-derived TWS after inversion technique on the GPS time series (authors calculations).
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Figure 9. The average monthly drought index for the time frame between January 2013 and December 2021, using monthly GPCC data. The drought is depicted in colors ranging from yellow to red, with the severity of the drought increasing from mild (0 to −1) to moderate (up to −1.5), severe (−1.5 to −2), and extremely severe (below −2). Conversely, the wet is represented by a range of blue hues, with the level of wetness increasing from mild (0 to 1) to moderate (up to 1.5), severe (1.5 to 2), and extremely severe (above 2) (authors calculations).
Figure 9. The average monthly drought index for the time frame between January 2013 and December 2021, using monthly GPCC data. The drought is depicted in colors ranging from yellow to red, with the severity of the drought increasing from mild (0 to −1) to moderate (up to −1.5), severe (−1.5 to −2), and extremely severe (below −2). Conversely, the wet is represented by a range of blue hues, with the level of wetness increasing from mild (0 to 1) to moderate (up to 1.5), severe (1.5 to 2), and extremely severe (above 2) (authors calculations).
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Figure 10. The GWS over the MKA using GRACE and GPS. (a) the GWS trend using GRACE, (b) the GWS trend using GPS, (c) the GWS trend using WGHM, and (d) the GWS time series; the orange line represents GPS, the blue line represents GRACE, while the green line represents WGHM-derived GWS (authors calculations).
Figure 10. The GWS over the MKA using GRACE and GPS. (a) the GWS trend using GRACE, (b) the GWS trend using GPS, (c) the GWS trend using WGHM, and (d) the GWS time series; the orange line represents GPS, the blue line represents GRACE, while the green line represents WGHM-derived GWS (authors calculations).
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Figure 11. The GWS’s PCA and EOF modes were estimated using GPS and GRACE. The first and second PCs are represented at the left by the characters (a,b). Whereas this orange line represents GPS, the blue line shows the GRACE. The first EOF mode from GPS and GRACE, respectively, is shown in (c,d) on the right side. However, the second EOF mode from the same tools is represented by (e,f). While the gradient of red is positive values, the gradient of blue is negative values (authors’ calculations).
Figure 11. The GWS’s PCA and EOF modes were estimated using GPS and GRACE. The first and second PCs are represented at the left by the characters (a,b). Whereas this orange line represents GPS, the blue line shows the GRACE. The first EOF mode from GPS and GRACE, respectively, is shown in (c,d) on the right side. However, the second EOF mode from the same tools is represented by (e,f). While the gradient of red is positive values, the gradient of blue is negative values (authors’ calculations).
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Figure 12. The average climate factors in MKA. There are two bars in the figure, green for ET and blue for Pr. There are three time series: an orange Tm time series, a purple time series derived from GWS using GPS, and a brown time series derived from GRACE (authors calculations).
Figure 12. The average climate factors in MKA. There are two bars in the figure, green for ET and blue for Pr. There are three time series: an orange Tm time series, a purple time series derived from GWS using GPS, and a brown time series derived from GRACE (authors calculations).
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Figure 13. A time series graph showing GWS and the bar chart of the ENSO index. The top section of the graph illustrates different GWS types (GRACE, GPS, GWS derived from WGHM), yellow box shows El Niño events, while the lower section shows the ENSO index (authors calculations).
Figure 13. A time series graph showing GWS and the bar chart of the ENSO index. The top section of the graph illustrates different GWS types (GRACE, GPS, GWS derived from WGHM), yellow box shows El Niño events, while the lower section shows the ENSO index (authors calculations).
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Table 1. The GWS trend over the MKA were estimated using GPS, GRACE and WGHM.
Table 1. The GWS trend over the MKA were estimated using GPS, GRACE and WGHM.
GWSGWS Trend (mm/Year)
2013–20192013–2021
GPS-derived GWS2.37 ± 0.092.59 ± 0.12
GRACE-derived GWS1.52 ± 0.111.41 ± 0.08
WGHM-derived GWS1.98 ± 0.08-
Table 2. The GWS’s EOF modes ratio were estimated using GPS and GRACE.
Table 2. The GWS’s EOF modes ratio were estimated using GPS and GRACE.
GWSEOF-1 (%)EOF-2 (%)
GPS-derived GWS71.8328.17
GRACE-derived GWS68.9231.08
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Mohasseb, H.A.; Shen, W.; Jiao, J.; Wu, Q. Groundwater Storage Variations in the Main Karoo Aquifer Estimated Using GRACE and GPS. Water 2023, 15, 3675. https://doi.org/10.3390/w15203675

AMA Style

Mohasseb HA, Shen W, Jiao J, Wu Q. Groundwater Storage Variations in the Main Karoo Aquifer Estimated Using GRACE and GPS. Water. 2023; 15(20):3675. https://doi.org/10.3390/w15203675

Chicago/Turabian Style

Mohasseb, Hussein A., Wenbin Shen, Jiashuang Jiao, and Qiwen Wu. 2023. "Groundwater Storage Variations in the Main Karoo Aquifer Estimated Using GRACE and GPS" Water 15, no. 20: 3675. https://doi.org/10.3390/w15203675

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