Using Satellite-Based Terrestrial Water Storage Data: A Review

Land water storage plays a key role for the Earth's climate, natural ecosystems, and human activities. Since the launch of the first Gravity Recovery and Climate Experiment (GRACE) mission in 2002, spaceborne observations of changes in terrestrial water storage (TWS) have provided a unique, global perspective on natural and human-induced changes in freshwater resources. Even though they have become much used within the broader Earth system science community, space-based TWS datasets still incorporate important and case-specific limitations which may not always be clear to users not familiar with the underlying processing algorithms. Here, we provide an accessible and illustrated overview of the measurement concept, of the main available data products, and of some frequently encountered technical terms and concepts. We summarize concrete recommendations on how to use TWS data in combination with other hydrological or climatological datasets, and guidance on how to avoid possible pitfalls. Finally, we provide an overview of some of the main applications of GRACE TWS data in the fields of hydrology and climate science. This review is written with the intention of supporting future research and facilitating the use of satellite-based terrestrial water storage datasets in interdisciplinary contexts.

Patched Local Lunar Gravity Solutions Using GRAIL Data

We present a method to determine local gravity fields for the Moon using Gravity Recovery and Interior Laboratory (GRAIL) data. We express gravity as gridded gravity anomalies on a sphere, and we estimate adjustments to a background global start model expressed in spherical harmonics. We processed GRAIL Ka-band range-rate data with a short-arc approach, using only data over the area of interest. We determine our gravity solutions using neighbor smoothing constraints. We divided the entire Moon into 12 regions and 2 polar caps, with a resolution of 0.15 ° × 0.15 ° (which is equivalent to degree and order 1199 in spherical harmonics), and determined the optimal smoothing parameter for each area by comparing localized correlations between gravity and topography for each solution set. Our selected areas share nodes with surrounding areas and they are overlapping. To mitigate boundary effects, we patch the solutions together by symmetrically omitting the boundary parts of overlapping solutions. Our new solution has been iterated, and it has improved correlations with topography when compared to a fully iterated global model. Our method requires fewer resources, and can easily handle regionally varying resolution or constraints. The smooth model describes small-scale features clearly, and can be used in local studies of the structure of the lunar crust.

Validation of GRACE and GRACE-FO Mascon Data for the Study of Polar Motion Excitation

In this study, we calculate the hydrological plus cryospheric excitation of polar motion (hydrological plus cryospheric angular momentum, HAM/CAM) using mascon solutions based on observations from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions. We compare and evaluate HAM/CAM computed from GRACE and GRACE-FO mascon data provided by the Jet Propulsion Laboratory (JPL), the Center for Space Research (CSR), and the Goddard Space Flight Center (GSFC). A comparison with HAM obtained from the Land Surface Discharge Model is also provided. An analysis of HAM/CAM and HAM is performed for overall variability, trends, and seasonal and non-seasonal variations. The HAM/CAM and HAM estimates are validated using the geodetic residual time series (GAO), which is an estimation of the hydrological plus cryospheric signal in geodetically observed polar motion excitation. In general, all mascon datasets are found to be equally suitable for the determination of overall, seasonal, and non-seasonal HAM/CAM oscillations, but some differences in trends remain. The use of an ellipsoidal correction, implemented in the newest solution from CSR, does not noticeably affect the consistency between HAM/CAM and GAO. Analysis of the data from the first two years of the GRACE-FO mission indicates that the current accuracy of HAM/CAM from GRACE-FO mascon data meets expectations, and the root mean square deviation of HAM/CAM components are between 5 and 6 milliarcseconds. The findings from this study can be helpful in assessing the role of satellite gravimetry in polar motion studies and may contribute towards future improvements to GRACE-FO data processing.

Preliminary Estimation and Validation of Polar Motion Excitation from Different Types of the GRACE and GRACE Follow-On Missions Data

The Gravity Recovery and Climate Experiment (GRACE) mission has provided global observations of temporal variations in the gravity field resulting from mass redistribution at the surface and within the Earth for the period 2002–2017. Although GRACE satellites are not able to realistically detect the second zonal parameter (ΔC20) of geopotential associated with the flattening of the Earth, they can accurately determine variations in degree-2 order-1 (ΔC21, ΔS21) coefficients that are proportional to variations in polar motion. Therefore, GRACE measurements are commonly exploited to interpret polar motion changes due to variations in the global mass redistribution, especially in the continental hydrosphere and cryosphere. Such impacts are usually examined by computing the so-called hydrological polar motion excitation (HAM) and cryospheric polar motion excitation (CAM), often analyzed together as HAM/CAM. The great success of the GRACE mission and the scientific robustness of its data contributed to the launch of its successor, GRACE Follow-On (GRACE-FO), which began in May 2018 and continues to the present. This study presents the first estimates of HAM/CAM computed from GRACE-FO data provided by three data centers: Center for Space Research (CSR), Jet Propulsion Laboratory (JPL), and GeoForschungsZentrum (GFZ). In this paper, the data series is computed using different types of GRACE/GRACE-FO data: ΔC21, ΔS21 coefficients of geopotential, gridded terrestrial water storage anomalies, and mascon solutions. We compare and evaluate different methods of HAM/CAM estimation and examine the compatibility between CSR, JPL, and GFZ data. We also validate different HAM/CAM estimations using precise geodetic measurements and geophysical models. Analysis of data from the first 19 months of GRACE-FO shows that the consistency between GRACE-FO-based HAM/CAM and observed hydrological/cryospheric signals in polar motion is similar to the consistency obtained for the initial period of the GRACE mission, worse than the consistency received for the best GRACE period, and higher than the consistency obtained for the terminal phase of the GRACE mission. In general, the current quality of HAM/CAM from GRACE Follow-On meets expectations. In the following months, after full calibration of the instruments, this accuracy is expected to increase.

Introducing an Improved GRACE Global Point-Mass Solution—A Case Study in Antarctica

In the so-called point-mass modeling, surface densities are represented by point masses, providing only an approximated solution of the surface integral for the gravitational potential. Here, we propose a refinement for the point-mass modeling based on Taylor series expansion in which the zeroth-order approximation is equivalent to the point-mass solution. Simulations show that adding higher-order terms neglected in the point-mass modeling reduces the error of inverted mass changes of up to 90% on global and Antarctica scales. The method provides an alternative to the processing of the Level-2 data from the Gravity Recovery and Climate Experiment (GRACE) mission. While the evaluation of the surface densities based on improved point-mass modeling using ITSG-Grace2018 Level-2 data as observations reveals noise level of approximately 5.77 mm, this figure is 5.02, 6.05, and 5.81 mm for Center for Space Research (CSR), Goddard Space Flight Center (GSFC), and Jet Propulsion Laboratory (JPL) mascon solutions, respectively. Statistical tests demonstrate that the four solutions are not significant different (95% confidence) over Antarctica Ice Sheet (AIS), despite the slight differences seen in the noises. Therefore, the estimated noise level for the four solutions indicates the quality of GRACE mass changes over AIS. Overall, AIS shows a mass loss of −7.58 mm/year during 2003–2015 based on the improved point-mass solution, which agrees with the values derived from mascon solutions.

Improved Estimation of Regional Surface Mass Variations from GRACE Intersatellite Geopotential Differences Using a Priori Constraints

We presented an improved method for estimation of regional surface mass variations from the Gravity Recovery and Climate Experiment (GRACE)-derived precise intersatellite geopotential differences using a priori constraints. An alternative analytic formula was proposed to incorporate the K-band ranging (KBR) range rate into the improved energy balance equation, and precise geopotential differences were estimated from GRACE Level-1B data based on the remove-compute-restore (RCR) technique, which avoids the long-wavelength gravity signals being absorbed by empirical parameters. To reduce the ill condition for inversion of regional mass variations from geopotential differences, a priori information from hydrological models was used to construct the constraint equations, and the optimal regularization parameters were adaptively determined based on iterative least-squares estimation. To assess our improved method, a case study of regional mass variations’ inversion was carried out over South America on 2° × 2° grids at monthly intervals from January 2005 to December 2010. The results show that regional mascon solutions inverted from geopotential differences estimated by the RCR technique using hydrological models as a priori constraints can retain more signal energy and enhance regional mass variation inversion. The spatial distributions and annual amplitudes of geopotential difference-based regional mascon solutions agree well with the official GRACE mascon solutions, although notable differences exist in spatial patterns and trends, especially in small basins. In addition, our improved method can robustly estimate the mascon solutions, which are less affected by the a priori information. The results from the case study have clearly demonstrated the feasibility and effectiveness of the proposed method.

Hydropower dam operation strongly controls Lake Victoria's freshwater storage variability

River impoundments strongly modify the global water cycle and terrestrial water storage (TWS) variability. Given the susceptibility of global water cycle to climate change and anthropogenic influence, the synthesis of science with sustainable reservoir operation strategy is required as part of an integrated approach to water management. Here, we take advantage of new approaches combining state-of-the-art computational models and a novel satellite-based reservoir operation scheme to spatially and temporally decompose Lake Victoria's TWS, which has been dam-controlled since 1954. A ground-based lake bathymetry is merged with a global satellite-based topography to accurately represent absolute water storage, and radar altimetry data is integrated in the hydrodynamic model as a proxy of reservoir operation practices. Compared against an idealized naturalized system (i.e., no anthropogenic impacts) over 2003-2019, reservoir operation shows a significant impact on water elevation, extent, storage and outflow, controlling lake dynamics and TWS. For example, compared to Gravity Recovery and Climate Experiment (GRACE) data, reservoir operation improved correlation and root mean square error of basin-wide TWS simulations by 80% and 54%, respectively. Results also show that lake water storage is 20% higher under dam control and basin-wide surface water storage contributes 64% of TWS variability. As opposed to existing reservoir operation schemes for large-scale models, the proposed model simulates spatially distributed surface water processes and does not require human water demand estimates. Our proposed approaches and findings contribute to the understanding of Lake Victoria's water dynamics and can be further applied to quantify anthropogenic impacts on the global water cycle.

Determination of the Regularization Parameter to Combine Heterogeneous Observations in Regional Gravity Field Modeling

Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBFs) for regional gravity field refinement. In this process, regularization is in most cases inevitable, and choosing an appropriate value for the regularization parameter is a crucial issue. This study discusses the drawbacks of two frequently used methods for choosing the regularization parameter, which are the L-curve method and the variance component estimation (VCE). To overcome their drawbacks, two approaches for the regularization parameter determination are proposed, which combine the L-curve method and VCE. The first approach, denoted as “VCE-Lc”, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights, the L-curve method is applied to determine the regularization parameter. In the second approach, called “Lc-VCE”, the L-curve method determines first the regularization parameter, and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. To evaluate and compare the performance of the two proposed methods with the L-curve method and VCE, all these four methods are applied in six study cases using four types of simulated observations in Europe, and their modeling results are compared with the validation data. The RMS errors (w.r.t the validation data) obtained by VCE-Lc and Lc-VCE are smaller than those obtained from the L-curve method and VCE in all the six cases. VCE-Lc performs the best among these four tested methods, no matter if using SRBFs with smoothing or non-smoothing features. These results prove the benefits of the two proposed methods for regularization parameter determination when different data sets are to be combined.

Recovery of Rapid Water Mass Changes (RWMC) by Kalman Filtering of GRACE Observations

We demonstrate a new approach to recover water mass changes from GRACE satellite data at a daily temporal resolution. Such a product can be beneficial in monitoring extreme weather events that last a few days and are missing by conventional monthly GRACE data. The determination of the distribution of these water mass sources over networks of juxtaposed triangular tiles was made using Kalman Filtering (KF) of daily GRACE geopotential difference observations that were reduced for isolating the continental hydrology contribution of the measured gravity field. Geopotential differences were obtained from the along-track K-Band Range Rate (KBRR) measurements according to the method of energy integral. The recovery approach was validated by inverting synthetic GRACE geopotential differences simulated using GLDAS/WGHM global hydrology model outputs. Series of daily regional and global KF solutions were estimated from real GRACE KBRR data for the period 2003–2012. They provide a realistic description of hydrological fluxes at monthly time scales, which are consistent with classical spherical harmonics and mascons solutions provided by the GRACE official centers but also give an intra-month/daily continuity of these variations.

GRACE improves seasonal groundwater forecast initialization over the U.S

We evaluate the impact of Gravity Recovery and Climate Experiment data assimilation (GRACE-DA) on seasonal hydrological forecast initialization over the U.S., focusing on groundwater storage. GRACE-based terrestrial water storage (TWS) estimates are assimilated into a land surface model for the 2003-2016 period. Three-month hindcast (i.e., forecast of past events) simulations are initialized using states from the reference (no data assimilation) and GRACE-DA runs. Differences between the two initial hydrological condition (IHC) sets are evaluated for two forecast techniques at 305 wells where depth-to-water-table measurements are available. Results show that using GRACE-DA-based IHC improves seasonal groundwater forecast performance in terms of both RMSE and correlation. While most regions show improvement, degradation is common in the High Plains, where withdrawals for irrigation practices affect groundwater variability more strongly than the weather variability, which demonstrates the need for simulating such activities. These findings contribute to recent efforts towards an improved U.S. drought monitor and forecast system.

Analysis of Groundwater and Total Water Storage Changes in Poland Using GRACE Observations, In-situ Data, and Various Assimilation and Climate Models

The Gravity Recovery and Climate Experiment (GRACE) observations have provided global observations of total water storage (TWS) changes at monthly intervals for over 15 years, which can be useful for estimating changes in GWS after extracting other water storage components. In this study, we analyzed the TWS and groundwater storage (GWS) variations of the main Polish basins, the Vistula and the Odra, using GRACE observations, in-situ data, GLDAS (Global Land Data Assimilation System) hydrological models, and CMIP5 (the World Climate Research Programme’s Coupled Model Intercomparison Project Phase 5) climate data. The research was conducted for the period between September 2006 and October 2015. The TWS data were taken directly from GRACE measurements and also computed from four GLDAS (VIC, CLM, MOSAIC, and NOAH) and six CMIP5 (FGOALS-g2, GFDL-ESM2G, GISS-E2-H, inmcm4, MIROC5, and MPI-ESM-LR) models. The GWS data were obtained by subtracting the model TWS from the GRACE TWS. The resulting GWS values were compared with in-situ well measurements calibrated using porosity coefficients. For each time series, the trends, spectra, amplitudes, and seasonal components were computed and analyzed. The results suggest that in Poland there has been generally no major TWS or GWS depletion. Our results indicate that when comparing TWS values, better compliance with GRACE data was obtained for GLDAS than for CMIP5 models. However, the GWS analysis showed better consistency of climate models with the well results. The results can contribute toward selection of an appropriate model that, in combination with global GRACE observations, would provide information on groundwater changes in regions with limited or inaccurate ground measurements.

Regularization and error characterization of GRACE mascons

We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results with comparisons to independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget; i.e. the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.

Separation and Recovery of Geophysical Signals Based on the Kalman Filter with GRACE Gravity Data

Monthly gravitational field solutions as spherical harmonic coefficients produced by the GRACE satellite mission require post-processing to reduce the effects of shortwave-length noises and north–south stripe errors. However, the spatial smoothing and de-striping filter commonly used in the post-processing step will either reduce spatial resolution or remove short-wavelength features of geophysical signals, mainly at high latitudes. Here, by using prior covariance information that reflects the spatial and temporal features of the geophysical signals and the correlated errors derived from the synthetic model, together with the covariance matrix of the formal errors for the monthly gravity spherical harmonic coefficients, we apply the Kalman filter to separate the geophysical signal from GRACE Level-2 data and simultaneously to estimate the correlated errors. By increasing the number of observations, the iterative process is applied to update the state vector and covariance in the Kalman filter because the prior information is not accurate. Due to the inevitable truncation error, multiple gridded-gain factors method considering different temporal frequencies has been developed to recover the geophysical signal. The results show that the Kalman filter can reduce the high-frequency noises and correlated errors remarkably. When compared with the commonly used filter, no spatial filter (such as Gaussian filter) is used in the Kalman filter. Therefore, the estimated signal preserves its natural resolution, and more detailed information is retained. It shows good consistency when compared with mascon solutions in both secular trend and annual amplitude.

Terrestrial Water Storage in African Hydrological Regimes Derived from GRACE Mission Data: Intercomparison of Spherical Harmonics, Mass Concentration, and Scalar Slepian Methods

Spherical harmonics (SH) and mascon solutions are the two most common types of solutions for Gravity Recovery and Climate Experiment (GRACE) mass flux observations. However, SH signals are degraded by measurement and leakage errors. Mascon solutions (the Jet Propulsion Laboratory (JPL) release, herein) exhibit weakened signals at submascon resolutions. Both solutions require a scale factor examined by the CLM4.0 model to obtain the actual water storage signal. The Slepian localization method can avoid the SH leakage errors when applied to the basin scale. In this study, we estimate SH errors and scale factors for African hydrological regimes. Then, terrestrial water storage (TWS) in Africa is determined based on Slepian localization and compared with JPL-mascon and SH solutions. The three TWS estimates show good agreement for the TWS of large-sized and humid regimes but present discrepancies for the TWS of medium and small-sized regimes. Slepian localization is an effective method for deriving the TWS of arid zones. The TWS behavior in African regimes and its spatiotemporal variations are then examined. The negative TWS trends in the lower Nile and Sahara at -1.08 and -6.92 Gt/year, respectively, are higher than those previously reported.

High-resolution local gravity model of the south pole of the Moon from GRAIL extended mission data

We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6° by 1/6° (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40°. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models.

KEY POINTS

We present a high-resolution gravity model of the south pole of the Moon Improved correlations with topography to higher degrees than global models Improved fits to the data and reduced striping that is present in global models.