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GRACE-derived ice-mass variations over Greenland by accounting for leakage effects
Abstract
After more than 6 years in full operational mode, the Gravity Recovery and Climate Experiment (GRACE) satellite mission provides the opportunity to derive global secular mass changes from space-geodetic observations. Crucial for a reliable estimate of secular mass changes is the ability to correct for spectral and spatial leakage effects. In order to account for any leakage signal, we present and apply a four-step procedure, including a validation step based on forward gravity modeling. Most notably, our method is characterized by the separation and quantification of individual leakage sources. We test and apply our procedure to the Greenland area, which exhibits the strongest secular trend signal. On the basis of simulation studies, we demonstrate that leakage-out effects are dominant for the Greenland area, and if not accounted for, mass-change rates will be underestimated. Analyzing time-variable GRACE gravity fields covering 6 whole years (August 2002 to July 2008, inclusive), we estimate the ice-volume loss over Greenland to be 177 ± 12 km3/a. This value is the average derived from monthly gravity field models provided by CSR, GFZ and JPL, with individual contributions of 242 ± 14 km3/a, 194 ± 24 km3/a and 96 ± 23 km3/a, respectively. We highlight that without taking leakage effects into account, mass-change amplitudes over Greenland are reduced by a factor of 2. Despite the rather large spread of the results among GRACE processing centers, our results are in better agreement with the findings from alternative GRACE analysis methods and InSAR observations.
Supplementary resource (1)
Data
January 2012
... The gravity recovery and climate experiment (GRACE) satellite provides considerable information about Greenland's mass loss. The GRACE measurements, the gravity anomalies derived from the microwave ranging between two satellites from 2002 to 2016, suffer from noise and leakage effects (Baur, Kuhn, and Featherstone 2009). Signal leakage occurs due to the spatial averaging, spectral resolution, and cut-off spherical harmonics (Hippel and Harig 2019). ...
... One of the methods to solve the GRACE signal leakage is the forward modelling (FM) in which the geographical area is defined by a boundary and the localized signal is retrieved in an iterative process. This method can solve the landocean leakage but other noise components are amplified and hence signals are lost at the edges (Baur, Kuhn, and Featherstone 2009). ...
... At short time intervals, due to the movement of water in an area, the surface mass fluctuations are observed. These changes are caused by the circulation of water among the atmosphere, oceans, continents, glaciers, and polar ice (Baur, Kuhn, and Featherstone 2009). By singular value decomposition and the assumptions made by War et al. (1998), the surface density changes can be extended to the spherical harmonic series. ...
Monitoring the melting of Greenland ice using various sensors is of great importance due to global sea level rise. The mass changes in Greenland can be observed with the GRACE (Gravity Recovery and Climate Experiment) mission from 2002 to 2016. The GRACE limitations and noise are due to the geometrical and instrumental properties along its orbit, which requires investigations for further improvement. The innovation of this research is to introduce a new method in four-dimensional (4D) wavelet decomposition (WD) for increasing the efficiency of the GRACE signal, used for the reconstruction of the Greenland mass changes. The results show that the overall downward trend in the west Greenland coast is 25.25 ± 6.95 cm/year, and the highest decline rate is 33.60 ± 6.23 cm/year from 2013 to 2016. The northern regions of Greenland have less mass loss than the west and south. For verification, the 4D WD output has been compared with the CryoSat-2 results from 2011 to 2016. The GRACE and CryoSat-2 show a significant correlation of 0.62, which indicates an improvement of 0.18 compared to the forward modelling. The 4D WD improves the overall performance of the reconstructed signal in the frequency time-space domain and reduces the noise in each dimension.
... Although the GRACE data noises can be suppressed by different kinds of filters, the filter technique itself will lead to GRACE signal leakage and attenuation too (Wahr et al. 1998;Tang et al. 2012). Generally, this leakage error includes two types, that is, 'leakagein' error, signal in the surrounding area leaks into interested area and 'leakage-out' error, signal in interested area leaks into the surrounding area (Klees et al. 2007;Baur et al. 2009). Both errors can occur at global and regional scale due to the nature of 'spatial averaging' for any filters. ...
... To reduce the leakage error, some useful methods had been proposed. For example, Baur et al. (2009) presented a four-step procedure which used the total land mass change and land mass plus mass 1776 D. Mu et al. change in selected leakage area to calculate the so-called 'amplification factor'. This factor can help restore the 'true' total mass change in land. ...
... This factor can help restore the 'true' total mass change in land. Baur et al. (2009) applied this method to the Greenland ice sheet trend estimate. In contrast to spatial domain, Jacob et al. (2012) designed a sensitivity kernel in spectral domain to recover the 'true' mass change. ...
Filtering is a necessary step in the Gravity Recovery and Climate Experiment (GRACE) data processing, but leads to signal leakage and attenuation obviously, and adversely affects the quality of global and regional mass change estimates. We propose to use the Tikhonov regularization technique with the L-curve method to solve a correction equation which can reduce the leakage error caused by filter involved in GRACE data processing.We first demonstrate that the leakage error caused by the Gaussian filter can be well corrected by our regularization technique with simulation studies in Greenland and Antarctica. Furthermore, our regularization technique can restore the spatial distribution of original mass changes. For example, after applying the regularization method to GRAEC data (2003-2012), we find that GRACE mass changes tend to move from interior to coastal area in Greenland, which are consistent with recent other studies. After being corrected for glacial isostatic adjustment effect, our results show that the ice mass loss rates were 274 ± 30 and 107 ± 34 Gt yr⁻¹ in Greenland and Antarctica from 2003 to 2012, respectively. And a 10 ± 4 Gt yr⁻¹ increase rate in Greenland interior is also detected. © The Authors 2016. Published by Oxford University Press on behalf of The Royal Astronomical Society.
... One type is the "leakage-in" error, caused by signals from adjacent areas leaking to interest one. The other type is the "leakage-out" error, which signals leakage is opposite to the "leakage-in" [12]. ...
... For equation (11), ̅ is obtained by the method described in sec 3.1. the scale factor s is calculated by the equation (12). We skip over the process of derivation and give the equation as, ...
The accuracy of estimating changes in terrestrial water storage (TWS) using Gravity Recovery and Climate Experiment (GRACE) level-2 products is limited by the leakage effect resulting from post-processing and the weaker signal magnitude in adjacent areas. TWS anomaly in Dnieper River basin, where characteristic with medium scale and adjacent weak TWS anomaly, is estimate in this work. Two categories of leakage error repaired method (including forward modeling, Data-driven, single and multiple scaling factor) are employed. Root mean square error (RMSE) and Nash-Sutcliffe Efficiency (NSE) are used to evaluate the efficiency of methods. Compare to independent methods, TWS anomaly inverted by multiple scaling factor depending on CPC Soil Moisture model is more accurate in terms with RMSE 2.32 and NSE 0.88, which scaling factors corresponding to trend term 1.02, annual term 1.04, and semi-annual term 1.14. Further, comprehensive climate insights behind of the TWS anomaly were confirmed. The temperate continental climate of this River basin is shown, according to the variation of TWS anomaly in spatial domain. Snowmelt is significant role in TWS anomaly of Dnieper River basin, which is accord with the precipitation record and the 14 years temperature spatial distribution of February. Overall, we compare TWS anomaly recovered by single and multiple scaling method, the leakage signal originates mainly from semi-annual term of the TWS anomaly.
... The high-precision time-variable gravity signal is the most basic and direct physical quantity reflecting the geodynamic characteristics of various environments in which the density of the medium changes [1,2]. Since the early part of the 21st century, earth observations from space by platforms such as the GRACE satellites have been developing continuously, and time-variable gravity signals acquired on the global scale for more than 10 years have been used widely in geoscience, hydrology, astronomy, and other related fields [3][4][5][6][7]. In comparison with satellite gravimetry, ground-based gravity measurements obtained at regular intervals at fixed stations on Earth's surface are much closer to the field source, and the observed gravity signals can overcome the space resolution shortage (below 300 km) of gravity satellites. ...
... (5) Irrespective of how the number of AG values changes in a survey campaign, the calibrated SF changes almost synchronously, and the ratio between the two instruments remains broadly the same. (6) The difference between the two AG stations involved in the calibration process should cover no less than half that of the maximum GD in the network, and the difference of the SFs are no more than 100 ppm. ...
Ground-based time-variable gravimetry with high accuracy is an important approach in monitoring geodynamic processes. The uncertainty of instruments including scale factor (SF) and drift rate are the primary factors affect the quality of observation data. Differing from the conventional gravity adjustment procedure, this study adopted the modified Bayesian gravity adjustment (MBGA) method, which accounts for the nonlinear drift rate, and where the SF is considered as one of the hyperparameters estimated using Akaike’s Bayesian information criterion. Based on the terrestrial time-variable gravity datasets (2018–2020) from the southeastern Tibetan Plateau, errors caused by nonlinear drift rate and SF were processed quantitatively through analysis of the gravity difference (GD) residuals and the mutual difference of the GD. Additionally, cross validation from absolute gravity (AG) values was also applied. Results suggest that: (1) the drift rate of relavive instruments show nonlinear characteristics, and owing to their different spring features, the drift rate of CG-5 is much larger than that of LCR-G gravimeters; (2) the average bias between the original and optimized SF of the CG-5 gravimeters is approximately 169 ppm, while that of the LCR-G is no more than 63 ppm; (3) comparison of the differences in gravity values (GV) suggests that the uncertainty caused by the nonlinear drift rate is smaller than that attributable to SF. Overall, the novel approach adopted in this study was found effective in removing errors, and shown to be adaptive and robust for large-scale hybrid surface gravity campaign which providing high accuracy gravity data for the geoscience research.
... Due to a lack of in situ measurements, satellite remote sensing techniques have primarily been used to monitor GrIS changes. These techniques involve radar altimetry (the Ice, Clouds, and Land Elevation Satellite (ICESat) mission and CryoSat-2) [4][5][6][7], microwave radar (Cryosat, ERS-1/2, Envisat, Geosat, etc.) [8,9], satellite gravity (the Gravity Recovery and Climate Experiment (GRACE)) [10][11][12][13], and Global Navigation Satellite Systems (GNSS, such as GPS) [1,[14][15][16]. ...
... This effect causes inaccurate results, particularly in ocean-land areas [34]. It significantly attenuates the amplitudes and biases of mass loss estimates in Greenland [10,[34][35][36][37]. To reduce the ocean-land leakage effect, we applied a forward modeling technique [34] of GRACE monthly water storages changes results. ...
The Greenland Ice Sheet (GrIS) is losing mass at a rate that represents a major contribution to global sea-level rise in recent decades. In this study, we use the Gravity Recovery and Climate Experiment (GRACE) data to retrieve the time series variations of the GrIS from April 2002 to June 2017. We also estimate the mass balance from the RACMO2.3 and ice discharge data in order to obtain a comparative analysis and cross-validation. A detailed analysis of long-term trend and seasonal and inter-annual changes in the GrIS is implemented by GRACE and surface mass balance (SMB) modeling. The results indicate a decrease of −267.77 ± 8.68 Gt/yr of the GrIS over the 16-year period. There is a rapid decline from 2002 to 2008, which accelerated from 2009 to 2012 before declining relatively slowly from 2013 to 2017. The mass change inland is significantly smaller than that detected along coastal regions, especially in the southeastern, southwestern, and northwestern regions. The mass balance estimates from GRACE and SMB minus ice discharge (SMB-D) are very consistent. The ice discharge manifests itself mostly as a long-term trend, whereas seasonal mass variations are largely attributed to surface mass processes. The GrIS mass changes are mostly attributed to mass loss during summer. Summer mass changes are highly correlated with climate changes.
... An issue associated with estimated mass variations from GRACE data is the signal leakage. In the context of GRACE monthly solution, leakage effects are mainly due to the band-limited nature of the representation of the field in terms of Stokes's coefficients and the post-processing procedures to reduce the stripes (Baur et al., 2009). The latter might not be an issue here since the Stokes's coefficients have not been filtered. ...
... Consequently, the accuracy of surface mass changes derived from GRACE depends on the ability to identify, quantify, and remove leakage signals. There are many methods available to deal with leakage effects (see, e.g., Baur et al., 2009;Chen et al., 2006;Guo et al., 2010;Klees et al., 2008;Swenson and Wahr, 2002;Tang et al., 2012;Vishwakarma et al., 2017;Wiese et al., 2016). In this study, an approach that can be applied to a global set of surface densities covering the continents and that relies only on the GRACE data itself was considered. ...
The hydrology of the Third Pole, Asia's freshwater tower, has shown considerable sensitivity to the impacts of climate change and human interventions, which affect the headwaters of many rivers that originate therein. For example, the Yangtze River has its basin (YRB) experiencing wetness of terrestrial water storage (TWS), which rainfall seems to be the primary source as inferred from the previous studies. Consequently, it is crucial to understand the contributions of each TWS's sub-domain - i.e., groundwater (GWS); total water content (TWC) stored as soil moisture, ice/snow, and canopy; and the surface water (SWS) storages - on YRB's wetness. Hence, SWS, from altimetry and imagery satellites, and TWC, from Global Land Data Assimilation System, are inverted considering the same basis function as for TWS from the Gravity Recovery and Climate Experiment, which account for the differences in the resolutions inherent in each product. Furthermore, a tie-in signal approach is used to fit the temporal patterns of GWS, TWC, and SWS to TWS (i.e., the observations). Results show improvements in the reconstructed GWS series concerning standard deviation, correlation coefficient, and NashSutcliffe efficiency of 22%, 27%, and 120%, respectively, regarding the use of the TWS-budget equation. The reconstructed time series of GWS, TWC, and SWS present an increase of 1.76, 2.69, and 0.14 mm per year (mm/yr) and that YRB loses water stored at its aquifers 55% of the time (regarding 2003-2016 period) based on the quantile function of storage (QFS). The QFS's slope shows that TWS has a fast and small storage potential w.r.t. GWS since inland waters and soil moisture reflect the dryness impacting TWS first. Despite the evidence of an increase of 19.05 mm/yr in annual precipitation, which seems to explain the bulk in TWS, further investigation to characterize controls on TWS memory within YRB still necessary.
... For instance, it significantly attenuates amplitudes and biases of mass loss estimates in Greenland [40][41][42]. Various methods have been developed and applied to mitigate a leakage effect at global and regional scales [40][41][42][43][44][45][46][47]. A typical example is to isolate continental and oceanic mass-change signals either in the spatial or in the spectral domains. ...
... This can be done by disregarding oceanic margins to some distance from the coast (e.g., 300 km) in order to estimate the oceanic signal and correcting it for leakage errors caused by a continental hydrological signal [47]. Another method uses a basin average function [43][44][45][46]. This method could efficiently correct for a spatial leakage effect over larger regions, but assumptions of a numerical simulation limits its effectiveness. ...
The monitoring of water storage variations is essential not only for the management of water resources, but also for a better understanding of the impact of climate change on hydrological cycle, particularly in Tibet. In this study, we estimated and analyzed changes of the total water budget on the Tibetan Plateau from the Gravity Recovery And Climate Experiment (GRACE) satellite mission over 15 years prior to 2017. To suppress overall leakage effect of GRACE monthly solutions in Tibet, we applied a forward modeling technique to reconstruct hydrological signals from GRACE data. The results reveal a considerable decrease in the total water budget at an average annual rate of −6.22 ± 1.74 Gt during the period from August 2002 to December 2016. In addition to the secular trend, seasonal variations controlled mainly by annual changes in precipitation were detected, with maxima in September and minima in December. A rising temperature on the plateau is likely a principal factor causing a continuous decline of the total water budget attributed to increase melting of mountain glaciers, permafrost, and snow cover. We also demonstrate that a substantial decrease in the total water budget due to melting of mountain glaciers was partially moderated by the increasing water storage of lakes. This is evident from results of ICESat data for selected major lakes and glaciers. The ICESat results confirm a substantial retreat of mountain glaciers and an increasing trend of major lakes. An increasing volume of lakes is mainly due to an inflow of the meltwater from glaciers and precipitation. Our estimates of the total water budget on the Tibetan Plateau are affected by a hydrological signal from neighboring regions. Probably the most significant are aliasing signals due to ground water depletion in Northwest India and decreasing precipitation in the Eastern Himalayas. Nevertheless, an integral downtrend in the total water budget on the Tibetan Plateau caused by melting of glaciers prevails over the investigated period.
... Due to the different orbital altitudes and ground track patterns of the satellites, and due to the different observation techniques used, the gravity fields derived differ in their spherical harmonic and corresponding spatial resolution [22]. The truncation of the spherical harmonic expansion of the gravity field leads to spatial leakage that has to be taken into account when comparing the results (e.g., [4,[23][24][25][26]). Furthermore, the high-resolution GRACE gravity fields commonly are smoothed to suppress noise in the high-degree coefficients (e.g., [27][28][29]). ...
... The truncation of the spherical harmonic expansion at a certain maximum degree causes signal leakage (e.g., [23][24][25][26]). To demonstrate this effect, we simulate a mass layer with uniform mass distribution within the island of Greenland, while the mass over the rest of the globe is set to zero. ...
Satellite gravimetry allows for determining large scale mass transport in the system Earth and to quantify ice mass change in polar regions. We provide, evaluate and compare a long time-series of monthly gravity field solutions derived either by satellite laser ranging (SLR) to geodetic satellites, by GPS and K-band observations of the GRACE mission, or by GPS observations of the three Swarm satellites. While GRACE provides gravity signal at the highest spatial resolution, SLR sheds light on mass transport in polar regions at larger scales also in the pre-and post-GRACE era. To bridge the gap between GRACE and GRACE Follow-On, we also derive monthly gravity fields using Swarm data and perform a combination with SLR. To correctly take all correlations into account, this combination is performed on the normal equation level. Validating the Swarm/SLR combination against GRACE during the overlapping period January 2015 to June 2016, the best fit is achieved when down-weighting Swarm compared to the weights determined by variance component estimation. While between 2014 and 2017 SLR alone slightly overestimates mass loss in Greenland compared to GRACE, the combined gravity fields match significantly better in the overlapping time period and the RMS of the differences is reduced by almost 100 Gt. After 2017 both, SLR and Swarm indicate moderate mass gain in Greenland.
... In addition, the application of filtering moves gravity anomalies from one region to another region. Generally speaking, after applying a smoothing kernel some parts of the signals inside an area of interest leak out from it or alternatively signals from outside leak into the area of interest (e.g., Baur et al., 2009;Chen et al., 2007). These issues become more critical for basin-scale studies, especially where the sizes of the basins are small in comparison to the spatial resolution of GRACE (e.g., Longuevergne et al., 2010;Yeh et al., 2006). ...
... Several methods have been put forward to mitigate spatial leakage effects in TWS estimations from L2 products. These methods can largely be categorised into the following three groups (i) those that numerically estimate the leakages (leakage in and out) using the averaging kernels (e.g., Baur et al., 2009;Longuevergne et al., 2010;Seo and Wilson, 2005), (ii) those that are based on scaling factors derived from synthetic data (e.g., Landerer and Swenson, 2012;Long et al., 2015), and (iii) those that use inversion for simultaneous signal separation and leakage reduction (e.g., Frappart et al., 2011Frappart et al., , 2016Wouters and Schrama, 2007). From the first group, Swenson and Wahr (2002) developed an isotropic kernel using a Lagrange multiplier filter to best balance signal and leakage errors over a basin of interest. ...
The Gravity Recovery And Climate Experiment (GRACE) satellite mission provides time-variable gravity fields that are commonly used to study regional and global terrestrial total water storage (TWS) changes. These estimates are superimposed by different error sources such as the north–south stripes in the spatial domain and spectral/spatial leakage errors, which should be reduced before use in hydrological applications. Although different filtering methods have been developed to mitigate these errors, their performances are known to vary between regions. In this study, a Kernel Fourier Integration (KeFIn) filter is proposed, which can significantly decrease leakage errors over (small) river basins through a two-step post-processing algorithm. The first step mitigates the measurement noise and the aliasing of unmodelled high-frequency mass variations, and the second step contains an efficient kernel to decrease the leakage errors. To evaluate its performance, the KeFIn filter is compared with commonly used filters based on (i) basin/gridded scaling factors and (ii) ordinary basin averaging kernels. Two test scenarios are considered that include synthetic data with properties similar to GRACE TWS estimates within 43 globally distributed river basins of various sizes and application of the filters on real GRACE data. The KeFIn filter is assessed against water flux observations through the water balance equations as well as in-situ measurements. Results of both tests indicate a remarkable improvement after applying the KeFIn filter with leakage errors reduced in 34 out of the 43 assessed river basins and an average improvement of about 23.38% in leakage error reduction compared to other filters applied in this study.
... Leakage effects, where signals spread spatially and are not concentrated directly over the area of mass variation, are a major challenge (Baur et al. 2009). The approach proposed by Tang et al. (2012)is used to correct for leakage effects, which relies only on GRACE data and can be applied globally. ...
... For Equation (11), g c is obtained by the method described in Section 3.1. The scale factor s is calculated using Equation (12). We skip over the process of derivation and give the equation as, ...
The accuracy of estimating changes in terrestrial water storage (TWS) using Gravity Recovery and Climate Experiment (GRACE) level-2 products is limited by the leakage effect resulting from post-processing and the weak signal magnitude in adjacent areas. The TWS anomaly from 2003 to 2016 in the Dnieper River basin, with characteristics of medium scale and an adjacent weak TWS anomaly area, are estimated in this work. Two categories of leakage error repair approaches (including forward modeling, data-driven, single, and multiple scaling factor approaches) are employed. Root mean square error (RMSE) and Nash–Sutcliffe Efficiency (NSE) are used to evaluate the efficiency of approaches. The TWS anomaly inverted by the forward modeling approach (FM) is more accurate in terms of RMSE 3.04 and NSE 0.796. We compared single and multiple scaling approaches for the TWS anomaly and found that leakage signals mostly come from semi-annual terms. From the recovered results demonstrated in the spatial domain, the South of Dnieper River basin is more sensitive to the leakage effect because of it is adjacent to a weak hydrological signal region near the Black Sea. Further, comprehensive climate insights and physical mechanisms behind the TWS anomaly were confirmed. The temperate continental climate of this river basin is shown according to the variation in TWS anomaly in the spatial domain. Snowmelt plays a significant role in the TWS anomaly of the Dnieper River basin, following the precipitation record and the 14-year temperature spatial distribution for February. We compared single and multiple scaling approaches for the TWS anomaly and found that leakage signals mostly come from semi-annual terms.
... northeast Canada, which are not a part of the ice sheet. This is especially a problem in Northern Greenland (Baur et al., 2009;Barletta et al., 2013). Similarly, in Antarctica, the surrounding ocean creates a leakage error (Horwath and Dietrich, 2009;Chen et al., 2015). ...
The time series of observations from NASA’s latest satellite laser altimetry, the Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) are now mature to revisit the methodology for estimating surface elevation change and mass balance of ice sheets as proposed by Sørensen et al. (2011). Following the original ICESat study, we combine the derived ICESat-2 surface elevation change estimates with modelled changes of both the firn and the vertical bedrock to derive the total mass balance of the ice sheets, during the northern hemisphere mass balance years of October 2018 to September 2021. The method of converting the surface elevation change to mass balance change has been refined to obtain more reliable mass balance results for both ice sheets. From 2018 to 2021, we find that the grounded ice sheet in Antarctica has lost 135.7±27.3 Gt year-1, and the Greenland ice sheet 237.5±14.0 Gt year-1. Compared to 2003–2008, the ICESat-2 derived mass change of the Greenland ice sheet has a similar magnitude; however, the spatial pattern is changed and we observe reduced ice loss around Jakobshavn Isbræ and in the southeast accompanied by increased loss almost everywhere else and especially in the northern sector of the ice sheet. Our results show pervasive ice sheet loss across much of Greenland in recent years and an increase in loss from Antarctica compared to earlier studies. Parallels between the two ice sheets revealed by ICESat-2 data reflect atmospheric and oceanic drivers and show the importance of understanding ice sheets as components within the Earth system.
... Different methods have been applied to the GRACE/GRACE-FO Level-2 (L2) data, i.e., the monthly sets of spherical harmonic coefficients (SHCs) describing the Earth's gravitational potential (Stokes coefficients), to conclude on the causing mass changes. A wide range of studies have made use of different variants of the regional integration approach [4] and have applied it both in the space (e.g., [5]) and in the spectral domain (e.g., [6,7]). Mass concentration (mascon) approaches have been applied to L2 data both in the space (e.g., [8]) and in the spectral domain (e.g., [7]). ...
We derived gravimetric mass change products, i.e., gridded and basin-averaged mass changes, for the Antarctic Ice Sheet (AIS) from time-variable gravity-field solutions acquired by the Gravity Recovery and Climate Experiment (GRACE) mission and its successor GRACE-FO, covering more than 18 years. For this purpose, tailored sensitivity kernels (TSKs) were generated for the application in a regional integration approach. The TSKs were inferred in a formal optimization approach minimizing the sum of both propagated mission errors and leakage errors. We accounted for mission errors by means of an empirical error covariance model, while assumptions on signal variances of potential sources of leakage were used to minimize leakage errors. To identify the optimal parameters to be used in the TSK generation, we assessed a set of TSKs by quantifying signal leakage from the processing of synthetic data and by inferring the noise level of the derived basin products. The finally selected TSKs were used to calculate mass change products from GRACE/GRACE-FO Level-2 spherical harmonic solutions covering 2002-04 to 2020-07. These products were compared to external data sets from satellite altimetry and the input–output method. For the period under investigation, the mass balance of the AIS was quantified to be −90.9±43.5 Gt a−1, corresponding to a mean sea-level rise of 0.25±0.12 mm a−1.
... The most commonly used global-scale remote-sensing based TWS dataset is the Gravity Recovery and Climate Experiment (GRACE) satellite data (Tapley et al., 2004 andTapley et al., 2019). Since March 2002, GRACE TWSA has been widely applied in estimating groundwater storage changes Li et al., 2019;Wang et al., 2020;Yeh et al., 2006), river discharge (Ehalt Macedo et al., 2019;Xie et al., 2019), evapotranspiration (Long et al., 2014;Pan et al., 2017), and the changing mass of ice sheets (Baur et al., 2009;Velicogna et al., 2020) and glaciers (Ciracì et al., 2020;Schrama et al., 2014). These GRACE applications have provided important insights on the variability of regional-to-global TWS and more general for the entire water cycle. ...
Terrestrial water storage (TWS) is a vital component in global hydrologic cycle with direct linkage to water resources availability and hydrologic extremes. Assessing the uncertainty in TWS projections are fundamentally important for developing counter-measures against impacts of climate change on water resources and disasters. This study presents a global-scale evaluation of model agreement and uncertainty in TWS anomaly (TWSA) simulations within the ISIMIP 2b framework by comparison with the 2006–2016 Gravity Recovery and Climate Experiment (GRACE) data. The total 24 members of ISIMIP2b ensembles considered here include the permutations of 6 global water models (GWMs: CLM4.5, H08, LPLmL, MATSIRO, PCR-GLOBWB, WaterGAP2) simulations forced by 4 global climate models (GCMs: GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR, MIROC5) under RCP2.6 and RCP6.0 scenarios. Results show that the fraction of global land area with the same sign between the ISIMIP2b ensemble mean and GRACE TWSA is 47.5% and 47.3% under RCP2.6 and RCP6.0, respectively. The ensemble mean reproduces the negative (positive) TWSA in southern North America, southwestern Asia, northern and central Africa (central South America and northern Europe) under both scenarios. >50% of ensemble members agree with GRACE TWS better in the sign of drying trend than wetting trend over the global land. The interannual TWS variations among ensemble members show better agreement in North America and Europe than other continents. >80% of ensemble members simulate larger (smaller) TWS seasonal amplitude than GRACE in North America, Europe, and Asia (South America, Africa, and Australia). GWM is found to be the main source of uncertainty in TWS simulations in North America, Europe, and Asia (>55%), while GCM uncertainty is the dominant uncertainty source in South America, Africa, and Australia (>45%).
... Studying the amplitude and phase changes among Gaussian-filtered GRACE solutions with different averaging radii also lead to the development of efficient methods for the correction of leakage effects. These methods are applicable to both spatial (Baur et al., 2009;Baur and Sneeuw, 2011;Chen et al., 2015;Mu et al., 2017) and basinscale (Klees et al., 2007;Landerer and Swenson, 2012;Longuevergne et al., 2010;Vishwakarma et al., 2016Vishwakarma et al., , 2017 estimates of GRACE-derived mass changes. In order to account for the correlated nature of GRACE errors, some simple non-isotropic Gaussian filters have also been designed (Han et al., 2005b;Guo et al., 2010). ...
The isotropic Gaussian filter has been used extensively in Gravity Recovery and Climate Experiment (GRACE) temporal gravity field solutions, and is still being applied to GRACE Follow-On products to remove high-frequency errors and improve the estimation of mass transport events on the Earth’s surface. For such applications, the only known rigorous method to calculate the spherical harmonic coefficients of an isotropic Gaussian filter is by the use of a second-order recurrence relation. As an alternative, an approximate expression is also used frequently. In this paper, we provide some additional expressions for the calculation of isotropic Gaussian filter kernels in the spherical harmonic domain. Specifically, we derive a new recurrence relation, a closed-form expression, expressions involving modified Bessel functions of the first kind, and a new approximate expression. We also examine and compare them from a computational viewpoint. The results of our numerical investigations indicate that the new recurrence relation and the closed-form expression are unstable in a way similar to the second-order recurrence relation that has been used so far. The expressions involving modified Bessel functions, and particularly the ones using exponentially scaled modified Bessel functions, provide a simple, elegant and stable way of calculating isotropic Gaussian filter coefficients, since routines for their stable evaluation are readily available in many programming languages. Alternatively, the new approximate expression can be used, which is also stable and offers better accuracy than previous approximations.
... This can be considered a limitation for gravimetric observations of mass redistributions, called signal leakage between ocean and land. Therefore, an underestimation happens in mass changes on land or ocean [154]. Thus, leakage correction is necessary for the coastal regions to avoid underestimating mass changes [155]. ...
As discussed in the previous part of this review paper, Remote Sensing (RS) creates unprecedented opportunities by providing a variety of systems with different characteristics to study and monitor oceans. Part 1 of this review paper was dedicated to reviewing passive RS systems and their main applications in the ocean. Here, in part 2, seven active RS systems, including scatterometers, altimeters, gravimeters, Synthetic Aperture Radar (SAR), Light Detection and Ranging (LiDAR), Sound Navigation and Ranging (SONAR), High-Frequency (HF) radars are comprehensively reviewed. For consistency, this part is structured similarly to part 1. The aforementioned systems, along with their characteristics and primary applications, are introduced in separate sections. This review paper provides useful information to all students and researchers who are interested in the oceanographic applications of active RS systems.
... Several techniques have been proposed for the estimation and removal of ice mass leakage from GRACE data, by modeling the spatial distribution of ice mass changes. Baur et al. (2009) developed a four-step procedure for estimating the magnitude and geometry of leakage effects. Their method in based on the amplification of the total mass changes in the study area using forward modeling and analysis of the total mass change in an extended area. ...
The need for a reliable land hydrology model that can monitor the amount of water stored on and beneath the Earth’s surface on a regional and global scale has become very important, especially in overpopulated areas or regions that already suffer from shortage of freshwater. The main objective of this thesis is to examine the hydrology signal in North America using a combination of land hydrology models and satellite gravimetry products coming from the GRACE satellite mission. Our analysis emphasizes on the post-processing of GRACE data. More specifically, we define a detailed framework for the extraction of hydrological signals from GRACE data by removing the contribution of non-hydrologic geophysical components and using advanced processing techniques. In order to carry out this objective, we improve the most frequently-used filtering methods for the suppression of correlated errors from GRACE data, and develop more refined algorithms for their implementation. We formulate a selective decorrelation of GRACE data using machine learning and show that our new approach mitigates the over-filtering effects of the conventional decorrelation. We also solve the instability and inaccuracy problems related to the calculation of isotropic Gaussian filter coefficients and develop new expressions that simplify their evaluation. We assess the GRACE data and the hydrology models, and find a satisfactory level of agreement between them, with an averaged RMS difference of 3.9 cm in terms of equivalent water height. We then combine these independent datasets and develop two combined hydrology models for the monitoring of monthly terrestrial water storage and groundwater storage variations. We examine their seasonal and long-term variations and provide useful insights for the spatiotemporal evolution of water masses in North America from 2003 to 2014. For the most part, North America is affected by negative long-term trends of terrestrial and ground water changes that are more evident in Hudson Bay and southern North America, whereas strong accumulation of water masses is observed in central North America. The combined models developed in this study provide a basis for the continuous satellite-based monitoring of land hydrology in North America and can be used for the improved management of water resources.
... In order to study the variations in the mass distribution of the water (snow, ice) storage near the Earth surface, satellite gravity measurements are expressed by means of the so-called equivalent water height, which is directly connected to surface mass density (i.e., mass/area) [9,40,41]. To suppress the errors in monthly gravity solutions that grow with harmonic degree (short scales, high-frequency noise), a Gaussian smoothing filter is usually applied; for Greenland we chose its radius to be 200 km (cf., [42]). ...
Over the last two decades, a small group of researchers repeatedly crossed the Greenland interior skiing along a 700-km long route from east to west, acquiring precise GNSS measurements at exactly the same locations. Four such elevation profiles of the ice sheet measured in 2002, 2006, 2010 and 2015 were differenced and used to analyze the surface elevation change. Our goal is to compare such locally measured GNSS data with independent satellite observations. First, we show an agreement in the rate of elevation change between the GNSS data and satellite radar altimetry (ERS, Envisat, CryoSat-2). Both datasets agree well (2002–2015), and both correctly display local features such as an elevation increase in the central part of the ice sheet and a sharp gradual decline in the surface heights above Jakobshavn Glacier. Second, we processed satellite gravimetry data (GRACE) in order for them to be comparable with local GNSS measurements. The agreement is demonstrated by a time series at one of the measurement sites. Finally, we provide our own satellite gravimetry (GRACE, GRACE-FO, Swarm) estimate of the Greenland mass balance: first a mild decrease (2002–2007: −210 ± 29 Gt/yr), then an accelerated mass loss (2007–2012: −335 ± 29 Gt/yr), which was noticeably reduced afterwards (2012–2017: −178 ± 72 Gt/yr), and nowadays it seems to increase again (2018–2019: −278 ± 67 Gt/yr).
... While geocenter variations and GIA play a minor role in Greenland, the area is known for signal leaking out in the surrounding ocean. To compensate for this, we fetch back the signal from a 100-km offshore zone following the approach in Baur et al. (2009). The GIA effect is again reduced using the model from A et al. (2012). ...
A new approach to recover time-variable gravity fields from satellite laser ranging (SLR) is presented. It takes up the concept of lumped coefficients by representing the temporal changes of the Earth’s gravity field by spatial patterns via combinations of spherical harmonics. These patterns are derived from the GRACE mission by decomposing the series of monthly gravity field solutions into empirical orthogonal functions (EOFs). The basic idea of the approach is then to use the leading EOFs as base functions in the gravity field modelling and to adjust the respective scaling factors straightforward within the dynamic orbit computation; only for the lowest degrees, the spherical harmonic coefficients are estimated separately. As a result, the estimated gravity fields have formally the same spatial resolution as GRACE. It is shown that, within the GRACE time frame, both the secular and the seasonal signals in the GRACE time series are reproduced with high accuracy. In the period prior to GRACE, the SLR solutions are in good agreement with other techniques and models and confirm, for instance, that the Greenland ice sheet was stable until the late 1990s. Further validation is done with the first monthly fields from GRACE Follow-On, showing a similar agreement as with GRACE itself. Significant differences to the reference data only emerge occasionally when zooming into smaller river basins with strong interannual mass variations. In such cases, the approach reaches its limits which are set by the low spectral sensitivity of the SLR satellites and the strong constraints exerted by the EOFs. The benefit achieved by the enhanced spatial resolution has to be seen, therefore, primarily in the proper capturing of the mass signal in medium or large areas rather than in the opportunity to focus on isolated spatial details.
... To reduce spatial leakage, various filtering methods have been implemented which are categorized into the following three groups. 1) Estimation of in and out leakage with averaging kernels have been attempted by Seo and Wilson (2005); Han et al. (2005); Baur et al. (2009); Swenson and Wahr (2002); and Longuevergne et al. (2010). 2) Some filtering techniques are based on scaling factors that are obtained from artificial data (e.g., Landerer and Swenson, 2012;Long et al., 2016). ...
Global climate change and anthropogenic impacts lead to alterations in the water cycle, water resource availability and the frequency and intensity of floods and droughts. As a result, developing effective techniques such as hydrological modeling is essential to monitor and predict water storage changes. However, inaccuracies and uncertainties in different aspects of modeling, due to simplification of meteorological physical processes, data limitations and inaccurate climate forcing data limit the reliability of hydrological models. Satellite remote sensing datasets, especially Terrestrial Water Storage (TWS) data which can be obtained from Gravity Recovery and Climate Experiment (GRACE), provide a new and valuable source of data which can augment our understanding of the hydrologic cycle. Merging these new observations with hydrological models can effectively enhance the model performance using advanced statistical and numerical methods, which is known as data assimilation. Assimilation of new observations constrain the dynamics of the model based on uncertainties associated with both model and data, which can introduce missing water storage signals e.g., anthropogenic and extreme climate change effects. Assimilation of GRACE TWS data into hydrological models is a challenging task as provision should be made for handling the errors and then merging them with hydrological models using efficient assimilation techniques. The goal of this paper is to provide an in-depth overview of recent studies on assimilating GRACE TWS data into hydrological models and shed light on their limitations, challenges and progress. We present a comprehensive review of some challenges with GRACE TWS data assimilation into a hydrological model including GRACE TWS errors e.g., the correlated noise of high-frequency mass variations and spatial leakage errors, and how to work with GRACE TWS data errors to use the potential of GRACE TWS data as much as possible. We provide a review of the benefits and limitations of available data assimilation techniques with emphasis on the capability of sequential methods for hydrological applications.
... Satellite remote-sensing techniques have primarily been used to detect changes in the GrIS, such as the Global Navigation Satellite Systems technique [1,9,10], satellite altimetry [11][12][13][14][15], and satellite gravity [16][17][18][19]. The Gravity Recovery and Climate Experiment (GRACE) space mission in the terrestrial gravity field from space has been successfully used to monitor the mass changes in Greenland from temporal variations in space [20][21][22][23]. The mass changes of the GrIS detected by GRACE are the sum of mass variations in the glacial dynamic mass balance (ice discharge) and the surface mass balance (SMB) [8,[24][25][26][27], but GRACE observations cannot directly separate these physical causes. ...
Although a significant effort has been dedicated to studying changes in the mass budget of
the Greenland Ice Sheet (GrIS), mechanisms behind these changes are not yet fully understood. In this study, we address this issue by investigating the link between climate controls and mass changes of the GrIS between August 2002 and June 2017. We estimate the GrIS mass changes based on averaging the Gravity Recovery and Climate Experiment (GRACE) monthly gravity field solutions from four processing data centers. We then investigate the possible impact of different climate variables on the GrIS mass changes using the North Atlantic Oscillation (NAO), temperature, precipitation, and the 700 hPa wind retrieved from the ERA-5 reanalysis. Results indicate a decrease of −267.77 ± 32.67 Gt/yr in the total mass of the GrIS over the 16-year period. By quantifying the relationship between climate controls and mass changes, we observe that mass changes in different parts of Greenland have varying sensitivity to climate controls. The NAO mainly controls mass changes in west Greenland, where the summertime NAO modulations have a greater impact on the summer mass loss than the wintertime NAO modulations have on the winter mass gain. The GrIS mass changes are correlated spatially with summer temperature, especially in southwest Greenland. Mass balance changes in northwest Greenland are mostly affected by wind anomalies. These new findings based on wind anomalies indicate that the summer atmospheric circulation anomalies control surface temperature and snow precipitation and consequently affect mass changes in different parts of Greenland.
... The contribution is in the range of 0.36~0.50 mm yr −1 [18,20,21] Even within the different periods, using the same type of GRACE data still leads to errors in the results. Generally, the source of error is not only the difference in the research period, as for the same data product, the error obtained during the same period is relatively large. ...
The melting of the polar ice caps is considered to be an essential factor for global sea-level rise and has received significant attention. Quantitative research on ice cap mass changes is critical in global climate change. In this study, GRACE JPL RL06 data under the Mascon scheme based on the dynamic method were used. Greenland, which is highly sensitive to climate change, was selected as the study area. Greenland was divided into six sub-research regions, according to its watersheds. The spatial–temporal mass changes were compared to corresponding temperature and precipitation statistics to analyze the relationship between changes in ice sheet mass and climate change. The results show that: (i) From February 2002 to September 2019, the rate of change in the Greenland Ice Sheet mass was about −263 ± 13 Gt yr−1 and the areas with the most substantial ice sheet loss and climate changes were concentrated in the western and southern parts of Greenland. (ii) The mass balance of the Greenland Ice Sheet during the study period was at a loss, and this was closely related to increasing trends in temperature and precipitation. (iii) In the coastal areas of western and southern Greenland, the rate of mass change has accelerated significantly, mainly because of climate change.
... One needs to take care when attributing the absolute trend signal. The uncertainty of the TWS trend is estimated based on one standard deviation of the three GRACE mascons, which seems different from some studies (Baur et al., 2009;Scanlon et al., 2018) using leakage and measurement errors. ...
Terrestrial water storage (TWS) changes are driven by internal climate variability, external natural climate change, external human‐caused climate change, and human water management. Spatiotemporal patterns of TWS change and attribution can help understand the water cycle process and refine water management in a region. Here, the spatiotemporal changes in the TWS in China between 2003 and 2016 are analyzed based on three monthly mass concentration (mascon) data products from the Gravity Recovery and Climate Experiment (GRACE) satellites, and the possible drivers are investigated using multiple precipitation products, land surface models, and multisource remote sensing and socioeconomic data. Six major TWS change regions are detected, including negative trends in northwestern China, the southeastern Tibetan Plateau, and northern China and positive trends in western China, southern China, and northeastern China. Two global hydrological models, WaterGAP and PCR‐GLOBWB, substantially underestimate the TWS changes relative to GRACE. Four land surface models (CLM 2.0, VIC, MOSAIC, and NOAH 3.3) from the Global Land Data Assimilation System version 2.1 show large model uncertainties in simulating the TWS trend. A statistical attribution indicates that ice melting under human‐caused climate change is a driver of decreasing TWS in northwestern China and the southeastern Tibetan Plateau that cannot be ignored, while human water use is largely responsible for groundwater depletion in northern China. The increasing TWS in southern China and northeastern China is likely caused by precipitation increases, and the increasing TWS in western China is probably a result of precipitation increases and water supplementation from ice melting.
... Therefore, the separation into the contributions of the individual subsystems of the Earth still remains a challenge. There exists a large number of papers concerning the reduction of leakage effects in GRACE-derived mass variations of the continental hydrosphere (e.g., Klees et al. 2007;Longuevergne et al. 2010;Landerer and Swenson 2012;Vishwakarma et al. 2016Vishwakarma et al. , 2017Khaki et al. 2018), oceans (e.g., Chambers 2006Chambers and Bonin 2012;Peralta-Ferris et al. 2014) and cryosphere (e.g., Baur et al. 2009;King et al. 2012;Velicogna and Wahr 2013;Chen et al. 2015;Mu et al. 2017). Many of these techniques depend on geophysical model information such as the forward modelling approaches (additive, multiplicative and scaling) which are designed for specific subsystems of the Earth or regions. ...
Abstract Polar motion is caused by mass redistribution and motion within the Earth system. The GRACE (Gravity Recovery and Climate Experiment) satellite mission observed variations of the Earth’s gravity field which are caused by mass redistribution. Therefore GRACE time variable gravity field models are a valuable source to estimate individual geophysical mass-related excitations of polar motion. Since GRACE observations contain erroneous meridional stripes, filtering is essential to retrieve meaningful information about mass redistribution within the Earth system. However filtering reduces not only the noise but also smoothes the signal and induces leakage of neighboring subsystems into each other. We present a novel approach to reduce these filter effects in GRACE-derived equivalent water heights and polar motion excitation functions which is based on once- and twice-filtered gravity field solutions. The advantages of this method are that it is independent from geophysical model information, works on global grid point scale and can therefore be used for mass variation estimations of several subsystems of the Earth. A closed-loop simulation reveals that due to application of the new filter effect reduction approach the uncertainties in GRACE-derived polar motion excitations can be decreased from 12–48% to 5–29%, especially for the oceanic excitations. Comparisons of real GRACE data with model-based oceanic excitations show that the agreement can be improved by up to 15 percentage points.
... For example, Velicogna et al. [26][27][28] earlier used GRACE data to study the mass balance of Greenland ice sheet, which concluded that the total melting rate of the Greenland ice sheet showed an increasing trend of 248 ± 36 km 3 /a, and an acceleration of −30 ± 11 Gt/yr 2 ; Ramilli et al. [29] estimated that the melting rate of the Greenland ice sheet was −109 ± 9 Gt/a from 2002 to 2005; Slobbe et al. [30] used GRACE post-processing data to compare Greenland ice sheet mass changes from four different organizations. The results indicated that the different data sources caused different results; Baur et al. [31] explored the annual average Greenland ice sheet melting with a rate of 162 ± 11 km 3 /a through GRACE RL04 data during Joodaki et al. [32] found that the mass of the Greenland ice sheet melted at the rate of −166 ± 20 Gt/a and the acceleration of melting was −32 ± 6 Gt/a by GRACE RL04 data from 2002 to 2011; Lu Fei et al. [33] found that the melting speed and acceleration of the ice sheet were −157.8 ± 11.3 Gt/a and −17.7 ± 4.5 Gt/a 2 , respectively, through GRACE RL05 data from 2003 to 2012. In addition, the melting rate significantly increased after 2010, from −132.2 Gt/a in 2003-2009to −252.5 Gt/a in 2010-2012Forsberg et al. [34] concluded that the mass change rate of the Greenland ice sheet was 265 ± 25 Gt/a, and the correlation coefficient was 0.72 with the global mean sea level change. ...
With the warming of the global climate, the mass loss of the Greenland ice sheet is intensifying, having a profound impact on the rising of the global sea level. Here, we used Gravity Recovery and Climate Experiment (GRACE) RL06 data to retrieve the time series variations of ice sheet mass in Greenland from January 2003 to December 2015. Meanwhile, the spatial changes of ice sheet mass and its relationship with land surface temperature are studied by means of Theil–Sen median trend analysis, the Mann–Kendall (MK) test, empirical orthogonal function (EOF) analysis, and wavelet transform analysis. The results showed: (1) in terms of time, we found that the total mass of ice sheet decreases steadily at a speed of −195 ± 21 Gt/yr and an acceleration of −11 ± 2 Gt/yr2 from 2003 to 2015. This mass loss was relatively stable in the two years after 2012, and then continued a decreasing trend; (2) in terms of space, the mass loss areas of the Greenland ice sheet mainly concentrates in the southeastern, southwestern, and northwestern regions, and the southeastern region mass losses have a maximum rate of more than 27 cm/yr (equivalent water height), while the northeastern region show a minimum rate of less than 3 cm/yr, showing significant changes as a whole. In addition, using spatial distribution and the time coefficients of the first two models obtained by EOF decomposition, ice sheet quality in the southeastern and northwestern regions of Greenland show different significant changes in different periods from 2003 to 2015, while the other regions showed relatively stable changes; (3) in terms of driving factors temperature, there is an anti-phase relationship between ice sheet mass change and land surface temperature by the mean XWT-based semblance value of −0.34 in a significant oscillation period variation of 12 months. Meanwhile, XWT-based semblance values have the largest relative change in 2005 and 2012, and the smallest relative change in 2009 and 2010, indicating that the influence of land surface temperature on ice sheet mass significantly varies in different years.
... The correction methods can be classified in terms of the application for which they were developed (for example: for ice sheets, for hydrology, and for land-ocean signal leakage), or in terms of the source of the correction quantity (for example: model-dependent and data-driven) [6,[19][20][21][24][25][26][27][28][29]. Since in this article we are focusing on land-hydrology from GRACE, we choose the correction methods relevant for hydrological investigations only. ...
The mass change information from the Gravity Recovery And Climate Experiment (GRACE) satellite mission is available in terms of noisy spherical harmonic coefficients truncated at a maximum degree (band-limited). Therefore, filtering is an inevitable step in post-processing of GRACE fields to extract meaningful information about mass redistribution in the Earth-system. It is well known from previous studies that a number can be allotted to the spatial resolution of a band-limited spherical harmonic spectrum and also to a filtered field. Furthermore, it is now a common practice to correct the filtered GRACE data for signal damage due to filtering (or convolution in the spatial domain). These correction methods resemble deconvolution, and, therefore, the spatial resolution of the corrected GRACE data have to be reconsidered. Therefore, the effective spatial resolution at which we can obtain mass changes from GRACE products is an area of debate. In this contribution, we assess the spatial resolution both theoretically and practically. We confirm that, theoretically, the smallest resolvable catchment is directly related to the band-limit of the spherical harmonic spectrum of the GRACE data. However, due to the approximate nature of the correction schemes and the noise present in GRACE data, practically, the complete band-limited signal cannot be retrieved. In this context, we perform a closed-loop simulation comparing four popular correction schemes over 255 catchments to demarcate the minimum size of the catchment whose signal can be efficiently recovered by the correction schemes. We show that the amount of closure error is inversely related to the size of the catchment area. We use this trade-off between the error and the catchment size for defining the potential spatial resolution of the GRACE product obtained from a correction method. The magnitude of the error and hence the spatial resolution are both dependent on the correction scheme. Currently, a catchment of the size ≈63,000 km 2 can be resolved at an error level of 2 cm in terms of equivalent water height.
... Given the importance of monitoring wet-snow properties for hydrology, synthetic aperture radar (SAR) retrieval approaches have been proposed, since passive approaches are not sensitive to dry snow parameters. Gravimetric techniques represent another alternative to microwavebased measurement of snow depth (Baur et al., 2009), but the approach is limited by the large spatial and coarse temporal characteristics of such sensors (Niu et al., 2007). In the light of the non-selection of ESA's CoreH2O as an Earth Explore mission, there remains a need for high-resolution active microwave sensors with high revisit times to more effectively capture the dynamics of wet-snow in diverse terrain. ...
In just the past 5 years, the field of Earth observation has progressed beyond the offerings of conventional space-agency-based platforms to include a plethora of sensing opportunities afforded by CubeSats, unmanned aerial vehicles (UAVs), and smartphone technologies that are being embraced by both for-profit companies and individual researchers. Over the previous decades, space agency efforts have brought forth well-known and immensely useful satellites such as the Landsat series and the Gravity Research and Climate Experiment (GRACE) system, with costs typically of the order of 1 billion dollars per satellite and with
concept-to-launch timelines of the order of 2 decades (for new missions).
More recently, the proliferation of smartphones has helped to miniaturize
sensors and energy requirements, facilitating advances in the use of
CubeSats that can be launched by the dozens, while providing ultra-high (3–5 m) resolution sensing of the Earth on a daily basis. Start-up companies that did not exist a decade ago now operate more satellites in orbit than any space agency, and at costs that are a mere fraction of traditional satellite missions. With these advances come new space-borne measurements, such as real-time high-definition video for tracking air pollution, storm-cell
development, flood propagation, precipitation monitoring, or even for
constructing digital surfaces using structure-from-motion techniques. Closer
to the surface, measurements from small unmanned drones and tethered
balloons have mapped snow depths, floods, and estimated evaporation at
sub-metre resolutions, pushing back on spatio-temporal constraints and
delivering new process insights. At ground level, precipitation has been
measured using signal attenuation between antennae mounted on cell phone
towers, while the proliferation of mobile devices has enabled
citizen scientists to catalogue photos of environmental conditions, estimate
daily average temperatures from battery state, and sense other
hydrologically important variables such as channel depths using commercially
available wireless devices. Global internet access is being pursued via high-altitude balloons, solar planes, and hundreds of planned satellite launches, providing a means to exploit the internet of things as an entirely new measurement domain. Such global access will enable real-time collection of data from billions of smartphones or from remote research platforms. This future will produce petabytes of data that can only be accessed via cloud storage and will require new analytical approaches to interpret. The extent to which today's hydrologic models can usefully ingest such massive data
volumes is unclear. Nor is it clear whether this deluge of data will be
usefully exploited, either because the measurements are superfluous,
inconsistent, not accurate enough, or simply because we lack the capacity to
process and analyse them. What is apparent is that the tools and techniques
afforded by this array of novel and game-changing sensing platforms present
our community with a unique opportunity to develop new insights that advance
fundamental aspects of the hydrological sciences. To accomplish this will
require more than just an application of the technology: in some cases, it
will demand a radical rethink on how we utilize and exploit these new
observing systems.
... km), ρ ave is the average density of the Earth (5515 kg/m 3 ), ϱ w is the average density of water (1000 kg/ m 3 ), k l is the load Love numbers of degree l, P lm are the normalized associated Legendre function of degree l and order m with l max = 60 and ΔY lm are the normalized complex spherical harmonic coefficients of temporal anomalies of the geoid after subtracting the long term mean. The regularisation filter leads to leakage and attenuation of the signal's amplitude (e.g., Wouters and Schrama, 2007;Baur et al., 2009), hence a scaling factor was computed following Landerer and Swenson (2012) in order to account for the geophysical signal loss, which occurred during the pre-processing of GRACE data. Specifically, the scale factor was empirically derived using GLDAS-derived total water storage content (see more details in Section 3.5). ...
By combining satellite altimetry with Gravity Recovery and Climate Experiment derived terrestrial water storage-TWS (2002-2014), this study used a two-step procedure based on spherical harmonic synthesis and statistical decomposition to support the understanding of the Volta basin’s natural hydrology and its freshwater systems. Results indicate that Lake Volta contributed 41.6% to the observed increase in TWS over the basin during the 2002 – 2014 period. The statistical decomposition of TWS over the basin (after removing the Lake’s water storage) resulted in a statistically significant (α = 0.05) loss of 59.5 ± 8.5 mm/yr of TWS in the lower Volta region of the basin between 2007 and 2011. This trend is attributed to a base flow recession resulting from the negative trends in precipitation around the lower Volta (2002 − 2014) and limited river flows of the Volta river system. While it also coincides with observed decline in net precipitation (-15 mm/yr), the long dry periods in the basin (2001−2007) also contributed to this storage depletion. The Lake Volta shows sensitivity to incoming flows of the Volta river system with a lag spanning between less than one and up to two years. In addition to this, a 4 − 5 year cycle in the clustering of dry and wet periods resulting from the impact of climate variability on the basin was noticed.
... Given the importance of monitoring wet-snow properties for hydrology, synthetic aperture radar (SAR) retrieval approaches have also been proposed, since passive approaches are not sensitive to dry snow parameters. Gravimetric techniques represent another alternative to microwave based measurement approaches for snow depth (Baur et al., 2009), but the approach is limited by the large spatial and coarse temporal characteristics of such sensors (Niu et al., 2007). In light of the non-selection of ESA's CoreH2O as an 30 ...
In just the past five years, the field of Earth observation has evolved from the relatively staid approaches of government space agencies into a plethora of sensing opportunities afforded by CubeSats, Unmanned Aerial Vehicles (UAVs), and smartphone technologies that have been embraced by both for-profit companies and individual researchers. Over the previous decades, space agency efforts have brought forth well-known and immensely useful satellites such as the Landsat series and the Gravity 5 Research and Climate Experiment (GRACE) system, with costs typically on the order of one billion dollars per satellite and with concept-to-launch timelines on the order of two decades (for new missions). More recently, the proliferation of smartphones has helped to miniaturise sensors and energy requirements, facilitating advances in the use of CubeSats that can be launched by the dozens, while providing 3–5 m resolution sensing of the Earth on a daily basis. Start-up companies that did not exist five years ago now operate more satellites in orbit than any space agency and at costs that are a mere fraction of an 10 agency mission. With these advances come new space-borne measurements, such as high-definition video for understanding real-time cloud formation, storm development, flood propagation, precipitation tracking, or for constructing digital surfaces using structure-from-motion techniques. Closer to the surface, measurements from small unmanned drones and tethered balloons have mapped snow depths, floods, and estimated evaporation at sub-meter resolution, pushing back on spatiotemporal constraints and delivering new process insights. At ground level, precipitation has been measured using signal 15 attenuation between antennae mounted on cell phone towers, while the proliferation of mobile devices has enabled citizenscience to record photos of environmental conditions, estimate daily average temperatures from battery state, and enable the measurement of other hydrologically important variables such as channel depths using commercially available wireless devices. Global internet access is being pursued via high altitude balloons, solar planes, and hundreds of planned satellite launches, providing a means to exploit the Internet of Things as a new measurement domain. Such global access will enable 20 real-time collection of data from billions of smartphones or from remote research platforms. This future will produce petabytes of data that can only be accessed via cloud storage and will require new analytical approaches to interpret. The extent to which today's hydrologic models can usefully ingest such massive data volumes is not clear. Nor is it clear whether this deluge of data will be usefully exploited, either because the measurements are superfluous, inconsistent, not accurate enough, or simply because we lack the capacity to process and analyse them. What is apparent is that the tools and techniques afforded by this 25 array of novel and game-changing sensing platforms presents our community with a unique opportunity to develop new insights that advance fundamental aspects of the hydrological sciences. To accomplish this will require more than just an application of the technology: in some cases, it will demand a radical rethink on how we utilise and exploit these new observation platforms to enhance our understanding of the Earth system.
Water storage changes in the soil can be observed on a global scale with different types of satellite remote sensing. While active or passive microwave sensors are limited to the upper few centimeters of the soil, satellite gravimetry can detect changes in the terrestrial water storage (TWS) in an integrative way, but it cannot distinguish between storage variations in different compartments or soil depths. Jointly analyzing both data types promises novel insights into the dynamics of subsurface water storage and of related hydrological processes. In this study, we investigate the global relationship of (1) several satellite soil moisture products and (2) non-standard daily TWS data from the Gravity Recovery and Climate Experiment/Follow-On (GRACE/GRACE-FO) satellite gravimetry missions on different timescales. The six soil moisture products analyzed in this study differ in the post-processing and the considered soil depth. Level 3 surface soil moisture data sets of the Soil Moisture Active Passive (SMAP) and Soil Moisture and Ocean Salinity (SMOS) missions are compared to post-processed Level 4 data products (surface and root zone soil moisture) and the European Space Agency Climate Change Initiative (ESA CCI) multi-satellite product. On a common global 1∘ grid, we decompose all TWS and soil moisture data into seasonal to sub-monthly signal components and compare their spatial patterns and temporal variability. We find larger correlations between TWS and soil moisture for soil moisture products with deeper integration depths (root zone vs. surface layer) and for Level 4 data products. Even for high-pass filtered sub-monthly variations, significant correlations of up to 0.6 can be found in regions with a large, high-frequency storage variability. A time shift analysis of TWS versus soil moisture data reveals the differences in water storage dynamics with integration depth.
Since the 1990s, the climate in the Amur River Basin (ARB) has changed, and large-scale wetlands in the region have been reclaimed for paddy fields. The study of the influence of climate change and agricultural expansion on groundwater storage is of great significance to the evaluation of regional water resource balance and the promotion of ecological protection and agricultural development. In this work, the groundwater storage anomaly (GWSA) in the ARB and its drivers were analyzed for the period 2003–2016 using Gravity Recovery and Climate Experiment (GRACE) satellite data, a Global Land Data Assimilation System model, and in situ observations of groundwater levels. Results indicated that 1) the GWSA in the ARB increased at a rate of 2.0–2.4 mm/yr from 2003 to 2016; the GWSA in the upper reaches of the ARB increased, whereas the GWSA in the middle and lower reaches decreased during the study period. 2) The GWSA in the middle and lower reaches of the ARB was greatly influenced by temperature (Tmp) and evapotranspiration (ET). Tmp was positively correlated with GWSA, whereas ET was negatively correlated with GWSA (p < 0.05). 3) Extreme rainfall had a delayed effect on groundwater recharge. Wetland degradation and agricultural development were the main factors causing the decrease of the GWSA in the middle and lower reaches of the ARB. In summary, temperature and evapotranspiration affect groundwater storage by regulating the water–heat balance, wetland reclamation reduces the regional storage capacity, and the irrigation required for reclaimed farmland is the main source of groundwater loss.
The launch of the Gravity Recovery and Climate Experiment (GRACE) satellite in 2002 resulted in new capabilities to track changes in continental water storage and the acceleration of the global water cycle. It contributed to addressing the challenges posed by lack of or limited observational data for freshwater (including groundwater, soil moisture, lakes, and reservoirs) monitoring, and is now considered an important “tool in the box” in quantitative large-scale hydrology. GRACE satellite observations are now helping with freshwater accounting and improving our understanding of climate change and anthropogenic influence on changes in terrestrial water storage on different spatial scales (local, regional, and global). The use of GRACE to strengthen capacity in water resources assessment and to identify risk associated with climate change and human water consumption means it will continue to be an important tool for the future. The broad applications of GRACE-satellite in water resources, Earth and planetary science, and climate science attest to this. This chapter discusses GRACE as one of the novel satellite hydrology missions upon which the concept and definition of remote sensing hydrology is based. The principles behind the GRACE mission, its processing chains, and hydrological applications are also detailed.
The signal leakage effect in the use of the Gravity Recovery and Climate Experiment (GRACE) level‐2 products limits the accuracy of the mass inversion, especially in small spatial scales (less than ∼100,000 km²). In this study, we try to use GRACE observation to evaluate the basin mass changes in Finland, where the basins are quite small (less than 93,000 km²) and the accurate mass inversion is challenging. To this end, we carry out a series of numerical simulation experiments and optimize the parameters of the GRACE inversion methods. We propose a hybrid inversion strategy, which takes the differences of both inversion methods and basins into consideration. This strategy is expected to achieve the statistically optimal estimation of the basin mass changes in Finland with Nash‐Sutcliffe Efficiency values ranging from 0.82 to 0.92, corresponding to Index Of Agreement values from 0.95 to 0.98. Further, based on ∼19.7 years of real GRACE data, we analyze the seasonal and interannual terrestrial water storage (TWS) changes in Finland. We find that snow plays a key role in the annual cycle of the TWS change. A remarkable phase difference (∼5 months) between TWS and precipitation is mainly attributed to the effects of snow accumulation and melting. We also find that there is an obvious interannual oscillation with a period of ∼3.8 years in the TWS change of Finland, which seems to be a superposition effect of the real hydrological signal and the tide aliasing error.
In GHA, satellites and new technology have proven to be game changers in FAO’s emergency efforts over the past years. Remote-sensing tools continue to help FAO to lead the way and break new ground in terms of reaching remote rural or previously inaccessible areas, especially in times of COVID-19. These tools not only inform rescue and response operations, they promote flood preparedness and contingency planning. In addition, information systems have been geared almost exclusively to the collection of performance data that are relevant to crop production areas, using a combination of remote sensing and field data-gathering networks to provide early warning of emerging food insecurity situations [13].
This study focused upon the estimation and analysis of terrestrial water storage (TWS changes) across the Canadian landscape. The estimation was performed using Gravity Recovery and Climate Experiment (GRACE) data from April 2002 to June 2017, and GRACE Follow-On (GRACE-FO) observations from June 2018 to December 2019. Removing the gravity effects of Glacial Isostatic Adjustment (GIA) signals and leakage is required to have realistic estimations of TWS changes in the Canadian landmass. In this study, GIA correction was based on a regional-scale modeling of uplift rate. To evaluate the performance compared to the latest GIA models, a comparison was made to uplift rate derived from 149 GPS stations over the study area. Refined TWS changes showed strong seasonal patterns (between −160 mm and 80 mm). The slope of the trend was positive (6.6 mm/year) for the period combining both GRACE and GRACE-FO. The trend increases to 45 mm/year over the 17-year period across central Canada, especially in regions surrounding Hudson Bay. For GRACE, maximum TWS variations occurred between February and April; for GRACE-FO, it occurred with a 2-month lag earlier during the short period being considered. Uncertainties in TWS variations that were derived by GRACE increased towards the end of the mission. Uncertainty for GRACE-FO is lower than that at the beginning of GRACE. The TWS changes extracted from the used approach were compared to Mascon solutions TWS changes products (GRCTellus JPL MSCNv02 and CSR MSCNv02), by using two steps: 1) the Water Global Assessment Prognosis hydrological model (WGHM), and 2) TWS changes derived from in-situ precipitation and potential evapotranspiration data. In all the cases our approach provided the best correlations and lower root mean square errors, compared to the Mascon products.
Nile River Basin (NRB)’s overall water movement expressed through the hydrological cycle is characterised by a simple water balance equation: \(\bigtriangleup S =P-E-Q\), where \(\bigtriangleup S\) is the basin’s total water storage (TWS representing the sum of groundwater, soil moisture, vegetation, and surface water), P the basin’s precipitation, E its evapotranspiration, and Q its runoff. Due to its sheer size of area of 3,400,000 km\(^{2}\) (see Section 2.3), monitoring changes in \(\bigtriangleup S, P, E, Q\) through “boots on the ground” ground-based (in-situ) observations is practically impossible and a daunting task indeed. On the one hand, the in-situ (ground-based products, e.g., [89]) data may be inaccessible while on the other hand, the mearger accessible data where available, might be inconsistent or suffer from missing data.
Lake Victoria Basin (LVB)’s overall water movement expressed through the hydrological cycle is characterised by a simple water balance equation: \(\bigtriangleup S =P-E-Q\), where \(\bigtriangleup S\) is the basin’s total water storage (TWS representing the sum of groundwater, soil moisture, vegetation, and surface water), P the basin’s precipitation, E its evapotranspiration, and Q its runoff.
Signal leakage between the land and ocean is a challenge in using Gravity Recovery and Climate Experiment (GRACE) observation data to study global mass redistributions. Although the leakage occurs in both directions, more attention has been paid to the land-to-ocean leakage and less to the ocean-to-land leakage. Here, we show that the ocean-to-land leakage is non-uniform and non-negligible and propose a new forward modelling method to fully consider bi-directional leakages with the help of the global Ocean ReAnalysis System ORAS5. This observation-driven model could significantly reduce the variations in ocean grids and thus decrease the ocean-to-land leakage. The results with different treatment of the ocean signal leakage are compared. We find that failing to consider the ocean-to-land leakage will cause an underestimation of ∼20 per cent in the seasonal variation and will introduce a bias of several giga-tons in the secular trend. Although the uniform and non-uniform model have similar results in the global average of seasonal mass variations, the non-uniform ocean model is necessary in most places, especially near the Arctic Ocean, the Sea of Japan and the Gulf of Carpentaria. Despite these achievements, we also point out that there is still much room for improvement in ocean mass models, particularly in long-term trends. Our results indicate the importance of the ocean-to-land leakage correction in the mass estimation in coastal land areas using the GRACE data.
Knowledge of the coastal ocean mass variations is important for understanding the ocean climate and sea level change. However, estimates of coastal ocean mass variations have been perplexed due to poor representativeness of previous Gravity Recovery and Climate Experiment (GRACE) data across the land/ocean boundary. We here use GRACE mascon solutions to investigate the coastal ocean mass variations (within 400 km band) at global and regional scales. GRACE mascon solutions are advanced by spatial constraints and leakage correction. For the global mean, it is found that mascons ocean mass variations are in rough agreement with those inferred from satellite altimeter and an ocean analysis; the agreement is better on seasonal scales (6.4 ± 0.5 mm annual amplitude for the mascons and 7.3 ± 0.7 mm annual amplitude for the inferred); on the other hand, large differences are shown for the linear trend (2.1 ± 0.1 mm yr⁻¹ for the mascons and 3.2 ± 0.1 mm yr⁻¹ for the inferred), indicating that it is far from closing the coastal sea level budget. At regional scales, high consistency between mascons and the inferred is observed over two shallow areas, that is, Europe coast and East China coast, whose annual amplitudes are 24 ± 5 and 42 ± 3 mm, respectively. Ocean mass variations are not well captured by mascons over other regions (e.g. Africa coast, Indian coast and North and South America coast). Possible explanations include (1) the steric component plays a more important role in sea level, consequently resulting in weak mass signal and (2) the performance of mascons varies with locations. We find that mascon solutions show better variability (especially seasonal cycles) than do the traditional spherical harmonic coefficients, suggesting that mascons applied with spatial constraints improve the coastal ocean mass variability.
Satellite gravimetry data acquired by the Gravity Recovery and Climate Experiment (GRACE) allows to derive the temporal evolution in ice mass for both the Antarctic Ice Sheet (AIS) and the Greenland Ice Sheet (GIS). Various algorithms have been used in a wide range of studies to generate Gravimetric Mass Balance (GMB) products. Results from different studies may be affected by substantial differences in the processing, including the applied algorithm, the utilised background models and the time period under consideration. This study gives a detailed description of an assessment of the performance of GMB algorithms using actual GRACE monthly solutions for a prescribed period as well as synthetic data sets. The inter-comparison exercise was conducted in the scope of the European Space Agency’s Climate Change Initiative (CCI) project for the AIS and GIS, and was, for the first time, open to everyone. GMB products generated by different groups could be evaluated and directly compared against each other. For the period from 2003-02 to 2013-12, estimated linear trends in ice mass vary between −99 Gt/yr and −108 Gt/yr for the AIS and between −252 Gt/yr and −274 Gt/yr for the GIS, respectively. The spread between the solutions is larger if smaller drainage basins or gridded GMB products are considered. Finally, findings from the exercise formed the basis to select the algorithms used for the GMB product generation within the AIS and GIS CCI project.
In order to fully appreciate the contribution of geoinformatics in monitoring climate change caused by increase in temperature, a distinction between weather and climate , on one hand, and climate variability and climate change , on the other hand, is essential.
GNSS satellites such as GPS are playing an increasingly crucial role in tracking low earth orbiting (LEO) remote sensing satellites at altitudes below 3000 km with accuracies of better than 10 cm (Yunck in IEEE Trans Geosci Remote Sens 28:108–116 1990, [2]). These remote sensing satellites employ a precise global network of GNSS, GRACE (Gravity Recovery And Climate Experiment) and Altimetry ground receivers operating in concert with receivers onboard the LEO satellites, with all estimating the satellites’ orbits, GPS orbits, and selected ground locations simultaneously (Yunck in IEEE Trans Geosci Remote Sens 28:108–116 1990, [2]).
When assessing remote sensing data, nighttime light data have shortcomings that can be attributed to sensor limitations and the influence of the natural environment. Signal leakage errors in nighttime light data were identified in this study. A regression model was created to reduce signal leakage error by selecting sampling points in coastal area. Lighting variations in Edogawa between 2008 and 2013 were compared based on the Defense Meteorological Satellite Program’s nighttime light data. The lighting variation characteristics in Edogawa from 1992 to 2012 at 5-year intervals were also analyzed. The results show that the 2002 FIFA World Cup held in Japan led Edogawa’s light digital number values to peak in 2002. The annual Edogawa lighting changes from 2007 to 2013 were also explored. The 2008 global financial crisis led to the lowest compounded night light index and average digital number in Edogawa during these 7 years.
In order to address the contributions of GNSS to monitor climate change caused by increase in temperature, a distinction between weather and climate on one hand, and climate variability and climate change on the other hand is essential.
GNSS satellites such as GPS are playing an increasingly crucial role in tracking low earth orbiting (LEO) remote sensing satellites at altitudes below 3000 km with accuracies of better than 10 cm [2]
We present a state-of-the-art approach of passive-ocean Modified Radial Basis Functions (MRBFs) that improves the recovery of time-variable gravity fields from GRACE. As is well known, spherical harmonics (SHs), which are commonly used to recover gravity fields, are orthogonal basis functions with global coverage. However, the chosen SH truncation involves a global compromise between data coverage and obtainable resolution, and strong localized signals may not be fully captured. Radial basis functions (RBFs) provide another representation, which has been proposed in earlier works to be better suited to retrieve regional gravity signals. In this paper, we propose a MRBF approach by embedding the known coastal geometries in the RBF parameterization and imposing global mass conservation and equilibrium behavior of the oceans. Our hypothesis is that, with this physically justified constraint, the GRACE-derived gravity signals can be more realistically partitioned into the land and ocean contributions along the coastlines. We test this new technique to invert monthly gravity fields from GRACE level-1b observations covering 2005-2010, for which the numerical results indicate that: (1) MRBF-based solutions reduce the number of parameters by approximately 10%, and allow for more flexible regularization when compared to ordinary RBF solutions; and (2) the MRBF-derived mass flux is better confined along coastal areas. The latter is particularly tested in the Southern Greenland, and our results indicate that the trend of mass loss from the MRBF solutions is approximately 11% larger than that from the SH solutions, and approximately 4% ∼ 6% larger than that of RBF solutions.
Water on continents is a fundamental reservoir of the global hydrological cycle. It plays a major role for Earth's climate via its exchanges with the atmosphere (precipitation and evapotranspiration) and the oceans (outflow of rivers), the regulation of energy flow and biogeochemical flow. Despite its importance, estimations of water stored on land remains uncertain, as much on a regional scale as a global one. This is due to a lack of in situ measurement networks which prevents continuous monitoring of the different hydrological reservoirs. Even though such monitoring is possible thanks to a few local measurement networks, our current knowledge of the water cycle mainly originates from global hydrological models, for which the capabilities of simulating the exchanges between the different reservoirs from regional to global scales suffer from significant limitations. This is mainly due to the absence of certain hydrological reservoirs in modeling, such as floodplains and groundwater tables, as well as forcing errors. Notably, forcing from rain, that has inhomogeneous quality depending on the region of the world considered, is a major issue. In addition this is the shortage of information, on a small scale, for certain parameters, such as the nature of the soil and vegetation cover and their evolution. © 2016 ISTE Press Ltd Published by Elsevier Ltd All rights reserved.
We derive the mass balance of Greenland ice sheet from the Gravity Recovery and Climate Experiment (GRACE) for the period January 2003–October 2014. We have found an ice mass loss with peak amplitude of −15 cm/yr in the southeastern and northwestern parts, and an acceleration of −2.5 cm/yr2 in the southwestern region. Global warming is a well-known suspected triggering factor of ice melting. We use MODIS-derived Ice Surface Temperature (IST), and continuous and cross wavelet transforms have been determined to investigate the common power and relative phase between GRACE derived time-series of ice mass changes and IST time-series. Results indicate a high common power between the two time-series for the whole study period, but with different time patterns.
Watersheds draining into the Gulf of Alaska (GoA) experience large
seasonal and inter-annual variations of water in the form of rain, snow,
and ice, but accurate constraints on these variations have been
difficult to obtain. Over larger geographic regions, water variations
can be inferred directly from the Gravity Recovery and Climate
Experiment (GRACE) data. However, because GoA variations occur over such
a small region, the inferred average value of water flux increases as
the applied smoothing of the GRACE data decreases. We use this observed
scaling together with scaling results obtained from forward models to
infer a seasonal amplitude of 115 +/- 20 km3 of water and an
average contribution to sea level rise over the two years of data of
0.31 +/- 0.09 mm/yr. These results suggest that accelerated melting that
began in the late 1990s, as inferred from altimetry, continues unabated.
The GRACE mission is designed to track changes in the Earth's gravity
field for a period of five years. Launched in March 2002, the two GRACE
satellites have collected nearly two years of data. A span of data
available during the Commissioning Phase was used to obtain initial
gravity models. The gravity models developed with this data are more
than an order of magnitude better at the long and mid wavelengths than
previous models. The error estimates indicate a 2-cm accuracy uniformly
over the land and ocean regions, a consequence of the highly accurate,
global and homogenous nature of the GRACE data. These early results are
a strong affirmation of the GRACE mission concept.
1] The temporal variations in the Earth's gravity field caused by fluctuations in terrestrial water mass can be inferred from changes in GRACE monthly gravity field solutions. Such methods have limited spatial resolution due to a necessary and possibly arbitrary truncation and smoothing of the coefficients. Limiting the temporal resolution to one month was necessary to solve the gravity field by a global representation. Our alternative method uses GRACE satellite-to-satellite tracking and accelerometer data to obtain the along-track geopotential differences and directly estimate the temporal gravity variations regionally. This method was tested on the estimation of hydrological mass anomaly over the Amazon and Orinoco river basins. Compared to conventional spherical harmonic methods, the spatial extent of the estimated GRACE water height anomaly achieved finer resolution and is shown to follow more closely the boundaries of the river basins and significant systematic variation could be discerned at 15-day temporal resolutions.
1] The satellite Gravity Recovery and Climate Experiment (GRACE) provides data describing monthly changes in the geoid, which are closely related to changes in vertically integrated terrestrial water storage. Unlike conventional point or gridded hydrologic measurements, such as those from rain gauges, stream gauges, rain radars, and radiometric satellite images, GRACE data are sets of Stokes coefficients in a truncated spherical harmonic expansion of the geoid. Swenson and Wahr [2002] describe techniques for constructing spatial averaging kernels, with which the average change in vertically integrated water storage within a given region can be extracted from a set of Stokes coefficients. This study extends that work by applying averaging kernels to a realistic synthetic GRACE gravity signal derived in part from a large-scale hydrologic model. By comparing the water storage estimates inferred from the synthetic GRACE data with the water storage estimates predicted by the same hydrologic model, we are able to assess the accuracy of the GRACE estimates and to compare the performance of different averaging kernels. We focus specifically on recovering monthly water storage variations within North American river basins. We conclude that GRACE will be capable of estimating monthly changes in water storage to accuracies of better than 1 cm of water thickness for regions having areas of 4.0 Á 10 5 km 2 or larger. Accuracies are better for larger regions. The water storage signal of the Mississippi river basin (area = 3.9 Á 10 6 km 2), for example, can be obtained to better than 5 mm. For regional-to global-scale water balance analyses, this result indicates that GRACE will provide a useful, direct measure of seasonal water storage for river-basin water balance analyses; such data are without precedent in hydrologic analysis.
1] We use 22 monthly GRACE (Gravity Recovery and Climate Experiment) gravity fields to estimate the linear trend in Greenland ice mass during 2002 – 2004. We recover a decrease in total ice mass of 82 ± 28 km 3 of ice per year, consistent with estimates from other techniques. Our uncertainty estimate is dominated by the effects of GRACE measurement errors and errors in our post glacial rebound (PG) correction. The main advantages of GRACE are that it is sensitive to the entire ice sheet, and that it provides mass estimates with only minimal use of supporting physical assumptions or ancillary data.
1] We estimate mass trends over Antarctica using gravity variations observed by the Gravity Recovery and Climate Experiment (GRACE) satellite mission during its first 3.5 years (April 2002– November 2005). An image of surface mass trends is constructed from 1° Â 1° pixels over the entire continent, and shows two prominent features, a region of mass loss along the coast of West Antarctica, and one of accumulation in East Antarctica. After adjusting for bias due to smoothing and to GRACE's limited spatial resolution, and removing post glacial rebound (PGR) effects, the rate in West Antarctica is À77 ± 14 km 3 /year, similar to a recent estimate of ice mass loss from satellite altimetry and remote sensing data. The prominent East Antarctic feature in the Enderby Land region has a rate of +80 ± 16 km 3 /year. Published snow/ice mass rates from remote sensing measurements indicate approximate ice mass balance in this region, suggesting that this feature is either from unquantified snow accumulation in this region or more likely due to unmodeled PGR.
Four different basin functions are developed to estimate water storage variations within individual river basins from time variations in the Stokes coefficients now available from the GRACE mission. The four basin functions are evaluated using simulated data. Basin functions differ in how they minimize effects of three major error sources: measurement error; leakage of signal from one region to another; and errors in the atmospheric pressure field removed during GRACE data processing. Three of the basin functions are constant in time, while the fourth changes monthly using information about the signal (hydrologic and oceanic load variations). To test basin functions performance, Stokes coefficient variations from land and ocean models are synthesized, and error levels 50 and 100 times greater than pre-launch GRACE error estimate are used to corrupt them. Errors at 50 times pre-launch estimates approximately simulate current GRACE data. GRACE recovery of water storage variations is attempted for five different river basins (Amazon, Mississippi, Lena, Huang He and Oranje), representing a variety of sizes, locations, and signal variance. In the large basins (Amazon, Mississippi and Lena), water storage variations are recovered successfully at both error levels. As the error level increases from 50 to 100 times, basin functions change their shape, yielding less atmospheric pressure error and more leakage error. Amplitude spectra of measurement and atmospheric pressure errors have different shapes, but the best results are obtained when both are used in basin function design. When high-quality information about the signal is available, for example from climate and ocean models, changing the basin function each month can reduce leakage error and improve estimates of time variable water storage within basins.
Monthly gravity field estimates made by the twin Gravity Recovery and Climate Experiment (GRACE) satellites have a geoid height accuracy of 2 to 3 millimeters at a spatial resolution as small as 400 kilometers. The annual cycle in the geoid variations, up to 10 millimeters in some regions, peaked predominantly in the spring and fall seasons. Geoid variations observed over South America that can be largely attributed to surface water and groundwater changes show a clear separation between the large Amazon watershed and the smaller watersheds to the north. Such observations will help hydrologists to connect processes at traditional length scales (tens of kilometers or less) to those at regional and global scales.
Using satellite radar interferometry observations of Greenland, we detected widespread glacier acceleration below 66° north
between 1996 and 2000, which rapidly expanded to 70° north in 2005. Accelerated ice discharge in the west and particularly
in the east doubled the ice sheet mass deficit in the last decade from 90 to 220 cubic kilometers per year. As more glaciers
accelerate farther north, the contribution of Greenland to sea-level rise will continue to increase.
Using measurements of time-variable gravity from the Gravity Recovery and Climate Experiment satellites, we determined mass
variations of the Antarctic ice sheet during 2002–2005. We found that the mass of the ice sheet decreased significantly, at
a rate of 152 ± 80 cubic kilometers of ice per year, which is equivalent to 0.4 ± 0.2 millimeters of global sea-level rise
per year. Most of this mass loss came from the West Antarctic Ice Sheet.
Using time-variable gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) satellite mission, we estimate
ice mass changes over Greenland during the period April 2002 to November 2005. After correcting for the effects of spatial
filtering and limited resolution of GRACE data, the estimated total ice melting rate over Greenland is –239 ± 23 cubic kilometers
per year, mostly from East Greenland. This estimate agrees remarkably well with a recent assessment of –224 ± 41 cubic kilometers
per year, based on satellite radar interferometry data. GRACE estimates in southeast Greenland suggest accelerated melting
since the summer of 2004, consistent with the latest remote sensing measurements.
In 2001 the Intergovernmental Panel on Climate Change projected the contribution to sea level rise from the Greenland ice sheet to be between -0.02 and +0.09 m from 1990 to 2100 (ref. 1). However, recent work has suggested that the ice sheet responds more quickly to climate perturbations than previously thought, particularly near the coast. Here we use a satellite gravity survey by the Gravity Recovery and Climate Experiment (GRACE) conducted from April 2002 to April 2006 to provide an independent estimate of the contribution of Greenland ice mass loss to sea level change. We detect an ice mass loss of 248 +/- 36 km3 yr(-1), equivalent to a global sea level rise of 0.5 +/- 0.1 mm yr(-1). The rate of ice loss increased by 250 per cent between the periods April 2002 to April 2004 and May 2004 to April 2006, almost entirely due to accelerated rates of ice loss in southern Greenland; the rate of mass loss in north Greenland was almost constant. Continued monitoring will be needed to identify any future changes in the rate of ice loss in Greenland.
Mass changes of the Greenland Ice Sheet resolved by drainage system regions were derived from a local mass concentration analysis
of NASA–Deutsches Zentrum für Luftund Raumfahrt Gravity Recovery and Climate Experiment (GRACE mission) observations. From
2003 to 2005, the ice sheet lost 101 ± 16 gigaton/year, with a gain of 54 gigaton/year above 2000 meters and a loss of 155
gigaton/year at lower elevations. The lower elevations show a large seasonal cycle, with mass losses during summer melting
followed by gains from fall through spring. The overall rate of loss reflects a considerable change in trend (–113 ± 17 gigaton/year)
from a near balance during the 1990s but is smaller than some other recent estimates.
The Gravity Recovery and Climate Experiment (GRACE) was designed to
measure variations in the Earth's gravity field from space at monthly
intervals. Researchers have used these data to measure changes in water
mass over various regions, including the global oceans and continental
ice sheets covering Greenland and Antarctica. However, GRACE data must
be smoothed in these analyses and the effects of geocenter motions are
not included. In this study, we examine what effect each of these has in
the computation of ocean mass trends using a simulation of ice melting
on Greenland, Antarctica, and mountain glaciers. We find that the
recovered sea level change is systematically lower when coefficients are
smoothed and geocenter terms are not included. Assuming current
estimates of ice melting, the combined error can be as large as 30-50%
of the simulated sea level rise. This is a significant portion of the
long-term sea level change signal, and needs to be considered in any
application of GRACE data to estimating long-term trends in sea level
due to gain of water mass from melting ice.
The static deformation of an elastic half-space by surface pressure is reviewed. A brief mention is made of methods for solving the problem when the medium is plane stratified, but the major emphasis is on the solution for spherical, radially stratified, gravitating earth models. Love-number calculations are outlined, and from the Love numbers, Green's functions are formed for the surface mass-load boundary-value problem. Tables of mass-load Green's functions, computed for realistic earth models, are given, so that the displacements, tilts, accelerations, and strains at the earth's surface caused by any static load can be found by evaluating a convolution integral over the loaded region.
We use twenty-two monthly GRACE (Gravity Recovery and Climate Experiment) gravity fields to recover nonsecular mass change in Greenland. The results show large seasonal variability. We compare with modeled precipitation, evaporation, and runoff derived from ERA40 (the 40-year ECMWF Re-Analysis of the global atmosphere). The model's seasonal amplitude is controlled by runoff and agrees reasonably well with GRACE. Both GRACE and the model show an April/May maximum. But the GRACE results show a delayed minimum relative to the model. This difference is probably associated with omissions in the runoff model, ice discharge, subglacial hydrology, mass loss by blowing-snow, and hydrology in ice-free regions. The discrepancy is smaller, but still significant, for south Greenland alone. When we include a proxy for ice discharge the agreement is improved.
Recently reprocessed GRACE gravity fields are found to provide reliable ocean mass anomalies down to 500 km regional averages when comparing them to mass observations obtained from sterically corrected Jason 1 altimetry and simulated mass anomalies derived from the Ocean Model for Circulation and Tides (OMCT). Beside the assessment of systematic shortcomings of GRACE, Jason 1 and OMCT estimates, robust signals of mass anomalies in the North Pacific and in various regions of the Southern Ocean are identified in all three independent data sets. Correlations of up to 0.8 and rms values of differences of around 2 hPa indicate that uncertainties are well below the expected monthly mean mass signals of up to 6 hPa rms in these regions. By means of output of the numerical ocean model, mass anomalies are related to changes in barotropic ocean currents, providing in turn the opportunity to infer barotropic current anomalies from GRACE observations, and therefore principally allowing to monitor climate relevant changes of ocean currents from satellite observations.
The GRACE satellite mission, scheduled for launch in 2001, is designed to map out the Earth's gravity field to high accuracy every 2-4 weeks over a nominal lifetime of 5 years. Changes in the gravity field are caused by the redistribution of mass within the Earth and on or above its surface. GRACE will thus be able to constrain processes that involve mass redistribution. In this paper we use output from hydrological, oceanographic, and atmospheric models to estimate the variability in the gravity field (i.e., in the geoid) due to those sources. We develop a method for constructing surface mass estimates from the GRACE gravity coefficients. We show the results of simulations, where we use synthetic GRACE gravity data, constructed by combining estimated geophysical signals and simulated GRACE measurement errors, to attempt to recover hydrological and oceanographic signals. We show that GRACE may be able to recover changes in continental water storage and in seafloor pressure, at scales of a few hundred kilometers and larger and at timescales of a few weeks and longer, with accuracies approaching 2 mm in water thickness over land, and 0.1 mbar or better in seafloor pressure.
Sea level rises and falls as the temperature and salinity of the water column varies, which is known as steric sea level. Sea level also changes as water mass is redistributed within the ocean or is added or removed. Satellite radar altimeters measure the combination of both effects, while the Gravity Recovery and Climate Experiment (GRACE) was designed to measure time variable gravity caused by movement of water mass. Theoretically, altimetry and GRACE data can be combined in order to compute the steric sea level variations. We test this by combining current GRACE and Jason 1 altimeter data and comparing against steric sea level observations. We will describe how to properly combine the altimetry and GRACE data, commenting on important corrections that need to be applied to each data type. Using empirical orthogonal function (EOF) analysis, we examine the leading modes of seasonal variability and find that using GRACE improves the ability to recover the dominant mode of steric sea level variability over using altimetry alone. The RMS error of the GRACE ocean mass variations is estimated to be about 2 cm of sea level at a 1000 km smoothing radius. Although this is larger than initially predicted from the GRACE mission, it is still significantly smaller than the recovered signal in several regions of the ocean.
Monthly mass variations within the Earth system produce temporal gravity changes, which are observable by the NASA/GFZ Gravity Recovery and Climate Experiment (GRACE) twin-satellite system. Mass load changes with spatial scales larger than 1000 km have been observed using conventional filters based on a Gaussian smoother, which applies a weight to GRACE spherical harmonic (SH) coefficients depending only on SH degree. This practice is consistent with a degree-dependent error model for GRACE monthly geopotential solutions. The Gaussian filters effectively dampen all power of ill-determined higher-degree components in the estimates. However, the spatial sampling provided by GRACE yields errors that vary with both SH degree and order. The consequence is that maps of spatial loads shall not be smoothed with an isotropic (degree-only) filter, but shall be constructed using anisotropic smoothing thus also yielding better spatial resolution in latitude. We have developed a non-isotropic filter to optimize the smoothing of GRACE temporal gravity observations by considering the degree- and order-dependent quality of GRACE estimates, the latter analysed from the correlation with the predicted signals of hydrologic and ocean models. In order to retain GRACE coefficients in the filtering process that show reasonable correlation with the geophysical (hydrology and ocean) models, we applied Gaussian-type smoothing but with averaging radius depending on the order of the geopotential coefficient estimates. Applied to 2 yr of GRACE data, we showed that the resulting non-isotropic filter yields enhanced GRACE signals with significantly higher resolution in latitude and the same resolution in longitude without reducing the accuracy as compared to the conventional Gaussian smoother.
The Gravity Recovery and Climate Experiment, GRACE, will deliver monthly averages of the spherical harmonic coefficients describing the Earth's gravity field, from which we expect to infer time-variable changes in mass, averaged over arbitrary regions having length scales of a few hundred kilometers and larger, to accuracies of better than 1 cm of equivalent water thickness. These data will be useful for examining changes in the distribution of water in the ocean, in snow and ice on polar ice sheets, and in continental water and snow storage. We describe methods of extracting regional mass anomalies from GRACE gravity coefficients. Spatial averaging kernels were created to isolate the gravity signal of individual regions while simultaneously minimizing the effects of GRACE observational errors and contamination from surrounding glacial, hydrological, and oceanic gravity signals. We then estimated the probable accuracy of averaging kernels for regions of arbitrary shape and size.
1] Gravity fields produced by the Gravity Recovery and Climate Experiment (GRACE) satellite mission require smoothing to reduce the effects of errors present in short wavelength components. As the smoothing radius decreases, these errors manifest themselves in maps of surface mass variability as long, linear features generally oriented north to south (i.e., stripes). The presence of stripes implies correlations in the gravity field coefficients. Here we examine the spectral signature of these correlated errors, and present a method to remove them. Finally, we apply the filter to a model of surface-mass variability to show that the filter has relatively little degradation of the underlying geophysical signals we seek to recover.
Monthly GRACE gravity field models from the three science processing centers (CSR, GFZ, and JPL) are analyzed for the period from February 2003 to April 2005 over the ocean. The data are used to estimate maps of the mass component of sea level at smoothing radii of 500 km and 750 km. In addition to using new gravity field models, a new filter has been applied to estimate and remove systematic errors i n the coefficients that cause erroneous patterns in the maps of equivalent water level. The filter is described and its effects are discussed. The GRACE maps have been evaluated using a residual analysis with maps of altimeter sea level from Jason-1 corrected for steric variations using the World Ocean Atlas 2001 monthly climatology. The mean uncertainty of GRACE maps determined from an average of data from all 3 processing centers is estimated to be less than 1.8 cm RMS at 750 km smoothing and 2.4 cm at 500 km smoothing, which is better than was found previously using the first generation GRACE gravity fields.
The isostatic adjustment of a radially stratified visco-elastic spheroid is treated using space-time Green functions for the associated surface mass load boundary value problem. These impulse response functions are convolved with a Heaviside function to give the time dependent deformation of the planet which would be produced by a unit point mass brought up from infinity at t= 0 and allowed to remain on the surface. The resulting ’ Heaviside Green functions ’ can be employed to simulate all of the important signatures of glacial isostatic adjustment. Given a space-time dependent surface mass load consisting of ice sheet ablation histories and a model of the simultaneous filling of the ocean basins, these source terms are simply convolved with the Heaviside Green function appropriate to a specific response signature. A realistic model of the spatial distribution of the main late Pleistocene ice loads and of their temporal disintegration is constructed. The response of two visco-elastic earth models is computed and compared to a global set of relaxation data (relative sea-level curves). On the basis of this initial comparison of theory and observation the possibility that the lower mantle has a viscosity which is significantly in excess of the viscosity of the upper mantle is excluded. In addition, clear evidence of the presence of the lithosphere has been found in relaxation data from sites which were near the edge of the Laurentide ice sheet. Such data should therefore prove useful as a basis for analysis of lateral variations in lithosphere thickness. Further extensions of the calculation are suggested.
Throughout 2004 the GRACE (Gravity Recovery And Climate Experiment) orbit contracted slowly to yield a sparse repeat track of 61 revolutions every 4 days on 19 September 2004. As a result, we show from linear perturbation theory that geopotential information previously available to fully resolve a gravity field every month of 120 120 (degree by order) in spherical harmonics was compressed then into about one-fourth of the necessary observation space. We estimate from this theory that the ideal gravity field resolution in September 2004 was only about 30 30. More generally, we show that any repeat-cycle mission for geopotential recovery with full resolution LנL requires the number of orbit-revolutions-to-repeat to be greater than 2L.
We estimate the mean steric sea level variations over the 60°S-60°N oceanic domain for the recent period (from August 2002 to April 2006), by combining sea level data from Jason-1 altimetry with time-variable gravity data from GRACE. The observed global mean sea level change from satellite altimetry results in total from steric plus ocean mass change. As GRACE measurements averaged over the ocean represents the ocean mass change component only, the difference between GRACE and altimetry observations provides an estimate of the mean steric sea level. Two different sets of GRACE geoid solutions (the GRGS EIGEN-GL04 and the GFZ EIGEN-GRACE04S products) have been used. Each GRACE data set ranges over approximately 3 yr or more (August 2002-April 2006 for the GRGS geoids and February 2003-February 2006 for the GFZ geoids).
We use satellite gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) as an indication of mass change to study potential long-term mountain glacial melting in southern Alaska and West Canada. The first 3.5 yr of GRACE monthly gravity data, spanning April 2002–November 2005, show a prominent glacial melting trend in the mountain regions around the Gulf of Alaska (GOA). GRACE-observed surface mass changes correlate remarkably well with available mass balance data at Gulkana and Wolverine, two benchmark glaciers of the U.S. Geological Survey (USGS), although the GRACE signals are smaller in magnitude. In addition, terrestrial water storage (TWS) changes estimated from an advanced land surface model show significant mass loss in this region during the same period. After correcting for the leakage errors and removing TWS contributions using model estimates, we conclude that GRACE-observed glacial melting in the GOA mountain region is equivalent to ∼ − 101 ± 22 km3/yr, which agrees quite well with the assessment of ∼ − 96 ± 35 km3/yr based on airborne laser altimetry data, and is consistent with an earlier estimate based on the first 2 yr of GRACE data. This study demonstrates the significant potentials of satellite gravity measurements for monitoring mountain glacial melting and regional climate change.
We propose a new estimate of the mass balance of the West/East Antarctica and Greenland ice sheets from GRACE for the recent period (July 2002–March 2005) and compute the corresponding contribution to the global mean sea level. We use new GRACE geoid solutions provided by the Groupe de Recherche en Géodésie Spatiale (GRGS/CNES), at the resolution of ∼ 400 km and sampled at 10-day interval. In the three regions, significant interannual variations are observed, which we approximate as linear trends over the short time span of analysis. Over Greenland, an apparent total volume loss of 119 +/− 10 cu km/yr water is observed. For the Antarctica ice sheet, a bimodal behaviour is apparent, with volume loss amounting to 88 +/− 10 cu km/yr water in the West, and increase in the East amounting to 72 +/− 20 cu km/yr water. These GRACE results are affected by land hydrology contamination and glacial isostatic adjustment (GIA) of the solid Earth since last deglaciation. We correct for both land hydrology contamination (using a global hydrological model) and GIA using the ICE-4G model for Greenland and the IJ05 model for Antarctica. Corrected for both land hydrology contamination and GIA, GRACE volume rates are − 129 +/− 15 cu km/yr, − 107 +/− 23 cu km/yr and + 67 +/− 28 cu km/yr for Greenland, West Antarctica and East Antarctica respectively. In terms of sea level rise, the GRACE-based ice sheets contributions are + 0.36 +/− 0.04 mm/yr for Greenland, + 0.30 +/− 0.06 mm/yr for West Antarctica and − 0.19 +/− 0.07 for East Antarctica for the time interval of study. The total Antarctica contribution to sea level over this short time span is thus slightly positive (+ 0.11 +/− 0.09 mm/yr). The ice sheets together contribute to a sea level rise of 0.47 +/− 0.1 mm/yr. The results reported here are in qualitative agreement with recent estimates of the mass balance of the ice sheets based on GRACE and with those based upon other remote sensing observations. Due to the very short sampling time span for which the GRACE data are available, it is not yet possible to distinguish between interannual oscillations and long-term trend associated with climate change.
By delivering monthly maps of the gravity field, the GRACE project allows the determination of tiny time variations of the Earth's gravity and particularly the effects of fluid mass redistributions at the surface of the Earth. However, GRACE data represent vertically integrated gravity measurements, thus are the sum of all mass redistributions inside the Earth's system (atmosphere, oceans and continental water storage, plus solid Earth). In this paper, we apply a generalized least-squares inverse approach, previously developed by [1] [G. Ramillien, A. Cazenave, O. Brunau, Global time-variations of hydrological signals from GRACE satellite gravimetry, Geophys. J. Int. 158 (2004) 813–826.], to estimate, from the monthly GRACE geoids, continental water storage variations (and their associated uncertainties) over a 2-year time span (April 2002 to May 2004). Tests demonstrating the robustness of the method are presented, including the separation between liquid water reservoirs (surface waters + soil moisture + groundwaters) and snow pack contributions. Individual monthly solutions of total land water storage from GRACE, with a spatial resolution of ∼ 660 km, are presented for the 2-year time span. We also derive the seasonal cycle map. We further estimate water volume changes over eight large river basins in the tropics and compare with model predictions. Finally, we attempt to estimate an average value of the evapotranspiration over each river basin, using the water balance equation which links temporal change in water volume to precipitation, evapotranspiration and runoff. Amplitudes of the GRACE-derived evapotranspiration are regionally consistent to the predictions of global hydrological models.
Convolutions on the sphere with corresponding convolution theorems are developed for one and two dimensional functions. Some of these results are used in a study of isotropic smoothing operators or filters. Well known filters in Fourier spectral analysis, such as the rectangular, Gaussian, and Hanning filters, are adapted for data on a sphere. The low-pass filter most often used on gravity data is the rectangular (or Pellinen) filter. However, its spectrum has relatively large sidelobes; and therefore, this filter passes a considerable part of the upper end of the gravity spectrum. The spherical adaptations of the Gaussian and Hanning filters are more efficient in suppressing the high-frequency components of the gravity field since their frequency response functions are strongly field since their frequency response functions are strongly tapered at the high frequencies with no, or small, sidelobes. Formulas are given for practical implementation of these new filters.