Monthly Gravity Research Articles

GRACE 위성 중력자료를 활용한 한반도의 평균 수자원변화량 산정

대부분의 수문자료는 지상관측을 통해 얻어진다. 그러나 어떤 지역은 접근이 어렵거나 장기적인 관측에 어려움이 있기 때문에 지상관측을 대체하거나 보완할 새로운 방법이 요구된다. 시 공간적 한계를 극복할 수 있는 대안으로 미항공우주국 NASA에서 2002년 지구 중력장을 측정하는 GRACE(Gravity Recovery And Climate Experiment) 인공위성 자료가 존재한다. 본 연구에서는 GRACE Level-2 중력자료를 이용하여 공간평활화 반경별(0 km, 300 km, 500 km)로 한반도의 수자원변화량(GRACE-based TWSC)을 산정하였다. 산정된 결과의 타당성을 검증하기 위해, 지상 수문 관측자료를 이용한 수자원 변화량(land-based TWSC)과의 비교를 시도하였다. Land-based TWSC는 WAMIS의 강우량, 증발 산량 및 GLDAS의 유출량 자료를 이용해 계산하였다. GRACE-based TWSC와 land-based TWSC의 RMSE 검정 결과, 공간평활화 반경 500 km의 위성자료가 한반도에 가장 적합한 것으로 나타났다. 한반도의 월별 평균 TWSC는 0.986 cm/month로 나타났고, 이러한 큰 변화폭 때문에 안정적수자원 확보를 위한 대처 방안의 마련이 필요한 것으로 평가된다. Most hydrologic data are obtained by ground observations. New observation methods are needed for some regions to overcome difficulties in accessibility and durability of long-term observation. In 2002, NASA launched twin satellites named GRACE which were designed to measure the gravitational field of the earth. Using the GRACE monthly gravity level-2 data, we calculated terrestrial water storage change (TWSC) of the Korean peninsula in various spatial smoothing radii (0 km, 300 km, 500 km). For the validation of GRACE-based TWSC, we compared it with land-based TWSC which was obtained using the ground observation data: precipitation and evaporation from WAMIS, and runoff from GLDAS. According to the mean square-error test, GRACE-based TWSC best fits the land-based one at 500 km smoothing radius. The variation of the terrestrial water storage in the Korean peninsula turned out to be 0.986 cm/month, which means that appropriate measures should be prepared for sustainable water resources management.

Estimation of mass change trends in the Earth’s system on the basis of GRACE satellite data, with application to Greenland

The Gravity Recovery and Climate Experiment (GRACE) satellite mission measures the Earth’s gravity field since March 2002. We propose a new filtering procedure for post-processing GRACE-based monthly gravity field solutions provided in the form of spherical harmonic coefficients. The procedure is tuned for the optimal estimation of linear trends and other signal components that show a systematic behavior over long time intervals. The key element of the developed methodology is the statistically optimal Wiener-type filter which makes use of the full covariance matrices of noise and signal. The developed methodology is applied to determine the mass balance of the Greenland ice sheet, both per drainage system and integrated, as well as the mass balance of the ice caps on the islands surrounding Greenland. The estimations are performed for three 2-year time intervals (2003–2004, 2005–2006, and 2007–2008), as well as for the 6-year time interval (2003–2008). The study confirms a significant difference in the behavior of the drainage systems over time. The average 6-year rate of mass loss in Greenland is estimated as 165 ± 15 Gt/year. The rate of mass loss of the ice caps on Ellesmere Island (together with Devon Island), Baffin Island, Iceland, and Svalbard is found to be 22 ± 4, 21 ± 6, 17 ± 9, and 6 ± 2 Gt/year, respectively. All these estimates are corrected for the effect of glacial isostatic adjustment.

Separation of mass signals within GRACE monthly gravity field models by means of empirical orthogonal functions

Since 2002 the two GRACE satellites observe the time varying gravity signal mainly caused by the sum of mass variations within the Earth subsystems ocean, atmosphere, and continental hydrosphere. It is a challenging problem to separate the integral GRACE signal and to identify and quantify the mass variations of the individual subsystems. This work proves first by a closed loop simulation that such a decomposition is successful by means of empirical orthogonal functions (EOF) derived from geophysical models and a least-squares adjustment with a multivariate Gauss–Markov model with time coefficients parameterized. The geophysical models are used to synthesize GRACE observations which are subsequently separated leading to time coefficients coinciding with those of the predefined models. In a second step the separation is performed with real, unfiltered time series of 5years of monthly GRACE gravity field models (with atmospheric and oceanic background models reconstructed) and a limited number of EOFs. The reconstructed time coefficients are in good agreement with the original ones and exhibit high correlations (0.70 for ocean, 0.91 for atmosphere and 0.93 for continental hydrosphere). Analysis of GRACE residuals and the correlation among the time coefficients substantiate a successful identification.

Reducing errors in the GRACE gravity solutions using regularization

The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth’s monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003–Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE.

Radial and tangential gravity rates from GRACE in areas of glacial isostatic adjustment

In areas dominated by Glacial Isostatic Adjustment (GIA), the free-air gravity anomaly rate can be converted to uplift rate to good approximation by using a simple spectral relation. We provide quantitative comparisons between gravity rates derived from monthly gravity field solutions (GFZ Potsdam, CSR Texas, IGG Bonn) from the Gravity Recovery and Climate Experiment (GRACE) satellite mission with uplift rates measured by GPS in these areas. The band-limited gravity data from the GRACE satellite mission can be brought to very good agreement with the point data from GPS by using scaling factors derived from a GIA model (the root-mean-square of differences is 0.55 mm yr-1 for a maximum uplift rate signal of 10 mm yr-1). The root-mean-square of the differences between GRACE derived uplift rates and GPS derived uplift rates decreases with increasing GRACE time period to a level below the uncertainty that is expected from GRACE observations, GPS measurements and the conversion from gravity rate to uplift rate. With the current length of time-series (more than 8 yr) applying filters and a hydrology correction to the GRACE data does not reduce the root-mean-square of differences significantly. The smallest root-mean-square was obtained with the GFZ solution in Fennoscandia and with the CSR solution in North America. With radial gravity rates in excellent agreement with GPS uplift rates, more information on the GIA process can be extracted from GRACE gravity field solutions in the form of tangential gravity rates, which are equivalent to a rate of change in the deflection of the vertical scaled by the magnitude of gravity rate vector. Tangential gravity rates derived from GRACE point towards the centre of the previously glaciated area, and are largest in a location close to the centre of the former ice sheet. Forward modelling showed that present day tangential gravity rates have maximum sensitivity between the centre and edge of the former ice sheet, while radial gravity rates are most sensitive in the centre of the former ice sheet. As a result, tangential gravity rates offer constraints on a two-layer mantle viscosity profile that are different from radial gravity rates, which can be exploited in future GIA studies.

Integration of GRACE (Gravity Recovery and Climate Experiment) data with traditional data sets for a better understanding of the time-dependent water partitioning in African watersheds

Monthly (71 months) Gravity Recovery and Climate Experiment (GRACE) gravity field solutions acquired over North and Central Africa (August 2002–July 2008) were destriped, smoothed (250 km; Gaussian), and converted to equivalent water thickness. These data were analyzed in a geographic information system environment together with relevant data sets (e.g., topography, geology, remote sensing) to assess the utility of GRACE for monitoring elements of hydrologic systems on local scales. The following were observed over the Niger, Congo, and Nile Basins: (1) large persistent anomalies (standard deviation, SD > 10 cm) on SD images over periods of 2–7 yr; (2) anomalous areas originate at mountainous source areas that receive high precipitation, extend downslope toward mountain foothills, and often continue along main channels, wetlands, or lakes that drain these areas; (3) time-series analyses over anomalous areas showed that seasonal mass variation lags behind seasonal precipitation; and (4) seasonal mass variations showed progressive shift in phase and decrease in amplitude with distance from the mountainous source areas. Results indicate that (1) the observed temporal mass variations are largely controlled by elements of the hydrologic cycle (e.g., runoff, infiltration, groundwater flow) and have not been obscured by noise, as previously thought; and (2) it is possible to use GRACE to investigate the temporal local responses of a much larger suite of hydrologic systems (watersheds, lakes, rivers, and marshes) and domains (source areas and lowlands) within watersheds and subbasins worldwide.

GRACE gravity field modeling with an investigation on correlation between nuisance parameters and gravity field coefficients

The GRACE (Gravity Recovery And Climate Experiment) monthly gravity models have been independently produced and published by several research institutions, such as Center for Space Research (CSR), GeoForschungsZentrum (GFZ), Jet Propulsion Laboratory (JPL), Centre National d’Etudes Spatiales (CNES) and Delft Institute of Earth Observation and Space Systems (DEOS). According to their processing standards, above institutions use the traditional variational approach except that the DEOS exploits the acceleration approach. The background force models employed are rather similar. The produced gravity field models generally agree with one another in the spatial pattern. However, there are some discrepancies in the gravity signal amplitude between solutions produced by different institutions. In particular, 10%–30% signal amplitude differences in some river basins can be observed. In this paper, we implemented a variant of the traditional variational approach and computed two sets of monthly gravity field solutions using the data from January 2005 to December 2006. The input data are K-band range-rates (KBRR) and kinematic orbits of GRACE satellites. The main difference in the production of our two types of models is how to deal with nuisance parameters. This type of parameters is necessary to absorb low-frequency errors in the data, which are mainly the aliasing and instrument errors. One way is to remove the nuisance parameters before estimating the geopotential coefficients, called NPARB approach in the paper. The other way is to estimate the nuisance parameters and geopotential coefficients simultaneously, called NPESS approach. These two types of solutions mainly differ in geopotential coefficients from degree 2 to 5. This can be explained by the fact that the nuisance parameters and the gravity field coefficients are highly correlated, particularly at low degrees. We compare these solutions with the official and published ones by means of spectral analysis. It is found that our solutions are, in general, consistent with others in the spatial pattern. The water storage variations of the Amazon, Chari and Ganges river basins have also been computed. The variations computed with the NPARB approach are closer to those produced by JPL and DEOS solutions, while the variations produced with the NPESS approach are in good agreement with those produced by the CSR and GFZ solutions. A simulation study is implemented with considering realistic noise and low-frequency error. The two approaches are used to recover the true model. The NPESS solution appears closer to the true one. Therefore we are inclined to estimate the nuisance parameters simultaneously with the geopential coefficients.

DEOS Mass Transport model (DMT-1) based on GRACE satellite data: methodology and validation

SUMMARY The DEOS Mass Transport release 1 (DMT-1) model has been produced on the basis of intersatellite K-band ranging data acquired by the GRACE satellite mission. The functional model exploited in the data processing can be considered as a variant of the acceleration approach. Each element of the data vector is defined as a linear combination of three successive range measurements and can be interpreted as the line-of-sight projection of a weighted average of intersatellite accelerations. As such, the data vector can be directly linked to parameters of the gravitational field. In this way, a series of unconstrained monthly gravity field solutions is produced, each of which is defined as a set of spherical harmonic coefficients complete to degree 120. At the post-processing stage, the unconstrained solutions are filtered with a statistically optimal Wiener-type filter based on full covariance matrices of noise and signal. As such, the DMT-1 model is free from along-track artefacts, which are typical for many other GRACE gravity models. The accuracy of the DMT-1 model has been analysed in different ways. First, the signals observed in areas with minimal mass variations (Sahara, East Antarctica and the middle of the Pacific Ocean) are analysed and interpreted as an upper bound of the noise in the DMT-1 model. It is concluded that the pointwise errors after filtering are of the order of 2–3 cm in terms of equivalent water heights. For the mean mass variations in an area of 10 6 km 2 , the corresponding error reduces to 1.5–2 cm. Second, a time-series of mass variations in the Marie Byrd Land (Antarctica) has been analysed, where the true signal (mostly caused by postglacial rebound) is expected to be close to a linear trend. The rms of the post-fit residuals is found to be 3.3 cm, which is consistent with the error analysis in areas with minimal mass variations. Thirdly, the DMT-1 model has been applied to estimate mass variations in 2003–2006 in Lake Victoria (Africa), where a large drop of water level is observed in recent years. The obtained linear trend (−31 ± 3c m yr −1 ) is in good agreement with that derived from the satellite altimetry data (−35 ± 1c m yr −1 ).

Significance of secular trends of mass variations determined from GRACE solutions

Abstract Since 2002 the Earth’s gravity field is globally observed by the Gravity Recovery and Climate Experiment (GRACE) satellite mission. The GRACE monthly gravity field solutions, available from several analysis centres, reflect mass variations in the atmosphere, hydrosphere and geosphere. Due to correlated noise contained in these solutions, it is, however, first necessary to apply an appropriate filtering technique. The resulting, smoothed time series are applied not only to determine variations with different periodic signatures (e.g., seasonal, short and medium-term), but to derive long-periodic mass variations and secular trends as well. As the GRACE monthly solutions always show the integral effect of all mass variations, for separation of single processes, like the GIA (Glacial isostatic adjustment)-related mass increase in Fennoscandia, appropriate reduction models (e.g. from hydrology) are necessary. In this study we show for the example of the Fennoscandian uplift area that GRACE solutions from different analysis centres yield considerably different secular trends. Furthermore, it turns out that the inevitable filtering of the monthly gravity field models affects not only the amplitudes of the signals, but also their spatial resolution and distribution such as the spatial form of the detected signals. It also becomes evident that the determination of trends has to be performed together with the determination of periodic components. All periodic terms which are really contained in the data, and only such, have to be included. The restricted time span of the available GRACE measurements, however, limits the separation of long-periodic and secular signals. It is shown that varying the analysis time span affects the results considerably. Finally, a reduction of hydrological signals from the detected integral secular trends using global hydrological models (WGHM, LaDWorld, GLDAS) is attempted. The differences among the trends resulting from different models illustrate that the state-of-the-art hydrology models are not suitable for this purpose as yet. Consequently, taking the GRACE monthly gravity field solutions from one centre, choosing a single filter and applying an insufficiently reliable reduction model leads sometimes to a misinterpretation of considered geophysical processes. Therefore, one has to be cautious with the final interpretation of the results.

Residual ocean tide signals from satellite altimetry, GRACE gravity fields, and hydrodynamic modelling

Improvements of a global state-of-the art ocean tide model are identified and quantified by applying three independent approaches, namely (i) empirical ocean tide analysis of multimission altimeter data, (ii) evaluation of GRACE data and gravity field models and (iii) high resolution hydrodynamic modelling. Although these approaches have different capabilities to sense ocean tides they obtain results which are basically consistent one with each other. The analysis of altimeter data clearly identifies significant residual amplitudes over shallow water for all major diurnal and semidiurnal constituents and the non-linear tide M4. GRACE data and the time-series of monthly gravity field models exhibit-on a larger scale-residual ocean tide signals over much the same areas. The analysis of dynamic residuals of hydrodynamic modelling with data assimilation proves the validity of linear dynamics in the deep ocean and shows correlation of dynamic residuals with energy dissipation in these areas.

On the influence of the ground track on the gravity field recovery from high–low satellite-to-satellite tracking missions: CHAMP monthly gravity field recovery using the energy balance approach revisited

In this paper, the influence of the ground track coverage on the quality of a monthly gravity field solution is investigated for the scenario of a high–low satellite- to-satellite tracking mission. Data from the CHAllenging Minisatellite Payload (champ) mission collected in the period April 2002 to February 2004 has been used to recover the gravity field to degree and order 70 on a monthly basis. The quality is primarily restricted by the accuracy of the instruments. Besides, champ passed through a 31/2 repeat mode three times during the period of interest resulting in an insufficient spatial sampling and a degraded solution. Contrary to the rule of thumb by Colombo (The global mapping of gravity with two satellites, Publications on Geodesy, vol 7(3), Netherlands Geodetic Commission, The Netherlands, 263 pp, 1984), see also Wagner (J Geod 80(2): 94–103, 2006), we found that the monthly solutions themselves could be recovered to about degree 30, not 15. In order to improve the monthly gravity solutions, two strategies have been developed: the restriction to a low degree, and the densification of the sampling by the introduction of additional sensitive measurements from contemporaneous satellite missions. The latter method is tested by combining the champ measurements with data from the Gravity Recovery And Climate Experiment (grace). Note that the two grace satellites are considered independent here, i.e. no use is made of the K-band ranging data. This way, we are able to almost entirely remove the influence of the ground track leaving the accuracy of the instruments as the primary restriction on the quality of a monthly solution. These findings are especially interesting for the upcoming swarm-mission since it will consist of a similar configuration as the combined champ and (grace) missions.

GRACE‐derived ice‐mass variations over Greenland by accounting for leakage effects

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−1. 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−1, −194 ± 24 km3 a−1 and −96 ± 23 km3 a−1, 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.

Implications of postseismic gravity change following the great 2004 Sumatra‐Andaman earthquake from the regional harmonic analysis of GRACE intersatellite tracking data

We report Gravity Recovery and Climate Experiment (GRACE) satellite observations of coseismic displacements and postseismic transients from the great Sumatra‐Andaman Islands (thrust event; Mw ∼9.2) earthquake in December 2004. Instead of using global spherical harmonic solutions of monthly gravity fields, we estimated the gravity changes directly using intersatellite range‐rate data with regionally concentrated spherical Slepian basis functions every 15‐day interval. We found significant step‐like (coseismic) and exponential‐like (postseismic) behavior in the time series of estimated coefficients (from May 2003 to April 2007) for the spherical Slepian functions. After deriving coseismic slip estimates from seismic and geodetic data that spanned different time intervals, we estimated and evaluated postseismic relaxation mechanisms with alternate asthenosphere viscosity models. The large spatial coverage and uniform accuracy of our GRACE solution enabled us to clearly delineate a postseismic transient signal in the first 2 years of postearthquake GRACE data. Our preferred interpretation of the long‐wavelength components of the postseismic gravity change is biviscous viscoelastic flow. We estimated a transient viscosity of 5 × 1017 Pa s and a steady state viscosity of 5 × 1018–1019 Pa s. Additional years of the GRACE observations should provide improved steady state viscosity estimates. In contrast to our interpretation of coseismic gravity change, the prominent postearthquake positive gravity change around the Nicobar Islands is accounted for by seafloor uplift with less postseismic perturbation in intrinsic density in the region surrounding the earthquake.

The design of an optimal filter for monthly GRACE gravity models

SUMMARY Most applications of the publicly released Gravity Recovery and Climate Experiment monthly gravity field models require the application of a spatial filter to help suppressing noise and other systematic errors present in the data. The most common approach makes use of a simple Gaussian averaging process, which is often combined with a ‘destriping’ technique in which coefficient correlations within a given degree are removed. As brute force methods, neither of these techniques takes into consideration the statistical information from the gravity solution itself and, while they perform well overall, they can often end up removing more signal than necessary. Other optimal filters have been proposed in the literature; however, none have attempted to make full use of all information available from the monthly solutions. By examining the underlying principles of filter design, a filter has been developed that incorporates the noise and full signal variance–covariance matrix to tailor the filter to the error characteristics of a particular monthly solution. The filter is both anisotropic and nonsymmetric, meaning it can accommodate noise of an arbitrary shape, such as the characteristic stripes. The filter minimizes the mean-square error and, in this sense, can be considered as the most optimal filter possible. Through both simulated and real data scenarios, this improved filter will be shown to preserve the highest amount of gravity signal when compared to other standard techniques, while simultaneously minimizing leakage effects and producing smooth solutions in areas of low signal.

Gravity model determination from the GRACE mission

The Gravity Recovery and Climate Experiment (GRACE) is a collaborative NASA and DLR mission whose satellites were launched on March 17, 2002 as the first of the Earth System Science Pathfinder (ESSP) Missions. The purpose of the GRACE mission is to characterize the spatial and temporal variations in the Earth’s mass, through precise measurements of its gravity field. This is accomplished by using micron level inter-satellite range measurements to determine monthly solutions for the Earth’s global gravity field. The GRACE mission has provided 82 monthly solutions that have led to unprecedented improvements in the mean gravity field accuracy and a seven-year record of monthly gravity signals associated with the global mass flux. This continuous, multi-year record of monthly measurements supports investigations that characterize the seasonal cycle of mass transport between the oceans, land, and atmosphere; observes its inter-annual variability; and monitors the secular trends in mass transport. In the following discussion, the overall mission concept is described, the approach to the gravity model determination is discussed, and the mission progress is partially summarized.

Spatiospectral localization of global geopotential fields from the Gravity Recovery and Climate Experiment (GRACE) reveals the coseismic gravity change owing to the 2004 Sumatra‐Andaman earthquake

Regional mass fluxes owing to transport and adjustment within the Earth system that are implicitly contained in the monthly Gravity Recovery and Climate Experiment (GRACE) global geopotential coefficients are revealed by localizing global spectra using spatiospectrally concentrated window functions. We have analyzed 45 monthly global GRACE harmonic coefficient series in order to find the coseismic signature associated with the 2004 great Sumatra‐Andaman earthquake. A significant gravity change after the earthquake is found in the time series of the GRACE coefficients after localization with a single band‐limited window centered near the north of the island of Sumatra. This change is undetectable from the original global coefficients or from coefficients localized elsewhere on the globe. A step function with its discontinuity at 26 December 2004 usefully models the coseismic gravity change. The localized GRACE coefficients contain the jumps (associated with the earthquake) up to degree and order 55, although not all of them within this band produce changes that are statistically significant. The gravity change calculated from the localized GRACE coefficients displays 30 μGal peak‐to‐peak variations that are very well correlated with an independently derived seismic model based on elastic dislocation theory.

Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models

We discuss a new method for approximately decorrelating and non-isotropically filtering the monthly gravity fields provided by the gravity recovery and climate experiment (GRACE) twin-satellite mission. The procedure is more efficient than conventional Gaussian-type isotropic filters in reducing stripes and spurious patterns, while retaining the signal magnitudes. One of the problems that users of GRACE level 2 monthly gravity field solutions fight is the effect of increasing noise in higher frequencies. Simply truncating the spherical harmonic solution at low degrees causes the loss of a significant portion of signal, which is not an option if one is interested in geophysical phenomena on a scale of few hundred to few thousand km. The common approach is to filter the published solutions, that is to convolve them with an isotropic kernel that allows an interpretation as smoothed averaging. The downside of this approach is an amplitude bias and the fact that it neither accounts for the variable data density that increases towards the poles where the orbits converge nor for the anisotropic error correlation structure that the solutions exhibit. Here a relatively simple regularization procedure will be outlined, which allows one to take the latter two effects into account, on the basis of published level 2 products. This leads to a series of approximate decorrelation transformations applied to the monthly solutions, which enable a successive smoothing to reduce the noise in the higher frequencies. This smoothing effect may be used to generate solutions that behave, on average over all possible directions, very close to Gaussian-type filtered ones. The localizing and smoothing properties of our non-isotropic kernels are compared with Gaussian kernels in terms of the kernel variance and the resulting amplitude bias for a standard signal. Examples involving real GRACE level 2 fields as well as geophysical models are used to demonstrate the techniques. With the new method, we find that the characteristic striping pattern in the GRACE solutions are much more reduced than Gaussian-filtered solutions of comparable signal amplitude and root mean square.

Errors of regional mass variations inferred from GRACE monthly solutions

Error correlations in current GRACE monthly gravity field models strongly affect the errors of inferred regionally averaged mass variations (RMV). To demonstrate this, we develop an empirical method which roughly estimates scaling factors to convert error bars computed by ignoring error correlations into more realistic error bars for RMV. For current solutions by CSR and GFZ, we find factors in the order of 2 or more for near‐polar regions and below one for near‐equatorial regions. A comparison of RMV computed from the CSR and the GFZ models for Greenland, Antarctica and the Amazon basin supports our findings. We discuss consequences on error assessment and error separation. For example, previously published GRACE‐derived RMV of Greenland may be still strongly affected by errors in the GRACE products.

Observing seasonal bottom pressure variability in the North Pacific with GRACE

Using monthly gravity field solutions from GRACE together with output from an ocean model we assess the ability of GRACE to observe seasonal ocean bottom pressure variability in the North Pacific. First, the spatial structure and temporal evolution of the long‐term mean seasonal bottom pressure cycle in the North Pacific is characterised in the context of the ocean model. It is then shown that a mean seasonal cycle based on a limited subset of the model output corresponding to the intervals over which the GRACE monthly solutions were formed is representative of this long‐term seasonal cycle. It is therefore concluded that the significant features of the seasonal cycle should be present in the GRACE data. Agreement is found between the ocean model and GRACE estimates of the bottom pressure seasonal cycle, thus demonstrating the worth of GRACE as a tool for studying ocean dynamics.

Seasonal variation of ocean bottom pressure derived from Gravity Recovery and Climate Experiment (GRACE): Local validation and global patterns

The Gravity Recovery and Climate Experiment (GRACE) processing centers at the GeoForschungsZentrum Potsdam (GFZ) and the University of Texas Center for Space Research (UTCSR) provide time series of monthly gravity field solutions covering the period since mission launch in March 2002. Although the achieved accuracy still remains an order of magnitude below the mission's baseline goal, these time series have successfully been used to study terrestrial phenomena such as water storage variations. Over the oceans, the monthly gravity field solutions can be converted into estimates of the fluctuating ocean bottom pressure (OBP), which is the sum of atmospheric and oceanic mass variations. The GRACE products may be validated against in situ OBP observations which are available from a ground truth site in the tropical northwest Atlantic Ocean. Large differences are observed between the in situ and GRACE‐derived OBP which are investigated by comparing the tidal and nontidal ocean models used at GFZ and UTCSR for dealiasing short‐term (<2 months) mass variations from satellite measurements. Results show that the barotropic nontidal and tide models need improvement at periods shorter than 1 day and longer than 2 weeks. On a global scale the monthly OBP fields from GRACE generally overestimate the variability compared to ocean general circulation models, especially in tropical regions. This may be attributed to continuing deficiencies in GRACE data processing. Nevertheless, there is some initial evidence that GRACE possesses the potential to observe large‐scale averages of bottom pressure fluctuations.