Satellite Gravity Missions Research Articles

Short‐term transport variability of the Antarctic Circumpolar Current from satellite gravity observations

Ocean bottom pressure gradients deduced from the satellite gravity mission Gravity Recovery and Climate Experiment (GRACE) were previously shown to provide barotropic transport variations of the Antarctic Circumpolar Current (ACC) with up to monthly resolution. Here, bottom pressure distributions from GRACE with monthly (GFZ RL04) and higher temporal resolution (CNES/GRGS with 10 days, ITG‐GRACE2010 with daily resolution) are evaluated over the ACC area. Even on time scales shorter than 10 days, correlations with in situ bottom pressure records frequently exceed 0.6 with positive explained variances, giving evidence that high‐frequency nontidal ocean mass variability is captured by the daily ITG‐GRACE2010 solutions not already included in the applied background models. Bottom pressure is subsequently taken to calculate the barotropic component of the ACC transport variability across Drake Passage. For periods longer than 30 days, transport shows high correlations between 0.4 and 0.5 with several tide gauge records along the coast of Antarctica. Still significant correlations around 0.25 are obtained even for variability with periods shorter than 10 days. Since transport variations are predominantly affected by time‐variable surface winds, GRACE‐based transports are contrasted against an atmospheric index of the Southern Annular Mode (SAM), which represents the Southern Hemispheric wind variability. Correlations between the SAM and GRACE‐based transports are consistently higher than correlations between any of the available sea level records in all frequency bands considered, indicating that GRACE is indeed able to accurately observe a hemispherically consistent pattern of bottom pressure (and hence ACC transport) variability that is otherwise at least partially masked in tide gauge records due to local weather effects, sea ice presence and steric signals.

Mass balance and mass loss acceleration of the Greenland ice sheet (2002 - 2011) from GRACE gravity data

Mass balance and mass loss acceleration of the Greenland ice sheet (2002 - 2011) from GRACE gravity dataWe examine the magnitude and acceleration of the Greenland ice sheet mass loss between 2002 and 2011. We use monthly observations of time-variable gravity from the Gravity Recovery and Climate Experiment (GRACE) satellite gravity mission. The Greenland mass loss during this time period is not a constant, but accelerating with time. We have used a quadratic trend in addition to a linear trend, which is usually applied to the GRACE monthly time series of ice mass changes, to show that it better represents GRACE observations. Results of computations provide a mass decrease of -166±20 Gigatonne per year (Gt/yr) by using a linear trend and -111±21 Gt/yr by fitting a quadratic trend to the monthly time series. Quadratic fitting shows that the mass loss increases from -121 Gt/yr in 2002 - 2003 to -210 Gt/yr in 2006 - 2007 and -271 Gt/yr in 2010 - 2011 with an acceleration of -32±6 Gt/yr2 in 2002 - 2011. This implies that the Greenland ice sheet contribution to sea level rise becomes larger with time. Contrary to recent studies, we use a non-isotropic filter whose degree of smoothing corresponds to a Gaussian filter with a radius of 340 km. Stripping effects in the GRACE data, C20 effect, and leakage effects are applied.

On the combination of high-resolution and satellite-only global gravity models

The issue of combining high-resolution gravity models, based on observations taken on the Earth surface, with those derived from satellite-only observations is of increasing importance, due to the new data provided by gravity satellite missions, CHAMP, GRACE and GOCE. The paper addresses this issue with a twofold purpose. On the one hand, it is an attempt to discuss and assess general concepts, well known in literature, such as achievable resolution, regularization in the least-squares sense or in an infinite dimensional setup, combination criteria, symmetry and block diagonal structures. In particular, as for the symmetry question, a well-defined result, generalizing known facts, is derived. On the other hand, the outcomes of the general discussion are specifically applied to the combination of a high-resolution model (e.g. EGM08) with a GOCE gravity model estimated by the so-called space-wise approach. Small numerical examples are developed to clarify the property of the proposed solution.

Terrestrial water variations in the North China Plain revealed by the GRACE mission

Using eight years of time-variant gravity measurements from the GRACE gravity satellite mission, we estimate monthly terrestrial water storage variations in the North China Plain between August 2002 and August 2010. We find that during this period, the water storage is not constant but accelerate at a rate of −1.1 cm/yr over time. The study confirms that the relatively long-term trend of water storage in the North China Plain (by 13-point moving average) is consistent well with that by linear fitting. Two hydrological models, CPC and GLDAS, are adopted in calculating surface water variations, with results indicating that they agree with those of GRACE. Furthermore, rates of −0.6 cm/yr for surface water variations and −0.5 cm/yr for groundwater variations are found in the North China Plain during the study period. Decrease of rainfall and the groundwater over-exploitation are possibly the main causes for groundwater depletion in the North China Plain. The results will be helpful for better understanding climatic changes and provide reference for the management of water resources and the establishment of policies on preventing and alleviating natural hazards.

Estimating high frequency ocean bottom pressure variability

[1] Knowledge of variability in ocean bottom pressure (pb) at periods < 60 days is essential for minimizing aliasing in satellite gravity missions. We assess how well we know such rapid, non-tidal pb signals by analyzing in-situ bottom pressure recorder (BPR) data and available global estimates from two very different modeling approaches. Estimated pb variance is generally lower than that measured by the BPRs, implying the presence of correlated model errors. Deriving uncertainties from differencing the model estimates can thus severely underestimate the aliasing errors. Removing estimated series from BPR data tends to reduce the variance by up to ∼5 cm2 but residual variance is still ∼5–20 cm2 and not negligible relative to expected variance in climate pb signals. The residual pb variability can be correlated over hundreds of kilometers. Results indicate the need to improve estimates of rapid pb variability in order to minimize aliasing noise in current and future satellite-based pb observations.

GOCE, Satellite Gravimetry and Antarctic Mass Transports

In 2009 the European Space Agency satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) was launched. Its objectives are the precise and detailed determination of the Earth’s gravity field and geoid. Its core instrument, a three axis gravitational gradiometer, measures the gravity gradient components V xx , V yy , V zz and V xz (second-order derivatives of the gravity potential V) with high precision and V xy , V yz with low precision, all in the instrument reference frame. The long wavelength gravity field is recovered from the orbit, measured by GPS (Global Positioning System). Characteristic elements of the mission are precise star tracking, a Sun-synchronous and very low (260 km) orbit, angular control by magnetic torquing and an extremely stiff and thermally stable instrument environment. GOCE is complementary to GRACE (Gravity Recovery and Climate Experiment), another satellite gravity mission, launched in 2002. While GRACE is designed to measure temporal gravity variations, albeit with limited spatial resolution, GOCE is aiming at maximum spatial resolution, at the expense of accuracy at large spatial scales. Thus, GOCE will not provide temporal variations but is tailored to the recovery of the fine scales of the stationary field. GRACE is very successful in delivering time series of large-scale mass changes of the Antarctic ice sheet, among other things. Currently, emphasis of respective GRACE analyses is on regional refinement and on changes of temporal trends. One of the challenges is the separation of ice mass changes from glacial isostatic adjustment. Already from a few months of GOCE data, detailed gravity gradients can be recovered. They are presented here for the area of Antarctica. As one application, GOCE gravity gradients are an important addition to the sparse gravity data of Antarctica. They will help studies of the crustal and lithospheric field. A second area of application is ocean circulation. The geoid surface from the gravity field model GOCO01S allows us now to generate rather detailed maps of the mean dynamic ocean topography and of geostrophic flow velocities in the region of the Antarctic Circumpolar Current.

Verification of heights above global mean sea level from high-degree global geopotential models by using leveling data

The dedicated satellite gravity missions CHAllenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity field and steady-state Ocean Circulation Explorer (GOCE) and their recent and expected Global Geopotential Models (GGMs) present new opportunities for the determination of gravity-related heights. Global Positioning System (GPS), the recent GGMs, and reference value W0 are used to study the construction of different height systems and verify high-degree global geopotential models. This approach matches well with all theoretical basics of height systems. The presented numerical strategy is independent of height anomaly and geoid undulation computation. Using the International Terrestrial Reference Frame (ITRF) coordinates at 47 GPS stations of the Turkish National Vertical Control Network (TNVCN), the gravity potential values are computed based on new-generation GGMs. The computed gravity potentials are converted into different height systems. A global mean sea level represented by a geoid potential has been taken as reference for the heights. The GGM-derived geopotential numbers, Helmert orthometric, and Molodensky normal heights at the GPS stations are compared against the results from precise leveling. The numerical application demonstrates that three types of gravity-related heights can be determined with a similar accuracy level (12 cm). When long-term deformations such as tectonic activity and possible land subsidence/uplift effects on the heights of benchmarks of the TNVCN are taken into account, the obtained results are significant, and also, under the light of the dedicated satellite gravity missions, high-resolution GGMs such as EGM2008 have an important potential for the realization of a unified height system. The experimental study shows a datum bias of 38 2 cm between the TNVCN datum and the global datum.

Water storage variations of the Yangtze, Yellow, and Zhujiang river basins derived from the DEOS Mass Transport (DMT-1) model

In general, China is short of water resources and some regions even experience a shortage of daily water supply. This could threaten the stability and economic development of the nation. A study on the water storage variations is especially important for the water management and storage prediction in three largest river basins of China, namely, Yangtze, Yellow, and Zhujiang, where the most dense population and leading economic regions are located. The satellite gravity mission GRACE (Gravity Recovery and Climate Experiment) provides an opportunity to macroscopically identify water (or mass) variations in the Earth’s system with a spatial resolution of 300–400 km and a temporal resolution of about one month. We use the first release of the DEOS (Delft Institute of Earth Observation and Space Systems) Mass Transport (DMT-1) model based on GRACE data to analyze water storage changes in the three river basins. The DMT-1 model consists of monthly solutions, which are computed using an innovative methodology. The methodology includes, in particular, the application of a statistically optimal Wiener-type filter based on full variance-covariance matrices of noise and signal. This results in particularly sharp mass variation maps. Taking one monthly solution as an example, we compare the results derived from the DMT-1 model with ones produced with the standard post-processing scheme based on a combination of the de-striping and Gaussian filtering. The comparison shows that the DMT-1 model outperforms the other models and is suitable for the analysis of the mass changes in river basins. A subset of the DMT-1 solutions in the interval between February 2003 and May 2008 is used to estimate the secular trends and seasonal variations for the three river basins. The estimated trends show that the water storage of the Yellow River basin does not have significant changes, while the Zhujiang and Yangtze river basins have a large and statistically significant water storage increase. The estimation of seasonal variations demonstrates that the water storage variations in Yangtze and Zhujiang river basins are almost in the same phase. The amplitude of variations in the Zhujiang River basin is larger than that in Yangtze. No clear annual variations are observed in the Yellow River basin. The observed water storage variations generally coincide with the observations and conclusions presented in the hydrological reports of the Chinese Ministry of Water Resources.

The 2009 exceptional Amazon flood and interannual terrestrial water storage change observed by GRACE

The Gravity Recovery and Climate Experiment (GRACE) satellite gravity mission provides a new capability for measuring extreme climate events, such as floods and droughts associated with large‐scale terrestrial water storage (TWS) change. GRACE gravity measurements show significant TWS increases in the lower Amazon basin in the first half of 2009, clearly associated with the exceptional flood season in that region. The extended record of GRACE monthly gravity solutions reveals the temporal and spatial evolution of both nonseasonal and interannual TWS change in the Amazon basin over the 7 year mission period from April 2002 to August 2009. GRACE observes a very dry season in 2002–2003 and an extremely wet season in 2009. In March 2009 (approximately the peak of the recent Amazon flood), total TWS surplus in the entire Amazon basin is ∼624 ± 32 Gt, roughly equal to U.S. water consumption for a year. GRACE measurements are consistent with precipitation data. Interannual TWS changes in the Amazon basin are closely connected to ENSO events in the tropical Pacific. The 2002–2003 dry season is clearly tied to the 2002–2003 El Niño and the 2009 flood to the recent La Niña event. The most significant contribution of this study in the area of water resources is to confront the hydrological community with the latest results of the GRACE satellite mission and further demonstrates the unique strength of GRACE and follow‐up satellite gravity observations for measuring large‐scale extreme climate events.

On global and regional spectral evaluation of global geopotential models

Spectral evaluation of global geopotential models (GGMs) is necessary to recognize the behaviour of gravity signal and its error recorded in spherical harmonic coefficients and associated standard deviations. Results put forward in this wise explain the whole contribution of gravity data in different kinds that represent various sections of the gravity spectrum. This method is more informative than accuracy assessment methods, which use external data such as GPS-levelling. Comparative spectral evaluation for more than one model can be performed both in global and local sense using many spectral tools. The number of GGMs has grown with the increasing number of data collected by the dedicated satellite gravity missions, CHAMP, GRACE and GOCE. This fact makes it necessary to measure the differences between models and to monitor the improvements in the gravity field recovery. In this paper, some of the satellite-only and combined models are examined in different scales, globally and regionally, in order to observe the advances in the modelling of GGMs and their strengths at various expansion degrees for geodetic and geophysical applications. The validation of the published errors of model coefficients is a part of this evaluation. All spectral tools explicitly reveal the superiority of the GRACE-based models when compared against the models that comprise the conventional satellite tracking data. The disagreement between models is large in local/regional areas if data sets are different, as seen from the example of the Turkish territory.

On the combination of global and local data in collocation theory

Due to the successful operation of dedicated satellite gravity missions, nowadays high-accuracy global gravity field models have become available. This triggers the challenge to optimally combine this long to medium wavelength gravity field information derived from space-borne data with high-resolution terrestrial gravity data. In this paper, the least squares collocation concept is revised with the attempt to consistently unify the combination procedure in such a way that the full information contained in both data sets is merged. For example, in local or regional geoid determination the remove-restore method is usually applied only partially taking into account the accuracy of the global model coefficients used for the long-wavelength reduction. The key advantage of the extended formulation is the fact that it automatically accounts for the error covariance of all data types involved. The applicability, feasibility and performance of the proposed method is investigated in the frame of numerical closed-loop simulations. The two main fields of application, i.e., the improvement of a global gravity field model by terrestrial gravity field data, and, vice versa, the support to a regional geoid solution by the incorporation of a global gravity field model, have been analyzed and assessed. Although applied under simplified conditions, it could be shown that the method works and is practically applicable.

Spread of ice mass loss into northwest Greenland observed by GRACE and GPS

Greenland's main outlet glaciers have more than doubled their contribution to global sea level rise over the last decade. Recent work has shown that Greenland's mass loss is still increasing. Here we show that the ice loss, which has been well‐documented over southern portions of Greenland, is now spreading up along the northwest coast, with this acceleration likely starting in late 2005. We support this with two lines of evidence. One is based on measurements from the Gravity Recovery and Climate Experiment (GRACE) satellite gravity mission, launched in March 2002. The other comes from continuous Global Positioning System (GPS) measurements from three long‐term sites on bedrock adjacent to the ice sheet. The GRACE results provide a direct measure of mass loss averaged over scales of a few hundred km. The GPS data are used to monitor crustal uplift caused by ice mass loss close to the sites. The GRACE results can be used to predict crustal uplift, which can be compared with the GPS data. In addition to showing that the northwest ice sheet margin is now losing mass, the uplift results from both the GPS measurements and the GRACE predictions show rapid acceleration in southeast Greenland in late 2003, followed by a moderate deceleration in 2006. Because that latter deceleration is weak, southeast Greenland still appears to be losing ice mass at a much higher rate than it was prior to fall 2003. In a more general sense, the analysis described here demonstrates that GPS uplift measurements can be used in combination with GRACE mass estimates to provide a better understanding of ongoing Greenland mass loss; an analysis approach that will become increasingly useful as long time spans of data accumulate from the 51 permanent GPS stations recently deployed around the edge of the ice sheet as part of the Greenland GPS Network (GNET).

Apparent geocenter oscillations in Global Navigation Satellite Systems solutions caused by the ionospheric effect of second order

The international reference ionosphere (IRI2007) and International Geomagnetic Reference Field (IGRF2005) models are used to create a worldwide model of apparent Global Navigation Satellite Systems (GNSS) site displacements due to unmodeled higher‐order ionospheric delays for different time, seasons, and phases of the solar activity cycle. It is shown that diurnal and seasonal variability of the higher‐order ionospheric delays causes apparent oscillations of the geometric center of the Earth's figure as determined by GNSS. The amplitude of the oscillations in the z direction reaches 2.5 mm for the semiannual and 3.5 mm for 11 year components when satellite orbits are considered fixed and degree 1 parameterization is used. Failure to account for the higher‐order ionospheric delay when performing precise orbit determination for space‐borne receivers, flying above, while the ground‐based fiducial network is located below the ionosphere, will result in biases between the ground and the space segment. Such biases, changing with time and location, can cause difficulties in interpretation of results from satellite altimetry and satellite gravity missions, as systematic biases in orbital parameters can be interpreted as manifestations of geophysical processes. On the basis of the results presented, it is recommended to introduce the modeling of the second‐order ionospheric delay in routine GNSS processing for global geodetic networks, especially in view of the forthcoming solar activity maximum.

Orbit Determination and Sea Level Rise: How Astrodynamics Informs Us About the Climate

Advancements in satellite tracking systems, Earth-gravity field models, and the definition of the terrestrial reference frame have led to significant improvements in the orbit determination for low Earth orbit satellites over the last few decades. These improvements have allowed climate-driven variations in the hydrosphere to be detected for the first time. The monitoring of global mean sea level variations was not originally a goal of satellite altimeter missions such as TOPEX/Poseidon, but now they are measured with an accuracy of ∼4 mm every 10 days because of improvements in the orbit determination (radial component ∼1 cm) and other advances. Similarly, satellite gravity missions such as GRACE have allowed time-variable gravity to become a major scientific objective, with monthly estimates of changes in global ocean mass with an accuracy of 2 mm. Taking advantage of these measurements for climate change studies will require multidecadal time-series using multiple satellite missions that may be tracked by different techniques and methods as technology evolves. For this reason, maintenance and improvement of the terrestrial reference frame is a critical component of an overall plan to monitor the Earth’s water reservoirs from space.

Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE

We use monthly measurements of time‐variable gravity from the GRACE (Gravity Recovery and Climate Experiment) satellite gravity mission to determine the ice mass‐loss for the Greenland and Antarctic Ice Sheets during the period between April 2002 and February 2009. We find that during this time period the mass loss of the ice sheets is not a constant, but accelerating with time, i.e., that the GRACE observations are better represented by a quadratic trend than by a linear one, implying that the ice sheets contribution to sea level becomes larger with time. In Greenland, the mass loss increased from 137 Gt/yr in 2002–2003 to 286 Gt/yr in 2007–2009, i.e., an acceleration of −30 ± 11 Gt/yr2 in 2002–2009. In Antarctica the mass loss increased from 104 Gt/yr in 2002–2006 to 246 Gt/yr in 2006–2009, i.e., an acceleration of −26 ± 14 Gt/yr2 in 2002–2009. The observed acceleration in ice sheet mass loss helps reconcile GRACE ice mass estimates obtained for different time periods.

General formulations of global co-seismic deformations caused by an arbitrary dislocation in a spherically symmetric earth model-applicable to deformed earth surface and space-fixed point

Based on the authors' previous work, co-seismic deformations for a spherical symmetric earth model are summarized and reformulated. Unified expressions presented herein accommodate physical deformations: displacement, potential, gravity, geoid and strain changes. The corresponding Green's functions are derived by combining spheroidal and toroidal deformations. Sign errors in previous publications are corrected in these new formulas. These expressions are developed basically for a deformed earth surface because most traditional geodetic measurements are performed on the terrain surface. However, through development of space geodetic techniques, such as the satellite gravity missions, co-seismic gravity changes can be detected from space. In this case, the above dislocation theory (e.g., the co-seismic gravity change) cannot be applied directly to the observed data because the data do not include surface crustal deformation (the free air gravity change). Correspondingly, the contribution by the vertical displacement part must be removed from the traditional expressions. For this purpose, we present the corresponding expressions applicable to space observations. Some numerical technical problems are discussed. In addition, a smoothing technique is necessary to damp the high-frequency contribution so that the theory can be applied reasonably. Global co-seismic deformations caused by the 2004 Sumatra—Andaman earthquake (M9.3) are studied as an application of the new Green's function. That earthquake caused a global deformation detected by GPS, strain metres and even a satellite gravity mission. These global deformations are calculated based on the derived Green's functions and the seismic-wave derived earth model. A segment-summation scheme is used considering the slip distribution on a limited fault plane. The results are useful for interpreting observed deformations, especially those in the far field. The earthquake reveals global co-seismic deformations and effects of spherical curvature and the earth's layered structure. Comparisons between results for a spherical earth mode and a half-space model show a large discrepancy at an epicentral distance of about 1000 km, implying that effects of spherical curvature and layer structure are considerably large. In addition, the theoretical results are compared with the real observed strain steps, horizontal displacements and gravity changes caused by that earthquake. Good agreement validates the results of the current theoretical work. Finally, we discuss the application the above theory to the GRACE data through several case studies.

On the spectral consistency of the altimetric ocean and geoid surface: a one-dimensional example

Geoid models from the new generation of satellite gravity missions, such as GRACE and GOCE, in combination with sea surface from satellite altimetry allow to obtain absolute dynamic ocean topography with rather high spatial resolution and accuracy. However, this implies combination of data with fundamentally different characteristics and different spatial resolutions. Spectral consistency would imply the removal of the short-scale features of the altimetric sea surface height by filtering, to provide altimetric data consistent with the resolution of the geoid field. The goal must be to lose as little as possible from the high precision of the altimetric signal. Using a one-dimensional example we show how the spectrum is changing when a function defined only on a limited domain (ocean in the real case) is extended or not as to cover the complete domain (the whole sphere in the real case). The results depend on the spectral characteristics of the altimetric signal and of the applied filter. Referring to the periodicity condition, as it is requested in the case of Fourier analysis, the action of the two classical filters (Ideal Low Pass and Gauss filter) and of two alternative procedures (wavelets and Slepian) is studied.

Trend of China land water storage redistribution at medi- and large-spatial scales in recent five years by satellite gravity observations

The GRACE (Gravity Recovery and Climate Experiment) satellite gravity mission has provided a new method to study land water mass redistribution at medi- and long-spatial scales in recent years. We estimate continental water mass redistribution in China using GRACE observations during 2003 to 2007. The results show some large regions with increase or decrease of land water mass storage in the central northern region, Tibetan Plateau, the Three Gorges region, the place where Qinghai, Sichuan and Gansu provinces meet, and the Altun Mountains region in the Xinjiang Uygur Autonomous Region. In the first two regions, it is obvious that water (ice) mass storages are decreasing. Water mass in the central northern region decreases at a linear rate of 2.4 cm/a equivalent water height, equal to 5.2 billion cubic meters per year during the five years’ period, and water mass depletion in Hebei Province is ∼ 4.5 billion cubic meters per year in the same period, which is consistent with the average water mass depletion of 4.0 billion cubic meters per year of overused underground water in the recent 30 years estimated by Hebei Province Water Resources Bureau. Furthermore, GRACE can detect the water mass accumulation of ∼ 5 cm equivalent water height within the region spreading over about 0.12 million square kilometers due to the Three Gorges dam construction in June 2003. We also find a water mass gain of ∼ 1.1 cm/a in the areas where Qinghai, Sichuan and Gansu provinces meet. This indicates that the climate of these regions has been becoming gradually humid in recent years.

Assessment of systematic errors in the surface gravity anomalies over North America using the GRACE gravity model

SUMMARY The surface gravity data collected via traditional techniques such as ground-based, shipboard and airborne gravimetry describe precisely the local gravity field, but they are often biased by systematic errors. On the other hand, the spherical harmonic gravity models determined from satellite missions, in particular, recent models from CHAMP and GRACE, homogenously and accurately describe the low-degree components of the Earth’s gravity field. However, they are subject to large omission errors. The surface and satellite gravity data are therefore complementary in terms of spectral composition. In this paper, we aim to assess the systematic errors of low spherical harmonic degrees in the surface gravity anomalies over North America using a GRACE gravity model. A prerequisite is the extraction of the low-degree components from the surface data to make them compatible with GRACE data. Three types of methods are tested using synthetic data: low-pass filtering, the inverse Stokes integral, and spherical harmonic analysis. The results demonstrate that the spherical harmonic analysis works best. Eighty-five per cent of difference between the synthetic gravity anomalies generated from EGM96 and GGM02S from degrees 2 to 90 can be modelled for a region covering North America and neighbouring areas. Assuming EGM96 is developed solely from the surface gravity data with the same accuracy and GGM02S errorless, one way to understand the 85 per cent difference is that it represents the systematic error from the region of study, while the remaining 15 per cent originates from the data outside of the region. To estimate systematic errors in the surface gravity data, Helmert gravity anomalies are generated from both surface and GRACE data on the geoid. Their differences are expanded into surface spherical harmonics. The results show that the systematic errors for degrees 2 to 90 range from about −6 to 13 mGal with a RMS value of 1.4 mGal over North America. A few significant data gaps can be identified from the resulting error map. The errors over oceans appear to be related to the sea surface topography. These systematic errors must be taken into consideration when the surface gravity data are used to validate future satellite gravity missions.

Uncertainties in atmospheric surface pressure fields from global analyses

Operational analyses from the U.S. National Centers for Environmental Prediction (NCEP) and the European Centre for Medium‐Range Weather Forecasts (ECMWF) provide, among other quantities, atmospheric surface pressure. This field is especially useful for data processing and interpretation of altimeter and gravity satellite missions like Jason‐1 and GRACE (Gravity Recovery and Climate Experiment). Quantitative use of this pressure field, however, requires knowledge of its uncertainties. To assess these uncertainties, we compare NCEP and ECMWF analyses of surface pressure to an extensive set of surface barometric observations for the period 2001–2005, both land‐ and ocean‐based, as well as to each other. Differences between each analysis and the observations are quite similar, indicating that both analyses generally fit the station observations equally well. Such differences, including both bias and variance about the bias, are largest over parts of the Southern Ocean, and over Asia, central Africa, and Antarctica. These bias and variance differences between the NCEP and ECMWF surface pressure fields change only slightly over the period of study. More importantly, though, such differences are substantially smaller than those found by previous studies for an earlier period (1993–1995), suggesting recent improvements in both analyses. The largest differences are found over high latitudes, particularly over Antarctica, and in the respective winter hemisphere. Much of the differences occur on rapid timescales, though with a significant portion at timescales longer than 1–2 months. The potential impact of such uncertainties on de‐aliasing and interpreting sea level and gravity data from altimeter and GRACE missions is discussed.