Geoid and Gravity in Earth Sciences – An Overview

Precise global geoid and gravity anomaly information serves essentially three different kinds of applications in Earth sciences: gravity and geoid anomalies reflect density anomalies in oceanic and continental lithosphere and the mantle; dynamic ocean topography as derived from the combination of satellite altimetry and a global geoid model can be directly transformed into a global map of ocean surface circulation; any redistribution or exchange of mass in Earth system results in temporal gravity and geoid changes. After completion of the dedicated gravity satellite missions GRACE and GOCE a high standard of global gravity determination, both of the static and of the time varying field will be attained. Thus, it is the right time to investigate the future needs for improvements in the various fields of Earth sciences and to define the right strategy for future gravity field satellite missions.     

Meltwater and the global ocean conveyor: northern versus southern connections

The sensitivity of the ocean circulation to changes in North Atlantic surface fluxes has become a major factor in explaining climate variability. The role of the Antarctic Bottom Water in modulating this variability has received much less attention, limiting the development of a complete understanding of decadal to millennial time-scale climate change. New analyses indicate that the southern deepwater source may change dramatically (e.g., experience a decrease of as much as two thirds during last 800 years). Such change can substantially alter the ocean circulation patterns of the last millennium. Additional analyses indicate that the Southern Hemisphere led the Northern Hemisphere changes in some of the glacial cycles of Pleistocene, implying a seesaw-type oscillation of the global ocean conveyor. The potential for melting of sea ice and ice sheets in the Antarctica associated with global warming can cause a further slowdown of the southern deepwater source. These results demand an assessment of the role of the Southern Ocean in driving changes of the global ocean circulation and climate. Systematic model simulation targeting the ocean circulation response to changes in surface salinity in the high latitudes of both Northern and Southern Hemispheres demonstrate that meltwater impacts in one hemisphere may lead to a strengthening of the thermohaline conveyor driven by the source in the opposite hemisphere. This, in turn, leads to significant changes in poleward heat transport. Further, meltwater events can lead to deep-sea warming and thermal expansion of abyssal water, that in turn cause a substantial sea-level change even without a major ice sheet melting.     

Shallow ocean overturning and the heat and carbon content of the Glacial Tropical Ocean

Mechanisms affecting the heat and carbon content of the Glacial Tropical Ocean (21,000 years BP) remain controversial. Exchange with the deep ocean via vertical mixing and the overturning circulation is one aspect that is clearly relevant to greenhouse gas concentrations and future climate change. We examined evidence of the possible role of the shallow overturning contribution on the Glacial Tropical Ocean temperature and carbonate ion concentration. Compared to the present, we find that the Glacial tropical upper ocean (0–1000 m) had enhanced vertical gradients in temperature and carbonate ion concentration, reduced turbulent diffusivity (vertical mixing rate) (by 20% or more), and weakened Ekman pumping in middle-latitudes, all consistent with reduced shallow overturning. The weakened property exchanges between the tropical upper ocean and the ocean below (cold with high total dissolved carbon-dioxide concentration) provide a unified explanation for both the unexpectedly-small sea surface cooling and the lower carbon-dioxide content in the Glacial tropical upper ocean and the atmosphere.     

Simulations of the impact of orbital forcing and ocean on the Asian summer monsoon during the Holocene

The importance of orbital forcing and ocean impact on the Asian summer monsoon in the Holocene is investigated by comparing simulations with a fully coupled ocean–atmosphere general circulation model (FOAM) and with the atmospheric component of this model (FSSTAM) forced with prescribed modern sea-surface temperatures (SSTs). The results show: (1) the ocean amplifies the orbitally-induced increase in African monsoon precipitation, makes somewhat increase in southern India and damps the increase over the southeastern China. (2) The ocean could change the spatial distribution and local intensity of the orbitally-induced latitudinal atmospheric oscillation over the southeastern China and the subtropical western Pacific Ocean. (3) The orbital forcing mostly enhances the Asian summer precipitation in the FOAM and FSSTAM simulations. However, the ocean reduces the orbitally-induced summer precipitation and postpones the time of summer monsoon onset over the Asian monsoon region. (4) The orbital forcing considerably enhances the intensity of upper divergence, which is amplified by ocean further, over the eastern hemisphere. But the divergence is weaker in the FOAM simulations than in the FSSTAM simulations when the orbital forcing is fixed. (5) The orbital forcing can enhance the amplitude of precipitation variability over the subtropical Africa, the southeastern China and northwestern China, inversely, reduce it over central India and North China in the FOAM and FSSTAM simulations. The ocean obviously reduces the amplitude of precipitation variability over most of the Asian monsoon regions in the fixed orbital forcing simulations. (6) The areas characterized by increased summer precipitation in the long-term mean are mostly characterized by increased amplitude of short-term variability, whereas regions characterized by decreased precipitation are primarily characterized by decreased amplitude of short-term variability. However, the influences of orbital forcing or dynamical ocean on regional climate depend on the model.     

Ice Mass Balance and Ice Dynamics from Satellite Gravity Missions

An overview of advances in ice research which can be expected from future satellite gravity missions is given. We compare present and expected future accuracies of the ice mass balance of Antarctica which might be constrained to 0.1–0.3 mm/year of sea level equivalent by satellite gravity data. A key issue for the understanding of ice mass balance is the separation of secular and interannual variations. For this aim, one would strongly benefit from longer uninterrupted time series of gravity field variations (10 years or more). An accuracy of 0.01 mm/year for geoid time variability with a spatial resolution of 100 km would improve the separability of ice mass balance from mass change due to glacial isostatic adjustment and enable the determination of regional variations in ice mass balance within the ice sheets. Thereby the determination of ice compaction is critical for the exploitation of such high accuracy data. A further benefit of improved gravity field models from future satellite missions would be the improvement of the height reference in the polar areas, which is important for the study of coastal ice processes. Sea ice thickness determination and modelling of ice bottom topography could be improved as well.     

Marine‐target craters on Mars? An assessment study

Abstract— Observations of impact craters on Earth show that a water column at the target strongly influences lithology and morphology of the resultant crater. The degree of influence varies with the target water depth and impactor diameter. Morphological features detectable in satellite imagery include a concentric shape with an inner crater inset within a shallower outer crater, which is cut by gullies excavated by the resurge of water. In this study, we show that if oceans, large seas, and lakes existed on Mars for periods of time, marine‐target craters must have formed. We make an assessment of the minimum and maximum amounts of such craters based on published data on water depths, extent, and duration of putative oceans within “contacts 1 and 2,” cratering rate during the different oceanic phases, and computer modeling of minimum impactor diameters required to form long‐lasting craters in the seafloor of the oceans. We also discuss the influence of erosion and sedimentation on the preservation and exposure of the craters. For an ocean within the smaller “contact 2” with a duration of 100,000 yr and the low present crater formation rate, only ?1–2 detectable marine‐target craters would have formed. In a maximum estimate with a duration of 0.8 Gyr, as many as 1400 craters may have formed. An ocean within the larger “contact 1‐Meridiani,” with a duration of 100,000 yr, would not have received any seafloor craters despite the higher crater formation rate estimated before 3.5 Gyr. On the other hand, with a maximum duration of 0.8 Gyr, about 160 seafloor craters may have formed. However, terrestrial examples show that most marine‐target craters may be covered by thick sediments. Ground penetrating radar surveys planned for the ESA Mars Express and NASA 2005 missions may reveal buried craters, though it is uncertain if the resolution will allow the detection of diagnostic features of marine‐target craters. The implications regarding the discovery of marine‐target craters on Mars is not without significance, as such discoveries would help address the ongoing debate of whether large water bodies occupied the northern plains of Mars and would help constrain future paleoclimatic reconstructions.     

Effects of anthropogenic intervention in the land hydrologic cycle on global sea level rise

Recent studies suggest that anthropogenic modification of land hydrology (e.g. through groundwater mining, dam building, irrigation, deforestation, wetlands drainage, and urbanization) could significantly impact sea-level rise, although the magnitude and sign of this effect have been widely debated. This paper attempts a comprehensive overview of the effects of human activities on land hydrology. Estimates are provided for the volumes of water associated with each of the major anthropogenic processes and the corresponding equivalent in sea level.Groundwater mining; and runoff from paved and built-up areas are two major sources of water added to the ocean. In contrast, storage of water behind dams, losses through percolation, and evapotranspiration from irrigated fields withhold water that would otherwise flow to the sea. The net effect of these processes holds back the equivalent of 0.8 +- 0.4 mm/yr from sea-level rise. This is a magnitude comparable to, but in the opposite direction from the currently observed sea-level rise of 1–2 mm/yr. These estimates are still preliminary, awaiting better documentation. Coupling of improved land hydrology models with GCMs will help in analysis of feedbacks, especially the partitioning of water among runoff, infiltration, and evaporation.     

Constraints on interpretation of the Eltanin impact from numerical simulations

The results of numerical simulations of the Eltanin impact are combined with the available geological data in order to reconstruct the impact dynamics and to get some constraints on the impact parameters. Numerical simulations show that the Eltanin projectile size should be less than 2 km for a 45° oblique impact and less than 1.5 km for a vertical impact. On the other hand, we demonstrate that the projectile diameter cannot be considerably smaller than 1 km; otherwise, the impact‐induced water flow cannot transport eroded sediments across large distances. The maximum displacement approximately equals the water crater radius and rapidly decreases with increasing distances. Numerical simulations also show that ejecta deposits strongly depend on impact angle and projectile size and, therefore, cannot be used for reliable estimates of the initial projectile mass. The initial amplitudes of tsunami‐like waves are estimated. The presence of clay‐rich sediments, typical for the abyssal basins in cores PS2709 and PS2708 on the Freeden Seamounts (Bellingshausen Sea, Southern Ocean) combined with numerical data allow us to suggest a probable point of impact to the east of the seamounts. The results do not exclude the possibility that a crater in the ocean bottom may exist, but such a structure has not been found yet.     

Efficient Determination of Global Gravity Field from Satellite-to-satellite Tracking Mission

The gravity field dedicated satellite missions like CHAMP, GRACE, and GOCE are supposed to map the Earth's global gravity field with unprecedented accuracy and resolution. New models of the Earth's static and time-variable gravity fields will be available every month as one of the science products from GRACE. A method for the efficient gravity field recovery is presented using in situ satellite-to-satellite observations at altitude and results on static as well as temporal gravity field recovery are shown. Considering the energy relationship between the kinetic energy of the satellite and the gravitational potential, the disturbing potential observations can be computed from the orbital state vector, using high-low GPS tracking data, low–low satellite-to-satellite GRACE measurements, and data from 3-axis accelerometers. The solution method is based on the conjugate gradient iterative approach to efficiently recover the gravity field coefficients and approximate error covariance up to degree and order 120 every month. Based on the monthly GRACE noise-only simulation, the geoid was obtained with an accuracy of a few cm and with a resolution (half wavelength) of 160 km. However, the geoid accuracy can become worse by a factor of 6–7 because of spatial aliasing. The approximate error covariance was found to be a very good accuracy measure of the estimated coefficients, geoid, and gravity anomaly. The temporal gravity field, representing the monthly mean continental water mass redistribution, was recovered in the presence of measurement noise and high frequency temporal variation. The resulting recovered temporal gravity fields have about 0.3 mm errors in terms of geoid height with a resolution of 670 km.     

Settling of metal droplets in a terrestrial magma ocean: On the correction of the Stokes velocity

The formation of magma oceans on at least the major terrestrial planets is widely assumed even if the full accretion history and early evolution of terrestrial planets is discussed rather controversial. Various processes occur within these magma oceans, among them the settling of small iron drops and their chemical equilibration with the silicate environment. Different models were proposed to explain the differentiation within a magma ocean. In order to model a magma ocean and give constraints about settling time of iron droplets, a constant velocity is used in most models, which is calculated using Stokes’ famous formula. According to the other model parameters this assumption is invalid, since Stokes’ assumption of a creeping flow is violated. However, former models investigated the behaviour of a large number of droplets, which makes it is impossible to solve the flow around each single iron drop. We introduce a model, in which the flow around iron drops in a molten silicate environment is computed using the appropriate hydrodynamic equations. We investigate the terminal velocity of a single drop descending through a magma ocean and additionally study the effects of the presence of other obstacles in the neighbourhood. We determine a new mean velocity, which may serve as an input parameter for the existent models of magma oceans. Although we used a full fluid-dynamical approach, the velocity computed with our model is not very different from the simple Stokes case and thus proves that the former assumptions were legitimate and can be used in future as well as the new velocity presented here.     

大气、陆地水储量和海水质量分布变化与地球低阶引力场球谐系数的关系

大气、固体地球及海洋组成了一个复杂、变化的地球动力学系统，这一系统中的任一质量分布变化都将产生地球引力场变化。采用全球7000多个地面气象台站的月平均降水及温度资料、NCEP提供气压月均值、TOPEX／Poseidon卫星测高资料和WOA98海水温度及盐度模型计算了大气、陆地水储量和海水质量分布变化引起地球低阶引力场系数变化。比较综合大气、陆地水储量和海水质量分布变化对带谐项J2，J3，J4影响的计算结果和人卫激光卫星的测定结果，可以看出，大气、陆地水储量和海水质量分布变化是引起地球低阶引力场系数周年变化的重要激发源。     

中国地壳运动网络的海潮位移改正

采用CSR4．0全球海潮模型，顾及中国近海海潮图，计算了海潮中8个主要潮波（M2,N2,S2,K2,O1,P1,Q1,K1波）引起的中国地壳运动观测网中测站的海潮位移改正，文中也讨论了海潮模型和格林函数对海潮位移改正的影响，作为实例，把海潮影响加入GAMIT软件，用实测GPS数据检核出海潮对GPS基线向量的影响，结果显示了海洋负荷潮引起测站位移和GPS基线向量改变的最大值大约分别为2厘米和2毫米。     

Enceladus: A hypothesis for bringing both heat and chemicals to the surface

The eruptive plumes and large heat flow (～15 GW) observed by Cassini in the South Polar Region of Enceladus may be expressions of hydrothermal activity inside Enceladus. We hypothesize that a subsurface ocean is the heat reservoir for thermal anomalies on the surface and the source of heat and chemicals necessary for the plumes. The ocean is believed to contain dissolved gases, mostly CO₂ and is found to be relatively warm (～0 °C). Regular tidal forces open cracks in the icy crust above the ocean. Ocean water fills these fissures. There, the conditions are met for the upward movement of water and the dissolved gases to exsolve and form bubbles, lowering the bulk density of the water column and making the pressure at its bottom less than that at the top of the ocean. This pressure difference drives ocean water into and up the conduits toward the surface. This transportation mechanism supports the thermal anomalies and delivers heat and chemicals to the chambers from which the plumes erupt. Water enters these chambers and there its bubbles pop and loft an aerosol mist into the ullage. The exiting plume gas entrains some of these small droplets. Thus, nonvolatile chemical species in ocean water can be present in the plume particles. A CO₂ equivalent-gas molar fraction of ～4 × 10^?4 for the ocean is sufficient to support the circulation. A source of heat is needed to keep the ocean warm at ～0 °C (about two degrees above its freezing point). The source of heat is unknown, but our hypothesis is not dependent on any particular mechanism for producing the heat.     

Liquid water oceans in ice giants

Aptly named, ice giants such as Uranus and Neptune contain significant amounts of water. While this water cannot be present near the cloud tops, it must be abundant in the deep interior. We investigate the likelihood of a liquid water ocean existing in the hydrogen-rich region between the cloud tops and deep interior. Starting from an assumed temperature at a given upper tropospheric pressure (the photosphere), we follow a moist adiabat downward. The mixing ratio of water to hydrogen in the gas phase is small in the photosphere and increases with depth. The mixing ratio in the condensed phase is near unity in the photosphere and decreases with depth; this gives two possible outcomes. If at some pressure level the mixing ratio of water in the gas phase is equal to that in the deep interior, then that level is the cloud base. The gas below the cloud base has constant mixing ratio. Alternately, if the mixing ratio of water in the condensed phase reaches that in the deep interior, then the surface of a liquid ocean will occur. Below this ocean surface, the mixing ratio of water will be constant. A cloud base occurs when the photospheric temperature is high. For a family of ice giants with different photospheric temperatures, the cooler ice giants will have warmer cloud bases. For an ice giant with a cool enough photospheric temperature, the cloud base will exist at the critical temperature. For still cooler ice giants, ocean surfaces will result. A high mixing ratio of water in the deep interior favors a liquid ocean. We find that Neptune is both too warm (photospheric temperature too high) and too dry (mixing ratio of water in the deep interior too low) for liquid oceans to exist at present. To have a liquid ocean, Neptune's deep interior water to gas ratio would have to be higher than current models allow, and the density at 19 kbar would have to be ≈0.8 g/cm³. Such a high density is inconsistent with gravitational data obtained during the Voyager flyby. In our model, Neptune's water cloud base occurs around 660 K and 11 kbar, and the density there is consistent with Voyager gravitational data. As Neptune cools, the probability of a liquid ocean increases. Extrasolar “hot Neptunes,” which presumably migrate inward toward their parent stars, cannot harbor liquid water oceans unless they have lost almost all of the hydrogen and helium from their deep interiors.     

Analysis of 208 U.S. Navy orbits for the satellite 1970-47B at 14th-order resonance

The orbit of 1970-47B passed very slowly through 14th-order resonance, and the changes in orbital inclination and eccentricity have been analysed over a 4-year period, from January 1977 to January 1981, using 208 U.S. Navy orbits. The analysis has yielded values for three pairs of lumped harmonic coefficients of 14th order, which have accuracies equivalent to 0.4, 1.5 and 2.0 cm in geoid height. Three pairs of values of 28th-order lumped harmonic coefficients were also obtained, and the best of these has a standard deviation (S.D.) corresponding to an accuracy of 0.7 cm in geoid height. The lumped harmonic coefficients have been compared with the corresponding values from the latest geopotential models, and agreement is satisfactory.     

Sea level budget over 2003–2008: A reevaluation from GRACE space gravimetry,satellite altimetry and Argo

From the IPCC 4th Assessment Report published in 2007, ocean thermal expansion contributed by ～ 50% to the 3.1 mm/yr observed global mean sea level rise during the 1993–2003 decade, the remaining rate of rise being essentially explained by shrinking of land ice. Recently published results suggest that since about 2003, ocean thermal expansion change, based on the newly deployed Argo system, is showing a plateau while sea level is still rising, although at a reduced rate (～ 2.5 mm/yr). Using space gravimetry observations from GRACE, we show that recent years sea level rise can be mostly explained by an increase of the mass of the oceans. Estimating GRACE-based ice sheet mass balance and using published estimates for glaciers melting, we further show that ocean mass increase since 2003 results by about half from an enhanced contribution of the polar ice sheets – compared to the previous decade – and half from mountain glaciers melting. Taking also into account the small GRACE-based contribution from continental waters (< 0.2 mm/yr), we find a total ocean mass contribution of ～ 2 mm/yr over 2003–2008. Such a value represents ～ 80% of the altimetry-based rate of sea level rise over that period. We next estimate the steric sea level (i.e., ocean thermal expansion plus salinity effects) contribution from: (1) the difference between altimetry-based sea level and ocean mass change and (2) Argo data. Inferred steric sea level rate from (1) (～ 0.3 mm/yr over 2003–2008) agrees well with the Argo-based value also estimated here (0.37 mm/yr over 2004–2008). Furthermore, the sea level budget approach presented in this study allows us to constrain independent estimates of the Glacial Isostatic Adjustment (GIA) correction applied to GRACE-based ocean and ice sheet mass changes, as well as of glaciers melting. Values for the GIA correction and glacier contribution needed to close the sea level budget and explain GRACE-based mass estimates over the recent years agree well with totally independent determinations.     

The effect of gravitational and pressure torques on Titan's length-of-day variations

Cassini radar observations show that Titan's spin is slightly faster than synchronous spin. Angular momentum exchange between Titan's surface and the atmosphere over seasonal time scales corresponding to Saturn's orbital period of 29.5 year is the most likely cause of the observed non-synchronous rotation. We study the effect of Saturn's gravitational torque and torques between internal layers on the length-of-day (LOD) variations driven by the atmosphere. Because static tides deform Titan into an ellipsoid with the long axis approximately in the direction to Saturn, non-zero gravitational and pressure torques exist that can change the rotation rate of Titan. For the torque calculation, we estimate the flattening of Titan and its interior layers under the assumption of hydrostatic equilibrium. The gravitational forcing by Saturn, due to misalignment of the long axis of Titan with the line joining the mass centers of Titan and Saturn, reduces the LOD variations with respect to those for a spherical Titan by an order of magnitude. Internal gravitational and pressure coupling between the ice shell and the interior beneath a putative ocean tends to reduce any differential rotation between shell and interior and reduces further the LOD variations by a few times. For the current estimate of the atmospheric torque, we obtain LOD variations of a hydrostatic Titan that are more than 100 times smaller than the observations indicate when Titan has no ocean as well as when a subsurface ocean exists. Moreover, Saturn's torque causes the rotation to be slower than synchronous in contrast to the Cassini observations. The calculated LOD variations could be increased if the atmospheric torque is larger than predicted and or if fast viscous relaxation of the ice shell could reduce the gravitational coupling, but it remains to be studied if a two order of magnitude increase is possible and if these effects can explain the phase difference of the predicted rotation variations. Alternatively, the large differences with the observations may suggest that non-hydrostatic effects in Titan are important. In particular, we show that the amplitude and phase of the calculated rotation variations are similar to the observed values if non-hydrostatic effects could strongly reduce the equatorial flattening of the ice shell above an internal ocean.     

Multi-frequency electromagnetic sounding of the Galilean moons

Induced magnetic fields provide the unique possibility to sound the conductive interior of planetary bodies. Such fields are caused by external time-variable magnetic fields. We investigate temporal variations of the jovian magnetospheric field at multiple frequencies at the positions of the Galilean moons and analyze possible responses due to electromagnetic induction within multi-layered interior models of all four satellites. At the jovian satellites the magnetic field varies with the synodic rotation period of Jupiter’s internal field (about 10 h), fractions of this period (e.g., 1/2 and 1/3) due to higher order harmonics of the internal field, the orbital periods of the satellites (∼40 h at Io to ∼400 h at Callisto) and the solar rotation period (about 640 h) and its harmonics due to variabilities of the magnetopause field. To analyze these field variations, we use a magnetospheric model that includes the jovian internal field, the current sheet field and fields due to the magnetopause boundary currents. With this model we calculate magnetic amplitude spectra for each satellite orbit. These spectra provide the strengths of the inducing signals at the different frequencies for all magnetic components. The magnetic fields induced in the interiors of the satellites are then determined from response functions computed for different multi-layer interior models including conductive cores and ocean layers of various conductivities and thicknesses. Based on these results we discuss what information about the ocean and core layers can be deduced from the analysis of induction signals at multiple frequencies. Even moderately thick and conductive oceans produce measurable signal strengths at several frequencies for all satellites. The conductive cores cause signals which will be hardly detectable. Our results show that mutual induction occurs between the core and the ocean. We briefly address this effect and its implications for the analysis of induced field data. We further note that close polar orbits are preferable for future Jupiter system missions to investigate the satellites interiors.     

用球函数方法计算东亚测站的综合海潮负荷参数(英)

用球谐函数方法（SHM）计算了由Schwiderski海潮图和日本海海潮图引起的M2,S2,K1和O1各分潮波的综合海潮负荷参数.计算中采用了Pagiatakis（1990）地球模型的负荷Love数.结果表明SHM具有更高的计算效率和计算精度．为了真正实现±毫米的VLBI地壳运动测定精度和±0.1微伽的绝对重力测量精度,对未来海潮图模型,特别是日本海的海潮图模型的精度要求作了讨论．计算结果还表明不同地球模型的负荷Love数对计算的测站位移之差为0.7毫米,在目前测量精度下尚可以不作考虑.中国近海的海潮M2波对台北,上海,Daejeon,Okinawa,和Kagosima站的径向和水平分量位移影响可分别达±22．4～±1．0毫米和±05-±5.5毫米,表明中国近海高精度的海潮图模型对东亚测站的地壳运动高精度测量是十分重要的．     

The accuracy of geopotential models

Extensive tests of two recent geopotential models (GEM 7 and 8) have been made with observations not used in the solutions. Several other recent models are also evaluated. These tests show the accuracy of the satellite derived model (GEM 7, with 400 coefficients) to be about 4.3 m (r.m.s.) with respect to the global geoid surface. The corresponding accuracy of the combined satellite and surface gravimetry model (GEM 8, with 706 coefficients) is found to be 3.9m (r.m.s.). These results include a calibration for the commission errors of the coefficients in the models and an estimate of the errors from omitted coefficients. For GEM 7, the formal precision (commission errors) of the solution gives 0.7 m for the geoid error which after calibration increases to 2.4 m.

Independent observations used in this assessment include: 159 lumped coefficients from 35 resonant orbits of 1 and 9 through 15 revolutions per day, two sets of (8, 8) fields derived from optical-only and laser-only data, sets of zonal and resonant coefficients derived from largely independent sources and geoid undulations measured by satellite altimetry. In addition, the accuracy of GEM 7 has been judged by the gravimetry in GEM 8. The ratio of estimated commission to formal error in GEM 7 and 8 ranges from 2 to 5 in these tests.