Measuring the Distribution of Ocean Mass Using GRACE

The Gravity Recovery and Climate Experiment (GRACE), which was successfully launched March 17, 2002, has the potential to create a new paradigm in satellite oceanography with an impact perhaps as large as was observed with the arrival of precision satellite altimetry via TOPEX/Poseidon (T/P) in 1992. The simulations presented here suggest that GRACE will be able to monitor non-secular changes in ocean mass on a global basis with a spatial resolution of ≈500 km and an accuracy of ≈3 mm water equivalent. It should be possible to recover global mean ocean mass variations to an accuracy of ≈1 mm, possibly much better if the atmospheric pressure modeling errors can be reduced. We have not considered the possibly significant errors that may arise due to temporal aliasing and secular gravity variations. Secular signals from glacial isostatic adjustment and the melting of polar ice mass are expected to be quite large, and will complicate the recovery of secular ocean mass variations. Nevertheless, GRACE will provide unprecedented insight into the mass components of sea level change, especially when combined with coincident satellite altimeter measurements. Progress on these issues would provide new insight into the response of sea level to climate change. This revised version was published online in August 2006 with corrections to the Cover Date.     

What Might GRACE Contribute to Studies of Post Glacial Rebound?

The NASA/DLR satellite gravity mission GRACE, launched in March, 2002, will map the Earth's gravity field at scales of a few hundred km and greater, every 30 days for five years. These data can be used to solve for time-variations in the gravity field with unprecedented accuracy and resolution. One of the many scientific problems that can be addressed with these time-variable gravity estimates, is post glacial rebound (PGR): the viscous adjustment of the solid Earth in response to the deglaciation of the Earth's surface following the last ice age. In this paper we examine the expected sensitivity of the GRACE measurements to the PGR signal, and explore the accuracy with which the PGR signal can be separated from other secular gravity signals. We do this by constructing synthetic GRACE data that include contributions from a PGR model as well as from a number of other geophysical processes, and then looking to see how well the PGR model can be recovered from those synthetic data. We conclude that the availability of GRACE data should result in improved estimates of the Earth's viscosity profile. This revised version was published online in August 2006 with corrections to the Cover Date.     

Error Characteristics Estimated from Champ,GRACE and GOCE Derived Geoids and from Satellite Altimetry Derived Mean Dynamic Topography

This paper presents a review of geoid error characteristics of three satellite gravity missions in view of the general problem of separating scientifically interesting signals from various noise sources. The problem is reviewed from the point of view of two proposed applications of gravity missions, one is the observation of the mean oceanic circulation whereby an improved geoid model is used as a reference surface against the long term mean sea level observed by altimetry. In this case we consider the presence of mesoscale variability during assimilation of derived surface currents in inverse models. The other experiment deals with temporal changes in the gravity field observed by GRACE in which case a proposed experiment is to monitor changes in the geoid in order to detect geophysical interesting signals such as variations in the continental hydrology and non-steric ocean processes. For this experiment we will address the problem of geophysical signal contamination and the way it potentially affects monthly geoid solutions of GRACE. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ocean Tides in GRACE Monthly Averaged Gravity Fields

The GRACE mission will map the Earth's gravity fields and its variations with unprecedented accuracy during its 5-year lifetime. Unless ocean tide signals and their load upon the solid earth are removed from the GRACE data, their long period aliases obscure more subtle climate signals which GRACE aims at. In this analysis the results of Knudsen and Andersen (2002) have been verified using actual post-launch orbit parameter of the GRACE mission. The current ocean tide models are not accurate enough to correct GRACE data at harmonic degrees lower than 47. The accumulated tidal errors may affect the GRACE data up to harmonic degree 60. A study of the revised alias frequencies confirm that the ocean tide errors will not cancel in the GRACE monthly averaged temporal gravity fields. The S₂ and the K₂ terms have alias frequencies much longer than 30 days, so they remain almost unreduced in the monthly averages. Those results have been verified using a simulated 30 days GRACE orbit. The results show that the magnitudes of the monthly averaged values are slightly higher than the previous values. This may be caused by insufficient sampling to fully resolve and reduce the tidal signals at short wavelengths and close to the poles. This revised version was published online in August 2006 with corrections to the Cover Date.     

V: SEA LEVEL: Benefits of GRACE and GOCE to sea level studies

The recently published Third Assessment Reports of the Intergovernmental Panel on Climate Change have underlined the scientific interest in, and practical importance of past and potential future sea level changes. Space gravity missions will provide major benefits to the understanding of the past, and, thereby, in the prediction of future, sea level changes in many ways. The proposal for the GOCE mission described well the improvements to be expected from improved gravity field and geoid models in oceanography (for example, in the measurement of the time-averaged, or ‘steady state’, ocean surface circulation and better estimation of ocean transports), in geophysics (in the improvement of geodynamic models for vertical land movements), in geodesy (in positioning of tide gauge data into the same reference frame as altimeter data, and in improvement of altimeter satellite orbits), and possibly in glaciology (in improved knowledge of bedrock topography and ice sheet mass fluxes). GRACE will make many important steps towards these ‘steady state’ aims. However, its main purpose is the provision of oceanographic (and hydrological and meteorological) temporally-varying gravity information, and should in effect function as a global ‘bottom pressure recorder’, providing further insight into the 3-D temporal variation of the ocean circulation, and of the global water budget in general. This paper summaries several of these issues, pointing the way towards improved accuracy of prediction of future sea level change. This revised version was published online in August 2006 with corrections to the Cover Date.     

Resolution Needed for an Adequate Determination of the Mean Ocean Circulation from Altimetry and an Improved Geoid

The sea surface topography observed by satellite altimetry is a combination of the geoid and of the ocean dynamic topography. Satellite altimetry has thus the potential to supply quasi-global maps of mean sea surface heights from which the mean geostrophic surface ocean currents can be derived, provided that the geoid is known with a sufficient absolute accuracy. At present, however, given the limited accuracy of the best available geoid, altimetric mean sea surface topographies have been derived only up to degree 15 or so, i.e. for wavelengths of approximately 2000 km and larger. CHAMP, GRACE, and the future GOCE missions are dedicated to the improvement of the Earth's gravity field from space. Several studies have recently investigated the impact of these improvements for oceanography, concluding to reductions of uncertainties on the oceanic flux estimates as large as a factor of 2 in the regions of intense an narrow currents. The aim of this paper is to focus on what are the typical horizontal scales of the mean dynamic topography of the ocean, and to compare their characteristics to the error estimates expected from altimetry and these future geoids. It gives also an illustration of the oceanic features that will be resolved by the combination of altimetry and the GRACE and GOCE geoids. It further reassesses the very demanding requirements in term of accuracy and resolution agreed in the design of these new gravity missions for ocean science applications. The present study relies on recent very high-resolution numerical Ocean General Circulation Model simulations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Feasibility,and Contribution to Ocean Circulation Studies,of Ocean Bottom Pressure Determination

An assessment is presented of the probable magnitude of ocean signals causing aliasing in ocean bottom pressure measurements from the GRACE satellite mission. Even after modelling as much of the high frequency signal as possible, variability between 1 mbar (in quiet ocean regions) and 10 mbar (on some shelves) is likely to remain. Interpretation of the resulting retrievals will therefore rely on the facts that the satellite sampling will average the aliasing signal to some extent, and that the spatial patterns of aliased signal and true signal will be different. To this end, a theoretical argument is given, and supported by model diagnostics, suggesting that observable bottom pressure signals will be strongly constrained by the shape of the ocean floor. The modelled magnitudes offer the prospect of significant detectable signals and, while the model accuracy can be called into question, there are hints from Earth rotation and satellite orbit measurements that significant mass redistributions occur in the ocean. It seems certain that we will learn something new about the oceans from GRACE. This revised version was published online in August 2006 with corrections to the Cover Date.     

冰雪条件下机场跑道摩擦系数建模与仿真研究

机场跑道摩擦系数是评价机场跑道道面质量的重要参数。在考虑冬季跑道道面压实雪厚度和摩擦热形成的润滑水膜作用下建立了冰雪道面半融状态摩擦系数计算模型。使用Matlab数值仿真软件对所建模型进行了仿真。数值仿真结果表明,摩擦系数模型建模合理,摩擦系数计算数据与实测数据比较吻合。对摩擦系数的测试实践有一定的理论指导意义。     

How Well Do Experimental Results on Large Samples of Gas-Laden Amorphous Ice Duplicate Deep Impact’s Findings?

The findings of Deep Impact on the structure and composition of Tempel-1 are compared with our experimental results on large (20 cm diameter and up to 10 cm high) samples of gas-laden amorphous ice which does not contain dust. The mechanical ～tensile strength inferred for Tempel-1: up to 12 kPa is close to our experimental findings of 2–4 kPa. This means that Tempel-1 is as fluffy as our very fluffy, talcum like, ice sample. The thermal inertia: 30<I<100 W?K^?1?m^?2?s^1/2 is close to our value of 80. The density of 350±250 kg?m^?3, is close to our value of 250–300 kg?m^?3, taking into account an ice/silicate ratio of 1 in the comet, while we study pure ice. Surface morphological features, such as non-circular depressions and chaotic terrain, were observed in our experiments. The only small increase in the gas/water vapor ratio pre- and post-impact, suggest that in the area excavated by the impactor, the 135 K front did not penetrate deeper than a few meters. Altogether, the agreement between the findings of Deep Impact and our experimental results point to a loose agglomerate of ice grains (with a silicate-organic core), which was formed by a very gentle aggregation of the ice grains, without compaction.     

The chemical profiles of polar ice on Earth and Mars: What we read from the first; what we could read from the second

An analogy is drawn between the current knowledge on terrestrial snow and ice-cap chemistry and the possible composition of snowfall and ice caps of Mars. Terrestrial snowfall reflects the composition of the Earth's atmosphere. Snow cover further interacts with the atmosphere and is the recipient of aerosol and particulate fall-out. The snow is transformed to firn and ice and the chemical signatures become locked into the perennial ice sheets. The chemical profiles of ice thus constitute environmental records of the Earth's past. By considering the present knowledge on the hydrologie cycle of Mars and the chemistry of the atmosphere, a simple analogous model for the chemical profile of the North polar ice cap is proposed. Three major constituents of the ice are discussed: water ice, dust, and occluded air bubbles. The seasonal fluctuations and interannual variability of these components are examined as possible chemical signatures for the dating of ice, elucidating hydrologie processes, and recording long-term climatic change. The model of the north polar cap in summer consists of water-ice fine-dust layers (30–200 m thick) sandwiched between annual dust layers of variable size distribution and thickness (< 1m– > 66 m). The water ice is subjected to metamorphism and grain growth. The interpretation of the physico-chemical profile could lead to increased knowledge on the recent climatic past (1,000–2,000 years), hydrologic reservoirs, and seasonal cycles in the atmospheric dynamics of the planet.     

迎风面三维积冰过程中水膜流动的计算方法

对影响迎风面三维积冰过程的冰层表面水膜流动进行分析,建立描述其流动的数学模型,引入在流动前锋下游预设薄水膜的方法处理其在表面干区的流动推进过程,提出超过临界厚度的水膜被吹除的方法处理角状冰下游局部水膜被吹离表面的现象.通过对翼型-平板结构中翼型上的冰形对比和水膜流动规律分析,验证了该水膜流动数学模型的合理性和计算方法的可行性.研究表明:与Messinger模型相比,积冰模型中引入水膜流动后,可以较好地模拟三维明冰积冰,同时明冰极限的模拟结果也更接近试验值;冰层表面的水膜厚度约为10-5m,流动速度约为10-2m/s.      

Long Term Climate Records from Polar Ice

One of the great challenges in climate research is to investigate the principal mechanisms that control global climatic changes and an effective way to learn more about it, is the reconstruction of past climate changes. The most important sources of information about such changes and the associated composition of the atmosphere are the two large ice caps of Greenland and Antarctica. Analysis of ice cores is the most powerful means we have to determine how climate has changed over the last few climatic cycles, and to relate this to changes in atmospheric composition, in particular to concentrations of the principal greenhouse gases – CO₂, CH₄ and N₂O (carbon dioxide, methane, and nitrous oxide).Transitions from cold ice age climates to warmer interstadials have always been accompanied by an increase of the atmospheric concentration of the three principal greenhouse gases. This increase has been, at least for CO₂, vital for the ending of glacial epochs. A highly simplified course of events for the past four transitions would then be as follows: first, changing orbital parameters initiated the end of the glacial epoch; second, an increase in greenhouse gases then amplified the weak orbital signal; third, in the second half of the transition, warming was further amplified by decreasing albedo, caused by melting of the large ice sheets in the Northern Hemisphere going parallel with a change of the ocean circulation.The isotopic records of Greenland ice cores show evidence for fast and drastic climatic changes during the last glacial epoch. Possible causes and mechanisms of such changes and their significance as global climatic events are discussed here. Ice core results also enable the reaction of the environment to past global changes to be investigated.It will also be discussed how reliable stable isotope records are as a local temperature proxy and how representative paleoclimatic results from Greenland and Antarctica are in relation to global climate.     

Origin of Comet Nuclei and Dynamics

We present a review of the main physical features of comet nuclei, their birthplaces and the dynamical processes that allow some of them to reach the Sun’s neighborhood and become potentially detectable. Comets are thought to be the most primitive bodies of the solar system although some processing—for instance, melting water ice in their interiors and collisional fragmentation and reaccumulation—could have occurred after formation to alter their primordial nature. Their estimated low densities (a few tenths g?cm^?3) point to a very fluffy, porous structure, while their composition rich in water ice and other highly volatile ices point to a formation in the region of the Jovian planets, or the trans-neptunian region. The main reservoir of long-period comets is the Oort cloud, whose visible radius is ～3.3×10⁴ AU. Yet, the existence of a dense inner core cannot be ruled out, a possibility that would have been greatly favored if the solar system formed in a dense galactic environment. The trans-neptunian object Sedna might be the first discovered member that belongs to such a core. The trans-neptunian population is the main source of Jupiter family comets, and may be responsible for a large renovation of the Oort cloud population.     

Present-Day Sea Level Change: Observations and Causes

We investigate climate-related processes causing variations of the global mean sea level on interannual to decadal time scale. We focus on thermal expansion of the oceans and continental water mass balance. We show that during the 1990s where global mean sea level change has been measured by Topex/Poseidon satellite altimetry, thermal expansion is the dominant contribution to the observed 2.5 mm/yr sea level rise. For the past decades, exchange of water between continental reservoirs and oceans had a small, but not totally negligible contribution (about 0.2 mm/yr) to sea level rise. For the last four decades, thermal contribution is estimated to about 0.5 mm/yr, with a possible accelerated rate of thermosteric rise during the 1990s. Topex/Poseidon shows an increase in mean sea level of 2.5 mm/yr over the last decade, a value about two times larger than reported by historical tide gauges. This would suggest that there has been significant acceleration of sea level rise in the recent past, possibly related to ocean warming. This revised version was published online in August 2006 with corrections to the Cover Date.     

Core Formation and Mantle Differentiation on Mars

Geochemical investigation of Martian meteorites (SNC meteorites) yields important constraints on the chemical and geodynamical evolution of Mars. These samples may not be representative of the whole of Mars; however, they provide constraints on the early differentiation processes on Mars. The bulk composition of Martian samples implies the presence of a metallic core that formed concurrently as the planet accreted. The strong depletion of highly siderophile elements in the Martian mantle is only possible if Mars had a large scale magma ocean early in its history allowing efficient separation of a metallic melt from molten silicate. The solidification of the magma ocean created chemical heterogeneities whose ancient origin is manifested in the heterogeneous ¹⁴²Nd and ¹⁸²W abundances observed in different meteorite groups derived from Mars. The isotope anomalies measured in SNC meteorites imply major chemical fractionation within the Martian mantle during the life time of the short-lived isotopes ¹⁴⁶Sm and ¹⁸²Hf. The Hf-W data are consistent with very rapid accretion of Mars within a few million years or, alternatively, a more protracted accretion history involving several large impacts and incomplete metal-silicate equilibration during core formation. In contrast to Earth early-formed chemical heterogeneities are still preserved on Mars, albeit slightly modified by mixing processes. The preservation of such ancient chemical differences is only possible if Mars did not undergo efficient whole mantle convection or vigorous plate tectonic style processes after the first few tens of millions of years of its history.     

The Lunar Gravity Ranging System for the Gravity Recovery and Interior Laboratory (GRAIL) Mission

The Lunar Gravity Ranging System (LGRS) flying on NASA’s Gravity Recovery and Interior Laboratory (GRAIL) mission measures fluctuations in the separation between the two GRAIL orbiters with sensitivity below 0.6 microns/Hz^1/2. GRAIL adapts the mission design and instrumentation from the Gravity Recovery and Climate Experiment (GRACE) to a make a precise gravitational map of Earth’s Moon. Phase measurements of Ka-band carrier signals transmitted between spacecraft with line-of-sight separations between 50 km to 225 km provide the primary observable. Measurements of time offsets between the orbiters, frequency calibrations, and precise orbit determination provided by the Global Positioning System on GRACE are replaced by an S-band time-transfer cross link and Deep Space Network Doppler tracking of an X-band radioscience beacon and the spacecraft telecommunications link. Lack of an atmosphere at the Moon allows use of a single-frequency link and elimination of the accelerometer compared to the GRACE instrumentation. This paper describes the implementation, testing and performance of the instrument complement flown on the two GRAIL orbiters.     

Tidal Models in a New Era of Satellite Gravimetry

The high precision gravity measurements to be made by recently launched (and recently approved) satellites place new demands on models of Earth, atmospheric, and oceanic tides. The latter is the most problematic. The ocean tides induce variations in the Earth's geoid by amounts that far exceed the new satellite sensitivities, and tidal models must be used to correct for this. Two methods are used here to determine the standard errors in current ocean tide models. At long wavelengths these errors exceed the sensitivity of the GRACE mission. Tidal errors will not prevent the new satellite missions from improving our knowledge of the geopotential by orders of magnitude, but the errors may well contaminate GRACE estimates of temporal variations in gravity. Solar tides are especially problematic because of their long alias periods. The satellite data may be used to improve tidal models once a sufficiently long time series is obtained. Improvements in the long-wavelength components of lunar tides are especially promising. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Prediction of CO Outgassing from Comets Hale-Bopp and Wirtanen

The gas flux from a volatile icy-dust mixture is computed using a comet nucleus thermal model in order to study the evolution of CO outgassing during several apparitions from long-period Comet Hale-Bopp and short-period Comet Wirtanen. The comet model assumes a spherical, porous body containing a dust component, one major ice component (H₂O), and one minor ice component of higher volatility (CO). The initial chemical composition is assumed to be homogeneous. The following processes are taken into account: heat and gas diffusion inside the rotating nucleus; release of outward diffusing gas from the comet nucleus; chemical differentiation by sublimation of volatile ices in the surface layers and recondensation of gas in deeper, cooler layers. A 2-D time dependent solution is obtained through the dependence of the boundary conditions on the local solar illumination as the nucleus rotates. The model for Comet Hale-Bopp was compared with observational measurements (Biver et al., 1999). The best agreement was obtained for a model with amorphous water ice and CO, assuming that a part of the latter is trapped by the water ice, another part is condensed as an independent ice phase. The model confirms that sublimation of CO ice at large heliocentric distance produces a gradual increase in the comet's activity as it approaches the Sun. Crystallization of amorphous water ice begins at 7 AU from the Sun, but no outbursts were found. Seasonal effects and thermal inertia of the nucleus material lead to larger CO outgassing rates as the comet recedes from the Sun. In the second part of this work the model was run with the orbital parameters of Comet Wirtanen. Unlike Comet Hale-Bopp, the predicted CO outgassing from Comet Wirtanen is almost constant throughout its orbit. Such behavior can be explained by a thermally evolved and chemically differentiated comet nucleus. This revised version was published online in June 2006 with corrections to the Cover Date.     

Subsurface Water Oceans on Icy Satellites: Chemical Composition and Exchange Processes

The state of knowledge about the structure and composition of icy satellite interiors has been significantly extended by combining direct measurements from spacecraft, laboratory experiments, and theoretical modeling. The existence of potentially habitable liquid water reservoirs on icy satellites is dependent on the radiogenic heating of the rock component, additional contributions such as the dissipation of tidal energy, the efficiency of heat transfer to the surface, and the presence of substances that deplete the freezing point of liquid water. This review summarizes the chemical evolution of subsurface liquid water oceans, taking into account a number of chemical processes occuring in aqueous environments and partly related to material exchange with the deep interior. Of interest are processes occuring at the transitions from the liquid water layer to the ice layers above and below, involving the possible formation of clathrate hydrates and high-pressure ices on large icy satellites. In contrast, water-rock exchange is important for the chemical evolution of the liquid water layer if the latter is in contact with ocean floor rock on small satellites. The composition of oceanic floor deposits depends on ambient physical conditions and ocean chemistry, and their evolutions through time. In turn, physical properties of the ocean floor affect the circulation of oceanic water and related thermal effects due to tidally-induced porous flow and aqueous alteration of ocean floor rock.