Gravity

@article{doi1010160016003259901851,
    title = "The earth and its gravity field",
    year = "1959",
    journal = "Journal of the Franklin Institute",
    url = "https://doi.org/10.1016/0016-0032(59)90185-1",
    doi = "10.1016/0016-0032(59)90185-1",
    openalex = "W4255498853"
}

@article{doi10106313060812,
    author = "Heiskanen, W. and Meinesz, F. A. Vening and Korff, S. A.",
    title = "The Earth and Its Gravity Field",
    year = "1959",
    journal = "Physics Today",
    url = "https://doi.org/10.1063/1.3060812",
    doi = "10.1063/1.3060812",
    openalex = "W2052723438"
}

@misc{heiskanen1959the1,
    author = "Heiskanen, W. A. and Meinesz, F. A. V",
    title = "The Earth and Its Gravity Field",
    year = "1959",
    howpublished = "New York, McGraw-Hill Book Co., 470 p",
    note = "talkorigins\_source = {true}; raw\_reference = {Heiskanen, W. A., and Meinesz, F. A. V., 1959, The Earth and Its Gravity Field: New York, McGraw-Hill Book Co., 470 p.}"
}

The static deformation of an elastic half‐space by surface pressure is reviewed. A brief mention is made of methods for solving the problem when the medium is plane stratified, but the major emphasis is on the solution for spherical, radially stratified, gravitating earth models. Love‐number calculations are outlined, and from the Love numbers, Green's functions are formed for the surface mass‐load boundary‐value problem. Tables of mass‐load Green's functions, computed for realistic earth models, are given, so that the displacements, tilts, accelerations, and strains at the earth's surface caused by any static load can be found by evaluating a convolution integral over the loaded region.

@article{doi101029rg010i003p00761,
    author = "Farrell, William E.",
    title = "Deformation of the Earth by surface loads",
    year = "1972",
    journal = "Reviews of Geophysics",
    abstract = "The static deformation of an elastic half‐space by surface pressure is reviewed. A brief mention is made of methods for solving the problem when the medium is plane stratified, but the major emphasis is on the solution for spherical, radially stratified, gravitating earth models. Love‐number calculations are outlined, and from the Love numbers, Green's functions are formed for the surface mass‐load boundary‐value problem. Tables of mass‐load Green's functions, computed for realistic earth models, are given, so that the displacements, tilts, accelerations, and strains at the earth's surface caused by any static load can be found by evaluating a convolution integral over the loaded region.",
    url = "https://doi.org/10.1029/rg010i003p00761",
    doi = "10.1029/rg010i003p00761",
    openalex = "W2159268657",
    references = "doi101029jz065i012p04151, doi101029jz068i002p00485, doi101098rsta19700005, doi101111j1365246x1971tb03593x, doi10119011439771, doi1023072003554, doi1023072300274, doi1023072310412, openalexw1535035979, openalexw1590241584, openalexw2130958463, openalexw2171369888"
}

Solar evolution implies, for contemporary albedos and atmospheric composition, global mean temperatures below the freezing point of seawater less than 2.3 aeons ago, contrary to geologic and paleontological evidence. Ammonia mixing ratios of the order of a few parts per million in the middle Precambrian atmosphere resolve this and other problems. Possible temperature evolutionary tracks for Earth and Mars are described. A runaway greenhouse efect will occur on Earth about 4.5 aeons from now, when clement conditions will prevail on Mars.

@article{doi101126science177404352,
    author = "Sagan, Carl and Mullen, George",
    title = "Earth and Mars: Evolution of Atmospheres and Surface Temperatures",
    year = "1972",
    journal = "Science",
    abstract = "Solar evolution implies, for contemporary albedos and atmospheric composition, global mean temperatures below the freezing point of seawater less than 2.3 aeons ago, contrary to geologic and paleontological evidence. Ammonia mixing ratios of the order of a few parts per million in the middle Precambrian atmosphere resolve this and other problems. Possible temperature evolutionary tracks for Earth and Mars are described. A runaway greenhouse efect will occur on Earth about 4.5 aeons from now, when clement conditions will prevail on Mars.",
    url = "https://doi.org/10.1126/science.177.4043.52",
    doi = "10.1126/science.177.4043.52",
    openalex = "W1986601098",
    references = "doi101073pnas316153, doi101126science1603829729"
}

Abstract Computer programs based on the exact calculations of the gravity and magnetic anomalies of polygonal prisms are faster in operation and more accurate than previous programs based on the numerical integration of polygonal laminas. The prism programs also are of more general application than existing computer programs that are based on the exact gravity and magnetic effects of rectangular prisms. There are no restrictions on the use of the exact formula for the gravitational attraction of a polygonal prism, but the formulas for the magnetic effect are restricted in that demagnetization is not considered, and a finite answer is not obtained in the unrealistic circumstance where an observation point coincides with an edge of the prism.Least-squares methods permit calculation of the gravity or magnetic effect of models without knowledge of the density or magnetization contrasts, respectively, by comparison of the observed anomalies with theoretical dimensionless values to determine contrasts as regression coefficients. The coefficient of correlation provides a goodness of fit estimate that helps model evaluation. After calculating a magnetic terrain correction for an outcrop of Quaternary dacite and andestite near Clear Lake, Calif., an improvement of the coefficient of correlation from 88 to the 92 percent level indicates that this volcanic unit probably extends at least 150 m beneath the surface. Application of a magnetic terrain correction to disconnected outcrops of Tertiary andesite, eliminates most of a prominent v-shaped magnetic anomaly south of the San Juan Mountains, Colo.

@article{doi10119011440645,
    author = "Plouff, Donald",
    title = "Gravity and magnetic fields of polygonal prisms and application to magnetic terrain corrections",
    year = "1976",
    journal = "Geophysics",
    abstract = "Abstract Computer programs based on the exact calculations of the gravity and magnetic anomalies of polygonal prisms are faster in operation and more accurate than previous programs based on the numerical integration of polygonal laminas. The prism programs also are of more general application than existing computer programs that are based on the exact gravity and magnetic effects of rectangular prisms. There are no restrictions on the use of the exact formula for the gravitational attraction of a polygonal prism, but the formulas for the magnetic effect are restricted in that demagnetization is not considered, and a finite answer is not obtained in the unrealistic circumstance where an observation point coincides with an edge of the prism.Least-squares methods permit calculation of the gravity or magnetic effect of models without knowledge of the density or magnetization contrasts, respectively, by comparison of the observed anomalies with theoretical dimensionless values to determine contrasts as regression coefficients. The coefficient of correlation provides a goodness of fit estimate that helps model evaluation. After calculating a magnetic terrain correction for an outcrop of Quaternary dacite and andestite near Clear Lake, Calif., an improvement of the coefficient of correlation from 88 to the 92 percent level indicates that this volcanic unit probably extends at least 150 m beneath the surface. Application of a magnetic terrain correction to disconnected outcrops of Tertiary andesite, eliminates most of a prominent v-shaped magnetic anomaly south of the San Juan Mountains, Colo.",
    url = "https://doi.org/10.1190/1.1440645",
    doi = "10.1190/1.1440645",
    openalex = "W2101611497"
}

Astronomers have long noted that the Earth does not rotate uniformly about an axis fixed in the planet, that both the length-of-day and the direction of the rotation axis vary periodically and irregularly by small amounts. These variations are an immediate consequence of the Earth not being a rigid body. In this book Professor Lambeck discusses the irregular nature of this motion and the geophysical mechanisms responsible for it. A complete analysis of these causes requires a discussion of solid Earth physics, magnetohydrodynamics, oceanography and meteorology. The study of the Earth's rotation is therefore of interest not only to astronomers who wish to explain their observations, but also to many geophysicists who use the astronomers' observations to understand better the Earth's response to a variety of applied forces. The author emphasizes the important contributions made over the last 15 years, this progress being in part a consequence of the overall progress in geophysics and planetary physics and of the developments in space science and technology, which not only require that the Earth's motion be precisely known but which also have provided new and precise methods for monitoring this motion. This book is suitable for geophysicists, astronomers and geodesists who are actively engaged in research as well as for graduate students.

@book{doi101017cbo9780511569579,
    author = "Lambeck, Kurt",
    title = "The Earth\&\#39;s Variable Rotation",
    year = "1980",
    booktitle = "Cambridge University Press eBooks",
    abstract = "Astronomers have long noted that the Earth does not rotate uniformly about an axis fixed in the planet, that both the length-of-day and the direction of the rotation axis vary periodically and irregularly by small amounts. These variations are an immediate consequence of the Earth not being a rigid body. In this book Professor Lambeck discusses the irregular nature of this motion and the geophysical mechanisms responsible for it. A complete analysis of these causes requires a discussion of solid Earth physics, magnetohydrodynamics, oceanography and meteorology. The study of the Earth's rotation is therefore of interest not only to astronomers who wish to explain their observations, but also to many geophysicists who use the astronomers' observations to understand better the Earth's response to a variety of applied forces. The author emphasizes the important contributions made over the last 15 years, this progress being in part a consequence of the overall progress in geophysics and planetary physics and of the developments in space science and technology, which not only require that the Earth's motion be precisely known but which also have provided new and precise methods for monitoring this motion. This book is suitable for geophysicists, astronomers and geodesists who are actively engaged in research as well as for graduate students.",
    url = "https://doi.org/10.1017/cbo9780511569579",
    doi = "10.1017/cbo9780511569579",
    openalex = "W3036341826"
}

It is proposed that magnetic field arises naturally in neutron stars as a consequence of thermal effects occurring in their outer crusts. The heat flux through the crust, which is carried mainly by degenerate electrons, can give rise to a possible thermoelectric instability in the solid crust which causes horizontal magnetic field components to grow exponentially with time. However, in order for the thermally driven growth to exceed ohmic decay, either the electron collision time must exceed existing estimates by a factor ∼ 3 or the surface layers comprise helium. A second instability is possible if the liquid phase that lies above the solid crust also contains a horizontal magnetic field. The heat flux will drive circulation which should amplify the field strength provided that there is a seed field in excess of ∼ 108 G. If either of these two instabilities develops the field will quickly grow to a strength of ∼ 1012 G, where the instabilities become non-linear. Further growth will saturate when either the magnetic stress exceeds the lattice yield stress or the temperature perturbations become non-linear, both of which occur at a subsurface field strength of ∼ 1014 G; the corresponding surface field strength is ∼ 1012 G. Further evolution of the magnetic field should lead to long-range order and yield neutron star magnetic dipole moments ∼ 1030 G cm3, comparable with those observed. Newly-formed neutron stars should be able to develop their dipole moments in a hundred thousand years and maintain them for as long as heat flows through the crust. Thereafter, the dipole moment should decay in several million years, as observed in the case of most radio pulsars. Neutron stars that are formed spinning rapidly, like that in the Crab Nebula, should be able to grow magnetic fields far more rapidly since their rotational energy can also be tapped to drive thermoelectric currents. The interiors of neutron stars in binary systems may be heated by the energy released by accreting matter. The resulting heat flux may cause the production of magnetic fields in these objects. Binary pulsars, with their unusually low and persistent fields, have probably passed through this phase.

@article{doi101093mnras20441025,
    author = "Blandford, R. D. and Applegate, James H. and Hernquist, Lars",
    title = "Thermal origin of neutron star magnetic fields",
    year = "1983",
    journal = "Monthly Notices of the Royal Astronomical Society",
    abstract = "It is proposed that magnetic field arises naturally in neutron stars as a consequence of thermal effects occurring in their outer crusts. The heat flux through the crust, which is carried mainly by degenerate electrons, can give rise to a possible thermoelectric instability in the solid crust which causes horizontal magnetic field components to grow exponentially with time. However, in order for the thermally driven growth to exceed ohmic decay, either the electron collision time must exceed existing estimates by a factor ∼ 3 or the surface layers comprise helium. A second instability is possible if the liquid phase that lies above the solid crust also contains a horizontal magnetic field. The heat flux will drive circulation which should amplify the field strength provided that there is a seed field in excess of ∼ 108 G. If either of these two instabilities develops the field will quickly grow to a strength of ∼ 1012 G, where the instabilities become non-linear. Further growth will saturate when either the magnetic stress exceeds the lattice yield stress or the temperature perturbations become non-linear, both of which occur at a subsurface field strength of ∼ 1014 G; the corresponding surface field strength is ∼ 1012 G. Further evolution of the magnetic field should lead to long-range order and yield neutron star magnetic dipole moments ∼ 1030 G cm3, comparable with those observed. Newly-formed neutron stars should be able to develop their dipole moments in a hundred thousand years and maintain them for as long as heat flows through the crust. Thereafter, the dipole moment should decay in several million years, as observed in the case of most radio pulsars. Neutron stars that are formed spinning rapidly, like that in the Crab Nebula, should be able to grow magnetic fields far more rapidly since their rotational energy can also be tapped to drive thermoelectric currents. The interiors of neutron stars in binary systems may be heated by the energy released by accreting matter. The resulting heat flux may cause the production of magnetic fields in these objects. Binary pulsars, with their unusually low and persistent fields, have probably passed through this phase.",
    url = "https://doi.org/10.1093/mnras/204.4.1025",
    doi = "10.1093/mnras/204.4.1025",
    openalex = "W1977245296"
}

In order to obtain a dynamically consistent relationship between the geoid and the earth's response to internal buoyancy forces, we have calculated potential and surface deformation Love numbers for internal loading. These quantities depend on the depth and harmonic degree of loading. They can be integrated as Green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts. Spherically symmetric, self‐gravitating flow models are constructed for a variety of radial Newtonian viscosity variations and flow configurations including both whole mantle and layered convection. We demonstrate that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound, much less than the time scale for significant change in the convective flow pattern, by calculating relaxation times for a series of spherically symmetric viscous earth models. For uniform mantle viscosity the geoid signature due to boundary deformations is larger than that due to internal loads, resulting in net negative geoid anomalies for positive density contrasts. Geoid anomalies from intermediate‐wavelength density contrasts are amplified by up to an order of magnitude. Geoid anomalies are primarily the result of density contrasts in the interior of convecting layers; density contrasts near layer boundaries are almost completely compensated. Layered mantle convection results in smaller geoid anomalies than mantle‐wide flow for a given density contrast. Viscosity stratification leads to more complicated spectral signatures. Because of the sensitivity of the dynamic response functions to model parameters, forward models for the geoid can be used to combine several sources of geophysical data (e.g., subducted slab locations, seismic velocity anomalies, surface topography) to constrain better the structure and viscosity of the mantle.

@article{doi101029jb089ib07p05987,
    author = "Richards, Mark A. and Hager, Bradford H.",
    title = "Geoid anomalies in a dynamic Earth",
    year = "1984",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "In order to obtain a dynamically consistent relationship between the geoid and the earth's response to internal buoyancy forces, we have calculated potential and surface deformation Love numbers for internal loading. These quantities depend on the depth and harmonic degree of loading. They can be integrated as Green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts. Spherically symmetric, self‐gravitating flow models are constructed for a variety of radial Newtonian viscosity variations and flow configurations including both whole mantle and layered convection. We demonstrate that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound, much less than the time scale for significant change in the convective flow pattern, by calculating relaxation times for a series of spherically symmetric viscous earth models. For uniform mantle viscosity the geoid signature due to boundary deformations is larger than that due to internal loads, resulting in net negative geoid anomalies for positive density contrasts. Geoid anomalies from intermediate‐wavelength density contrasts are amplified by up to an order of magnitude. Geoid anomalies are primarily the result of density contrasts in the interior of convecting layers; density contrasts near layer boundaries are almost completely compensated. Layered mantle convection results in smaller geoid anomalies than mantle‐wide flow for a given density contrast. Viscosity stratification leads to more complicated spectral signatures. Because of the sensitivity of the dynamic response functions to model parameters, forward models for the geoid can be used to combine several sources of geophysical data (e.g., subducted slab locations, seismic velocity anomalies, surface topography) to constrain better the structure and viscosity of the mantle.",
    url = "https://doi.org/10.1029/jb089ib07p05987",
    doi = "10.1029/jb089ib07p05987",
    openalex = "W2063287321",
    references = "doi1010160033589478900339, doi101029jb082i002p00239, doi101029jb083ib12p05989, doi101029jb086ib06p04843, doi101029jb089ib07p05929, doi101029jb089ib07p05953, doi101029jb089ib07p06003, doi101038089471a0, doi101111j1365246x1976tb01253x, doi101111j1365246x1982tb04976x, openalexw1624331985, openalexw2128978199, passey1981upper"
}

@book{doi101007bfb0010546,
    author = "Sanso, Fernando and Rummel, Reinhard 1945-",
    title = "Theory of Satellite Geodesy and Gravity Field Determination",
    year = "1989",
    booktitle = "Lecture notes in earth sciences",
    url = "https://doi.org/10.1007/bfb0010546",
    doi = "10.1007/bfb0010546",
    openalex = "W1481738552"
}

@article{doi101016003192018990263x,
    author = "Cross, PA",
    title = "Lecture notes in Earth sciences",
    year = "1989",
    journal = "Physics of The Earth and Planetary Interiors",
    url = "https://doi.org/10.1016/0031-9201(89)90263-x",
    doi = "10.1016/0031-9201(89)90263-x",
    openalex = "W2931574751"
}

@book{doi1010079783642520617,
    author = "Burša, Milan and Pěč, Karel",
    title = "Gravity Field and Dynamics of the Earth",
    year = "1993",
    url = "https://doi.org/10.1007/978-3-642-52061-7",
    doi = "10.1007/978-3-642-52061-7",
    openalex = "W1580334432",
    references = "doi10100797836425206175, doi10100797836425206176"
}

Three-dimensional numerical simulations of the geodynamo suggest that a super- rotation of Earth's solid inner core relative to the mantle is maintained by magnetic coupling between the inner core and an eastward thermal wind in the fluid outer core. This mechanism, which is analogous to a synchronous motor, also plays a fundamental role in the generation of Earth's magnetic field.

@article{doi101126science27452941887,
    author = "Glatzmaier, GA and Roberts, PH",
    title = "Rotation and Magnetism of Earth's Inner Core.",
    year = "1996",
    journal = "Science (New York, N.Y.)",
    abstract = "Three-dimensional numerical simulations of the geodynamo suggest that a super- rotation of Earth's solid inner core relative to the mantle is maintained by magnetic coupling between the inner core and an eastward thermal wind in the fluid outer core. This mechanism, which is analogous to a synchronous motor, also plays a fundamental role in the generation of Earth's magnetic field.",
    url = "https://pubmed.ncbi.nlm.nih.gov/8943197/",
    doi = "10.1126/science.274.5294.1887",
    pmid = "8943197"
}

The implementation of the Global Positioning System (GPS) network of satellites and the development of small, high‐performance instrumentation to receive GPS signals have created an opportunity for active remote sounding of the Earth's atmosphere by radio occultation at comparatively low cost. A prototype demonstration of this capability has now been provided by the GPS/MET investigation. Despite using relatively immature technology, GPS/MET has been extremely successful [Ware et al., 1996; Kursinski et al., 1996], although there is still room for improvement. The aim of this paper is to develop a theoretical estimate of the spatial coverage, resolution, and accuracy that can be expected for atmospheric profiles derived from GPS occultations. We consider observational geometry, attenuation, and diffraction in defining the vertical range of the observations and their resolution. We present the first systematic, extensive error analysis of the spacecraft radio occultation technique using a combination of analytical and simulation methods to establish a baseline accuracy for retrieved profiles of refractivity, geopotential, and temperature. Typically, the vertical resolution of the observations ranges from 0.5 km in the lower troposphere to 1.4 km in the middle atmosphere. Results indicate that useful profiles of refractivity can be derived from ∼60 km altitude to the surface with the exception of regions less than 250 m in vertical extent associated with high vertical humidity gradients. Above the 250 K altitude level in the troposphere, where the effects of water are negligible, sub‐Kelvin temperature accuracy is predicted up to ∼40 km depending on the phase of the solar cycle. Geopotential heights of constant pressure levels are expected to be accurate to ∼10 m or better between 10 and 20 km altitudes. Below the 250 K level, the ambiguity between water and dry atmosphere refractivity becomes significant, and temperature accuracy is degraded. Deep in the warm troposphere the contribution of water to refractivity becomes sufficiently large for the accurate retrieval of water vapor given independent temperatures from weather analyses [Kursinski et al., 1995]. The radio occultation technique possesses a unique combination of global coverage, high precision, high vertical resolution, insensitivity to atmospheric particulates, and long‐term stability. We show here how these properties are well suited for several applications including numerical weather prediction and long‐term monitoring of the Earth's climate.

@article{doi10102997jd01569,
    author = "Kursinski, E. R. and Hajj, G. A. and Schofield, J. T. and Linfield, R. P. and Hardy, Kenneth R.",
    title = "Observing Earth's atmosphere with radio occultation measurements using the Global Positioning System",
    year = "1997",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "The implementation of the Global Positioning System (GPS) network of satellites and the development of small, high‐performance instrumentation to receive GPS signals have created an opportunity for active remote sounding of the Earth's atmosphere by radio occultation at comparatively low cost. A prototype demonstration of this capability has now been provided by the GPS/MET investigation. Despite using relatively immature technology, GPS/MET has been extremely successful [Ware et al., 1996; Kursinski et al., 1996], although there is still room for improvement. The aim of this paper is to develop a theoretical estimate of the spatial coverage, resolution, and accuracy that can be expected for atmospheric profiles derived from GPS occultations. We consider observational geometry, attenuation, and diffraction in defining the vertical range of the observations and their resolution. We present the first systematic, extensive error analysis of the spacecraft radio occultation technique using a combination of analytical and simulation methods to establish a baseline accuracy for retrieved profiles of refractivity, geopotential, and temperature. Typically, the vertical resolution of the observations ranges from 0.5 km in the lower troposphere to 1.4 km in the middle atmosphere. Results indicate that useful profiles of refractivity can be derived from ∼60 km altitude to the surface with the exception of regions less than 250 m in vertical extent associated with high vertical humidity gradients. Above the 250 K altitude level in the troposphere, where the effects of water are negligible, sub‐Kelvin temperature accuracy is predicted up to ∼40 km depending on the phase of the solar cycle. Geopotential heights of constant pressure levels are expected to be accurate to ∼10 m or better between 10 and 20 km altitudes. Below the 250 K level, the ambiguity between water and dry atmosphere refractivity becomes significant, and temperature accuracy is degraded. Deep in the warm troposphere the contribution of water to refractivity becomes sufficiently large for the accurate retrieval of water vapor given independent temperatures from weather analyses [Kursinski et al., 1995]. The radio occultation technique possesses a unique combination of global coverage, high precision, high vertical resolution, insensitivity to atmospheric particulates, and long‐term stability. We show here how these properties are well suited for several applications including numerical weather prediction and long‐term monitoring of the Earth's climate.",
    url = "https://doi.org/10.1029/97jd01569",
    doi = "10.1029/97jd01569",
    openalex = "W2120653142",
    references = "doi101029gm029p0130, doi10106312809772, doi1017159caj1991847309"
}

The GRACE satellite mission, scheduled for launch in 2001, is designed to map out the Earth's gravity field to high accuracy every 2–4 weeks over a nominal lifetime of 5 years. Changes in the gravity field are caused by the redistribution of mass within the Earth and on or above its surface. GRACE will thus be able to constrain processes that involve mass redistribution. In this paper we use output from hydrological, oceanographic, and atmospheric models to estimate the variability in the gravity field (i.e., in the geoid) due to those sources. We develop a method for constructing surface mass estimates from the GRACE gravity coefficients. We show the results of simulations, where we use synthetic GRACE gravity data, constructed by combining estimated geophysical signals and simulated GRACE measurement errors, to attempt to recover hydrological and oceanographic signals. We show that GRACE may be able to recover changes in continental water storage and in seafloor pressure, at scales of a few hundred kilometers and larger and at timescales of a few weeks and longer, with accuracies approaching 2 mm in water thickness over land, and 0.1 mbar or better in seafloor pressure.

@article{doi10102998jb02844,
    author = "Wahr, John and Molenaar, Mery and Bryan, Frank O.",
    title = "Time variability of the Earth's gravity field: Hydrological and oceanic effects and their possible detection using GRACE",
    year = "1998",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "The GRACE satellite mission, scheduled for launch in 2001, is designed to map out the Earth's gravity field to high accuracy every 2–4 weeks over a nominal lifetime of 5 years. Changes in the gravity field are caused by the redistribution of mass within the Earth and on or above its surface. GRACE will thus be able to constrain processes that involve mass redistribution. In this paper we use output from hydrological, oceanographic, and atmospheric models to estimate the variability in the gravity field (i.e., in the geoid) due to those sources. We develop a method for constructing surface mass estimates from the GRACE gravity coefficients. We show the results of simulations, where we use synthetic GRACE gravity data, constructed by combining estimated geophysical signals and simulated GRACE measurement errors, to attempt to recover hydrological and oceanographic signals. We show that GRACE may be able to recover changes in continental water storage and in seafloor pressure, at scales of a few hundred kilometers and larger and at timescales of a few weeks and longer, with accuracies approaching 2 mm in water thickness over land, and 0.1 mbar or better in seafloor pressure.",
    url = "https://doi.org/10.1029/98jb02844",
    doi = "10.1029/98jb02844",
    openalex = "W1990931465",
    references = "doi1010160031920181900467, doi10102990jb01583, doi101029rg010i003p00761, doi101126science2655169195"
}

The notable absence of radio pulsars having measured magnetic dipole surface field strengths above $B_0\\sim 3\\times 10^{13}$ Gauss naturally raises the question of whether this forms an upper limit to pulsar magnetization. Recently there has been increasing evidence that neutron stars possessing higher dipole spin-down fields do in fact exist, including a growing list of anomalous X-ray pulsars (AXPs) with long periods and spinning down with high period derivatives, implying surface fields of $10^{14}$--$10^{15}$ Gauss. Furthermore, the recently reported X-ray period and period derivative for the Soft Gamma-ray Repeater (SGR) source SGR1806-20 suggest a surface field around $10^{15}$ Gauss. None of these high-field pulsars have yet been detected as radio pulsars. We propose that high-field pulsars should be radio-quiet because electron-positron pair production in their magnetospheres, thought to be essential for radio emission, is efficiently suppressed in ultra-strong fields ($B_0\\gtrsim 4\\times 10^{13}$ Gauss) by the action of photon splitting, a quantum electrodynamical process in which a photon splits into two. Our computed radio quiescence boundary in the radio pulsar $P-\\dot P$ diagram, where photon splitting overtakes pair creation, is located just above the boundary of the known radio pulsar population, neatly dividing them from the AXPs. We thus identify a physical mechanism that defines a new class of high-field radio-quiet neutron stars that should be detectable by their pulsed emission at X-ray and perhaps $\\gamma$-ray energies.

@article{doi101086311679,
    author = "Baring, Matthew G. and Harding, A. K.",
    title = "Radio-Quiet Pulsars with Ultrastrong Magnetic Fields",
    year = "1998",
    journal = "The Astrophysical Journal",
    abstract = "The notable absence of radio pulsars having measured magnetic dipole surface field strengths above $B\_0\\sim 3\\times 10^{13}$ Gauss naturally raises the question of whether this forms an upper limit to pulsar magnetization. Recently there has been increasing evidence that neutron stars possessing higher dipole spin-down fields do in fact exist, including a growing list of anomalous X-ray pulsars (AXPs) with long periods and spinning down with high period derivatives, implying surface fields of $10^{14}$--$10^{15}$ Gauss. Furthermore, the recently reported X-ray period and period derivative for the Soft Gamma-ray Repeater (SGR) source SGR1806-20 suggest a surface field around $10^{15}$ Gauss. None of these high-field pulsars have yet been detected as radio pulsars. We propose that high-field pulsars should be radio-quiet because electron-positron pair production in their magnetospheres, thought to be essential for radio emission, is efficiently suppressed in ultra-strong fields ($B\_0\\gtrsim 4\\times 10^{13}$ Gauss) by the action of photon splitting, a quantum electrodynamical process in which a photon splits into two. Our computed radio quiescence boundary in the radio pulsar $P-\\dot P$ diagram, where photon splitting overtakes pair creation, is located just above the boundary of the known radio pulsar population, neatly dividing them from the AXPs. We thus identify a physical mechanism that defines a new class of high-field radio-quiet neutron stars that should be detectable by their pulsed emission at X-ray and perhaps $\\gamma$-ray energies.",
    url = "https://doi.org/10.1086/311679",
    doi = "10.1086/311679",
    openalex = "W2151402465"
}

Abstract We present two methods for inverting surface gravity data to recover a 3-D distribution of density contrast. In the first method, we transform the gravity data into pseudomagnetic data via Poisson's relation and carry out the inversion using a 3-D magnetic inversion algorithm. In the second, we invert the gravity data directly to recover a minimum structure model. In both approaches, the earth is modeled by using a large number of rectangular cells of constant density, and the final density distribution is obtained by minimizing a model objective function subject to fitting the observed data. The model objective function has the flexibility to incorporate prior information and thus the constructed model not only fits the data but also agrees with additional geophysical and geological constraints. We apply a depth weighting in the objective function to counteract the natural decay of the kernels so that the inversion yields depth information. Applications of the algorithms to synthetic and field data produce density models representative of true structures. Our results have shown that the inversion of gravity data with a properly designed objective function can yield geologically meaningful information.

@article{doi10119011444302,
    author = "Li, Yaoguo and Oldenburg, Douglas W.",
    title = "3-D inversion of gravity data",
    year = "1998",
    journal = "Geophysics",
    abstract = "Abstract We present two methods for inverting surface gravity data to recover a 3-D distribution of density contrast. In the first method, we transform the gravity data into pseudomagnetic data via Poisson's relation and carry out the inversion using a 3-D magnetic inversion algorithm. In the second, we invert the gravity data directly to recover a minimum structure model. In both approaches, the earth is modeled by using a large number of rectangular cells of constant density, and the final density distribution is obtained by minimizing a model objective function subject to fitting the observed data. The model objective function has the flexibility to incorporate prior information and thus the constructed model not only fits the data but also agrees with additional geophysical and geological constraints. We apply a depth weighting in the objective function to counteract the natural decay of the kernels so that the inversion yields depth information. Applications of the algorithms to synthetic and field data produce density models representative of true structures. Our results have shown that the inversion of gravity data with a properly designed objective function can yield geologically meaningful information.",
    url = "https://doi.org/10.1190/1.1444302",
    doi = "10.1190/1.1444302",
    openalex = "W2332990274",
    references = "doi10119011438369"
}

A new model of the Earth's gravity field, called GRIM5‐S1, was prepared in a joint German‐French effort. The solution is based on satellite orbit perturbation analysis and exploits tracking data from 21 satellites to solve simultaneously for the gravitational and ocean tide potential and tracking station positions. The satellite‐only solution results in a homogeneous representation of the geoid with an approximation error of about 45 cm in terms of 5×5 degree block mean values, and performs globally better in satellite orbit restitution than any previous gravity field model. The GRIM5 normals, which were generated taking into account the latest computational standards, shall be the reference for use during the coming geopotential satellite mission CHAMP and should provide new standards in computing orbits of next altimetric missions like Jason and ENVISAT. The GRIM5‐S1 normals also give the basis for the tracking/surface data combined solution GRIM5‐C1.

@article{doi1010292000gl011721,
    author = "Biancale, R. and Balmino, G. and Lemoine, Jean‐Michel and Marty, Jean‐Charles and Moynot, B. and Barlier, F. and Exertier, P. and Laurain, O. and Gégout, Pascal and Schwintzer, P. and Reigber, Christoph and Bode, Albert and König, Rolf and Massmann, Franz‐Heinrich and Raimondo, Jean‐Claude and Schmidt, Roland and Zhu, Sheng Yuan",
    title = "A new global Earth's gravity field model from satellite orbit perturbations: GRIM5‐S1",
    year = "2000",
    journal = "Geophysical Research Letters",
    abstract = "A new model of the Earth's gravity field, called GRIM5‐S1, was prepared in a joint German‐French effort. The solution is based on satellite orbit perturbation analysis and exploits tracking data from 21 satellites to solve simultaneously for the gravitational and ocean tide potential and tracking station positions. The satellite‐only solution results in a homogeneous representation of the geoid with an approximation error of about 45 cm in terms of 5×5 degree block mean values, and performs globally better in satellite orbit restitution than any previous gravity field model. The GRIM5 normals, which were generated taking into account the latest computational standards, shall be the reference for use during the coming geopotential satellite mission CHAMP and should provide new standards in computing orbits of next altimetric missions like Jason and ENVISAT. The GRIM5‐S1 normals also give the basis for the tracking/surface data combined solution GRIM5‐C1.",
    url = "https://doi.org/10.1029/2000gl011721",
    doi = "10.1029/2000gl011721",
    openalex = "W2004117811"
}

We study the effects of very strong magnetic fields on the equation of state (EOS) in multicomponent, interacting matter by developing a covariant description for the inclusion of the anomalous magnetic moments of nucleons. For the description of neutron star matter, we employ a field-theoretical approach which permits the study of several models which differ in their behavior at high density. Effects of Landau quantization in ultra-strong magnetic fields ($B>10^{14}$ Gauss) lead to a reduction in the electron chemical potential and a substantial increase in the proton fraction. We find the generic result for $B>10^{18}$ Gauss that the softening of the EOS caused by Landau quantization is overwhelmed by stiffening due to the incorporation of the anomalous magnetic moments of the nucleons. In addition, the neutrons become completely spin polarized. The inclusion of ultra-strong magnetic fields leads to a dramatic increase in the proton fraction, with consequences for the direct Urca process and neutron star cooling. The magnetization of the matter never appears to become very large, as the value of $|H/B|$ never deviates from unity by more than a few percent. Our findings have implications for the structure of neutron stars in the presence of large frozen-in magnetic fields.

@article{doi101086309010,
    author = "Broderick, Avery E. and Prakash, M. and Lattimer, James M.",
    title = "The Equation of State of Neutron Star Matter in Strong Magnetic Fields",
    year = "2000",
    journal = "The Astrophysical Journal",
    abstract = "We study the effects of very strong magnetic fields on the equation of state (EOS) in multicomponent, interacting matter by developing a covariant description for the inclusion of the anomalous magnetic moments of nucleons. For the description of neutron star matter, we employ a field-theoretical approach which permits the study of several models which differ in their behavior at high density. Effects of Landau quantization in ultra-strong magnetic fields ($B>10^{14}$ Gauss) lead to a reduction in the electron chemical potential and a substantial increase in the proton fraction. We find the generic result for $B>10^{18}$ Gauss that the softening of the EOS caused by Landau quantization is overwhelmed by stiffening due to the incorporation of the anomalous magnetic moments of the nucleons. In addition, the neutrons become completely spin polarized. The inclusion of ultra-strong magnetic fields leads to a dramatic increase in the proton fraction, with consequences for the direct Urca process and neutron star cooling. The magnetization of the matter never appears to become very large, as the value of $|H/B|$ never deviates from unity by more than a few percent. Our findings have implications for the structure of neutron stars in the presence of large frozen-in magnetic fields.",
    url = "https://doi.org/10.1086/309010",
    doi = "10.1086/309010",
    openalex = "W2039300833",
    references = "doi101086312104"
}

Topography and gravity measured by the Mars Global Surveyor have enabled determination of the global crust and upper mantle structure of Mars. The planet displays two distinct crustal zones that do not correlate globally with the geologic dichotomy: a region of crust that thins progressively from south to north and encompasses much of the southern highlands and Tharsis province and a region of approximately uniform crustal thickness that includes the northern lowlands and Arabia Terra. The strength of the lithosphere beneath the ancient southern highlands suggests that the northern hemisphere was a locus of high heat flow early in martian history. The thickness of the elastic lithosphere increases with time of loading in the northern plains and Tharsis. The northern lowlands contain structures interpreted as large buried channels that are consistent with northward transport of water and sediment to the lowlands before the end of northern hemisphere resurfacing.

@article{doi101126science28754591788,
    author = "Zuber, M. T. and Solomon, Sean C. and Phillips, R. J. and Smith, David E. and Tyler, G. L. and Aharonson, O. and Balmino, G. and Banerdt, W. B. and Head, J. W. and Johnson, C. L. and Lemoine, F. G. and McGovern, P. J. and Neumann, G. A. and Rowlands, D. D. and Zhong, Shijie",
    title = "Internal Structure and Early Thermal Evolution of Mars from Mars Global Surveyor Topography and Gravity",
    year = "2000",
    journal = "Science",
    abstract = "Topography and gravity measured by the Mars Global Surveyor have enabled determination of the global crust and upper mantle structure of Mars. The planet displays two distinct crustal zones that do not correlate globally with the geologic dichotomy: a region of crust that thins progressively from south to north and encompasses much of the southern highlands and Tharsis province and a region of approximately uniform crustal thickness that includes the northern lowlands and Arabia Terra. The strength of the lithosphere beneath the ancient southern highlands suggests that the northern hemisphere was a locus of high heat flow early in martian history. The thickness of the elastic lithosphere increases with time of loading in the northern plains and Tharsis. The northern lowlands contain structures interpreted as large buried channels that are consistent with northward transport of water and sediment to the lowlands before the end of northern hemisphere resurfacing.",
    url = "https://doi.org/10.1126/science.287.5459.1788",
    doi = "10.1126/science.287.5459.1788",
    openalex = "W2104652753",
    references = "doi101029jb090ib14p12623, doi101126science2845415790, doi101126science28454191495"
}

Mantle Convection in the Earth and Planets is a comprehensive synthesis of all aspects of mantle convection within the Earth, the terrestrial planets, the Moon, and the Galilean satellites of Jupiter. The book includes up-to-date discussions of the latest research developments that have revolutionized our understanding of the Earth and the planets. It is suitable as a text for graduate courses in geophysics and planetary physics, and as a supplementary reference for use at the undergraduate level. It is also an invaluable review for researchers in the broad fields of the Earth and planetary sciences including seismologists, tectonophysicists, geodesists, mineral physicists, volcanologists, geochemists, geologists, mineralogists, petrologists, paleomagnetists, planetary geologists, and meteoriticists. The book features a comprehensive index, an extensive reference list, numerous illustrations (many in color) and major questions that focus the discussion and suggest avenues of future research.

@book{doi101017cbo9780511612879,
    author = "Schubert, G. and Turcotte, Donald L. and Olson, Peter",
    title = "Mantle Convection in the Earth and Planets",
    year = "2001",
    booktitle = "Cambridge University Press eBooks",
    abstract = "Mantle Convection in the Earth and Planets is a comprehensive synthesis of all aspects of mantle convection within the Earth, the terrestrial planets, the Moon, and the Galilean satellites of Jupiter. The book includes up-to-date discussions of the latest research developments that have revolutionized our understanding of the Earth and the planets. It is suitable as a text for graduate courses in geophysics and planetary physics, and as a supplementary reference for use at the undergraduate level. It is also an invaluable review for researchers in the broad fields of the Earth and planetary sciences including seismologists, tectonophysicists, geodesists, mineral physicists, volcanologists, geochemists, geologists, mineralogists, petrologists, paleomagnetists, planetary geologists, and meteoriticists. The book features a comprehensive index, an extensive reference list, numerous illustrations (many in color) and major questions that focus the discussion and suggest avenues of future research.",
    url = "https://doi.org/10.1017/cbo9780511612879",
    doi = "10.1017/cbo9780511612879",
    openalex = "W1594412726"
}

The similarity of rotation periods of, the anomalous X-ray pulsars (AXPs), the soft gamma ray repeaters (SGRs) and the dim thermal neutron stars (DTNs) suggests a common mechanism with an asymptotic spindown phase through the propeller and early accretion stages. The DTNs are in the propeller stage. Their luminosities arise from frictional heating in the neutron star. If the 8.4 s rotation period of the DTN RXJ 0720.4-3125 is close to its rotational equilibrium period, the propeller torque indicates a magnetic field in the 10$^{12}$ Gauss range. The mass inflow rate onto the propeller is of the order of the AXP accretion rates. The limited range of rotation periods, taken to be close to equilibrium periods, and magnetic fields in the range 5 E11- 5 E12 Gauss correspond to mass inflow rates 3.2 E14 gm/s < \\dot{M} < 4.2 E17 gm/s. Observed spindown rates of the AXPs and SGRs also fit in with these fields rather than magnetar fields periods. The source of the mass inflow is a remnant accretion disk formed as part of the fallback during the supernova explosion. These classes of sources thus represent the alternative pathways for those neutron stars that do not become radio pulsars. For the highest mass inflow rates the propeller action may support enough circumstellar material so that the optical thickness to electron scattering destroys the X-ray beaming, and the rotation period is not observable. These are the radio quiet neutron stars (RQNSs) at the centers of supernova remnants Cas A, Puppis A, RCW 103 and 296.5+10.

@article{doi101086321393,
    author = "Alpar, M. A.",
    title = "On Young Neutron Stars as Propellers and Accretors with Conventional Magnetic Fields",
    year = "2001",
    journal = "The Astrophysical Journal",
    abstract = "The similarity of rotation periods of, the anomalous X-ray pulsars (AXPs), the soft gamma ray repeaters (SGRs) and the dim thermal neutron stars (DTNs) suggests a common mechanism with an asymptotic spindown phase through the propeller and early accretion stages. The DTNs are in the propeller stage. Their luminosities arise from frictional heating in the neutron star. If the 8.4 s rotation period of the DTN RXJ 0720.4-3125 is close to its rotational equilibrium period, the propeller torque indicates a magnetic field in the 10$^{12}$ Gauss range. The mass inflow rate onto the propeller is of the order of the AXP accretion rates. The limited range of rotation periods, taken to be close to equilibrium periods, and magnetic fields in the range 5 E11- 5 E12 Gauss correspond to mass inflow rates 3.2 E14 gm/s < \\dot{M} < 4.2 E17 gm/s. Observed spindown rates of the AXPs and SGRs also fit in with these fields rather than magnetar fields periods. The source of the mass inflow is a remnant accretion disk formed as part of the fallback during the supernova explosion. These classes of sources thus represent the alternative pathways for those neutron stars that do not become radio pulsars. For the highest mass inflow rates the propeller action may support enough circumstellar material so that the optical thickness to electron scattering destroys the X-ray beaming, and the rotation period is not observable. These are the radio quiet neutron stars (RQNSs) at the centers of supernova remnants Cas A, Puppis A, RCW 103 and 296.5+10.",
    url = "https://doi.org/10.1086/321393",
    doi = "10.1086/321393",
    openalex = "W2156454222",
    references = "doi101086312104"
}

Using three months of GPS satellite‐to‐satellite tracking and accelerometer data of the CHAMP satellite mission, a new long‐wavelength global gravity field model, called EIGEN‐1S, has been prepared in a joint German‐French effort. The solution is derived solely from analysis of satellite orbit perturbations, i.e. independent of oceanic and continental surface gravity data. EIGEN‐1S results in a geoid with an approximation error of about 20 cm in terms of 5 × 5 degree block mean values, which is an improvement of more than a factor of 2 compared to pre‐CHAMP satellite‐only gravity field models. This impressive progress is a result of CHAMP's tailored orbit characteristics and dedicated instrumentation, providing continuous tracking and direct on‐orbit measurements of non‐gravitational satellite accelerations.

@article{doi1010292002gl015064,
    author = "Reigber, Christoph and Balmino, G. and Schwintzer, P. and Biancale, R. and Bode, Albert and Lemoine, Jean‐Michel and König, Rolf and Loyer, Sylvain and Neumayer, H. and Marty, Jean‐Charles and Barthelmes, Franz and Pérosanz, F. and Zhu, Shen Yuan",
    title = "A high‐quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN‐1S)",
    year = "2002",
    journal = "Geophysical Research Letters",
    abstract = "Using three months of GPS satellite‐to‐satellite tracking and accelerometer data of the CHAMP satellite mission, a new long‐wavelength global gravity field model, called EIGEN‐1S, has been prepared in a joint German‐French effort. The solution is derived solely from analysis of satellite orbit perturbations, i.e. independent of oceanic and continental surface gravity data. EIGEN‐1S results in a geoid with an approximation error of about 20 cm in terms of 5 × 5 degree block mean values, which is an improvement of more than a factor of 2 compared to pre‐CHAMP satellite‐only gravity field models. This impressive progress is a result of CHAMP's tailored orbit characteristics and dedicated instrumentation, providing continuous tracking and direct on‐orbit measurements of non‐gravitational satellite accelerations.",
    url = "https://doi.org/10.1029/2002gl015064",
    doi = "10.1029/2002gl015064",
    openalex = "W2156071113"
}

@book{doi1010079789401713337,
    author = "Beutler, Gerhard and Drinkwater, Mark R. and Rummel, Reiner and von Steiger, R.",
    title = "Earth Gravity Field from Space — From Sensors to Earth Sciences",
    year = "2003",
    booktitle = "Space sciences series of ISSI",
    url = "https://doi.org/10.1007/978-94-017-1333-7",
    doi = "10.1007/978-94-017-1333-7",
    openalex = "W1679808818"
}

@incollection{doi10100797894017133376,
    author = "Reigber, Christoph and Balmino, G. and Schwintzer, P. and Biancale, R. and Bode, Albert and Lemoine, Jean‐Michel and König, R. and Loyer, Sylvain and Neumayer, H. and Marty, Jean‐Charles and Barthelmes, Franz and Pérosanz, F. and Zhu, S. Y.",
    title = "Global Gravity Field Recovery Using Solely GPS Tracking and Accelerometer Data from CHAMP",
    year = "2003",
    booktitle = "Space sciences series of ISSI",
    url = "https://doi.org/10.1007/978-94-017-1333-7\_6",
    doi = "10.1007/978-94-017-1333-7\_6",
    openalex = "W2053510993"
}

@article{doi101007s0019000303158,
    author = "Visser, Pieter and Sneeuw, Nico and Gerlach, Christian",
    title = "Energy integral method for gravity field determination from satellite orbit coordinates",
    year = "2003",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-003-0315-8",
    doi = "10.1007/s00190-003-0315-8",
    openalex = "W2059078230"
}

@article{doi101016s0273117703001625,
    author = "Reigber, Ch. and Schwintzer, P. and Neumayer, Karl Hans and Barthelmes, Franz and König, R. and Förste, Ch. and Balmino, G. and Biancale, R. and Lemoine, Jean‐Michel and Loyer, Sylvain and Bruinsma, Sean and Pérosanz, F. and Fayard, T.",
    title = "The CHAMP-only earth gravity field model EIGEN-2",
    year = "2003",
    journal = "Advances in Space Research",
    url = "https://doi.org/10.1016/s0273-1177(03)00162-5",
    doi = "10.1016/s0273-1177(03)00162-5",
    openalex = "W2062752630",
    references = "doi10100797894017133376, doi101007bfb0010546, doi101007bfb0010552, doi101016003192018990263x, doi101016s0273117702002764, doi101023a1026217713133, doi1010292000gl011721, doi1010292002gl015064, doi10102992jc00095, openalexw2214184"
}

@article{doi101023a1026217713133,
    author = "Reigber, C. and Balmino, G. and Schwintzer, P. and Biancale, R. and Bode, A. and Lemoine, Jean‐Michel and König, R. and Loyer, Sylvain and Neumayer, H. and Marty, J.-C. and Barthelmes, Franz and Perosanz, F. and Zhu, S. Y.",
    title = "Global Gravity Field Recovery Using Solely GPS Tracking and Accelerometer Data from Champ",
    year = "2003",
    journal = "Space Science Reviews",
    url = "https://doi.org/10.1023/a:1026217713133",
    doi = "10.1023/a:1026217713133",
    openalex = "W4232336948"
}

Abstract. Various methods for kinematic and reduced-dynamic precise orbit determination (POD) of Low Earth Orbiters (LEO) were developed based on zero- and double-differencing of GPS carrier-phase measurements with and without ambiguity resolution. In this paper we present the following approaches in LEO precise orbit determination: – zero-difference kinematic POD, – zero-difference dynamic POD, – double-difference kinematic POD with and without ambiguity resolution, – double-difference dynamic POD with and without ambiguity resolution, – combined GPS/SLR reduced-dynamic POD. All developed POD approaches except the combination of GPS/SLR were tested using real CHAMP data (May 20-30, 2001) and independently validated with Satellite Laser Ranging (SLR) data over the same 11 days. With SLR measurements, additional combinations are possible and in that case one can speak of combined kinematic or combined reduced-dynamic POD. First results of such a combined GPS/SLR POD will be presented, too. This paper shows what LEO orbit accuracy may be achieved with GPS using different strategies including zerodifference and double-difference approaches. Kinematic versus dynamic orbit determination is presently an interesting issue that will also be discussed in this article.Key words. POD, kinematic orbit, dynamic orbit, LEO, CHAMP, ambiguity resolution, GPS, SLR

@article{doi105194adgeo1472003,
    author = "Švehla, Dražen and Rothacher, Markus",
    title = "Kinematic and reduced-dynamic precise orbit determination of low earth orbiters",
    year = "2003",
    journal = "Advances in geosciences",
    abstract = "Abstract. Various methods for kinematic and reduced-dynamic precise orbit determination (POD) of Low Earth Orbiters (LEO) were developed based on zero- and double-differencing of GPS carrier-phase measurements with and without ambiguity resolution. In this paper we present the following approaches in LEO precise orbit determination: – zero-difference kinematic POD, – zero-difference dynamic POD, – double-difference kinematic POD with and without ambiguity resolution, – double-difference dynamic POD with and without ambiguity resolution, – combined GPS/SLR reduced-dynamic POD. All developed POD approaches except the combination of GPS/SLR were tested using real CHAMP data (May 20-30, 2001) and independently validated with Satellite Laser Ranging (SLR) data over the same 11 days. With SLR measurements, additional combinations are possible and in that case one can speak of combined kinematic or combined reduced-dynamic POD. First results of such a combined GPS/SLR POD will be presented, too. This paper shows what LEO orbit accuracy may be achieved with GPS using different strategies including zerodifference and double-difference approaches. Kinematic versus dynamic orbit determination is presently an interesting issue that will also be discussed in this article.Key words. POD, kinematic orbit, dynamic orbit, LEO, CHAMP, ambiguity resolution, GPS, SLR",
    url = "https://doi.org/10.5194/adgeo-1-47-2003",
    doi = "10.5194/adgeo-1-47-2003",
    openalex = "W2113257274"
}

@article{doi101016jjog200407001,
    author = "Reigber, Christoph and Schmidt, Roland and Flechtner, Frank and König, Rolf and Meyer, Ulrich and Neumayer, Karl-Hans and Schwintzer, P. and Zhu, Sheng Yuan",
    title = "An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S",
    year = "2004",
    journal = "Journal of Geodynamics",
    url = "https://doi.org/10.1016/j.jog.2004.07.001",
    doi = "10.1016/j.jog.2004.07.001",
    openalex = "W2131076696",
    references = "doi10100735402680064, doi1010079783540383666, doi101007978366203482862, doi101007b138105, doi101007bfb0010552, doi1010292000gl011721, doi1010292001jc000888, doi1010292002gl015064, doi1010292003gl018622, doi101029jb074i022p05295"
}

Eleven monthly GRACE gravity field solutions are now available for analyses. We show those fields can be used to recover monthly changes in water storage, both on land and in the ocean, to accuracies of 1.5 cm of water thickness when smoothed over 1000 km. The amplitude of the annually varying signal can be determined to 1.0 cm. Results are 30% better for a 1500 km smoothing radius, and 40% worse for a 750 km radius. We estimate the annually varying component of water storage for three large drainage basins (the Mississippi, the Amazon, and a region draining into the Bay of Bengal), to accuracies of 1.0–1.5 cm.

@article{doi1010292004gl019779,
    author = "Wahr, John and Swenson, Sean and Zlotnicki, Victor and Velicogna, I.",
    title = "Time‐variable gravity from GRACE: First results",
    year = "2004",
    journal = "Geophysical Research Letters",
    abstract = "Eleven monthly GRACE gravity field solutions are now available for analyses. We show those fields can be used to recover monthly changes in water storage, both on land and in the ocean, to accuracies of 1.5 cm of water thickness when smoothed over 1000 km. The amplitude of the annually varying signal can be determined to 1.0 cm. Results are 30\% better for a 1500 km smoothing radius, and 40\% worse for a 750 km radius. We estimate the annually varying component of water storage for three large drainage basins (the Mississippi, the Amazon, and a region draining into the Bay of Bengal), to accuracies of 1.0–1.5 cm.",
    url = "https://doi.org/10.1029/2004gl019779",
    doi = "10.1029/2004gl019779",
    openalex = "W2046930921"
}

The GRACE mission is designed to track changes in the Earth's gravity field for a period of five years. Launched in March 2002, the two GRACE satellites have collected nearly two years of data. A span of data available during the Commissioning Phase was used to obtain initial gravity models. The gravity models developed with this data are more than an order of magnitude better at the long and mid wavelengths than previous models. The error estimates indicate a 2‐cm accuracy uniformly over the land and ocean regions, a consequence of the highly accurate, global and homogenous nature of the GRACE data. These early results are a strong affirmation of the GRACE mission concept.

@article{doi1010292004gl019920,
    author = "Tapley, B. D. and Bettadpur, Srinivas and Watkins, M. M. and Reigber, Ch.",
    title = "The gravity recovery and climate experiment: Mission overview and early results",
    year = "2004",
    journal = "Geophysical Research Letters",
    abstract = "The GRACE mission is designed to track changes in the Earth's gravity field for a period of five years. Launched in March 2002, the two GRACE satellites have collected nearly two years of data. A span of data available during the Commissioning Phase was used to obtain initial gravity models. The gravity models developed with this data are more than an order of magnitude better at the long and mid wavelengths than previous models. The error estimates indicate a 2‐cm accuracy uniformly over the land and ocean regions, a consequence of the highly accurate, global and homogenous nature of the GRACE data. These early results are a strong affirmation of the GRACE mission concept.",
    url = "https://doi.org/10.1029/2004gl019920",
    doi = "10.1029/2004gl019920",
    openalex = "W1588827410",
    references = "doi1010292003gl018622, doi10102992gl02824, doi10251424989, doi10251439749, openalexw2303808595, openalexw2335824682, openalexw2995376352"
}

We have used the new gravity field model GGM01C derived from GRACE data to reanalyze DORIS data from 1993.0 to 2003.2 using the Gipsy/Oasis software and a free‐network approach. We have estimated the position and velocity of each DORIS station in ITRF2000. In order to test the accuracy of these results, we have compared them to the positions and velocities of 43 collocated GPS stations using local ties and covariance information. DORIS results computed using the GGM01C gravity field instead of the EGM96 gravity field show a significantly improved external agreement with GPS. Position agreement of 12–26 mm was reduced to 10–13 mm and velocity agreement of 3.3–3.7 mm/yr was reduced to 2.4–3.3 mm/yr. This can be interpreted as an external test of the accuracy of the new GGM01C gravity field.

@article{doi1010292004gl020038,
    author = "Willis, Pascal and Heflin, M. B.",
    title = "External validation of the GRACE GGM01C gravity field using GPS and DORIS positioning results",
    year = "2004",
    journal = "Geophysical Research Letters",
    abstract = "We have used the new gravity field model GGM01C derived from GRACE data to reanalyze DORIS data from 1993.0 to 2003.2 using the Gipsy/Oasis software and a free‐network approach. We have estimated the position and velocity of each DORIS station in ITRF2000. In order to test the accuracy of these results, we have compared them to the positions and velocities of 43 collocated GPS stations using local ties and covariance information. DORIS results computed using the GGM01C gravity field instead of the EGM96 gravity field show a significantly improved external agreement with GPS. Position agreement of 12–26 mm was reduced to 10–13 mm and velocity agreement of 3.3–3.7 mm/yr was reduced to 2.4–3.3 mm/yr. This can be interpreted as an external test of the accuracy of the new GGM01C gravity field.",
    url = "https://doi.org/10.1029/2004gl020038",
    doi = "10.1029/2004gl020038",
    openalex = "W2093922341"
}

Monthly gravity field estimates made by the twin Gravity Recovery and Climate Experiment (GRACE) satellites have a geoid height accuracy of 2 to 3 millimeters at a spatial resolution as small as 400 kilometers. The annual cycle in the geoid variations, up to 10 millimeters in some regions, peaked predominantly in the spring and fall seasons. Geoid variations observed over South America that can be largely attributed to surface water and groundwater changes show a clear separation between the large Amazon watershed and the smaller watersheds to the north. Such observations will help hydrologists to connect processes at traditional length scales (tens of kilometers or less) to those at regional and global scales.

@article{doi101126science1099192,
    author = "Tapley, B. D. and Bettadpur, Srinivas and Ries, John and Thompson, Paul and Watkins, M. M.",
    title = "GRACE Measurements of Mass Variability in the Earth System",
    year = "2004",
    journal = "Science",
    abstract = "Monthly gravity field estimates made by the twin Gravity Recovery and Climate Experiment (GRACE) satellites have a geoid height accuracy of 2 to 3 millimeters at a spatial resolution as small as 400 kilometers. The annual cycle in the geoid variations, up to 10 millimeters in some regions, peaked predominantly in the spring and fall seasons. Geoid variations observed over South America that can be largely attributed to surface water and groundwater changes show a clear separation between the large Amazon watershed and the smaller watersheds to the north. Such observations will help hydrologists to connect processes at traditional length scales (tens of kilometers or less) to those at regional and global scales.",
    url = "https://doi.org/10.1126/science.1099192",
    doi = "10.1126/science.1099192",
    openalex = "W2092645526",
    references = "doi1010160022169495029656, doi101016s0921818198000472, doi1010291999wr900141, doi1010292001jb000576, doi1010292004gl019920, doi101038303757a0, doi101126science1089802, doi1011751520047719960770437tnyrp20co2, doi101175bams853381, openalexw1549124992"
}

▪ Abstract The 100 kyr quasiperiodic variation of continental ice cover, which has been a persistent feature of climate system evolution throughout the most recent 900 kyr of Earth history, has occurred as a consequence of changes in the seasonal insolation regime forced by the influence of gravitational n-body effects in the Solar System on the geometry of Earth's orbit around the Sun. The impacts of the changing surface ice load upon both Earth's shape and gravitational field, as well as upon sea-level history, have come to be measurable using a variety of geological and geophysical techniques. These observations are invertible to obtain useful information on both the internal viscoelastic structure of the solid Earth and on the detailed spatiotemporal characteristics of glaciation history. This review focuses upon the most recent advances that have been achieved in each of these areas, advances that have proven to be central to the construction of the refined model of the global process of glacial isostatic adjustment, denoted ICE-5G (VM2). A significant test of this new global model will be provided by the global measurement of the time dependence of the gravity field of the planet that will be delivered by the GRACE satellite system that is now in space.

@article{doi101146annurevearth32082503144359,
    author = "Peltier, W. R.",
    title = "GLOBAL GLACIAL ISOSTASY AND THE SURFACE OF THE ICE-AGE EARTH: The ICE-5G (VM2) Model and GRACE",
    year = "2004",
    journal = "Annual Review of Earth and Planetary Sciences",
    abstract = "▪ Abstract The 100 kyr quasiperiodic variation of continental ice cover, which has been a persistent feature of climate system evolution throughout the most recent 900 kyr of Earth history, has occurred as a consequence of changes in the seasonal insolation regime forced by the influence of gravitational n-body effects in the Solar System on the geometry of Earth's orbit around the Sun. The impacts of the changing surface ice load upon both Earth's shape and gravitational field, as well as upon sea-level history, have come to be measurable using a variety of geological and geophysical techniques. These observations are invertible to obtain useful information on both the internal viscoelastic structure of the solid Earth and on the detailed spatiotemporal characteristics of glaciation history. This review focuses upon the most recent advances that have been achieved in each of these areas, advances that have proven to be central to the construction of the refined model of the global process of glacial isostatic adjustment, denoted ICE-5G (VM2). A significant test of this new global model will be provided by the global measurement of the time dependence of the gravity field of the planet that will be delivered by the GRACE satellite system that is now in space.",
    url = "https://doi.org/10.1146/annurev.earth.32.082503.144359",
    doi = "10.1146/annurev.earth.32.082503.144359",
    openalex = "W2112363056",
    references = "doi1010160031920181900467, doi1010160033589478900339, doi101017s0033822200019123, doi10102990jb01583, doi101029jb073i022p07089, doi101029rg010i003p00761, doi101029rg012i004p00649, doi101029rg020i002p00219, doi101038342637a0, doi101038345405a0, doi10103835021035, doi101038364218a0, doi101046j1365246x199800541x, doi101111j1365246x1976tb01251x, doi101111j1365246x1976tb01253x, doi101111j1365246x1982tb04976x, doi101126science1072497, doi101126science2605109771, doi101126science2655169195, doi101126science28754612225, doi101126science28954861897, doi101144gsjgs15230437"
}

@incollection{doi10100735402680064,
    author = "Reigber, Christoph and Jochmann, H. and Wünsch, J. and Petrović, Svetozar and Schwintzer, P. and Barthelmes, Franz and Neumayer, Karl-Hans and König, Rolf and Förste, Christoph and Balmino, G. and Biancale, R. and Lemoine, Jean‐Michel and Loyer, Sylvain and Pérosanz, F.",
    title = "Earth Gravity Field and Seasonal Variability from CHAMP",
    year = "2005",
    url = "https://doi.org/10.1007/3-540-26800-6\_4",
    doi = "10.1007/3-540-26800-6\_4",
    openalex = "W2123374972",
    references = "doi101016s0273117703001625, doi1010292000jc000763, doi1011751525754120020030283gmolwa20co2"
}

@incollection{doi101007bfb0010552,
    author = "Reigber, Christoph",
    title = "Gravity field recovery from satellite tracking data",
    year = "2005",
    booktitle = "Lecture notes in earth sciences",
    url = "https://doi.org/10.1007/bfb0010552",
    doi = "10.1007/bfb0010552",
    openalex = "W1579726472"
}

@article{doi101007s0019000404132,
    author = "Mayer-G�rr, T. and Ilk, Karl Heinz and Eicker, Annette and Feuchtinger, Martin",
    title = "ITG-CHAMP01: a CHAMP gravity field model from short kinematic arcs over a one-year observation period",
    year = "2005",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-004-0413-2",
    doi = "10.1007/s00190-004-0413-2",
    openalex = "W2077680353",
    references = "doi10100735402680064, doi101007978364265590610, doi101007s001900020245x, doi101007s0019000203025, doi101007s0019000303158, doi101016s0273117703001625, doi101023a1008313405488, doi1010292000gl011721, doi1010292004gl019920, doi105194adgeo1472003"
}

@article{doi101007s001900050480z,
    author = "Tapley, B. D. and Ries, John and Bettadpur, Srinivas and Chambers, D. P. and Cheng, Minkang and Condi, F. and Gunter, B. C. and Kang, Zhigui and Nagel, Peter and Pastor, R. and Pekker, T. and Poole, S. R. and Wang, F.",
    title = "GGM02 – An improved Earth gravity field model from GRACE",
    year = "2005",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-005-0480-z",
    doi = "10.1007/s00190-005-0480-z",
    openalex = "W1977431270",
    references = "doi101007s0019000403941, doi101016s027311779900160x, doi1010292003gl018622, doi1010292004gl019779, doi1010292004gl019920, doi1010292004gl020038, doi10108001490410490465300, doi101126science1099192, doi10251424989, openalexw2303808595"
}

Abstract The gravity method was the first geophysical technique to be used in oil and gas exploration. Despite being eclipsed by seismology, it has continued to be an important and sometimes crucial constraint in a number of exploration areas. In oil exploration the gravity method is particularly applicable in salt provinces, overthrust and foothills belts, underexplored basins, and targets of interest that underlie high-velocity zones. The gravity method is used frequently in mining applications to map subsurface geology and to directly calculate ore reserves for some massive sulfide orebodies. There is also a modest increase in the use of gravity techniques in specialized investigations for shallow targets. Gravimeters have undergone continuous improvement during the past 25 years, particularly in their ability to function in a dynamic environment. This and the advent of global positioning systems (GPS) have led to a marked improvement in the quality of marine gravity and have transformed airborne gravity from a regional technique to a prospect-level exploration tool that is particularly applicable in remote areas or transition zones that are otherwise inaccessible. Recently, moving-platform gravity gradiometers have become available and promise to play an important role in future exploration. Data reduction, filtering, and visualization, together with low-cost, powerful personal computers and color graphics, have transformed the interpretation of gravity data. The state of the art is illustrated with three case histories: 3D modeling of gravity data to map aquifers in the Albuquerque Basin, the use of marine gravity gradiometry combined with 3D seismic data to map salt keels in the Gulf of Mexico, and the use of airborne gravity gradiometry in exploration for kimberlites in Canada.

@article{doi10119012133785,
    author = "Nabighian, Misac N. and Ander, Mark E. and Grauch, V.J.S. and Hansen, R. O. and LaFehr, T. R. and Li, Y. and Pearson, William C. and Peirce, John W. and Phillips, Jeffrey D. and Ruder, M. E.",
    title = "Historical development of the gravity method in exploration",
    year = "2005",
    journal = "Geophysics",
    abstract = "Abstract The gravity method was the first geophysical technique to be used in oil and gas exploration. Despite being eclipsed by seismology, it has continued to be an important and sometimes crucial constraint in a number of exploration areas. In oil exploration the gravity method is particularly applicable in salt provinces, overthrust and foothills belts, underexplored basins, and targets of interest that underlie high-velocity zones. The gravity method is used frequently in mining applications to map subsurface geology and to directly calculate ore reserves for some massive sulfide orebodies. There is also a modest increase in the use of gravity techniques in specialized investigations for shallow targets. Gravimeters have undergone continuous improvement during the past 25 years, particularly in their ability to function in a dynamic environment. This and the advent of global positioning systems (GPS) have led to a marked improvement in the quality of marine gravity and have transformed airborne gravity from a regional technique to a prospect-level exploration tool that is particularly applicable in remote areas or transition zones that are otherwise inaccessible. Recently, moving-platform gravity gradiometers have become available and promise to play an important role in future exploration. Data reduction, filtering, and visualization, together with low-cost, powerful personal computers and color graphics, have transformed the interpretation of gravity data. The state of the art is illustrated with three case histories: 3D modeling of gravity data to map aquifers in the Albuquerque Basin, the use of marine gravity gradiometry combined with 3D seismic data to map salt keels in the Gulf of Mexico, and the use of airborne gravity gradiometry in exploration for kimberlites in Canada.",
    url = "https://doi.org/10.1190/1.2133785",
    doi = "10.1190/1.2133785",
    openalex = "W2110931156",
    references = "doi1010160926985194900221, doi101029jz064i001p00049, doi10106313060812"
}

Using time-variable gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) satellite mission, we estimate ice mass changes over Greenland during the period April 2002 to November 2005. After correcting for the effects of spatial filtering and limited resolution of GRACE data, the estimated total ice melting rate over Greenland is -239 +/- 23 cubic kilometers per year, mostly from East Greenland. This estimate agrees remarkably well with a recent assessment of -224 +/- 41 cubic kilometers per year, based on satellite radar interferometry data. GRACE estimates in southeast Greenland suggest accelerated melting since the summer of 2004, consistent with the latest remote sensing measurements.

@article{doi101126science1129007,
    author = "Chen, Jianli and Wilson, Clark R. and Tapley, B. D.",
    title = "Satellite Gravity Measurements Confirm Accelerated Melting of Greenland Ice Sheet",
    year = "2006",
    journal = "Science",
    abstract = "Using time-variable gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) satellite mission, we estimate ice mass changes over Greenland during the period April 2002 to November 2005. After correcting for the effects of spatial filtering and limited resolution of GRACE data, the estimated total ice melting rate over Greenland is -239 +/- 23 cubic kilometers per year, mostly from East Greenland. This estimate agrees remarkably well with a recent assessment of -224 +/- 41 cubic kilometers per year, based on satellite radar interferometry data. GRACE estimates in southeast Greenland suggest accelerated melting since the summer of 2004, consistent with the latest remote sensing measurements.",
    url = "https://doi.org/10.1126/science.1129007",
    doi = "10.1126/science.1129007",
    openalex = "W1973491245",
    references = "doi1010160016703793904512, doi101016jjog200407001"
}

@article{doi101007s0019000701838,
    author = "Förste, Christoph and Schmidt, Roland and Stubenvoll, R. and Flechtner, Frank and Meyer, Ulrich and König, Rolf and Neumayer, H. and Biancale, R. and Lemoine, Jean‐Michel and Bruinsma, Sean and Loyer, Sylvain and Barthelmes, Franz and Esselborn, Saskia",
    title = "The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C",
    year = "2007",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-007-0183-8",
    doi = "10.1007/s00190-007-0183-8",
    openalex = "W2044582720",
    references = "doi101016jjog200407001, doi101016s0273117703001625"
}

Unlike the past International Terrestrial Reference Frame (ITRF) versions where global long‐term solutions were combined, the ITRF2005 uses as input data time series (weekly from satellite techniques and 24‐h session‐wise from Very Long Baseline Interferometry) of station positions and daily Earth Orientation Parameters (EOPs). The advantage of using time series of station positions is that it allows to monitor station non‐linear motion and discontinuities and to examine the temporal behavior of the frame physical parameters, namely the origin and the scale. The ITRF2005 origin is defined in such a way that it has zero translations and translation rates with respect to the Earth center of mass, averaged by the Satellite Laser Ranging (SLR) time series spanning 13 years of observations. Its scale is defined by nullifying the scale and its rate with respect to the Very Long Baseline Interferometry (VLBI) time series spanning 26 years of observations. The ITRF2005 orientation (at epoch 2000.0) and its rate are aligned to the ITRF2000 using 70 stations of high geodetic quality. The estimated level of consistency of the ITRF2005 origin (at epoch 2000.0) and its rate with respect to the ITRF2000 is respectively 0.1, 0.8, 5.8 mm and 0.2, 0.1, 1.8 mm/yr along the X, Y and Z ‐axis. We estimate the formal errors on these components to be 0.3 mm and 0.3 mm/yr. We believe that this low level of agreement between the two frame origins is most probably due to the poor SLR network geometry and its degradation over time. The ITRF2005 combination involving 84 co‐location sites revealed a scale inconsistency of 1 ppb (6.3 mm at the equator), at epoch 2000.0, and 0.08 ppb/yr between the SLR and VLBI long‐term solutions as obtained by the stacking of their respective time series. Possible causes of this inconsistency may include the poor SLR and VLBI networks and their co‐locations, local tie uncertainties, systematic effects and possible inconsistent model corrections used in the data analysis of both techniques. For the first time of the ITRF history, the ITRF2005 rigorous combination provides self‐consistent series of EOPs, including Polar Motion from VLBI and satellite techniques and Universal Time and Length of Day from VLBI only. A velocity field of 152 sites with an error less than 1.5 mm/yr is used to estimate absolute rotation poles of 15 tectonic plates that are consistent with the ITRF2005 frame. This new absolute plate motion model supersedes and significantly improves that of the ITRF2000 which involved six major tectonic plates.

@article{doi1010292007jb004949,
    author = "Altamimi, Z. and Collilieux, Xavier and Legrand, Juliette and Garayt, B. and Boucher, C.",
    title = "ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters",
    year = "2007",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "Unlike the past International Terrestrial Reference Frame (ITRF) versions where global long‐term solutions were combined, the ITRF2005 uses as input data time series (weekly from satellite techniques and 24‐h session‐wise from Very Long Baseline Interferometry) of station positions and daily Earth Orientation Parameters (EOPs). The advantage of using time series of station positions is that it allows to monitor station non‐linear motion and discontinuities and to examine the temporal behavior of the frame physical parameters, namely the origin and the scale. The ITRF2005 origin is defined in such a way that it has zero translations and translation rates with respect to the Earth center of mass, averaged by the Satellite Laser Ranging (SLR) time series spanning 13 years of observations. Its scale is defined by nullifying the scale and its rate with respect to the Very Long Baseline Interferometry (VLBI) time series spanning 26 years of observations. The ITRF2005 orientation (at epoch 2000.0) and its rate are aligned to the ITRF2000 using 70 stations of high geodetic quality. The estimated level of consistency of the ITRF2005 origin (at epoch 2000.0) and its rate with respect to the ITRF2000 is respectively 0.1, 0.8, 5.8 mm and 0.2, 0.1, 1.8 mm/yr along the X, Y and Z ‐axis. We estimate the formal errors on these components to be 0.3 mm and 0.3 mm/yr. We believe that this low level of agreement between the two frame origins is most probably due to the poor SLR network geometry and its degradation over time. The ITRF2005 combination involving 84 co‐location sites revealed a scale inconsistency of 1 ppb (6.3 mm at the equator), at epoch 2000.0, and 0.08 ppb/yr between the SLR and VLBI long‐term solutions as obtained by the stacking of their respective time series. Possible causes of this inconsistency may include the poor SLR and VLBI networks and their co‐locations, local tie uncertainties, systematic effects and possible inconsistent model corrections used in the data analysis of both techniques. For the first time of the ITRF history, the ITRF2005 rigorous combination provides self‐consistent series of EOPs, including Polar Motion from VLBI and satellite techniques and Universal Time and Length of Day from VLBI only. A velocity field of 152 sites with an error less than 1.5 mm/yr is used to estimate absolute rotation poles of 15 tectonic plates that are consistent with the ITRF2005 frame. This new absolute plate motion model supersedes and significantly improves that of the ITRF2000 which involved six major tectonic plates.",
    url = "https://doi.org/10.1029/2007jb004949",
    doi = "10.1029/2007jb004949",
    openalex = "W2102877934",
    references = "doi10102991gl01532"
}

@article{doi101016jpepi200806013,
    author = "Calcagno, Philippe and Chilès, Jean‐Paul and Courrioux, Gabriel and Guillen, Abel",
    title = "Geological modelling from field data and geological knowledge",
    year = "2008",
    journal = "Physics of The Earth and Planetary Interiors",
    url = "https://doi.org/10.1016/j.pepi.2008.06.013",
    doi = "10.1016/j.pepi.2008.06.013",
    openalex = "W1988045831",
    references = "doi101016jpepi200806014"
}

@article{doi101016jpepi200806014,
    author = "Guillen, A. and Calcagno, Philippe and Courrioux, Gabriel and Joly, A. and Ledru, Patrick",
    title = "Geological modelling from field data and geological knowledge",
    year = "2008",
    journal = "Physics of The Earth and Planetary Interiors",
    url = "https://doi.org/10.1016/j.pepi.2008.06.014",
    doi = "10.1016/j.pepi.2008.06.014",
    openalex = "W2104879404",
    references = "doi1010079789401713337, doi101007978940171333736, doi1010160146664x82900788, doi101016jpepi200806013, doi10102994jb03097, doi10106311699114, doi10108001621459194910483310, doi10113719780898717921, doi10119011440645, doi10119011444302, openalexw1574224119"
}

Orientation of a static or slow-moving rigid body can be determined from the measured gravity and local magnetic field vectors. Some formulation of the QUaternion ESTimator (QUEST) algorithm is commonly used to solve this problem. Triads of accelerometers and magnetometers are used to measure gravity and local magnetic field vectors in sensor coordinates. In the QUEST algorithm, local magnetic field measurements affect not only the estimation of yaw but also that of roll and pitch. Due to the deviations in the direction of the magnetic field vector between locations, it is not desirable to use magnetic data in calculations that are related to the determination of roll and pitch. This paper presents a geometrically intuitive 3-degree-of-freedom (3-DOF) orientation estimation algorithm with physical meaning [which is called the factored quaternion algorithm (FQA)], which restricts the use of magnetic data to the determination of the rotation about the vertical axis. The algorithm produces a quaternion output to represent the orientation. Through a derivation based on half-angle formulas and due to the use of quaternions, the computational cost of evaluating trigonometric functions is avoided. Experimental results demonstrate that the proposed algorithm has an overall accuracy that is essentially identical to that of the QUEST algorithm and is computationally more efficient. Additionally, magnetic variations cause only azimuth errors in FQA attitude estimation. A singularity avoidance method is introduced, which allows the algorithm to track through all orientations.

@article{doi101109tim2007911646,
    author = "Xiaoping, Yun and Bachmann, E.R. and McGhee, Robert B.",
    title = "A Simplified Quaternion-Based Algorithm for Orientation Estimation From Earth Gravity and Magnetic Field Measurements",
    year = "2008",
    journal = "IEEE Transactions on Instrumentation and Measurement",
    abstract = "Orientation of a static or slow-moving rigid body can be determined from the measured gravity and local magnetic field vectors. Some formulation of the QUaternion ESTimator (QUEST) algorithm is commonly used to solve this problem. Triads of accelerometers and magnetometers are used to measure gravity and local magnetic field vectors in sensor coordinates. In the QUEST algorithm, local magnetic field measurements affect not only the estimation of yaw but also that of roll and pitch. Due to the deviations in the direction of the magnetic field vector between locations, it is not desirable to use magnetic data in calculations that are related to the determination of roll and pitch. This paper presents a geometrically intuitive 3-degree-of-freedom (3-DOF) orientation estimation algorithm with physical meaning [which is called the factored quaternion algorithm (FQA)], which restricts the use of magnetic data to the determination of the rotation about the vertical axis. The algorithm produces a quaternion output to represent the orientation. Through a derivation based on half-angle formulas and due to the use of quaternions, the computational cost of evaluating trigonometric functions is avoided. Experimental results demonstrate that the proposed algorithm has an overall accuracy that is essentially identical to that of the QUEST algorithm and is computationally more efficient. Additionally, magnetic variations cause only azimuth errors in FQA attitude estimation. A singularity avoidance method is introduced, which allows the algorithm to track through all orientations.",
    url = "https://doi.org/10.1109/tim.2007.911646",
    doi = "10.1109/tim.2007.911646",
    openalex = "W2120665422",
    references = "doi101109tnsre2004827825, doi101109vrais1996490527, doi10111911484149, doi1011371006093, doi1011371007077, doi1011371008080, doi1015159780691211701, doi102307jctvx5wc3k, doi102514319717, openalexw1520013425"
}

@article{doi102312gfzb10308095,
    author = "Dill, Robert",
    title = "Hydrological model LSDM for operational Earth rotation and gravity field variations",
    year = "2008",
    journal = "Publication Database GFZ (GFZ German Research Centre for Geosciences)",
    url = "https://doi.org/10.2312/gfz.b103-08095",
    doi = "10.2312/gfz.b103-08095",
    openalex = "W2309328274"
}

Global gravity field recovery from satellite-to-satellite tracking data with the acceleration approach This thesis is focused on the development of new techniques for global gravity field recovery from high-low (hl) and low-low (ll) satellite-to-satellite tracking (SST) data.There are a number of approaches to global gravity field recovery known from literature, including the variational equations approach, short arc approach, energy balance approach and acceleration approach.The focus of the thesis is the acceleration approach with an aim to produce high-quality global gravity field models using real data from CHAMP and GRACE satellite missions.In the first part, the research is devoted to a refinement of CHAMP hl-SST data processing methodology, which was developed at DEOS earlier.The refinement includes two major updates.The first update is usage of smoothed kinematic orbits, instead of reduced-dynamic ones, in data processing.A procedure based on B-splines has been developed for smoothing kinematic orbits by means of a regularised least-squares adjustment.The second update is the implementation of a data noise estimation procedure from the data themselves, with the aim to obtain a statistically optimal gravity field solution.The refined procedure is used to compute both regularised and a non-regularised models from a nearly one-year set of CHAMP accelerations.The regularized model is proved to be better than the regularized ITG-CHAMP01E model, and slightly better than the older DEOS CHAMP-01C 70 model computed at DEOS.The non-regularized solution is compared to a few non-regularized CHAMP-only models produced by several research groups.The comparison shows that the obtained solution clearly outperforms most of the alternative models.In the second part of the research, the methodology of processing CHAMP hl-SST data is extended to the case of GRACE hl-SST data, including the GRACE kinematic baselines.The kinematic positions and baselines are processed both individually and jointly.It is found that the kinematic baselines themselves are, in general, not favorable for the derivation of gravity field models.We explain this, first of all, by a poor sensitivity of the baseline data to East-West variations of the gravity field.Nevertheless, kinematic baselines slightly improve the quality xii

@book{doi1054419rmsi6z,
    author = "Liu, Xianglin",
    title = "Global gravity field recovery from satellite-to-satellite tracking data with the acceleration approach",
    year = "2008",
    journal = "Publications on geodesy. New series",
    abstract = "Global gravity field recovery from satellite-to-satellite tracking data with the acceleration approach This thesis is focused on the development of new techniques for global gravity field recovery from high-low (hl) and low-low (ll) satellite-to-satellite tracking (SST) data.There are a number of approaches to global gravity field recovery known from literature, including the variational equations approach, short arc approach, energy balance approach and acceleration approach.The focus of the thesis is the acceleration approach with an aim to produce high-quality global gravity field models using real data from CHAMP and GRACE satellite missions.In the first part, the research is devoted to a refinement of CHAMP hl-SST data processing methodology, which was developed at DEOS earlier.The refinement includes two major updates.The first update is usage of smoothed kinematic orbits, instead of reduced-dynamic ones, in data processing.A procedure based on B-splines has been developed for smoothing kinematic orbits by means of a regularised least-squares adjustment.The second update is the implementation of a data noise estimation procedure from the data themselves, with the aim to obtain a statistically optimal gravity field solution.The refined procedure is used to compute both regularised and a non-regularised models from a nearly one-year set of CHAMP accelerations.The regularized model is proved to be better than the regularized ITG-CHAMP01E model, and slightly better than the older DEOS CHAMP-01C 70 model computed at DEOS.The non-regularized solution is compared to a few non-regularized CHAMP-only models produced by several research groups.The comparison shows that the obtained solution clearly outperforms most of the alternative models.In the second part of the research, the methodology of processing CHAMP hl-SST data is extended to the case of GRACE hl-SST data, including the GRACE kinematic baselines.The kinematic positions and baselines are processed both individually and jointly.It is found that the kinematic baselines themselves are, in general, not favorable for the derivation of gravity field models.We explain this, first of all, by a poor sensitivity of the baseline data to East-West variations of the gravity field.Nevertheless, kinematic baselines slightly improve the quality xii",
    url = "https://doi.org/10.54419/rmsi6z",
    doi = "10.54419/rmsi6z",
    openalex = "W1534189594",
    references = "doi10100735402680064, doi101007bf02149761, doi101016003192018990263x, doi1010292002jd003296, doi1010292004gl019920, doi1010292005gl025285, doi10102998jb02844, doi101029rg010i003p00761, doi101146annurevearth32082503144359, doi101175bams853381, doi1023073615195"
}

Author: Förste, Christoph et al.; Genre: Conference Paper; Finally published: 2008; Open Access; Title: EIGEN-GL05C - A new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation

@article{openalexw3006213641,
    author = "Förste, Christoph and Flechtner, Frank and Schmidt, Roland and Stubenvoll, R. and Rothacher, Markus and Kusche, Jürgen and Neumayer, Karl-Hans and Biancale, R. and Lemoine, J. and Barthelmes, Franz and Bruinsma, J. and König, Rolf and Meyer, Ulrich and Field, Gravity and Gravimetry, Geoengineering Centres and Satellites, Geoengineering Centres Earth Observing",
    title = "EIGEN-GL05C - A new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation",
    year = "2008",
    journal = "Publication Database GFZ (GFZ German Research Centre for Geosciences)",
    abstract = "Author: Förste, Christoph et al.; Genre: Conference Paper; Finally published: 2008; Open Access; Title: EIGEN-GL05C - A new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation",
    openalex = "W3006213641"
}

Three approaches are used to reduce the error in the satellite‐derived marine gravity anomalies. First, we have retracked the raw waveforms from the ERS‐1 and Geosat/GM missions resulting in improvements in range precision of 40% and 27%, respectively. Second, we have used the recently published EGM2008 global gravity model as a reference field to provide a seamless gravity transition from land to ocean. Third, we have used a biharmonic spline interpolation method to construct residual vertical deflection grids. Comparisons between shipboard gravity and the global gravity grid show errors ranging from 2.0 mGal in the Gulf of Mexico to 4.0 mGal in areas with rugged seafloor topography. The largest errors of up to 20 mGal occur on the crests of narrow large seamounts. The global spreading ridges are well resolved and show variations in ridge axis morphology and segmentation with spreading rate. For rates less than about 60 mm/a the typical ridge segment is 50–80 km long while it increases dramatically at higher rates (100–1000 km). This transition spreading rate of 60 mm/a also marks the transition from axial valley to axial high. We speculate that a single mechanism controls both transitions; candidates include both lithospheric and asthenospheric processes.

@article{doi1010292008jb006008,
    author = "Sandwell, David T. and Smith, Walter H. F.",
    title = "Global marine gravity from retracked Geosat and ERS‐1 altimetry: Ridge segmentation versus spreading rate",
    year = "2009",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "Three approaches are used to reduce the error in the satellite‐derived marine gravity anomalies. First, we have retracked the raw waveforms from the ERS‐1 and Geosat/GM missions resulting in improvements in range precision of 40\% and 27\%, respectively. Second, we have used the recently published EGM2008 global gravity model as a reference field to provide a seamless gravity transition from land to ocean. Third, we have used a biharmonic spline interpolation method to construct residual vertical deflection grids. Comparisons between shipboard gravity and the global gravity grid show errors ranging from 2.0 mGal in the Gulf of Mexico to 4.0 mGal in areas with rugged seafloor topography. The largest errors of up to 20 mGal occur on the crests of narrow large seamounts. The global spreading ridges are well resolved and show variations in ridge axis morphology and segmentation with spreading rate. For rates less than about 60 mm/a the typical ridge segment is 50–80 km long while it increases dramatically at higher rates (100–1000 km). This transition spreading rate of 60 mm/a also marks the transition from axial valley to axial high. We speculate that a single mechanism controls both transitions; candidates include both lithospheric and asthenospheric processes.",
    url = "https://doi.org/10.1029/2008jb006008",
    doi = "10.1029/2008jb006008",
    openalex = "W2081696323",
    references = "doi101007s001900050480z, doi10102996jb03223, doi10119011442837"
}

Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10‐daily or weekly mean fields. These solutions are derived independently for each time span, i.e., no correlation between the analyzed batches is considered. Following this procedure, an increase in temporal resolution is accompanied by a loss in accuracy. To avoid this problem, a new approach is followed, which takes into account the temporal correlations of the gravity field variations thus enabling the enhancement of the temporal resolution up to daily snapshots. The GRACE Level‐1B (L1B) instrument data processing is performed within the framework of a Kalman filter estimation procedure, where the information about the temporal correlation patterns can be derived from geophysical models. The WaterGAP hydrological model was analyzed to derive the required information in terms of an empirical auto‐covariance function. First results are presented and compared to GFZ‐RL04 monthly and weekly gravity field solutions.

@article{doi1010292009gl039564,
    author = "Kurtenbach, Enrico and Mayer‐Gürr, Torsten and Eicker, Annette",
    title = "Deriving daily snapshots of the Earth's gravity field from GRACE L1B data using Kalman filtering",
    year = "2009",
    journal = "Geophysical Research Letters",
    abstract = "Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10‐daily or weekly mean fields. These solutions are derived independently for each time span, i.e., no correlation between the analyzed batches is considered. Following this procedure, an increase in temporal resolution is accompanied by a loss in accuracy. To avoid this problem, a new approach is followed, which takes into account the temporal correlations of the gravity field variations thus enabling the enhancement of the temporal resolution up to daily snapshots. The GRACE Level‐1B (L1B) instrument data processing is performed within the framework of a Kalman filter estimation procedure, where the information about the temporal correlation patterns can be derived from geophysical models. The WaterGAP hydrological model was analyzed to derive the required information in terms of an empirical auto‐covariance function. First results are presented and compared to GFZ‐RL04 monthly and weekly gravity field solutions.",
    url = "https://doi.org/10.1029/2009gl039564",
    doi = "10.1029/2009gl039564",
    openalex = "W1991211725",
    references = "doi10100797836421022884"
}

important work on mass balance estimates for Greenland

@book{doi1054419hboxky,
    author = "Wittwer, T.",
    title = "Regional gravity field modeling with radial basis functions",
    year = "2009",
    journal = "Publications on geodesy. New series",
    abstract = "important work on mass balance estimates for Greenland",
    url = "https://doi.org/10.54419/hboxky",
    doi = "10.54419/hboxky",
    openalex = "W4312852549",
    references = "doi1054419rmsi6z"
}

@incollection{doi101007978364210228813,
    author = "Mayer‐Gürr, Torsten and Eicker, Annette and Kurtenbach, Enrico and Ilk, Karl-Heinz",
    title = "ITG-GRACE: Global Static and Temporal Gravity Field Models from GRACE Data",
    year = "2010",
    booktitle = "Advanced technologies in earth sciences",
    url = "https://doi.org/10.1007/978-3-642-10228-8\_13",
    doi = "10.1007/978-3-642-10228-8\_13",
    openalex = "W2147716655",
    references = "doi101007s0019000404132"
}

@incollection{doi10100797836421022884,
    author = "Flechtner, Frank and Dahle, Christoph and Neumayer, Karl Hans and König, Rolf and Förste, Christoph",
    title = "The Release 04 CHAMP and GRACE EIGEN Gravity Field Models",
    year = "2010",
    booktitle = "Advanced technologies in earth sciences",
    url = "https://doi.org/10.1007/978-3-642-10228-8\_4",
    doi = "10.1007/978-3-642-10228-8\_4",
    openalex = "W92931290",
    references = "doi10100735402680064, doi101007b138105, doi101007s0019000701838, doi101007s102360060086x, doi101016jjog200407001, doi1010292000gl012234, doi1010292000jc000763, doi1010292001jc001224, doi1010292002gl016473, doi1026153tsw12695, openalexw3006213641, openalexw3187485216"
}

(Abridged) Gamma-ray emission from pulsars has long been modeled using a vacuum dipole field. This approximation ignores changes in the field structure caused by the magnetospheric plasma and strong plasma currents. We present the first results of gamma-ray pulsar light curve modeling using the more realistic field taken from 3D force-free magnetospheric simulations. Having the geometry of the field, we apply several prescriptions for the location of the emission zone, comparing the light curves to observations. We find that the conventional two-pole caustic model fails to produce double-peak pulse profiles, mainly because the size of the polar cap in force-free magnetosphere is larger than the vacuum field polar cap. The conventional outer-gap model is capable of producing only one peak under general conditions, because a large fraction of open field lines does not cross the null charge surface. We propose a novel "separatrix layer" model, where the high-energy emission originates from a thin layer on the open field lines just inside of the separatrix that bounds the open flux tube. The emission from this layer generates two strong caustics on the sky map due to the effect we term "Sky Map Stagnation" (SMS). It is related to the fact that force-free field asymptotically approaches the field of a rotating split monopole, and the photons emitted on such field lines in the outer magnetosphere arrive to the observer in phase. The double-peak light curve is a natural consequence of SMS. We show that most features of the currently available gamma-ray pulsar light curves can be reasonably well reproduced and explained with the sepatratrix model using the force-free field. Association of the emission region with the current sheet will guide more detailed future studies of the magnetospheric acceleration physics.

@article{doi1010880004637x71521282,
    author = "Bai, Xue‐Ning and Spitkovsky, Anatoly",
    title = "MODELING OF GAMMA-RAY PULSAR LIGHT CURVES USING THE FORCE-FREE MAGNETIC FIELD",
    year = "2010",
    journal = "The Astrophysical Journal",
    abstract = {(Abridged) Gamma-ray emission from pulsars has long been modeled using a vacuum dipole field. This approximation ignores changes in the field structure caused by the magnetospheric plasma and strong plasma currents. We present the first results of gamma-ray pulsar light curve modeling using the more realistic field taken from 3D force-free magnetospheric simulations. Having the geometry of the field, we apply several prescriptions for the location of the emission zone, comparing the light curves to observations. We find that the conventional two-pole caustic model fails to produce double-peak pulse profiles, mainly because the size of the polar cap in force-free magnetosphere is larger than the vacuum field polar cap. The conventional outer-gap model is capable of producing only one peak under general conditions, because a large fraction of open field lines does not cross the null charge surface. We propose a novel "separatrix layer" model, where the high-energy emission originates from a thin layer on the open field lines just inside of the separatrix that bounds the open flux tube. The emission from this layer generates two strong caustics on the sky map due to the effect we term "Sky Map Stagnation" (SMS). It is related to the fact that force-free field asymptotically approaches the field of a rotating split monopole, and the photons emitted on such field lines in the outer magnetosphere arrive to the observer in phase. The double-peak light curve is a natural consequence of SMS. We show that most features of the currently available gamma-ray pulsar light curves can be reasonably well reproduced and explained with the sepatratrix model using the force-free field. Association of the emission region with the current sheet will guide more detailed future studies of the magnetospheric acceleration physics.},
    url = "https://doi.org/10.1088/0004-637x/715/2/1282",
    doi = "10.1088/0004-637x/715/2/1282",
    openalex = "W2162631736",
    references = "doi101046j13658711200003031x"
}

@article{doi101007s001900110467x,
    author = "Pail, Roland and Bruinsma, Sean and Migliaccio, Federica and Förste, Christoph and Goiginger, Helmut and Schuh, Wolf‐Dieter and Höck, Eduard and Reguzzoni, Mirko and Brockmann, Jan Martin and Abrikosov, O. A. and Veicherts, M. and Fecher, T. and Mayrhofer, R. and Krasbutter, Ina and Sansò, Fernando and Tscherning, C. C.",
    title = "First GOCE gravity field models derived by three different approaches",
    year = "2011",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-011-0467-x",
    doi = "10.1007/s00190-011-0467-x",
    openalex = "W2146645469",
    references = "doi10100797836421022884, doi101007s0019000404132, doi101007s0019001004017"
}

@article{doi101007s001900110482y,
    author = "Hirt, Christian and Gruber, Th. and Featherstone, W. E.",
    title = "Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights",
    year = "2011",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-011-0482-y",
    doi = "10.1007/s00190-011-0482-y",
    openalex = "W1986184974",
    references = "doi1010079789401713337"
}

Spectral analysis of data noise is performed in the context of gravity field recovery from inter-satellite ranging measurements acquired by the satellite gravimetry mission GRACE. The motivation of the study is two-fold: (i) to promote a further improvement of GRACE data processing techniques and (ii) to assist designing GRACE follow-on missions. The analyzed noise realizations are produced as the difference between the actual GRACE inter-satellite range measurements and the predictions based on state-of-the-art force models. The exploited functional model is based on the so-called “range combinations,” which can be understood as a finite-difference analog of inter-satellite accelerations projected onto the line-of-sight connecting the satellites. It is shown that low-frequency noise is caused by limited accuracy of the computed GRACE orbits. In the first instance, it leads to an inaccurate estimation of the radial component of the inter-satellite velocities. A large impact of this component stems from the fact that it is directly related to centrifugal accelerations, which have to be taken into account when the measured range-accelerations are linked with inter-satellite accelerations. Another effect of orbit inaccuracies is a miscalculation of forces acting on the satellites (particularly, the one described by the zero-degree term of the Earth’s gravitational field). The major contributors to the noise budget at high frequencies (above 9 mHz) are (i) ranging sensor errors and (ii) limited knowledge of the Earth’s static gravity field at high degrees. Importantly, we show that updating the model of the static field on the basis of the available data must be performed with a caution as the result may not be physical due to a non-unique recovery of high-degree coefficients. The source of noise in the range of intermediate frequencies (1–9 mHz), which is particularly critical for an accurate gravity field recovery, is not fully understood yet. We show, however, that it cannot be explained by inaccuracies in background models of time-varying gravity field. It is stressed that most of the obtained results can be treated as sufficiently general (i.e., applicable in the context of a statistically optimal estimation based on any functional model).

@article{doi101007s0019001105316,
    author = "Ditmar, P. and Encarnação, J. and Farahani, H. Hashemi",
    title = "Understanding data noise in gravity field recovery on the basis of inter-satellite ranging measurements acquired by the satellite gravimetry mission GRACE",
    year = "2011",
    journal = "Journal of Geodesy",
    abstract = "Spectral analysis of data noise is performed in the context of gravity field recovery from inter-satellite ranging measurements acquired by the satellite gravimetry mission GRACE. The motivation of the study is two-fold: (i) to promote a further improvement of GRACE data processing techniques and (ii) to assist designing GRACE follow-on missions. The analyzed noise realizations are produced as the difference between the actual GRACE inter-satellite range measurements and the predictions based on state-of-the-art force models. The exploited functional model is based on the so-called “range combinations,” which can be understood as a finite-difference analog of inter-satellite accelerations projected onto the line-of-sight connecting the satellites. It is shown that low-frequency noise is caused by limited accuracy of the computed GRACE orbits. In the first instance, it leads to an inaccurate estimation of the radial component of the inter-satellite velocities. A large impact of this component stems from the fact that it is directly related to centrifugal accelerations, which have to be taken into account when the measured range-accelerations are linked with inter-satellite accelerations. Another effect of orbit inaccuracies is a miscalculation of forces acting on the satellites (particularly, the one described by the zero-degree term of the Earth’s gravitational field). The major contributors to the noise budget at high frequencies (above 9 mHz) are (i) ranging sensor errors and (ii) limited knowledge of the Earth’s static gravity field at high degrees. Importantly, we show that updating the model of the static field on the basis of the available data must be performed with a caution as the result may not be physical due to a non-unique recovery of high-degree coefficients. The source of noise in the range of intermediate frequencies (1–9 mHz), which is particularly critical for an accurate gravity field recovery, is not fully understood yet. We show, however, that it cannot be explained by inaccuracies in background models of time-varying gravity field. It is stressed that most of the obtained results can be treated as sufficiently general (i.e., applicable in the context of a statistically optimal estimation based on any functional model).",
    url = "https://doi.org/10.1007/s00190-011-0531-6",
    doi = "10.1007/s00190-011-0531-6",
    openalex = "W2144839272",
    references = "doi1054419rmsi6z"
}

Land water storage plays a fundamental role in the West African water cycle and has an important impact on climate and on the natural resources of this region. However, measurements of land water storage are scarce at regional and global scales and especially in poorly instrumented endorheic regions, such as most of the Sahel, where little useful information can be derived from river flow measurements and basin water budgets. The Gravity Recovery and Climate Experiment (GRACE) satellite mission provides an accurate measurement of the terrestrial gravity field variations from which land water storage variations can be derived. However, their retrieval is not straightforward, and different methods are employed, which results in different water storage GRACE products. On the other hand, water storage can be estimated by land surface modeling forced with observed or satellite‐based boundary conditions, but such estimates can be highly model dependent. In this study, land water storage by six GRACE products and soil moisture estimations by nine land surface models (run within the framework of the African Monsoon Multidisciplinary Analysis Land Surface Intercomparison Project (ALMIP)) are evaluated over West Africa, with a particular focus on the Sahelian area. The water storage spatial distribution, including zonal transects, its seasonal cycle, and its and interannual variability, are analyzed for the years 2003–2007. Despite the nonnegligible differences among the various GRACE products and among the different models, a generally good agreement between satellite and model estimates is found over the West Africa study region. In particular, GRACE data are shown to reproduce well the water storage interannual variability over the Sahel for the 5 year study period. The comparison between satellite estimates and ALMIP results leads to the identification of processes needing improvement in the land surface models. In particular, our results point out the importance of correctly simulating slow water reservoirs as well as evapotranspiration during the dry season for accurate soil moisture modeling over West Africa.

@article{doi1010292009wr008856,
    author = "Grippa, Manuela and Kergoat, Laurent and Frappart, Frédéric and Araud, Quentin and Boone, Aaron and de Rosnay, Patricia and Lemoine, Jean‐Michel and Gascoin, Simon and Balsamo, Gianpaolo and Ottlé, Catherine and Decharme, Bertrand and Saux‐Picart, S. and Ramillien, Guillaume",
    title = "Land water storage variability over West Africa estimated by Gravity Recovery and Climate Experiment (GRACE) and land surface models",
    year = "2011",
    journal = "Water Resources Research",
    abstract = "Land water storage plays a fundamental role in the West African water cycle and has an important impact on climate and on the natural resources of this region. However, measurements of land water storage are scarce at regional and global scales and especially in poorly instrumented endorheic regions, such as most of the Sahel, where little useful information can be derived from river flow measurements and basin water budgets. The Gravity Recovery and Climate Experiment (GRACE) satellite mission provides an accurate measurement of the terrestrial gravity field variations from which land water storage variations can be derived. However, their retrieval is not straightforward, and different methods are employed, which results in different water storage GRACE products. On the other hand, water storage can be estimated by land surface modeling forced with observed or satellite‐based boundary conditions, but such estimates can be highly model dependent. In this study, land water storage by six GRACE products and soil moisture estimations by nine land surface models (run within the framework of the African Monsoon Multidisciplinary Analysis Land Surface Intercomparison Project (ALMIP)) are evaluated over West Africa, with a particular focus on the Sahelian area. The water storage spatial distribution, including zonal transects, its seasonal cycle, and its and interannual variability, are analyzed for the years 2003–2007. Despite the nonnegligible differences among the various GRACE products and among the different models, a generally good agreement between satellite and model estimates is found over the West Africa study region. In particular, GRACE data are shown to reproduce well the water storage interannual variability over the Sahel for the 5 year study period. The comparison between satellite estimates and ALMIP results leads to the identification of processes needing improvement in the land surface models. In particular, our results point out the importance of correctly simulating slow water reservoirs as well as evapotranspiration during the dry season for accurate soil moisture modeling over West Africa.",
    url = "https://doi.org/10.1029/2009wr008856",
    doi = "10.1029/2009wr008856",
    openalex = "W2087895072",
    references = "doi1054419rmsi6z"
}

[1] Satellite laser ranging (SLR) data were used to determine the variations in the Earth's principal figure axis represented by the degree 2 and order 1 geopotential coefficients: C21 and S21. Significant variations at the annual and Chandler wobble frequencies appear in the SLR time series when the rotational deformation or “pole tides” (i.e., the solid Earth and ocean pole tides) were not modeled. The contribution of the ocean pole tide is estimated to be only ∼8% of the total annual variations in the normalized coefficients: / based on the analysis of SLR data. The amplitude of the nontidal annual variation of is only ∼ 30% of from the SLR time series. The estimates of the annual variation in from SLR, the Gravity Recovery and Climate Experiment (GRACE) and polar motion excitation function, are in a good agreement. The nature of the linear trend for the Earth's figure axis determined by these techniques during the last several years is in general agreement but does not agree as well with results predicted from current glacial isostatic adjustment (GIA) models. The “fluid Love number” for the Earth is estimated to be ∼0.9 based on the position of the mean figure axis from the GRACE gravity model GGM03S and the mean pole defined by the IERS 2003 conventions. The estimate of / from GRACE and SLR provides an improved constraint on the relative rotation of the core. The results presented here indicate a possible tilt of the inner core figure axis of ∼2° and ∼3 arc sec displacement for the figure axis of the entire core.

@article{doi1010292010jb000850,
    author = "Cheng, Minkang and Ries, John and Tapley, B. D.",
    title = "Variations of the Earth's figure axis from satellite laser ranging and GRACE",
    year = "2011",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "[1] Satellite laser ranging (SLR) data were used to determine the variations in the Earth's principal figure axis represented by the degree 2 and order 1 geopotential coefficients: C21 and S21. Significant variations at the annual and Chandler wobble frequencies appear in the SLR time series when the rotational deformation or “pole tides” (i.e., the solid Earth and ocean pole tides) were not modeled. The contribution of the ocean pole tide is estimated to be only ∼8\% of the total annual variations in the normalized coefficients: / based on the analysis of SLR data. The amplitude of the nontidal annual variation of is only ∼ 30\% of from the SLR time series. The estimates of the annual variation in from SLR, the Gravity Recovery and Climate Experiment (GRACE) and polar motion excitation function, are in a good agreement. The nature of the linear trend for the Earth's figure axis determined by these techniques during the last several years is in general agreement but does not agree as well with results predicted from current glacial isostatic adjustment (GIA) models. The “fluid Love number” for the Earth is estimated to be ∼0.9 based on the position of the mean figure axis from the GRACE gravity model GGM03S and the mean pole defined by the IERS 2003 conventions. The estimate of / from GRACE and SLR provides an improved constraint on the relative rotation of the core. The results presented here indicate a possible tilt of the inner core figure axis of ∼2° and ∼3 arc sec displacement for the figure axis of the entire core.",
    url = "https://doi.org/10.1029/2010jb000850",
    doi = "10.1029/2010jb000850",
    openalex = "W2124662745",
    references = "doi101016jjog200407001"
}

[1] We review the sea-level and energy budgets together from 1961, using recent and updated estimates of all terms. From 1972 to 2008, the observed sea-level rise (1.8 ± 0.2 mm yr−1 from tide gauges alone and 2.1 ± 0.2 mm yr−1 from a combination of tide gauges and altimeter observations) agrees well with the sum of contributions (1.8 ± 0.4 mm yr−1) in magnitude and with both having similar increases in the rate of rise during the period. The largest contributions come from ocean thermal expansion (0.8 mm yr−1) and the melting of glaciers and ice caps (0.7 mm yr−1), with Greenland and Antarctica contributing about 0.4 mm yr−1. The cryospheric contributions increase through the period (particularly in the 1990s) but the thermosteric contribution increases less rapidly. We include an improved estimate of aquifer depletion (0.3 mm yr−1), partially offsetting the retention of water in dams and giving a total terrestrial storage contribution of −0.1 mm yr−1. Ocean warming (90% of the total of the Earth's energy increase) continues through to the end of the record, in agreement with continued greenhouse gas forcing. The aerosol forcing, inferred as a residual in the atmospheric energy balance, is estimated as −0.8 ± 0.4 W m−2 for the 1980s and early 1990s. It increases in the late 1990s, as is required for consistency with little surface warming over the last decade. This increase is likely at least partially related to substantial increases in aerosol emissions from developing nations and moderate volcanic activity.

@article{doi1010292011gl048794,
    author = "Church, John and White, Neil J. and Konikow, Leonard F. and Domingues, Catia M. and Cogley, J. Graham and Rignot, Eric and Gregory, Jonathan M. and van den Broeke, M. R. and Monaghan, Andrew J. and Velicogna, I.",
    title = "Revisiting the Earth's sea-level and energy budgets from 1961 to 2008",
    year = "2011",
    journal = "Geophysical Research Letters",
    abstract = "[1] We review the sea-level and energy budgets together from 1961, using recent and updated estimates of all terms. From 1972 to 2008, the observed sea-level rise (1.8 ± 0.2 mm yr−1 from tide gauges alone and 2.1 ± 0.2 mm yr−1 from a combination of tide gauges and altimeter observations) agrees well with the sum of contributions (1.8 ± 0.4 mm yr−1) in magnitude and with both having similar increases in the rate of rise during the period. The largest contributions come from ocean thermal expansion (0.8 mm yr−1) and the melting of glaciers and ice caps (0.7 mm yr−1), with Greenland and Antarctica contributing about 0.4 mm yr−1. The cryospheric contributions increase through the period (particularly in the 1990s) but the thermosteric contribution increases less rapidly. We include an improved estimate of aquifer depletion (0.3 mm yr−1), partially offsetting the retention of water in dams and giving a total terrestrial storage contribution of −0.1 mm yr−1. Ocean warming (90\% of the total of the Earth's energy increase) continues through to the end of the record, in agreement with continued greenhouse gas forcing. The aerosol forcing, inferred as a residual in the atmospheric energy balance, is estimated as −0.8 ± 0.4 W m−2 for the 1980s and early 1990s. It increases in the late 1990s, as is required for consistency with little surface warming over the last decade. This increase is likely at least partially related to substantial increases in aerosol emissions from developing nations and moderate volcanic activity.",
    url = "https://doi.org/10.1029/2011gl048794",
    doi = "10.1029/2011gl048794",
    openalex = "W2104706002",
    references = "doi1011751525754120020030283gmolwa20co2"
}

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.

@article{doi101007s0019001205805,
    author = "Siemes, Christian and Ditmar, P. and Riva, Riccardo and Slobbe, Cornelis and Liu, X. L. and Farahani, H. Hashemi",
    title = "Estimation of mass change trends in the Earth’s system on the basis of GRACE satellite data, with application to Greenland",
    year = "2012",
    journal = "Journal of Geodesy",
    abstract = "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.",
    url = "https://doi.org/10.1007/s00190-012-0580-5",
    doi = "10.1007/s00190-012-0580-5",
    openalex = "W2164504626",
    references = "doi1054419rmsi6z"
}

@article{doi101007s1071201292098,
    author = "Panet, Isabelle and Flury, Jakob and Biancale, R. and Gruber, Thomas and Johannessen, Johnny A. and van den Broeke, M. R. and van Dam, Tonie and Gégout, Pierre and Hughes, Christopher W. and Ramillien, Guillaume and Sasgen, Ingo and Seoane, Lucía and Thomas, Maik",
    title = "Earth System Mass Transport Mission (e.motion): A Concept for Future Earth Gravity Field Measurements from Space",
    year = "2012",
    journal = "Surveys in Geophysics",
    url = "https://doi.org/10.1007/s10712-012-9209-8",
    doi = "10.1007/s10712-012-9209-8",
    openalex = "W2070252593",
    references = "doi1010079789401713337"
}

@article{doi101016jjog201202006,
    author = "Kurtenbach, Enrico and Eicker, Annette and Mayer‐Gürr, Torsten and Holschneider, M. and Hayn, M. and Fuhrmann, M. and Kusche, Jürgen",
    title = "Improved daily GRACE gravity field solutions using a Kalman smoother",
    year = "2012",
    journal = "Journal of Geodynamics",
    url = "https://doi.org/10.1016/j.jog.2012.02.006",
    doi = "10.1016/j.jog.2012.02.006",
    openalex = "W2081496653",
    references = "doi10100797836421022884"
}

EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG‐GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area‐mean free‐air gravity anomalies defined on a 5 arc‐minute equiangular grid. This grid was formed by merging terrestrial, altimetry‐derived, and airborne gravity data. Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography. EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159. Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/Leveling values are on the order of ±5 to ±10 cm. EGM2008 vertical deflections over USA and Australia are within ±1.1 to ±1.3 arc‐seconds of independent astrogeodetic values. These results indicate that EGM2008 performs comparably with contemporary detailed regional geoid models. EGM2008 performs equally well with other GRACE‐based gravitational models in orbit computations. Over EGM96, EGM2008 represents improvement by a factor of six in resolution, and by factors of three to six in accuracy, depending on gravitational quantity and geographic area. EGM2008 represents a milestone and a new paradigm in global gravity field modeling, by demonstrating for the first time ever, that given accurate and detailed gravimetric data, a single global model may satisfy the requirements of a very wide range of applications.

@article{doi1010292011jb008916,
    author = "Pavlis, Nikolaos K. and Holmes, S. A. and Kenyon, S. and Factor, J. K.",
    title = "The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)",
    year = "2012",
    journal = "Journal of Geophysical Research Atmospheres",
    abstract = "EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed by a least squares combination of the ITG‐GRACE03S gravitational model and its associated error covariance matrix, with the gravitational information obtained from a global set of area‐mean free‐air gravity anomalies defined on a 5 arc‐minute equiangular grid. This grid was formed by merging terrestrial, altimetry‐derived, and airborne gravity data. Over areas where only lower resolution gravity data were available, their spectral content was supplemented with gravitational information implied by the topography. EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159. Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/Leveling values are on the order of ±5 to ±10 cm. EGM2008 vertical deflections over USA and Australia are within ±1.1 to ±1.3 arc‐seconds of independent astrogeodetic values. These results indicate that EGM2008 performs comparably with contemporary detailed regional geoid models. EGM2008 performs equally well with other GRACE‐based gravitational models in orbit computations. Over EGM96, EGM2008 represents improvement by a factor of six in resolution, and by factors of three to six in accuracy, depending on gravitational quantity and geographic area. EGM2008 represents a milestone and a new paradigm in global gravity field modeling, by demonstrating for the first time ever, that given accurate and detailed gravimetric data, a single global model may satisfy the requirements of a very wide range of applications.",
    url = "https://doi.org/10.1029/2011jb008916",
    doi = "10.1029/2011jb008916",
    openalex = "W2053987409",
    references = "doi101007s001900050480z, doi1010292004gl019920, doi1010292005gl025285, doi10102996jb03223, doi10102998eo00426, doi101126science27753341956"
}

We calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We present explicit formulas appropriate at zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. We demonstrate that the resulting expressions satisfy the canonical relations $\ensuremath{\Omega}=\ensuremath{-}{P}_{\ensuremath{\parallel}}$ and ${P}_{\ensuremath{\perp}}={P}_{\ensuremath{\parallel}}\ensuremath{-}MB$, with $M=\ensuremath{-}\ensuremath{\partial}\ensuremath{\Omega}/\ensuremath{\partial}B$ being the magnetization of the system. We numerically calculate the resulting pressure anisotropy for a gas of protons and a gas of neutrons and demonstrate that the inclusion of the anomalous magnetic increases the level of pressure anisotropy in both cases.

@article{doi101103physrevd86125032,
    author = "Strickland, Michael and Dexheimer, Verônica and Menezes, Débora P.",
    title = "Bulk properties of a Fermi gas in a magnetic field",
    year = "2012",
    journal = "Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology",
    abstract = "We calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We present explicit formulas appropriate at zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. We demonstrate that the resulting expressions satisfy the canonical relations $\ensuremath{\Omega}=\ensuremath{-}{P}\_{\ensuremath{\parallel}}$ and ${P}\_{\ensuremath{\perp}}={P}\_{\ensuremath{\parallel}}\ensuremath{-}MB$, with $M=\ensuremath{-}\ensuremath{\partial}\ensuremath{\Omega}/\ensuremath{\partial}B$ being the magnetization of the system. We numerically calculate the resulting pressure anisotropy for a gas of protons and a gas of neutrons and demonstrate that the inclusion of the anomalous magnetic increases the level of pressure anisotropy in both cases.",
    url = "https://doi.org/10.1103/physrevd.86.125032",
    doi = "10.1103/physrevd.86.125032",
    openalex = "W2140400799",
    references = "doi101086312104"
}

Abstract Reprocessed Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) gravity gradient data were combined with data from Laser Geodynamics Satellite (LAGEOS) 1/2 and Gravity Recovery and Climate Experiment (GRACE) to generate a satellite‐only gravity field model to degree 260 using the direct approach, named DIR‐R4. When compared to Earth Gravitational Model 2008 (EGM2008), it is more accurate at low to medium resolution thanks to GOCE and GRACE data. When compared to earlier releases of ESA GOCE models, it is more accurate at high degrees owing to the larger amount of data ingested. It is also slightly more accurate than ESA's fourth release of the time‐wise model (TIM‐R4), as demonstrated by GPS/leveling, orbit determination tests, and an oceanographic evaluation. According to the formal, probably too optimistic by a factor of 2–2.5, cumulated geoid (1.3 cm) and gravity anomaly (0.4 mGal) errors at 100 km resolution, the GOCE mission objectives have been reached.

@article{doi101002grl50716,
    author = "Bruinsma, Sean and Förste, Christoph and Abrikosov, O. A. and Marty, Jean‐Charles and Rio, Marie‐Helene and Mulet, Sandrine and Bonvalot, Sylvain",
    title = "The new ESA satellite‐only gravity field model via the direct approach",
    year = "2013",
    journal = "Geophysical Research Letters",
    abstract = "Abstract Reprocessed Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) gravity gradient data were combined with data from Laser Geodynamics Satellite (LAGEOS) 1/2 and Gravity Recovery and Climate Experiment (GRACE) to generate a satellite‐only gravity field model to degree 260 using the direct approach, named DIR‐R4. When compared to Earth Gravitational Model 2008 (EGM2008), it is more accurate at low to medium resolution thanks to GOCE and GRACE data. When compared to earlier releases of ESA GOCE models, it is more accurate at high degrees owing to the larger amount of data ingested. It is also slightly more accurate than ESA's fourth release of the time‐wise model (TIM‐R4), as demonstrated by GPS/leveling, orbit determination tests, and an oceanographic evaluation. According to the formal, probably too optimistic by a factor of 2–2.5, cumulated geoid (1.3 cm) and gravity anomaly (0.4 mGal) errors at 100 km resolution, the GOCE mission objectives have been reached.",
    url = "https://doi.org/10.1002/grl.50716",
    doi = "10.1002/grl.50716",
    openalex = "W1810381590",
    references = "doi101007s0019000404132"
}

In the event of a termination of the Gravity Recovery and Climate Experiment (GRACE) mission before the launch of GRACE Follow‐On (due for launch in 2017), high‐low satellite‐to‐satellite tracking (hl‐SST) will be the only dedicated observing system with global coverage available to measure the time‐variable gravity field (TVG) on a monthly or even shorter time scale. Until recently, hl‐SST TVG observations were of poor quality and hardly improved the performance of Satellite Laser Ranging observations. To date, they have been of only very limited usefulness to geophysical or environmental investigations. In this paper, we apply a thorough reprocessing strategy and a dedicated Kalman filter to Challenging Minisatellite Payload (CHAMP) data to demonstrate that it is possible to derive the very long‐wavelength TVG features down to spatial scales of approximately 2000 km at the annual frequency and for multi‐year trends. The results are validated against GRACE data and surface height changes from long‐term GPS ground stations in Greenland. We find that the quality of the CHAMP solutions is sufficient to derive long‐term trends and annual amplitudes of mass change over Greenland. We conclude that hl‐SST is a viable source of information for TVG and can serve to some extent to bridge a possible gap between the end‐of‐life of GRACE and the availability of GRACE Follow‐On.

@article{doi101002jgrb50283,
    author = "Weigelt, Matthias and van Dam, Tonie and Jäggi, Adrian and Prange, Lars and Tourian, Mohammad J. and Keller, Wolfgang and Sneeuw, Nico",
    title = "Time‐variable gravity signal in Greenland revealed by high‐low satellite‐to‐satellite tracking",
    year = "2013",
    journal = "Journal of Geophysical Research Solid Earth",
    abstract = "In the event of a termination of the Gravity Recovery and Climate Experiment (GRACE) mission before the launch of GRACE Follow‐On (due for launch in 2017), high‐low satellite‐to‐satellite tracking (hl‐SST) will be the only dedicated observing system with global coverage available to measure the time‐variable gravity field (TVG) on a monthly or even shorter time scale. Until recently, hl‐SST TVG observations were of poor quality and hardly improved the performance of Satellite Laser Ranging observations. To date, they have been of only very limited usefulness to geophysical or environmental investigations. In this paper, we apply a thorough reprocessing strategy and a dedicated Kalman filter to Challenging Minisatellite Payload (CHAMP) data to demonstrate that it is possible to derive the very long‐wavelength TVG features down to spatial scales of approximately 2000 km at the annual frequency and for multi‐year trends. The results are validated against GRACE data and surface height changes from long‐term GPS ground stations in Greenland. We find that the quality of the CHAMP solutions is sufficient to derive long‐term trends and annual amplitudes of mass change over Greenland. We conclude that hl‐SST is a viable source of information for TVG and can serve to some extent to bridge a possible gap between the end‐of‐life of GRACE and the availability of GRACE Follow‐On.",
    url = "https://doi.org/10.1002/jgrb.50283",
    doi = "10.1002/jgrb.50283",
    openalex = "W1500800118",
    references = "doi101007s0019001004017"
}

@article{doi101007s0019001306503,
    author = "Farahani, H. Hashemi and Ditmar, P. and Klees, R. and Liu, X. and Zhao, Qilong and Guo, Jing",
    title = "The static gravity field model DGM-1S from GRACE and GOCE data: computation, validation and an analysis of GOCE mission’s added value",
    year = "2013",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-013-0650-3",
    doi = "10.1007/s00190-013-0650-3",
    openalex = "W2012385759",
    references = "doi1054419rmsi6z"
}

Given a solar luminosity LAr = 0.75L0 at the beginning of the Archean 3.8 Ga ago, where L0 is the present-day one, if the heliocentric distance, r, of the Earth was rAr = 0.956r0, the solar irradiance would have been as large as IAr = 0.82I0. It would have allowed for a liquid ocean on the terrestrial surface, which, otherwise, would have been frozen, contrary to the empirical evidence. By further assuming that some physical mechanism subsequently displaced the Earth towards its current distance in such a way that the irradiance stayed substantially constant over the entire Archean from 3.8 to 2.5 Ga ago, a relative recession per year as large as r˙/r ≈3.4 × 10−11 a−1 would have been required. Although such a figure is roughly of the same order of magnitude of the value of the Hubble parameter 3.8 Ga ago HAr = 1.192H0 = 8.2 × 10−11 a−1, standard general relativity rules out cosmological explanations for the hypothesized Earth’s recession rate. Instead, a class of modified theories of gravitation with nonminimal coupling between the matter and the metric naturally predicts a secular variation of the relative distance of a localized two-body system, thus yielding a potentially viable candidate to explain the putative recession of the Earth’s orbit. Another competing mechanism of classical origin that could, in principle, allow for the desired effect is the mass loss, which either the Sun or the Earth itself may have experienced during the Archean. On the one hand, this implies that our planet should have lost 2% of its present mass in the form of eroded/evaporated hydrosphere. On the other hand, it is widely believed that the Sun could have lost mass at an enhanced rate, due to a stronger solar wind in the past for not more than ≈ 0.2–0.3 Ga.

@article{doi103390galaxies1030192,
    author = "Iorio, Lorenzo",
    title = "A Closer Earth and the Faint Young Sun Paradox: Modification of the Laws of Gravitation or Sun/Earth Mass Losses?",
    year = "2013",
    journal = "Galaxies",
    abstract = "Given a solar luminosity LAr = 0.75L0 at the beginning of the Archean 3.8 Ga ago, where L0 is the present-day one, if the heliocentric distance, r, of the Earth was rAr = 0.956r0, the solar irradiance would have been as large as IAr = 0.82I0. It would have allowed for a liquid ocean on the terrestrial surface, which, otherwise, would have been frozen, contrary to the empirical evidence. By further assuming that some physical mechanism subsequently displaced the Earth towards its current distance in such a way that the irradiance stayed substantially constant over the entire Archean from 3.8 to 2.5 Ga ago, a relative recession per year as large as r˙/r ≈3.4 × 10−11 a−1 would have been required. Although such a figure is roughly of the same order of magnitude of the value of the Hubble parameter 3.8 Ga ago HAr = 1.192H0 = 8.2 × 10−11 a−1, standard general relativity rules out cosmological explanations for the hypothesized Earth’s recession rate. Instead, a class of modified theories of gravitation with nonminimal coupling between the matter and the metric naturally predicts a secular variation of the relative distance of a localized two-body system, thus yielding a potentially viable candidate to explain the putative recession of the Earth’s orbit. Another competing mechanism of classical origin that could, in principle, allow for the desired effect is the mass loss, which either the Sun or the Earth itself may have experienced during the Archean. On the one hand, this implies that our planet should have lost 2\% of its present mass in the form of eroded/evaporated hydrosphere. On the other hand, it is widely believed that the Sun could have lost mass at an enhanced rate, due to a stronger solar wind in the past for not more than ≈ 0.2–0.3 Ga.",
    url = "https://doi.org/10.3390/galaxies1030192",
    doi = "10.3390/galaxies1030192",
    openalex = "W2016703604",
    references = "doi101016jnewast201105003"
}

Given a solar luminosity L_Ar = 0.75 L_0 at the beginning of the Archean 3.8 Gyr ago, where L_0 is the present-day one, if the heliocentric distance r of the Earth was r_Ar = 0.956 r_0, the solar irradiance would have been as large as I_Ar = 0.82 I_0. It would allowed for a liquid ocean on the terrestrial surface which, otherwise, would have been frozen, contrary to the empirical evidence. By further assuming that some physical mechanism subsequently displaced the Earth towards its current distance in such a way that the irradiance stayed substantially constant over the entire Archean from 3.8 Gyr to 2.5 Gyr ago, a relative recession rate as large as \dot r/r \simeq 3.4 x 10^-11 yr^-1 would have been required. Although such a figure is roughly of the same order of magnitude of the value of the Hubble parameter 3.8 Gyr ago H_Ar = 1.192 H_0 = 8.2 x 10^-11 yr^-1, standard general relativity rules out cosmological explanations for the hypothesized Earth' s recession rate. Instead, a class of modified theories of gravitation with nonminimal coupling between the matter and the metric naturally predicts a secular variation of the relative distance of a localized two-body system, thus yielding a potentially viable candidate to explain the putative recession of the Earth' s orbit. Another competing mechanism of classical origin which could, in principle, allow for the desired effect is the mass loss which either the Sun or the Earth itself may have experienced during the Archean. On the one hand, this implies that our planet should have lost 2% of its present mass in the form of eroded/evaporated hydrosphere which, thus, should have been two orders of magnitude larger than now. On the other hand, it is widely believed that the Sun could have lost mass at an enhanced rate due to a stronger solar wind in the past for not more than \sim 0.2-0.3 Gyr.

@article{openalexw3104865967,
    author = "Iorio, Lorenzo",
    title = "A Closer Earth and the Faint Young Sun Paradox: Modification of the Laws of Gravitation, or Sun/Earth Mass Losses?",
    year = "2013",
    abstract = "Given a solar luminosity L\_Ar = 0.75 L\_0 at the beginning of the Archean 3.8 Gyr ago, where L\_0 is the present-day one, if the heliocentric distance r of the Earth was r\_Ar = 0.956 r\_0, the solar irradiance would have been as large as I\_Ar = 0.82 I\_0. It would allowed for a liquid ocean on the terrestrial surface which, otherwise, would have been frozen, contrary to the empirical evidence. By further assuming that some physical mechanism subsequently displaced the Earth towards its current distance in such a way that the irradiance stayed substantially constant over the entire Archean from 3.8 Gyr to 2.5 Gyr ago, a relative recession rate as large as \dot r/r \simeq 3.4 x 10^-11 yr^-1 would have been required. Although such a figure is roughly of the same order of magnitude of the value of the Hubble parameter 3.8 Gyr ago H\_Ar = 1.192 H\_0 = 8.2 x 10^-11 yr^-1, standard general relativity rules out cosmological explanations for the hypothesized Earth' s recession rate. Instead, a class of modified theories of gravitation with nonminimal coupling between the matter and the metric naturally predicts a secular variation of the relative distance of a localized two-body system, thus yielding a potentially viable candidate to explain the putative recession of the Earth' s orbit. Another competing mechanism of classical origin which could, in principle, allow for the desired effect is the mass loss which either the Sun or the Earth itself may have experienced during the Archean. On the one hand, this implies that our planet should have lost 2\% of its present mass in the form of eroded/evaporated hydrosphere which, thus, should have been two orders of magnitude larger than now. On the other hand, it is widely believed that the Sun could have lost mass at an enhanced rate due to a stronger solar wind in the past for not more than \sim 0.2-0.3 Gyr.",
    openalex = "W3104865967",
    references = "doi101016jnewast201105003"
}

@article{doi101007s0019001406912,
    author = "Schall, Judith and Eicker, Annette and Kusche, Jürgen",
    title = "The ITG-Goce02 gravity field model from GOCE orbit and gradiometer data based on the short arc approach",
    year = "2014",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-014-0691-2",
    doi = "10.1007/s00190-014-0691-2",
    openalex = "W2007657257",
    references = "doi1010079789401713337"
}

@article{doi101016jicarus201404007,
    author = "Baland, Rose‐Marie and Tobie, G. and Lefèvre, A. and Hoolst, Tim Van",
    title = "Titan’s internal structure inferred from its gravity field, shape, and rotation state",
    year = "2014",
    journal = "Icarus",
    url = "https://doi.org/10.1016/j.icarus.2014.04.007",
    doi = "10.1016/j.icarus.2014.04.007",
    openalex = "W2091111783",
    references = "doi101016jicarus201404006"
}

Continuous observations of temporal variations in the Earth's gravity field have recently become available at an unprecedented resolution of a few hundreds of kilometers. The gravity field is a product of the Earth's mass distribution, and these data-provided by the satellites of the Gravity Recovery And Climate Experiment (GRACE)-can be used to study the exchange of mass both within the Earth and at its surface. Since the launch of the mission in 2002, GRACE data has evolved from being an experimental measurement needing validation from ground truth, to a respected tool for Earth scientists representing a fixed bound on the total change and is now an important tool to help unravel the complex dynamics of the Earth system and climate change. In this review, we present the mission concept and its theoretical background, discuss the data and give an overview of the major advances GRACE has provided in Earth science, with a focus on hydrology, solid Earth sciences, glaciology and oceanography.

@article{doi101088003448857711116801,
    author = "Wouters, Bert and Bonin, J. A. and Chambers, D. P. and Riva, Riccardo and Sasgen, Ingo and Wahr, John",
    title = "GRACE, time-varying gravity, Earth system dynamics and climate change",
    year = "2014",
    journal = "Reports on Progress in Physics",
    abstract = "Continuous observations of temporal variations in the Earth's gravity field have recently become available at an unprecedented resolution of a few hundreds of kilometers. The gravity field is a product of the Earth's mass distribution, and these data-provided by the satellites of the Gravity Recovery And Climate Experiment (GRACE)-can be used to study the exchange of mass both within the Earth and at its surface. Since the launch of the mission in 2002, GRACE data has evolved from being an experimental measurement needing validation from ground truth, to a respected tool for Earth scientists representing a fixed bound on the total change and is now an important tool to help unravel the complex dynamics of the Earth system and climate change. In this review, we present the mission concept and its theoretical background, discuss the data and give an overview of the major advances GRACE has provided in Earth science, with a focus on hydrology, solid Earth sciences, glaciology and oceanography.",
    url = "https://doi.org/10.1088/0034-4885/77/11/116801",
    doi = "10.1088/0034-4885/77/11/116801",
    openalex = "W1969374828",
    references = "doi10100797836421022884, doi101111j1365246x201104952x, doi1054419rmsi6z"
}

Multiple coronal and heliospheric models have been recently upgraded at the Community Coordinated Modeling Center (CCMC), including the Wang-Sheeley-Arge (WSA)-Enlil model, MHD-Around-a-Sphere (MAS)-Enlil model, Space Weather Modeling Framework (SWMF), and heliospheric tomography using interplanetary scintillation data. To investigate the effects of photospheric magnetograms from different sources, different coronal models, and different model versions on the model performance, we run these models in 10 combinations. Choosing seven Carrington rotations in 2007 as the time window, we compare the modeling results with the Operating Mission as Nodes on the Internet data for near-Earth space environment during the late declining phase of solar cycle 23. Visual comparison is proved to be a necessary addition to the quantitative assessment of the models' capabilities in reproducing the time series and statistics of solar wind parameters. The MAS-Enlil model captures the time patterns of solar wind parameters better, while the WSA-Enlil model matches with the time series of normalized solar wind parameters better. Models generally overestimate slow wind temperature and underestimate fast wind temperature and magnetic field. Using improved algorithms, we have identified magnetic field sector boundaries (SBs) and slow-to-fast stream interaction regions (SIRs) as focused structures. The success rate of capturing them and the time offset vary largely with models. For this quiet period, the new version of MAS-Enlil model works best for SBs, while heliospheric tomography works best for SIRs. The new version of SWMF with more physics added needs more development. General strengths and weaknesses for each model are diagnosed to provide an unbiased reference to model developers and users.

@article{doi1010022015sw001174,
    author = "Jian, L. K. and MacNeice, P. J. and Taktakishvili, A. L. and Odstrčil, D. and Jackson, B. V. and Yu, Hsiu-Shan and Riley, Pete and Соколов, И. В. and Evans, R. M.",
    title = "Validation for solar wind prediction at Earth: Comparison of coronal and heliospheric models installed at the CCMC",
    year = "2015",
    journal = "Space Weather",
    abstract = "Multiple coronal and heliospheric models have been recently upgraded at the Community Coordinated Modeling Center (CCMC), including the Wang-Sheeley-Arge (WSA)-Enlil model, MHD-Around-a-Sphere (MAS)-Enlil model, Space Weather Modeling Framework (SWMF), and heliospheric tomography using interplanetary scintillation data. To investigate the effects of photospheric magnetograms from different sources, different coronal models, and different model versions on the model performance, we run these models in 10 combinations. Choosing seven Carrington rotations in 2007 as the time window, we compare the modeling results with the Operating Mission as Nodes on the Internet data for near-Earth space environment during the late declining phase of solar cycle 23. Visual comparison is proved to be a necessary addition to the quantitative assessment of the models' capabilities in reproducing the time series and statistics of solar wind parameters. The MAS-Enlil model captures the time patterns of solar wind parameters better, while the WSA-Enlil model matches with the time series of normalized solar wind parameters better. Models generally overestimate slow wind temperature and underestimate fast wind temperature and magnetic field. Using improved algorithms, we have identified magnetic field sector boundaries (SBs) and slow-to-fast stream interaction regions (SIRs) as focused structures. The success rate of capturing them and the time offset vary largely with models. For this quiet period, the new version of MAS-Enlil model works best for SBs, while heliospheric tomography works best for SIRs. The new version of SWMF with more physics added needs more development. General strengths and weaknesses for each model are diagnosed to provide an unbiased reference to model developers and users.",
    url = "https://doi.org/10.1002/2015sw001174",
    doi = "10.1002/2015sw001174",
    openalex = "W1852780072",
    references = "doi1010292012ja017782"
}

@article{doi101007s0019001407878,
    author = "Dobslaw, Henryk and Bergmann-Wolf, Inga and Dill, Robert and Forootan, Ehsan and Klemann, Volker and Kusche, Jürgen and Sasgen, Ingo",
    title = "The updated ESA Earth System Model for future gravity mission simulation studies",
    year = "2015",
    journal = "Journal of Geodesy",
    url = "https://doi.org/10.1007/s00190-014-0787-8",
    doi = "10.1007/s00190-014-0787-8",
    openalex = "W2028199218",
    references = "doi102312gfzb10308095"
}

The time variable Earth’s gravity field contains information about the mass transport within the system Earth, i.e., the relationship between mass variations in the atmosphere, oceans, land hydrology, and ice sheets. For many years, satellite laser ranging (SLR) observations to geodetic satellites have provided valuable information of the low-degree coefficients of the Earth’s gravity field. Today, the Gravity Recovery and Climate Experiment (GRACE) mission is the major source of information for the time variable field of a high spatial resolution. We recover the low-degree coefficients of the time variable Earth’s gravity field using SLR observations up to nine geodetic satellites: LAGEOS-1, LAGEOS-2, Starlette, Stella, AJISAI, LARES, Larets, BLITS, and Beacon-C. We estimate monthly gravity field coefficients up to degree and order 10/10 for the time span 2003–2013 and we compare the results with the GRACE-derived gravity field coefficients. We show that not only degree-2 gravity field coefficients can be well determined from SLR, but also other coefficients up to degree 10 using the combination of short 1-day arcs for low orbiting satellites and 10-day arcs for LAGEOS-1/2. In this way, LAGEOS-1/2 allow recovering zonal terms, which are associated with long-term satellite orbit perturbations, whereas the tesseral and sectorial terms benefit most from low orbiting satellites, whose orbit modeling deficiencies are minimized due to short 1-day arcs. The amplitudes of the annual signal in the low-degree gravity field coefficients derived from SLR agree with GRACE K-band results at a level of 77 %. This implies that SLR has a great potential to fill the gap between the current GRACE and the future GRACE Follow-On mission for recovering of the seasonal variations and secular trends of the longest wavelengths in gravity field, which are associated with the large-scale mass transport in the system Earth.

@article{doi101007s0019001508251,
    author = "Sośnica, Krzysztof and Jäggi, Adrian and Meyer, Ulrich and Thaller, Daniela and Beutler, Gerhard and Arnold, Daniel and Dach, Rolf",
    title = "Time variable Earth’s gravity field from SLR satellites",
    year = "2015",
    journal = "Journal of Geodesy",
    abstract = "The time variable Earth’s gravity field contains information about the mass transport within the system Earth, i.e., the relationship between mass variations in the atmosphere, oceans, land hydrology, and ice sheets. For many years, satellite laser ranging (SLR) observations to geodetic satellites have provided valuable information of the low-degree coefficients of the Earth’s gravity field. Today, the Gravity Recovery and Climate Experiment (GRACE) mission is the major source of information for the time variable field of a high spatial resolution. We recover the low-degree coefficients of the time variable Earth’s gravity field using SLR observations up to nine geodetic satellites: LAGEOS-1, LAGEOS-2, Starlette, Stella, AJISAI, LARES, Larets, BLITS, and Beacon-C. We estimate monthly gravity field coefficients up to degree and order 10/10 for the time span 2003–2013 and we compare the results with the GRACE-derived gravity field coefficients. We show that not only degree-2 gravity field coefficients can be well determined from SLR, but also other coefficients up to degree 10 using the combination of short 1-day arcs for low orbiting satellites and 10-day arcs for LAGEOS-1/2. In this way, LAGEOS-1/2 allow recovering zonal terms, which are associated with long-term satellite orbit perturbations, whereas the tesseral and sectorial terms benefit most from low orbiting satellites, whose orbit modeling deficiencies are minimized due to short 1-day arcs. The amplitudes of the annual signal in the low-degree gravity field coefficients derived from SLR agree with GRACE K-band results at a level of 77 \%. This implies that SLR has a great potential to fill the gap between the current GRACE and the future GRACE Follow-On mission for recovering of the seasonal variations and secular trends of the longest wavelengths in gravity field, which are associated with the large-scale mass transport in the system Earth.",
    url = "https://doi.org/10.1007/s00190-015-0825-1",
    doi = "10.1007/s00190-015-0825-1",
    openalex = "W422590001",
    references = "doi101007s0019001004017"
}

@article{doi101016jasr201510035,
    author = "Jäggi, Adrian and Dahle, Christoph and Arnold, Daniel and Bock, H. and Meyer, Ulrich and Beutler, Gerhard and van den IJssel, José",
    title = "Swarm kinematic orbits and gravity fields from 18 months of GPS data",
    year = "2015",
    journal = "Advances in Space Research",
    url = "https://doi.org/10.1016/j.asr.2015.10.035",
    doi = "10.1016/j.asr.2015.10.035",
    openalex = "W2199758187",
    references = "doi101007s0019000600299, doi101007s0019001004017"
}

In this work, the Laser Ranged Satellites Experiment (LARASE) is presented. This is a research program that aims to perform new refined tests and measurements of gravitation in the field of the Earth in the weak field and slow motion (WFSM) limit of general relativity (GR). For this objective we use the free available data relative to geodetic passive satellite lasers tracked from a network of ground stations by means of the satellite laser ranging (SLR) technique. After a brief introduction to GR and its WFSM limit, which aims to contextualize the physical background of the tests and measurements that LARASE will carry out, we focus on the current limits of validation of GR and on current constraints on the alternative theories of gravity that have been obtained with the precise SLR measurements of the two LAGEOS satellites performed so far. Afterward, we present the scientific goals of LARASE in terms of upcoming measurements and tests of relativistic physics. Finally, we introduce our activities and we give a number of new results regarding the improvements to the modelling of both gravitational and non-gravitational perturbations to the orbit of the satellites. These activities are a needed prerequisite to improve the forthcoming new measurements of gravitation. An innovation with respect to the past is the specialization of the models to the LARES satellite, especially for what concerns the modelling of its spin evolution, the neutral drag perturbation and the impact of Earth's solid tides on the satellite orbit.

@article{doi101088026493813215155012,
    author = "Lucchesi, David and Anselmo, Luciano and Bassan, M. and Pardini, Carmen and Peron, Roberto and Pucacco, Giuseppe and Visco, M.",
    title = "Testing the gravitational interaction in the field of the Earth via satellite laser ranging and the Laser Ranged Satellites Experiment (LARASE)",
    year = "2015",
    journal = "Classical and Quantum Gravity",
    abstract = "In this work, the Laser Ranged Satellites Experiment (LARASE) is presented. This is a research program that aims to perform new refined tests and measurements of gravitation in the field of the Earth in the weak field and slow motion (WFSM) limit of general relativity (GR). For this objective we use the free available data relative to geodetic passive satellite lasers tracked from a network of ground stations by means of the satellite laser ranging (SLR) technique. After a brief introduction to GR and its WFSM limit, which aims to contextualize the physical background of the tests and measurements that LARASE will carry out, we focus on the current limits of validation of GR and on current constraints on the alternative theories of gravity that have been obtained with the precise SLR measurements of the two LAGEOS satellites performed so far. Afterward, we present the scientific goals of LARASE in terms of upcoming measurements and tests of relativistic physics. Finally, we introduce our activities and we give a number of new results regarding the improvements to the modelling of both gravitational and non-gravitational perturbations to the orbit of the satellites. These activities are a needed prerequisite to improve the forthcoming new measurements of gravitation. An innovation with respect to the past is the specialization of the models to the LARES satellite, especially for what concerns the modelling of its spin evolution, the neutral drag perturbation and the impact of Earth's solid tides on the satellite orbit.",
    url = "https://doi.org/10.1088/0264-9381/32/15/155012",
    doi = "10.1088/0264-9381/32/15/155012",
    openalex = "W1629328301",
    references = "doi1010079789401713337, doi101029jb090ib11p09301, doi101029jb090ib11p09312"
}

Abstract The intense plume activity at the South Pole of Enceladus together with the recent detection of libration hints at an internal water ocean underneath the outer ice shell. However, the interpretation of gravity, shape, and libration data leads to contradicting results regarding the depth of ocean/ice interface and the total volume of the ocean. Here we develop an interior structure model consisting of a rocky core, an internal ocean, and an ice shell, which satisfies simultaneously the gravity, shape, and libration data. We show that the data can be reconciled by considering isostatic compensation including the effect of a few hundred meter thick elastic lithosphere. Our model predicts that the core radius is 180–185 km, the ocean density is at least 1030 kg/m 3, and the ice shell is 18–22 km thick on average. The ice thicknesses are reduced at poles decreasing to less than 5 km in the south polar region.

@article{doi1010022016gl068634,
    author = "Čadek, Ondřej and Tobie, G. and Hoolst, Tim Van and Massé, M. and Choblet, G. and Lefèvre, A. and Mitri, Giuseppe and Baland, Rose‐Marie and Běhounková, Marie and Bourgeois, Olivier and Trinh, Anthony",
    title = "Enceladus's internal ocean and ice shell constrained from Cassini gravity, shape, and libration data",
    year = "2016",
    journal = "Geophysical Research Letters",
    abstract = "Abstract The intense plume activity at the South Pole of Enceladus together with the recent detection of libration hints at an internal water ocean underneath the outer ice shell. However, the interpretation of gravity, shape, and libration data leads to contradicting results regarding the depth of ocean/ice interface and the total volume of the ocean. Here we develop an interior structure model consisting of a rocky core, an internal ocean, and an ice shell, which satisfies simultaneously the gravity, shape, and libration data. We show that the data can be reconciled by considering isostatic compensation including the effect of a few hundred meter thick elastic lithosphere. Our model predicts that the core radius is 180–185 km, the ocean density is at least 1030 kg/m 3, and the ice shell is 18–22 km thick on average. The ice thicknesses are reduced at poles decreasing to less than 5 km in the south polar region.",
    url = "https://doi.org/10.1002/2016gl068634",
    doi = "10.1002/2016gl068634",
    openalex = "W2406857419",
    references = "doi101016jicarus201404006"
}

The new release AIUB-RL02 of monthly gravity models from GRACE GPS and K-Band range-rate data is based on reprocessed satellite orbits referring to the reference frame IGb08. The release is consistent with the IERS2010 conventions. Improvements with respect to its predecessor AIUB-RL01 include the use of reprocessed (RL02) GRACE observations, new atmosphere and ocean dealiasing products (RL05), an upgraded ocean tide model (EOT11A), and the interpolation of shallow ocean tides (admittances). The stochastic parametrization of AIUB-RL02 was adapted to include daily accelerometer scale factors, which drastically reduces spurious signal at the 161 day period in C20 and at other low degree and order gravity field coefficients. Moreover, the correlation between the noise in the monthly gravity models and solar activity is considerably reduced in the new release. The signal and the noise content of the new AIUB-RL02 monthly gravity fields are studied and calibrated errors are derived from their non-secular and non-seasonal variability. The short-period time-variable signal over the oceans, mostly representing noise, is reduced by 50% with respect to AIUB-RL01. Compared to the official GFZ-RL05a and CSR-RL05 monthly models, the AIUB-RL02 stands out by its low noise at high degrees, a fact emerging from the estimation of seasonal variations for selected river basins and of mass trends in polar regions. Two versions of the monthly AIUB-RL02 gravity models, with spherical harmonics resolution of degree and order 60 and 90, respectively, are available for the time period from March 2003 to March 2014 at the International Center for Global Earth Models (ICGEM) or from ftp://ftp.unibe.ch/aiub/GRAVITY/GRACE

@article{doi101093gjiggw081,
    author = "Meyer, Ulrich and Jäggi, Adrian and Jean, Y. and Beutler, Gerhard",
    title = "AIUB-RL02: an improved time-series of monthly gravity fields from GRACE data",
    year = "2016",
    journal = "Geophysical Journal International",
    abstract = "The new release AIUB-RL02 of monthly gravity models from GRACE GPS and K-Band range-rate data is based on reprocessed satellite orbits referring to the reference frame IGb08. The release is consistent with the IERS2010 conventions. Improvements with respect to its predecessor AIUB-RL01 include the use of reprocessed (RL02) GRACE observations, new atmosphere and ocean dealiasing products (RL05), an upgraded ocean tide model (EOT11A), and the interpolation of shallow ocean tides (admittances). The stochastic parametrization of AIUB-RL02 was adapted to include daily accelerometer scale factors, which drastically reduces spurious signal at the 161 day period in C20 and at other low degree and order gravity field coefficients. Moreover, the correlation between the noise in the monthly gravity models and solar activity is considerably reduced in the new release. The signal and the noise content of the new AIUB-RL02 monthly gravity fields are studied and calibrated errors are derived from their non-secular and non-seasonal variability. The short-period time-variable signal over the oceans, mostly representing noise, is reduced by 50\% with respect to AIUB-RL01. Compared to the official GFZ-RL05a and CSR-RL05 monthly models, the AIUB-RL02 stands out by its low noise at high degrees, a fact emerging from the estimation of seasonal variations for selected river basins and of mass trends in polar regions. Two versions of the monthly AIUB-RL02 gravity models, with spherical harmonics resolution of degree and order 60 and 90, respectively, are available for the time period from March 2003 to March 2014 at the International Center for Global Earth Models (ICGEM) or from ftp://ftp.unibe.ch/aiub/GRAVITY/GRACE",
    url = "https://doi.org/10.1093/gji/ggw081",
    doi = "10.1093/gji/ggw081",
    openalex = "W2328481248",
    references = "doi101007s0019001004017"
}

Over the years, a compact, superconducting gravity gradiometer has been discussed, with the potential for important applications in planetary science, the measurement of gravity waves, and even early warning against earthquakes. Its test-mass dynamics, levitation, and successful operation still need to be verified, though. This study describes the design and construction of the instrument, and reports detailed results and the issues encountered along the way. The data suggest that this promising technology could deliver otherwise unobtainable gravity maps, which can be translated to planetary structural data.

@article{doi101103physrevapplied8064024,
    author = "Griggs, C. E. and Moody, M. V. and Norton, Ronald S. and Paik, Ho Jung and Venkateswara, Krishna",
    title = "Sensitive Superconducting Gravity Gradiometer Constructed with Levitated Test Masses",
    year = "2017",
    journal = "Physical Review Applied",
    abstract = "Over the years, a compact, superconducting gravity gradiometer has been discussed, with the potential for important applications in planetary science, the measurement of gravity waves, and even early warning against earthquakes. Its test-mass dynamics, levitation, and successful operation still need to be verified, though. This study describes the design and construction of the instrument, and reports detailed results and the issues encountered along the way. The data suggest that this promising technology could deliver otherwise unobtainable gravity maps, which can be translated to planetary structural data.",
    url = "https://doi.org/10.1103/physrevapplied.8.064024",
    doi = "10.1103/physrevapplied.8.064024",
    openalex = "W2777498598",
    references = "doi1010079789401713337"
}

The Gravity Recovery and Climate Experiment (GRACE) satellite mission, which was in operation from March 2002 to June 2017, was the first remote sensing mission to provide temporal variations of Terrestrial Water Storage (TWS), which is the sum of the water masses that were contained in the soil column (i.e., snow, surface water, soil moisture, and groundwater), at a spatial resolution of a few hundred kilometers. As in situ level measurements are generally not sufficiently available for monitoring groundwater changes at the regional-scale, this unique dataset, combined with external information, is widely used to quantify the interannual variations of groundwater storage in the world’s major aquifers. GRACE-based groundwater changes revealed significant aquifer depletion over large regions, such as the Middle East, the northwest India aquifer, the North China Plain aquifer, the Murray-Darling Basin in Australia, the High Plains, and the California Central Valley aquifers in the United States of America (USA), but were also used to estimate groundwater-related parameters such as the specific yield, which relates groundwater level to storage, or to define the indices of groundwater depletion and stress. In this review, the approaches used for estimating groundwater storage variations are presented along with the main applications of GRACE data for groundwater monitoring. Issues that were related to the use of GRACE-based TWS are also addressed.

@article{doi103390rs10060829,
    author = "Frappart, Frédéric and Ramillien, Guillaume",
    title = "Monitoring Groundwater Storage Changes Using the Gravity Recovery and Climate Experiment (GRACE) Satellite Mission: A Review",
    year = "2018",
    journal = "Remote Sensing",
    abstract = "The Gravity Recovery and Climate Experiment (GRACE) satellite mission, which was in operation from March 2002 to June 2017, was the first remote sensing mission to provide temporal variations of Terrestrial Water Storage (TWS), which is the sum of the water masses that were contained in the soil column (i.e., snow, surface water, soil moisture, and groundwater), at a spatial resolution of a few hundred kilometers. As in situ level measurements are generally not sufficiently available for monitoring groundwater changes at the regional-scale, this unique dataset, combined with external information, is widely used to quantify the interannual variations of groundwater storage in the world’s major aquifers. GRACE-based groundwater changes revealed significant aquifer depletion over large regions, such as the Middle East, the northwest India aquifer, the North China Plain aquifer, the Murray-Darling Basin in Australia, the High Plains, and the California Central Valley aquifers in the United States of America (USA), but were also used to estimate groundwater-related parameters such as the specific yield, which relates groundwater level to storage, or to define the indices of groundwater depletion and stress. In this review, the approaches used for estimating groundwater storage variations are presented along with the main applications of GRACE data for groundwater monitoring. Issues that were related to the use of GRACE-based TWS are also addressed.",
    url = "https://doi.org/10.3390/rs10060829",
    doi = "10.3390/rs10060829",
    openalex = "W2803686615",
    references = "doi101007s001900050480z, doi101016jjog200407001"
}

Abstract Earth System Models (ESMs) are essential tools for understanding and predicting global change, but they cannot explicitly resolve hillslope‐scale terrain structures that fundamentally organize water, energy, and biogeochemical stores and fluxes at subgrid scales. Here we bring together hydrologists, Critical Zone scientists, and ESM developers, to explore how hillslope structures may modulate ESM grid‐level water, energy, and biogeochemical fluxes. In contrast to the one‐dimensional (1‐D), 2‐ to 3‐m deep, and free‐draining soil hydrology in most ESM land models, we hypothesize that 3‐D, lateral ridge‐to‐valley flow through shallow and deep paths and insolation contrasts between sunny and shady slopes are the top two globally quantifiable organizers of water and energy (and vegetation) within an ESM grid cell. We hypothesize that these two processes are likely to impact ESM predictions where (and when) water and/or energy are limiting. We further hypothesize that, if implemented in ESM land models, these processes will increase simulated continental water storage and residence time, buffering terrestrial ecosystems against seasonal and interannual droughts. We explore efficient ways to capture these mechanisms in ESMs and identify critical knowledge gaps preventing us from scaling up hillslope to global processes. One such gap is our extremely limited knowledge of the subsurface, where water is stored (supporting vegetation) and released to stream baseflow (supporting aquatic ecosystems). We conclude with a set of organizing hypotheses and a call for global syntheses activities and model experiments to assess the impact of hillslope hydrology on global change predictions.

@article{doi1010292018wr023903,
    author = "Fan, Ying and Clark, Martyn and Lawrence, David M. and Swenson, Sean and Band, Lawrence E. and Brantley, Susan L. and Brooks, P. D. and Dietrich, W. E. and Flores, Alejandro N. and Grant, Gordon E. and Kirchner, James W. and Mackay, D. S. and McDonnell, Jeffrey J. and Milly, P. C. D. and Sullivan, Pamela and Tague, C. and Ajami, Hoori and Chaney, Nathaniel W. and Hartmann, Andreas and Hazenberg, P. and McNamara, J. P. and Pelletier, Jon D. and Perket, J. and Freund, Elham Rouholahnejad and Wagener, Thorsten and Zeng, Xubin and Beighley, R. Edward and Buzan, Jonathan and Huang, Maoyi and Livneh, Ben and Mohanty, Binayak P. and Nijssen, Bart and Safeeq, Mohammad and Shen, Chaopeng and van Verseveld, Willem and Volk, John and Yamazaki, Dai",
    title = "Hillslope Hydrology in Global Change Research and Earth System Modeling",
    year = "2019",
    journal = "Water Resources Research",
    abstract = "Abstract Earth System Models (ESMs) are essential tools for understanding and predicting global change, but they cannot explicitly resolve hillslope‐scale terrain structures that fundamentally organize water, energy, and biogeochemical stores and fluxes at subgrid scales. Here we bring together hydrologists, Critical Zone scientists, and ESM developers, to explore how hillslope structures may modulate ESM grid‐level water, energy, and biogeochemical fluxes. In contrast to the one‐dimensional (1‐D), 2‐ to 3‐m deep, and free‐draining soil hydrology in most ESM land models, we hypothesize that 3‐D, lateral ridge‐to‐valley flow through shallow and deep paths and insolation contrasts between sunny and shady slopes are the top two globally quantifiable organizers of water and energy (and vegetation) within an ESM grid cell. We hypothesize that these two processes are likely to impact ESM predictions where (and when) water and/or energy are limiting. We further hypothesize that, if implemented in ESM land models, these processes will increase simulated continental water storage and residence time, buffering terrestrial ecosystems against seasonal and interannual droughts. We explore efficient ways to capture these mechanisms in ESMs and identify critical knowledge gaps preventing us from scaling up hillslope to global processes. One such gap is our extremely limited knowledge of the subsurface, where water is stored (supporting vegetation) and released to stream baseflow (supporting aquatic ecosystems). We conclude with a set of organizing hypotheses and a call for global syntheses activities and model experiments to assess the impact of hillslope hydrology on global change predictions.",
    url = "https://doi.org/10.1029/2018wr023903",
    doi = "10.1029/2018wr023903",
    openalex = "W2916772745",
    references = "doi1010022015wr017037, doi1010291998rg900002, doi1011751525754120020030283gmolwa20co2"
}

Abstract ITSG‐Grace2018 is a new series of GRACE‐only gravity field solutions based on reprocessed GRACE observation data (L1B RL03) and the latest atmosphere and ocean dealiasing product (AOD1B RL06). It includes unconstrained monthly and constrained daily solutions, as well as a high‐resolution static gravity field. Compared to the previous ITSG release, we implemented a number of improvements within the processing chain and use updated background models. In an effort to better model all known error sources, we propagate synthetic orientation uncertainties of the star camera assembly to the antenna offset correction for intersatellite ranging observations. This enables the disentanglement of the stationary noise of the K‐Band system and the nonstationary noise of the antenna offset correction. We further incorporated uncertainties of the atmosphere and ocean dealiasing product to reduce temporal aliasing effects. To mitigate errors in the applied ocean tide model, we used constrained GRACE estimates of selected tidal constituents as an additional background model. Variability over quiet ocean areas suggests a 27% to 46% lower noise level compared to the current spherical harmonic solutions of the official processing centers (300 km Gaussian filter applied). To ensure that the low noise floor is not accompanied by signal loss, we examined drainage basin averages, which showed consistent amplitudes with the official GRACE time series. These evaluations lead to the conclusion that ITSG‐Grace2018 is a state‐of‐the‐art GRACE time series which exhibits an excellent signal‐to‐noise ratio.

@article{doi1010292019jb017415,
    author = "Kvas, Andreas and Behzadpour, Saniya and Ellmer, Matthias and Klinger, Beate and Strasser, Sebastian and Zehentner, Norbert and Mayer‐Gürr, Torsten",
    title = "ITSG‐Grace2018: Overview and Evaluation of a New GRACE‐Only Gravity Field Time Series",
    year = "2019",
    journal = "Journal of Geophysical Research Solid Earth",
    abstract = "Abstract ITSG‐Grace2018 is a new series of GRACE‐only gravity field solutions based on reprocessed GRACE observation data (L1B RL03) and the latest atmosphere and ocean dealiasing product (AOD1B RL06). It includes unconstrained monthly and constrained daily solutions, as well as a high‐resolution static gravity field. Compared to the previous ITSG release, we implemented a number of improvements within the processing chain and use updated background models. In an effort to better model all known error sources, we propagate synthetic orientation uncertainties of the star camera assembly to the antenna offset correction for intersatellite ranging observations. This enables the disentanglement of the stationary noise of the K‐Band system and the nonstationary noise of the antenna offset correction. We further incorporated uncertainties of the atmosphere and ocean dealiasing product to reduce temporal aliasing effects. To mitigate errors in the applied ocean tide model, we used constrained GRACE estimates of selected tidal constituents as an additional background model. Variability over quiet ocean areas suggests a 27\% to 46\% lower noise level compared to the current spherical harmonic solutions of the official processing centers (300 km Gaussian filter applied). To ensure that the low noise floor is not accompanied by signal loss, we examined drainage basin averages, which showed consistent amplitudes with the official GRACE time series. These evaluations lead to the conclusion that ITSG‐Grace2018 is a state‐of‐the‐art GRACE time series which exhibits an excellent signal‐to‐noise ratio.",
    url = "https://doi.org/10.1029/2019jb017415",
    doi = "10.1029/2019jb017415",
    openalex = "W2968421659",
    references = "doi102312gfzb10308095"
}

Abstract Ocean tides produce significant gravitational perturbations that affect near‐Earth orbiting spacecraft. The gravitational potential induced by tidal mass redistribution is routinely modeled for global gravity analysis and orbit determination, although generally by assuming a spherical Earth and a uniform seawater density. The inadequacy of these simplifications is here addressed. We have developed an accurate yet efficient algorithm to compute the ocean tidal geopotential, allowing for Earth's elliptical shape and variable seawater density. Using this new computation, we find that (1) the effect of ellipticity is several percent of the tide signal over mid to high‐latitude regions, which is comparable to elevation error in the state‐of‐the‐art ocean tide models; (2) the effect of seawater density variations on the potential is as large as 2–3 cm in water‐height equivalent, primarily in deep water where density increases 2%–3% from compressibility. Our analysis of new Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) laser ranging interferometer measurements reveals evident errors when ellipticity and density variations are ignored. When accounted for, the GRACE‐FO residual tidal gravity perturbations are reduced by half, depending on the adopted tide model; only the remaining half likely represents actual model elevation error. The use of a spherical surface and a uniform seawater density is no longer tenable given the precision of gravity measurements from GRACE and GRACE‐FO satellites.

@article{doi1010292020jc016774,
    author = "Han, Shin‐Chan and Ghobadi‐Far, Khosro and Ray, Richard D. and Papanikolaou, Thomas",
    title = "Tidal Geopotential Dependence on Earth Ellipticity and Seawater Density and Its Detection With the GRACE Follow‐On Laser Ranging Interferometer",
    year = "2020",
    journal = "Journal of Geophysical Research Oceans",
    abstract = "Abstract Ocean tides produce significant gravitational perturbations that affect near‐Earth orbiting spacecraft. The gravitational potential induced by tidal mass redistribution is routinely modeled for global gravity analysis and orbit determination, although generally by assuming a spherical Earth and a uniform seawater density. The inadequacy of these simplifications is here addressed. We have developed an accurate yet efficient algorithm to compute the ocean tidal geopotential, allowing for Earth's elliptical shape and variable seawater density. Using this new computation, we find that (1) the effect of ellipticity is several percent of the tide signal over mid to high‐latitude regions, which is comparable to elevation error in the state‐of‐the‐art ocean tide models; (2) the effect of seawater density variations on the potential is as large as 2–3 cm in water‐height equivalent, primarily in deep water where density increases 2\%–3\% from compressibility. Our analysis of new Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) laser ranging interferometer measurements reveals evident errors when ellipticity and density variations are ignored. When accounted for, the GRACE‐FO residual tidal gravity perturbations are reduced by half, depending on the adopted tide model; only the remaining half likely represents actual model elevation error. The use of a spherical surface and a uniform seawater density is no longer tenable given the precision of gravity measurements from GRACE and GRACE‐FO satellites.",
    url = "https://doi.org/10.1029/2020jc016774",
    doi = "10.1029/2020jc016774",
    openalex = "W3097844678",
    references = "doi101016jicarus2019113412"
}

Abstract. GOCO06s is the latest satellite-only global gravity field model computed by the GOCO (Gravity Observation Combination) project. It is based on over a billion observations acquired over 15 years from 19 satellites with different complementary observation principles. This combination of different measurement techniques is key in providing consistently high accuracy and best possible spatial resolution of the Earth's gravity field. The motivation for the new release was the availability of reprocessed observation data for the Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE), updated background models, and substantial improvements in the processing chains of the individual contributions. Due to the long observation period, the model consists not only of a static gravity field, but comprises additionally modeled temporal variations. These are represented by time-variable spherical harmonic coefficients, using a deterministic model for a regularized trend and annual oscillation. The main focus within the GOCO combination process is on the proper handling of the stochastic behavior of the input data. Appropriate noise modeling for the observations used results in realistic accuracy information for the derived gravity field solution. This accuracy information, represented by the full variance–covariance matrix, is extremely useful for further combination with, for example, terrestrial gravity data and is published together with the solution. The primary model data consisting of potential coefficients representing Earth's static gravity field, together with secular and annual variations, are available on the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/, last access: 11 June 2020). This data set is identified with the following DOI: https://doi.org/10.5880/ICGEM.2019.002 (Kvas et al., 2019b). Supplementary material consisting of the full variance–covariance matrix of the static potential coefficients and estimated co-seismic mass changes is available at https://ifg.tugraz.at/GOCO (last access: 11 June 2020).

@article{doi105194essd13992021,
    author = "Kvas, Andreas and Brockmann, Jan Martin and Krauß, Sandro and Schubert, Till and Gruber, Thomas and Meyer, Ulrich and Mayer‐Gürr, Torsten and Schuh, Wolf‐Dieter and Jäggi, Adrian and Pail, Roland",
    title = "GOCO06s – a satellite-only global gravity field model",
    year = "2021",
    journal = "Earth system science data",
    abstract = "Abstract. GOCO06s is the latest satellite-only global gravity field model computed by the GOCO (Gravity Observation Combination) project. It is based on over a billion observations acquired over 15 years from 19 satellites with different complementary observation principles. This combination of different measurement techniques is key in providing consistently high accuracy and best possible spatial resolution of the Earth's gravity field. The motivation for the new release was the availability of reprocessed observation data for the Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE), updated background models, and substantial improvements in the processing chains of the individual contributions. Due to the long observation period, the model consists not only of a static gravity field, but comprises additionally modeled temporal variations. These are represented by time-variable spherical harmonic coefficients, using a deterministic model for a regularized trend and annual oscillation. The main focus within the GOCO combination process is on the proper handling of the stochastic behavior of the input data. Appropriate noise modeling for the observations used results in realistic accuracy information for the derived gravity field solution. This accuracy information, represented by the full variance–covariance matrix, is extremely useful for further combination with, for example, terrestrial gravity data and is published together with the solution. The primary model data consisting of potential coefficients representing Earth's static gravity field, together with secular and annual variations, are available on the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/, last access: 11 June 2020). This data set is identified with the following DOI: https://doi.org/10.5880/ICGEM.2019.002 (Kvas et al., 2019b). Supplementary material consisting of the full variance–covariance matrix of the static potential coefficients and estimated co-seismic mass changes is available at https://ifg.tugraz.at/GOCO (last access: 11 June 2020).",
    url = "https://doi.org/10.5194/essd-13-99-2021",
    doi = "10.5194/essd-13-99-2021",
    openalex = "W3048387442",
    references = "doi101007s0019001004017"
}

Abstract With a small fraction of marginal subduction zones, the driving mechanism for the North American plate motion is in debate. We construct global mantle flow models simultaneously constrained by geoid and plate motions to investigate the driving forces for the North American plate motion. By comparing the model with only near‐field subducting slabs and that with global subducting slabs, we find that the contribution to the motion of the North American plate from the near‐field Aleutian, central American, and Caribbean slabs is small. In contrast, other far‐field slabs, primarily the major segments around western Pacific subduction margins, provide the dominant large‐scale driving forces for the North American plate motion. The coupling between far‐field slabs and the North American plate suggests a new form of active plate interactions within the global self‐organizing plate tectonic system. We further evaluate the extremely slow seismic velocity anomalies associated with the shallow partial melt around the southwestern North America. Interpreting these negative seismic shear‐velocity anomalies as purely thermal origin generates considerably excessive resistance to the North American plate motion. A significantly reduced velocity‐to‐density scaling for these negative seismic shear‐velocity anomalies must be incorporated into the construction of the buoyancy field to predict the North American plate motion. We also examine the importance of lower mantle buoyancy including the ancient descending Kula‐Farallon plates and the active upwelling below the Pacific margin of the North American plate. Lower mantle buoyancy primarily affects the amplitudes, as opposed to the patterns of both North American and global plate motions.

@article{doi1010292021gc009808,
    author = "Liu, Shangxin and King, Scott D.",
    title = "Dynamics of the North American Plate: Large‐Scale Driving Mechanism From Far‐Field Slabs and the Interpretation of Shallow Negative Seismic Anomalies",
    year = "2022",
    journal = "Geochemistry Geophysics Geosystems",
    abstract = "Abstract With a small fraction of marginal subduction zones, the driving mechanism for the North American plate motion is in debate. We construct global mantle flow models simultaneously constrained by geoid and plate motions to investigate the driving forces for the North American plate motion. By comparing the model with only near‐field subducting slabs and that with global subducting slabs, we find that the contribution to the motion of the North American plate from the near‐field Aleutian, central American, and Caribbean slabs is small. In contrast, other far‐field slabs, primarily the major segments around western Pacific subduction margins, provide the dominant large‐scale driving forces for the North American plate motion. The coupling between far‐field slabs and the North American plate suggests a new form of active plate interactions within the global self‐organizing plate tectonic system. We further evaluate the extremely slow seismic velocity anomalies associated with the shallow partial melt around the southwestern North America. Interpreting these negative seismic shear‐velocity anomalies as purely thermal origin generates considerably excessive resistance to the North American plate motion. A significantly reduced velocity‐to‐density scaling for these negative seismic shear‐velocity anomalies must be incorporated into the construction of the buoyancy field to predict the North American plate motion. We also examine the importance of lower mantle buoyancy including the ancient descending Kula‐Farallon plates and the active upwelling below the Pacific margin of the North American plate. Lower mantle buoyancy primarily affects the amplitudes, as opposed to the patterns of both North American and global plate motions.",
    url = "https://doi.org/10.1029/2021gc009808",
    doi = "10.1029/2021gc009808",
    openalex = "W4213205349",
    references = "doi101093gjiggz036"
}

SUMMARY In this study, we developed a new method that can significantly accelerate the forward modelling of gravity fields generated by large-scale tesseroids while keeping the computational accuracy as high as possible. The cost of the high efficiency is that the method only works under the assumptions that (1) all tesseroids in the same latitude band have the same horizontal dimension, (2) the computation points are located at the same surface level and aligned with the horizontal centres of tesseroids and (3) each tesseroid has a constant or linearly varying density. The new method first integrates the kernel function of the Newton’s volume integral analytically in the radial direction to eliminate its dependence on the vertical dimension of the tesseroid, and then expands the integrated kernel function into a Taylor series up to a certain order. Because the Taylor series expansion term of the integrated kernel function is an odd or even function of the difference between the longitudes of the tesseroid and computation point, there exist shifting or swapping symmetry relations among the gravity field of tesseroids. Consequently, the shifting or swapping symmetry is extended to the tesseroids with unequal vertical dimensions. Numerical experiments using the spherical shell model are conducted to verify the effectiveness of the new method. The results show that the computational speed of the new method is about 30 times faster than that of the traditional method, which employs the Gauss–Legendre quadrature rule and a 2-D adaptive subdivision approach, while keeping almost the same computational accuracy. When applying the new method to an ice shell with unequal thicknesses, the results reveal that the relative errors of calculating V, Vz and Vzz are smaller than 10−8, 10−6 and 10−4, respectively if the Taylor series expansion is truncated at order 4, while the computational time consumed by the new method is about 7 times less than that of the traditional method. Finally, the influence of the truncation order on the computational accuracy and the strategies for dividing the latitude band into several parts to further improve the accuracy are discussed.

@article{doi101093gjiggac136,
    author = "Zeng, Xianghang and Wan, Xiaoyun and Lin, Miao and Wang, Wenbin",
    title = "Gravity field forward modelling using tesseroids accelerated by Taylor series expansion and symmetry relations",
    year = "2022",
    journal = "Geophysical Journal International",
    abstract = "SUMMARY In this study, we developed a new method that can significantly accelerate the forward modelling of gravity fields generated by large-scale tesseroids while keeping the computational accuracy as high as possible. The cost of the high efficiency is that the method only works under the assumptions that (1) all tesseroids in the same latitude band have the same horizontal dimension, (2) the computation points are located at the same surface level and aligned with the horizontal centres of tesseroids and (3) each tesseroid has a constant or linearly varying density. The new method first integrates the kernel function of the Newton’s volume integral analytically in the radial direction to eliminate its dependence on the vertical dimension of the tesseroid, and then expands the integrated kernel function into a Taylor series up to a certain order. Because the Taylor series expansion term of the integrated kernel function is an odd or even function of the difference between the longitudes of the tesseroid and computation point, there exist shifting or swapping symmetry relations among the gravity field of tesseroids. Consequently, the shifting or swapping symmetry is extended to the tesseroids with unequal vertical dimensions. Numerical experiments using the spherical shell model are conducted to verify the effectiveness of the new method. The results show that the computational speed of the new method is about 30 times faster than that of the traditional method, which employs the Gauss–Legendre quadrature rule and a 2-D adaptive subdivision approach, while keeping almost the same computational accuracy. When applying the new method to an ice shell with unequal thicknesses, the results reveal that the relative errors of calculating V, Vz and Vzz are smaller than 10−8, 10−6 and 10−4, respectively if the Taylor series expansion is truncated at order 4, while the computational time consumed by the new method is about 7 times less than that of the traditional method. Finally, the influence of the truncation order on the computational accuracy and the strategies for dividing the latitude band into several parts to further improve the accuracy are discussed.",
    url = "https://doi.org/10.1093/gji/ggac136",
    doi = "10.1093/gji/ggac136",
    openalex = "W4225516641",
    references = "doi101016jicarus2019113412"
}

Abstract There are numerous applications in geodesy and other geo-sciences in which the gravitational potential effect or other functions of the potential are computed by forward modelling from a given mass distribution. Different volume discretisations, e.g. prisms, tesseroids or mass layers are used. In order to control the numerical realisation of the forward calculation in the practical application, e.g. in reduction tasks, these evaluation programs should be verified against rigorous analytical solutions. In this contribution, a closed analytical solution for the potential of an ellipsoidal shell as a test body is presented. Furthermore, we derive the respective closed formulae for the gravity vector and the gravity gradient tensor. Program implementations of the tesseroid approach are compared on the basis of this ellipsoidal mass arrangement. For the practical usage, fast-converging expansions in spherical harmonics are provided in addition. The derivation of the formulae is based on a closed solution of the potential of a homogeneous ellipsoid for computation points situated on the rotation axis, which then is extended to the external space.

@article{doi101007s00190023017331,
    author = "Seitz, Kurt and Heck, Bernhard and Abd-Elmotaal, Hussein A.",
    title = "External gravitational field of a homogeneous ellipsoidal shell: a reference for testing gravity modelling software",
    year = "2023",
    journal = "Journal of Geodesy",
    abstract = "Abstract There are numerous applications in geodesy and other geo-sciences in which the gravitational potential effect or other functions of the potential are computed by forward modelling from a given mass distribution. Different volume discretisations, e.g. prisms, tesseroids or mass layers are used. In order to control the numerical realisation of the forward calculation in the practical application, e.g. in reduction tasks, these evaluation programs should be verified against rigorous analytical solutions. In this contribution, a closed analytical solution for the potential of an ellipsoidal shell as a test body is presented. Furthermore, we derive the respective closed formulae for the gravity vector and the gravity gradient tensor. Program implementations of the tesseroid approach are compared on the basis of this ellipsoidal mass arrangement. For the practical usage, fast-converging expansions in spherical harmonics are provided in addition. The derivation of the formulae is based on a closed solution of the potential of a homogeneous ellipsoid for computation points situated on the rotation axis, which then is extended to the external space.",
    url = "https://doi.org/10.1007/s00190-023-01733-1",
    doi = "10.1007/s00190-023-01733-1",
    openalex = "W4378901074",
    references = "doi101016jicarus2019113412"
}

This planetary boundaries framework update finds that six of the nine boundaries are transgressed, suggesting that Earth is now well outside of the safe operating space for humanity. Ocean acidification is close to being breached, while aerosol loading regionally exceeds the boundary. Stratospheric ozone levels have slightly recovered. The transgression level has increased for all boundaries earlier identified as overstepped. As primary production drives Earth system biosphere functions, human appropriation of net primary production is proposed as a control variable for functional biosphere integrity. This boundary is also transgressed. Earth system modeling of different levels of the transgression of the climate and land system change boundaries illustrates that these anthropogenic impacts on Earth system must be considered in a systemic context.

@article{doi101126sciadvadh2458,
    author = "Richardson, Katherine and Steffen, Will and Lucht, Wolfgang and Bendtsen, Jørgen and Cornell, Sarah and Donges, Jonathan F. and Drüke, Markus and Fetzer, Ingo and Bala, Govindasamy and von Bloh, Werner and Feulner, Georg and Fiedler, Stephanie and Gerten, Dieter and Gleeson, Tom and Hofmann, Matthias and Huiskamp, Willem and Kummu, Matti and Mohan, Chinchu and Nogués‐Bravo, David and Petri, Stefan and Porkka, Miina and Rahmstorf, Stefan and Schaphoff, Sibyll and Thonicke, Kirsten and Tobian, Arne and Virkki, Vili and Wang‐Erlandsson, Lan and Weber, L. and Rockström, Johan",
    title = "Earth beyond six of nine planetary boundaries",
    year = "2023",
    journal = "Science Advances",
    abstract = "This planetary boundaries framework update finds that six of the nine boundaries are transgressed, suggesting that Earth is now well outside of the safe operating space for humanity. Ocean acidification is close to being breached, while aerosol loading regionally exceeds the boundary. Stratospheric ozone levels have slightly recovered. The transgression level has increased for all boundaries earlier identified as overstepped. As primary production drives Earth system biosphere functions, human appropriation of net primary production is proposed as a control variable for functional biosphere integrity. This boundary is also transgressed. Earth system modeling of different levels of the transgression of the climate and land system change boundaries illustrates that these anthropogenic impacts on Earth system must be considered in a systemic context.",
    url = "https://doi.org/10.1126/sciadv.adh2458",
    doi = "10.1126/sciadv.adh2458",
    openalex = "W4386706488",
    references = "doi1010022015rg000482, doi101002joc3711, doi101016jtree201508009, doi101021acsest1c04158, doi101038nature11018, doi101038nature25138, doi101046j13652486200300569x, doi101073pnas1711842115, doi101126scienceabn7950, doi1011751525754120020030283gmolwa20co2, doi105194essd99272017"
}

Abstract Relativistic corrections are essential for time transformations between geocentric, solar system barycentric, and lunicentric reference systems to account for differences in gravitational potential and relative motion. As the primary reference for Earth-based systems, Terrestrial Time (TT) provides the foundation for precise synchronization across spatial and temporal frameworks. To ensure consistency with TT, Barycentric Dynamical Time (TDB) must exhibit no average rate difference from TT. Although the International Astronomical Union has established resolutions for transformations between TT and TDB, extending these frameworks to define a lunar surface timescale (TL) is essential for advancing lunar exploration. This paper derives the (TL − TT) transformation, quantifying a secular drift of 56.0256 μ s day −1 and periodic terms, with the largest amplitude of ∼0.470 μ s at the mean anomalistic period. Additionally, the TT -compatible spatial scale and Lorentz contraction of Moon-centered positional coordinates are computed, achieving subnanosecond timing precision. These transformations, implemented in JPL ephemeris generation software, provide a robust framework for high-fidelity relativistic models of lunar timekeeping, enabling further refinements and supporting navigation, communication, and scientific operations in cis-lunar space.

@article{doi10384715384357adcc18,
    author = "Turyshev, Slava G. and Williams, J. G. and Boggs, D. H. and Park, Ryan S.",
    title = "Relativistic Time Transformations between the Solar System Barycenter, Earth, and Moon",
    year = "2025",
    journal = "The Astrophysical Journal",
    abstract = "Abstract Relativistic corrections are essential for time transformations between geocentric, solar system barycentric, and lunicentric reference systems to account for differences in gravitational potential and relative motion. As the primary reference for Earth-based systems, Terrestrial Time (TT) provides the foundation for precise synchronization across spatial and temporal frameworks. To ensure consistency with TT, Barycentric Dynamical Time (TDB) must exhibit no average rate difference from TT. Although the International Astronomical Union has established resolutions for transformations between TT and TDB, extending these frameworks to define a lunar surface timescale (TL) is essential for advancing lunar exploration. This paper derives the (TL − TT) transformation, quantifying a secular drift of 56.0256 μ s day −1 and periodic terms, with the largest amplitude of ∼0.470 μ s at the mean anomalistic period. Additionally, the TT -compatible spatial scale and Lorentz contraction of Moon-centered positional coordinates are computed, achieving subnanosecond timing precision. These transformations, implemented in JPL ephemeris generation software, provide a robust framework for high-fidelity relativistic models of lunar timekeeping, enabling further refinements and supporting navigation, communication, and scientific operations in cis-lunar space.",
    url = "https://doi.org/10.3847/1538-4357/adcc18",
    doi = "10.3847/1538-4357/adcc18",
    openalex = "W4410524686",
    references = "doi101007s1056901395236"
}