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A debris flow barrier is a structure used to prevent erosion caused by debris flow, and is typically installed in countries with mountainous areas, such as Korea. However, owing to earth pressure, several debris flow barriers become damaged. Geofoam is a reinforcement material widely used in the design of debris flow barriers, not only in dams/retaining walls but also in bridges and landscaping. The purpose of this study was to examine the lateral earth pressure reduction effect of geofoam on debris flow barriers, and to find an optimized geofoam shape that satisfies specific conditions. In this study, the debris flow barrier, backfill, geofoam, and foundation were modeled using ABAQUS, a two-dimensional finite element method program. Models A-C were simulated and compared at backfill lengths of 10, 20, and 40 m. The debris flow barrier model was used at a mountain slope of 25°. To determine the geofoam shape and analyze the stability coefficients for sliding and overturning, ten diverse scenarios were considered. According to the results, Scenario 10, with a reversed triangle shape of geofoam, was the most effective in all cases, which reduces the earth pressure significantly. In the case of Model C, a reversed triangle geofoam reinforcement reduces the lateral earth pressure on the backside of the structure by an average of 34.43%. [ABSTRACT FROM AUTHOR]

Precise knowledge of geocenter motion, i.e., the relative motion between the Earth's center of mass (CM) and the center of figure of the Earth's surface (CF), is crucial to high-stakes geodetic applications such as sea-level rise monitoring with satellite altimetry or the establishment of regional and global mass budgets with satellite gravimetry. The computation of the latest release of the International Terrestrial Reference Frame, ITRF2020, involved the estimation of a field of seasonal motions for a global network of geodetic stations, expressed with respect to CM, as sensed by satellite laser ranging, from which the translational part represents seasonal geocenter motion. This paper presents two different methods to isolate seasonal geocenter motion from the field of ITRF2020 seasonal station motions, among which a new method based on a direct weighted average of seasonal station motions, with station-specific weights chosen so as to provide a better approximation of CF than the standard network shift approach. The ITRF2020 annual geocenter motion model thus obtained is then compared with other recent geodetic and geophysical estimates. Although different sub-groups of estimates with relatively good internal consistency may be identified, the overall scatter of recent geodetic estimates remains at the level of several mm, i.e., close to the amplitude of annual geocenter motion itself. Efforts toward reconciling seasonal geocenter motion estimates therefore still appear necessary. Meanwhile, it would seem safe to assume that seasonal geocenter motion models, in particular those currently used in satellite altimetry and satellite gravimetry, are still uncertain. [ABSTRACT FROM AUTHOR]

Understanding the external and internal geodynamical processes shaping the Earth is challenging. Physical, chemical, and biological processes form the ground surface over time. Erosion, weathering, transporting, and sedimentation are the natural processes that shape landscapes. However, the continuous interactions of external geodynamic drivers, such as water, wind, and biota, play vital roles in shaping the Earth's surface. These complex and interconnected processes impact the landscape and environment, making it essential to comprehend them to predict evolution, variability, and changes. This Topical Collection (TC) is a comprehensive set of over 54 articles (to date, it has over 16,500 accesses and 119 citations) focused on Earth's processes and environment in a changing world. It was grounded in paying tribute to the legacy of the outstanding Spanish geomorphologist, geographer, and honorific Professor Augusto Pérez-Alberti, whose thoughtful contributions have significantly advanced the understanding of earth processes, particularly glacial and periglacial processes, sedimentary dynamics, hydromorphology, and coastal geomorphology. Understanding the geodynamics of the processes that shape Earth systems is critical to protecting and preserving ecosystems, landscapes, natural resources, and communities' well-being. [ABSTRACT FROM AUTHOR]

The relative roles of protoplanetary differentiation versus late accretion in establishing Earth's life-essential volatile element inventory are being hotly debated. To address this issue, we employ first-principles calculations to investigate nitrogen (N) isotope fractionation during Earth's accretion and differentiation. We find that segregation of an iron core would enrich heavy N isotopes in the residual silicate, while evaporation within a H2-dominated nebular gas produces an enrichment of light N isotope in the planetesimals. The combined effect of early planetesimal evaporation followed by core formation enriches the bulk silicate Earth in light N isotopes. If Earth is comprised primarily of enstatite-chondrite-like material, as indicated by other isotope systems, then late accretion of carbonaceous-chondrite-like material must contribute ~ 30–100% of the N budget in present-day bulk silicate Earth. However, mass balance using N isotope constraints shows that the late veneer contributes only a limited amount of other volatile elements (e.g., H, S, and C) to Earth. The late veneer impacts Earth's nitrogen budget while exhibiting limited effects on other volatile elements, according to first-principles calculations of N-isotope fractionation during Earth's accretion and differentiation. [ABSTRACT FROM AUTHOR]

Oxygen in marine sediments regulates many key biogeochemical processes, playing a crucial role in shaping Earth's climate and benthic ecosystems. In this context, branched glycerol dialkyl glycerol tetraethers (brGDGTs), essential biomarkers in paleoenvironmental research, exhibit an as-yet-unresolved association with sediment oxygen conditions. Here, we investigated brGDGTs in sediments from three deep-sea regions (4045 to 10,100 m water depth) dominated by three respective trench systems and integrated the results with in situ oxygen microprofile data. Our results demonstrate robust correlations between diffusive oxygen uptake (DOU) obtained from microprofiles and brGDGT methylation and isomerization degrees, indicating their primary production within sediments and their strong linkage with microbial diagenetic activity. We establish a quantitative relationship between the Isomerization and Methylation index of Branched Tetraethers (IMBT) and DOU, suggesting its potential validity across deep-sea environments. Increased brGDGT methylation and isomerization likely enhance the fitness of source organisms in deep-sea habitats. Our study positions brGDGTs as a promising tool for quantifying benthic DOU in deep-sea settings, where DOU is a key metric for assessing sedimentary organic carbon degradation and microbial activity. Xiao et al. uncover a strong linkage between marine bacterial tetraether lipids and benthic oxygen uptake in deepsea trench regions, indicating their potential for assessing microbial diagenetic activity and organic carbon degradation. [ABSTRACT FROM AUTHOR]

GRACE and GRACE Follow-On (FO) missions provide time-variable gravity field models of unprecedented quality that allow for the hydrological, oceanic, and ice mass change studies on a global scale. However, the very low-degree coefficients derived from GRACE and GRACE-FO are of inferior quality due to thermal effects acting on satellites and malfunctioning of the onboard accelerometers. Therefore, C20 and C30 coefficients describing the Earth's oblateness and the pear shape of the Earth, respectively, are being replaced by values derived from satellite laser ranging (SLR) in the standard GRACE solutions. This study assesses the impact of the replacement of low-degree gravity field coefficients in GRACE/GRACE-FO solutions by SLR data on the trend and seasonal signals of ice mass changes in Greenland and Antarctica. We found that the replacement of the low-degree gravity field coefficients changes the estimates of trends by 4, 8, and 22 Gt/year in Greenland, West, and East Antarctica, respectively, depending on the source of SLR coefficients and period for which the coefficients are replaced. In SLR and GRACE solutions, all coefficients of the same order and the same parity of degrees are strongly correlated. Therefore, replacing only two selected coefficients may lead to a biased solution. Thus, we propose to combine GRACE with SLR solutions up to a degree and order 10 × 10 to properly consider the sensitivity of each of the techniques to gravity field coefficients, instead of replacing two coefficients from SLR in GRACE solutions. The combined solution reduces the residual trend of post-glacial rebound from 1.2 to 0.9 Gt/year and from − 57.8 to − 57.0 Gt/year in Scandinavia and South Canada, respectively, when compared to GRACE/GRACE-FO solutions with the replacement of coefficients. The SLR-GRACE combination reduces the noise in the GRACE/GRACE-FO solutions by 8%, from 38 to 35 Gt, in the Fennoscandia region. In the periods when GRACE is at the end of its mission and observations are disrupted, the weights adjust the contribution from SLR and GRACE based on relative ratio of variances from each techniques. Thus, the combined solutions are more consistent with independent geophysical models of glacial isostatic adjustment, and the combinations are affected by smaller noise than the standard GRACE solutions and properly account for different sensitivities of SLR and GRACE techniques to low-degree time-variable gravity field coefficients. [ABSTRACT FROM AUTHOR]

An algorithm and a program for transformation of gravity anomalies for large territories are presented. They use a spherical shape of the Earth and the geodetic coordinates of measuring points. The calculations employ the "quasi-ellipsoidal" model of V.V. Kavraisky, which allows the transition from the geodetic to the spherical coordinate system with increased accuracy. The algorithm is based on a sourcewise approximation of the field values located at the nodes of a regular grid with the latitude-dependent depths of the equivalent sources. To determine the source masses, the system of linear algebraic equations is solved by the steepest descent gradient method with an accelerated calculation of the step. The results of transformation of the gravitational field in the Bouguer reduction for the Kuril Island arc, the adjacent water and land areas located within 40°–54° N, 142°–162° E and having a total area of about 2.4 mln km2, are presented. A slight difference between the results of recalculating the gravity anomalies into the upper half-space using the "spherical" and "quasi-ellipsoidal" models of the Earth is experimentally established. [ABSTRACT FROM AUTHOR]

The real shape of the earth is approximated closer to an ellipsoidal curvature other than a homogeneous half-space. Therefore, the use of the dislocation theory of homogeneous half-space for the farthest epicentral distance brings an error. This study investigates the far-filed effect of dislocation modeling of homogeneous half-space due to the ellipsoidal curvature of the Earth. The co-seismic displacement in South Korea is used for the dislocation modeling of the Tohoku-Oki (TO) Japan earthquake as one of the numerical examples. The obtained slip by using geodetic measurements in South Korea is compared with the measured slip of Japan's geodetic measurements. Analysis of modeled results showed that the obtained result with accuracy is lower than around 20%. Therefore, the study concludes that it can be an error in the use of the dislocation modeling theory of homogeneous half-space for the farthest epicentral distance. [ABSTRACT FROM AUTHOR]

LARES 2, successfully launched on July 13, 2022, is a new generation laser-ranged satellite. LARES is an acronym for LAser RElativity Satellite. The first LARES satellite was successfully launched on February 13, 2012 with the ESA-ASI-AVIO launch vehicle VEGA. LARES 2 was injected with extremely high precision onto a high-altitude orbit at about 5900 km altitude with the new ESA-ASI-AVIO launch vehicle VEGA C. Laser-ranged satellites have many applications, including to test Einstein's theory of general relativity. The main general relativistic phenomenon that LARES 2 will test with high accuracy is the dragging of inertial frames, or frame-dragging. It will also test other aspects and principles of fundamental physics and general relativity, such as the weak equivalence principle at the foundation of viable gravitational theories. Frame-dragging is the name Einstein himself gave in 1913 to an intriguing phenomenon of general relativity which implies that a current of mass-energy, such as the rotation of a body, will generate spacetime curvature. Frame-dragging has a key role in high energy astrophysics, e.g., in the generation of gravitational waves by the collision of two black holes to form a rotating black hole. Frame-dragging by the rotating Earth was measured to a few percent accuracy by combining the data of the satellites LARES, LAGEOS and LAGEOS 2 (Ciufolini et al. in Eur Phys J C 79:872, 2019). LARES 2, thanks to its extremely high injection precision, is projected to improve the test of frame-dragging by at least an order of magnitude. LARES 2 has also relevant applications in space geodesy and geodynamics, e.g., in the study of the shape of the Earth and in the determination of the International Terrestrial Reference Frame (ITRF) by improving the determination of the Earth center of mass and by contributing to a better determination of its rotation axis. [ABSTRACT FROM AUTHOR]

Io is the most volcanically-active object in the solar system. The moon ejects a tonne per second of sulphur-rich gases that fill the vast magnetosphere of Jupiter and drives million-amp electrical currents that excite strong auroral emissions. We present the case for including a detailed study of Io within Voyage 2050 either as a standalone mission or as a contribution to a NASA New Frontiers mission, possibly within a Solar System theme centred around current evolutionary or dynamical processes. A comprehensive investigation will provide answers to many outstanding questions and will simultaneously provide information on processes that have formed the landscapes of several other objects in the past. A mission investigating Io will also study processes that have shaped the Earth, Moon, terrestrial planets, outer planet moons, and potentially extrasolar planets. The aim would be simple – tracing the mass and energy flows in the Io-Jupiter system. [ABSTRACT FROM AUTHOR]

This study addresses the problems and shortcomings of the traditional field geomagnetic diurnal variation reduction method, the single-observatory reference method, by applying the Taylor polynomial model to establish a spatial reference field for diurnal variation reduction based on geomagnetic network data and comparing the results of the two methods. The findings are as follows: 1. The Taylor polynomial spatial reference field method can effectively describe the spatial distribution pattern of the geomagnetic field, and its results are more accurate and reliable than those of the single-observatory reference method. 2. The results obtained by the proposed method are more uniform and stable than those obtained by the single-observatory reference method, and they are closer to the theoretical shape of Earth's crustal magnetic field changes. 3. While applying the proposed method on earthquakes, it optimizes the display of seismomagnetic information and has good application values. [ABSTRACT FROM AUTHOR]

Traditional conversion from gravity Stokes coefficients into the surface mass, e.g., in the GRACE(-FO) applications, presumes the Earth as a perfect sphere that is apparently against the reality. Recent studies manage to correct the conversion by considering the Earth's oblateness, in another word, the Earth is treated as an ellipsoid. However, the Earth's geometry is far more complicated due to the topography, so that neither a sphere nor an ellipsoid is exact. Evidences from recent studies and this one demonstrate that any geometrical approximation of the Earth shape like a presumed sphere will inevitably lead to a bias in the surface mass estimation from GRACE gravity fields, resulting in a possible misinterpretation of geophysical signals that may occur in polar regions or mountain areas. In this context, we propose an iterative scaling factor method to numerically realize a more accurate surface mass estimate, considering a more realistic geometry of the Earth including its oblateness, topography and geoid undulation. Verified with a series of simulations, the proposed method is found to be efficient (less than four iterations), reliable (after a broad range of tests) and universally accurate (reducing at least 80% of the bias). Relative to our method, the mean linear trend in 2002–2015 estimated from GRACE under an ideal spherical Earth is found to be underestimated by about 3.1% and 5.5% over Greenland and West Antarctica, respectively. Among the trend underestimation, the topography-related contribution takes up − 0.5% (0.79 Gt/yr, the negative sign denotes an overestimation) and − 0.4% (0.34 Gt/yr), respectively. Although the value is small, it is a systematic bias worth considering, for example, it is greater than the influence (0.3 Gt/yr on the trend estimation over West Antarctica) by switching atmospherical de-aliasing products from RL05 to RL06. Besides, the topography-induced bias rapidly increases to 2.7% (0.26 mm/yr) at mountain Himalayas, which is even larger than the ellipsoid-induced bias (0.19 mm/yr). Based on the results obtained so far, the topography-induced bias is found to be roughly one order of magnitude smaller than GRACE's present measurement error; nevertheless, it will be relevant once the GRACE is improved toward its baseline accuracy. In particular, the topography correction should be considered for NGGM that expects to map the Earth gravity field in an unprecedented accuracy and spatial resolution. [ABSTRACT FROM AUTHOR]

The coexistence of divergent (spreading ridge) and convergent (subduction zone) plate boundaries at which lithosphere is respectively generated and destroyed is the hallmark of plate tectonics. Here, we document temporally- and spatially-associated Neoarchean (2.55–2.51 Ga) rock assemblages with mid-ocean ridge and supra-subduction-zone origins from the Angou Complex, southern North China Craton. These assemblages record seafloor spreading and contemporaneous subduction initiation and mature arc magmatism, respectively, analogous to modern divergent and convergent plate boundary processes. Our results provide direct evidence for lateral plate motions in the late Neoarchean, and arguably the operation of plate tectonics, albeit with warmer than average Phanerozoic subduction geotherms. Further, we surmise that plate tectonic processes played an important role in shaping Earth's surficial environments during the Neoarchean and Paleoproterozoic. This study reports coexisting Neoarchean divergent and convergent plate boundary rock assemblages, providing new evidence for the operation of plate tectonics 2.55–2.51 billion years ago; and also suggests the subduction zone was warm then. [ABSTRACT FROM AUTHOR]

Transformation toward a sustainable future requires an earth stewardship approach to shift society from its current goal of increasing material wealth to a vision of sustaining built, natural, human, and social capital—equitably distributed across society, within and among nations. Widespread concern about earth's current trajectory and support for actions that would foster more sustainable pathways suggests potential social tipping points in public demand for an earth stewardship vision. Here, we draw on empirical studies and theory to show that movement toward a stewardship vision can be facilitated by changes in either policy incentives or social norms. Our novel contribution is to point out that both norms and incentives must change and can do so interactively. This can be facilitated through leverage points and complementarities across policy areas, based on values, system design, and agency. Potential catalysts include novel democratic institutions and engagement of non-governmental actors, such as businesses, civic leaders, and social movements as agents for redistribution of power. Because no single intervention will transform the world, a key challenge is to align actions to be synergistic, persistent, and scalable. [ABSTRACT FROM AUTHOR]

The human visual perceptual system is highly sensitive to biological motion (BM) but less sensitive to its inverted counterpart. This perceptual inversion effect may stem from our selective sensitivity to gravity-constrained life motion signals and confer an adaptive advantage to creatures living on Earth. However, to what extent and how such selective sensitivity is shaped by the Earth's gravitational field is heretofore unexplored. Taking advantage of a spaceflight experiment and its ground-based analog via 6° head-down tilt bed rest (HDTBR), we show that prolonged microgravity/HDTBR reduces the inversion effect in BM perception. No such change occurs for face perception, highlighting the particular role of gravity in regulating kinematic motion analysis. Moreover, the reduced BM inversion effect is associated with attenuated orientation-dependent neural responses to BM rather than general motion cues and correlated with strengthened functional connectivity between cortical regions dedicated to visual BM processing (i.e., pSTS) and vestibular gravity estimation (i.e., insula). These findings suggest that the neural computation of gravity may act as an embodied constraint, presumably implemented through visuo-vestibular interaction, to sustain the human brain's selective tuning to life motion signals. Utilizing spaceflight and its ground-based analog, the authors show how the Earth's gravity sustains the human brain's orientation-dependent sensitivity to biological motion signals based on neural computations of visual and vestibular gravitational cues. [ABSTRACT FROM AUTHOR]

Aeolian sand transport is a major process shaping landscapes on Earth and on diverse celestial bodies. Conditions favoring bimodal sand transport, with fine-grain saltation driving coarse-grain reptation, give rise to the evolution of megaripples with a characteristic bimodal sand composition. Here, we derive a unified phase diagram for this special aeolian process and the ensuing nonequilibrium megaripple morphodynamics by means of a conceptually simple quantitative model, grounded in the grain-scale physics. We establish a well-preserved quantitative signature of bimodal aeolian transport in the otherwise highly variable grain size distributions, namely, the log-scale width (Krumbein phi scale) of their coarse-grain peaks. A comprehensive collection of terrestrial and extraterrestrial data, covering a wide range of geographical sources and environmental conditions, supports the accuracy and robustness of this unexpected theoretical finding. It could help to resolve ambiguities in the classification of terrestrial and extraterrestrial sedimentary bedforms. Megaripples are sand landforms found in wind-blown environments. A newly identified characteristic signature of the underlying bimodal sand transport process is found in the grain-size distribution on megaripples and could lend insight into transport conditions on Earth and other planetary bodies. [ABSTRACT FROM AUTHOR]

Mass extinctions have repeatedly shaped global biodiversity. The Cretaceous-Paleogene (K-Pg) mass extinction caused the demise of numerous vertebrate groups, and its aftermath saw the rapid diversification of surviving mammals, birds, frogs, and teleost fishes. However, the effects of the K-Pg extinction on the evolution of snakes—a major clade of predators comprising over 3,700 living species—remains poorly understood. Here, we combine an extensive molecular dataset with phylogenetically and stratigraphically constrained fossil calibrations to infer an evolutionary timescale for Serpentes. We reveal a potential diversification among crown snakes associated with the K-Pg mass extinction, led by the successful colonisation of Asia by the major extant clade Afrophidia. Vertebral morphometrics suggest increasing morphological specialisation among marine snakes through the Paleogene. The dispersal patterns of snakes following the K-Pg underscore the importance of this mass extinction event in shaping Earth's extant vertebrate faunas. Snakes are one of the most successful groups of living vertebrates, but the timing of their diversification is unclear. Combining molecular clocks, fossils, and biogeography, Klein et al. show that snakes experienced a diversification, and underwent dispersal, around the time of the end-Cretaceous mass extinction. [ABSTRACT FROM AUTHOR]

Abstract—Modeling the relative motion of large crustal blocks vitally depends on an adequate description of the forces acting between the blocks. To describe motion at high strain rates, it proved necessary to assume a dry friction to depend on the shear strain rate and, in some cases, on the amplitude of fault side displacement. The best known examples of large-scale motions with dynamically decreasing friction are long-runout rock avalanches and gravity-driven collapsing of the transitional cavities of large impact craters. In this work, the experience is discussed of using the model of acoustic fluidization as a factor of a temporary decrease in friction to quantitatively simulate impact crater shape on the Earth and other planetary bodies. Immediate promising ways to find more adequate models are outlined. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has exposed an interconnected and tightly coupled globalized world in rapid change. This article sets the scientific stage for understanding and responding to such change for global sustainability and resilient societies. We provide a systemic overview of the current situation where people and nature are dynamically intertwined and embedded in the biosphere, placing shocks and extreme events as part of this dynamic; humanity has become the major force in shaping the future of the Earth system as a whole; and the scale and pace of the human dimension have caused climate change, rapid loss of biodiversity, growing inequalities, and loss of resilience to deal with uncertainty and surprise. Taken together, human actions are challenging the biosphere foundation for a prosperous development of civilizations. The Anthropocene reality—of rising system-wide turbulence—calls for transformative change towards sustainable futures. Emerging technologies, social innovations, broader shifts in cultural repertoires, as well as a diverse portfolio of active stewardship of human actions in support of a resilient biosphere are highlighted as essential parts of such transformations. [ABSTRACT FROM AUTHOR]

A view is often more than just a piece of landscape, framed by the gaze and evoking emotion. Without diminishing these obvious 'tourism-important' advantages of a view, it is noteworthy that in itself it might play the role of an interpretative tool, especially for large-scale phenomena, the knowledge and understanding of which is the goal of geotourism. In this paper, we analyze the importance of scenic drives and trails for tourism, particularly geotourism, focusing on their ability to create conditions for experiencing the dynamically changing landscapes in which lies knowledge of the natural processes shaping the Earth's surface and the methods and degree of its resource exploitation. The issues are found in both wider and local contexts. A more detailed insight has been conducted on the basis of two, although in some sense peripheral, tourism regions from the Sudeten Mountains (southwestern Poland): Lasocki Grzbiet (a ridge) and Pasmo Lesistej (a small range). The subjects of the investigation were complex: the geotourism potential of selected viewpoints located on the most scenic routes (mostly paths and forest tracks) as well as the problems of maintenance, conservation, and protection of their educational value. Our work is based on desk and field research supported by results of GIS visibility analyses (conducted in the QGIS program). [ABSTRACT FROM AUTHOR]

Green's functions (GFs) for elastic deformation due to unit slip on the fault plane comprise an essential tool for estimating earthquake rupture and underground preparation processes. These estimation results are often applied to generate important information for public such as seismic and tsunami hazard assessments. So, it is important to minimize the distortion of the estimation results on the numerical models used for calculating GFs to guarantee assessment reliability. For this purpose, we here calculated GFs based on a numerical model that is of high fidelity to obtain realistic topography and subsurface structural models of the Earth. We targeted two well-known subduction zones in Japan, the Nankai Trough and the Japan Trench. For these subduction zones, databases for realistic topography and subsurface structural models of the Earth are available in the "Japan integrated velocity structure model version 1", which was proposed for earthquake hazard assessments conducted by the Japanese government. Furthermore, we eliminated the inconsistency in processing calculated GFs and space geodetic observation data for surface displacements, which is often overlooked, by using the same coordinate system. The ellipsoidal shape of the Earth, which is often approximated with a projected plane or a spherical shape, was also incorporated by faithfully following the definitions of the coordinate systems in Geodetic Reference System 1980, which is the global standard for space geodesy. To calculate elastic GFs based on such high-fidelity subduction zone databases with the ellipsoidal shape of the Earth, we introduced the finite element (FE) method. In the FE meshes, the resolution of the topography and subsurface structure is the same as that of the original databases. Recent development of the state-of-the-art computation techniques for the rapid calculation of crustal deformation using large-scale FE models allows for GF calculation based on such a high-fidelity model. However, it is generally not easy to perform such calculations. Thus, we released a library for the GFs calculated with 1-km grid spacing on the ground surface in this study to the geoscience community on a web server, aiming to contribute more reliable seismic and tsunami hazard assessment. [ABSTRACT FROM AUTHOR]

Quantitative indicators of the influence of the shape of the Earth (ellipsoidal with modern polar compression or spherical) on the characteristics of its irradiation calculated without taking into account the changes in the solar activity have been obtained. The differences between specific energies as well as intensities of irradiation of the ellipsoid (and its parts) and sphere (and its parts) on the average over a tropical year and in its parts (half-years, months) have been revealed. It is found from the data on the Earth's motion in the interval of the tropical years from 3000 BC to AD 2999 that, at a constant intensity of solar irradiance, each of the two annual irradiation characteristics for the sphere is 0.085% higher than one for the ellipsoid. The monthly irradiation specific energy for the sphere is almost constant, and one for the ellipsoid varies with a scatter 0.043% of the average value (minima at the equinoxes and maxima at the solstices). The monthly irradiation intensities for the sphere and ellipsoid vary synchronously with a scatter 5.98% relative to the average value (the minimum occurs in the third month and the maximum in the ninth). The seasonality for a hemisphere (absolute value of the difference between irradiation specific energies for a hemisphere in different half-year periods) in the case of the ellipsoidal Earth is on the average 0.223% higher than in the case of the spherical Earth. The maximum of differences in the semiannual irradiation specific energies (and similarly in the semiannual irradiation intensities) in the latitudinal zones of the sphere and ellipsoid is positive and the minimum is negative. In the first half of the year, the maximum and minimum are observed in the zones 45°–50° S and 10°–15° N. In the second half of the year, the maximum and minimum are observed in zones 45°–50° N and 10°–15° S. It is found on the basis of the data from 1978–2008 that the differences in the intensities of irradiation of the sphere and ellipsoid are comparable with the variations in the total solar irradiance (TSI) associated with the changes in solar activity. The mean absolute value of the annual TSI anomaly is 14.01% greater than the average annual difference in the intensities of irradiation of the sphere and ellipsoid. The average absolute value of the monthly TSI anomaly exceeds the average monthly difference in the intensities of the irradiation of the sphere and ellipsoid by 23.37%. [ABSTRACT FROM AUTHOR]

This document is a correction notice for a research paper titled "Geodynamic processes of the southeastern Neo-Tethys Ocean and the formation mechanism of the curved subduction system in Southeast Asia." The original paper contained errors, specifically in Figure 1. The corrected figure and figure caption are provided in the correction notice. The corrections do not impact the results or conclusions of the paper. The original article can be found online. [Extracted from the article]

Biotically-mediated weathering helps to shape Earth's surface. For example, plants expend carbon (C) to mobilize nutrients in forms whose relative abundances vary with depth. It thus is likely that trees' nutrient acquisition strategies—their investment in rooting systems and exudates—may function differently following disturbance-induced changes in depth of rooting zones and soil nutrient stocks. These changes may persist across centuries. We test the hypothesis that plant C allocation for nutrient acquisition is depth dependent as a function of rooting system development and relative abundances of organic vs. mineral nutrient stocks. We further posit that patterns of belowground C allocation to nutrient acquisition reveal anthropogenic signatures through many decades of forest regeneration. To test this idea, we examined fine root abundances and rooting system C in organic acid exudates and exo-enzymes in tandem with depth distributions of organically- and mineral-bound P stocks. Our design permitted us to estimate C tradeoffs between organic vs. mineral nutrient benefits in paired forests with many similar aboveground traits but different ages: post-agricultural mixed-pine forests and older reference hardwoods. Fine roots were more abundant throughout the upper 2 m in reference forest soils than in regenerating stands. Rooting systems in all forests exhibited depth-dependent C allocations to nutrient acquisition reflecting relative abundances of organic vs. mineral bound P stocks. Further, organic vs. mineral stocks underwent redistribution with historic land use, producing distinct ecosystem nutritional economies. In reference forests, rooting systems are allocating C to relatively deep fine roots and low-C exudation strategies that can increase mobility of mineral-bound P stocks. Regenerating forests exhibit relatively shallower fine root distributions and more diverse exudation strategies reflecting more variable nutrient stocks. We observed these disparities in rooting systems' depth and nutritional mechanisms even though the regenerating forests have attained aboveground biomass stocks similar to those in reference hardwood forests. These distinctions offer plausible belowground mechanisms for observations of continued C sink strength in relatively old forests, and have implications for soil C fates and soil development on timescales relevant to human lifetimes. As such, depth-dependent nutrient returns on plant C investments represent a subtle but consequential signal of the Anthropocene. [ABSTRACT FROM AUTHOR]

We became interested in investigating the origin of the length of the metre as a basis of the metric system after reading Ken Alder's 2002 book "The measure of all things", where we learnt that the metre we use in all our length measurements is about 0.2 millimetres shorter than it was supposed to be. That does not sound like being too far off, but when one realizes that the metre was supposed to be one ten-millionth part of the Earth quadrant, the 0.2 mm translates to a 2 km error in the Earth quadrant. Even with the instruments available at the end of the eighteenth century, when these geodetic measurements were carried out by a couple of French geodesists, the error of 2 km in the Earth quadrant was a little too large to expect. Particularly so as both these gentlemen, Méchain and Delambre, had a reputation of being excellent and very careful observers. When we read in the two geodesists' 1806 Opus Magnum, Base du système métrique décimal ou mesure de l'arc du méridian, that Legendre, when he compared their 1806 results with the results of their predecessors and contemporaries, said: "I'd suspect the irregularities of the local [gravity] attraction on the plumb-line [to be at play here]", our interest was definitely aroused. Indeed, the analyses described in this paper confirm Legendre's suspicion: while the error due to the neglect of gravity field is responsible for about 95% of the total error, the error in the meridian length measurements amounts to less than 2% of the total error and the error due to a wrong assumption of the Earth's shape contributed about 3% of the total error. If the careful work of Méchain and Delambre was the only source of error, the metre nowadays would be too long only by less than 4 μm instead of being short by 197 μm. The bulk of the difference is made by not taking the effect of gravity field into account; that they could not have done because the needed gravity field features were not yet known. [ABSTRACT FROM AUTHOR]

Highlights from the article: The third contribution 'Ill-Posed Problems: Operator Methodologies of Resolution and Regularization', with 114 pages was written by Will Freedmen and M. Zuhair Nashed. The sixth contribution "Oblique Stochastic Boundary Value Problem" with 26 pages was written by Martin Grothaus and Thomas Raskop. After the preliminaries, the multipole methods for splines are presented, the fast multipole method for splines with illustrations, and the parameter choice methods for spline approximation. To work with inverse gravimetry, the Newton volume integral is presented first, then the ill-posedness of the gravimetry problem, the mollifier methods, and the reproducing kernel Hilbert space methods.

Planetary dynamics of century-long Earth shape changes is studied based on the approximation of the physical Earth surface by a biaxial ellipsoid. Trends in century-long changes of Earthshape parameters were revealed from the analysis of the following data: modern GNSS measurements on permanent stations in the Northern and Southern hemispheres and paleoreconstruction models of continental and ocean surfaces. [ABSTRACT FROM AUTHOR]

Are the National Geodetic Survey's surface gravity data sufficient for supporting the computation of a 1 cm-accurate geoid? This paper attempts to answer this question by deriving a few measures of accuracy for this data and estimating their effects on the US geoid. We use a data set which comprises $${\sim }1.4$$ million gravity observations collected in 1,489 surveys. Comparisons to GRACE-derived gravity and geoid are made to estimate the long-wavelength errors. Crossover analysis and $$K$$-nearest neighbor predictions are used for estimating local gravity biases and high-frequency gravity errors, and the corresponding geoid biases and high-frequency geoid errors are evaluated. Results indicate that 244 of all 1,489 surface gravity surveys have significant biases $${>}2$$ mGal, with geoid implications that reach 20 cm. Some of the biased surveys are large enough in horizontal extent to be reliably corrected by satellite-derived gravity models, but many others are not. In addition, the results suggest that the data are contaminated by high-frequency errors with an RMS of $${\sim }2.2$$ mGal. This causes high-frequency geoid errors of a few centimeters in and to the west of the Rocky Mountains and in the Appalachians and a few millimeters or less everywhere else. Finally, long-wavelength ( $${>}3^{\circ }$$) surface gravity errors on the sub-mGal level but with large horizontal extent are found. All of the south and southeast of the USA is biased by +0.3 to +0.8 mGal and the Rocky Mountains by $$-0.1$$ to $$-0.3$$ mGal. These small but extensive gravity errors lead to long-wavelength geoid errors that reach 60 cm in the interior of the USA. [ABSTRACT FROM AUTHOR]

One of the main objectives of ESA's Gravity Field and Steady-State Ocean Circulation mission GOCE (Gravity field and steady-state ocean circulation mission, ) is to allow global unification of height systems by directly providing potential differences between benchmarks in different height datum zones. In other words, GOCE provides a globally consistent and unbiased geoid. If this information is combined with ellipsoidal (derived from geodetic space techniques) and physical heights (derived from leveling/gravimetry) at the same benchmarks, datum offsets between the datum zones can be determined and all zones unified. The expected accuracy of GOCE is around 2-3 cm up to spherical harmonic degree n ≈ 200. The omission error above this degree amounts to about 30 cm which cannot be neglected. Therefore, terrestrial residual gravity anomalies are necessary to evaluate the medium and short wavelengths of the geoid, i.e. one has to solve the Geodetic Boundary Value Problem (GBVP). The theory of height unification by the GBVP approach is well developed, see e.g. Colombo (A World Vertical Network. Report 296, Department of Geodetic Science and Surveying, ) or Rummel and Teunissen (Bull Geod 62:477-498, ). Thereby, it must be considered that terrestrial gravity anomalies referring to different datum zones are biased due to the respective datum offsets. Consequently, the height reference surface of a specific datum zone deviates from the unbiased geoid not only due to its own datum offset ( direct bias term) but is also indirectly affected by the integration of biased gravity anomalies. The latter effect is called the indirect bias term and it considerably complicates the adjustment model for global height unification. If no satellite based gravity model is employed, this error amounts to about the same size as the datum offsets, i.e. 1-2 m globally. We show that this value decreases if a satellite-only gravity model is used. Specifically for GOCE with n ≈ 200, the error can be expected not to exceed the level of 1 cm, allowing the effect to be neglected in practical height unification. The results are supported by recent findings by Gatti et al. (J Geod, ). [ABSTRACT FROM AUTHOR]

Regional height systems do not refer to a common equipotential surface, such as the geoid. They are usually referred to the mean sea level at a reference tide gauge. As mean sea level varies (by ±1 to 2 m) from place to place and from continent to continent each tide gauge has an unknown bias with respect to a common reference surface, whose determination is what the height datum problem is concerned with. This paper deals with this problem, in connection to the availability of satellite gravity missions data. Since biased heights enter into the computation of terrestrial gravity anomalies, which in turn are used for geoid determination, the biases enter as secondary or indirect effect also in such a geoid model. In contrast to terrestrial gravity anomalies, gravity and geoid models derived from satellite gravity missions, and in particular GRACE and GOCE, do not suffer from those inconsistencies. Those models can be regarded as unbiased. After a review of the mathematical formulation of the problem, the paper examines two alternative approaches to its solution. The first one compares the gravity potential coefficients in the range of degrees from 100 to 200 of an unbiased gravity field from GOCE with those of the combined model EGM2008, that in this range is affected by the height biases. This first proposal yields a solution too inaccurate to be useful. The second approach compares height anomalies derived from GNSS ellipsoidal heights and biased normal heights, with anomalies derived from an anomalous potential which combines a satellite-only model up to degree 200 and a high-resolution global model above 200. The point is to show that in this last combination the indirect effects of the height biases are negligible. To this aim, an error budget analysis is performed. The biases of the high frequency part are proved to be irrelevant, so that an accuracy of 5 cm per individual GNSS station is found. This seems to be a promising practical method to solve the problem. [ABSTRACT FROM AUTHOR]

Movement and searching behaviors at diverse spatial scales are important for understanding how animals interact with their environment. Although the shapes of branches and the voids in arboreal habitats seem likely to affect searching behaviors, their influence is poorly understood. To gain insights into how both environmental structure and the attributes of an animal may affect movement and searching, we compared the three-dimensional exploratory movements of snakes in the dark on two simulated arboreal surfaces (disc and horizontal cylinder). Most of the exploratory movements of snakes in the dark were a small fraction of the distances they could reach while bridging gaps in the light. The snakes extended farther away from the edge of the supporting surface at the ends of the cylinder than from the sides of the cylinder or from any direction from the surface of the disc. The exploratory movements were not random, and the surface shape and three-dimensional directions had significant interactive effects on how the movements were structured in time. Thus, the physical capacity for reaching did not limit the area that was explored, but the shape of the supporting surface and the orientation relative to gravity did create biased searching patterns. [ABSTRACT FROM AUTHOR]

In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ″ × 3″ resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes' formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure. [ABSTRACT FROM AUTHOR]

Recently it was proved that the classical formula for computing the geoid to quasigeoid separation (GQS) by the Bouguer gravity anomaly needs a topographic correction. Here we generalize the modelling of the GQS not only to Bouguer types of anomalies, but also to arbitrary reductions of topographic gravity. Of particular interest for practical applications should be isostatic and Helmert types of reductions, which provide smaller and smoother components, more suitable for interpolation and calculation, than the Bouguer reduction. [ABSTRACT FROM AUTHOR]

The effect of the Earth's compression on the physical libration of the Moon is studied using a new vector method. The moment of gravitational forces exerted on the Moon by the oblate Earth is derived considering second order harmonics. The terms in the expression for this moment are arranged according to their order of magnitude. The contribution due to a spherically symmetric Earth proves to be greater by a factor of 1.34 × 10 than a typical term allowing for the oblateness. A linearized Euler system of equations to describe the Moon's rotation with allowance for external gravitational forces is given. A full solution of the differential equation describing the Moon's libration in longitude is derived. This solution includes both arbitrary and forced oscillation harmonics that we studied earlier (perturbations due to a spherically symmetric Earth and the Sun) and new harmonics due to the Earth's compression. We posed and solved the problem of spinorbital motion considering the orientation of the Earth's rotation axis with regard to the axes of inertia of the Moon when it is at a random point in its orbit. The rotation axes of the Earth and the Moon are shown to become coplanar with each other when the orbiting Moon has an ecliptic longitude of L = 90° or L = 270°. The famous Cassini's laws describing the motion of the Moon are supplemented by the rule for coplanarity when proper rotations in the Earth-Moon system are taken into account. When we consider the effect of the Earth's compression on the Moon's libration in longitude, a harmonic with an amplitude of 0.03″ and period of T = 9.300 Julian years appears. This amplitude exceeds the most noticeable harmonic due to the Sun by a factor of nearly 2.7. The effect of the Earth's compression on the variation in spin angular velocity of the Moon proves to be negligible. [ABSTRACT FROM AUTHOR]

Background and aims: RootScan is a program for semi-automated image analysis of anatomical traits in root cross-sections. Methods: RootScan uses pixel thresholds to separate the cross-section from its background and to divide it into tissue regions. Area measurements and object counts are performed within various regions of interest. A graphical user interface permits the user to see which regions are selected, to edit those selections, and to rate and comment on the data. The structure of the program allows for organized workflow and increased data collection efficiency. Results: The program collects data on more than 20 variables per image including areas of the cross-section, stele, cortex, aerenchyma lacunae, xylem vessels, and counts of cortical cells and cell files. An increased rate of data collection allows collection of four times more variables in less time than is possible with current methods. Correlation analysis shows that RootScan data is equal or greater in accuracy than data collected with Photoshop. Conclusions: Compared with currently available tools, this software offers considerable improvements in the amount and quality of data, ease of use, and time needed for data collection. RootScan permits phenotypic scoring of physiologically and agronomically important traits on a large number of genotypes. [ABSTRACT FROM AUTHOR]

Precise information of geoid undulations is essential for obtaining the orthometric heights from Global Positioning System (GPS) measurements over any region; apart from providing the information of subsurface density distribution. This paper presents computation of geoid undulations over a part of southern Indian region from terrestrial gravity and elevation data using remove-restore technique that involves spherical Fast Fourier Transform (FFT) to compute 'Stokes' coefficients. Computed geoid undulations are compared with geoid obtained from global geopotential models such as EGM2008 and EIGEN-GRACE02S and measured GPS-levelling records at 67 locations. Statistical analysis of comparison suggests that the computed gravimetric geoid model has a good match with the geoid determined from GPS-levelling with rms of 0.1 m whereas EGM2008 has 0.46 m. The differences of GPS-levelling with EGM2008 at majority of stations fall in the range of ±0.5 m, which indicates that EGM2008 may be used for orthometric height determination with an accuracy of <0.5 m in the south Indian region and offers a reasonably good transformation platform from ellipsoid to local datum. However, local determination of geoid is necessary for better accuracy of orthometric height from GPS. The gravimetric geoid calculated from the available gravity data shows considerable improvement to the global model and can be used to achieve orthometric height with an accuracy of 0.1 m. [ABSTRACT FROM AUTHOR]

The mean dynamic topography (MDT) can be computed as the difference between the mean sea level (MSL) and a gravimetric geoid. This requires that both data sets are spectrally consistent. In practice, it is quite common that the resolution of the geoid data is less than the resolution of the MSL data, hence, the latter need to be low-pass filtered before the MDT is computed. For this purpose conventional low-pass filters are inadequate, failing in coastal regions where they run into the undefined MSL signal on the continents. In this paper, we consider the use of a bandlimited, spatially concentrated Slepian basis to obtain a low-resolution approximation of the MSL signal. We compute Slepian functions for the oceans and parts of the oceans and compare the performance of calculating the MDT via this approach with other methods, in particular the iterative spherical harmonic approach in combination with Gaussian low-pass filtering, and various modifications. Based on the numerical experiments, we conclude that none of these methods provide a low-resolution MSL approximation at the sub-decimetre level. In particular, we show that Slepian functions are not appropriate basis functions for this problem, and a Slepian representation of the low-resolution MSL signal suffers from broadband leakage. We also show that a meaningful definition of a low-resolution MSL over incomplete spherical domains involves orthogonal basis functions with additional properties that Slepian functions do not possess. A low-resolution MSL signal, spectrally consistent with a given geoid model, is obtained by a suitable truncation of the expansions of the MSL signal in terms of these orthogonal basis functions. We compute one of these sets of orthogonal basis functions using the Gram-Schmidt orthogonalization for spherical harmonics. For the oceans, we could construct an orthogonal basis only for resolutions equivalent to a spherical harmonic degree 36. The computation of a basis with a higher resolution fails due to inherent instabilities. Regularization reduces the instabilities but destroys the orthogonality and, therefore, provides unrealistic low-resolution MSL approximations. More research is needed to solve the instability problem, perhaps by finding a different orthogonal basis that avoids it altogether. [ABSTRACT FROM AUTHOR]

The Global Geopotential Models (GGMs) are very significant because of their usefulness in determination of the parameters like geoidal undulations, height anomalies, gravity anomalies, and so on. In this paper, first, we review the calculation of such parameters and then present the GGMCalc software, which is prepared in Fortran 95 under GNU/Linux Operating System. This software is capable of using the files presented by the International Center for Global Earth Models (ICGEM) directly without need to apply any changes on them. The software is completely structural and user friendly and could be used conveniently for academic purposes. [ABSTRACT FROM AUTHOR]

We present a method to estimate the difference between quasigeoid and geoid heights globally from the Earth Gravitational Model EGM08 and a related topographic model. The numerical computations with the standard topographic density of 2.67 g/cm show that the maximum and minimum of the separations are estimated to 5.47 m and −0.11 m on the Tibet plateau and in the Indian Ocean, respectively. These estimates do not consider possible topographic density variations, which result in topographic bias changes proportional to the topographic elevation squared. Assuming such density changes of 10% from the standard value, the separation may change up to 5 dm. [ABSTRACT FROM AUTHOR]

As the number of Earth geopotential models (EGM) grows with the increasing number of data collected by dedicated satellite gravity missions, CHAMP, GRACE and GOCE, measuring the differences among the models and monitoring the improvements in gravity field recovery are required. This study assesses the performance of recent EGMs derived from CHAMP, GRACE, and other data in comparison to the earlier two models in Turkish territory. Also the improvement capacities of these EGMs using local terrestrial data are inspected with two different approaches. In the first approach, the spherical harmonic coefficients of EGMs are modified depending on the local gravity data. In the second part, the original EGMs with their maximum harmonic expansions are employed in Remove Compute Restore algorithm for high resolution local geoid modelling. The assessment results with the local terrestrial data exhibited large disagreements among the models in Turkey. The outputs from regional improvements of EGMs using the gravity observations clarified the important role of the ground truth data contribution in geopotential models. The validations of the computed high resolution geoids rely on the EGMs at the GNSS/levelling networks, having 451 and 309 benchmarks, provided an absolute accuracy by means of standard deviations of the geoid height differences around 20 cm. These results from the final stage of the case study provide a comparison among the EGMs by means of their fit to the local gravity field. [ABSTRACT FROM AUTHOR]

The forthcoming GRAV-D gravimetric geoid model over the United States is to be updated regularly to account for changes in geoid height. Its baseline precision is to be at the 10-20 mm level over non-mountainous regions. The aim of this study is to provide an estimate of the magnitude, time scale, and spatial footprint of geoid height change over North America, from mass redistribution processes of hydrologic, cryospheric and solid Earth nature. Geoid height changes from continental water storage changes over the past 50 years and predicted over the next century are evaluated and are highly dependent on the used model. Groundwater depletion from anthropogenic pumping in regional scale aquifers may lead to geoid changes of 10 mm magnitude every 50-100 years. The GRACE time varying gravity fields are used to (i) assess the errors in a glacial isostatic adjustment model, which, if used to correct the GRAV-D model, may induce errors at the 10 mm geoid height level after ~20 years, (ii), evaluate geoid height change over ice mass loss regions of North America, which, if they remain unchanged in the future, may lead to geoid height changes at the 10 mm level in under a decade and (iii), compute sea level rise and its effect on the geoid, which is found to be negligible. Coseismic gravitational changes from past North American earthquakes are evaluated, and lead to geoid change at the 10-mm level for only the largest thrust earthquakes. Finally, geoid change from volcanic processes are assessed and found to be significant with respect to the GRAV-D geoid model baseline precision for cataclysmic events, such as that of the 1980 Mt. St. Helens eruption. Recommendations on how to best monitor geoid change in the future are given. [ABSTRACT FROM AUTHOR]

While it is obvious that large-scale gravity studies should account for the sphericity of the Earth, each case should be examined. If a geometry model is very large for the 3D-gravity calculation, it cannot be correctly defined in Cartesian coordinates. Because of the Earth's curvature it is necessary to use spherical coordinates, the importance of which is shown in this paper. The calculation of the gravity for a cylinder reveals, 1 m above the center of the cylinder, a relative difference of 13% between the models with Cartesian and spherical coordinates. [ABSTRACT FROM AUTHOR]

Important though indirect information about the internal structure of Venus is provided by its topography and geoid. In the last decades this information has been used to constrain the Venus mantle viscosity structure and its dynamic regime. Recently, the geodynamic inversion of the Venus' geoid and topography resulted in a group of best fitting viscosity profiles. We use these viscosity models here as an input to our mantle convection code. We carry out simulations of the Venus' mantle evolution in a 3D spherical shell with depth dependent viscosity and check whether the character of the dynamic topography and the geoid represented by their power spectra fits the observed quantities. We compare the results with several other models obtained for different viscosity stratifications (constant, constant with highly viscous lithosphere, linear increase of viscosity). Further, we estimate the effect of other factors such as internal heating and varying Rayleigh number. We use a 2D spherical axisymmetric convection code to study the effect of lateral viscosity variations. In these 2D models we monitor the topography and the geoid developing above the axisymmetric plume and compare them with the observed elevations of Venus' geoid and topography in several Regia. Though none of the models fits observed data perfectly, we can generally conclude, that the best fit between the observed and predicted quantities is reached for viscosity profiles with 200 km thick lithosphere followed by a gradual increase of viscosity with depth and with the upper mantle viscosity of 2 × 10 Pa s. For all viscosity profiles the predicted geoid and topography spectra match the observed ones only up to the degree 40, thus indicating other than dynamic origin of these quantities for higher degrees. [ABSTRACT FROM AUTHOR]

The vertical gradients of gravity anomaly and gravity disturbance can be related to horizontal first derivatives of deflection of the vertical or second derivatives of geoidal undulations. These are simplified relations of which different variations have found application in satellite altimetry with the implicit assumption that the neglected terms-using remove-restore-are sufficiently small. In this paper, the different simplified relations are rigorously connected and the neglected terms are made explicit. The main neglected terms are a curvilinear term that accounts for the difference between second derivatives in a Cartesian system and on a spherical surface, and a small circle term that stems from the difference between second derivatives on a great and small circle. The neglected terms were compared with the dynamic ocean topography (DOT) and the requirements on the GOCE gravity gradients. In addition, the signal root-mean-square (RMS) of the neglected terms and vertical gravity gradient were compared, and the effect of a remove-restore procedure was studied. These analyses show that both neglected terms have the same order of magnitude as the DOT gradient signal and may be above the GOCE requirements, and should be accounted for when combining altimetry derived and GOCE measured gradients. The signal RMS of both neglected terms is in general small when compared with the signal RMS of the vertical gravity gradient, but they may introduce gradient errors above the spherical approximation error. Remove-restore with gravity field models reduces the errors in the vertical gravity gradient, but it appears that errors above the spherical approximation error cannot be avoided at individual locations. When computing the vertical gradient of gravity anomaly from satellite altimeter data using deflections of the vertical, the small circle term is readily available and can be included. The direct computation of the vertical gradient of gravity disturbance from satellite altimeter data is more difficult than the computation of the vertical gradient of gravity anomaly because in the former case the curvilinear term is needed, which is not readily available. [ABSTRACT FROM AUTHOR]

A new gravimetric geoid model, USGG2009 (see Abbreviations), has been developed for the United States and its territories including the Conterminous US (CONUS), Alaska, Hawaii, Guam, the Commonwealth of the Northern Mariana Islands, American Samoa, Puerto Rico and the US Virgin Islands. USGG2009 is based on a 1′ × 1′ gravity grid derived from the NGS surface gravity data and the DNSC08 altimetry-derived anomalies, the SRTM-DTED1 3′′ DEM for its topographic reductions, and the global geopotential model EGM08 as a reference model. USGG2009 geoid heights are compared with control values determined at 18,398 Bench Marks over CONUS, where both the ellipsoidal height above NAD 83 and the Helmert orthometric height above NAVD 88 are known. Correcting for the ellipsoidal datum difference, this permits a comparison of the geoid heights to independent data. The standard deviation of the differences is 6.3 cm in contrast to 8.4 cm for its immediate predecessor- USGG2003. To minimize the effect of long-wavelength errors that are known to exist in NAVD88, these comparisons were made on a state-by-state basis. The standard deviations of the differences range from 3-5 cm in eastern states to about 6-9 cm in the more mountainous western states. If the GPS/Bench Marks-derived geoid heights are corrected by removing a GRACE-derived estimate of the long-wavelength NAVD88 errors before the comparison, the standard deviation of their differences from USGG2009 drops to 4.3 cm nationally and 2-4 cm in eastern states and 4-8 in states with a maximum error of 26.4 cm in California and minimum of −32.1 cm in Washington. USGG2009 is also compared with geoid heights derived from 40 tide-gauges and a physical dynamic ocean topography model in the Gulf of Mexico; the mean of the differences is 3.3 cm and their standard deviation is 5.0 cm. When USGG2009-derived deflections of the vertical are compared with 3,415 observed surface astro-geodetic deflections, the standard deviation of the differences in the N-S and E-W components are 0.87′′ and 0.94′′, respectively. [ABSTRACT FROM AUTHOR]

The phenomenon of the rise of the Scandinavian shield during the Holocene and the concomitant fall in level of the Baltic Sea has been investigated for centuries. Already in medieval times, there were reports about the coastlines of the Gulf of Bothnia that are full of relevant observations. During the eighteenth century, scientists such as Celsius and Linnaeus collected observations such as these. The result was that the search for the possible explanations of this rise-and-fall phenomenon intensified. The generally favoured explanation was that there was an active sinking of sea level in the Baltic rather than an active rising of the land surface in Fennoscandia. This was because water was seen as mobile, in contrast to a 'terra firma'. The relevant discussion was often emotional, and here, we try to illustrate it using material from the Geologenarchiv Freiburg (von Hoff, von Buch and Goethe). No more than a few decades later, it became obvious by the theory of Ice Age that both the sea level and the land could be mobile (eustatic sea level changes-glacial isostasy). Additionally, of course, plate tectonics had some influence: Norway is situated at the western end of the Eurasian plate and is part of a passive continental margin. There are still open research problems, many of which can be addressed using modern methods of satellite-based geophysics and geodesy. Some other aspects as the permanent uplift trend of Scandinavia since the Cambrium or the rhythmic to and fro of magma in the upper mantle during the Pleistocene are mentioned. [ABSTRACT FROM AUTHOR]

Three GOCE-based gravity field solutions have been computed by ESA's high-level processing facility and were released to the user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest, that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200 can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1-2 cm geoid accuracy with 100 km spatial resolution can be achieved. [ABSTRACT FROM AUTHOR]

Today air-gravimetry is a versatile technique to quickly collect gravity data over large regions, where terrestrial gravity data are sparse and/or of poor quality. The method requires the data to be downward continued to sea level for use in geoid determination, an inverse problem operation that calls for smoothing of the data and/or the kernel function involved (in either spectral or space domain). In this purely theoretical study we avoid this separate computational step by performing direct geoid estimation by so-called spectral combination/filtering of the data, which includes terrestrial gravimetry, airgravimetry, an Earth Gravitational Model (EGM) as well as their signal and error degree variances. Each derived geoid estimator is presented as the sum of one or two integral formulas and the harmonic series of the EGM together with the expected mean square error of the estimator. The article is limited to a theoretical study, leaving its practical tests for future investigation. [ABSTRACT FROM AUTHOR]

Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method for computation of area mean gravity anomalies in ellipsoidal approximation ('ellipsoidal area means') by applying a simple ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM quasigeoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available as area mean values. [ABSTRACT FROM AUTHOR]