Correction to Variations of Ice Bed Coupling Beneath and Beyond Ice Streams: The Force Balance

A geometrical force balance that links stresses to ice bed coupling along a flow band of an ice sheet was developed in 1988 for longitudinal tension in ice streams and published 4 years later. It remains a work in progress. Now gravitational forces balanced by forces producing tensile, compressive, basal shear, and side shear stresses are all linked to ice bed coupling by the floating fraction phi of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how phi varies along these flow bands where surface and bed topography are known: phi = h(O)/h(I) with h(O) being ice thickness h(I) at x = 0 for x horizontal and positive upslope from grounded ice margins. This captures the basic fact in glaciology: the height of ice depends on how strongly ice couples to the bed. It shows how far a high convex ice sheet (phi = 0) has gone in collapsing into a low flat ice shelf (phi = 1). Here phi captures ice bed coupling under an ice stream and h(O) captures ice bed coupling beyond ice streams.

On the Pulling Power of Ice Streams

Gravity wants to pull an ice sheet to the center of the Earth, but cannot because the Earth's crust is in the way, so ice is pushed out sideways instead. Or is it? The ice sheet "sees" nothing preventing it from spreading out except air, which is much less massive than ice. Therefore, does not ice rush forward to fill this relative vacuum; does not the relative vacuum suck ice into it, because Nature abhors a vacuum? If so, the ice sheet is not only pulled downward by gravity, it is also pulled outward by the relative vacuum. This pulling outward will be most rapid where the ice sheet encounters least resistance. The least resistance exists along the bed of ice streams, where ice-bed coupling is reduced by a basal water layer, especially if the ice stream becomes afloat and the floating part is relatively unconfined around its perimeter and unpinned to the sea floor. Ice streams are therefore fast currents of ice that develop near the margins of an ice sheet where these conditions exist. Because of these conditions, ice streams pull ice out of ice sheets and have pulling power equal to the longitudinal gravitational pulling force multiplied by the ice-stream velocity. These boundary conditions beneath and beyond ice streams can be quantified by a basal buoyancy factor that provides a life-cycle classification of ice streams into inception, growth, mature, declining and terminal stages, during which ice streams disintegrate the ice sheet. Surface profiles of ice streams are diagnostic of the stage in a life cycle and, hence, of the vitality of the ice sheet.

Variations of Ice Bed Coupling Beneath and Beyond Ice Streams: The Force Balance

A geometrical force balance that links stresses to ice bed coupling along a flow band of an ice sheet was developed in 1988 for longitudinal tension in ice streams and published 4 years later. It remains a work in progress. Now gravitational forces balanced by forces producing tensile, compressive, basal shear, and side shear stresses are all linked to ice bed coupling by the floating fraction phi of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how phi varies along these flow bands where surface and bed topography are known: phi = h(O)/h(I) with h(O) being ice thickness h(I) at x = 0 for x horizontal and positive upslope from grounded ice margins. This captures the basic fact in glaciology: the height of ice depends on how strongly ice couples to the bed. It shows how far a high convex ice sheet (phi = 0) has gone in collapsing into a low flat ice shelf (phi = 1). Here phi captures ice bed coupling under an ice stream and h(O) captures ice bed coupling beyond ice streams.

Geometrical Force Balance in Glaciology

The analytical force balance traditionally used in glaciology relates gravitational forcing to ice surface slope for sheet flow and to ice basal buoyancy for shelf flow. It is unable to represent stream flow as a transition from sheet flow to shelf flow by having gravitational forcing gradually passing from being driven by surface slope to being driven by basal buoyancy downslope along the length of an ice steam. This is a serious defect, because ice streams discharge up to 90% of ice from ice sheets into the sea. The defect is overcome by using a geometrical force balance that includes basal buoyancy, represented by the ratio of basal water pressure to ice overburden pressure, as a source of gravitational forcing. When combined with the mass balance, the geometrical force balance provides a holistic approach to ice flow in which resistance to gravitational flow must be summed upstream from the calving front of an ice shelf. This is not done in the analytical force balance, and it provides the ice-thinning rate required by gravitational collapse of ice sheets as interior ice is downdrawn by ice streams.

Calculating Basal Thermal Zones Beneath the Antarctic Ice Sheet

A procedure is presented for using a simple flowline model to calculate the fraction of the bed that is thawed beneath present-day ice sheets, and therefore for mapping thawed, frozen, melting and freezing basal thermal zones. The procedure is based on the proposition, easily demonstrated, that variations in surface slope along ice flowlines are due primarily to variations in bed topography and ice-bed coupling, where ice-bed coupling for sheet flow is represented by the basal thawed fraction. This procedure is then applied to the central flowlines of flow bands on the Antarctic ice sheet where accumulation rates, surface elevations and bed topography are mapped with sufficient accuracy, and where sheet flow rather than stream flow prevails. In East Antarctica, the usual condition is a low thawed fraction in subglacial highlands, but a high thawed fraction in subglacial basins and where ice converges on ice streams. This is consistent with a greater depression of the basal melting temperature and a slower rate of conducting basal heat to the surface where ice is thick, and greater basal frictional heat production where ice flow is fast, as expected for steady-state flow. This correlation is reduced or even reversed where steady-state flow has been disrupted recently, notably where ice-stream surges produced the Dibble and Dalton Iceberg Tongues, both of which are now stagnating. In West Antarctica, for ice draining into the Pine Island Bay polynya of the Amundsen Sea, the basal thawed fraction is consistent with a prolonged and ongoing surge of Pine Island Glacier and with a recently initiated surge of Thwaites Glacier. For ice draining into the Ross Ice Shelf, long ice streams extend nearly to the West Antarctic ice divide. Over the rugged bed topography near the ice divide, no correlation consistent with steady-state sheet flow exists between ice thickness and the basal thawed fraction. The bed is wholly thawed beneath ice streams, even where stream flow is slow. This is consistent with ongoing gravitational collapse of ice entering the Ross Sea embayment and with unstable flow in the ice streams.

A Model Study of the Circulation in the Pearl River Estuary (PRE) and Its Adjacent Coastal Waters: 1. Simulations and Comparison with Observations

The Princeton Ocean Model is used to study the circulation features in the Pearl River Estuary and their responses to tide, river discharge, wind, and heat flux in the winter dry and summer wet seasons. The model has an orthogonal curvilinear grid in the horizontal plane with variable spacing from 0.5 km in the estuary to 1 km on the shelf and 15 sigma levels in the vertical direction. The initial conditions and the subtidal open boundary forcing are obtained from an associated larger-scale model of the northern South China Sea. Buoyancy forcing uses the climatological monthly heat fluxes and river discharges, and both the climatological monthly wind and the realistic wind are used in the sensitivity experiments. The tidal forcing is represented by sinusoidal functions with the observed amplitudes and phases. In this paper, the simulated tide is first examined. The simulated seasonal distributions of the salinity, as well as the temporal variations of the salinity and velocity over a tidal cycle are described and then compared with the in situ survey data from July 1999 and January 2000. The model successfully reproduces the main hydrodynamic processes, such as the stratification, mixing, frontal dynamics, summer upwelling, two-layer gravitational circulation, etc., and the distributions of hydrodynamic parameters in the Pearl River Estuary and coastal waters for both the winter and the summer season.

Impact of Earth radiation pressure on LAGEOS orbits and on the global scale

The indirect solar radiation pressure caused by reflected or re-emitted radiation by the Earth’s surface is an important non-gravitational force perturbing the orbits of geodetic satellites (Rubincam and Weiss, 1986; Martin and Rubincam, 1996). In the case of LAGEOS this acceleration is of the order of 15% of the direct solar radiation pressure. Therefore, Earth radiation pressure has a non-negligible impact not only on LAGEOS orbits, but also on the SLR-derived terrestrial reference frame. We investigate the impact of the Earth radiation pressure on LAGEOS orbits and on the SLR-derived parameters. Earth radiation pressure has a remarkable impact on the semi-major axes of the LAGEOS satellites, causing a systematic reduction of 1.5 mm. The infrared Earth radiation causes a reduction of about 1.0 mm and the Earth’s reflectivity of 0.5 mm of the LAGEOS’ semi-major axes. The global scale defined by the SLR network is changed by 0.07 ppb, when applying Earth radiation pressure. The resulting station heights differ by 0.5-0.6 mm in the solution with and without Earth radiation pressure. However, when range biases are estimated, the height differences are absorbed by the range biases, and thus, the station heights are not shifted.

Mass transport around comets and its impact on the seasonal differences in water production rates

Comets are surrounded by a thin expanding atmosphere, and although the nucleus' gravity is small, some molecules and grains, possibly with the inclusion of ices, can get transported around the nucleus through scattering (atoms/molecules) and gravitational pull (grains). Based on the obliquity of the comet, it is also possible that volatile material and icy grains get trapped in regions, which are in shadow until the comet passes its equinox. When the Sun rises above the horizon and the surface starts to heat up, this condensed material starts to desorb and icy grains will sublimate off the surface, possibly increasing the comet's neutral gas production rate on the outbound path. In this paper we investigate the mass transport around the nucleus, and based on a simplified model, we derive the possible contribution to the asymmetry in the seasonal gas production rate that could arise from trapped material released from cold areas once they come into sunlight. We conclude that the total amount of volatiles retained by this effect can only contribute up to a few percent of the asymmetry observed in some comets.

Measuring gbar with AEgIS, progress and perspectives

AEgIS experiment’s main goal is to measure the local gravitational acceleration of antihydrogen¯g and thus perform a direct test of the weak equivalence principle with antimatter. In the first phase of the experiment the aim is to measure ¯g with 1% relative precision. This paper presents the antihydrogen production method and a description of some components of the experiment, which are necessary for the gravity measurement. Current status of the AE¯gIS experimental apparatus is presented and recent commissioning results with antiprotons are outlined. In conclusion we discuss the short-term goals of the AE¯gIS collaboration that will pave the way for the first gravity measurement in the near future.

The AEgIS experiment at CERN for the measurement of antihydrogen gravity acceleration

The Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy (AEgIS) experiment is conducted by an international collaboration based at CERN whose aim is to perform the first direct measurement of the gravitational acceleration of antihydrogen in the local field of the Earth, with Δg/g = 1% precision as a first achievement. The idea is to produce cold (100 mK) antihydrogen ( ¯H) through a pulsed charge exchange reaction by overlapping clouds of antiprotons, from the Antiproton Decelerator (AD) and positronium atoms inside a Penning trap. The antihydrogen has to be produced in an excited Rydberg state to be subsequently accelerated to form a beam. The deflection of the antihydrogen beam can then be measured by using a moir´e deflectometer coupled to a position sensitive detector to register the impact point of the anti-atoms through the vertex reconstruction of their annihilation products. After being approved in late 2008, AEgIS started taking data in a commissioning phase in 2012. This paper presents an outline of the experiment with a brief overview of its physics motivation and of the state-of-the-art of the g measurement on antimatter. Particular attention is given to the current status of the emulsion-based position detector needed to measure the ¯H sag in AEgIS.

A moiré deflectometer for antimatter

The precise measurement of forces is one way to obtain deep insight into the fundamental interactions present in nature. In the context of neutral antimatter, the gravitational interaction is of high interest, potentially revealing new forces that violate the weak equivalence principle. Here we report on a successful extension of a tool from atom optics—the moiré deflectometer—for a measurement of the acceleration of slow antiprotons. The setup consists of two identical transmission gratings and a spatially resolving emulsion detector for antiproton annihilations. Absolute referencing of the observed antimatter pattern with a photon pattern experiencing no deflection allows the direct inference of forces present. The concept is also straightforwardly applicable to antihydrogen measurements as pursued by the AEgIS collaboration. The combination of these very different techniques from high energy and atomic physics opens a very promising route to the direct detection of the gravitational acceleration of neutral antimatter.

AEgIS experiment: Towards antihydrogen beam production for antimatter gravity measurements

AEgIS (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) is an experiment that aims to perform the first direct measurement of the gravitational acceleration g of antihydrogen in the Earth’s field. A cold antihydrogen beam will be produced by charge exchange reaction between cold antiprotons and positronium excited in Rydberg states. Rydberg positronium (with quantum number n between 20 and 30) will be produced by a two steps laser excitation. The antihydrogen beam, after being accelerated by Stark effect, will fly through the gratings of a moir´e deflectometer. The deflection of the horizontal beam due to its free fall will be measured by a position sensitive detector. It is estimated that the detection of about 103 antihydrogen atoms is required to determine the gravitational acceleration with a precision of 1%. In this report an overview of the AEgIS experiment is presented and its current status is described. Details on the production of slow positronium and its excitation with lasers are discussed.

Improved star camera attitude data and their effect on the gravity field

Efforts are ongoing to decrease the noise of the GRACE gravity field models and hence to arrive closer to the GRACE baseline. The most significant error sources belong the untreated errors in the observation data and the imperfections in the background models. The recent study (Bandikova&Flury,2014) revealed that the current release of the star camera attitude data (SCA1B RL02) contain noise systematically higher than expected by about a factor 3-4. This is due to an incorrect implementation of the algorithms for quaternion combination in the JPL processing routines. Generating improved SCA data requires that valid data from both star camera heads are available which is not always the case because the Sun and Moon at times blind one camera. In the gravity field modeling, the attitude data are needed for the KBR antenna offset correction and to orient the non-gravitational linear accelerations sensed by the accelerometer. Hence any improvement in the SCA data is expected to be reflected in the gravity field models. In order to quantify the effect on the gravity field, we processed one month of observation data using two different approaches: the celestial mechanics approach (AIUB) and the variational equations approach (ITSG). We show that the noise in the KBR observations and the linear accelerations has effectively decreased. However, the effect on the gravity field on a global scale is hardly evident. We conclude that, at the current level of accuracy, the errors seen in the temporal gravity fields are dominated by errors coming from sources other than the attitude data.

The effective Planck mass and the scale of inflation

Observable quantities in cosmology are dimensionless, and therefore independent of the units in which they are measured. This is true of all physical quantities associated with the primordial perturbations that source cosmic microwave background anisotropies such as their amplitude and spectral properties. However, if one were to try and infer an absolute energy scale for inflation—a priori, one of the more immediate corollaries of detecting primordial tensor modes—one necessarily makes reference to a particular choice of units, the natural choice for which is Planck units. In this note, we discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales. The uncertainty in the former relative to the latter has to do with the unknown spectrum of universally coupled particles between laboratory scales and the putative scale of inflation. These intermediate particles could be in hidden as well as visible sectors or could also be associated with Kaluza–Klein resonances associated with a compactification scale below the scale of inflation. We discuss various implications for cosmological observables.

GRAIL gravity field determination using the Celestial Mechanics Approach

The NASA mission GRAIL (Gravity Recovery and Interior Laboratory) inherited its concept from the GRACE (Gravity Recovery and Climate Experiment) mission to determine the gravity field of the Moon. We present lunar gravity fields based on the data of GRAIL’s primary mission phase. Gravity field recovery is realized in the framework of the Celestial Mechanics Approach, using a development version of the Bernese GNSS Software along with Ka-band range-rate data series as observations and the GNI1B positions provided by NASA JPL as pseudo-observations. By comparing our results with the official level-2 GRAIL gravity field models we show that the lunar gravity field can be recovered with a high quality by adapting the Celestial Mechanics Approach, even when using pre-GRAIL gravity field models as a priori fields and when replacing sophisticated models of non-gravitational accelerations by appropriately spaced pseudo-stochastic pulses (i.e., instantaneous velocity changes). We present and evaluate two lunar gravity field solutions up to degree and order 200 – AIUB-GRL200A and AIUB-GRL200B. While the first solution uses no gravity field information beyond degree 200, the second is obtained by using the official GRAIL field GRGM900C up to degree and order 660 as a priori information. This reduces the omission errors and demonstrates the potential quality of our solution if we resolved the gravity field to higher degree.