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NASA NTRS1992

Antarctic lakes (above and beneath the ice sheet): Analogues for Mars

The perennial ice covered lakes of the Antarctic are considered to be excellent analogues to lakes that once existed on Mars. Field studies of ice covered lakes, paleolakes, and polar beaches were conducted in the Bunger Hills Oasis, Eastern Antarctica. These studies are extended to the Dry Valleys, Western Antarctica, and the Arctic. Important distinctions were made between ice covered and non-ice covered bodies of water in terms of the geomorphic signatures produced. The most notable landforms produced by ice covered lakes are ice shoved ridges. These features form discrete segmented ramparts of boulders and sediments pushed up along the shores of lakes and/or seas. Sub-ice lakes have been discovered under the Antarctic ice sheet using radio echo sounding. These lakes occur in regions of low surface slope, low surface accumulations, and low ice velocity, and occupy bedrock hollows. The presence of sub-ice lakes below the Martian polar caps is possible. The discovery of the Antarctic sub-ice lakes raises possibilities concerning Martian lakes and exobiology.

Rice, J. W., Jr.↗

NASA NTRS1993

The role of the margins in ice stream dynamics

At first glance, it would appear that the bed of the active ice stream plays a much more important role in the overall force balance than do the margins, especially because the ratio of the half-width to depth for a typical ice stream is large (15:1 to 50:1). On the other hand, recent observations indicate that at least part of the ice stream is underlain by a layer of very weak till (shear strength about 2 kPa), and this weak basal layer would then imply that some or all of the resistive drag is transferred to the margins. In order to address this question, a detailed velocity profile near Upstream B Camp, which extends from the center of the ice stream, across the chaotic shear margin, and onto the Unicorn, which is part of the slow-moving ice sheet was measured. Comparison of this observed velocity profile with finite-element models of flow shows several interesting features. First, the shear stress at the margin is on the order of 130 kPa, while the mean value along the bed is about 15 kPa. Integration of these stresses along the boundaries indicates that the margins provide 40 to 50 percent, and the bed, 60 to 40 percent of the total resistive drag needed to balance the gravitational driving stress in this region. (The range of values represents calculations for different values of surface slope.) Second, the mean basal stress predicted by the models shows that the entire bed cannot be blanketed by the weak till observed beneath upstream B - instead there must be a distribution of weak till and 'sticky spots' (e.g., 85 percent till and 15 percent sticky spots of resistive stress equal to 100 kPa). If more of the bed were composed of weak till, then the modeled velocity would not match that observed. Third, the ice must exhibit an increasing enhancement factor as the margins are approached (E equals 10 in the chaotic zone), in keeping with laboratory measurements on ice under prolonged shear strain. Also, there is either a narrow zone of somewhat stiffer ice (E equals 5) outward of the shear margin, or the bed is frozen there. And last, the high shear stress and strain rate found at the margin are likely to cause significant viscous heating (q) in the marginal ice. The increase in temperature is proportional to qX/u, where X is the width of the shear zone and u is the transverse velocity component bringing cold ice in from the ice sheet outside the shear zone. Near upstream B, this heating is likely to cause an increase in temperature of 4 to 10 K. Plans are to measure this temperature increase in a series of bore holes near the margin during the 1992-93 field season, as well as to provide a more detailed description of the velocity field there.

Echelmeyer, Keith↗

NASA NTRS1993

The Arctic Ocean ice balance - A Kalman smoother estimate

The methodology of Kalman filtering and smoothing is used to integrate a 7-year time series of buoy-derived ice motion fields and satellite passive microwave observations. The result is a record of the concentrations of open water, first-year ice, and multiyear ice that we believe is better than the estimates based on the microwave data alone. The Kalman procedure interprets the evolution of the ice cover in terms of advection, melt, growth, ridging, and aging of first-year into multiyear ice. Generally, the regions along the coasts of Alaska and Siberia and the area just north of Fram Strait are sources of first-year ice, with the rest of the Arctic Ocean acting as a sink for first-year ice via ridging and aging. All the Arctic Ocean except for the Beaufort and Chukchi seas is a source of multiyear ice, with the Chukchi being the only internal multiyear ice sink. Export through Fram Strait is a major ice sink, but we find only about two-thirds the export and greater interannual variation than found in previous studies. There is no discernible trend in the area of multiyear ice in the Arctic Ocean during the 7 years.

Thomas, D. R.↗

NASA NTRS1993

Homogeneous ice nucleation and supercooled liquid water in orographic wave clouds

This study investigates ice nucleation mechanisms in cold lenticular wave clouds, a cloud type characterized by quasi-steady-state air motions and microphysical properties. It is concluded that homogeneous ice nucleation is responsible for the ice production in these clouds at temperatures below about -33 C. The lack of ice nucleation observed above -33 C indicates a dearth of ice-forming nuclei, and hence heterogeneous ice nucleation, in these clouds. Aircraft measurements in the temperature range -31 to -41 C show the following complement of simultaneous and abrupt changes in cloud properties that indicate a transition from the liquid phase to ice: disappearance of liquid water; decrease in relative humidity from near water saturation to ice saturation; increase in mean particle size; change in particle concentration; and change in temperature due to the release of latent heat. A numerical model of cloud particle growth and homogeneous ice nucleation is used to aid in interpretation of our in situ measurements. The abrupt changes in observed cloud properties compare favorably, both qualitatively and quantitatively, with results from the homogeneous ice nucleation model. It is shown that the homogeneous ice nucleation rates from the measurements are consistent with the temperature-dependent rates employed by the model (within a factor of 100, corresponding to about 1 C in temperature) in the temperature range -35 deg to -38 C. Given the theoretical basis of the modeled rates, it may be reasonable to apply them throughout the -30 to -50 C temperature range considered by the theory.

Heymsfield, Andrew J.↗

NASA NTRS1955

Statistical Survey of Icing Data Measured on Scheduled Airline Flights over the United States and Canada from November 1951 to June 1952

A statistical survey and a preliminary analysis are made of icing data collected from scheduled flights over the United States and Canada from November 1951 to June 1952 by airline aircraft equipped with NACA pressure-type icing-rate meters. This interim report presents information obtained from a continuing program sponsored by the NACA with the cooperation of the airlines. An analysis of over 600 icing encounters logged by three airlines operating in the United States, one operating in Canada and one operating up the coast to Alaska, is presented. The icing conditions encountered provided relative frequencies of many icing-cloud variables, such as horizontal extent, vertical thickness, temperatures, icing rate, liquid-water content, and total ice accumulation. Liquid-water contents were higher than data from earlier research flights in layer-type clouds but slightly lower than previous data from cumulus clouds. Broken-cloud conditions, indicated by intermittent icing, accounted for nearly one-half of all the icing encounters. About 90 percent of the encounters did not exceed a distance of 120 miles, and continuous icing did not exceed 50 miles for 90 percent of the unbroken conditions. Icing cloud thicknesses measured during climbs and descents were less than 4500 feet for 90 percent of the vertical cloud traverses.

Perkins, Porter J↗

NASA NTRS1956

Heat-requirements for Ice Protection of a Cyclically Gas-heated, 36 Degree Swept Airfoil with Partial-span Leading-edge Slat

Heating requirements for satisfactory cyclic de-icing over a wide range of icing and operating conditions have been determined for a gas-heated, 36deg swept airfoil of 6.9-foot chord with a partial-span leading-edge slat. Comparisons of heating requirements and effectiveness were made between the slatted and unslatted portions of the airfoil. Studies were also made comparing cyclic de-icing with continuous anti-icing, and cycll.cde-icing systems with and without leading-edge ice-free parting strips. De-icing heat requirements were approximately the same with either heated or unheated parting strips because of the aerodynamic effects of the 36deg sweep angle and the spanwise saw-tooth profile of leading-edge glaze-ice deposits. Cyclic de-icing heat-source requirements were found to be one-fourth or less of the heat requirements for complete anti-icing. The primary factors that affected the performance of the cyclic de-icing heating system were ambient air temperature, heat distribution, and thermal lag.

Gray, Vernon H↗

NASA NTRS1993

Retrieval of ice thickness from polarimetric SAR data

We describe a potential procedure for retrieving ice thickness from multi-frequency polarimetric SAR data for thin ice. This procedure includes first masking out the thicker ice types with a simple classifier and then deriving the thickness of the remaining pixels using a model-inversion technique. The technique used to derive ice thickness from polarimetric observations is provided by a numerical estimator or neural network. A three-layer perceptron implemented with the backpropagation algorithm is used in this investigation with several improved aspects for a faster convergence rate and a better accuracy of the neural network. These improvements include weight initialization, normalization of the output range, the selection of offset constant, and a heuristic learning algorithm. The performance of the neural network is demonstrated by using training data generated by a theoretical scattering model for sea ice matched to the database of interest. The training data are comprised of the polarimetric backscattering coefficients of thin ice and the corresponding input ice parameters to the scattering model. The retrieved ice thickness from the theoretical backscattering coefficients is compare with the input ice thickness to the scattering model to illustrate the accuracy of the inversion method. Results indicate that the network convergence rate and accuracy are higher when multi-frequency training sets are presented. In addition, the dominant backscattering coefficients in retrieving ice thickness are found by comparing the behavior of the network trained backscattering data at various incidence angels. After the neural network is trained with the theoretical backscattering data at various incidence anges, the interconnection weights between nodes are saved and applied to the experimental data to be investigated. In this paper, we illustrate the effectiveness of this technique using polarimetric SAR data collected by the JPL DC-8 radar over a sea ice scene.

Kwok, R.↗

NASA NTRS1994

Rime-, mixed- and glaze-ice evaluations of three scaling laws

This report presents the results of tests at NASA Lewis to evaluate three icing scaling relationships or 'laws' for an unheated model. The laws were LWC x time = constant, one proposed by a Swedish-Russian group and one used at ONERA in France. Icing tests were performed in the NASA Lewis Icing Research Tunnel (IRT) with cylinders ranging from 2.5- to 15.2-cm diameter. Reference conditions were chosen to provide rime, mixed and glaze ice. Scaled conditions were tested for several scenarios of size and velocity scaling, and the resulting ice shapes compared. For rime-ice conditions, all three of the scaling laws provided scaled ice shapes which closely matched reference ice shapes. For mixed ice and for glaze ice none of the scaling laws produced consistently good simulation of the reference ice shapes. Explanations for the observed results are proposed, and scaling issues requiring further study are identified.

Anderson, David N.↗

NASA NTRS1994

Ice surface temperature retrieval from AVHRR, ATSR, and passive microwave satellite data: Algorithm development and application

One essential parameter used in the estimation of radiative and turbulent heat fluxes from satellite data is surface temperature. Sea and land surface temperature (SST and LST) retrieval algorithms that utilize the thermal infrared portion of the spectrum have been developed, with the degree of success dependent primarily upon the variability of the surface and atmospheric characteristics. However, little effort has been directed to the retrieval of the sea ice surface temperature (IST) in the Arctic and Antarctic pack ice or the ice sheet surface temperature over Antarctica and Greenland. The reason is not one of methodology, but rather our limited knowledge of atmospheric temperature, humidity, and aerosol vertical, spatial and temporal distributions, the microphysical properties of polar clouds, and the spectral characteristics of snow, ice, and water surfaces. Over the open ocean the surface is warm, dark, and relatively homogeneous. This makes SST retrieval, including cloud clearing, a fairly straightforward task. Over the ice, however, the surface within a single satellite pixel is likely to be highly heterogeneous, a mixture of ice of various thicknesses, open water, and snow cover in the case of sea ice. Additionally, the Arctic is cloudy - very cloudy - with typical cloud cover amounts ranging from 60-90 percent. There are few observations of cloud cover amounts over Antarctica. The goal of this research is to increase our knowledge of surface temperature patterns and magnitudes in both polar regions, by examining existing data and improving our ability to use satellite data as a monitoring tool. Four instruments are of interest in this study: the AVHRR, ATSR, SMMR, and SSM/I. Our objectives are as follows. Refine the existing AVHRR retrieval algorithm defined in Key and Haefliger (1992; hereafter KH92) and applied elsewhere. Develop a method for IST retrieval from ATSR data similar to the one used for SST. Further investigate the possibility of estimating surface temperature from passive microwave data (in conjunction with AVHRR clear sky samples) through the use of 'effective emissivities' and physical relationships between skin temperature and subsurface temperature. Use the general method outlined in MK93 to calculate a 12-year record of clear sky equivalent surface temperatures, or possibly all-sky snow-ice interface physical temperatures, from SMMR and SSM/I, compare these temperatures to climatologies, ECMWF modeled surface temperatures, and surface temperatures predicted by a 2-D ice model. And intercompare several ice surface retrieval methods and validate them against ground measurements from the Swiss Camp on the Greenland ice sheet. Additionally, we intend to develop a surface temperature product based on AVHRR data and possibly blended with drifting buoy and meteorological station temperatures.

Key, Jeff↗

NASA NTRS1994

Backscatter characteristics of the winter ice cover in the Beaufort Sea

The microwave backscatter statistics of the sea ice cover in the winter Beaufort Sea are characterized using C band synthetic aperture radar (SAR) data collected by the European Earth Resources Satellite 1. Sea ice backscatter signatures were sampled from SAR image data collected during the winter of 1991-1992 and winter of 1992-1993. The spatial and temporal variabilities of the backscatter signatures of different ice types are discussed. The results show considerable seasonal stability of the backscatter signature of multiyear ice as well as of first-year ice. Small amplitude regional variations of the multiyear ice backscatter can be observed. Consistent contrast between multiyear ice and first-year ice is maintained throughout the season. The highest radiometric variability is observed in sea ice in leads. On the basis of these observations the backscatter from the principal ice types (multiyear and first-year) are consistent with scatterometer observations and can be easily identified under winter conditions. Correlations of the regional variations of multiyear ice signatures to physical processes are suggested.

Kwok, Ronald↗

NASA NTRS1995

Polarimetric signatures of sea ice. 1: Theoretical model

Physical, structral, and electromagnetic properties and interrelating processes in sea ice are used to develop a composite model for polarimetric backscattering signatures of sea ice. Physical properties of sea ice constituents such as ice, brine, air, and salt are presented in terms of their effects on electromagnetic wave interactions. Sea ice structure and geometry of scatterers are related to wave propagation, attenuation, and scattering. Temperature and salinity, which are determining factors for the thermodynamic phase distribution in sea ice, are consistently used to derive both effective permittivities and polarimetric scattering coefficients. Polarmetric signatures of sea ice depend on crystal sizes and brine volumes, which are affected by ice growth rates. Desalination by brine expulsion, drainage, or other mechanisms modifies wave penetration and scattering. Sea ice signatures are further complicated by surface conditions such as rough interfaces, hummocks, snow cover, brine skim, or slush layer. Based on the same set of geophysical parameters characterizing sea ice, a composite model is developed to calculate effective permittivities and backscattering covariance matrices at microwave frequencies to interpretation of sea ice polarimetric signatures.

Nghiem, S. V.↗

NASA NTRS1995

Polarimetric signatures of sea ice. 2: Experimental observations

Experimental observations of polarimetric signatures are presented for sea ice in the Beaufort Sea under cold winter conditions and interpreted with the composite model developed in Part 1. Polarimetric data were acquired in March 1988 with the Jet Propulsion Laboratory multifrequency airborne synthetic aperture radar (SAR) during the Beaufort Sea Flight Campaign. The experimental area was located near 75 N latitude and spanned 140 deg-145 deg W longitude. Selected sea ice scenes contain various ice types, including multiyear, thick first-year, and thin lead ice. Additionally, the C band SAR on the first European Remote Sensing Satellite provides supplementary backscattering data of winter Beaufort Sea ice for small incident angles (20 deg-26 deg) at vertical polarization. Sea ice characterization and environment data used in the model were collected at the Applied Physics Laboratory drifting ice station to the northeast of Prudhoe Bay; additional data from field and laboratory experiments are also utilized in this analysis. The model related sea ice polarimetric backscattering signatures to physical, structural, and electromagnetic properties of sea ice. Scattering mechanisms contributing to sea ice signatures are explained, and sensitivies of polarimetric signatures to sea ice characterization parameters are studied.

Nghiem, S. V.↗

NASA NTRS1995

Polarimetric Signatures of Sea Ice: Theoretical Model - Part 1

Physical, structural, and electromagnetic properties and interrelating processes in sea ice are used to develop a composite model for polarimetric backscattering signatures of sea ice. Physical properties of sea ice constituents such as ice, brine, air, and salt are presented in terms of their effects on electromagnetic wave interactions. Sea ice structure and geometry of scatterers are related to wave propagation, attenuation, and scattering. Temperature and salinity, which are determining factors for the thermodynamic phase distribution in sea ice, are consistently used to derive both effective permittivities and polarimetric scattering coefficients. Polarimetric signatures of sea ice depend on crystal sizes and brine volumes, which are affected by ice growth rates. Desalination by brine expulsion, drainage, or other mechanisms modifies wave penetration and scattering. Sea ice signatures are further complicated by surface conditions such as rough interfaces, hummocks, snow cover, brine skim, or slush layer. Based on the same set of geophysical parameters characterizing sea ice, a composite model is developed to calculate effective permittivities and backscattering covariance matrices at microwave frequencies for interpretation of sea ice polarimetric signatures.

Nghiem, S. V.↗

NASA NTRS1999

External Sources of Water for Mercury's Putative Ice Deposits

Radar images have revealed the possible presence of ice deposits in Mercury's polar regions. Although thermal models indicate that water ice can be stable in permanently shaded regions near Mercury's poles, the ultimate source of the water remains unclear. We use stochastic models and other theoretical methods to investigate the role of external sources in supplying Mercury with the requisite amount of water. By extrapolating the current terrestrial influx of interplanetary dust particles to that at Mercury, we find that continual micrometeoritic bombardment of Mercury over the last 3.5 byr could have resulted in the delivery of (3-60) x 10(exp 16) grams of water ice to the permanently shaded regions at Mercury's poles (equivalent to an average ice thickness of 0.8-20 m). Erosion by micrometeoritic impact on exposed ice deposits could reduce the above value by about a half. For comparison, the current ice deposits on Mercury are believed to be somewhere between approx. 2 and 20 m thick. Using a Monte Carlo model to simulate the impact history of Mercury, we find that asteroids and comets can also deliver an amount of water consistent with the observations. Impacts from Jupiter-family comets over the last 3.5 billion years can supply (0.1-200) x 10(exp 16) grams of water to Mercury's polar regions (corresponding to ice deposits 0.05-60 m thick), Halley-type comets can supply (0.2-20) x 10(exp 16) grams of water to the poles (0.07-7 m of ice), and asteroids can provide (0.4-20) x 10(exp 16) grams of water to the poles (0.1-8 m of ice). Although all these external sources are nominally sufficient to explain the estimated amount of ice currently at Mercury's poles, impacts by a few large comets and/or asteroids seem to provide the best explanation for both the amount and cleanliness of the ice deposits on Mercury. Despite their low population estimates in the inner solar system, Jupiter-family comets are particularly promising candidates for delivering water to Mercury because they have a larger volatile content than asteroids and more favorable orbital and impact characteristics than Halley-type comets.

Moses, Julianne I.↗

NASA NTRS1998

Computer Modeling of the Thermal Conductivity of Cometary Ice

The main objective of this research was to estimate the thermal conductivity of cometry ices from computer simulations of model amorphous ices. This was divided into four specific tasks: (1) Generating samples of amorphous water ices at different microporosities; (2) Comparing the resulting molecular structures of the ices with experimental results, for those densities where data was available; (3) Calculating the thermal conductivities of liquid water and bulk amorphous ices and comparing these results with experimentally determined thermal conductivities; and (4) Investigating how the thermal conductivity of amorphous ice depends upon the microscopic porosity of the samples. The thermal conductivity was found to be only weakly dependent on the microstructure of the amorphous ice. In general, the amorphous ices were found to have thermal conductivities of the same order of magnitude as liquid water. This is in contradiction to recent experimental estimates of the thermal conductivity of amorphous ice, and it is suggested that the extremely low value obtained experimentally is due to larger-scale defects in the ice, such as cracks, but it is not an intrinsic property of the bulk amorphous ice.

Bunch, Theodore E.↗

NASA NTRS2000

Remote Sensing of In-Flight Icing Conditions: Operational, Meteorological, and Technological Considerations

Remote-sensing systems that map aircraft icing conditions in the flight path from airports or aircraft would allow icing to be avoided and exited. Icing remote-sensing system development requires consideration of the operational environment, the meteorological environment, and the technology available. Operationally, pilots need unambiguous cockpit icing displays for risk management decision-making. Human factors, aircraft integration, integration of remotely sensed icing information into the weather system infrastructures, and avoid-and-exit issues need resolution. Cost, maintenance, power, weight, and space concern manufacturers, operators, and regulators. An icing remote-sensing system detects cloud and precipitation liquid water, drop size, and temperature. An algorithm is needed to convert these conditions into icing potential estimates for cockpit display. Specification development requires that magnitudes of cloud microphysical conditions and their spatial and temporal variability be understood at multiple scales. The core of an icing remote-sensing system is the technology that senses icing microphysical conditions. Radar and microwave radiometers penetrate clouds and can estimate liquid water and drop size. Retrieval development is needed; differential attenuation and neural network assessment of multiple-band radar returns are most promising to date. Airport-based radar or radiometers are the most viable near-term technologies. A radiometer that profiles cloud liquid water, and experimental techniques to use radiometers horizontally, are promising. The most critical operational research needs are to assess cockpit and aircraft system integration, develop avoid-and-exit protocols, assess human factors, and integrate remote-sensing information into weather and air traffic control infrastructures. Improved spatial characterization of cloud and precipitation liquid-water content, drop-size spectra, and temperature are needed, as well as an algorithm to convert sensed conditions into a measure of icing potential. Technology development also requires refinement of inversion techniques. These goals can be accomplished with collaboration among federal agencies including NASA, the FAA, the National Center for Atmospheric Research, NOAA, and the Department of Defense. This report reviews operational, meteorological, and technological considerations in developing the capability to remotely map in-flight icing conditions from the ground and from the air.

Ryerson, Charles C.↗

NASA NTRS1997

Year-Round Pack Ice in the Weddell Sea, Antarctica: Response and Sensitivity to Atmospheric and Oceanic Forcing

Using a dynamic-thermodynamic numerical sea-ice model, external oceanic and atmospheric forcings on sea ice in the Weddell Sea are examined to identify physical processes associated with the seasonal cycle of pack ice, and to identify further the parameters that coupled models need to consider in predicting the response of the pack ice to climate and ocean-circulation changes. In agreement with earlier studies, the primary influence on the winter ice-edge maximum extent is air temperature. Ocean heat flux has more impact on the minimum-ice-edge extent and in reducing pack-ice thickness, especially in the eastern-Weddell Sea. Low relative humidity enhances ice growth in thin ice and open-water regions, producing a more realistic ice edge along the coastal areas of the western-Weddell Sea where dry continental air has an impact. The modeled extent of the Weddell summer pack is equally sensitive to ocean heat flux and atmospheric relative humidity variations with the more dynamic responses being from the atmosphere. Since the atmospheric regime in the eastern Weddell is dominated by marine intrusions from lower latitudes, with high humidity already, it is unlikely that either the moisture trans- port could be further raised or that it could be significantly lowered because of its distance from the continent (the lower humidity source). Ocean heat-transport variability is shown to lead to overall ice thinning in the model response and is a known feature of the actual system, as evidenced by the occurrence of the Weddell Polynya in the mid 1970s.

Geiger, Cathleen A.↗

NASA NTRS1999

Measuring Greenland Ice Mass Variation With Gravity Recovery and the Climate Experiment Gravity and GPS

The response of the Greenland ice sheet to climate change could significantly alter sea level. The ice sheet was much thicker at the last glacial maximum. To gain insight into the global change process and the future trend, it is important to evaluate the ice mass variation as a function of time and space. The Gravity Recovery and Climate Experiment (GRACE) mission to fly in 2001 for 5 years will measure gravity changes associated with the current ice variation and the solid earth's response to past variations. Our objective is to assess the separability of different change sources, accuracy and resolution in the mass variation determination by the new gravity data and possible Global Positioning System (GPS) bedrock uplift measurements. We use a reference parameter state that follows a dynamic ice model for current mass variation and a variant of the Tushingham and Peltier ICE-3G deglaciation model for historical deglaciation. The current linear trend is also assumed to have started 5 kyr ago. The Earth model is fixed as preliminary reference Earth model (PREM) with four viscoelastic layers. A discrete Bayesian inverse algorithm is developed employing an isotropic Gaussian a priori covariance function over the ice sheet and time. We use data noise predicted by the University of Texas and JPL for major GRACE error sources. A 2 mm/yr uplift uncertainty is assumed for GPS occupation time of 5 years. We then carry out covariance analysis and inverse simulation using GRACE geoid coefficients up to degree 180 in conjunction with a number of GPS uplift rates. Present-day ice mass variation and historical deglaciation are solved simultaneously over 146 grids of roughly 110 km x 110 km and with 6 time increments of 3 kyr each, along with a common starting epoch of the current trend. For present-day ice thickness change, the covariance analysis using GRACE geoid data alone results in a root mean square (RMS) posterior root variance of 2.6 cm/yr, with fairly large a priori uncertainties in the parameters and a Gaussian correlation length of 350 km. Simulated inverse can successfully recover most features in the reference present-day change. The RMS difference between them over the grids is 2.8 cm/yr. The RMS difference becomes 1.1 cm/yr when both are averaged with a half Gaussian wavelength of 150 km. With a fixed Earth model, GRACE alone can separate the geoid signals due to past and current load fairly well. Shown are the reference geoid signatures of direct and elastic effects of the current trend, the viscoelastic effect of the same trend starting from 5 kyr ago, the Post Glacial Rebound (PGR), and the predicted GRACE geoid error. The difference between the reference and inverse modeled total viscoelastic signatures is also shown. Although past and current ice mass variations are allowed the same spatial scale, their geoid signals have different spatial patterns. GPS data can contribute to the ice mass determination as well. Additional information is contained in the original.

Wu, Xiao-Ping↗