estimation of sampling efficiency of the big spring number eight bsne sampler at different heights based on sand particle size in the taklimakan desert abstract the big spring number eight bsne sampler is an important and widely used instrument in studies of aeolian sand transport its sampling efficiency is an important parameter and varies with particle size however little is known about the variations in sampling efficiency caused by the differences in particle size with height the variations in particle size with height from 10 to 200 cm were obtained from a field experiment at four sites in the taklimakan desert from may 2010 to april 2011 the variation in the sampling efficiency of the bsne sampler with particle size was estimated based on previous studies and a wind tunnel experiment it was found that the average particle size decreased with height above ground from 10 to 200 cm at three experimental sites while at the other site it decreased from 10 to 15 cm and then slightly increased the percentage distribution of particle sizes with height was similar for sizes below 63 m and between 125 and 200 m at all experimental sites but there were differences in the percentage of size classes between 63 and 125 m and above 200 m the sampling efficiencies ranged from 66 27 to 58 98 64 97 to 57 47 56 04 to 52 76 and 72 07 to 58 9 at the four sites respectively with an average of 64 84 to 57 03 at heights from 10 to 200 cm after correcting for sampling efficiency the amount of aeolian sand that passed through a section of 100 cm width 200 cm height increased by 44 5 52 1 78 8 and 26 4 at the four sites respectively with an average of 50 5 these results indicate that the sampling efficiency of the device needs to be considered when making observations across a gradient of particle sizes

long period variations in gravity field caused by mantle anelasticity a numerical perturbation approach is used to assess the effect of mantle anelasticity on the earth s zonal response coefficient the zonal geopotential coefficient j2 and the orbital node of geodetic satellites the theoretical predictions are used to compare solutions of elastic ocean tide models and tides observed by geodetic satellites for mr m m ssa and s a the discrepancies between the satellite observed tides and the solution from schwiderski and recent altimetric ocean tide models can be partly explained by the predicted effect of mantle anelasti city at mf and m m frequencies approximately 80 of the observed semiannual variation in 2 by geodetic satellites can be attributed to the tidal deformation from anelasticity and from the classical equilibrium ocean the predicted for the 18 6 year tide was computed for an earth with an anelastic mantle and a nonequilibrium ocean the range of the lower and upper bounds of for the 18 6 year tide is from 0 345 to 0 377 in amplitude and from 6 o to 3 o in phase with preferred amplitude of 0 365 and phase of 0 o8

field wind erosion measurements with big spring number eight bsne and modified wilson and cook mwac samplers article i nfo the aim of this study was to compare the horizontal mass flux hmf of aeolian sediment obtained from field wind erosion measurements with the modified wilson and cook mwac and big spring number eight bsne and to analyze the effectiveness of exponential power logarithmic and rational equations to calculate the horizontal mass transport hmt for each sampler type with this purpose wind erosion was measured on fine sandy loam soil in 10 erosion events between december 4 2008 and july 1 2009 the relative efficiency of the mwac related to bsne rew b quotient between the hmf of mwac and the hmf of bsne multiplied by 100 was 247 while rew bobtained from the absolute efficiency of the bsne 85 to 95 and mwac 44 to 120 found in previous studies was between 51 and 141 the rew b increased with height as a consequence of the wind speed increase and particle size decrease which reduces the efficiency of the bsne while the efficiency of the mwac remains constant depending on the equation used the hmt of mwac was from 2 1 to 2 53 times higher than the hmt of bsne indicating that if the hmf is corrected by the rew b found in this study the hmt obtained with the mwac and bsne is similar the hmt obtained from exponential equations was 16 higher than the power equation and 62 and 11 lower than logarithmic and rational equations respectively in spite of this the hmt obtained with different equations presented a good relationship with each other pb0 05 indicating that the hmt can be corrected and compared between equations this study shows that the hmf and hmt data obtained from field measurements with the bsne and mwac are different nevertheless comparable measurements of wind erosion can be obtained with both samplers taking into account the relative efficiency and the relationship between equations found in this study

dendrogeomorphic reconstruction of past snow avalanche events in bâlea glacial valley făgăras massif southern carpathians romanian carpathians abstract snow avalanches are a major hazard in the southern carpathians romanian carpathians and cause damage to transportation routes or infrastructure and losses of human lives in these mountains the scientific understanding of avalanches is still poor the main objectives of this study were to reconstruct spatio temporal patterns of avalanche events to complement written records in the b lea glacial valley located in the central part of northern slope of the f g ras massif and to identify the winter weather conditions responsible for avalanche occurrence using a dendrogeomorphologic approach the analysis was based on tree ring series from 293 affected picea abies trees in four avalanche tracks our results from tree ring records yielded 24 and 17 snow avalanches in the 1867 2012 chronology in first and second track 24 and 12 snow avalanches in the 1870 2012 chronology in third and in fourth track the tree ring based analysis of the 586 extracted increment cores allowed the identification of 853 growth disturbances related to past avalanche activity the most frequent response is found as reaction wood 64 1 followed by abrupt growth changes 20 6 traumatic resin ducts 13 and callus tissue 2 3 a total of 77 event years with aai 10 were reconstructed the reconstruction revealed five high magnitude avalanches aai 30 25 medium magnitude avalanches 20 aai 30 and 47 small magnitude avalanches 10 aai 20 the return period values vary between 16 7 and 23 6 years based on the reconstructed chronologies our analyses identified 13 cases of synchronicity of events with aai 10 this synchronicity indicates the decisive role of local weather conditions which are responsible for the occurrence of extreme snow avalanches the weather conditions triggering extreme avalanche correspond with high amounts of snowfall and consequently thick snowpack even if the largest snowfalls are not necessarily associated with extreme avalanches

large scale mass redistribution in the oceans 1993 2001 1 a recent study of satellite laser ranging measurements by cox and chao 2002 indicates that large scale mass redistribution has caused a rapid change in earth s dynamic oblateness j2 since 1998 using satellite altimeter observations and two runs of an ocean general circulation models ogcm we examine mass variations in the oceans and their estimated effect on j2 combined altimeter and ogcm results indicate variations similar to the j2 changes in 1998 and predict considerably larger oceanic effects on the j2 anomaly than purely ogcm estimates suggesting that the oceans should not be ruled out by any means as a significant source of this interesting geodetic anomaly until they have been studied further

near bed mass flux profiles in aeolian sand transport high resolution measurements in a wind tunnel vertical profiles of the streamwise mass flux of blown sand in the near bed 17 mm region are analysed from high resolution measurements made using an optical sensor in a wind tunnel this analysis is complemented by detailed measurements of mass flux and mean velocity profiles throughout the boundary layer depth 0 17 m using passive chambered sand traps of small dimensions and armoured thermal anemometers respectively the data permit a preliminary analysis of the relations between the observed forms of the profiles of near bed fluid stress and horizontal mass flux within a carefully conditioned boundary layer profiles of mass flux density are found to be characterized by three regions of differing gradient with transitions at about 2 mm and 19 mm above the bed the exponential decay of mass flux with height is confirmed for elevations above 19 mm and when plotted as a function of u 2 g a parameter of mean vertical trajectory height in saltation the gradient of mass flux in this region scales with the wake corrected friction velocity u where u 0 30 m s 1 a separate near bed region of more intense transport below 19 mm is identified which carries 80 per cent of the total mass flux this region is evident in some previous field and wind tunnel data but not in profiles simulated by numerical models ventilated passive sand traps underestimate mass flux in this region by 37 per cent at slow or moderate wind speeds a third significant region below 2 mm is observed these regions are likely to be related to grain populations in successive saltation low energy ejections and intermittent bed contact respectively optical measurements reveal locally high grain concentrations at some elevations below 5 mm these heights scale with transport rate mass flux gradient and wind speed copyright 1999 john wiley sons ltd

long period perturbations in starlette orbit and tide solution continuous and dynamically consistent orbits have been computed using satellite laser ranging slr data to starlette for a one year period during 1976 and 1977 and the three year period from 1983 through 1985 a low degree and order ocean tide solution consisting of a total of 66 tidal parameters from 14 tidal constituents was obtained in a combined solution using both the one and three year starlette orbits an enhanced model of the schwiderski 1980 tide solution was used both as the a priori and the background tide model the model contains 368 tidal coefficients from 21 tidal constituents yearly values for the second degree annual tides sa which produce seasonal variations on the starlette node were obtained also these variations were found to have year to year fluctuations of more than 25 about the mean value and produced significant long period perturbations in the starlette orbit the starlette tide solution is in good agreement with the schwiderski tide solutions and with other satellite solutions including multi satellite tide solutions the average uncertainties are approximately 0 1 cm for the estimated semidiurnal and diurnal tides and 0 4 cm for the long period tides the discrepancies of effective k2 inferred from the starlette tide solution and other tide solutions are less than 0 01 the tide solutions were evaluated using orbit fits of a three year lageos and a one year starlette long arc the results indicate that the starlette tide solution produces significantly improved orbit fits for both lageos and starlette the uncertainties for the estimated tide model coefficients were used to predict tidal errors for the lageos orbit and were found to be consistent with the apparent tidal errors present in this orbit the computed secular change in the moon s mean motion due to tidal dissipation is 24 8 0 8 arc second century2 which is in good agreement with the results obtained from other investigations

the global geodynamic effect of the macquarie ridge earthquake besides generating seismic waves which eventually dissipate an earthquake also generates a static displacement field everywhere within the earth this global displacement field rearranges the earth s mass distribution causing the earth s rotational properties and gravitational field to change the size of these changes depends in general upon the size of the earthquake the macquarie ridge earthquake of may 23 1989 is considered to be the largest earthquake to have occurred since the 1977 sumba and tonga events as such the coseismic effect of this earthquake upon the earth s length of day polar motion and low degree harmonic coefficients of the gravitational field are computed it is found that this earthquake should have caused the length of day to decrease by 0 06 mu sec the position of the mean rotation pole to shift 0 11 milli arcsec towards 323 degree e longitude and selected degree l 2 5 gravitational field coefficients to change by about 1 part in 10 sup 13 these changes are all smaller than can be detected by current observational techniques however changes of this size could perhaps be detected in the future with the implementation of proposed improvements to the techniques of monitoring the earth s rotation and especially for the low degree gravitational field coefficients with the placement ofmore gps receivers onboard orbiting spacecraft less

a test of recent inferences of net polar ice mass balance based on long wavelength gravity abstracta comprehensive analysis of satellite datasets has estimated that the ice sheets of greenland west antarctica the antarctic peninsula and east antarctica experienced a net mass loss of 100 92 gt yr 1 over the period 1992 2000 and 298 58 gt yr 1 over the period 2000 11 representing an increase of 198 109 gt yr 1 between the two epochs the authors demonstrate that the time rate of change of the degree four zonal harmonic of earth s gravitational potential provides an independent check on these mass balances that is less sensitive to uncertainties that have contaminated previous analyses of the degree 2 zonal harmonic e g due to ongoing glacial isostatic adjustment gia solid earth body tides and core mantle coupling for the period 2000 11 the signal implied by the ice sheet mass flux cited above is 3 8 0 6 10 11 yr 1 whereas the change in the harmonic across the two epochs is 2 3 1 1 10 11 yr 1 in comparison using satellite laser ranging slr data the authors

lageos scientific results introduction the lageos spacecraft is unique in that both its design and orbital characteristics were specifically chosen for high resolution geodynamic studies using satellite laser ranging techniques since its launch in 1976 the precision of single shot ranging observations made on the satellite has improved from several decimeters to a few centimeters with this level of precision it is possible to use lageos data for studies of contemporary plate movement polar motion gravity earth rotation and earth and ocean tides inferences about mantle structure and dynamics angular momentum coupling between the earth and its atmosphere and perturbative effects acting on earth satellites are being extracted from the data this special issue of the journal of geophysical research presents the current research results derived from lageos data

postglacial rebound observed by lageos and the effective viscosity of the lower mantle sixty four observations of the orbital node made by the lageos satellite over a five year time interval reveal an acceleration of 8 1 or 1 8 x 10 to the 8 power arcseconds day 2 due to a source which is not presently modeled in the geodyn orbit determination computer program this acceleration cannot be explained by the ocean tide with 18 6 year period assuming it to be an equilibrium tide instead it seems to be due to postglacial rebound which changes the j 2 coefficient in the spherical harmonic expansion of the earth s gravitational field at the rate of 8 2 or 18 x 10 to the 19th power s this in turn accelerates the node this rate does not agree with the 32 x 10 to the 19th power s predicted by wu and peltier s 1982 l2 model which has upper and lower mantle effective viscosities of 10 to the 21st and 22nd powers pa s respectively it does agree well with their l1 model which gives about 10 x 10 to the 19th power s since the effective viscosity is 10 to the 21st power pa s throughout the entire mantle in the l1 model the results support the contentions that the efective viscosity is near 10 to the 21st power pa s everyhere in the mantle and this relatively low value for the effective viscosity may have permitted several degrees of polar wander due to glaciation during the quaternary ice age previously announced in star as n84 13705

local gravity anomalies produced by dislocation sources rundle 1978 and walsh and rice 1979 have shown that the change in the vertical component of gravity is proportional to uplift for a spherical source of dilatation and for slip on an infinitely long dip slip fault in the first case no free air gravity anomaly is produced and in the second case no bouguer gravity anomaly gravity anomalies due to other dislocation sources in three dimensions are as follows for strike slip faulting the ratio of the gravity change to uplift depends upon position however the gravity change contours are roughly similar to those corresponding to a zero free air gravity anomaly nor is the ratio constant for dip slip faulting except for the two special cases of dip slip on a vertical fault and horizontal slip on a horizontal fault neither of which produce a bouguer anomaly the bouguer anomaly produced by an open horizontal crack is the same as would be produced had the material within the crack been mined out without deforming the solid if the horizontal crack were filled with material of density equal to the host rock a good approximation to sill formation no bouguer anomaly is produced for cracks of other inclinations the ratio of gravity change to uplift is not constant thus dilatancy in general does not correspond to the absence of a free air anomaly as might be suggested by the special case of a spherical source of dilatation for two dimensional models a cylindrical source of dilatation produces no free air gravity anomaly dip slip faulting produces no bouguer anomaly and open cracks produce a bouguer anomaly equal to that which would be produced had the material within the crack been mined out without deforming the solid a two dimensional crack filled with material of density equal to that of the host rock would produce no bouguer anomaly jachens et al 1983 have reported temporal changes in gravity elevation and area strain along the san andreas fault in southern california such that the bouguer anomaly apparently remains unchanged and the uplift to strain ratio is about 100 km several dislocation mechanisms are proposed that fulfill these constraints but these mechanisms appear to be rather contrived and are not regarded as satisfactory explanations

effect of melting glaciers on the earth s rotation and gravitational field 1965 1984 summary yearly mass balance data for 85 glaciers in 13 of the 31 mountain glacier systems designated in meier s 1984 paper are averaged for the years 1965 1984 average rates of volume change for the 13 regions are compared to meier s 1984 estimates of glacial melting these data cover regions that account for about 74 per cent of the volume change estimated to have occurred in all the 31 mountain glacier systems from 1900 to 1984 the volume changes in the 13 regions tend to be less than those calculated by using changes in the volume of glaciers between 1900 and 1961 meier 1984 although the reason for this difference is not well known it could result from melting during the first half of the 20th century of ice accumulated during earlier periods or a decrease in the rise in atmospheric temperatures from 1945 to 1980 spatial and temporal empirical orthogonal functional analysis is used to bring out the similarities and differences among the 13 regions and identify those regions contributing most to the variance of the data set these regions are not necessarily those with the greatest average rates of volume change enough spatial variability is present to support the hypothesis that satellites may eventually be able to discern changes in the earth s glaciers through the gravitational field even though the signal from the mass change is small and changes in the gravitational field of the earth are contaminated with gravity signals from other mass changes on the earth s surface and interior zonal coefficients of the spherical harmonic expansion of the gravitational potential are calculated for yearly mass changes for these 13 regions up to i 8 there is little similarity at decadal periods between the polar motion excitation from mountain glacier systems and the observed excitation the majority of observed polar motion excitation could be due to other surface mass changes including continental water storage see for example chao 1988 the amplitude of the interannual excitation due to the glacial signal computed here is less than 10 per cent of the observed excitation and the secular trend of the excitation from melting glaciers in the 13 regions is about one quarter of that of the observed excitation yearly changes in the length of day lod are calculated from the glacial signals and compared to the observed yearly alod excess lod signal the contribution of glaciers to the total excess lod signal is less than one part in 150 of the observed signal as alod is caused mainly by core mantle coupling at decadal periods and atmospheric coupling at shorter periods the contributions to displacement of the centre of mass of the solid earth as seen by a satellite tracked from the earth s surface are calculated for the mountain glaciers and an 80 year record of global sea level for the glaciers the average displacements are as much as 1 mm over 20 years and for sea level the z coordinate of the average displacement is 5mm over its 80 year record interannual signals

constraints on short term mantle rheology from the j observation and the dispersion of the 18 6 y tidal love number abstract the nature of short term mantle rheology for timescales between the seismic frequency band and a few hundred years remains relatively unknown we have made use of two pieces of information which have emerged as a consequence of the recent acquisition of data from the lageos satellite to place some contraints on the rheological parameters of short term mantle rheology the first is the secular variation of the gravitational harmonic j the second is the amount of dispersion of the tidal love number for the 18 6 y tide which has been inferred to be 20 two types of rheology have been considered the first is a frequency dependent q rheology an analytical expression for the transformed shear modulus has been developed from the truncated retardation spectrum explicitly for this purpose the second anelastic rheology we have used is a standard linear solid where the parameters of importance are the relaxation strength and the short term viscosity 2 rheological parameters of the frequency dependent q model previously proposed by lambeck and nakiboglu to explain the dispersion of the tidal love number for a 18 6 y period are found to produce too much dispersion for the chandler wobble and to yield seismic q s between o 103 and o 104 for fundamental toroidal modes which are not compatible with the data we have used instead a three layer model consisting of an elastic lithosphere a mantle with a standard linear solid rheology whose debye peak lies beyond the long time cutoff of the retardation spectrum and an inviscid core for relaxation strength of around 1 and short term viscosity 2 j would result from earthquake excitation a sharp decrease of the tidal dispersion takes place for 2 5 1020 p and 1 0 for smaller values of relaxation strength 0 15 the maximum tidal dispersion is only 9 and decreases gradually as 2 is increased beyond 5 1020 p we have found that the maximum dispersion caused by the maxwell rheology is small around 5 even for asthenospheric viscosities of o 1018p these results suggest that the datum of 18 6 y tidal dispersion can be utilized eventually to place constraints on potential candidates of short term mantle rheology

mantle phase transitions and the free air gravity anomalies over fennoscandia and laurentia the interpretation of free air gravity anomalies over present day centers of postglacial rebound has always been controversial we show that the observed gravity anomalies over both fennoscandia and laurentia and the associated relative sea level variations since deglaciation are explicable with a simple newtonian viscoelastic model of the earth if the earth model includes the density jumps in the mantle associated with the phase transitions at 420 and 670 km depth the result has important implications for mantle convection since the observed free air anomalies are very sensitive to the viscosity of the mantle beneath the deepest phase transition

pleistocene deglaciation and the earth s rotation implications for mantle viscosity summary recent results from the analysis of postglacial rebound data suggest that the viscosity of the earth s mantle increases through the transition region models which fit both relative sea level and free air gravity data have viscosities which increase from a value near 1022 poise in the upper mantle beneath the lithosphere to a value of about 1023 poise in the lower mantle in this paper we analyse the effect of deglaciation upon the earth s rotation and thereby show that the observed secular trend polar wander evident in the ils ipms pole path and measurements of the non tidal acceleration of the length of day are both consistent with the viscosity profile deduced from postglacial rebound the two analyses are therefore mutually reinforcing

viscosity of the lower mantle as inferred from rotational data until recently most estimates of the deep mantle viscosity were based on analyses of postglacial uplifts and there were no serious estimates of the sensitivity of the derived viscosity solutions to variations of the input parameters such as those associated with the surface loading in this paper the viscosity of the lower mantle is arrived at by making comparisons of the observed secular motions of the earth s rotation axis with theoretical results from a layered viscoelastic rotating earth which has been subjected to glacial forcing our model consisting of an elastic lithosphere a two layer adiabatically stratified viscoelastic mantle and an inviscid core is essentially analytical and this makes it economically feasible to use as an aid in conducting an extensive sensitivity analysis of the lower mantle viscosity from changes in the parameters connected with the deglaciation phenomenon both sets of rotational data polar wander and nontidal deceleration of the length of the day have been employed to constrain the viscosity structure on the basis of this type of investigation the viscosity of the lower mantle is found invariably to be larger than that of the upper mantle and lies between 1 and 4 1022 p our results which just rely on the second degree harmonic of the strain field also lead to a determination of an upper bound to the thickness of the globally averaged lithosphere this value ranging between 130 and 190 km suggests that strong lateral heterogeneities between oceanic and continental plates may extend a few hundred kilometers into the upper mantle

time variability of the earth s gravity field hydrological and oceanic effects and their possible detection using grace the grace satellite mission scheduled for launch in 2001 is designed to map out the earth s gravity field to high accuracy every 2 4 weeks over a nominal lifetime of 5 years changes in the gravity field are caused by the redistribution of mass within the earth and on or above its surface grace will thus be able to constrain processes that involve mass redistribution in this paper we use output from hydrological oceanographic and atmospheric models to estimate the variability in the gravity field i e in the geoid due to those sources we develop a method for constructing surface mass estimates from the grace gravity coefficients we show the results of simulations where we use synthetic grace gravity data constructed by combining estimated geophysical signals and simulated grace measurement errors to attempt to recover hydrological and oceanographic signals we show that grace may be able to recover changes in continental water storage and in seafloor pressure at scales of a few hundred kilometers and larger and at timescales of a few weeks and longer with accuracies approaching 2 mm in water thickness over land and 0 1 mbar or better in seafloor pressure

power laws and snow avalanches 1 this paper presents evidence of frequency size power laws in several groups of snow avalanche paths other natural hazards such as earthquakes and forest fires exhibit similar power law relationships in addition an analysis of the response of one group of snow avalanche paths to storms through time demonstrates a power law between the response of the system and the binned frequency of those responses our results as well as our experience with these complex non linear systems are consistent with self organized criticality the practical implication of this work is that the frequency size relationship for small and medium sized avalanches may be useful for quantifying the risk of large snow avalanches within a group of avalanche paths

viscoelastic responses of a hard transition zone effects on postglacial uplifts and rotational signatures abstract recent studies from laboratory s karato 1989 and monte carlo inversion y ricard et al 1989 have argued that the transition zone between 400 and 670 km depth may be stiffer than the lower mantle and the upper mantle above it using a five layer viscoelastic spherical model we have calculated the transient displacements of postglacial rebound the induced polar motions and the temporal variations of the geopotential up to degree eight of the zonal coefficients we have compared two models a one with two viscoelastic layers separated at 670 km and b the other with three layers in which a hard garnet layer lies between the upper and lower mantle forward modelling shows that it may be possible to discern the presence of a hard garnet layer with a viscosity of at least ten times greater than the upper mantle on the basis of uplift data near the center of the former laurentide ice sheet and from polar wander and j 2 data temporal variations of higher gravity harmonics such as j 6 and j 8 can potentially place even tighter constraints on the rheological properties of the hard transition zone a lower mantle viscosity between 2 and 4 10 22 pa s is generally preferred in models with a garnet layer which may be as large as 50 times more viscous than the upper mantle

the slr secular gravity variations and their impact on the inference of mantle rheology and lithospheric thickness a long history of slr satellite laser ranging observations of the geodetic satellites lageos i lageos ii starlette and stella have been analyzed in order to estimate the time series of the low degree zonal coefficients in the earth gravity field up to degree six and derive their secular drifts the paper will point out the critical aspects of the analysis process and will compare the estimated zonal rates with other published results comparison of these zonal rates with the results of global viscoelastic earth models forced by pleistocenic deglaciation shows that the slr retrieved zonals and the lumped odd zonals can be used to infer the upper mantle viscosity and lithospheric thickness discrepancies in the viscosity profiles required to reproduce the different zonals seem to indicate ongoing mass redistribution over the earth

radial profile of mantle viscosity results from the joint inversion of convection and postglacial rebound observables we present new inferences of the radial profile of mantle viscosity that simultaneously fit long wavelength free air gravity harmonics associated with mantle convection and a large set of decay times estimated from the postglacial uplift of sites within previously glaciated regions hudson bay arctic canada and fennoscandia the relative sea level variation at these latter sites is constrained by age height pairs obtained by geological survey rather than the subjective trends which are commonly used in glacial isostatic adjustment gia studies our viscosity inferences are generated using two approaches first we adopt a relative viscosity profile which is known to provide a good fit to the free air gravity harmonics and determine an absolute scaling which yields a best fit to the gia decay time constraints second we perform an iterative nonlinear joint inversion of the two data sets in both cases our inferred profiles are characterized by a significant increase of viscosity 2 orders of magnitude with depth to values of 1022 pa s in the bottom half of the lower mantle the new viscosity profiles are shown to satisfy constraints based on the postglacial uplift of both fennoscandia the classic haskell 1935 number and hudson bay which have commonly been invoked to argue for an isoviscous mantle furthermore the models are used to predict a set of long wavelength signatures of the gia process these include predictions of gia induced variations in 1 the length of day over the late holocene period 2 the earth s precession constant and obliquity over the last 2 6 myr and 3 the present day zonal harmonics of the geopotential jl l 7 the predictions 1 and 3 bound the late holocene and ongoing mass flux between the large polar ice sheets greenland and antarctic and the global oceans to small values 0 4 mm yr equivalent eustatic sea level rise

spectroscopic analysis of global tide gauge sea level data summary yearly and monthly tide gauge sea level data from around the globe are fitted to numerically generated tidal data to search for the 18 6 yr lunar nodal tide and 14 month pole tide both tides are clearly evident in the results with amplitudes and phases that are consistent with a global equilibrium response global atmospheric pressure data are fitted to global monthly sea level data to study the response of the ocean to pressure fluctuations the global response of sea level to pressure is found to be inverted barometer at periods greater than 2 months a large coherence at 437 days between pressure and sea level data is found for the north sea baltic sea and the gulf of bothnia the results are not entirely conclusive but they tend to support o connor s 1986 suggestion that the apparent enhanced pole tide in these basins may be due to meteorological forcing rather than to a basin scale resonance finally global averages of tide gauge data after correcting for the effects of post glacial rebound on individual station records reveal an increase in sea level over the last 80 yr of between 1 1 and 1 9 mm yr as part of the process of removing the effects of post glacial rebound we fit those effects to the global tide gauge data and obtain very good agreement with results predicted from post glacial rebound models this tends to support the post glacial model results and it suggests that the global tide gauge data are indeed capable of resolving changes in sea level at the mm yr level

time variations in the earth s gravity field detectable with geopotential research mission intersatellite tracking the geopotential research mission grm is a proposed system of two artificial satellites in tandem drag free polar orbits of low altitude 160 km designed for a detailed global mapping of the earth s gravitational and magnetic fields the mission should provide a large amount of new information about the gravity field particularly over continents resolving spatial variations in the gravity field as short as 100 km half wavelength however grm should also perform a much more difficult task the detection of time variations in the gravity field among the effects which produce changes in the field that are large enough to be detected by the intersatellite millimeter wavelength 1 s precision grm sensor are the following 1 rebound from ancient deglaciation 2 very large dip slip earthquakes 3 detailed ocean tides and 4 the seasonal growth and decline of continental glacial fields in particular many nonzonal as well as zonal components affected by postglacial rebound should be detected in a 6 month grm mission repeat passes over the fault zones of earthquakes similar to alaska 1964 chile 1960 or sumbawa 1977 should reveal signal changes due to their earth movements the effect of ocean tides on the grm signal should be readily detectable over a broad band of frequencies even if all but 10 of the tides are correctly modeled continued geophysical interest in these now largely unobserved phenomena warrants extension of the grm mission to somewhat higher altitudes

mars change in axial tilt due to climate the average tilt of mars equator with respect to its orbital plane may have increased significantly over the age of the solar system obliquity oscillations might have induced changes in the climate which altered the mass distribution and hence the solar torque on the planet viscous deformation attributable to loading by the large polar caps expected at low obliquity may have induced secular changes in the axial tilt earth like effective viscosities can account for virtually the entire present obliquity of 24 4 degrees thus the present average tilt of mars may not be primordial

limits on lateral pressure gradients in the outer core from geodetic observations abstract lateral variations in pressure associated with flow at the core mantle boundary will produce deformations of the mantle it is shown here that geostrophically plausible pressure gradients are sufficient to produce measurable changes in the length of day polar motion j2 sea level tilt gravity and strain of these polar motion is the most discriminating and limits intra annual variations in the lateral pressure field at planetary wavelength to less than 104 pa satellite observations of changes in j2 are potentially even more useful however at present the time span of observations is short and the separation of a residual which might be due to a change in the distribution of pressure at the core mantle boundary from other causes such as post glacial rebound is ambiguous it is suggested that not more than 10 of the decade variations in the length of day may be caused by pressure fluctuations at the core mantle boundary

on the compensation of geoid anomalies due to subducting slabs candidate models of the forces that oppose the sinking of slabs are all constrained to produce results consistent with the following observation relative geoid highs which one assumes are due to slabs characteristically occur over subduction zones however certain models of subduction induced flow such as one based on a newtonian half space mantle yield surface depressions and concomitant geoid lows that more than fully compensate the geoid highs due to the slab alone this study has extended a published model of viscous corner flow in subduction zones in order to demonstrate that it can in certain cases produce the requisite net geoid highs specifically the relative geoid highs are produced if mantle flow is distinctly non newtonian stress exponent n 2 results in the form of geoid slope or horizontal gravity disturbance profiles are computed for typical values of the slab parameters they are compared with a representative profile of geoid slopes derived from seasat altimeter data in order to show qualitative similarities it is concluded that the effect of non newtonian flow as opposed to newtonian is to spread out the induced surface deformation thereby stretching out the regional compensation to wavelengths transverse to the trench of many thousand kilometers

numerical models of thermally and mechanically coupled two layer convection of highly viscous fluids summary numerical solutions for thermal convection of two superposed viscous fluid layers with the same thicknesses as the earth s upper and lower mantles and separated by a fixed horizontal interface are obtained at the onset of convection and in the nonlinear regime several heating configurations and thermal boundary conditions are considered including an isothermal bottom boundary a prescribed heat flux bottom boundary and internal heating with an insulated lower boundary at the onset of convection and with the same material properties in each layer the lower layer is more unstable than the upper layer and long horizontal wavelengths proportional to the lower layer thickness predominate for layers with sufficiently different material properties the upper layer can be more unstable and short horizontal wavelengths proportional to the upper layer thickness can predominate at the onset of convection when the material properties are chosen to make the two layers equally unstable there are two stability curve rayleigh number ra versus wavelength minima with the lower minimum at long wavelength linear stability results typify weakly nonlinear convection except when both layers are equally unstable when the layers have unequal stability the stable layer has a conductive temperature field and its flow is viscously driven by the convective flow in the unstable layer when the two layers are equally unstable both layers are separately convecting even at rayleigh numbers of only twice the critical value for convection onset at large enough supercritical ra the lower layer convects with a long wavelength cell even when linear stability theory predicts short wavelength cells the upper layer always begins convecting with short wavelength cells however the upper layer cell over the lower layer downwelling plume increases in size with increasing ra thus horizontal wavelength plate dimension for example cannot be used to discriminate between whole mantle and layered mantle convection mechanical coupling of the layers downwelling plume over upwelling plume occurs for all cases with the same material properties in each layer and for the case with the same ra in each layer when the material properties of the layers are sufficiently different to produce short wavelength cells at the onset of convection the upper layer has two thermally coupled cells downwelling plume over downwelling plume and a shear zone at the interface over both lower layer plumes a large 50 per cent of total temperature difference across the interface occurs in all cases examined implying that two layer mantle convection should also have a large temperature change across the 670 km discontinuity however temperature dependent viscosity may reduce the magnitude of this temperature difference interpretations of geoid anomalies over subduction zones and seismic traveltime anomalies of slabs should account for possible thermal coupling of separate upper and lower mantle convective systems

new constraints on transient lower mantle rheology and internal mantle buoyancy from glacial rebound data a model of mantle rheology which has an explicit transient component of its relaxation spectrum is shown to reconcile two apparently conflicting inferences of lower mantle viscosity if recent analyses of isostatic geoid anomalies are correct in requiring a large increase of viscosity with depth then the weak viscosity stratification demanded by postglacial rebound data implies the importance of such rheological behaviour at least in the earth s lower mantle

secular rotational motions and the mechanical structure of a dynamical viscoelastic earth we give a survey of the analytical methods for computing the linear responses of the rotational axis of a layered viscoelastic earth to surface loading the two classes of eigenspectra involving isostatic relaxation of the mantle and readjustment of the spin axis are emphasized as being essential for a uniformly valid description of polar wander the rotational responses due to the application of an equilibrium phase or a chemically layered boundary condition at the 670 km discontinuity are studied the displacement fields associated with rotational deformation are affected to a much greater extent by the amount of chemical enrichment than are the eigenfunctions associated with isostatic relaxation the present polar motion data from international latitude service i l s can be fit equally well by a pure chemical or an equilibrium phase boundary with a 9 change in density across the interface on the other hand responses from models with a smaller amount of chemical stratification 7 are not compatible with the data the secular variation of the earth s gravitational harmonic j2 is insensitive to the chemical nature of the 670 km discontinuity from the rotational data it is not possible to rule out the existence of a high viscosity region with values of o 1023 p at the bottom 500 km of the mantle although a solution with a relatively uniform viscosity profile o 1022p still can be found inferences of the globally averaged thickness of the elastic lithosphere from rotational data are not affected too much by the particular density stratification used for the lithosphere and upper mantle they lie in the range between 120 and 170 km

sediment transport by wind toward a general model a general model of eolian sediment transport by both saltation and suspension is developed saltation is analyzed through calculations of single trajectories given initial conditions of liftoff speed angle and spin profiles of particle concentration and mass flux generated by assuming that all trajectories are identical display distinct maxima at the top of the trajectory by incorporating the realistic distribution of trajectories that arises from the stochastic nature of grain impacts with a granular bed the model yields monotonic decreases in particle concentration and mass flux with height in accordance with published empirical data the analysis of suspension as the balance between downward advective flux as a result of the settling of grains and their upward diffusive flux as a result of turbulence results in concentration profiles that fall off as power laws with height also in accordance with empirical data a relation for reference level concentrations is presented for both blowing snow and dust profiles the solutions for saltation and suspension are combined to yield mass flux profiles for the entire range of grain sizes in the bed the saltation layer emerges naturally as that region where the total flux of saltating grains exceeds that of suspended grains the model points clearly to the need for further research on the stochastic grain bed interactions which control both the probability distribution of liftoff velocities in saltation and the production of fine particles in suspension

obliquity oblateness feedback are climatically sensitive values of obliquity dynamically unstable a new model is presented for feedback between rotational and climatic variations operative on time scales of 104 107 years due to the combined effect of planetary perturbations to the earth s orbit plane and luni solar torques on the oblate figure of the earth the obliquity varies by 1 on a 4 104 year time scale associated changes in the seasonal and latitudinal pattern of incident solar radiation cause major glaciations mass transport from the oceans to the polar ice sheets during these glaciations can change the gravitational oblateness of the earth by amounts approaching 1 as the rate of spin axis precession is directly proportional to the oblateness the climatically forced mass transport can by dynamically significant a simple parameterization of us coupled orbital rotational climatic system suggests that there is a strong tendency for the system to evolve away from climatically sensitive values of the obliquity this may explain the mid pleistocene transition from an obliquity dominated regime to the present regime in which most climatic variability is concentrated at longer 105 year periods

glacial isostatic adjustment and earth rotation refined constraints on the viscosity of the deepest mantle we explore the extent to which two properties of earth s present day rotational state may be applied to constrain the viscosity of the lower regions of the lower mantle the analysis builds upon recent advances in understanding the radial resolving power of the relative sea level data of postglacial rebound which have demonstrated anew that no significant increase of viscosity across the 660 km seismic discontinuity appears to be allowed by these data such observations do not constrain the viscosity of the mantle below about 1400 km depth however and here we estimate the average viscosity in this deepest region by invoking observations of the present day rate and direction of polar wander and the present day magnitude of the nontidal acceleration of the rate of planetary rotation since the rotational response to the glaciation cycle depends only upon the degree 2 spherical harmonic components of the induced deformation this response is expected to provide the most specific sampling possible of deep mantle properties our analysis is based upon the use of glacial excitation functions calculated from complete gravitationally self consistent solutions of the sea level equation for the most recent refinement of the history of ice sheet thickness variations across the last glacial interglacial transition namely the ice 4g model this analysis shows that when earth rotation observations are combined with relative sea level constraints the viscosity of the deepest mantle is required to be 1 order of magnitude higher than the viscosity of the upper part of the lower mantle such significant elevation of viscosity in the lowermost region of the lower mantle is also in accord with recent inferences based upon analysis of the nonhydrostatic geoid the analyses presented herein therefore suffice to effect a reconciliation between the requirements of these distinct geophysical observations

the rotation of the earth earth rotation studies are reviewed for the 1987 1990 time period it is noted that the emphasis in these studies has shifted from improvements in the observational techniques to interpreting and gaining greater understanding of the variations of the earth rotations there have been progressive improvements in the accuracy and the temporal resolution of earth rotation measurements

glacial isostatic adjustment and the free air gravity anomaly as a constraint on deep mantle viscosity summary a gravitationally self consistent theory for relative sea level variations forced by pleistocene deglaciation events is employed to explore the extent to which rsl and free air gravity observations together constrain the viscosity of the mantle beneath the seismic discontinuity at 670 km depth a trade off is revealed between errors in the assumed deglaciation history and errors in the inferred value of the viscosity of the lower mantle taking full account of such uncertainty plausible values of the viscosity beneath the transition region are bounded above by 1023 poise cgs units the preferred value is at least a factor of 2 lower than this and is strongly constrained by the observed free air gravity anomaly over hudson bay the calculations described in detail here show for the first time that the relatively large gravity anomalies observed over sites of wurm wisconsin deglaciation do not require any pronounced increase of mantle viscosity with depth in order to explain them

wind tunnel and field calibration of five aeolian sand traps the efficiency of five aeolian sand samplers was tested via wind tunnel experiments and field measurements the samplers were the big spring number eight bsne sampler the modified wilson and cooke mwac sampler the suspended sediment trap sustra the pollet catcher polca and the saltiphone in the wind tunnel the samplers were calibrated against an isokinetic sampler a modified sartorius sm 16711 sampler with adjustable flow rate and this for three sand types median diameter 132 194 and 287 m and five wind speeds ranging from 6 6 to 14 4 m s 1 in the field seven calibration tests of two weeks each were conducted the absolute efficiencies of the bsne mwac and polca are more or less comparable and vary between 70 and 120 depending on sediment size and wind speed for the sustra the efficiency is somewhat lower for fine sands and for wind speeds above 11 m s 1 finally the saltiphone can accurately detect the periods of saltation transport but in its current version the instrument is not accurate when measuring the absolute saltation flux the most recommendable sampler in the test is the mwac not only because of its high efficiency but also because its efficiency is independent of wind speed

the flux profile of a blowing sand cloud a wind tunnel investigation abstract the flux profile of a blowing sand cloud or the variation of blown sand flux with height is the reflection of blown sand particles that move in different trajectories and also the basis for checking drifting sand here we report the wind tunnel results of systematic tests of the flux profiles of different sized sands at different free stream wind velocities the results reveal that within the 60 cm near surface layer the decay of blown sand flux with height can be expressed by an exponential function q h a exp h b where q h is the blown sand transport rate at height h a and b are parameters that vary with wind velocity and sand size the significance of coefficient a and b in the function is defined a represents the transport rate in true creep and b implies the relative decay rate with height of the blown sand transport rate the true creep fraction the ratio of the sand transported on the surface h 0 to the total transport varies widely decreasing with both sand size and wind speed the flux profiles are converted to straight lines by plotting sand transport rate q h on a log scale the slope of the straight lines that represents the relative decay rate with height of sand transport rate decreases with an increase in free stream wind velocity and sand grain size implying that relatively more of the blown sand is transported to greater heights as grain size and wind speed increase the average saltating height represented by the height where 50 of the cumulative flux percentage occurs increases with both wind speed and grain size implying that saltation becomes more intense as grain size and or wind velocity increase

effect of the viscoelastic lithosphere on polar wander speed caused by the late pleistocene glacial cycles previous studies of the wander of the rotation pole associated with the late pleistocene glacial cycles indicate that the predicted polar wander speed is sensitive to the density jump at the 670 km discontinuity the thickness of the elastic lithosphere and the lower mantle viscosity in particular the m1 mode related to the density jump at 670 km depth has been shown to contribute a dominant portion of predicted polar wander speed for sufficiently small lower mantle viscosities in this study we examine the sensitivity of polar wander to variations in the viscosity of the viscoelastic lithosphere using simplified compressible maxwell viscoelastic earth models model calculations for earth models with a viscoelastic lithosphere of finite viscosity indicate that the contribution of the m1 mode is similar to those associated with the density discontinuity at the core mantle boundary c0 mode and the lithosphere l0 mode we speculate that this is due to the interaction between the m1 mode and the transient mode associated with the viscoelastic lithosphere which reduces the magnitude of polar wander rates therefore the m1 mode does not contribute a dominant portion of the predicted polar wander speed for earth models with a viscoelastic lithosphere of finite viscosity in this case predictions of polar wander speed as a function of lower mantle viscosity exhibit the qualitative form of an inverted parabola as predicted for the j 2 curve we caution however that these results are obtained for simplified earth models and the results for seismological earth models such as prem may be complicated by the interaction between the m1 mode and the large set of transient modes

secular variations in zonal harmonics of earth s geopotential and their implications for mantle viscosity and antarctic melting history due to the last deglaciation

effects of polar ice on the earth s rotation and gravitational potential summary gridded values of net surface accumulation rates for the antarctic and greenland ice sheets are used to estimate the contributions these two regions make to the earth s gravity and rotation the ice discharge from both ice sheets is adjusted so that the estimates of sea level contribution from both ice sheets fall within limits for present mass balance suggested by the committee on glaciology 1985 these sea level contributions are for antarctica 0 6 0 6 mm yr minus 1 and for greenland 0 1 0 4 mm yr 1 the contributions to the low order zonal harmonic coefficients of the earth s gravitational potential from antarctica are found to be between two and 10 times larger than the uncertainties of the zonal harmonics derived from satellite solutions for greenland the coefficients are within an order of magnitude of the uncertainties of the satellite solutions these results are not definitive they are presented to demonstrate that the ice sheets contribute to gravity in amounts that are within the limits of detection by satellite ranging methods the secular trends in the x and y components of observed polar motion excitation agree in magnitude and sign with the antarctic contributions for a model where the interior regions on the ice sheet undergo a net thinning and the coastal regions thicken for this model the boundary between the interior and coastal regions is set at the contour of constant accumulation of 0 28 m yr 1 water equivalent and the magnitude of the thickness change is set equal to the local accumulation rate the contributions from greenland to the secular trends in polar motion excitation and length of day are either smaller than or of opposite sign to the observed effects and are found to be smaller than those of antarctica the limited information on mass balance and ice discharge including calving of ice and refreezing of melt water for both ice sheets and the lack of measured data for land based water storage makes the results presented here highly speculative in addition the inelastic response of the earth to changes in surface mass loading is not considered here this delayed response can reduce the magnitude of the effects presented here by as much as 15 per cent if the loading is a linear trend spanning 100 yr and the correction can be larger for longer histories of loading see wahr et al 1992 these results suggest very approximate upper and lower limits for both inter annual and secular contributions of polar ice mass balance to earth rotation and gravity these limits are useful where they fall within the range of detectability using satellites

field measurement and numerical modelling of aeolian mass flux distributions on a sandy beach the vertical and horizontal distributions of aeolian mass flux were measured at oceano dunes california and these data were used to evaluate a numerical model of saltation grain size analyses showed that the distributions of the modal sediment size class corresponded closely to those of the total sediment population and modelling thus focused on replicating the distributions of the mean grain size although much previous work has assumed that the mean launch speed of saltating particles varies in proportion to shear velocity simulations using a constant mean launch speed were found to yield the closest approximations to the mass flux distributions observed in the field both exponential and gamma distributions of launch velocity produced realistic simulations although the latter approach required the inclusion of an additional reptation component to achieve good results a range of mean launch angles and an equivalent sphere correction were also found to generate comparable results providing the other input parameters could be varied freely all the modelling approaches overestimated the proportion of mass flux occurring at the bottom of the vertical distributions and underestimated the proportion occurring at the upwind end of the horizontal distributions no theoretical shortcoming that would account for these small but systematic discrepancies could be identified and experimental error thus represents a more plausible explanation the conclusion that mean grain launch speeds are essentially constant and independent of shear velocity suggests that the additional kinetic energy extracted by grains under more energetic wind conditions is largely transferred to the bed and that increases in the transport rate are therefore driven primarily by the ejection of additional grains it is suggested that the kinetic energy of rebounding grains is constrained by the ability of the bed to resist deformation equivalent to a plastic limit hence grains of larger mass diameter rebound from the bed at lower speeds and follow shorter lower trajectories as has been widely observed previously

debris flow activity and snow avalanches in a steep watershed of the valais alps switzerland dendrogeomorphic event reconstruction and identification of triggers debris flows and snow avalanches are common processes in the headwaters of steep watersheds worldwide in forested areas dendrogeomorphic analyses of trees affected by debris flows and snow avalanches have regularly been used to date past events previous studies have however almost never focused on both processes at once as snow avalanche impacts cannot easily be distinguished from debris flow scars in a similar way tree ring studies have often been limited to conifers and sites colonized with broad leaved forests have been widely disregarded we report on a case from the valais alps switzerland where past debris flow and snow avalanche activity was dated with intraseasonal precision using different broad leaved and conifer trees in total the analysis of 171 cores 34 wedges and 11 crosssections from 93 trees allowed identification of 20 debris flow and 3 snow avalanche events between a d 1930 and 2008 results also indicate that some of the events would have been missed without the sampling of broad leaved trees

mars reconnaissance orbiter radio science gravity investigation 1 the objectives of the mars reconnaissance orbiter mro radio science gravity investigation are to improve knowledge of the static structure and characterize the temporal variability of the martian gravitational field relevant to the planet s internal dynamics the structure and dynamics of the atmosphere and the orbital evolution of spacecraft at mars the investigation will utilize range rate and range measurements from x band and when available ka band tracking systems of the mro spacecraft mro will enable a considerable improvement in the spatial resolution and quality of mars global gravity field the low orbital periapsis of mro 255 km will yield gravity maps suitable for study of regional 102 km structure of the crust and lithosphere the addition of tracking data from the mars global surveyor and mars odyssey spacecraft also currently orbiting mars will be useful in decorrelating errors in spherical harmonic coefficients of the gravity field that will improve the quality of the static field studies of the low degree gravity field combined with measurements of rotational dynamics will permit insight about the structure of mars deep interior changes in the low degree spherical harmonic coefficients of the martian gravity field and in polar mass anomalies will be used to track the seasonal cycle of co2 exchange with the surface measurements of spacecraft drag will be used to estimate density variations in the atmosphere relevant to weather patterns and aerobraking of future spacecraft tracking observations will also be used to improve the ephemeris of mars and the masses of the martian moons

spatio temporal reconstruction of snow avalanche activity using tree rings pierres jean jeanne avalanche talus massif de l oisans france snow avalanches are a major threat in many parts of the alps where they periodically damage infrastructure disrupt transportation corridors or even cause loss of life nonetheless the spatial behavior of past avalanche activity and the analysis of areas affected during particular events remain often imprecise it was therefore the purpose of this study to reconstruct spatio temporal patterns of past avalanche activity on a forested avalanche talus in the french alps pierres jean jeanne talus massif de l oisans france a total of 232 european larches larix decidua mill with clear signs of snow wasting events was analyzed and growth disturbances gd related to avalanche activity was assessed such as tangential rows of traumatic resin ducts the onset of compression wood or abrupt growth suppression and release in total 901 gd were identified in the tree ring samples indicating that 20 high magnitude avalanches occurred between ad 1919 and 1994 the mean return period of snow avalanches was 4 years with a 26 probability that an avalanche occurs in any particular year interpolated maps allowed for explicit spatial estimates of return periods throughout the talus showing a rapid increase of return frequency from 2 5 to 50 years with increasing distance from the talus apex the distribution of avalanche years seems to be quite homogeneous in time with a gap between 1951 and 1959 snowfall from a nearby meteorological station saint christophe en oisans 10 km from the study site indicated that the five most recent high magnitude events on record occurred due to above average snowfall anomalies in december and january associated with abnormally low air temperatures findings suggest that a strong snow metamorphism under high temperature gradients in january could explain the occurrence of high magnitude snow avalanches 2010 elsevier b v all rights reserved

higher harmonic effects of the earth s gravitational field from post glacial rebound as observed by lageos recently long term orbital data from the artificial satellite lageos have been analyzed to determine the rate of post glacial rebound rubincam has compared the observed values against values derived from two realistic earth models wu peltier l1 l2 working with the second harmonic mode of excitation the data support model l1 with a uniform mantle viscosity of 1022 poise over l2 with a lower mantle viscosity of 1023 poise we find the higher degree harmonic contributions are significant and considerably strengthen the support for model l1 we perform such calculations using the same parameter values for glaciation as rubincam and also values due to peltier and coworkers we also show that a similar analysis of data from the satellite starlette is less likely to be as definitive as analysis of lageos data since there are significant contributions from very high harmonics indicating that the behavior of the earth must be known in much greater detail

continental lithospheric thickness and deglaciation induced true polar wander the secular drift of the earth s rotation pole which is evident in ils data is a memory of the planet of the last deglaciation event of the current ice age in order to fit the observed rate and direction of drift with an earth model whose viscosity profile is capable of reconciling the free air gravity and relative sea level data of postglacial rebound requires a lithospheric thickness which is substantially in excess of that which might be considered an appropriate average thickness for the entire planet this required thickness which is greater than 250 km is nevertheless in accord with independent estimates of the thickness of the continental lithosphere

present day secular variations in the zonal harmonics of earth s geopotential we develop a new formalism for the prediction of secular variations in the gravitational potential field of a spherically symmetric self gravitating maxwell viscoelastic planetary model subjected to an arbitrary surface load which may include a gravitationally self consistent ocean loading component the theory is applied to generate the most accurate predictions to date of the present day secular variations in the zonal harmonics of the geopotential the so called for degree arising as a consequence of the late pleistocene glacial cycles in this respect we use the very recent ice 3g reconstruction of the last late pleistocene deglaciation event tushingham and peltier 1991 a comparison of these predictions with those generated using simplified disk models of the ice sheets which have been used in all previous studies of the harmonics 2 indicates that the disk model approximation introduces unacceptably large errors at all spherical harmonic degrees except perhaps 2 predictions have also been made using a eustatic loading approximation also used in previous studies in place of a gravitationally self consistent ocean loading component and we have found that the resulting discrepancy is largest at degrees 2 8 and 10 in the case of the magnitude of the error incurred using the eustatic approximation can be as large as order 10 15 of the predicted value we have attributed this discrepancy to the present day net flux of water away from the equatorial regions arising from the remnant present day adjustment associated with the late pleistocene glacial cycles the effect represents a heretofore unrecognized contribution to the harmonics or alternatively the nontidal acceleration of earth s axial rate of rotation in terms of the latter the maximum anomaly in the length of day is approximately 1 7 s yr we also consider the sensitivity of the data to variations in the radial mantle viscosity profile by using a suite of forward calculations and an examination of frechet kernels the theory required for the computation of those kernels is described herein we find that the radial variation in sensitivity can be a strong function of the viscosity model used in the calculations for models with a uniform upper mantle viscosity um of 1021 pa s forward predictions of the harmonics exhibit a pronounced peak when a wide enough range of lower mantle viscosities lm are considered we denote the lm value at this peak as at the lowest degrees 4 frechet kernels computed for a series of increasing lm values 1021 pa s lm 1023 pa s indicate a migration of the dominant sensitivity of the data to variations in viscosity from regions below approximately 1200 km depth for to regions above this depth in the lower mantle for the sensitivity of the data to variations in the viscosity profile in the shallowest parts of the lower mantle for the case is also reflected in a set of forward calculations described herein as an example predictions made using earth models in which the viscosity above 1200 km depth is constrained to be 1021 pa s do not exhibit the multiple solutions characteristic of the um 1021 pa s calculations the same is true of earth models in which the upper mantle viscosity is weakened an order of magnitude to 1020 pa s the theory described herein is also applied to compute the signal 10 arising from the retreat of small ice sheets and glaciers described by meier 1984 and also from any potential variations in the mass of the antarctic and greenland ice sheets the present day signal due to the late pleistocene glacial cycles dominates the signal from meier s sources at all degrees except 3 in contrast the signal arising from mass variations in the antarctic and greenland ice sheets is potentially comparable to the former a comparison of observational constraints on the data with predictions of the postglacial rebound signal described in this paper in order to infer mantle rheology cannot proceed until constraints are placed on the present day mass flux of these large polar ice sheets we show that the constraints required are weakest at degrees 2 and 4 finally we outline a potentially important procedure for incorporating predictions of the signal due to the late pleistocene glacial cycles and meier s sources with an observational constraint on the datum to yield bounds on the present day net mass flux from the antarctic and greenland ice sheets a rigorous application of this procedure must wait until observational constraints on are reestablished in the literature

lithospheric thickness antarctic deglaciation history and ocean basin discretization effects in a global model of postglacial sea level change a summary of some sources of nonuniqueness the global model of postglacial relative sea level variations that has been developed over the past decade is employed to investigate the constraints that it may be invoked to place on the timing of the deglaciation of west antarctica the analyses presented here confirm the suggestion of p wu and w r peltier 1983 geophysical journal of the royal astronomical society74 377 450 that the model of this event employed inj a clark and c s lingle 1979quaternary research11 279 298 may be simply modified to rectify the misfits between theory and observation that are otherwise obtained at southern hemisphere sites a large number of southern hemisphere relative sea level data are shown to require that the retreat of antarctic ice substantially lagged the retreat of northern hemisphere ice if the deglaciation of antarctica was abrupt the time of onset of antarctic deglaciation is thereby shown to coincide with the time of most rapid northern hemisphere deglaciation sensitivity tests are performed which demonstrate that this result is relatively insensitive to the discretization employed to represent the ocean basins the only exception to this general rule obtains at some coastal sites at which a trade off is revealed between the delay of west antarctic melting and the thickness of the lithosphere required to reconcile the observed local variations of relative sea level at such sites which are all in the far field of the ice sheets some attention must be paid to the accuracy of the local finite element representation of the oceans and to the details of the antarctic deglaciation history

viscous gravitational relaxation summary this paper is concerned with a detailed examination of the response of maxwell models of the planet to surface mass loads particular attention is devoted to an examination of the factors which determine the isostatic response since the understanding of this response is crucial in a number of different geodynamic problems one particular example which we discuss in detail is concerned with the prediction of free air gravity anomalies produced by large scale deglaciation events using the methods developed here we are able to provide the first direct assessment of the importance of initial isostatic disequilibrium on the observed relative sea level variations and free air gravity anomalies forced by the melting of the laurentide ice sheet we are therefore able to estimate the extent to which such initial disequilibrium might influence the inference of mantle viscosity from isostatic adjustment data our calculations establish that free air gravity data although they are sensitive to the degree of initial disequilibrium provide an extremely high quality constraint upon the viscosity of the lower mantle

on the efficiency of vertical array aeolian field traps the efficiency of three vertical array field traps for measuring the distribution of aeolian mass transport with height was compared with measurements with an isokinetic trap the vertical traps seem to work adequately efficiency 80 at heights greater than 15 mm above the bed closer to the bed however the open array trap catches about 70 the two continuous arrays only about 50 because most of the transport takes place close to the surface the overall efficiency of the field traps ranges from 50 to 70 based on these wind tunnel tests we have developed a low single compartment wedge shaped trap its shape in combination with flow straighteners at the entrance minimizes stagnation effects so that the efficiency is 80 our data indicate that with the wedge trap used in combination with the vertical array aberdeen trap we can sample mass transport in the field during periods with unidirectional winds with an overall efficiency of the order of 80

pleistocene deglaciation and the global gravity field the present day global geoid and free air gravity anomaly signals induced by pleistocene deglaciation have been computed along with their secular variations a revised green function has been derived for the free air gravity anomaly and we find that an earth model with a lower mantle viscosity moderately larger than the upper mantle value satisfies observations of the anomaly over both hudson s bay and fennoscandia using this preferred earth model the predicted global geoid anomaly map is characterized by peak negative values of 36 7 9 4 and 21 9 m over hudson s bay northern europe and antarctica respectively and by a smooth small amplitude 2 5 m upwarping over the major ocean basins although the field has an order of magnitude less power than the observed there is a significant spatial correlation between the two inferences of mantle viscosity based upon comparisons between the observed geoid and the computed deglaciation induced anomaly are hampered by the large contribution from the convective circulation in the earth s mantle we have subtracted a predicted convection signal based on seismic tomography from the observed field however the residual geoid thus obtained is still too inaccurate to allow a useful comparison in contrast a filtered version of the observed geoid over canada which retains harmonic coefficients in the degree range 10 22 provides a relatively uncontaminated by convection datum that is indeed satisfied by the preferred earth model secular variations in the earth s gravitational field are naturally dominated by the signal from pleistocene deglaciation in this respect we compute zonal harmonics in the expansion of the present day rate of change of the geopotential and in particular we predict amplitudes comparable to that for the previously analysed j2 for j4 j5 j7 and j9 all of which reflect in large part the response due to the melting of the massive laurentide ice sheet this analysis suggests that measurement of these higher order secular variations of the zonal harmonics based upon analysis of long time series of lageos ranging data could provide very useful additional constraints on the radial variation of mantle viscosity these constraints along with all others described in this paper are shown to be relatively insensitive to assumptions concerning the deflection during the glacial isostatic adjustment process of the 400 and 670 km density discontinuities within the mantle

holocene fluvial valley fill sources of atmospheric mineral dust in the skeleton coast namibia western namibia is a significant global source of atmospheric mineral dust we investigate the relationship between dust and source sediments assessing the sustainability of dust flux remote sensing studies vickery and eckhardt 2013 have highlighted specific ephemeral fluvial systems as important contributors to dust flux including highlighting sections of valleys that are the origins of dust plumes in the period 2005 8 little is known however about the specific within valley dust sediment sources particularly whether dust is derived from modern ephemeral channel floors or older valley fill sediments many of which have been reported in the region stone and thomas 2013 as part of a region wide analysis of aeolian dust flux we investigate the sediment properties of atmospheric dust samples and valley sediments from the huab valley one of the principal regional dust sources trapped dust samples contain up to 88 very fine sand and silt when collected samples are disaggregated prior to analysis valley fill surface samples comprise 80 very fine sand and silt and the surface of the modern ephemeral channel 30 valley fill sediments were sampled at depths up to 3 6m below the present surface and reveal holocene depositional ages from 0 6 0 03ka back to 9 79 0 73ka these sediments contain 30 to 6 very fine sand and silt with levels decreasing with depth and age aeolian bedforms in the valley system nebkhas on the fill surface and climbing dunes on valley margins indicate that aeolian processes under the influence of strong seasonal easterly winds likely result in dust being winnowed out of the valley fill surfaces with sandy bedforms being constructed from the coarser component of the fill sediments the volume of valley fill sediment suggests dust sourced from holocene sediments is likely to continue into the future regardless of flow conditions in the modern channel system

mantle rheology and satellite signatures from present day glacial forcings we study the changes of the long wavelength portion of the earth s gravity field as a result of present day gladal discharges and the possible growth of the antarctic ice sheet we employ both maxwell and burgers body rheologies and find that there are significant differences in the responses between the two rheologies for time spans less than a century both present day gladal forcing and the ice buildup on antarctica can cause non negligible perturbations in j 2 of about one third the observed amount the contributions from the two mechanisms have opposite signs in j 2 only for i 3 and 6 do these cryospheric contributors act in concert with one another in disturbing the gravity field ali other degree harmonics up to 1 9 have opposite signs from these two excitations for a steady state lower mantle viscosity of 1022 pa s j 3 can attain a maximum value of around 1 5 x lo i1 yr 1 and j a value of 1 3 x io il yr i for current forcings these have signs opposite to those predicted for pleistocene deglaciation ali harmonics up to i 9 are sensitive to variations of the steady state vis cosity in the lower mantle even for time scales shorter than 100 years it is proposed that detailed satellite monitoring of present day ice movements in conjunction with geodetic satellite missions will eventually pro vide a viable alternative for estimating deep mantle viscosity useful in mantle convection models

the geoscience laser altimetry ranging system the geoscience laser altimetry ranging system glars is a planned highly precise laser distance measuring system to be used for geoscience measurements requiring extremely accurate geodetic observations from a space platform the system combines the attributes of a pointable laser ranging system making observations to retroreflectors placed on the ground with those of a nadir looking laser altimeter making height observations to ground ice sheet and oceanic surfaces in the ranging mode centimeter level precise baseline and station coordinate determinations will be made on grids consisting of 100 to 200 targets separated by distances from a few tens of kilometers to about 1000 km these measurements will be used for studies of seismic zone crustal deformations and tectonic plate motions ranging measurements will also be made to a coarser but globally distributed array of retroreflectors for both precise geodetic and orbit determination applications in the altimetric mode relative height determinations will be obtained with approximately decimeter vertical precision and 70 100 m horizontal resolution altimetric profiles consisting of nearly contiguous spots will be available when the system is operated at 40 pulses per second the height data will be used to study surface topography and roughness ice sheet and lava flow thickness and ocean dynamics waveform digitization will provide a measure of the vertical extent of topography within each footprint

time variable gravity signal of an anomalous redistribution of water mass in the extratropic pacific during 1998 2002 1 cox and chao 2002 reported the detection of a large anomaly in the time series of earth s dynamic oblateness j2 the lowest degree gravity spatial harmonic in the form of a positive jump since 1998 overshadowing the decreasing secular trend in j2 caused primarily by the postglacial rebound pgr here we report that recent data show that j2 has been rapidly returning toward normal with pgr considered since early 2001 in search of the geophysical and climatic causes for this 1998 2002 j2 anomaly we report an oceanographic event that took place in the extratropic north and south pacific basins that was found to match remarkably well with the time evolution of the anomaly we examine the leading nonseasonal extratropic pacific empirical orthogonal function principal component modes in the sea surface height ssh data from topex poseidon sea surface temperature sst data from the national center for environmental predictions and output fields of the estimating the circulation and the climate of the ocean ecco ocean general circulation model ogcm including ocean bottom pressure obp and temperature and salinity profiles the phenomenon appears to be part of the pacific decadal oscillation and temporal correlations are made however quantitatively the obp field of the ecco model predicts a j2 anomaly that is smaller in magnitude than the observed by a factor of about 3 we discuss various possibilities for reconciling this discrepancy in terms of inadequacies of present ogcms and considering other geophysical contributions a complete resolution of the j2 enigma awaits further studies

low degree gravity changes from grace earth rotation geophysical models and satellite laser ranging 1 several independent time series of variations c 21 s 21 and c 20 in earth s gravity field are compared for the period april 2002 to may 2007 we examine estimates from the gravity recovery and climate experiment grace earth rotation variations climate models and satellite laser ranging slr recently released grace solutions show significant improvement relative to earlier results especially for c 21 and s 21 at the annual period all estimates agree remarkably well and good correlation is found among time series at intraseasonal periods in general earth rotation values for c 21 and s 21 and slr values for c 20 agree best with grace estimates grace c 20 time series are contaminated by aliased ocean tide model errors slr c 21 and s 21 time series have been reported without an ocean pole tide opt correction and with an older solid earth pole tide sept model after correcting for opt and sept deficiencies slr c 21 and s 21 time series show improved agreement with other estimates

gia induced secular variations in the earth s long wavelength gravity field influence of 3 d viscosity variations abstract predictions of present day secular variations in the earth s long wavelength geopotential driven by glacial isostatic adjustment gia have previously been analyzed to infer the radial profile of mantle viscosity and to constrain ongoing cryospheric mass balance these predictions have been based on spherically symmetric earth models we explore the impact of lateral variations in mantle viscosity using a new finite volume formulation for computing the response of 3 d maxwell viscoelastic earth models the geometry of the viscosity field is constrained from seismic to mographic images of mantle structure while the amplitude of the lateral viscosity variations is tuned by a free parameter in the modeling we focus on the zonal j l harmonics for degrees l 2 8 and demonstrate that large scale lateral viscosity variations of two to three orders of magnitude have a modest 5 10 impact on predictions of j 2 in contrast predictions of higher degree harmonics show a much greater sensitivity to lateral variation in viscosity structure we conclude that future analyses of secular trends for degree l 2 estimated from ongoing grace champ satellite missions must incorporate gia predictions based on 3 d viscoelastic earth models

modeling and simulation of glacier avalanche a case study of gayari sector glaciers hazards assessment glacier avalanches are natural hazards that could damage infrastructures and threaten lives in high altitude mountainous terrains on april 7 2012 a massive ice avalanche struck a pakistani base at gayari sector saltoro valley and buried killed 148 soldiers and civilians keeping in view the catastrophe a study was designed with the objectives to 1 model and simulate the gayari sector glacier avalanche incident in terms of height extent velocity pressure and momentum 2 generate hazard risk assessment of possible other glacier avalanches in the saltoro valley through modeling and simulation and 3 suitability analysis of current camp sites and recommendation of new safe camps sites locations in the saltoro valley to simulate the gayari sector glacier event and other glacier possible avalanches a physical process based rapid mass movements ramms was used the ramms has two main components i e voellmy salm vs model and random kinetic energy which deals with variables such as avalanche height and the mean avalanche velocity during the course of simulation the suitability analysis of current camp sites were achieved using weighted overlay analysis with different constraints in arcgis spatial analyst the ramms model simulation of the gayari avalanche event predicted a maximum velocity of 74 ms 1 generating a pressure of 5074 kpa and attaining a height of 45 m whereas the predicted debris volume on the ground was 3 8145 million m 3 a good agreement was found between actual debris height and extent as compared with the ramms model output the ramms model simulated all the potential tributary glacier avalanches of saltoro valley very well the weighted overlay analyses in arcgis spatial analyst revealed that the existing camp sites are safe and were not threatened by the glacier avalanche hazard however it was recommended that the gayari camp should not be constructed at the same location and should be relocated to the proposed safe camp sites identified in this research study the proposed methodology developed in the current study could be applied in the siachen conflict zone for avalanche hazard risk analysis of all the camp sites located in the valley

a global geodetic reference frame from lageos ranging sl5 1ap a summary of the results obtained for a new comprehensive geodetic parameter solution from the analysis of lageos laser ranging data for the period may 1976 to the end of 1982 is presented estimates of each component of the polar motion and earth rotation the station coordinates the value of the earth s gravitational constant gm and the elements of the lageos orbit comprise this sl5 1ap solution the results differ from previously published values primarily through incorporation of more rigorous dynamic models for the ocean and solid earth tides the precision of the geodetic parameters are on average 5 marc sec polar motion 0 2 ms length of day better than 5 cm center of mass geodetic positioning 3 cm global baselines and 2 cm regional baselines an assessment of the contribution of systematic errors in the interstation distance determination is presented

interaction of cryospheric forcings with rotational dynamics has consequences for ice ages recent geological evidence1 2 suggests that several degrees of true polar wandering have occurred since the mid pliocene this rotational instability is supported by dynamical calculations3 of the spin axis of a layered viscoelastic earth which has been subjected to the periodic forcings characteristic of the late cenozoic ice age we propose here that polar wandering induced by the intrinsic response of the viscoelastic planet to such cryospheric forcings may be the underlying cause for the termination of the present ice age epoch

transient polar motions and the nature of the asthenosphere for short time scales the role of viscoelastic flows excited by earthquakes in driving short term polar motions is investigated analytically by means of a four layer model consisting of an elastic lithosphere a thin asthenosphere a mean mantle and an inviscid core we have employed a linear maxwell rheology throughout the entire mantle to describe large scale geodynamic processes for time spans less than 100 years the global displacement fields which contribute to the perturbations of the moment of inertia are calculated by solving a two point boundary value problem in which the forcing function is a dislocation source the elements of the perturbated inertia tensor are then employed directly in the liouville equations for determining the changes of the chandler wobble and the rate of the earth s rotation as a consequence of large earthquakes a complete set of solutions to the liouville equation is used for this problem this formulation requires the usage of two classes of eigenspectra one arising from isostatic reequilibration of the mantle due to faulting and the second set involving the gradual readjustment of the spin axis as a result of transient flows in the mantle we find that the polar motions depend sensitively on the viscosity structure of the asthenosphere and not at all on the underlying mantle on the basis of the observed polar motion data and the secular changes of the gravitational harmonic coefficient j2 we can rule out a global low viscosity zone with short term asthenospheric viscosities less than about 5 1018 pa s and widths greater than 50 km

erratum deglaciation effects on the rotation of the earth geophys j r astron soc vol 62 p 49 58 1980

generalized rheology and geophysical consequences abstract in some portions of the earth crust one finds stresses and creeps which are incompatible with the local geologic history and or the generally accepted rheological models of voigt or maxwell or standard linear solid also there is no reason to accept that the rheology of the earth is represented by mathematical formulae modeling combinations of simplicistic springs and dash pots which lead to represent the phenomenon by means of first order time derivatives of stress and or strains we describe here an attempt to obtain a rheological model for the lithosphere which is more realistic and flexible than the voigt the maxwell and the standard linear solid models which are generally used in geophysics and geology in this model the first order derivatives of maxwell stress strain relations are replaced by z order derivatives the resulting creep rates are variable functions of time as indicated by laboratory observations in the one dimensional case as well as in the case of the sphere the relaxation rate after a given time is a decreasing function of time a small value of z could explain the residual deviatoric stress present in the fennoscandia and canadian shields herget 1980 leijon et al 1981 and the deviatoric stress present in the rocky mountains and in the appalachian range caputo et al 1985 which seem stable and were formed many tens of millions of years ago a small value of z would also explain why the seismicity is decreasing with lithospheric age stein 1979 bergman and solomon 1980 but is still present 100 millions of years after the origin of the lithosphere which implies a relevant residual shear stress after long time if one wants to take into account the effect of temperature then one should consider that there is evidence that in some materials the creep rate is linearly increasing with temperature in the range between 100 c to 400 c caputo 1983 and that it is independent of the confining pressure then one would infer that the new viscosity parameter introduced with the model is decreasing with depth which would account for the deformation rates observed on the surface of the earth which should therefore be caused by the fast creep of the lower layers the rheological model gives more realistic values for the q of the mantle the variation of the node of lageos and that of ut1 are also discussed it is suggested that these variations may be caused by the cumulative rebounds due to several deglaciations and not by the last one only

climate friction a possible cause for secular drift of earth s obliquity we investigated one of the mechanisms of secular drift of earth s obliquity called climate friction due to the feedback from the periodic variation of solar insolation and the glacial cycles we estimated the change of the moment of inertia by utilizing maxwell type viscous earth models and assumed linearity between insolation variation and ice sheet variation we reproduced the feedback loop of insolation variation ice sheet variation change of the moment of inertia change of the motion of the rotational axis of earth including the standard theoretical results of the quasi periodic planetary perturbation our simulation resulted in a secular increasing drift of earth s obliquity which is induced by the time lag of ice sheet formation with respect to the solar insolation variation and time lag of viscous deformation of the solid earth with respect to the formation of ice sheets we have estimated a secular increase of the obliquity 0 4 10 m y which depends on the viscosity of the lower mantle and the degree of ice sheet development

polar wandering and the forced responses of a rotating multilayered viscoelastic planet changes in the earth s rotation produced by the waxing and waning of large mobile ice sheets can be used to infer the viscosity of the mantle from a comparison with the recent secular polar drift as revealed in the international latitude service data and also in the estimates of the nontidal acceleration of the length of the day we have developed by using an analytical approach a physical model of a rotating earth consisting of an elastic lithosphere a viscoelastic mantle and an inviscid core forcings from the two major ice sheets laurentide and fennoscandia have been considered sensitivity analysis of the parameters governing the external forcings such as the length and the time of termination of the deglaciation phase show in general that there exist two families of mean mantle viscosities 0 1022 p and 0 1023 p which can match the data satisfactorily however we find it an improvement to incorporate some amount of shrinkage from the antarctic ice sheet obtaining simultaneously a better fit with the two rotational data sets to the lower viscosity solutions hence forcings from the southern hemisphere may be able to remove the ambiguity associated with the extraction of mantle viscosity from rotational data we have also solved the initial value problem of the components of instantaneous angular velocity by means of the laplace transform for applied loads characterizing the continental ice sheets which since the mid pliocene have periodically expanded and contracted over the northern hemisphere in consequence of this continual forcing polar wander of around 5 10 degrees can take place for a mean mantle viscosity 0 1022 p recent reanalysis of paleomagnetic data in conjunction with hot spot tracks have revealed that several degrees of true polar wander could have occurred in the last 5 m y these calculations thus provide a physical explanation for the observed movement of the rotation axis membrane stresses of 0 10 bars can develop from this secular polar motion

perturbations of the earth s rotation and their implications for the present day mass balance of both polar ice caps summary the present day perturbations of the earth s rotation are sensitive to the glacial isostatic adjustment gia arising from the late pleistocene glacial cycles and also to the recent mass balance of polar ice caps in this study we evaluate the polar wander and the change of degreetwo harmonic of the earth s geopotential j 2 proportional to the rotation rate for four late pleistocene ice models we examine these perturbations as a function of lower and uppermantle viscosities and lithospheric thickness and rheology elastic or viscoelastic in which a compressible earth model with elasticity and density given by the seismological model prem is used by considering the observations and predictions including the gia process arising from the late pleistocene ice and recent mass balance of polar ice caps we discuss the recent mass balance of the antarctic and greenland ice sheets we also examine the effects of internal processes and the melting of mountain glaciers although this work is only preliminary the results shown below seem to be supported even if these effects are included two solutions are obtained for source areas of the recent antarctic melting we denote an equivalent sea level esl rise mm yr 1 from the greenland and antarctic ice sheets as gl and