Craig S. Lingle

Updated estimates of glacier volume changes in the western Chugach Mountains, Alaska, and a comparison of regional extrapolation methods

and 2001/2004. Average net balance rates ranged between � 3.1 to 0.16 m yr � 1 for the tidewater and � 1.5 to � 0.02 m yr � 1 for the nontidewater glaciers. We tested several methods for extrapolating these measurements to all the glaciers of the western Chugach Mountains using a process similar to cross validation. Predictions of individual glacier changes appear to be difficult, probably because of the effects of glacier dynamics, which on long (multidecadal) timescales, complicates the response of glaciers to climate. In contrast, estimates of regional contributions to rising sea level were similar for different methods, mainly because the large glaciers, whose changes dominated the regional total, were among those measured. For instance, the above sea level net balance rate of Columbia glacier (� 3.1 ± 0.08 km 3 yr � 1 water equivalent (weq) or an equivalent rise in sea level (SLE) of 0.0090 ± 0.0002 mm yr � 1 ) was nearly half of the total regional net balance rate of the western Chugach Mountain glaciers (� 7.4 ± 1.1 km 3 yr � 1 weq or 0.020 ± 0.003 mm yr � 1 SLE between 1950/1957 and 2001/2004). Columbia glacier is a rapidly retreating tidewater glacier that has lost mass through processes largely independent of climate. Tidewater glaciers should therefore be treated separately when performing regional extrapolations.

Analysis of the 1993-95 Bering Glacier (Alaska) surge using differential SAR interferometry

Differential spaceborne radar interferometry observations of West Bagley Icefield are used to measure surface velocity and topography. Bagley Icefield is the accumulation area fur Bering Glacier which surged in two phases from spring 1993 through summer 1905. The observations presented are based on data collected during the winter of 1992, prior to the surge, and during winter 1994 while the surge was in full progress. Both observation intervals correspond to 3 day repeat orbit phases of the ERS-I C-band SAR. This paper gives an overview of the algorithms used to derive surface-velocity vector fields and topography for valley glaciers from SAR images. The resulting high-resolution velocity data clearly show West Bagley Icefield accelerating from its quiescent pre-surge velocity by a factor of 2.7 in response to the Bering Glacier surge. Persistence of lnterfero-metric phase coherence and the relatively moderate degree of acceleration on the western arm of Bagley Icefield suggest that the velocity increase may have been caused by increased longitudinal stress gradients resulting from coupling to the surging main trunk of Bering Glacier.

Exact solutions to the thermomechanically coupled shallow-ice approximation: effective tools for verification

We describe exact solutions to the thermomechanically coupled shallow-ice approximation in three spatial dimensions. Although artificially constructed, these solutions are very useful for testing numerical methods. In fact, they allow us to verify a finite-difference scheme, that is, to show that the results of our numerical scheme converge to the correct continuum values as the grid is refined in three dimensions. Comparison of numerical results with exact solutions has helped us to precisely quantify and understand some of the numerical errors we are making. Our verified numerical scheme shows the basal temperature spokes which arose in the EISMINT (European Ice Sheet Modelling INiTiative) II intercomparison (Payne and others, 2000). A careful analysis describes these warm spokes as numerical errors which occur when the derivative of the strain-heating term with respect to the temperature is large. On the other hand, the appearance of basal temperature spokes in a verified numerical scheme strongly suggests that they are a feature of the EISMINT II experiment F continuum problem. In fact, they are clear evidence of an unstable equilibrium point of the continuum problem. This paper is a sequel to Bueler and others (2005), which addresses exact solutions and verification in the isothermal case.

Seasonal fluctuations in the advance of a tidewater glacier and potential causes : Hubbard Glacier, Alaska, USA

Satellite imagery has been used to acquire seasonal terminus positions of tidewater Hubbard Glacier, Alaska, USA, from 1992 to 2006. During this 15 year time period, the width-averaged advance of the entire terminus has been � 620 m at a mean rate of 35 m a -1 . Seasonal fluctuation of the terminus ranges from 150 to 200 m on average and varies spatially. A section of the terminus, near a narrow gap where the glacier has now twice closed off 40 km long Russell Fiord, exhibited little to no mean advance during this time period but displayed seasonal fluctuations of 300-500 m. Seasonal variability in surface ice speeds and surface sea-water temperatures was also observed; both are potential forcing mechanisms for terminus fluctuations. Seasonal changes in sea-water temperature of 10-128C, as well as seasonal changes in subglacial freshwater discharge, are inferred to influence calving and submarine melting at the terminus, driving seasonal variations. Displacements of the medial moraine separating Hubbard and Valerie Glaciers at the terminus suggest surge-like pulses of the latter, with a periodicity of several years. The timing of these pulses suggests they may influence the Hubbard terminus near Gilbert Point and have implications for future closures of Russell Fiord.

InSAR observations of the 1993-95 Bering Glacier (Alaska, U.S.A.) surge and a surge hypothesis

Time-varying accelerations were observed on Bagley Icefield during the 1993-95 surge of Bering Glacier, Alaska, U.S.A., using repeat-pass synthetic aperture radar interferometry. Observations were from datasets acquired during winter 1991/92 (pre-surge), winter 1993/94 (during the surge) and winter 1995/96 (post-surge). The surge is shown to have extended 110 km up the icefield from Bering Glacier to within 15 km or less of the flow divide. Acceleration and step-like velocity profiles are strongly associated with an along-glacier series of central phase bulls-eyes with diameters of 0.5-4 km. These bulls-eyes are interpreted to represent glacier surface rise/fall events of ∼3-30 cm during 1-3 day observation intervals and indicate possible migrating pockets of subglacial water. We present a surge hypothesis that relates late-summer climate to englacial water storage and thence to the subglacial water dynamics-pressurization, hydraulic jacking, depressurization and migration-suggested by our observations.

On Mertz and Ninnis Glaciers, East Antarctica

Two large glacier tongues, which extend substantially across the coastline of King George V Land in East Antarctica, have been studied by remote sensing (synthetic aperture radar, JERS-1). The tongue of Mertz Glacier is in a state of advance, while the Ninnis Glacier tongue is retreating. Some more specific points are: The distinctive surface structure and the form of the glacier tongues indicates that they are floating. While the tongue of Ninnis Glacier has lost about two-thirds of its area since 1913, the Mertz Glacier tongue has advanced substantially and has about doubled its areal extent over the same time period. The annual movement of the tongue of Mertz Glacier was determined as about 1.2 km. This is close to the value of the advance of the tip of the tongue since 1963, which was determined as 0.9 km year -1 .

Fast computation of a viscoelastic deformable Earth model for ice-sheet simulations

This report starts by describing the continuum model used by Lingle & Clark (1985) to approximate the deformation of the earth under changing ice sheet and ocean loads. That source considers a single ice stream, but we apply their underlying model to continent-scale ice sheet simulation. Their model combines Farrells (1972) elastic spherical earth with a viscous half-space overlain by an elastic plate lithosphere. The latter half-space model is derivable from calculations by Cathles (1975). For the elastic spherical earth we use Farrells tabulated Greens function, as do Lingle & Clark. For the half-space model, however, we propose and implement a significantly faster numerical strategy, a spectral collocation method (Trefethen 2000) based directly on the Fast Fourier Transform. To verify this method we compare to an integral formula for a disc load. To compare earth models we build an accumulation history from a growing similarity solution from (Bueler, et al. 2005) and and simulate the coupled (ice flow)-(earth deformation) system. In the case of simple isostasy the exact solution to this system is known. We demonstrate that the magnitudes of numerical errors made in approximating the ice-earth system are significantly smaller than pairwise differences between several earth models, namely, simple isostasy, the current standard model used in ice sheet simulation (Greve 2001, Hagdorn 2003, Zweck & Huybrechts 2005), and the Lingle & Clark model. Therefore further efforts to validate different earth models used in ice sheet simulations are, not surprisingly, worthwhile. 1. Two linear earth models and their Greens functions Lingle & Clark (1985) use as their fundamental tools the Greens functions of two different linear earth models. The Greens functions for these models are convolved with the load to compute (vertical) displacements of the earths surface. One finds an elastic displacement u E and a viscous displacement u V given a current load and a load history, respectively, as we will explain. The total displacement is then the sum u = u E + u V at any time. That is, the two linear models are superposed. The partial differential equations (PDEs) behind these Greens functions are linear. In this report we state these PDEs, which is, in the case of the second model, a nontrivial accomplishment (see section 3). We then approximately solve these PDEs in a demonstra-bly efficient manner. First, however, we describe the two models and their sources in the literature.Abstract The model used by Lingle and Clark (1985) to approximate the deformation of the Earth under a single ice stream is adapted to the purposes of continent-scale ice-sheet simulation. The model combines a layered elastic spherical Earth (Farrell, 1972) with a viscous half-space overlain by an elastic plate lithosphere (Cathles, 1975). For the half-space model we identify a new mathematical formulation, essentially a time-dependent partial differential equation, which generalizes and improves upon the standard elastic plate lithosphere with relaxing asthenosphere model widely used in ice-sheet simulation. The new formulation allows a significantly faster numerical strategy, a spectral collocation method based directly on the fast Fourier transform. We verify this method by comparing to an integral formula for a disk load. We also demonstrate that the magnitudes of numerical errors made in approximating coupled ice-flow/Earth-deformation systems are significantly smaller than pairwise differences between several Earth models. Our implementation of the Lingle and Clark (1985) model offers important features of spherical, layered, self-gravitating, viscoelastic Earth models without the computational expense.

Satellite Altimetry, Semivariograms, and Seasonal Elevation Changes in the Ablation Zone of West Greenland

Seasonal mean changes in the surface elevation of the ablation zone of West Greenland to 72 oN between spring 1985 and summer 1986 are measured using radar altimeter data from the 18-month Geosat Geodetic Mission. Semiva riograms are used to estimate the noise in the data as a function of pOSItIOn on the ice sheet. Mean elevation changes are computed by averaging the elevation differences measured at points where orbits ascending in latitude are later crossed by orbits descending in latitude (or the reverse) , with each cross-over difference weighted in proportion to the in verse square of the noise level in the neighborhood of the cross-over point. The mean surface ele vation of the ablation zone, relative to spring 1985, ran ged from 1.5 ± 0.6 m lower during summer 1985 to I. 7 ± 0.4 m higher during spring 1986.

Airborne and spaceborne DEM- and laser altimetry-derived surface elevation and volume changes of the Bering Glacier system, Alaska, USA, and Yukon, Canada, 1972-2006

Using airborne and spaceborne high-resolution digital elevation models and laser altimetry, we present estimates of interannual and multi-decadal surface elevation changes on the Bering Glacier system, Alaska, USA, and Yukon, Canada, from 1972 to 2006. We find: (1) the rate of lowering during 1972-95 was 0.9 � 0.1 m a -1 ; (2) this rate accelerated to 3.0 � 0.7 m a -1 during 1995-2000; and (3) during 2000-03 the lowering rate was 1.5 � 0.4 m a -1 . From 1972 to 2003, 70% of the area of the system experienced a volume loss of 191 � 17 km 3 , which was an area-average surface elevation lowering of 1.7 � 0.2 m a -1 . From November 2004 to November 2006, surface elevations across Bering Glacier, from McIntosh Peak on the south to Waxell Ridge on the north, rose as much as 53 m. Up-glacier on Bagley Ice Valley about 10 km east of Juniper Island nunatak, surface elevations lowered as much as 28 m from October 2003 to October 2006. NASA Terra/MODIS observations from May to September 2006 indicated muddy outburst floods from the Bering terminus into Vitus Lake. This suggests basal-englacial hydrologic storage changes were a contributing factor in the surface elevation changes in the fall of 2006.

Surging, accelerating surface lowering and volume reduction of the Malaspina Glacier system, Alaska, USA, and Yukon, Canada, from 1972 to 2006

Near-concurrent surges and multi-decadal surface-elevation changes on the Malaspina Glacier system Alaska, USA, and Yukon, Canada, were investigated using digital elevation models and laser altimetry from airborne and space-borne sensors. Surface-elevation changes on Seward Lobe in two time periods support a hypothesis of moraine folding by a mechanism of sequential surges alternating from southeast to south-southwest. The near-concurrent surges of Agassiz, Lower Seward and Marvine glaciers support a hypothesis of englacial water storage being a critical factor of surging. Acceleration of area-average surface lowering on the piedmont glaciers occurred, from 1.5 � 0.1 m a -1 between 1972 and 1999 to 2.3 � 0.3 m a -1 between 1999 and 2002. On the western half of Upper Seward Glacier, above 1600 m, acceleration of surface lowering occurred from 2000 to 2003 relative to that from 1976 to 2000, indicating an effect from the surge of Lower Seward Glacier. From 2003 to 2006, the rate of surface lowering on Upper Seward Glacier has moderated back to the pre-2000 rate, indicating a recovery of surface elevation following the surge. From 1972 to 2002, the Malaspina Glacier system lost 156 � 19 km 3 (ice equivalent) on an area of 3661 km 2 .