We have used airborne laser altimetry to estimate volume changes of 67 glaciers in Alaska from the mid-1950s to the mid-1990s. The average rate of thickness change of these glaciers was -0.52 m/year. Extrapolation to all glaciers in Alaska yields an estimated total annual volume change of -52 +/- 15 km3/year (water equivalent), equivalent to a rise in sea level (SLE) of 0.14 +/- 0.04 mm/year. Repeat measurements of 28 glaciers from the mid-1990s to 2000-2001 suggest an increased average rate of thinning, -1.8 m/year. This leads to an extrapolated annual volume loss from Alaska glaciers equal to -96 +/- 35 km3/year, or 0.27 +/- 0.10 mm/year SLE, during the past decade. These recent losses are nearly double the estimated annual loss from the entire Greenland Ice Sheet during the same time period and are much higher than previously published loss estimates for Alaska glaciers. They form the largest glaciological contribution to rising sea level yet measured.

Comparison of numerically computed solutions to exact (analytical) time-dependent solutions, when possible, is superior to intercomparison as a technique for verification of numerical models. At least two sources of such exact solutions exist for the isothermal shallow ice-sheet equation: similarity solutions and solutions with 'compensatory accumulation'. In this paper, we derive new similarity solutions with non-zero accumulation. We also derive exact solutions with (i) sinusoidalin-time accumulation and (ii) basal sliding. A specific test suite based on these solutions is proposed and used to verify a standard explicit finite-difference method. This numerical scheme is shown to reliably track the position of a moving margin while being characterized by relatively large thickness errors near the margin. The difficulty of approximating the margin essentially explains the rate of global convergence of the numerical method. A transformed version of the ice-sheet equation eliminates the singularity of the margin shape and greatly accelerates the convergence. We also use an exact solution to verify an often-used numerical approximation for basal sliding and we discuss improvements of existing benchmarks.

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.

[1] We used airborne altimetry measurements to determine the volume changes of 23 glaciers in the western Chugach Mountains, Alaska, United States, between 1950/1957. Average net balance rates ranged between À3.1 to 0.16 m yr À1 for the tidewater and À1.5 to À0.02 m yr À1 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 (À3.1 ± 0.08 km 3 yr À1 water equivalent (weq) or an equivalent rise in sea level (SLE) of 0.0090 ± 0.0002 mm yr

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