On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets

This three section report can be regarded as an extended appendix to (Bueler, Brown, and Lingle 2006). First we give the detailed construction of an exact solution to a standard continuum model of a cold, shallow, and thermocoupled ice sheet. The construction is by calculation of compensatory accumulation and heat source functions which make a chosen pair of functions for thickness and temperature into exact solutions of the coupled system. The solution we construct here is ``TestG'' in (Bueler and others, 2006) and the steady state solution ``Test F'' is a special case. In the second section we give a reference C implementation of these exact solutions. In the last section we give an error analysis of a finite difference scheme for the temperature equation in the thermocoupled model. The error analysis gives three results, first the correct form of the Courant-Friedrichs-Lewy (CFL) condition for stability of the advection scheme, second an equation for error growth which contributes to understanding the famous ``spokes'' of (Payne and others, 2000), and third a convergence theorem under stringent fixed geometry and smoothness assumptions.Comment: 16 pages, two C codes; extended appendix to Bueler, Brown, and Lingle, "Exact solutions to the thermocoupled shallow ice approximation: effective tools for verification," submitted to J. Glacio

Computation of a combined spherical-elastic and viscous-half-space earth model for ice sheet simulation

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 Farrell's (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 Farrell's tabulated Green's 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.Comment: 36 pages, 16 figures, 3 Matlab program

Carbon Pricing and the Transition from Voluntary to Mandatory Markets

The current national and global call for a coordinated and meaningful response to climate change concerns is certain to shift the United States from several regional and voluntary carbon markets today to a global compulsory market in the near future. In addition to the clear environmental benefits, this changing landscape will result in groups of carbon market "winners" and "losers" – some market segments will gain favor and market share while others will lose economic opportunity. The competitive disadvantage for traditional energy in a carbon-priced world will be a catalyst for market-driven innovations in renewable energy, and sustainable development. There are many opportunities where Austin and Texas stand to gain as larger carbon pricing components are realized. This primer looks to explore the political, economic, and design considerations that will affect the development of the carbon market.IC2 Institut

Age Constraints for an M31 Globular Cluster from Main Sequence Photometry

We present a color-magnitude diagram (CMD) of the globular cluster SKHB-312 in the Andromeda galaxy (M31), obtained with the Advanced Camera for Surveys on the Hubble Space Telescope. The cluster was included in deep observations taken to measure the star formation history of the M31 halo. Overcoming a very crowded field, our photometry of SKHB-312 reaches V ~ 30.5 mag, more than 1 mag below the main sequence turnoff. These are the first observations to allow a direct age estimate from the turnoff in an old M31 cluster. We analyze its CMD and luminosity function using a finely-spaced grid of isochrones that have been calibrated using observations of Galactic clusters taken with the same camera and filters. The luminosity difference between the subgiant and horizontal branches is ~0.2 mag smaller in SKHB-312 than in the Galactic clusters 47 Tuc and NGC 5927, implying SKHB-312 is 2-3 Gyr younger. A quantitative comparison to isochrones yields an age of 10 +2.5/-1 Gyr

Far-Ultraviolet Emission from Elliptical Galaxies at z=0.33

We present far-ultraviolet (far-UV) images of the rich galaxy cluster ZwCl1358.1+6245, taken with the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope (HST). When combined with archival HST observations, our data provide a measurement of the UV-to-optical flux ratio in 8 early-type galaxies at z=0.33. Because the UV flux originates in a population of evolved, hot, horizontal branch (HB) stars, this ratio is potentially one of the most sensitive tracers of age in old populations -- it is expected to fade rapidly with lookback time. We find that the UV emission in these galaxies, at a lookback time of 3.9 Gyr, is significantly weaker than it is in the current epoch, yet similar to that in galaxies at a lookback time of 5.6 Gyr. Taken at face value, these measurements imply different formation epochs for the massive ellipticals in these clusters, but an alternative explanation is a "floor" in the UV emission due to a dispersion in the parameters that govern HB morphology.Comment: 4 pages, Latex. 2 figures. Uses corrected version of emulateapj.sty and apjfonts.sty (included). Accepted for publication in ApJ Letter

Far infrared giant dipole resonances in neutral quantum dots

A resonance behaviour of the far infrared absorption probability at a frequency \sim N^{1/4} is predicted for clusters of N electron-hole pairs (2\le N\le 110) confined in disk-shaped quantum dots. For radially symmetric dots, the absorption is dominated by a Giant Dipole Resonance, which accounts for more than 98 % of the energy-weighted photoabsorption sum rule.Comment: final versio