Enthalpy-Based Models For Ice Sheets And Improving Understanding Of Cryo-Hydrologic Warming
Macpherson, Brian 1 ; Rajaram, Harihar 2
1 University of Å·ÃÀ¿Ú±¬ÊÓƵ Boulder, Department of Civil, Environmental, and Architectural Engineering
2 University of Å·ÃÀ¿Ú±¬ÊÓƵ Boulder, Department of Civil, Environmental, and Architectural Engineering
Our research focuses on two aspects of ice sheet thermodynamics - (i) comparsion of enthalpy and temperature-based approaches for incorporation into thermo-mechanical models, and (ii) refinement of thermodynamic models to incoroprate processes such as cryo-hydrologic warming in the wet snow and ablation zones.
Alternative formulations of thermodynamic equations for continua include temperature-based, and various types of enthalpy-based formulations. The enthalpy-based formulations are ideally suited to situations where phase change or temperate conditions are encountered. Ice sheet thermomechanical models often employ one-dimensional column implementations of vertical energy transport coupled to horizontal transport. We compare column models incorporating temperature-based, and two types of enthalpy-based approaches (apparent heat capacity and enthalpy gradient) under a range of conditions. Our comparison confirms that these approaches are mutually consistent, even in cases where temperate ice is encountered at some internal depth. However, there are distinct computational advantages to enthalpy-based methods that require no iteration to find the cold-temperate interface and compute temperature and water content directly from the state variable, enthalpy.
Cryo-hydrologic warming (CHW) is a recently proposed mechanism for the rapid thermal response of ice sheets to melt inputs resulting from a warming climate. CHW is expected to be a significant component of ice sheet thermodynamics, specifically in areas that have only recently begun to receive melt (the estimated upstream expansion of the area receiving melt is 10-20km along a wide swath in western Greenland). We evaluate the physical underpinnings of CHW using high-resolution enthalpy-based models surrounding water-filled englacial features. We demonstrate the potential warming influence of these englacial water bodies in isolation, and in conjunction with other mechanisms, including advection and strain heating. Our results suggest that significant warming (to the extent of a temperature change that doubles the value of the flow-law parameter "A") occurs within decadal time-scales. Our simulations also suggest that deep englacial water bodies are required for significant thermo-mechanical influence of CHW. Deep englacial water bodies are shown to produce greater warmth near the bed where large gradients in velocity result in stretching and efficient dissipation of latent heat. In some situations, CHW may induce cold to temperate transitions near the bed, within decadal time-scales, priming the bed to permit year-round basal sliding.
Aschwanden A., Bueler, E., Khroulev, C., and Blatter, H., 2012, An enthalpy formulation for glaciers and ice sheets: Journal of Glaciology, v. 58, p. 441–457.
Phillips, T., Rajaram, H., and Steffen, K., 2010, Cryo-hydrologic warming: A potential mechanism for rapid thermal response of ice sheets, Geophys. Res. Lett., v. 37, L20503