Numerical modelling

Models range from simple and conceptual to highly inclusive and complex, and underlie interpretation of all data sets (Huybrechts, this volume, Chapter 80). Of special note is the rise of the fully coupled, thermomechanical, three-dimensional models, which have grown and expanded greatly since the pioneering work of Mahaffy (1976). A suite of such models is summarized briefly in the European Ice Sheet Modelling Initiative (EISMINT) exercise (Payne et al., 2000; Payne & Baldwin, 2000).

Numerous new directions are being explored now in ice-flow modelling. Older models have largely relied either on the shallow-ice approximation (Hutter, 1983) appropriate for inland regions of ice sheets with spatial averages taken over horizontal distances of many ice thicknesses, or on the depth-averaged longitudinal deviatoric stress balance more appropriate for ice-shelf conditions (MacAyeal, 1992a), sometimes joining these end-to-end (Huybrechts, this volume, Chapter 80). Pioneering work is moving to inclusion of more stress terms, approaching but not yet using the full stress tensor (e.g. Schmeltz et al., 2002; Pattyn, 2003; Vieli & Payne, 2003). Inclusion of the multiple stresses is essential to address the central problems of ice streams, subglacial lakes, etc.

The tie between ice-core interpretation and ice-sheet flow is important, e.g. for interpreting accumulation rates from annual layer thicknesses, surface-temperature histories from borehole temperatures, and climatic temperature histories from surface-temperature histories correcting for thickness change (e.g. Alley et al., 1993; Cuffey et al., 1995). An especially interesting advance in this regard is the inclusion of tracers in ice-flow models, so that such characteristics as the age, latitude, longitude and surface elevation of deposition of ice can be simulated through long times and across space, showing the origin of ice collected in a core (Clarke & Marshall, 2002).

The strong anisotropy of a single ice crystal, together with the strong tendency for development and destruction of coordinated orientations of neighbouring crystals (preferred c-axis fabrics), can have major effects on the flow of ice sheets (e.g. Budd & Jacka, 1989; Thorsteinsson et al., 1999), with smaller effects from grain size and other characteristics of ice (Cuffey et al., 2000a). Attempts have been made and are being made to include these effects into ice-sheet models (e.g. Castlenau et al., 1997; Thorsteinsson, 2002; Faria et al., 2002), although the full evolution equations under the full stresses are not yet available (see 'Forensic glaciology', below).

Improved confidence in interpretation of ice-core palaeoclimatic histories will require improvements in this modelling.

The scale of the associated difficulties in 'handling' full stresses, anisotropy and tracers, together with the surface mass balance, water runoff and basal lubrication, till deformation, etc., is daunting. The main modelling groups are moving vigorously (see Huy-brechts, Payne and Gudmundsson, this volume, Chapters 80-82), but a fully integrated ice-flow model appears to be some distance off. The modelling of other key aspects of the Earth system is handled quite differently, with large and often stably funded groups (e.g. the Hadley Centre of the UK Meteorological Office, http://www.meto.gov.uk/research/hadleycentre/models/model-types.html, or the U.S. National Center for Atmospheric Research, http://www.ncar.ucar.edu) dedicated to long-term development of complete models and to providing community access to those models or their products.

At present, we lack community ice-flow models with the level of support, intercomparison, etc., expected from the main climate models. Incorporating full stress tensors, anisotropy, fabric development, till deformation, hydrology and more are great challenges. Despite the remarkable progress in ice-flow modelling, the piecemeal funding situation and limited available resources leave us somewhat pessimistic about the ability to really address the major problems rapidly. A few groups, not just one, with a mission and resources more like those of the atmospheric general-circulation-modelling community, would greatly change the situation. Given the major, or even preeminent, importance assumed by sea-level change in assessment of future impacts of changing climate (e.g. IPCC, 2001b), and the dominance of ice sheets as reservoirs of potential sea-level rise (IPCC, 2001a), the value of improvement of ice-flow models should be clear.

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