Mountain glacier models
Glacier models are used to investigate the important processes creating the world around us and for making predications for what the world might look like under different conditions, such as the last glacial. Glaciers are generally investigated using numerical, rather than physical (“laboratory”) models to describe relationships between mass balance, ice dynamics and climate. A review of reasons and procedures for modelling glaciers is given here.
Models of mountain (alpine) glaciers are applied to solve similar problems to those models used for polar ice sheets, but typically have a higher resolution (a smaller grid size) and need to consider the effects of steep and often variable bed slopes, and the transverse stresses found in valley glaciers. Numerical models of ice sheet flow based on the shallow ice approximation (e.g. Plummer and Phillips, 2003; MacGregor et al., 2009) are being developed into higher-order ice flow models that consider the transverse stresses in flowing ice, glacial erosion and sediment transport, for example by Egholm et al. (2011).
Simulation of glacial and periglacial landscape evolution of the initially fluvial (unglaciated) Panamint Range, California using the integrated second-order shallow ice approximation (Egholm et al., 2011).
Modelling philosophy: simplicity versus complexity
No matter how powerful the computer used or how impressive the model output, any model of a natural system is only as good as the authors’ understanding of the interaction between the physical laws that define their subject and the potential of simple small-scale interactions to produce large-scale complexity, more readily summarised as:
“All models are wrong, but some are useful” (Box and Draper, 1987)
Even if possible, it is not desirable to reproduce a natural system in all its inherent complexity—a model is a simplification that allows us to identify and test the sensitivity of a glacier to a range of variables, such as seasonality in mean annual air temperature, precipitation intensity or bed topography. An excellent discussion of simplicity versus complexity in modelling environmental systems is provided by Paola and Leeder (2011).
The model cart and the data horse
A model in itself is unlikely to be enough to test a hypothesis. Data from real glaciers are required both to parameterise a model, for which values from similar glaciers in other parts of the world may be used, e.g. glacier surface albedo (Cuffey and Paterson, 2010), and to define variables for the study glacier. Ideally, modelling and data collection are carried out together by the same researchers so that the requirements of the model drive the collection of appropriate data with which to test it: unfortunately, it is usually much easier to produce large volumes of model output than to collect a small amount of field data.
Modelling glaciers in the Southern Alps, New Zealand
The Southern Alps are a glaciated mountain range at an important location in the temperate climate zone as New Zealand is one of the few landmasses between 40–50°S. These glaciers are sensitive to climate change and research here aims to unravel links between Northern and Southern Hemisphere climate change.
Five recent studies have investigated New Zealand’s mountain glaciers and what they tell can us about Southern Hemisphere palaeoclimate: Golledge et al. (2012) reconstructed the entire Southern Alps icefield using the last glacial maximum (LGM) geomorphological record as field data. Tasman Glacier is a popular destination for glacier modellers: Anderson and Mackintosh (2012) constrained the effect of debris cover on the mass balance and McKinnon et al. (2012), investigated how a change in bed topography, produced by glacial erosion, drove recession of this glacier independent of climate change. Meanwhile, Doughty et al. (2012) focused on the Irishman Stream cirque, a tributary of the Tasman, to determine precisely when Lateglacial moraines formed. Further north, Rowan et al. (2012) investigated how drainage capture driven by advance of the LGM Rangitata and Ashburton Glaciers impacted on the proglacial sedimentary record. The three different models (Golledge, Rowan, McKinnon) used to simulate LGM glaciers all agreed on a climate scenario equivalent to 6–7°C colder than the present accompanied by a reduction in precipitation, and in agreement with other climate proxies such as pollen-based environmental reconstructions (Newnham et al., 2012), demonstrating the robustness of numerical glacier models to investigate palaeoclimate.
The glacier modellers’ bible:
Cuffey, K., Paterson, W., 2010. The Physics of Glaciers. Butterworth Heinemann, Oxford.
Practical research-driven guides:
Oerlemans, J., 2008. Minimal Glacier Models.
Oerlemans, J., 2010. The microclimate of valley glaciers [available from http://www.staff.science.uu.nl/~oerle102/ ]
A general introduction to modeling environmental systems:
Slingerland, R., and Kump, L., (2011) Mathematical Modeling of Earth’s Dynamical Systems: A Primer. Princeton University Press
Anderson, B., Mackintosh, A., 2012. Controls on mass balance sensitivity of maritime glaciers in the Southern Alps, New Zealand: The role of debris cover. J. Geophys. Res 117.
Box, G.E.P., Draper, N.R., 1987. Empirical model-building and response surfaces. John Wiley & Sons.
Doughty, A.M., Anderson, B.M., Mackintosh, A.N., Kaplan, M.R., Vandergoes, M.J., Barrell, D.J.A., Denton, G.H., Schaefer, J.M., Chinn, T.J.H., Putnam, A.E., 2012. Evaluation of Lateglacial temperatures in the Southern Alps of New Zealand based on glacier modelling at Irishman Stream, Ben Ohau Range. Quaternary Science Reviews 1–10.
Egholm, D.L., Pedersen, V.K., Knudsen, M.F., Larsen, N.K., 2011. Coupling the flow of ice, water, and sediment in a glacial landscape evolution model. Geomorphology 141-142, p.47-66.
Golledge, N.R., Mackintosh, A.N., Anderson, B.M., Buckley, K.M., Doughty, A.M., Barrell, D.J.A., Denton, G.H., Vandergoes, M.J., Andersen, B.G., Schaefer, J.M., 2012. Last Glacial Maximum climate in New Zealand inferred from a modelled Southern Alps icefield. Quaternary Science Reviews 46, 30–45.
MacGregor, K., Anderson, R.S., Waddington, E.D., 2009. Numerical modeling of glacial erosion and headwall processes in alpine valleys. Geomorphology 103, 189–204.
McKinnon K.A., Mackintosh, A., Anderson, B., Barrell, J.A., 2012, The influence of sub-glacial bed evolution on ice extent: a model-based evaluation of the Last Glacial Maximum Pukaki glacier, New Zealand. Quaternary Science Reviews (in press)
Newnham, R., McGlone, M., Moar, N., Wilmshurst, J., Vandergoes, M., 2012. The vegetation cover of New Zealand at the Last Glacial Maximum. Quaternary Science Reviews 1–13
Paola, C., Leeder, M.R., 2011. Simplicity versus complexity. Nature Forum 1–2.
Plummer, M., Phillips, F., 2003. A 2-D numerical model of snow/ice energy balance and ice flow for paleoclimatic interpretation of glacial geomorphic features. Quaternary Science Reviews 22, 1389–1406.
Rowan, A., Plummer, M., Brocklehurst, S., Jones, M., Schultz, D., 2012. Drainage capture and discharge variations driven by glaciation in the Southern Alps, New Zealand. Geology (in press)