Christian Schoof


EOS-South 356
(604) 822-6482

About my work

I am a mathematical and physical glaciologist whose main interest is the dynamics of ice sheets, such as those found in Antarctica and Greenland, and smaller mountain glaciers. My work focuses on fundamental aspects of ice sheet and glacier dynamics; see here for other research directions in the UBC glaciology group. I use a combination of modelling and observational approaches in my work.

The interest in these ice sheets stems mostly from the fact that they hold the key to future sea level, though sometimes the key to understanding them lies in the past. Some of the questions that motivate my work are: what controls the fast flow of ice streams, its spatial patterning and its ability change spontaneously in the absence of changes in external forcing? How do the dynamics of ice streams interact with the movement of grounding lines, where land-based ice turns into floating ice shelf? What drove the retreat of the West Antarctic Ice Sheet following the Last Glacial Maximum? How can large ice sheets such as the Laurentide disintegrate as quickly as they are known to have done? What caused the massive discharges of sediment-laden ice known as Heinrich events?

In order to answer these questions, the flow behaviour of ice sheets must be understood. Ice sheets accumulate snow in their interior where surface elevations are high. They lose mass at their margins, either through melting or through calving. Ice is transported between these regions by ice flow, and generally, the faster the rate of flow, the greater the rate of mass loss. Much of my work has concentrated on processes that can speed up ice flow and contribute to the rapid and irreversible disintegration of ice sheets.

Mountain glaciers also motivate much of my work. Their relevance is frequently more local in terms of regional water supplies and/or natural hazards. We also use them as a logistically simpler "natural laboratory" to understand fundamental process that are likely to affect ice sheets, but would be harder to observe there. Glaciers do a number of fascinating things that are interesting to theorize about and even more fascinating to observe directly. I am particularly interested in glacier surges, where a glacier switches from a slow to a fast flow state and then continues to flow fast even though it thins and the stresses acting on it become smaller. Another, related focus is the flow of melt water under glaciers, and the dynamics of lakes dammed by glacier ice.

A word about modelling and mathematics

The main objective of the modelling work in my group is to address processes that we do not understand well, or that are inadequately represented in large-scale computational models. Much of our theoretical work is aimed at developing process descriptions and prototyping computational approaches tto these hat can ultimately be implemented large-scale simulations, rather than running these simulations in my group, which requires a complementary skill set. Some examples of this work include the derivation of friction laws for glacier sliding from first principles, the development of self-consistent models for moisture transport in temperate ice, of subglacial hydrology and of ice stream shear margin migration.

In addition to working at the process scale, I also try to understand the implications of different processes on large-scale ice sheet and glacier dynamics through the use of reduced models, stripped to the minimal form in which all the relevant processes are retained self-consistently. This has the advantage of often making the essential physics behind some phenomenon clear in a way that a large-scale trawl through the parameter space of a computational model would not. Examples of this work include systematic studies of marine ice sheet dynamics and glacier or ice sheet surges.

To use the language of dynamical systems loosely, I'm not overly interested in computing the trajectory taken by an ice sheet as a dynamical system (though this is a worthwhile task that helps do things like predict future sea level rise). I am interested in the attractors of that dynamical system (like steady states, limit cycles etc), and in bifurcations that change the nature of these attractors. In practice, this means idenftifying things that you may have heard of as "tipping points" at which a large-scale change becomes inevitable as the result of a small change in forcing, like the ultimate disappearance of an ice sheet as the result of temperature increase.

The methods involved are a combination of mathematics and physics. In the mathematical sphere, I have a particular interest in asymptotic methods, partial differential equations, free boundary problems, applied complex analysis, dynamical systems, scientific computing, and in fluid dynamics in general.

A word about field work

We also conduct field work on glacier dynamics and hydraulics. This is motivated in part because mountain glaciers are a fascinating natural laboratory in which to confront theoretical ideas with reality. Mountain glaciers also allow processes that are likely to affect ice sheets to be observing in a logistically simpler setting, which often allows more detailed data to be collected. In collaboration with Gwenn Flowers at Simon Fraser University I have been developing a project in the St Elias Mountains, Yukon Territory, aimed at understanding the dynamics of a small valley glacier. A second project in collaboration with the Institute of Marine and Antarctic Studies in Hobart and the Australian Antarctic Division is focused on the Sorsdal Glacier in Princess Elizabeth Land. Field work requires a wide range of technical skills, and much of it is done collaboratively in order to bring all those skills together. My own focus has been on direct instrumentation, much of it in subglacial envrionments accessed by hot-water drilling.

Some examples of ongoing projects

Ice sheet dynamics: ice sheets are continent-sized bodies of land ice, kilometres thick. There are currently two of these, in places far from where most of us live: Greenland and Antarctica. They matter because they are so large. Take all that ice and dump it into the ocean, and sea levels will rise by tens of metres. This isn't going to happen in its entirety any time soon, but just a fraction of that sea level rise could have serious consequences for humans, especially as we tend to live and build infrastructure near coastlines. As we are looking at cold fresh water, potentially laden with sediment once it runs off the ice sheet, ice loss can also affect ocean circulation and nutrient cycling.

Ice sheets work by gathering snow fall in their interior. That mass gain has to be balanced by mass loss. As a polycrystalline solid, ice creeps. That is, it flows like a very viscous incompressible fluid - which is quite fun to watch when looking at multi-year time lapse images of large glaciers. Well, more fun than watching paint dry, anyway. The flow of ice is relevant because it transports mass from where there is net accumulation of snow to where net mass loss occurs, either near the ice sheet edge where surface elevations are lower and more ice melts in a year than snow falls, or at the coast where icebergs can be discharged.

A significant amount of our work has looked at so-called marine ice sheets, and at quantifying rates of mass loss using physics-based models. An ongoing thread in our work is to improve models of fracture formation and iceberg calving in ice sheets, and to understand how that affects ice flow. Other work in ice sheet dynamics in my group focuses on the fast flow of ice streams, and on thermomechanical effects: how do feedbacks between heat dissipation and ice temperature affect the flow of an ice sheet, and can they lead to spontaneous pattern formation and to rapid acceleration of ice flow?

Glacier hydrology and surges: Glaciers work like ice sheets except that they are smaller and usually supported by significant topography. Rather than flowing primarily sideways as an ice sheet does (ice sheets essentially spread under their own weight), glaciers tend to flow downhill. The basic picture of input and output is still the same: over an annual cycle, there is net snow accumulation at the top of the glacier, and net loss near the end, or snout. The length of a glacier may be largely dictated by topographic gradients (in the sense that a longer glacier would have a larger portion below its end-of-summer snow line and therefore lose more mass over a year), but the thickness of a glacier is largely dictated by ice flow: for a given snowfall rate and therefore of mass throughput, a faster flowing glacier will be thinner.

Glaciers flow viscously, but like ice sheets, they can also slide at their base. That sliding motion is facilitated by pressurized water at the glacier bed, which partially separates from ice and bed and weakens sediments at the bed. How does the water get there? Usually, we are looking at surface meltwater that drains through the ice to the bed and onward to the downstream end of the glacier. How that drainage system works is the main control on water pressure and therefore on sliding velocities.

Our ongoing research, a combination of field observation and modelling, tries to understand the basic physical processes that control the formation of a drainage system, as well as their dynamical effects - which can be quite dramatic, in the form of self-sustaining oscillations in glacier-dammed lakes (so called outburst floods) and glacier surges, in which glacier length and thickness oscillate as the result (potentially) of coupling between glacier geometry and the evolution of the subglacial drainage system.

A second thread of our work encompasses surface rather than basal hydrology: not only does surface hydrology dictate how water is delivered to the bed where there is a connection through the ice (usually in the form of so-called moulins, or near-vertical shafts in the ice), it also influences the process of iceberg calving through the accumulation of water in surface cracks, which can cause them to propagate downwards. This work has been focused on coastal East Antarctica, and is also a combination of fieldwork and modelling. (Before you ask - Antarctica is a magical place, but there are currently no further field deployments planned.)

Prospective graduate and undergraduate research students

If you're thinking of grad school, it's import to know what you're getting into. So I'm going to give you some fairly straight answers to questions you may not even have thought of about going grad school (not just in my group, but anywhere). First, the I'll give you the bad news (all the things that are hard), and then some of the good (research is rewarding!). If you can get through reading the bad news, that's a good sign: the common thread to success in grad school is tenacity.

First, the Canadian funding system does not realistically allow paying for fieldwork and full student salaries. (I could go on, but it's best summed up in the words of a colleague: "It's not a research funding system, it's a research prize system": the amount of funding that flows to a researcher typically depends on their previous performance, not on the cost of the proposed research. Illogical, but true.) A scholarship is therefore your best bet for entering graduate school at UBC. Scholarships available in Canada and at UBC are typically awarded competitively, so a strong performance in your last degree is essential. For Canadian applicants and permanent residents, note that NSERC funding applications for graduate scholarships have to be submitted in the autumn of the year before you plan to start your studies. To get full consideration for internal scholarships at UBC, your application to EOAS has to be complete with references by the start of January. EOAS typically requires you to have the equivalent of a thesis-based MSc before acceptance into the PhD program. (With satisfactory progress, you may be permitted to transfer from the EOAS MSc program into the PhD program without completing the MSc). There are some good reasons for the MSc-before-PhD requirement - committing to a four year PhD without prior graduate research experience is a risky thing to do, and MSc level research can help crystallize your own ideas about where you want to go with your future research.

The most important quality you need to have is the ability to be fully engaged with a research project for several years, and the desire - compulsion, really - to keep learning and get to the heart of whatever you're doing, no matter how frustrating. Especially when it gets frustrating. Two more closely related qualities you'll want to have in graduate school is a commitment to precision and detail, and the ability to extend what you've learnt into ideas of your own.

Another way of putting the above is this: if you've never felt truly challenged in your previous degree, that is probably not a good thing. Everyone meets their match in research, sooner or later, and what matters is how you deal with it - with the necessary help, of course. That is to say, it's good to know what it means to struggle with something but not give up, because that's likely to happen Likewise, if you've never felt compelled to take a project or assignment further than what the homework script asked for, you might want to ask yourself why you want to do graduate studies. Low-hanging fruit is likely to be few and far between, and you need to be fairly self-motivated. The whole point is that you're breaking new ground, so there is no guarantee of easy success, though hopefully your supervisor knows that there is a feasible route to results - that at least is how I design graduate projects.

Now the bit where I really spoil the fun: you also have to work working days like the rest of the population, and may often work longer days than the nine till five crowd. The pay is also pretty poor (you are at least initially being paid to learn!), and you have to be organized and disciplined about your work. Lastly (speaking from experience), if your *primary* motivation for wanting to come to Vancouver is outdoor recreation, that is great but please consider a different way of moving here. Someone out there is paying their taxes to support university research, and hence to pay your way in grad school.

If you're still reading...pursuing research is also a lot of fun, if you are patient. At its best, research gives you the sense of having discovered something new, something about the world around you, first for yourself, which you can then share with others.

So, if you are thinking about trying to pursue research in my group, and think theoretical work is your thing, strong mathematics and physics skills are key to success. You should have fluency in calculus, linear algebra, ordinary and ideally partial differential equations and their applications in physics (meaning, ideally you can solve problems in these areas without immediately having to look up the relevant methods, and use them reasonably regularly), Some background in pde-based continuum mechanics and in computational methods for differential equations is a bonus. Supervision through the Institute of Applied Mathematics is possible: there is a strong fluid dynamics presence across campus.

For the fieldwork- and data-oriented side of research in my group, experience with instrumentation (including the design aspect), experimental work and / or practical engineering are ideal, as are strong quantitative skills in the physical sciences in general, either in modelling (see above) or data analysis. You need to have a good grasp of physics and university-level mathematics. The ultimate aim is to generate high-quality data that can be used to test and further develop quantitative models of glaciological phenomena, so you will need to understand these models. If you actually want to go in the field, you also need a willingness to spend weeks living and working in cold and often wet but also very beautiful places - while probably never getting to explore much purely for fun.

On that note, the reality is that fieldwork consists of often repetitive tasks that require a lot of attention to detail and often long hours under physically demanding conditions, and an absolute need to stay safe that may be absent from your personal outdoor activities. (In plain English, if you go to do fieldwork, you will not be calling the shots as to what is an acceptable level of risk or how we operate in the field. If you can't live with that, you should fulfill your outdoor needs in a different way.) To add to all that, once you get back to camp in the evening, the day is not yet over, as there are usually plenty of camp tasks (cooking, cleaning, maintaining a bear fence etc) that need to be seen to. Basic outdoor and mountaineering skills (glacier travel, backcountry travel) or field logistics experience are useful, but I have had very successful field seasons with glacier novices. Above all, common sense and an ability to get on with others are great assets in the field. All of that being said, we do have a lot of fun in the field, and many students find unsupported science work in a wild, remote environment to be an intense and rewarding experience.

Sad but true

This is for all those who contact me by email and don't hear back: it's unlikely to be personal. The reality is that my inbox traffic is barely manageable. As a result, my responses involve something of a triage system: priority goes to my current students, graduate and undergraduates, existing collaborations, and other regular work obligations; I have to work from there. If your request falls outside of these, especially if it is more complex and a response potentially requires commitments on my part that I need to think through, it will take me longer to process - and i may never get around to it, simply because I'm swamped. I suspect this is not uncommon in my line of work, but most uf us don't talk about it. As I said, it's unlikely to be personal...

This has, unfortunately, affected responses to interest from potential graduate students. A particularly acute problem at the moment, since I am in the midst of writing a complicated grant proposal just as the graduate application deadline is approaching.

Graduate Students


48. Rada, C. and C. Schoof. 2018 Channelized, distributed, disconnected: subglacial drainage under a valley glacier in the Yukon. The Cryospere, 12, 2609–2636. pdf supplementary material

47. Haseloff, M., C. Schoof and O. Gagliardini. 2018. The role of subtemperate slip in thermally-driven ice stream margin migration. The Cryosphere, 12, 2545–2568. pdf supplementary material

46. Bach, E., V. Radic and C. Schoof. 2018. How sensitive are mountain glaciers to climate change? Insights from a block model. J. Glaciol, 247–258. doi: 10.1017/jog.2018.15 pdf;

45. Aso, N., V.C. Tsai, C. Schoof, G.E. Flowers, A. Whiteford and C. Rada. 2017. Seismologically observed spatio-temporal drainage activity at moulins. J. Geophys. Res.: Solid Earth, 122, 9095–9108.

44. Schoof, C., A.D. Davis and T.V. Popa. 2017. Boundary layer models for calving marine outlet glaciers. The Cryosphere. 11, 2283-2303.pdf supplementary material

43. Shugar, D.H., J.J. Clague, J.L. Best, C. Schoof, M.J. Willis, L. Copland and G.H. Roe.2017. River piracy and drainage basin reorganization led by climate-driven glacier retreat. Nature Geosci., 10,370–375

42. Jessop, D., A. Hogg, M. Gilbertson and C. Schoof. 2017. Steady and unsteady fluidised granular flows on slopes. J. Fluid. Mech., 827, 67–120. 15

41. Hewitt, I. and C. Schoof. 2017. Models for polythermal ice sheets and glaciers. The Cryosphere, 11,541–551 pdf

40. Robel, A.A., C. Schoof and E. Tziperman. 2016. Persistence and variability of ice-stream grounding lines on retrograde bed slopes. The Cryosphere 10, 1883-1896, doi:10.5194/tc-10- 1883-2016. pdf

39. Schoof, C. and I.J. Hewitt. 2016. A model for temperate ice incorporating gravity-driven moisture transport. Journal of Fluid Mechanics, 797, 504–535.pdf supplementary material

38. *Haseloff, M., C. Schoof and O. Gagliardini. 2015. A boundary layer model for ice stream margins. Journal of Fluid Mechanics, 781, 353–387, doi:10.1017/jfm.2015.503 pdf

37. Robel, A.A., C. Schoof and E. Tziperman. 2014. Rapid grounding line migration induced by internal ice stream variability. Journal of Geophysical Research, 119(11), 2430–2447, doi:10.1002/2014JF003251 pdf supplementary material

36. *Schoof, C., C.A. Rada, N.J. Wilson, G.E. Flowers and M. Haseloff. 2014. Oscillatory subglacial drainage in the absence of surface melt. The Cryosphere, 8,959–976, doi:10.5194/tc-8- 959-2014 pdf

35. Flowers, G.E., L. Copland and C.G. Schoof. 2014. Contemporary glacier processes and global change. Arctic, 67(1), 22–34, doi:10.14430/arctic4356.

34. Goldberg, D.N., C. Schoof and O. Sergienko, 2014. Stick-slip motion of an Antarctic Ice Stream: The effects of viscoelasticity. Journal of Geophysical Research, 119(7).15641580 doi: 10.1002/2014JF003132. pdf supplementary material

33. DeGiuli, E. and C. Schoof, 2014. On the granular stress-geometry equation. Europhysics Letters, 105, 28001 doi: 10.1209/0295-5075/105/28001

32. Werder, M.A., I.J. Hewitt, C.G. Schoof and G.E. Flowers. 2013. Modeling channelized and distributed subglacial drainage in two dimensions, Journal of Geophysical Research., 118,1-19, doi:10.1002/jgrf.20146 pdf

31. Robel, A.A., E. DeGiuli, C. Schoof and E. Tziperman, 2013. Dynamics of Ice Stream Temporal Variability: Modes, Scales and Hysteresis. Journal of Geophysical Research., 118, F925936, doi:10.1002/jgrf.20072. pdf supplementary material

30. Jarosch, A.H., C.G. Schoof and F.S. Anslow. 2013. Restoring mass conservation to shallow ice flow models over complex terrain. The Cryosphere, 7, 229-240. pdf

29. Schoof, C. and I.J. Hewitt. 2013. Ice sheet dynamics. Ann. Rev. Fluid Mech. 45, 217–239.

28. *Schoof, C. 2012. Thermally-driven migration of ice stream shear margins. J. Fluid Mech., 712, 552-578. pdf

27.Tziperman, E., D.S. Abbott, Y. Ashkenazy, H. Gildor, D. Pollard, C. Schoof and D.P. Schrag. 2012. Continental constriction and ocean ice cover thickness in a Snowball-Earth scenario. Journal of Geophysical Research., 117, C05016,, doi:10.1029/2011JC007730 16

26. Pattyn, F., C. Schoof, L. Perichon, R.C.A. Hindmarsh, E. Bueler, B. de Fleurian, G. Durand, O. Gagliardini, R. Gladstone, D. Goldberg, G.H. Gudmundsson, V. Lee, F.M. Nick, A.J. Payne, D. Pollard, O. Rybak, F. Saito, and A. Vieli. 2012. Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP. The Cryosphere 6, 573-588. pdf

25. Schoof, C., I.J. Hewitt and M.A. Werder. 2012. Flotation and free surface flow in a model for subglacial drainage. Part 1. Distributed drainage. J. Fluid Mech. 702, 126–156. pdf

24. Hewitt, I.J., C. Schoof and M.A. Werder. 2012. Flotation and free surface flow in a model for subglacial drainage. Part 2. Channel flow. J. Fluid Mech. 702, 157–188 pdf

23. Schoof, C. 2012. Marine Ice Sheet Stability. J. Fluid Mech., 698, 62–73 27. pdf

22. Schoof, C. 2011. Marine Ice Sheet Dynamics. Part 2: A Stokes Flow Contact Problem. J. Fluid Mech., 679, 122–155. pdf

21. Flowers, G.E., N. Roux, S. Pimentel and C.G. Schoof. 2011. Present dynamics and future prognosis of a slowly surging glacier. The Cryosphere, 5(1), 299–323

20. *Schoof, C. 2010. Ice sheet acceleration driven by melt supply variability. Nature, 468(7325), 803–806. pdf supplementary material

19. Pimentel, S., G.E. Flowers and C.G. Schoof. 2010 A hydrologically coupled higher-order flow-band model of ice dynamics with a Coulomb friction sliding law. J. Geophys. Res., 115, F04023, doi:10.1029/2009JF001621

18. Schoof, C., and R.C.A. Hindmarsh. 2010. Thin-film flows with wall slip: an asymptotic analysis of higher order glacier flow models, Quart. J. Mech. Appl. Math., 63(1), 73-114, doi:10.1093/qjmam/hbp025. pdf

17. Schoof, C. 2010. Coulomb friction and other sliding laws in a higher-order glacier flow model, Math. Models Meth. Appl. Sci. (M3AS), 20(1), 157-189. pdf

16. Creyts, T.T. and C.G. Schoof. 2009. Drainage through subglacial water sheets, J. Geophys. Res. 114(F04008), doi:10.1029/2008JF001215. pdf

15. Goldberg, D., D.M. Holland, and C. Schoof. 2009. Grounding line movement and ice shelf buttressing in marine ice sheets, J. Geophys. Res. 114(F04026), doi:10.1029/2008JF001227. pdf

14. Clarke, G.K.C., E. Berthier, C.G. Schoof and A.H. Jarosch. 2008. Neural networks applied to estimating subglacial topography and glacier volume. J. Climate. 22(8), 2146-2160.

13. Schoof, C.G. and G.K.C. Clarke. 2008. A model for spiral flows in basal ice and flute for- mation based on a Reiner-Rivlin rheology for glacial ice. J. Geophys. Res., 113(B5), B05204, doi:10.1029/2007JB004957. pdf

12. Schoof, C. 2007.Cavitation on deformable glacier beds. SIAM J. Appl. Math., 67(6), 1633– 1653. pdf

11. *Schoof, C. 2007. Ice sheet grounding line dynamics: steady states, stability and hysteresis. J. Geophys. Res., 112(F03S28), doi:10.1029/2006JF000664. 17 pdf

10. Schoof, C. 2007. Marine ice sheet dynamics. Part 1: The case of rapid sliding. J. Fluid Mech., 573, 27–55. pdf

9. Schoof, C. 2007. Pressure-dependent viscosity and interfacial instability in coupled ice- sediment flow. J. Fluid Mech., 570, 227–252. pdf

8. Schoof, C. 2006. A variational approach to ice-stream flow. J. Fluid Mech., 556, 227–251.pdf

7. Schoof, C. 2006. Variational methods for glacier flow over plastic till. J. Fluid Mech., 555, 299–320. pdf

6. Schoof, C. 2005. A note on inverting ice-stream surface data. J. Glaciol., 51(172), 181–182.

5. *Schoof, C. 2005. The effect of cavitation on glacier sliding. Proc. R. Soc. Lond. A, 461, 609–627, doi:10.1098/rspa.2004.1350. pdf

4. Schoof, C. 2004. On the mechanics of ice stream shear margins. J. Glaciol., 50(169), 208–218. pdf

3. Schoof, C. 2004. Bed topography and surges in ice streams. Geophys. Res. Letts., 31(6), L06401, doi:10.1029/2003GL018807. pdf

2. Schoof, C. 2003. The effect of bed topography on ice sheet dynamics. Cont. Mech. Thermodyn., 15(3), 295–307. doi: 10.1007/s00161-003-0119-3. pdf

1. Schoof, C. 2002. Basal perturbations under ice streams: form drag and surface expression. J. Glaciol., 48(162), 407–416. ;pdf