If Paterson’s classic text The physics of glaciers may be considered a bible of modern glaciology, then this recent book by Kees van der Veen is probably one of the newly unearthed gospels. Fundamentals of glacier dynamics preaches the basic mathematical techniques used by scientists in the analysis and understanding of glacier flow. Rather than provide an overview of current research interests, it gives a dedicated account of the nuts and bolts of better-established models and theories, and the rationale behind their interpretation and validation. Accompanying the wealth of mathematical detail is a concise explanation of the underlying assumptions and derivations. Both analytical and numerical solutions are discussed, as well as comparison of results with field data. A textbook with such emphasis on modelling has been long overdue in the glaciology world.
But the book is not just a compendium of models. Van der Veen pulls together different themes by his centrepiece — what is known as the force-budget technique. The stresses controlling glacier motion may be separated into their “lithostatic” and “resistive” components, and this enables momentum conservation to be viewed in terms of a balance between terms that represent the effects of gravity, basal traction, lateral drag and longitudinal stress. As argued by Van der Veen, this facilitates a clearer visualization of the workings of the equations than if (perhaps more commonly) the isotropic–deviatoric stress decomposition were used. The author proceeds to demonstrate this in a variety of applications, covering the dynamical aspects of ice-sheet, valley-glacier, ice-shelf and ice-stream flows alike.
Not surprisingly, the structure of the book is straightforward, starting with developing the elementary tools and ending with models of the grand ice sheets of Greenland and Antarctica. Chapter one contains a brisk introduction to ice and climate; here, readers less familiar with the geosciences may find the prose rather dry and unstimulating. But though the book certainly does not open with a bang, it makes up with what follows. Chapters two to four give excellent accounts of the deformation behaviour of ice, the governing equations of glacier flow, and basal sliding. Once the scene is set, chapters five to nine follow through with a competent treatment of various topics in glacier mechanics and thermodynamics, with impressive continuity and coherence. These include laminar flow, flows dominated by longitudinal stresses or lateral drag, temperature control on ice viscosity, parameterization of surface energy balance and mass balance, and so on. Many classical results and some of their more sophisticated counterparts are there, ranging from Vialov’s ice-sheet profile, Robin’s solution for the temperature distribution in an ice sheet, Weertman’s equations for ice-shelf spreading, to the more recent numerical models by Huybrechts and others. Steady-state and time-dependent models are both considered. Particularly valuable are frequent references to the technicalities of numerical solution, although these are limited to finite-difference methods. (The entirety of chapter eight is devoted to these.) Then chapter nine steps back to take a broader look at glacier fluctuations and potential feedback mechanisms in glaciers by invoking low-order models. The final three chapters deal with more specific modelling problems concerning mountain glaciers, Greenland and Antarctica, respectively, each beginning with a succinct summary of the physical characteristics of these ice masses.
A key to the book, and a major difference between it and earlier ones, is the way in which the mathematics is presented. Throughout, the style of writing is somewhat similar to Paterson’s, but here the subject matter is tightly focused in order to illustrate the modelling approach. The author discusses the merits and weaknesses of each model at hand, so that the effect of successive refinements or approximations can be well appreciated. The presentation is tailored for course-teaching at graduate level, assuming only a basic background in calculus and differential equations. The book is therefore also much more accessible than the earlier works of Hutter and Lliboutry, and is likely to occupy an important niche in the market. In this introductory textbook, Van der Veen clearly achieves the goals he has set out.
At a deeper level, Van der Veen is also quite successful at getting across the philosophy of mathematical modelling. In isolated places, his writing hints at the endless cycle of iteration between model-building and field measurements, whereby our understanding is advanced. For instance, my favourite passage, found in chapter five, cautions that “there is nothing wrong with developing hypothetical models, but claims that such models apply to actual glaciers or ice sheets, when measurements indicate otherwise, reveal more about the modeller than the model about the glacier” (p. 132). How delightful and appropriate!
Having said many good things, the book is not without blemishes. The competent reader will notice that a large number of equations appearing in the text are plagued by errors. Though many of these are typographical and relatively easy to correct, this is nevertheless a nuisance. Other than that, the text is well illustrated and adequately cross-referenced. If you want to know about things like subglacial till, ice cores or glacial geomorphology, then there are much better places to look. But if your main interest is to acquire the skills to model glacier motion, this book should certainly be high on your shopping list. The more experienced researcher will also find it useful as a reference and teaching aid.
