As computing power and speed have grown ever more sophisticated models of dynamic phenomena have emerged, particularly those that focus on meteorology and climatology. Weather and climate models apply to the thin spherical shell that constitutes Earth’s atmosphere. They consider incoming solar radiation and longer wavelength thermal radiation emitted by the surface sources and sinks of available power, linked to the convective circulation of energy and matter, most importantly water as gas, aerosols, liquid and ice in atmosphere and oceans. Such general circulation models depend on immensely complex equations that relate to the motions of viscous media on a rotating sphere, modulated by other aspects of the outermost Earth: the absorptive and reflective properties of the materials from which it is composed – air, rocks, soils, vegetation, water in liquid, solid and gaseous forms; different means whereby energy is shifted – speeds of currents and wind, adiabatic heating and cooling, latent heat, specific heat capacity of materials and more still. The models also have to take into account the complex forms taken by circulation on account of Coriolis’ Effect, density variations in air and oceans, and the topography of land and ocean floor. The phrase ‘and much more besides’ isn’t really adequate for such an enormous turmoil, for the whole caboodle has chaotic tendencies in time as well as 3-D space. The fact that such modelling does enable weather forecasting that we can believe together with meaningful forward and backward ‘snapshots’ of overall climate depends on increasing amounts of empirical data about what is happening, where and when. Models of this kind are also increasingly able to address issues of why such and such outcomes occur, an important example being the teleconnections between major weather events around the globe and phenomena such as the El Nino-Southern Oscillation – the periodic fluctuation of ocean movements, winds and sea-surface temperatures over the tropical eastern Pacific Ocean.

The Earth’s lithosphere and deeper mantle in essence present much the same challenge to modellers. Silicate materials circulate convectively in a thick spherical shell so that radiogenic heat and some from core formation can escape to keep the planet in thermal balance.  There are differences, the obvious ones being sheer scale and a vastly more sluggish pace, but most important are the interactions between materials with very different viscosities; the ability of the deep mantle to move by plastic deformation while the lithosphere moves as rigid, brittle plates. For geophysicists interested in modelling there are other differences; information that bears on the system is orders of magnitude less, its precision is much poorer and all of it is based on measurement of proxies. For instance, information on temperature comes from variations in seismic wave speed given by analysis of arrival times at surface observatories of different kinds of wave emitted by individual earthquakes. That is, from seismic tomography, itself a product of immensely complex computation. Temptation by computing power and the basic equations of fluid dynamics, however, has proved hard to resist and the first results of a general circulation model for the solid Earth have emerged (Mallard, C. et al. 2016. Subduction controls the distribution and fragmentation of Earth’s tectonic plates. Nature, v. 535, p. 140-143).

As the title suggests, the authors’ main objective was understanding what controls the variety of lithospheric tectonic plates, particularly how strain becomes localised at plate boundaries. They used a circulation model for an idealised planet and examined several levels of a plastic limit at which the rigidity of the lithosphere drops to localise strain. At low levels the lithosphere develops many plate boundaries, and as the plastic limit increases so the lithosphere ends up with increasingly fewer plates and eventually a rigid ‘lid’. The modelling also identified divergent and convergent margins, i.e. mid-ocean ridges and subduction zones. The splitting in two of a single plate must form two triple junctions, whose type is defined by the kinds of plate boundary that meet: ridges; subduction zones; transform faults. Both the Earth and the models show significantly more triple junctions associated with subduction than with extension, despite the fact that ridges extend further than do subduction zones. And these trench-associated triple junctions are mainly those dividing smaller plates. This suggests that it is subduction that focuses fragmentation of the lithosphere, and the degree of fragmentation is controlled by the lithosphere’s strength. There is probably a feedback between mantle convection and lithosphere strength, suggesting that an earlier, hotter Earth had more plates but operated with fewer, larger plates as it cooled to the present. But that idea is not new at all, although the modelling gives support to what was once mere conjecture.