Many scientists now use the power of computer models to advance their subjects. But there is a choice: to simplify complex systems or to include more detail. Modelling the intricate processes of sedimentary geology is a case in point.
In modelling, simplicity isn't simple
Before computing became widespread, quantitative modelling usually required simplification — spherical cows1, if you like — to render complex problems tractable. Fields such as sedimentary geology that are only now becoming quantitative present a dilemma: is there any reason not to skip the first steps and go directly to the most detailed models we can create? Do we really need spherical cows?
I think that the evolution of relatively mature quantitative fields through a stage of creating simplified models was a matter of more than lack of access to large computers. It cultivated an essential counterpart to attention to detail, which is attention to what is truly essential. In general, complexity is ordered and hierarchical2, which among other things means that it is not additive. Simple interactions at small scales can produce complex behaviours at larger scales; and complicated small-scale processes can add up to relatively simple large-scale dynamics2,3,4. The discipline imposed by simplification forces one to seek out these effects.
The dynamics and stratigraphy of Earth's surface offer abundant examples of the power of insightful simplification. A generation of reduced-complexity models of landscapes showed how the interplay of simple rules could reproduce major features of tributary-channel networks. Similar approaches, with comparable results, have been applied to such features as stream braiding, sorted sediment patterns, bedforms, beach cusps, coastal morphology and river deltas. In each of these cases, simplified representations of the complex small-scale mechanics of flow and/or sediment motion capture the self-organization processes that create apparently complex patterns.
Moving up in scale, river 'long profiles' reflect the net effect of the complex, nonlinear mechanics of turbulent flow and sediment transport acting at small scales. Yet for many purposes, long-profile evolution can be represented by relatively simple diffusion models. And emerging evidence suggests that important aspects of large-scale downstream variability in depositional systems, including grain size and channel architecture, can be understood in terms of first-order sediment mass balance.
Traditional training in disciplines such as sedimentary geology understandably emphasizes attention to detail; this can easily carry over into a tendency to think that adding more detail to models is always better. If the goal is simply to produce realistic-looking simulations, this may be correct. But, as Philip England (personal communication) has pointed out, the danger in creating fully detailed models of complex systems is ending up with two things you don't understand — the system you started with, and your model of it.
Simplification is essential if the goal is insight. Models with fewer moving parts are easier to grasp, more clearly connect cause and effect, and are harder to fiddle to match observations. Even when they are only partially correct, simplified models can serve as reference cases5, a kind of intellectual geoid that lets us subtract first-order dynamics and focus on what is anomalous and idiosyncratic. But we will never find out what simple models can teach us if it becomes an article of faith that the systems we work on are irreducibly complex.
The convergence of high-resolution observational data, peta-scale computing and the obvious complexity of natural systems does make imaginary animals seem a little quaint. But understanding what is really essential requires simplification, which in turn requires imagination — the ability to see beyond what is in front of us — and a willingness to be wrong. Perhaps some day a computer will surprise us by proposing spherical cows. Until then, may they continue to remind us that simulation is not the same as understanding.
Complexity and the memory of landscape
The sedimentary record extends over more than 4.5 billion years and is the source for many inferences concerning Earth's history. Over this vast time, Earth has presented many faces, but there is no long-term trend because dynamic processes arise from a multiplicity of variables and time's arrow prevents future recurrence of the totality of past conditions. Yet Earth has certainly 'evolved', if only in the sense that it is always changing in response to the to-and-fro and up-and-down of tectonics, the position of continents and oceans, atmospheric composition, and the solar constant.Orbital parameters and organic evolution are other changing factors. The Pythagoreans had some of this in mind with their idea of the world in a state of constant flux. The concept also lies at the heart of the interdependence of material things recognized by Zen6 and other philosophies, going back to the Stoics.
In a simple world, solution of the Navier–Stokes equation, which describes fluid flow, would probably suffice to solve problems in what J. J. Thomson7 memorably referred to as 'out-of-doors physics'. Such disciplines comprise sedimentology, hydrology, geomorphology and other areas of surface environmental dynamics. However, the 'memory effect' makes it impossible for computational schemes to solve the Navier–Stokes equation for naturally evolving fluid flows (chaos theory outwits the weather forecasters in the end). Also, forces at work on the environment result in additional nonlinear effects. Nature is thus inherently complex, refuses to keep to boundary conditions, and is influenced by the pervasive variables of solid geology, climate change and life forms.
The best environmental science recognizes complexity and seeks to write computer code that can at least include influential variables. Take two examples: complex physical feedbacks in sediment transport8, and models linking climate, vegetation and soil erosion9. The former arise when flowing fluid transports solids that affect pressure and viscous forces, and influence fluid accelerations. The latter must deal with the linked complexity of all natural landscapes. The logic of a recent algorithm9 proceeds as: climate (monthly mean temperature/precipitation) → soil vegetation growth → soil infiltration properties → weather (daily storm events) → run-off → soil erosion potential. It is difficult to see the point in accepting landscape or sediment-routing models that ignore such fundamentals as seasonal water balance and vegetation growth. On the downside, attention to geology and the chemical weathering of rock is still not satisfactorily addressed.
What is the modern geologist to make of all this, for geophysicists contribute little practical help in the field examination of rock? In my opinion, there can be no general theory, only the effects of competing causes. We must try to interpret the rock record by attempting to assign true cause to stratigraphic events that originated in ancient landscapes. For example, what does a pulse of sediment signify? Is there such a thing as stratigraphic equilibrium? What are the timescales of sedimentary response to changes in environmental variables? Can we deconvolve such concatenated variables?
What we really need in 'out-of-doors physics' is a recognition of, on the one hand, the complexity of what I call the ambioscape, being the totality of spatial, environmental and geological variables that define a particular landscape, and, on the other hand, the limits to the explanatory power of self-similarity10.
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Paola, C., Leeder, M. Simplicity versus complexity. Nature 469, 38–39 (2011). https://doi.org/10.1038/469038a
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