The ‘stochastic river’: The use of budget-capacity modelling as a basis for predicting long-term properties of stratigraphic successions

Sediment budget and sedimentation capacity are basic variables that can be used to describe the operation of sedimentation systems of all types; they are generalisations of sediment supply and accommodation. The sediment budget at a site is defined as the net flux of sediment across the site's boundaries; the sedimentation capacity is a measure of the deviation from equilibrium of the sedimentation system concerned. The operation of a sedimentation system is described by first specifying the system's budget-capacity relationship; this is most conveniently done by providing a probabilistic means of predicting budget from capacity. Once the budget-capacity relationship has been specified, a model of the system is constructed; this model follows the general rules put forward in the budget-capacity theory of sedimentation. The model enables the prediction of the patterns of deposition, stasis and erosion that the system will produce in time; from these patterns can then be determined the properties of the stratigraphic successions the system is expected to leave behind. There are many kinds of budget-capacity model. One of these, the ‘stochastic river’, is particularly useful in predicting long-term regularities in the stratigraphic thickness-time relationship. The ‘stochastic river’ is a two-dimensional budget-capacity model that mimics an idealised single-channel river. It is composed of a large number of similar sedimentation systems linked together in a chain, with each system fed exclusively from its upstream neighbour. The systems are continually perturbed by having their capacities altered by various external factors; these may be long-term regional-scale factors such as tectonically-induced basement subsidence and isostatic adjustment, as well as short-term local-scale factors such as changes in river discharge. The capacity perturbations are modelled as being driven by a random process; the perturbations of adjacent systems are spatially and temporally coupled. This ‘stochastic river’ reproduces many of the patterns of transport, deposition and erosion found in modern river systems. In particular, it reproduces the irregularly alternating, downstream-migrating patterns of deposition and erosion that result, for instance, in the development, migration and amalgamation of bars in gravel-bed rivers.