Towards the identification of scaling relations in drainage basin sediment budgets

Drainage basin sediment budgets concern inputs, storages and outputs of sediments, and solutes through monitored cross-sections at the mouth of basins or at the base of individual slopes. The question under consideration is whether, and to what extent, it is possible to transfer knowledge from one spatial scale to another. The answer hinges on the question of scale invariance of (a) individual processes of sediment and solute transfer and (b) aggregate sediment budgets. Scale invariance of a number of hydrologic parameters has been established but, in general, with a few exceptions, geomorphic parameters are subject to scale distortion. By inference, but not yet established by experimental or field evidence, scale invariance of sediment budgets is improbable. There is therefore a priority to explore scaling relations in sediment budgets so as to determine the precise extent of scale distortion that is present. In this paper, five ways of identifying scaling relations in drainage basin sediment budgets are identified: (1) a fractal approach; (2) a theory hierarchy approach; (3) a non-linear dynamic systems approach; (4) a panarchy approach; and, (5) a hybrid approach. There are no “a priori” bases for selection of any one of these approaches until further field research and modeling of sediment and solute fluxes has been completed.