Scaling laws for aggradation, denudation and progradation rates: the case for time-scale invariance at sediment sources and sinks

Abstract Linear rates of sediment aggradation and fluvial incision are inverse functions of measurement interval, a generic consequence of unsteadiness in the underlying processes. This effect results from a one-dimensional approach–that is, vertical rates determined at a single location–and significantly complicates comparisons of rates at different timescales. Mass conservation imposes an important but underutilized constraint; sediment by-passing or eroded from one location must deposit somewhere else. Over the long term, sediment generation and deposition must balance. In principle, the effects of unsteadiness could be eliminated if the total volume of sediment eroded or deposited over different intervals could be measured. In practice, however, obtaining such three-dimensional data from an individual site is virtually impossible. Here, we advance from one- to two-dimensional rate data. We present two new global compilations of data: denudation rates of fluvial uplands; and lateral migration (progradation) rates of siliciclastic lowland and marine systems, from ripple to shelf-slope scale. Important new findings are: (1) upland denudation rates determined from specific sediment yield show little or no dependence of rate on time interval; (2) in the transfer zone between sediment source and sink, rates of erosion and deposition balance over all scales; and (3) progradation mirrors aggradation over all timescales. The product of progradation and aggradation is independent of timescale, implying that global sediment flux into the world’s oceans has been constant on the order of 10 0 m 2 /yr, from scales of months to tens of millions of years. Results show that global rates of denudation and accumulation are time invariant with appropriate spatial averaging; however, site-specific application remains a daunting challenge.