JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, F00A06, doi:10.1029/2009JF001266, 2009 Real and apparent changes in sediment deposition rates through time Rina Schumer1 and Douglas J. Jerolmack2 Received 15 January 2009; revised 11 May 2009; accepted 2 July 2009; published 30 September 2009. [1] Field measurements show that estimated sediment deposition rate decreases as a power law function of the measurement interval. This apparent decrease in sediment deposition has been attributed to completeness of the sedimentary record; the effect arises because of incorporation of longer hiatuses in deposition as averaging time is increased. We demonstrate that a heavy-tailed distribution of periods of nondeposition (hiatuses) produces this phenomenon and that observed accumulation rate decreases as tgÀ1, over multiple orders of magnitude, where 0 < g 1 is the parameter describing the tail of the distribution of quiescent period length. By using continuous time random walks and limit theory, we can estimate the actual average deposition rate from observations of the surface location over time. If geologic and geometric constraints place an upper limit on the length of hiatuses, then average accumulation rates approach a constant value at very long times. Our model suggests an alternative explanation for the apparent increase in global sediment accumulation rates over the last 5 million years. Citation: Schumer, R., and D. J. Jerolmack (2009), Real and apparent changes in sediment deposition rates through time, J. Geophys. Res., 114, F00A06, doi:10.1029/2009JF001266. 1. Introduction pattern as the ‘‘Sadler effect.’’ Sadler [1981] recognized that this decrease likely results from the intermittent nature of [2] Estimating erosion and deposition rates through geo- sediment deposition. To better understand this, consider logic time is a foundation of geomorphology and sedimen- modern sediment accumulation around the globe. If we tology. Measured rates provide information about the nature measure sedimentation everywhere it is occurring, we may and pace of landscape evolution. Modern sediment dating estimate a large value for the average global accumulation techniques, coupled with biological and chemical proxies rate. If we instead consider all basins, including ones for air temperature, precipitation and altitude, promise experiencing nondeposition or erosion, we would estimate continued progress in unraveling the coupling of erosion/ a much smaller value. We can infer that in the temporal deposition, tectonics, and climate change. Because sediment evolution of one particular basin, there will be hiatuses in transport processes on the Earth’s surface respond to glacial deposition interleaved with intervals of accumulation. cycles and tectonic motions, changes in denudation and Localized, instantaneous rates of deposition (or erosion) accumulation rates through geologic time are expected. are controlled only by the dynamics of sediment transport. Resolving these changes and attributing them to specific Over long timescales, however, deposition rates are limited forcing mechanisms is a key challenge. For example, much by the generation of accommodation space, typically the recent research has documented a global increase in sedi- slow process of tectonic subsidence. As an example, con- ment accumulation rates since the late Cenozoic ( 5Mato sider deposition at a point on a river delta undergoing present; Figures 1 and 2 [Zhang et al., 2001; Molnar, 2004; constant subsidence. Migrating dunes have deposition local- Kuhlemann et al., 2001]). Those studies present compelling ized on steep downstream faces, while the longer upstream evidence that enhanced climate variability beginning in the faces reerode most deposited sediment. In addition, signif- late Cenozoic has continually destabilized landscapes and icant sediment transport only occurs during large annual led to enhanced erosion in upland environments. floods, so during most of the year little river sediment [3] It is well known that measured deposition rates deposits at any point on the delta. Following centuries to decrease systemically with measurement duration (Figure 3) millennia of channel deposition, a river will avulse to a new for virtually all depositional environments in which there location and abandon the old channel. The abandoned are sufficient data, with intervals ranging from minutes to section of the delta will flood for millennia because of millions of years [Sadler, 1981, 1999]. Here we refer to this continued subsidence, until the river eventually returns to 1 begin deposition anew. The result is that hiatuses would Division of Hydrologic Sciences, Desert Research Institute, Reno, dominate the depositional history at any place on the delta, Nevada, USA. 2Department of Earth and Environmental Science, University of and would have a wide distribution in time, even under Pennsylvania, Philadelphia, Pennsylvania, USA. steady climate and tectonic conditions. Geologic evidence strongly supports the notion that hiatuses are common while Copyright 2009 by the American Geophysical Union. deposition is rare, such that stratigraphy records only a very 0148-0227/09/2009JF001266 F00A06 1of12 F00A06 SCHUMER AND JEROLMACK: REAL AND APPARENT DEPOSITION RATES F00A06 Figure 1. Global values for seafloor sediment accumula- tion [after Hay et al., 1988; Molnar, 2004]. Note that data are separated into bins with an interval of 5 million years. In this context, accumulation during the last 5 million years appears to abruptly increase. Figure 3. Representative ‘‘Sadler plot’’ showing sediment accumulation rates as a function of measurement interval for small fraction of Earth surface evolution [Sadler, 1981; siliciclastic shelf deposits. Data are log-bin averaged and Tipper, 1983]. Sadler [1981] hypothesized that the apparent represent thousands of measurements for each different decrease in accumulation rate with increasing measurement environment. At long timescales, some data appear to interval arises because of incorporation of longer hiatuses in gradually converge toward a constant rate. deposition as averaging time is increased. [4] Observations in natural rivers show that sediment rarely is conveyed steadily downstream, but instead pulses 2008]. Mechanisms responsible for these fluctuations in in an unpredictable fashion [Leopold et al., 1964; Gomez et fluvial systems include (in increasing length and timescale): al., 2002]. Careful laboratory experiments with constant the direct influence of turbulence on grain entrainment boundary conditions have produced large-scale fluctuations [Schmeeckle and Nelson, 2003; Sumer et al., 2003] and in bed load transport rates [Singh et al., 2009] and for grain-grain interactions in a river bed [Drake et al., 1988]; shoreline migration in a fan delta [Kim and Jerolmack, migration of bed forms [e.g., Jerolmack and Mohrig, Figure 2. Volumetric erosion rates for the last 10 Myr from the Eastern Alps (data from Kuhlemann et al. [2001]). Rates were estimated from measurements of sediment accumulation in basins around the Alps and were corrected for compaction. The curve may be thought of equivalently as sediment accumulation rate. Inset shows data plotted on a log-log scale. 2of12 F00A06 SCHUMER AND JEROLMACK: REAL AND APPARENT DEPOSITION RATES F00A06 2005a]; river avulsion and channel migration [Jerolmack tion for compaction. Modeling the generation of stratigra- and Paola, 2007]; and large-scale slope fluctuations in a phy as a stochastic process has a long history beginning river delta [Kim and Jerolmack, 2008]. Nonlinear thresholds with Kolmogorov [1951]. The idea is that location of the exist in many other types of transport systems as well. sediment surface is the sum of past depositional and Regardless of their origin, the net effect of such nonlinear- erosional periods, represented by positive or negative ities is that sediment transport is intermittent and rates ‘‘jumps’’ creating a stratigraphic column. Given indepen- typically vary widely in space and time even under steady dent and identically distributed (IID) particle jump vectors forcing. Several studies indicate that a large portion of Yn, location of the sediment surface at time t is stratigraphy may be the record of the stochastic variability of sediment transport itself, rather than changes in forcing Xt=Dt [Sadler and Strauss, 1990; Paola and Borgman, 1991; StðÞ¼ Yi; ð1Þ Pelletier and Turcotte, 1997; Jerolmack and Mohrig, i¼1 2005b; Jerolmack and Sadler, 2007; Kim and Jerolmack, 2008]. where Dt is the time between jumps. As equation (1) [5] Unequivocal demonstration of real changes in accu- implies, the focus of these stochastic models has been on the mulation rate through geologic time, such as the postulated nature of depositional and erosional periods that affect the late Cenozoic increase of Molnar [2004], requires that these location of the sediment surface S(t) in space. These have rates are measured over a constant interval of time t included exponentially distributed bed thickness [e.g., [Gardner et al., 1987]. This is rarely possible with real Dacey, 1979] and skewed distributions that produce biased data, however, where modern rates are measured over short random walks and lead to a negative dependence of Vobs on t time intervals while historical and geological rates are [Tipper, 1983]. measured over longer and longer intervals [Sadler, 1981, [7] Others have used the continuous scaling limit of the 1999]. For example, Hay et al. [1988] presented data on classical random