Real and Apparent Changes in Sediment Deposition Rates Through Time

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 tγ−1, over multiple orders of magnitude, where 0 \u3c γ ≤ 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

The Stratigraphic Filter and Bias in Measurement of Geologic Rates

Erosion and deposition rates estimated from the stratigraphic record frequently exhibit a power-law dependence on measurement interval. This dependence can result from a power-law distribution of stratigraphic hiatuses. By representing the stratigraphic filter as a stochastic process called a reverse ascending ladder, we describe a likely origin of power-law hiatuses, and thus, rate scaling. While power-law hiatuses in certain environments can be a direct result of power-law periods of stasis (no deposition or erosion), they are more generally the result of randomness in surface fluctuations irrespective of mean subsidence or uplift. Autocorrelation in fluctuations can make hiatuses more or less heavy-tailed, but still exhibit power-law characteristics. In addition we show that by passing stratigraphic data backward through the filter, certain statistics of surface kinematics from their formative environments can be inferred

The Physical Basis for Anomalous Diffusion in Bed Load Transport

Recent studies have observed deviation from normal (Fickian) diffusion in sediment tracer dispersion that violates the assumption of statistical convergence to a Gaussian. Nikora et al. (2002) hypothesized that particle motion at short time scales is superdiffusive because of inertia, while long-time subdiffusion results from heavy-tailed rest durations between particle motions. Here we test this hypothesis with laboratory experiments that trace the motion of individual gravels under near-threshold intermittent bed load transport (0.027 \u3c τ* \u3c 0.087). Particle behavior consists of two independent states: a mobile phase, in which indeed we find superdiffusive behavior, and an immobile phase, in which gravels distrained from the fluid remain stationary for long durations. Correlated grain motion can account for some but not all of the superdiffusive behavior for the mobile phase; invoking heterogeneity of grain size provides a plausible explanation for the rest. Grains that become immobile appear to stay at rest until the bed scours down to an elevation that exposes them to the flow. The return time distribution for bed scour is similar to the distribution of rest durations, and both have power law tails. Results provide a physical basis for scaling regimes of anomalous dispersion and the time scales that separate these regimes

Fractal Patterns in Riverbed Morphology Produce Fractal Scaling of Water Storage Times

River topography is famously fractal, and the fractality of the sediment bed surface can produce scaling in solute residence time distributions. Empirical evidence showing the relationship between fractal bed topography and scaling of hyporheic travel times is still lacking. We performed experiments to make high-resolution observations of streambed topography and solute transport over naturally formed sand bedforms in a large laboratory flume. We analyzed the results using both numerical and theoretical models. We found that fractal properties of the bed topography do indeed affect solute residence time distributions. Overall, our experimental, numerical, and theoretical results provide evidence for a coupling between the sand-bed topography and the anomalous transport scaling in rivers. Larger bedforms induced greater hyporheic exchange and faster pore water turnover relative to smaller bedforms, suggesting that the structure of legacy morphology may be more important to solute and contaminant transport in streams and rivers than previously recognized

A 50,000-year record of lake-level variations and overflow from Owens Lake, eastern California, USA

A continuous lake-level curve was constructed for Owens Lake, eastern California by integrating lake-core data and shoreline geomorphology with new wind-wave and sediment entrainment modeling of lake-core sedimentology. This effort enabled refinement of the overflow history and development of a better understanding of the effects of regional and global climate variability on lake levels of the paleo-Owens River system during the last 50,000 years. The elevations of stratigraphic sites, plus lake bottom and spillway positions were corrected for vertical tectonic deformation using a differential fault-block model to estimate the absolute hydrologic change of the watershed-lake system. New results include 14C dating of mollusk shells in shoreline deposits, plus post-IR-IRSL dating of a suite of five beach ridges and OSL dating of spillway alluvial and deltaic deposits in deep boreholes. Geotechnical data show the overflow area is an entrenched channel that had erodible sills composed of unconsolidated fluvial-deltaic and alluvial sediment at elevations of ∼1113–1165 m above mean sea level. Owens Lake spilled most of the time at or near minimum sill levels, controlled by a bedrock sill at ∼1113 m. Nine major transgressions at ∼40.0, 38.7, 23.3, 19.3, 15.6, 13.8, 12.8, 11.6, and 10.6 ka reached levels ∼10–45 m above the bedrock sill. Several major regressions at or below the bedrock sill from 36.9 to 28.5 ka, and at ∼17.8, 12.9, and 10.4–8.8 ka indicate little to no overflow during these times. The latest period of overflow occurred ∼10–20 m above the bedrock sill from ∼8.4 to 6.4 ka that was followed by closed basin conditions after ∼6.4 ka. Previous lake core age-depth models were revised by accounting for sediment compaction and using no reservoir correction for open basin conditions, thereby reducing discrepancies between Owens Lake shoreline and lake-core proxy records. The integrated analysis provides a continuous 50 ka lake-level record of hydroclimate variability along the south-central Sierra Nevada that is consistent with other shoreline and speleothem records in the southwestern U.S

Sediment residence time distributions: theory and application from bed elevation measurements

[1] Travel distance and residence time probability distributions are the key components of stochastic models for coarse sediment transport. Residence time for individual grains is difficult to measure, and residence time distributions appropriate to field and laboratory settings are typically inferred theoretically or from overall transport characteristics. However, bed elevation time series collected using sonar transducers and lidar can be translated into empirical residence time distributions at each elevation in the bed and for the entire bed thickness. Sediment residence time at a given depth can be conceptualized as a stochastic return time process on a finite interval. Overall sediment residence time is an average of residence times at all depths weighted by the likelihood of deposition at each depth. Theory and experiment show that when tracers are seeded on the bed surface, power law residence time will be observed until a timescale set by the bed thickness and bed fluctuation statistics. After this time, the long-time (global) residence time distribution will take exponential form. Crossover time is the time of transition from power law to exponential behavior. The crossover time in flume studies can be on the order of seconds to minutes, while that in rivers can be days to years

Multiscaling Fractional Advection-Dispersion Equations and Their Solutions

rocesses; 3250 Mathematical Geophysics: Fractals and multifractals; 5104 Physical Properties of Rocks: Fracture and flow; 5139 Physical Properties of Rocks: Transport properties; KEYWORDS: fractional, dispersion, fractal, fracture, anomalous, transport Citation: Schumer, R., D. A. Benson, M. M. Meerschaert, and B. Baeumer, Multiscaling fractional advection-dispersion equations and their solutions, Water Resour. Res., 39(1), 1022, doi:10.1029/2001WR001229, 2003. 1. Introduction [2] Hundreds of studies have proposed modeling techniques to address the super-Fickian transport of solutes in aquifers. Among them are fractional advection-dispersion equations (ADEs), analytical equations that employ fractional derivatives in describing the growth and scaling of diffusion-like plume spreading. Fractional ADEs are the limiting equations governing continuous time random walks (CTRW) with arbitrary particle jump length distribution and finite mean waiting time distribution [Compte, 1996]. T

Displacement characteristics of coarse fluvial bed sediment

[1] Previous work highlights the need for data collection to identify appropriate models for temporal evolution of tracer dispersal in rivers. Results of 64 gravel-bed field tracer experiments covering a wide range of flow and sediment supply regimes are compiled here to determine the probabilistic character of gravel transport. We focus on whether particle travel distances and waits are thin- or heavy-tailed. While heavy-tailed travel distance distributions are observed between successive monitoring events in different hydrological and sediment supply regimes, heavy-tailedness does not persist through total travel distance over multiple monitoring events, suggesting that individual monitoring events occur before particle travel distance exceeds the characteristic correlation length for the channel (such that particles that start in fast paths remain in fast paths and particles in slow paths remain in slow paths). After a large number of transport events, super-diffusive spreading was not observed at any of the gravel bed streams. Continuous-time tracking of x, y, z coordinates of tracers in natural streams is necessary to capture exact step and waiting time distributions