Vamsi Ganti

Normal and anomalous diffusion of gravel tracer particles in rivers

Received 12 December 2008; revised 16 November 2009; accepted 10 December 2009; published 4 May 2010. [1] One way to study the mechanism of gravel bed load transport is to seed the bed with marked gravel tracer particles within a chosen patch and to follow the pattern of migration and dispersal of particles from this patch. In this study, we invoke the probabilistic Exner equation for sediment conservation of bed gravel, formulated in terms of the difference between the rate of entrainment of gravel into motion and the rate of deposition from motion. Assuming an active layer formulation, stochasticity in particle motion is introduced by considering the step length (distance traveled by a particle once entrained until it is deposited) as a random variable. For step lengths with a relatively thin (e.g., exponential) tail, the above formulation leads to the standard advection‐diffusion equation for tracer dispersal. However, the complexity of rivers, characterized by a broad distribution of particle sizes and extreme flood events, can give rise to a heavy‐tailed distribution of step lengths. This consideration leads to an anomalous advection‐diffusion equation involving fractional derivatives. By identifying the probabilistic Exner equation as a forward Kolmogorov equation for the location of a randomly selected tracer particle, a stochastic model describing the temporal evolution of the relative concentrations is developed. The normal and anomalous advection‐diffusion equations are revealed as its long‐time asymptotic solution. Sample numerical results illustrate the large differences that can arise in predicted tracer concentrations under the normal and anomalous diffusion models. They highlight the need for intensive data collection efforts to aid the selection of the appropriate model in real rivers.

Testing morphodynamic controls on the location and frequency of river avulsions on fans versus deltas: Huanghe (Yellow River), China

A mechanistic understanding of river avulsion location and frequency is needed to predict the growth of alluvial fans and deltas. The Huanghe, China, provides a rare opportunity to test emerging theories because its high sediment load produces regular avulsions at two distinct nodes. Where the river debouches from the Loess plateau, avulsions occur at an abrupt decrease in bed slope and reoccur at a time interval (607 yrs) consistent with a channel-filling timescale set by the superelevation height of the levees. Downstream, natural deltaic avulsions reoccur at a timescale that is fast (7 yrs) compared to channel-filling timescale due to large stage-height variability during floods. Unlike the upstream node, deltaic avulsions cluster at a location influenced by backwater hydrodynamics and show evidence for episodic downstream migration in concert with progradation of the shoreline, providing new expectations for the interplay between avulsion location, frequency, shoreline rugosity and delta morphology.

Small crater modification on Meridiani Planum and implications for erosion rates and climate change on Mars

A morphometric and morphologic catalog of ~100 small craters imaged by the Opportunity rover over the 33.5 km traverse between Eagle and Endeavour craters on Meridiani Planum shows craters in six stages of degradation that range from fresh and blocky to eroded and shallow depressions ringed by planed off rim blocks. The age of each morphologic class from <50–200 ka to ~20 Ma has been determined from the size-frequency distribution of craters in the catalog, the retention age of small craters on Meridiani Planum, and the age of the latest phase of ripple migration. The rate of degradation of the craters has been determined from crater depth, rim height, and ejecta removal over the class age. These rates show a rapid decrease from ~1 m/Myr for craters <1 Ma to ~ <0.1 m/Myr for craters 10–20 Ma, which can be explained by topographic diffusion with modeled diffusivities of ~10−6 m2/yr. In contrast to these relatively fast, short-term erosion rates, previously estimated average erosion rates on Mars over ~100 Myr and 3 Gyr timescales from the Amazonian and Hesperian are of order <0.01 m/Myr, which is 3–4 orders of magnitude slower than typical terrestrial rates. Erosion rates during the Middle-Late Noachian averaged over ~250 Myr, and ~700 Myr intervals are around 1 m/Myr, comparable to slow terrestrial erosion rates calculated over similar timescales. This argues for a wet climate before ~3 Ga in which liquid water was the erosional agent, followed by a dry environment dominated by slow eolian erosion.

Quantitative bounds on morphodynamics and implications for reading the sedimentary record

Sedimentary rocks are the archives of environmental conditions and ancient planetary surface processes that led to their formation. Reconstructions of Earths past surface behaviour from the physical sedimentary record remain controversial, however, in part because we lack a quantitative framework to deconvolve internal dynamics of sediment-transport systems from environmental signal preservation. Internal dynamics of landscapes--a consequence of the coupling between bed topography, sediment transport and flow dynamics (morphodynamics)--result in regular and quasiperiodic landforms that abound on the Earth and other planets. Here, using theory and a data compilation of morphodynamic landforms that span a wide range of terrestrial, marine and planetary depositional systems, we show that the advection length for settling sediment sets bounds on the scales over which internal landscape dynamics operate. These bounds provide a universal palaeohydraulic reconstruction tool on planetary surfaces and allow for quantitative identification of depositional systems that may preserve tectonic, climatic and anthropogenic signals.

Time scale bias in erosion rates of glaciated landscapes

Averaging time scale bias may produce an apparent acceleration of measured erosion rates in glaciated landscapes. Deciphering erosion rates over geologic time is fundamental for understanding the interplay between climate, tectonic, and erosional processes. Existing techniques integrate erosion over different time scales, and direct comparison of such rates is routinely done in earth science. On the basis of a global compilation, we show that erosion rate estimates in glaciated landscapes may be affected by a systematic averaging bias that produces higher estimated erosion rates toward the present, which do not reflect straightforward changes in erosion rates through time. This trend can result from a heavy-tailed distribution of erosional hiatuses (that is, time periods where no or relatively slow erosion occurs). We argue that such a distribution can result from the intermittency of erosional processes in glaciated landscapes that are tightly coupled to climate variability from decadal to millennial time scales. In contrast, we find no evidence for a time scale bias in spatially averaged erosion rates of landscapes dominated by river incision. We discuss the implications of our findings in the context of the proposed coupling between climate and tectonics, and interpreting erosion rate estimates with different averaging time scales through geologic time.

Experimental river delta size set by multiple floods and backwater hydrodynamics

Experimental delta lobe size is controlled by bed adjustment to transient floods within the backwater zone. River deltas worldwide are currently under threat of drowning and destruction by sea-level rise, subsidence, and oceanic storms, highlighting the need to quantify their growth processes. Deltas are built through construction of sediment lobes, and emerging theories suggest that the size of delta lobes scales with backwater hydrodynamics, but these ideas are difficult to test on natural deltas that evolve slowly. We show results of the first laboratory delta built through successive deposition of lobes that maintain a constant size. We show that the characteristic size of delta lobes emerges because of a preferential avulsion node—the location where the river course periodically and abruptly shifts—that remains fixed spatially relative to the prograding shoreline. The preferential avulsion node in our experiments is a consequence of multiple river floods and Froude-subcritical flows that produce persistent nonuniform flows and a peak in net channel deposition within the backwater zone of the coastal river. In contrast, experimental deltas without multiple floods produce flows with uniform velocities and delta lobes that lack a characteristic size. Results have broad applications to sustainable management of deltas and for decoding their stratigraphic record on Earth and Mars.

Slope, grain size, and roughness controls on dry sediment transport and storage on steep hillslopes

Existing hillslope sediment transport models developed for low-relief, soil-mantled landscapes are poorly suited to explain the coupling between steep rocky hillslopes and headwater channels. Here we address this knowledge gap using a series of field and numerical experiments to inform a particle-based model of sediment transport by dry ravel—a mechanism of granular transport characteristic of steep hillslopes. We find that particle travel distance increases as a function of the ratio of particle diameter to fine-scale ( 1 m) topographic variability associated with rocky landscapes. Applying a 2-D dry-ravel-routing model to lidar-derived surface topography, we show how spatial patterns of local and nonlocal transport control connectivity between hillslopes and steep headwater channels that generate debris flows through failure of ravel-filled channels following wildfire. Our results corroborate field observations of a patchy transition from soil-mantled to bedrock landscapes and suggest that there is a dynamic interplay between sediment storage, roughness, grain sorting, and transport even on hillslopes that well exceed the angle of repose.

Avulsion cycles and their stratigraphic signature on an experimental backwater-controlled delta

River deltas grow in large part through repeated cycles of lobe construction and channel avulsion. Understanding avulsion cycles is important for coastal restoration and ecology, land management, and flood hazard mitigation. Emerging theories suggest that river avulsions on lowland deltas are controlled by backwater hydrodynamics; however, our knowledge of backwater-controlled avulsion cycles is limited. Here we present results from an experimental delta that evolved under persistent backwater hydrodynamics achieved through variable flood discharges, shallow bed slopes, and subcritical flows. The experimental avulsion cycles consisted of an initial phase of avulsion setup, an avulsion trigger, selection of a new flow path, and abandonment of the parent channel. Avulsions were triggered during the largest floods (78% of avulsions) after the channel was filled by a fraction (0.3 ± 0.13) of its characteristic flow depth at the avulsion site, which occurred in the upstream part of the backwater zone. The new flow path following avulsion was consistently one of the shortest paths to the shoreline, and channel abandonment occurred through temporal decline in water flow and sediment delivery to the parent channel. Experimental synthetic stratigraphy indicates that bed thicknesses were maximum at the avulsion sites, consistent with our morphologic measurements of avulsion setup and the idea that there is a record of avulsion locations and thresholds in sedimentary rocks. Finally, we discuss the implications of our findings within the context of sustainable management of deltas, their stratigraphic record, and predicting avulsions on deltas.

Erosional surfaces in the Upper Cretaceous Castlegate Sandstone (Utah, USA): Sequence boundaries or autogenic scour from backwater hydrodynamics?

Sequence stratigraphy relies on the identification of unconformity-bound sedimentary packages in order to understand variations in sediment supply, subsidence, and eustasy, which are themselves controlled by external (allogenic) drivers such as climate and tectonics. However, intrinsic (autogenic) river dynamics can also create a rich stratigraphic architecture in the absence of allogenic changes. Here, we outline scaling relationships for the expected depth and length scales of autogenic scour resulting from non-uniform flows in coastal rivers, and apply these relationships to the Upper Cretaceous Castlegate Sandstone—a classic fluvial sandstone unit in the Book Cliffs of Utah (USA). Theoretical and experimental work suggests that hydrodynamics within the backwater reach of coastal rivers—the zone of non-uniform flow that extends upstream of the river mouth—causes spatially extensive erosion during floods; this in turn creates erosional surfaces within fluvio-deltaic stratigraphy that may appear similar to sequence boundaries. Results demonstrate that scour patterns within the Castlegate Sandstone are consistent with the predictions of backwater-induced scours, and show how allogenic versus autogenic erosional surfaces can be parsed within fluvio-deltaic stratigraphy. INTRODUCTION Sequence stratigraphy is based on the identification of genetically related rock sequences contained between major erosional unconformities referred to as “sequence boundaries” (e.g., Van Wagoner et al., 1987; Catuneanu and Zecchin, 2013; Ainsworth et al., 2017). Sequence boundaries are often interpreted as signals of relative sea-level fall, which results in incision and the formation of significant erosional surfaces (Fig. 1A). Variations in sediment supply, subsidence, and eustasy can contribute to the development of a sequence boundary; these are thought to be controlled primarily by allogenic forces—climate and tectonics (Schlager, 1993). However, recent studies have demonstrated that autogenic dynamics in fluvio-deltaic systems can mask or overprint allogenic signals (Best and Ashworth, 1997; Jerolmack and Paola, 2010; Ganti et al., 2014b; Mikeš et al., 2015; Li et al., 2016), and there is growing recognition of the role that autogenic processes (e.g., delta-lobe switching, auto-retreat) may play in determining stratigraphic architecture (e.g., Strong and Paola, 2008; Catuneanu and Zecchin, 2013; Hampson, 2016). This presents a significant challenge for fluvial sequence stratigraphy: the erosional unconformities that define sequences might be generated by allogenic and/ or autogenic processes. It is therefore critical to understand the conditions under which allogenic and autogenic signals overlap in order to untangle them in the rock record. Non-uniform flows affect sediment transport and erosional patterns in coastal rivers. The backwater reach of a river is the distal zone of nonuniform flow due to the boundary condition of near constant water surface elevation at the river mouth (Lane, 1957), which can extend hundreds of kilometers inland for large, low gradient rivers (Lamb et al., 2012). Recent field, experimental and theoretical work demonstrate that backwater hydrodynamics significantly affect sediment dispersal (Lamb et al., 2012; Nittrouer et al., 2012), river avulsion locations (Jerolmack and Swenson, 2007; Chatanantavet et al., 2012; Ganti et al., 2014a), and river lateral migration (Lamb et al., 2012; Fernandes et al., 2016); these ideas are beginning to be incorporated into conceptual models and interpretations of stratigraphic architecture (Blum et al., 2013; Colombera et al., 2016; Fernandes et al., 2016; Durkin et al., 2017). However, workers have yet to address the stratigraphic implications for the observation that coastal rivers may scour deeply within the backwater zone during large floods (Lamb et al., 2012; Chatanantavet and Lamb, 2014), potentially leaving widespread erosional surfaces. We hypothesized that autogenic scour resulting from river floods in backwater zones can produce an identifiable stratigraphic fingerprint and developed predictive relationships for the spatial scales of these autogenic scours. We evaluated this hypothesis through examination of Cretaceous fluvio-deltaic deposits of the Castlegate Sandstone in the Book Cliffs of Utah (USA)—a locality where modern concepts in fluvial sequence stratigraphy were developed (e.g., Van Wagoner, 1991, 1995). EROSIONAL SCOURS FROM BACKWATER HYDRODYNAMICS The backwater reach is characterized by nonuniform flows, where during low water discharge, the flow decelerates toward the river mouth leading to net deposition; and during large floods, the flow accelerates toward the river mouth leading to net erosion (Lane, 1957; Lamb et al., 2012; Nittrouer et al., 2012). The length of the backwater zone (Lb) scales with the characteristic bankfull flow depth (hc) and the river bed slope (S): Lb ~hc/S (e.g., Jerolmack and Swenson, GEOLOGY, August 2018; v. 46; no. 8; p. 707–710 | GSA Data Repository item 2018257 | https:// doi .org /10 .1130 /G40273 .1 | Published online XX Month 2018