Michael P. Lamb

Is the critical Shields stress for incipient sediment motion dependent on channel‐bed slope?

Data from laboratory flumes and natural streams show that the critical Shields stress for initial sediment motion increases with channel slope, which indicates that particles of the same size are more stable on steeper slopes. This observation is contrary to standard models that predict reduced stability with increasing slope due to the added downstream gravitational force. Processes that might explain this discrepancy are explored using a simple force-balance model, including increased drag from channel walls and bed morphology, variable friction angles, grain emergence, flow aeration, and changes to the local flow velocity and turbulent fluctuations. Surprisingly, increased drag due to changes in bed morphology does not appear to be the cause of the slope dependency because both the magnitude and trend of the critical Shields stress are similar for flume experiments and natural streams, and significant variations in bed morphology in flumes is unlikely. Instead, grain emergence and changes in local flow velocity and turbulent fluctuations seem to be responsible for the slope dependency due to the coincident increase in the ratio of bed-roughness scale to flow depth (i.e., relative roughness). A model for the local velocity within the grain-roughness layer is proposed based on a 1-D eddy viscosity with wake mixing. In addition, the magnitude of near-bed turbulent fluctuations is shown to depend on the depth-averaged flow velocity and the relative roughness. Extension of the model to mixed grain sizes indicates that the coarser fraction becomes increasingly difficult to transport on steeper slopes.

Deposition, exhumation, and paleoclimate of an ancient lake deposit, Gale crater, Mars

Ancient lake system at Gale crater Since 2012, the Curiosity rover has been diligently studying rocky outcrops on Mars, looking for clues about past water, climate, and habitability. Grotzinger et al. describe the analysis of a huge section of sedimentary rocks near Gale crater, where Mount Sharp now stands (see the Perspective by Chan). The features within these sediments are reminiscent of delta, stream, and lake deposits on Earth. Although individual lakes were probably transient, it is likely that there was enough water to fill in low-lying depressions such as impact craters for up to 10,000 years. Wind-driven erosion removed many of these deposits, creating Mount Sharp. Science, this issue p.10.1126/science.aac7575, see also p. 167 Mount Sharp now stands where there was once a large intercrater lake system. [Also see Perspective by Chan] INTRODUCTION Remote observational data suggest that large bodies of standing water existed on the surface of Mars in its early history. This would have required a much wetter climate than that of the present, implying greater availability of water on a global basis and enhanced potential for global habitability. However, based on assumptions of a vast water inventory and models of atmospheric erosion, theoretical studies suggest a climate that was wetter but not by enough to sustain large lakes, even in depressions such as impact craters. RATIONALE The Mars Science Laboratory mission’s rover, Curiosity, provides the capability to test hypotheses about Mars’s past climate. The focus of the mission is the exploration of a ~5-km-high mountain, Aeolis Mons (informally known as Mount Sharp), located near the center of the ~140-km-wide Gale impact crater. Mount Sharp is underlain by hundreds of meters of sedimentary rock strata deposited ~3.6 billion to 3.2 billion years ago. These sediments accumulated in aqueous environments, recording the history of Mars’s ancient climate. Because of Curiosity’s ability to study these strata where they are exposed near the base of Mount Sharp, we can directly test the hypothesis that large impact craters were capable of accumulating and storing water as lakes for substantial periods of time. RESULTS Over the course of 2 years, Curiosity studied dozens of outcrops distributed along a ~9-km transect that also rose ~75 m in elevation. Image data were used to measure the geometry and grain sizes of strata and to survey the textures associated with sediment deposition and diagenesis. Erosion of Gale’s northern crater wall and rim generated gravel and sand that were transported southward in shallow streams. Over time, these stream deposits advanced toward the crater interior, transitioning downstream into finer-grained (sand-sized), southward-advancing delta deposits. These deltas marked the boundary of an ancient lake where the finest (mud-sized) sediments accumulated, infilling both the crater and its internal lake basin. After infilling of the crater, the sedimentary deposits in Gale crater were exhumed, probably by wind-driven erosion, creating Mount Sharp. The ancient stream and lake deposits are erosional remnants of superimposed depositional sequences that once extended at least 75 m, and perhaps several hundreds of meters, above the current elevation of the crater floor. Although the modern landscape dips northward away from Mount Sharp, the ancient sedimentary deposits were laid down along a profile that projected southward beneath Mount Sharp and indicate that a basin once existed where today there is a mountain. CONCLUSION Our observations suggest that individual lakes were stable on the ancient surface of Mars for 100 to 10,000 years, a minimum duration when each lake was stable both thermally (as liquid water) and in terms of mass balance (with inputs effectively matching evaporation and loss of water to colder regions). We estimate that the stratigraphy traversed thus far by Curiosity would have required 10,000 to 10,000,000 years to accumulate, and even longer if overlying strata are included. Though individual lakes may have come and gone, they were probably linked in time through a common groundwater table. Over the long term, this water table must have risen at least tens of meters to enable accumulation of the delta and lake deposits observed by Curiosity in Gale crater. Inclined strata in the foreground dip southward toward Mount Sharp and represent ancient delta deposits. These deposits transition into strata in the mid-field that were deposited in ancient lakes. The buttes and mesas in the background contain younger deposits that overlie and postdate the lake deposits beneath Mount Sharp. The outcrop in the foreground is about 6 m wide, and the buttes and mesas in the background are hundreds of meters wide and tens of meters high. The image has been white-balanced. [Credit: NASA/Caltech/JPL/MSSS] The landforms of northern Gale crater on Mars expose thick sequences of sedimentary rocks. Based on images obtained by the Curiosity rover, we interpret these outcrops as evidence for past fluvial, deltaic, and lacustrine environments. Degradation of the crater wall and rim probably supplied these sediments, which advanced inward from the wall, infilling both the crater and an internal lake basin to a thickness of at least 75 meters. This intracrater lake system probably existed intermittently for thousands to millions of years, implying a relatively wet climate that supplied moisture to the crater rim and transported sediment via streams into the lake basin. The deposits in Gale crater were then exhumed, probably by wind-driven erosion, creating Aeolis Mons (Mount Sharp).

A model for fluvial bedrock incision by impacting suspended and bed load sediment

[1] A mechanistic model is derived for the rate of fluvial erosion into bedrock by abrasion from uniform size particles that impact the bed during transport in both bed and suspended load. The erosion rate is equated to the product of the impact rate, the mass loss per particle impact, and a bed coverage term. Unlike previous models that consider only bed load, the impact rate is not assumed to tend to zero as the shear velocity approaches the threshold for suspension. Instead, a given sediment supply is distributed between the bed and suspended load by using formulas for the bed load layer height, bed load velocity, logarithmic fluid velocity profile, and Rouse sediment concentration profile. It is proposed that the impact rate scales linearly with the product of the near-bed sediment concentration and the impact velocity and that particles impact the bed because of gravitational settling and advection by turbulent eddies. Results suggest, unlike models that consider only bed load, that the erosion rate increases with increasing transport stage (for a given relative sediment supply), even for transport stages that exceed the onset of suspension. In addition, erosion can occur if the supply of sediment exceeds the bed load transport capacity because a portion of the sediment load is transported in suspension. These results have implications for predicting erosion rates and channel morphology, especially in rivers with fine sediment, steep channel-bed slopes, and large flood events.

Can springs cut canyons into rock

Amphitheater-headed valleys on Earth and Mars are often assumed to result from erosion by emerging spring water (i.e., seepage erosion or groundwater sapping) rather than by surface runoff. The origin of such valleys has implications for landscape evolution on Earth and the hydrologic cycle and associated potential for life on other planets. In this paper we explore the evidence for seepage erosion in bedrock to address whether valley morphology can be used as a diagnostic indicator of seepage erosion. Seepage erosion is an important process in loose sediment where hydraulic forces cause grain detachment, often resulting in amphitheater-headed valleys. However, the extension of these processes to resistant rock is uncertain. In sedimentary rocks, groundwater might control the shape and rate of valley formation. It is possible, however, that seepage plays only a secondary role to runoff processes. This seems likely in basaltic valleys on Earth, where little evidence exists for seepage erosion. Since the ability of seepage to erode bedrock valleys remains unclear and because many amphitheater-headed valleys were probably carved by other processes, seepage erosion should not be inferred based solely on valley form.

Spatial and temporal trends for water-flow velocity and bed-material sediment transport in the lower Mississippi River

Where rivers near the coastline, the receiving basin begins to influence flow, and gradually varied, nonuniform flow conditions arise. The section of the river affected by nonuniform flow is typically referred to as the backwater segment, and for large lowland rivers, this portion of the river can extend many hundreds of kilometers above the outlet. River morphology and kinematics vary in the backwater segment; however, these channel properties have not been explicitly related to properties of the flow and sediment-transport fields. This study examines the influence of spatially and temporally varying flow velocity and sediment transport on channel properties for the lower 800 km of the Mississippi River, a section of the river that includes the backwater segment. Survey transects (n = 2650) were used to constrain the cross-sectional area of water flow every ∼312 m along the Mississippi River channel for eight successive intervals of water discharge. Assuming conservation of water discharge, the local flow velocity was calculated at each transect by dividing water discharge by the local measurement of cross-sectional flow area. Calculated flow velocity was converted to total bed stress using a dimensionless friction coefficient that was determined by optimizing the match between a predicted and a measured water-surface profile. Estimates for the skin-friction component of the total bed stress were produced from the values for total shear stress using a form-drag correction. These skin-friction bed-stress values were then used to model bed-material transport. Results demonstrate that in the lower Mississippi River, cross-sectional flow area increases downstream during low- and moderate-water discharge. This generates a decrease in calculated water-flow velocity and bed-material transport. During high-water discharge, the trend is reversed: Cross-sectional flow area decreases downstream, producing an increase in calculated water-flow velocity and bed-material transport. An important contribution of this work is the identification of a downstream reversal in the trend for channel cross-sectional area due to variable water discharge. By accounting for the spatial divergences in sediment transport predicted over an average annual hydrograph, we demonstrate the tendency for channel-bed aggradation in much of the backwater reach of the Mississippi River (150–600 km above the outlet); however, a region of channel-bed erosion is calculated for the final 150 km. These results help to explain the spatial variability of channel morphology and kinematics for the lower Mississippi River, and they can be extended to other lowland river systems near the coastline.

Formation of amphitheater-headed valleys by waterfall erosion after large-scale slumping on Hawai'i

Amphitheater-headed valleys are common on the surfaces of Earth and Mars. The abrupt terminations of these valleys at their headwalls have been used extensively to argue for valley erosion from springs (i.e., seepage erosion or groundwater sapping) rather than surface runoff. This interpretation has significant implications for Martian hydrology and the associated prospects for life. A connection between channel form and the erosion processes induced by groundwater, however, has not been demonstrated in resistant rock. Perhaps the most widely cited terrestrial analogs for Martian amphitheater-headed valleys in basalt are the spectacular canyons of Kohala, Hawai‘i. Here we present new field observations and topographic analyses of the amphitheater-headed Kohala valleys. We found no evidence for intensively weathered rocks or alcoves around springs at valley headwalls. Instead, valley-head erosion appears to be dominated by waterfall plunge pools. Stream flow from peak annual precipitation events exceeds spring discharge by more than an order of magnitude, and such flow is responsible for evacuation of the coarse sediment that lines the streams. Bathymetric surveys along the Kohala coast have revealed a large submarine landslide, the Polol Slump, directly offshore of the Kohala valleys. We propose that the headscarp of this massive landslide is expressed as the present-day 400 m Kohala sea cliffs. As dominant streams poured over this headscarp as waterfalls, vertical plunge pool erosion and undercutting caused upstream propagation of knickpoints, eventually producing amphitheater-headed valleys. Island subsidence rates and the ages of volcanic eruptions and submarine terraces indicate that the average rate of valley headwall advance is as high as 60 mm/yr. We propose a simple expression for upslope headwall propagation by vertical waterfall erosion based on abrasion by impacting sediment particles in plunge pools. This model indicates that head-wall propagation depends nonlinearly on the sediment flux passing over the waterfall and linearly on the ratio of kinetic versus potential energy of sediment impacts. After the Polol Slump, many streams did not form upslope-propagating waterfalls because they had smaller discharges due to a radial drainage pattern and fault-bounded drainage divides, which prevented runoff from the wetter summit of the volcano. A threshold for headwall propagation due to sediment supply or sediment-transport capacity is consistent with the model. Island subsidence following valley formation has resulted in alluviation of the valley floors, which has created the observed U-shaped valley cross sections. Our interpretation implies that surface runoff can carve amphitheater-headed valleys and that seepage erosion cannot be inferred based solely on valley form on Earth, Mars, or other planets.

Formation of Box Canyon, Idaho, by megaflood: implications for seepage erosion on Earth and Mars

Amphitheater-headed canyons have been used as diagnostic indicators of erosion by groundwater seepage, which has important implications for landscape evolution on Earth and astrobiology on Mars. Of perhaps any canyon studied, Box Canyon, Idaho, most strongly meets the proposed morphologic criteria for groundwater sapping because it is incised into a basaltic plain with no drainage network upstream, and approximately 10 cubic meters per second of seepage emanates from its vertical headwall. However, sediment transport constraints, 4He and 14C dates, plunge pools, and scoured rock indicate that a megaflood (greater than 220 cubic meters per second) carved the canyon about 45,000 years ago. These results add to a growing recognition of Quaternary catastrophic flooding in the American northwest, and may imply that similar features on Mars also formed by floods rather than seepage erosion.

Valley formation and methane precipitation rates on Titan

Branching valley networks near the landing site of the Huygens probe on Titan imply that fluid has eroded the surface. The fluid was most likely methane, which forms several percent of Titans atmosphere and can exist as a liquid at the surface. The morphology of the valley networks and the nature of Titans surface environment are inconsistent with a primary valley formation process involving thermal, chemical, or seepage erosion. The valleys were more likely eroded mechanically by surface runoff associated with methane precipitation. If mechanical erosion did occur, the flows must first have been able to mobilize any sediment accumulated in the valleys. We develop a model that links precipitation, open-channel flow, and sediment transport to calculate the minimum precipitation rate required to mobilize sediment and initiate erosion. Using data from two monitored watersheds in the Alps, we show that the model is able to predict precipitation rates in small drainage basins on Earth. The calculated precipitation rate is most sensitive to the sediment grain size. For a grain diameter of 1–10 cm, a range that brackets the median size observed at the Huygens landing site, the minimum precipitation rate required to mobilize sediment in the nearby branching networks is 0.5–15 mm hr^(−1). We show that this range is reasonable given the abundance of methane in Titans atmosphere. These minimum precipitation rates can be compared with observations of tropospheric cloud activity and estimates of long-term methane precipitation rates to further test the hypothesis that runoff eroded the valleys.

Backwater and river plume controls on scour upstream of river mouths: Implications for fluvio‐deltaic morphodynamics

Sediment flux from rivers to oceans is the fundamental driver of fluvio-deltaic morphodynamics and continental margin sedimentation, yet sediment transport across the river-to-marine boundary is poorly understood. Coastal rivers typically are affected by backwater, a zone of spatially decelerating flow that is transitional between normal flow upstream and the offshore river plume. Flow deceleration in the backwater zone, as well as spreading of the offshore plume, should render rivers highly depositional near their mouths, leading to sedimentation and eventual elimination of the backwater zone at steady state. This reasoning is counter to observations of riverbed scour, erosional bed forms, and long-lived backwater zones near the mouths of some coastal rivers (e.g., Mississippi River, United States). To explain these observations, we present a quasi-2-D model of a coupled fluvial backwater and offshore river plume system and apply it to the Mississippi River. Results show that during high-discharge events the normal-flow depth can become larger than the water depth at the river mouth resulting in drawdown of the water surface, spatial acceleration of flow, and erosion of the riverbed. As proposed by Lane (1957), the transition to drawdown and erosion is ultimately forced by spreading of the offshore river plume. This points to the need to model coupled river and river plume systems with a dynamic backwater zone under a suite of discharges to accurately capture fluvio-deltaic morphodynamics and connectivity between fluvial sediment sources and marine depositional sinks.

Backwater controls of avulsion location on deltas

River delta complexes are built in part through repeated river-channel avulsions, which often occur about a persistent spatial node creating delta lobes that form a fan-like morphology. Predicting the location of avulsions is poorly understood, but it is essential for wetland restoration, hazard mitigation, reservoir characterization, and delta morphodynamics. Following previous work, we show that the upstream distance from the river mouth where avulsions occur is coincident with the backwater length, i.e., the upstream extent of river flow that is affected by hydrodynamic processes in the receiving basin. To explain this observation we formulate a fluvial morphodynamic model that is coupled to an offshore spreading river plume and subject it to a range of river discharges. Results show that avulsion is less likely in the downstream portion of the backwater zone because, during high-flow events, the water surface is drawn down near the river mouth to match that of the offshore plume, resulting in river-bed scour and a reduced likelihood of overbank flow. Furthermore, during low-discharge events, flow deceleration near the upstream extent of backwater causes enhanced deposition locally and a reduced channel-fill timescale there. Both mechanisms favor preferential avulsion in the upstream part of the backwater zone. These dynamics are fundamentally due to variable river discharges and a coupled offshore river plume, with implications for predicting delta response to climate and sea level change, and fluvio-deltaic stratigraphy.