J. D. Stock

Geologic constraints on bedrock river incision using the stream power law

Denudation rate in unextended terranes is limited by the rate of bedrock channel incision, often modeled as work rate on the channel bed by water and sediment, or stream power. The latter can be generalized as KA m S n , where K represents the channel beds resistance to lowenng (whose variation with lithology is unknown), A is drainage area (a surrogate for discharge), S is local slope, and m and n are exponents whose values are debated. We address these uncertainties by simulating the lowering of ancient river profiles using the finite difference method. We vary m, n, and K to match the evolved profile as closely as possible to the corresponding modern river profile over a time period constrained by the age of the mapped paleoprofiles. We find at least two end-member incision laws, KA 0.3-0.5 S for Australian rivers with stable base levels and K f A 0.1-0.2 S n for rivers in Kauai subject to abrupt base level change. The long-term lowering rate on the latter expression is a function of the frequency and magnitude of knickpoint erosion, characterized by K f Incision patterns from Japan and California could follow either expression. If they follow the first expression with m = 0.4, K varies from 10 -7 -10 -6 m 0.2 /yr for granite and metamorphic rocks to 10 -5 -10 -4 m 0.2 /yr for volcaniclastic rocks and 10 -4 -10 -2 m 0.2 /yr for mudstones. This potentially large variation in K with lithology could drive strong variability in the rate of long-term landscape change, including denudation rate and sediment yield.

Geomorphic Transport Laws for Predicting Landscape form and Dynamics

A geomorphic transport law is a mathematical statement derived from a physical principle or mechanism, which expresses the mass flux or erosion caused by one or more processes in a manner that: 1) can be parameterized from field measurements, 2) can be tested in physical models, and 3) can be applied over geomorphically significant spatial and temporal scales. Such laws are a compromise between physics-based theory that requires extensive information about materials and their interactions, which may be hard to quantify across real landscapes, and rules-based approaches, which cannot be tested directly but only can be used in models to see if the model outcomes match some expected or observed state. We propose that landscape evolution modeling can be broadly categorized into detailed, apparent, statistical and essential realism models and it is the latter, concerned with explaining mechanistically the essential morphodynamic features of a landscape, in which geomorphic transport laws are most effectively applied. A limited number of studies have provided verification and parameterization of geomorphic transport laws for: linear slope-dependent transport, non-linear transport due to dilational disturbance of soil, soil production from bedrock, and river incision into bedrock. Field parameterized geomorphic transport laws, however, are lacking for many processes including landslides, debris flows, surface wash, and glacial scour. We propose the use of high- resolution topography, as initial conditions, in landscape evolution models and explore the applicability of locally parameterized geomorphic transport laws in explaining hillslope morphology in the Oregon Coast Range. This modeling reveals unexpected morphodynamics, suggesting that the use of real landscapes with geomorphic transport laws may provide new insights about the linkages between process and form.

Erosion of steepland valleys by debris flows

Episodic debris flows scour the rock beds of many steepland valleys. Along recent debris-flow runout paths in the western United States, we have observed evidence for bedrock lowering, primarily by the impact of large particles entrained in debris flows. This evidence may persist to the point at which debris-flow deposition occurs, commonly at slopes of less than ∼0.03–0.10. We find that debris-flow–scoured valleys have a topographic signature that is fundamentally different from that predicted by bedrock river-incision models. Much of this difference results from the fact that local valley slope shows a tendency to decrease abruptly downstream of tributaries that contribute throughgoing debris flows. The degree of weathering of valley floor bedrock may also decrease abruptly downstream of such junctions. On the basis of these observations, we hypothesize that valley slope is adjusted to the long-term frequency of debris flows, and that valleys scoured by debris flows should not be modeled using conventional bedrock river-incision laws. We use field observations to justify one possible debris-flow incision model, whose lowering rate is proportional to the integral of solid inertial normal stresses from particle impacts along the flow and the number of upvalley debris-flow sources. The model predicts that increases in incision rate caused by increases in flow event frequency and length (as flows gain material) downvalley are balanced by rate reductions from reduced inertial normal stress at lower slopes, and stronger, less weathered bedrock. These adjustments lead to a spatially uniform lowering rate. Although the proposed expression leads to equilibrium long-profiles with the correct topographic signature, the crudeness with which the debris-flow dynamics are parameterized reveals that we are far from a validated debris-flow incision law. However, the vast extent of steepland valley networks above slopes of ∼0.03–0.10 illustrates the need to understand debris-flow incision if we hope to understand the evolution of steep topography around the world.

Field measurements of incision rates following bedrock exposure: Implications for process controls on the long profiles of valleys cut by rivers and debris flows

Until recently, published rates of incision of bedrock valleys came from indirect dating of incised surfaces. A small but growing literature based on direct measurement reports short-term bedrock lowering at geologically unsustainable rates. We report observations of bedrock lowering from erosion pins monitored over 1–7 yr in 10 valleys that cut indurated volcanic and sedimentary rocks in Washington, Oregon, California, and Taiwan. Most of these channels have historically been stripped of sediment. Their bedrock is exposed to bed-load abrasion, plucking, and seasonal wetting and drying that comminutes hard, intact rock into plates or equant fragments that are removed by higher fl ows. Consequent incision rates are proportional to the square of rock tensile strength, in agreement with experimental results of others. Measured rates up to centimeters per year far exceed regional long-term erosionrate estimates, even for apparently minor sediment-transport rates. Cultural artifacts on adjoining strath terraces in Washington and Taiwan indicate at least several decades of lowering at these extreme rates. Lacking sediment cover, lithologies at these sites lower at rates that far exceed long-term rock-uplift rates. This rate disparity makes it unlikely that the long profi les of these rivers are directly adjusted to either bedrock hardness or rock-uplift rate in the manner predicted by the stream power law, despite the observation that their profi les are well fi t by power-law plots of drainage area vs. slope. We hypothesize that the threshold of motion of a thin sediment mantle, rather than bedrock hardness or rock-uplift rate, controls channel slope in weak bedrock lithologies with tensile strengths below ~3–5 MPa. To illustrate this hypothesis and to provide an alternative interpretation for power-law plots of area vs. slope, we combine Shields’ threshold transport concept with measured hydraulic relationships and downstream fi ning rates. In contrast to fl uvial reaches, none of the hundreds of erosion pins we installed in steep valleys recently scoured to bedrock by debris fl ows indicate any postevent fl uvial lowering. These results are consistent with episodic debris fl ows as the primary agent of bedrock lowering in the steepest parts of the channel network above ~0.03–0.10 slope.

Covariation of climate and long-term erosion rates across a steep rainfall gradient on the Hawaiian island of Kaua‘i

Erosion of volcanic ocean islands creates dramatic landscapes, modulates Earth’s carbon cycle, and delivers sediment to coasts and reefs. Because many volcanic islands have large climate gradients and minimal variations in lithology and tectonic history, they are excellent natural laboratories for studying climatic effects on the evolution of topography. Despite concerns that modern sediment fl uxes to island coasts may exceed long-term fl uxes, little is known about how erosion rates and processes vary across island interiors, how erosion rates are infl uenced by the strong climate gradients on many islands, and how modern island erosion rates compare to long-term rates. Here, we present new measurements of erosion rates over 5 yr to 5 m.y. timescales on the Hawaiian island of Kaua‘i, across which mean annual precipitation ranges from 0.5 to 9.5 m/yr. Eroded rock volumes from basins across Kaua‘i indicate that million-year-scale erosion rates are correlated with modern mean annual precipitation and range from 8 to 335 t km –2 yr –1 . In

Controls on alluvial fan long-profiles

Water and debris flows exiting confined valleys have a tendency to deposit sediment on steep fans. On alluvial fans where water transport of gravel predominates, channel slopes tend to decrease downfan from ~0.10–0.04 to ~0.01 across wide ranges of climate and tectonism. Some have argued that this pattern reflects grain-size fining downfan such that higher threshold slopes are required just to entrain coarser particles in the waters of the upper fan, whereas lower slopes are required to entrain finer grains downfan (threshold hypothesis). An older hypothesis is that slope is adjusted to transport the supplied sediment load, which decreases downfan as deposition occurs (transport hypothesis). We have begun to test these hypotheses for alluvial fan long-profiles using detailed hydraulic and particle-size data in sediment transport models. On four alluvial fans in the western U.S., we find that channel hydraulic radiiare largely 0.5–0.9 m at fan heads, decreasing to 0.1–0.2 m at distal margins. We find that median gravel diameter does not change systematically along the upper 60%–80% of active fan channels as slope declines, so downstream gravel fining cannot explain most of the observed channel slope reduction. However, as slope declines, channel-bed sand cover increases systematically downfan from areal fractions of <20% above fan heads to distal fan values in excess of 70%. As a result, entrainment thresholds for bed material might decrease systematically downfan, leading to lower slopes. However, current models of this effect alone tend to underpredict downfan slope changes. This is likely due to off-channel gravel deposition. Calculations that match observed fan long-profiles require an exponential decline in gravel transport rate, so that on some fans approximately half of the load must be deposited off channel every ~0.20–1.4 km downfan. This leads us to hypothesize that some alluvial fan long-profiles are statements about the rate of overbank deposition of coarse particles downfan, a process for which there is currently no mechanistic theory.

Paleohydrology of arid southeastern maui, hawaiian islands, and its implications for prehistoric human settlement

Abstract Arid slopes on the southeastern side of Maui are densely covered with archaeological remains of Hawaiian settlement from the late prehistoric to early postcontact period (ca. A.D. 1500–1860). Permanent habitation sites, agricultural features, and religious structures indicate perennial occupation and farming in a subregion called Kahikinui, yet there is presently no year-round water source. We explore the possibility that postcontact deforestation led to the loss of either (1) perennial channel flow or (2) perennial springs or seeps. To investigate the first possibility, we estimated ancient peak flows on 11 ephemeral channels in Kahikinui using field measurements and paleohydrology. Peak-flow estimates (3–230 m3/s) for a given drainage area are smaller than those for current perennial Maui streams, but are equivalent to gauged peak flows from ephemeral and intermittent streams in the driest regions of Hawai’i and Maui islands. This is consistent with the long-term absence of perennial channel flow in Kahikinui. On the other hand, others have shown that canopy fog-drip in Hawai’i can be greater than rainfall and thus a large part of groundwater recharge. Using isolated live remnants and snags, we estimate the former extent of the forest upstream from archaeological sites. We use rough estimates of the loss of fog-drip recharge caused by deforestation and apply a simple, steady-state hydrologic model to calculate potential groundwater table fall. These order-of-magnitude estimates indicate that groundwater could have fallen by a minimum of several meters, abandoning perennial seeps. This is consistent with archaeological evidence for former perennial seeps, such as stonewalls enclosing potential seeps to protect them. Although longer-term reductions in rainfall cannot be ruled out as a factor, deforestation and loss of fog-drip recharge are obvious and more immediate reasons for a recent loss of perennial water in Kahikinui, Maui.

Vegetation influences on infiltration in Hawaiian soils: Infiltration in Hawaiian Soils

Ecohydrology. 2018;11:e1973. https://doi.org/10.1002/eco.1973 Abstract Changes in vegetation communities caused by removing trees, introducing grazing ungulates, and replacing native plants with invasive species have substantially altered soil infiltration processes and rates in Hawaii. These changes directly impact run‐off, erosion, plant‐available water, and aquifer recharge. We hypothesize that broad vegetation communities can be characterized by distributions of field‐saturated hydraulic conductivity (Kfs). We used 290 measurements of Kfs calculated from infiltration tests from 5 of the Hawaiian Islands to show this effect. We classified the data using 3 broad ecosystem categories: grasses, trees and shrubs, and bare soil. The soils of each site have coevolved with past and present ecological communities without significant mechanical disturbance by agriculture or urban development. Geometric mean values Kfs are 203 mm/hr for soils hosting trees and shrubs, 50 mm/hr for grasses, and 13 mm/hr for bare soil. Differences are statistically significant at the 95% confidence level. These examples show that it is feasible to make maps of relative Kfs based on field and ecosystem data. These ecosystem trends can be used to estimate ongoing changes to run‐off and recharge from climate and land use change. Greater Kfs for ecosystems with primarily trees and shrubs suggests that management decisions concerning reforestation or other changes of vegetation can have substantial hydrologic impacts.

Dust on a Hawaiian volcano: A regional model using field measurements to estimate transport and deposition: Quantifying Rates of Dust Transport and Deposition on Mauna Kea, HI

The western slopes of Hawaii’s Mauna Kea volcano are mantled by fine-grained soils, the record of volcanic airfall and eolian deposition. Where exposed, strong winds transport this sediment across West Hawaii, affecting tourism and local communities with decreased air and water quality. Operations on US Army’s Ke’amuku Maneuver Area (KMA) have the potential to increase dust flux from these deposits. The USGS established 18 ground monitoring sites and sampling locations surrounding KMA. For over 3 years, each station measured vertical and horizontal dust flux, while co-located anemometers measured wind speed and direction. We used these datasets to develop a parsimonious regional model for dust supply and transport to assess whether KMA is a net dust sink or source. We found that dust transport is most highly correlatedwith thresholdwind speeds of 8m/s.We used this value as the regional average threshold wind speed for dust entrainment. Using a model that partitions measured horizontal dust flux into inwardand outward-directed components, we estimate that KMA is currently a net dust sink. Geochemical analysis of dust samples illustrates that local organics and carbonate make up 64% of dust mass, the remainder being volcanic silt and fine sand. Measured vertical dust deposition rates of 0.006mm/yr are similar to 0.004mm/yr of deposition predicted from taking the divergence of dust across KMA’s boundary. These rates are low compared with pre-historic rates of ~0.2–0.3mm/yr, from radiocarbon dating of buried soils. KMA’s soils record persistent deposition over millennia, at rates that imply episodic dust storms. Such events created a soil-mantled landscape in the middle of a largely Pleistocene rocky landscape. A substantial portion of fine-grained soils in other leeward Hawaiian Island landscapes may have formed from similar eolian deposition, and not direct weathering of parent rock. Published 2018. This article is a U.S. Government work and is in the public domain in the USA.