David Jon Furbish

The illusion of diffusion: Field evidence for depth-dependent sediment transport

Soil-covered upland landscapes are common in much of the habitable world, and our understanding of their evolution as a function of different climatic, tectonic, and geologic regimes is important across a wide range of disciplines. Erosion laws direct quantitative study of the processes shaping Earths surface and form the basis of landscape evolution modeling, but are based on limited field data. Here we use in situ-produced cosmogenic 1 0 Be and 2 6 Al concentrations from granitic saprolite to quantify an exponential decline in soil production with increasing soil thickness for a new field site in Point Reyes, California. Results are similar to soil production functions from two different, previously studied field sites, and are used with extensive measurements of soil thickness to quantify depth-integrated sediment transport flux. Plots of calculated sediment fluxes against the product of soil depth and hillslope gradient provide the first field-based evidence that soil transport is a nonlinear, depth-dependent function. Data from all sites suggest that the widely used linear diffusion equation is only appropriate for shallow gradient, convex-up regions, while the depth-dependent transport law is more broadly applicable. Quantifying both the mobile soil thickness and landscape morphology is therefore critical to understanding how landscapes evolve.

On the shape and widening of salt marsh creeks

We have developed a model that simulates aspects of initial channel formation in a youthful salt marsh environment. The model mimics the evolution of the cross section of a channel by coupling calculations of bottom shear stresses caused by tidal motions with erosion, taking into account the deposition of cohesive sediments. The simulations characterize flow in a reference cross section that includes an incipient channel zone and a marsh surface zone, with assigned water surface level and initial bottom elevation. This model mimics key characteristics of salt marshes where discharges due to tidal motion repeat in time with approximately the same magnitude and water surface level. Significant reductions in the tidal prism due to increasing bottom elevation above mean sea level, however, are not treated. Rather, the model is suitable for youthful salt marshes where relatively large water depths are maintained. Prolonged deposition reduces the area available for flow and thereby changes the shear stress distribution at the bottom, leading locally to erosion and alteration of the channel cross section. The simulations suggest that two mechanisms contribute to the longitudinal widening exhibited by salt marsh channels, which typically is disproportionately greater than that exhibited by river channels. The short duration of the maximum discharge (spring tide) and corresponding erosion rates, when compared with deposition rates, prevent the channel from reaching a deep, narrow equilibrium configuration. Furthermore, autoconsolidation of cohesive sediments, often occurring in salt marsh environments, leads to a downward increase in the resistance of the sediment to erosion. As scour occurs locally, the flow encounters more resistant sediment layers; so rather than deepening the channel over a narrow zone, flow and bottom stresses become more uniformly distributed leading to a wider channel than would otherwise occur in the absence of autoconsolidation. Based on flow and sediment properties estimated for the Venice Lagoon, Italy, simulations are consistent with observations of salt marsh creeks at this location.

Rain splash of dry sand revealed by high‐speed imaging and sticky paper splash targets

[1] Rain splash transport of sediment on a sloping surface arises from a downslope drift of grains displaced ballistically by raindrop impacts. We use high-speed imaging of drop impacts on dry sand to describe the drop-to-grain momentum transfer as this varies with drop size and grain size and to clarify ingredients of downslope grain drift. The ‘‘splash’’ of many grains involves ejection of surface grains accelerated by grain-to-grain collisions ahead of the radially spreading front of a drop as it deforms into a saucer shape during impact. For a given sand size, splash distances are similar for different drop sizes, but the number of displaced grains increases with drop size in proportion to the momentum of the drop not infiltrated within the first millisecond of impact. We present a theoretical formulation for grain ejection which assumes that the proportion of ejected grains within any small azimuthal angular interval dq about the center of impact is proportional to the momentum density of the spreading drop within dq and that the momentum of ejected grains at angle q is, on average, proportional to the momentum of the spreading drop at q. This formulation, consistent with observed splash distances, suggests that downslope grain transport involves an asymmetry in both quantity and distance: more grains move downslope than upslope with increasing surface slope, and, on average, grains move farther downslope. This latter effect is primarily due to the radial variation in the surface-parallel momentum of the spreading drop. Surface-parallel transport increases approximately linearly with slope.

Stability of creeping soil and implications for hillslope evolution

The geomorphic behavior of a soil-mantled hillslope undergoing diffusive creep involves a coupling between changes in land surface elevation, soil transport rates, soil production, and soil thickness. A linear stability analysis suggests that the coupled response of the soil mantle to small perturbations in soil thickness or surface topography is influenced by two factors. The diffusive-like behavior of soil creep has a stabilizing effect wherein perturbations in land surface elevation are damped. The relation between the soil production rate and soil thickness may be either stabilizing or destabilizing. A monotonically decreasing production rate with soil thickness reinforces the stabilizing effect of diffusive land surface smoothing. An increasing production rate with soil thickness has a destabilizing effect wherein perturbations in soil thickness or the soil-bedrock interface are amplified, despite the presence of diffusive land surface smoothing. This coupled behavior is insensitive to the transport relation, whether the soil flux is proportional to the land surface gradient or to the product of the soil thickness and land surface gradient. The latter type of relation, nonetheless, could lead to a more complex hillslope form than might otherwise be expected for purely diffusive transport. Moreover, the response to periodic (sinusoidal) variations in the rate of stream downcutting at the lower hillslope boundary involves upslope propagation of coupled (damped) waveforms in the land surface and the soil-bedrock interface. The distance of upslope propagation goes with the square root of the product of the transport diffusion-like coefficient and the period of the downcutting rate. The upper part of the hillslope is therefore insensitive to relatively high-frequency variations in stream downcutting, so together with a stable behavior of the coupled soil-mantle-bedrock system, this part of the hillslope may exhibit a tendency toward uniform lowering, while the lower part behaves transiently. Conversely, in the presence of low-frequency variations in stream downcutting, hillslope morphology and soil thickness variations are more likely to reflect unsteady conditions over the entirety of the hillslope.

Influences of coarse bank roughness on flow within a sharply curved river bend

Abstract An experiment was performed to assess the influence of coarse bank roughness on flow within a sharply curved bend of the Ocklawaha Creek, a sand-bedded stream in northern Florida. This involved obtaining systematic measurements of flow velocity and water-surface topography when the outer bank was rough with natural vegetation, and obtaining an identical set of measurements after removing the vegetation and constructing a smooth wall along the outer bank. Results suggest that the roughness from bank vegetation systematically influences the flow field, particularly the secondary current strength and the position of the high-velocity core, because of its effect on the transverse boundary layer. The roughness essentially produces a backwater effect that inhibits outwardly directed surface flow from closely approaching the outer bank. This suppresses super-elevation on the outside bank and, therefore, weakens the inwardly directed transverse pressure gradient and secondary current. The flow is steered in a downstream direction, and the core of high velocity is nearly centered in the channel. In absence of roughness from vegetation, outwardly directed surface flows approach the outer bank more directly (and earlier in the bend), superelevation on the outside bank is enhanced, and the transverse pressure gradient and secondary current are strengthened. The core of high velocity is displaced toward the outer bank, and its magnitude is increased. Moreover, the streamwise position where the high-velocity core is closest to the outer bank shifts downstream from its position of closest approach in the presence of roughness. This, in principle, should contribute to asymmetrical bend migration, whereas migration in presence of roughness should be nearly in phase with bend curvature such that bends grow in amplitude, albeit slower, and with less asymmetry.

Spatial autoregressive structure in meander evolution

The migration of a river bend depends in part on the high flow velocities that characteristically impinge on its outside bank. Recent models have treated this in terms of a spatial convolution, whereby local bend migration is mathematically a weighted aggregate of up-stream curvature and bed topography. The convolution model can be tested using river migration data after it is discretized and recast into a finite autoregressive form. Published isochrones marking former positions of bends on the Beatton River, Canada, support the hypothesis that rates of bend migration follow a convolutional relation. In addition, a comparison of the underlying flow model with published flume experiments involving constant-curvature bends illustrates how it predicts the near-bank depth-averaged velocity associated with a forced-bar topography in absence of free bars. The autoregressive form of the model is equivalent to a stochastic linear-difference equation; this allows bend curvature to be treated as a random process. Cast in the frequency domain, the convolution model predicts that big bends tend to grow at the expense of little bends and curvature irregularities in complex trains; there exists no tendency for preferential growth of an intermediate bend size. The model also predicts the well-known shift of maximum migration rates to positions down-stream of curvature apexes and implies that the magnitude of this shift increases with decreasing bend size. Predicted shifts compare well with published, measured shifts on the Nishnabotna River, Iowa. The sensitivity of the meandering process to initial bend geometries and entrance flow conditions ensures that diverse bend shapes arise along freely migrating rivers independently of factors such as unsteady flow and nonuniform erodibility. No single geometrical form serves as an asymptotic, evolutionary state for individual bends.

Estimating depth-averaged velocities in rough ­channels

Profiles of streamwise velocity obtained from North Boulder Creek, Colorado, typically are non-logarithmic in form and exhibit the strong influence of form drag associated with coarse bed roughness. The spatially averaged profile is consistent with recent theoretical profile forms suggested for rough channels that are based on a partitioning of the total stress between a fluid part and a part associated with form drag on bed particles. Estimates of local depth-averaged velocity using algorithms that are based on several measurements in the flow column improve with explicit Riemann averaging, versus simple averaging, of the measurements. Estimates based on a single-point measurement at 0·6 of the flow depth, assuming a logarithmic or approximately logarithmic velocity profile, are the least reliable. Copyright

Annual precipitation and river discharges in Florida in response to El Niño- and La Niña-sea surface temperature anomalies

Abstract Statistical analysis proves that El Nino and La Nina are responsible for up to 40% of annual precipitation variations and up to 30% of river discharge variations in Florida. The analysis is based on 44-year records of precipitation from more than 30 gauge stations and stream discharge from 20 gauge stations distributed all across Florida Peninsula. The cross-correlation coefficients for both the sea surface temperature (SST) and precipitation data series, the SST and river data series are calculated after the SST data series, precipitation and river data series are prewhitened by an autoregressive moving average (ARMA) model (0, 1). The cross-correlations between the SST anomalies and both the precipitation and river discharge are positively significant. The conclusion is that a higher annual precipitation amount (a ‘wet’ year) is expected from an El Nino year, and a lower precipitation amount (a ‘dry’ year) is expected from a La Nina year. Large amounts of fresh water recharge into the estuary in an El Nino year and less fresh water recharges into an estuary in a La Nina year. Also a higher groundwater table is expected in an El Nino year, and a lower ground-water table is expected in a La Nina year. Assuming that SST anomalies are the input signals for a time-series analysis, the impulse response weights of both precipitation and river discharge to SST signals can be calculated due to their positive correlations. The impulse response weights can be used to build the linear transfer functions of precipitation, river discharge and SST signals. The annual precipitation and stream discharge amount therefore can be predicted from the SST anomalies. This can provide some guidance for the water management policy and planning.

Using chemical tracers in hillslope soils to estimate the importance of chemical denudation under conditions of downslope sediment transport

[1] We present a model of hillslope soils that couples the evolution of topography, soil thickness, and the concentration of constituent soil phases, defined as unique components of the soil with collective mass equal to the total soil mass. The model includes both sediment transport and chemical denudation. A simplified two-phase model is developed; the two phases are a chemically immobile phase, which has far lower solubility than the bulk soil and is not removed through chemical weathering (for example, zircon grains), and a chemically mobile phase that may be removed from the system through chemical weathering. Chemical denudation rates in hillslope soils can be measured using the concentration of immobile elements, but the enrichment of these immobile elements is influenced by spatial variations in chemical denudation rates and spatial variations in the chemical composition of a soil’s parent material. These considerations cloud the use of elemental depletion factors and cosmogenic nuclide-based total denudation rates used to identify the relationship between physical erosion and chemical weathering if these techniques do not account for downslope sediment transport. On hillslopes where chemical denudation rates vary in space, estimates of chemical denudation using techniques that do not account for downslope sediment transport and spatial variations in chemical denudation rates may be adequate where the chemical denudation rate is a significant fraction of the total denudation rate but are inadequate in regions where chemical weathering rates are small compared to the total denudation rate. We also examine relationships between transient mechanical and chemical denudation rates. Soil particle residence times may affect chemical weathering rates, and the relationship between total landscape-lowering rates and soil particle residence times can thus be quantified.

The use of sulfur hexafluoride (SF6) as a tracer of septic tank effluent in the Florida Keys

To determine the fate and movement of sewage derived contaminants and their possible interaction with surface waters in the Florida (USA) Keys, two types of experiments were conducted using SF6 as an artificial tracer. The first type of experiment examined fluid flow from septic tanks placed in Miami Oolite on Big Pine Key, where there is a shallow freshwater lens overlying saline groundwaters. Here groundwater transport rates were constrained to be between 0.11 and 1.87 m/h, travelling in an easterly direction. The second type of experiment took place on Key Largo where there is no freshwater aquifer and the matrix of the aquifer is solely the more porous Key Largo limestone. Here we injected the tracer into a shallow well which was screened from 0.6 to 10 m. This allowed us to evaluate groundwater movement in the shallow upper portion of the aquifer, the area to which inputs by septic tanks occur. Groundwater transport rates in the Upper Keys were as great as 3.7 m/h and were controlled by the Atlantic tide. SF 6 laden groundwater plumes moved back and forth due to tidal pumping and reached nearby surface waters within 8 h. q 1999 Elsevier Science B.V. All rights reserved.