Stochastic processes of soil production and transport: Erosion rates, topographic variation and cosmogenic nuclides in the Oregon Coast Range
ARJUN M. HEIMSATH1
*, WILLIAM E. DIETRICH2
, KUNIHIKO NISHIIZUMI3 AND ROBERT C. FINKEL4
1Department of Earth Sciences, 6105 Fairchild Hall, Dartmouth College, Hanover, NH 03755-3571, USA
2 Department of Geology and Geophysics, University of California, Berkeley, CA 94720, USA
3 Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
4 Center for Accelerator Mass Spectrometry, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
* Correspondence to: A. M. Heimsath, Department of Earth Sciences, 6105 Fairchild Hall, Dartmouth College, Hanover, NH 03755-3571, USA. E-mail: arjun.heimsath@dartmouth.edu
Contract/grant sponsor: NSF; contract/grant number: EAR-9527006.
Contract/grant sponsor: Cal Space; contract/grant number: IGPP-LLNL G596-05.
Earth Surf. Process. Landforms 26, 531–552 (2001)
ABSTRACT
Landscapes in areas of active uplift and erosion can only remain soil-mantled if the local production of soil equals or exceeds the local erosion rate. The soil production rate varies with soil depth, hence local variation in soil depth may provide clues about spatial variation in erosion rates. If uplift and the consequent erosion rates are sufficiently uniform in space and time, then there will be tendency toward equilibrium landforms shaped by the erosional processes. Soil mantle thickness would adjust such that soil production matched the erosion. Previous work in the Oregon Coast Range suggested that there may be a tendency locally toward equilibrium between hillslope erosion and sediment yield. Here results from a new methodology based oncosmogenic radionuclide accumulation in bedrock minerals at the base of the soil column are reported. We quantify how soil production varies with soil thickness in the southern Oregon Coast Range and explore further the issue of landscape equilibrium. Apparent soil production is determined to be an inverse exponential function of soil depth, with a maximum inferred production rate of 268 m Ma 1 occurring under zero soil depth. This rate depends, however, on the degree of weathering of the underlying bedrock. The stochastic and large-scale nature of soilproduction bybiogenic processesleads to large temporal and spatial variations in soil depth; the spatial variation of soil depth neither supports nor rejects equilibrium morphology. Our observed catchment-averaged erosion rate of 117 m Ma 1 is, however, similar to that estimated for the region by others, and to soil production rates under thin and intermediate soils typical for the steep ridges. We suggest that portions of the Oregon Coast Range may be eroding at roughly the same rate, but that local competition between drainage networks and episodic erosional events leads to landforms that are out of equilibrium locally and have a spatially varying soil mantle. Copyright 2001 John Wiley & Sons, Ltd.
KEY WORDS: erosion; soil production; landscape evolution; dynamic equilibrium; 10Be and 26Al
INTRODUCTION
Hilly and mountainous landscapes around the world are mantled with soil. In regions where external sources of sediment (e.g. aeolian and glacial deposition) are absent or negligible, the soil mantle is typically produced from the underlying bedrock. Gilbert (1877) first suggested that the rate of soil production from the underlying bedrock is a function of the depth of the soil mantle. We term this rate law the soil production function (Heimsath et al., 1997), defined as the relationship between soil depth and the rate of bedrock conversion to soil. The soil depth that sets the rate of soil production is a result of the balance between the soil production and erosion. If local soil depth is constant over time, the soil production rate equals the erosion rate, which equals the lowering rate of the land surface. Understanding the evolution rates of soil-mantled landscapes is furthered therefore by quantifying the soil production function (Anderson and Humphrey, 1989; Rosenbloom and Anderson, 1994; Dietrich et al., 1995; Heimsath et al., 1997). Heimsath et al. (1997, 1999, 2000) reported spatial variation of erosion rates, suggesting that the landscapes were out of the state of
Figure 1. (a) Site map showing the Coos Bay region as outlined by the rectangle on the state map of oregon. The shaded region labelled ‘Study Area’ is the field area shown in (b). (b) Shaded relief map of the field area in the Oregon Coast Range generated from laser altimetry elevation data. The two outlines represent a larger area of the landscape similar in morphology to the noses studies in the Headwall (HW) region and on the nose, Coos3, which are shown in detail for the area within the dashed lines in Figure 4a and b, respectively. The black triangle near the outlet of the HW catchment shows the location of the stream sediment samples, OR-16 and 17, from Sullivan Creek. The black diamond on the edge of the eastern subcatchment shows the location of OR-26, the only nuclide sample not in the HW study area. Adapted from Roering et al. (1999). (c) Oblique aerial photograph showing clear-cut slopes of the field area, looking due west such that the basin in the lower right corner corresponds to the second basin from the left edge of (b). Note the steep slopes, the ridge and valley topography, and the consistency of elevation on the main ridge crest dynamic equilibrium, as first conceptualized by Gilbert (1877, 1909) and then Hack (1960), where the landscape morphology is time-independent.
Figure 1. Continued
On actively eroding hilly landscapes, characterized by ridge and valley topography, the colluvial soil mantle is typically thin and is produced and transported by mechanical processes. Tree-throw, animal burrowing and similar processes, such as freeze–thaw and shrink–swell cycles, convert in-place bedrock to a mobile, often rocky, soil layer that is then transported downslope by the same actions (Lutz and Griswold, 1939; Lutz, 1960; Hole, 1981; Mitchell, 1988; Matsuoka, 1990; Schaetzl and Follmer, 1990; Norman et al., 1995; Paton et al., 1995). On steep slopes, shallow landsliding also transports material downslope, and may play a role in producing soil. While such processes are aided directly, and even accelerated, by chemical weathering of the bedrock, they are able to produce soil from bedrock irrespective of its weathered state. Previous quantification of the soil production function focused on low gradient topography developed on relatively homogenous bedrock, where the geomorphic processes could be characterized by simple rate laws (Heimsath et al., 1997, 1999, 2000).
In this paper we examine the steep, soil-mantled landscape of the Oregon Coast Range where we observed that stochastic processes of tree-throw and shallow landsliding may dominate soil production and transport. We apply the methods of Heimsath et al. (1999) to determine apparent soil production rates under such conditions, and specifically address the potential effects of these processes on our methods of using in situproduced cosmogenic nuclide concentrations as well as the landscape morphology to determine soil production rates. This paper also seeks to understand the competition between the spatial variation of processes and topography, which suggests large variations in local erosion rates, and the potential for dynamic equilibrium for the region, forwarded by Reneau and Dietrich (1991), who found hillslope erosion and sediment yield to be in an approximate balance over a range of spatial and temporal scales.
DISCUSSION
Soil production and transport processes at the Coos Bay field site are dominated by the mechanical disruption caused by burrowing animals and root penetration by Douglas fir trees. The stochastic nature of these largescale processes (compared to, for example, invertebrate soil production and root penetration by understorey vegetation) led to large variations in local soil thickness on the divergent noses. There were no observed relationships between curvature (as a proxy for soil production using a linear transport model) and soil depth as observed by Heimsath et al. (1997, 2000), or between erosion calculated from a non-linear transport model (e.g. Roering et al., 1999) and depth. Despite these variations in processes, however, there was a well-defined relationship between soil production rates from the radionuclide analyses and soil depth that we term here the apparent soil production function (Figure 5, Equation 15) because of the assumption of steady-state local soil depth used to determine the function. This discrepancy between the two methods highlights an interesting paradox that is not immediately resolvable.
The first implication of the stochastic conditions observed here on the cosmogenic nuclide method is that the soil depths observed in the field might not represent the long-term average soil under which the observed nuclide concentrations accumulated. The second implication is that the nuclide concentrations measured from the underlying bedrock might not represent the effect of the long-term average soil production rate at any given location. Both implications would suggest that results from the nuclide analyses would show considerably more scatter than observed here. Instead, if the observed depths do represent a local average depth, then the apparent relationship suggests that there is a strong tendency for soil production rates to decline with depth. The well-defined inverse exponential apparent soil production function is similar to the findings reported for northern California (Heimsath et al., 1997, 1999) and for southeastern Australia (Heimsath et al., 2000), from field areas without large-scale disturbances of the soil and soil–bedrock interface.
The only possibility of an artifactual relationship lies in the factor applied to correct the nuclide production rates for the slope and the shielding of the overlying soil thickness. If, for example, the central tendency for the weathered bedrock is to be eroding at some equilibrium rate (discussed below) irrespective of the overlying soil thickness, then nuclide concentrations measured in all samples would show some scatter around a mean value. Interpreting the nuclide concentrations using Equation 14 requires accounting for the shielding of the soil mantle and would lower the nuclide production rates for increasing soil depths. Lowering the nuclide production rates would lower the inferred soil production rates by Equation 14, thus potentially introducing an artifact due to the observed depth. An artifactual relationship would have a slope of about 0008 (=s/ , assuming an average moist soil density of 14 g cm 3 ), which is four times less steep than the slope of Equation 15, suggesting that the apparent soil production function reported here is not an artifact.
The potential effects of the non-steady-state erosion on the observed nuclide concentrations have been modelled numerically in several studies (Lal, 1991; Bierman and Steig, 1996; Small et al., 1997. Each of these models integrated their equivalent of Equation 12 under episodic (Lal, 1991; Small et al., 1997) and a step-function of (Bierman and Steig, 1996) erosion rates. While Lal (1991) modelled a very specific scenario where a rock erodes at a constant rate before and after a 50 cm thick ‘chip’ is removed instantaneously, Small et al. (1997) present a model applicable here. Their finite-difference model evaluates the potential error of determining erosion rates from nuclide concentrations that have accumulated under episodic erosion events that remove different amounts of rock at different time intervals. In all modelled cases they calculate the magnitude of error incurred by using the non-steady-state nuclide concentrations to infer steady-state erosion rates. By their modelled conditions the steady-state soil production rates that we report here would have between a 20 and 30 per cent error if the stochastic soil production processes remove 50 cm of bedrock at a time. The error would be larger (up to 200 per cent) if we sampled relatively recently after an episodic disturbance.
None of these models, however, accounted for the potential variation in a soil mantle shielding the sample. Heimsath and Barnes (unpublished data) have developed a similar numerical model that builds on the results of Bierman and Steig (1996) and Small et al. (1997) to add an analysis of the uncertainty caused by a variable soil mantle such as we faced here. Their results suggest that the episodically varying soil mantle could introduce an additional 10–20 per cent error into the inferred soil production rates, with the uncertainty increasing if a large event recently preceded the time of sampling. The conclusions reached, however, agree with both Bierman and Steig (1996) and Small et al. (1997), as well as with previous discussions by Lal (1991): the in situ-produced radionuclide method depends explicitly on the samples having a steady-state erosion history. Deviations from such a condition could lead to incorrect modelling of the exposure history and therefore incorrect interpretations of the radionuclide concentrations. In the absence of accurate knowledge of the exposure histories of samples, the best that can be done is to sample from locations that appear free from large-scale perturbations as we have done here. This remains an important point to make as further geomorphic applications are being tackled with radionuclide measurements.
While our observations and those of Schimdt (1999) show very clearly that stochastic and large-scale processes are occurring across the field area, we remain optimistic that our careful selection of nuclide sampling sites may have avoided the local effects of recent stochastic processes. Conversely, our sampling strategy for measuring soil depth for the morphometric analyses was to measure depths in a rough grid across the divergent parts of the landscape, seeking only to avoid any obvious disturbances on the landsurface, which therefore captured the uncorrelated variation of soil depth across the landscape. The scatter in our morphometric data is very similar to that observed by Schmidt (1999), although his estimates of colluvial production rates from morphometric analyses shows a weak inverse relationship.
Ahnert (1987) presents a compelling argument for how spatial variation of rock resistance to soil production can lead to variable soil depths on a one-dimensional landscape that tends toward equilibrium. His model posits a lower maximum soil production rate, 0 in Equation 5, for more resistant rock and evolves to a state where the exposed harder rock is lowering at the same rate as the soil-mantled, more easily erodible rock. Our nuclide results (Figure 5) suggest that such a scenario might help explain some of the depth variation, but the large variation in soil production rates for the more easily erodible rock suggests a more complicated interaction between hillslope processes and form. An important step toward resolving the paradox between morphometric observations and the apparent soil production function would be to quantify the role of bedrock strength and its resistance to mechanical weathering. Similarly, measurements to determine how the depth of the saprolite layer varies (e.g. Anderson, 1995), combined with correlating rock strength to soil production rates, would help link chemical weathering to soil production processes.
Many factors, from climate to tectonics, influence the evolution of a landscape. At a hillslope scale, the sediment production and transport processes directly influence the way a landscape changes. Most landscape evolution models simulate hillslope erosion as a steady-state process using a linear diffusion model, but Roering et al. (1999) present evidence that a non-linear transport model is appropriate for this field area. Morphometric analyses reported here cannot distinguish between the two models, but we specifically avoided the planar and steep slopes to remain out of the region where the non-linear model may predict sediment flux more closely than the linear model, as suggested by Roering et al. (1999). Irrespective of the transport law most applicable to the landscape – and it appears likely that a single transport law cannot adequately capture the processes (Heimsath et al., 2000; Braun, Heimsath and Chappell, 2001) – the evidence from Oregon is of a landscape shaped by the continuous interaction between stochastic hillslope processes and the driving forces of stream incision and tectonic uplift. Reneau and Dietrich (1991) suggest that this interaction approaches equilibrium tendencies at the landscape scale. Here, the apparent soil production function coupled with the observed variation in soil depth supports a state of local hillslope disequilibrium as discussed in Heimsath et al. (1997, 1999). The lack of morphometric relationships suggests, however, that the differences in soil production rates may act across the hillslope toward a uniformity of hillslope lowering rates over long time scales.
CONCLUSIONS
Here we report an apparent soil production function for a well-studied field site in the Oregon Coast Range. The well-defined exponential decline of soil production rates with increasing soil depths is similar to the functions reported elsewhere from field areas under very different climatic, tectonic and lithologic conditions in Marin County, California and southeastern Australia. This agreement suggests that there is a universal tendency for soil production rates to depend on the overlying soil thickness across hilly landscapes. As we have discussed before, and numerous recent models have applied, this relationship provides critical constraints for the processes of landscape evolution. The maximum soil production rate is, for example, the bound between transport-limited (soil-mantled) and weathering-limited (bedrock-dominated) landscapes and thus quantifies the maximum erosion rate under which a landscape can remain soil-mantled. This has important management implications in a landscape such as the Oregon Coast Range, where human land-use might be increasing erosion rates.
Morphometric analyses here did not yield the form of the soil production function, but provided evidence for the stochastic and large-scale nature of the soil production and transport processes. Field observations on the nature of soil production and removal show episodic processes of tree-throw, animal burrowing and shallow landsliding operating across the landscape. These processes lead to highly variable local soil depths over time and measurements of soil depth may only reflect an instantaneous snapshot of the soil depths across the landscape, rather than the long-term, steady-state soil thickness assumed for our nuclide interpretations. Stochastic processes also lead to highly variable erosion rates at the hillslope scale. Despite these variations, we conclude that the apparent soil production function reported here provides a valid and crucial quantification for the Oregon Coast Range landscape.
The study area is a small part of a landscape that is being shaped by a wide variety of processes. The catchment-averaged erosion rates determined by nuclide analyses here agree well with the rates determined by other methods across temporal and spatial scales for the Oregon Coast Range and suggest that there may be a tendency for uniformity of erosion at a large scale as suggested by Reneau and Dietrich (1991). Similarity in landscape form at the catchment scale supports this conclusion, while the highly variable hillslope processes highlight the local variation in erosion rates. While there may be some average erosion rate that applies to similar topography across the Oregon Coast Range, it is clear that local hillslopes are far from conditions of uniform lowering rates. The determination of an apparent soil production function for the region suggests that different parts of the landscape are lowering at rates that differ by over an order of magnitude depending on the thickness of the local soil mantle, and are therefore evolving in a highly dynamic manner
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