The humped soil production function

Introduction

When you walk across your favorite hill do you ever think about what you're walking on? Ever wonder what's beneath your feet and why it's there? If you've wondered about the soil that you're walking on, do you wonder what forces control whether you're walking on soil or not? Well, it turns out that understanding the processes that produce and move the soil around on hills is very important. Balances between soil production and erosion determine whether soil exists on a landscape, as well as how thick it might be. Soil presence and thickness, in turn, helps support much of the life that we are familiar with, play important roles in the hydrologic cycle, and are coupled with processes that impact the atmosphere. This vignette focuses on a soil-mantled, upland landscape in northern Australia to present soil production and transport rates for a landscape shaped by forces that cause it to be different from other landscapes used for similar studies.

Specifically, we present data to support a 'humped' soil production function, where the peak soil production rate occurs under a thin soil mantle (see Heimsath et al. (2009) for full article). Since G.K. Gilbert's first suggestion that soil production from weathered rock should depend on the depth of the soil above there is much debate on both the theory and the field evidence for soil production (Heimsath et al., 1997). Studies by Small et al. (1999) and Wilkinson et al. (2005) show data suggestive of a peak rate beneath some soil depth, but both papers report roughly uniform soil production rates with only the suggestion of a 'humped' function as discussed extensively in a different paper (Wilkinson and Humphreys, 2005). Small et al. focus on an alpine summit flat where the gently sloping landscape is punctuated by tors (free standing bedrock outcrops) and mantled with nearly constant veneer of scree (fractured rock). Their data are used to support a 'humped' function through a modeling study by Anderson (2002). Wilkinson et al. (2005) focus on the dramatic landscape of the Australian Blue Mountains, where rocky ridges have bands of exposed bedrock and towers. They compared their data with the Oregon Coast Range data of Heimsath et al. (2001b), and the southeastern Australia data (Heimsath et al., 2001a), and suggested a 'humped' function is an appropriate interpretation of the data.

Conceptual Framework and Field Area

The conceptual framework that we adopt here is used widely to understand soil production, landscape evolution, as well as to model the dynamic responses of the land surface to changes in climate and tectonic forces. Specifically, we are interested in the vertical lowering rate of the land surface. For a bedrock surface, this rate is simply the erosion rate of the rock surface. For a soil-mantled landscape, this is the rate of conversion of the underlying weathered bedrock to mobile soil: the soil production rate. Soil production rates have long been hypothesized and only recently documented to decline exponentially with increasing soil thickness in a relationship termed the soil production function (Heimsath et al., 1997). Field verification of this function helps quantify recent landscape evolution models, and the local steady state soil thickness assumption (soil thickness is roughly constant with time at any given place on a hillslope) was verified at one of the field areas initially explored in southeastern Australia (Heimsath et al., 2000).

This vignette is from a field site on Tin Camp Creek in northern Australia (Fig. 1). We collected bedrock, and river sediment samples for cosmogenic ¹⁰Be and ²⁶Al analyses to determine how erosion rates vary across a landscape used to understand erosional processes in the context of the uranium mining industry interests in the region. To get at the soil production rates we focused on the hillslopes (Fig. 2), where soils depths were either zero, or greater than about 30-40 cm (Fig. 3). Bedrock exposed on the hills showed significantly less weathering than the rock covered with soil. Vegetation is an open and very dry forest with seasonal grassland spread throughout the region. Rainfall of about 1400 mm/yr comes between October and April, with short, high-intensity storms that are normal for the tropical environments of northern Australia.

The 'Humped' Soil Production Function

Seven samples of weathered bedrock below different local soil depths show an exponential decline of soil production rates with increasing soil thickness (black filled circles, Fig. 3). Using these samples alone results in a soil production function that is remarkably similar to the function of Heimsath et al. from southeastern Australia: namely that SPR = 47e^-0.02*H, where SPR is the soil production rate (m/Ma) and H is the overlying soil depth (cm). When the erosion rates of exposed bedrock (shown by the cross-filled squares) are accounted for, averaging about 8 m/Ma, then the shape of the soil production function can be defined as being "humped." These data therefore support a long-hypothesized soil production function.

One of the questions that we ponder in our article about this study is why this particular landscape seems to be governed by a 'humped' soil production function, while the other landscapes where we have similar data seem to be governed by an exponential function. Turns out that we don't know exactly why, but there are a few options that may be narrowed with further study. The simplest explanation, initially supported by what we saw in the field, is the exposed rock is less chemically weathered than the rock below soil. To confirm this suggestion we need a detailed study of chemical weathering, which might show similarities between this landscape and the Oregon Coast Range and Blue Mountain studies.

A more complicated explanation highlights an interesting aspect of the humped soil production function. Namely, that because the peak rate is from weathered rock beneath about 35 cm of soil, the function suggests that a landscape is either going to be exposed bedrock or soil-covered with depths greater than 35 cm. Our observations do support this suggestion, but raise highlight an important problem about a landscape seemingly governed by a humped function: if exposed bedrock is eroding slowly, then it should stand out as tors above the surrounding landscape that is eroding more rapidly. Instead, we observed exposed rock flush with the ground surface. Further investigations of the details of how soil depth varies and the processes of soil erosion should help clear up this problem and better resolve the form of the soil production function.

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