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Climate, Uplift, Erosional Processes and Landscape Form: Clues from Physical Experiments

Les Hasbargen
SUNY College at Oneonta

Location

UTM coordinates and datum: none

Setting

Climate Setting: none
Tectonic setting: none
Type: Process


Click the images for a full-sized view.

Figure 1A Examples of steady state landscapes for varying forcing from rainfall and uplift.


Figure 1B Examples of steady state landscapes for varying forcing from rainfall and uplift.


Figure 1C Examples of steady state landscapes for varying forcing from rainfall and uplift.


Figure 2 Topographic measures as a function of the water-to-rock ratio, r/u.


Description

Erosional processes and rates of uplift strongly influence the overall shape of eroding landscapes. Uplift of a mass above base level increases the potential energy of the land. Uplift steepens stream profiles, energizing the streams, which then cut into the land mass. Thus, over longer time periods in uplifting landscapes, we expect increases in local relief between streams and ridges, and steeper stream channels. The topography roughens, and average slope increases.

But imagine that for the same rate of uplift, the landscape experiences a much higher rainfall rate. In this second case, for a drainage basin of the same size (and assume for now the same drainage density), the runoff is much higher. Greater discharges would equate to greater erosive potential, which would erode the landscape faster. Thus, over longer times, as erosion balances uplift across the landscape, stream gradients might be lower, and the local relief between streams and ridges might be lower as well.

Now let's consider one more key player in landscape development - the resistance of rocks to erosion. Imagine a landscape that is eroding at the same rate that it is uplifting. For this case, we will maintain a fixed uplift rate and constant climate condition, change the geology of the landscape. As rock resistance increases to mechanical erosion, greater forces are required to erode the substrate. If the dominant erosional mechanism streams and surface runoff, the increased resistance requires an increase in shear stress (greater depth and/or an increased stream gradient).

The thought experiment above, outlined more elegantly by G. K. Gilbert in his work on land sculpting (Gilbert, 1877) is somewhat difficult to test in natural field conditions. The time required to erode through enough rock for steady state conditions to exist is quite large - typically on the order of 100,000s of years. The large range in rock types, temporal and spatial variations in climate, the huge range in biologic activity across a landscape in space and time - all of these influence erosional processes, which in turn sculpt the land. Such variability impedes field tests of Gilbert's hypothesis. However, if one is content to study simplified versions of tectonism, climate, and landforms, numerical and physical models provide exciting and useful tools to explore landscape development and behavior. A substantial literature exists on numerical models of landscape evolution, and the reader is referred to Tucker and Whipple (2002) for an overview.

Physical experiments provide an additional perspective for evolving landscapes. In the last 10 years, researchers have developed several steady state erosion facilities (Hasbargen and Paola, 2000; Lague et al. 2003; Hasbargen, 2003; Hasbargen and Paola, 2003; Ouchi, 2004; Bonnet and Crave, 2006). In all of these facilities, a homogeneous erodible substrate forms the geology of the landscape. Typical choices for substrate include silt-size silica flour, a mix of silt-sand-clay, and fly ash (silt and fine sand mixed with minor amounts of clay). A rainfall-generating apparatus provides the climate for the model. The apparatus permits control over droplet size and the intensity of rainfall. The key component that makes the erosion experiments analogous to Gilbert's thought experiment is the introduction of constant tectonic forcing. Uplift of a land surface is often heterogeneous in natural settings, with large changes in the rate of uplift both in space and in time. The simplest case for uplift is a situation where uplift is spatially uniform (everywhere the same) and constant through time - a block uplift, if you will. Thus, at steady state conditions for block uplift, when erosion everywhere balances uplift, we would have a uniformly eroding landscape, and the form of the landscape would be directly related to the combined effects of uplift, climate, geologic erodibility, and the erosional processes. Uniform lowering of base level represents a simple way of implementing block uplift experimentally. If we choose a measure that characterizes in a general way the shape of the land, such as average slope (S), or local relief (R), we can state a relationship between the measure and forcing based on Gilbert's reasoning as follows. Slope and relief are directly proportional to uplift (U) and rock resistance (K), and inversely proportional to discharge (Q), or S,R ~ UK/Q

In a series of experiments with rock resistance held constant (silt-size material), Hasbargen varied U and Q in a oval basin ~ 1 m in diameter. As a measure of forcing, he utilized what he called the water-to-rock-ratio, r/u, which he defined as:
r/u = (R * rhow)/(U * rhor)
where R is the rainfall rate (Length/Time),
U is uplift rate (Length/Time)
rhow is the water density (Mass/Volume),
rhor is the rock density (Mass/Volume).

Note, r/u is dimensionless, and is analogous to Q/U. He found that erosional processes varied with the r/u, namely, that as r/u increased, surface runoff dominated the erosional processes. As r/u decreased, mass movements (landslides and debris flows) became more active. This had an effect on the landform, and on landform measures such as slope, relief, and to a lesser extent drainage density. Examples of the landform for r/u = 1, 6, and 8 appear below (Figures 1a, 1b, and 1c respectively). Note that for r/u = 1, each portion of the landscape experiences 1 unit of rainfall for each unit of uplift, for r/u = 6 each portion of the landscape experiences 6 units of rain for each unit of uplift, etc. For time lapse video of these experimental runs, go to Hasbargen's steady state eroding landscape web site: http://employees.oneonta.edu/hasbarle/LesWebSite-2002/research.htm, and scroll down to the time lapse videos.

Digital elevation models of the experimental landscapes permitted a quantitative extraction of a measure of landscape form for the forcing conditions. Several features were measured. These include valley area (a measure of drainage density), expressed as the fractional area of the landscape occupied by a stream (a/A, where the unit area is 7 mm x 7 mm cell); the area-slope intercept in the contributing area-slope relationship (based on a regression through the data), which describes how stream gradient decreases as contributing area increases; local slope, calculated as the average steepest descent slope (where the unit area is 7 mm x 7 mm cell); regional slope, derived from a regression through elevation as a function of distance from the outlet of the experimental basin; and maximum relief, defined as the difference between the highest and lowest points in the basin. Plots of these measures against r/u show consistent support for Gilbert's hypotheses (see Figure 2 below). Note that Gilbert did not directly make any predictions concerning drainage density, and indeed, the experimental data imply a very weak relation, if any. What physical experiments have allowed us to do is watch landscapes evolve, and observe how forcing from climate and uplift influences erosion processes, which in turn determine landscape form.

Associated References:

  • Bonnet, S., and Crave, A. Macroscale dynamics of experimental landscapes,in Buiter, S.J.H and Schreurs, G., eds., Analogue and numerical modeling of Crustal-scale processes, Geological Society of London Special publication 253, p.327-339, 2006.
  • Gilbert, G.K., Geology of the Henry Mountains: U.S. geographical and geological survey of the Rocky Mountain region: U.S. Government Printing Office, Washington, D.C., 160 p., 1877.
  • Hasbargen, L. E., and C. Paola, Landscape instability in an experimental drainage basin, Geology, 28, 1067-1070, 2000.
  • Hasbargen, Leslie E., and Chris Paola, How predictable is local erosion rate in eroding drainage basins? in Prediction in Geomorphology, eds. P. Wilcock and R. Iverson, AGU Geophysical Monograph 135, 2003.
  • Hasbargen, Leslie E., Erosion in Steady State Drainage Basins, unpublished doctoral dissertation, University of Minnesota - Twin Cities, 2003.
  • Lague, Dimitri, Alain Crave, and Philippe Davy, Laboratory experiments simulating the geomorphic response to tectonic uplift, Journal of Geophysical Research, vol. 108, NO. B1, 2003, doi:10.1029/2002JB001785, 2003.
  • Martin, Yvonne and Michael Church, Numerical modelling of landscape evolution: geomorphological perspectives, Progress in Physical Geography 2004; 28; 317, DOI: 10.1191/0309133304pp412ra.
  • Ouchi, Shunji, 2004, Effects of uplift rate on the development of experimental erosion landform, Geological Society of America Abstracts with Programs, Vol. 36, No. 5, p. 171.
  • Tucker, G.E., and Whipple, K.X., Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison, Journal of Geophysical Research, v. 107, no. B9, 2179, doi:10.1029/2001JB000162, 2002.

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