GEOLOGY 445 - GLACIAL GEOLOGY

LAB 6 - EROSION OF TROUGHS AND CIRQUES

Introduction

Glacial troughs have often been described as "U- shaped", and have been defined in more detail as parabolic, catenary, and a number of other shapes. A powerful method by which to describe the cross half-profile of a glacial trough or the profile of a cirque backwall involves fitting to the equation:

Y = aX^b

where Y is the height above valley floor on the profile, X is the distance from the valley centerline or cirque threshold, a is the intercept, and b is the exponent. Taking the logarithm of both sides:

log Y = log a + b*log X.

Thus, if the values are plotted on log/log paper, b is indicated by the slope of the line. If the valley is "V-shaped" (fluvial), Y = aX¹ and the log/log graph has a slope of 1. If the value of b is greater than 1 the valley side is parabolic, with higher values indicating a steeper parabola. Graf (1970) calculated b-values between 1.67 and 1.83 for mature glacial valleys, as opposed to a hypothesized optimal value of 2.  Cirque backwalls, on the other hand, have b values between 2 and 3 (Graf, 1976).  I wonder why that is?

Problem

POSE a working hypothesis which can be tested by determining b-values.

EXAMPLES:

• "The form of a glacial valley which has been eroded into bedrock should differ significantly from that of one deposited in till." Or
• "The limit of Pleistocene glaciation in a mountain valley should be marked by a change in b from about 2 to about 1." Or
• "Values of b on the inside of a bend in a glacial valley should exceed those on the outside of the bend due to accelerated erosion." Or
• "All other factors held equal, higher cirques should have higher b values than lower cirques because they have been occupied longer during the Pleistocene." Or...

TEST your hypothesis by selecting a research area, finding maps at a scale of 1:63,360 or larger, and plotting enough valley or cirque profiles to calculate a mean and standard deviation or to establish a linear regression or otherwise statistically evaluate your results.  Statistically, 30 measurements is considered a "statistical universe" (no significant difference would be expected even if the sample size were much higher), and 15 is considered statistically stable.  Teams of two, with one person investigating either side of the hypothesis, would work well.

A logical way to test would be to plot your cirque backwall or trough wall profiles, measured as distance from and above the valley centerline, in Excel with both axes set to logarithmic scales. IF the scales are the same on both axes, the slope of the line of data points can be manually scaled off the monitor.

You can also transform your data by taking the log of each value, then perform a linear regression with distance independent and height dependent (using "Tools", "Data Analysis", "Regression")  to let the computer calculate the slope.  If you do so, remember that regression requires pairs of matched data points (no missing data) and to select your points carefully within the elevations of interest.  Remember the trimline in the Spanish Creek valley?  "b" would be close to 2 below the trimline, but close to 1 above it!

EXAMPLE:  See sampleb.xls for a data set, graphs, and regression analysis.

DISCUSS the method, assumptions, and results.

Assuming that you do all your work within Excel, please pass in:

• Your discussion (~ 1 page)
• A graph of your valley cross-profiles or cirque long profiles
• A file or disk (in spreadsheet format) containing your data in column form:
  • Distance from valley centerline (cirque threshold)
  • log(Distance)
  • Elevation
  • Height above valley floor
  • log(Height)

REFERENCES:

• Graf, W. L., 1970, The geomorphology of the glacial valley cross-section. Arctic and Alpine Research, v. 2, p. 303- 312.
• Graf, W. L., 1976, Cirques as glacier locations.  Arctic and Alpine Research, v. 8, p. 79-90.