# Illustrating Hillslope Diffusion with Physical and Numerical Models

## Summary

This is a lab exercise that is done over two lab sessions. Students are first introduced to the diffusion equation as a theory for hillslope evolution. They then test this numerical theory by collecting data on hillslope erosion and curvature from a sand hillslope that is subjected to artificial rainfall for several time periods. Once tested, they then construct a numerical model in Excel of hillslope diffusion using the equations originally developed, and then use this model to simulate the evolution of their sand hillslope. This problem illustrates how numerical theories are developed, how we might test this theory with an analog model, how numerical models are constructed, and the limitations of numerical modeling.

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## Learning Goals

1. develop the math for a diffusional process
2. make predictions from this equation about how a hillslope would evolve through time
3. develop a numerical theory (here, the diffusion equation applied to slopes)
4. test this numerical theory with data from an analog model
5. construct a numerical model of hillslope diffusion, and compare it to the analog model results

## Context for Use

This exercise is done in a 300 level course on Surface Processes. The course prerequisite is one introductory geology course, and there are ~15-25 students in the course. The activity is used during two three-hour lab sessions, with the first lab for the analog model (Slope Lab I) and the second for the numerical model (Slope Lab II). I assume that students (with some prodding) can remember both simple algebra and that a delta symbol implies change in a variable. From work in previous labs, students have a basic working knowledge of Excel for data entry and Kaleidagraph for graphing (entire lab could be done using Excel alone). The lab takes place after several lectures discussing hillslope processes, including a basic introduction to hillslope diffusion. But, the majority of the learning about hillslope diffusion is done as part of the lab.

## Description and Teaching Materials

Lab 1 Handout (Microsoft Word 33kB Jun29 05)
Lab 2 Handout (Microsoft Word 268kB Jun29 05)
Excel Spreadsheets (Excel 92kB Mar17 05)
range.avi ( 12.1MB Jul22 05)
range2.avi ( 50MB Jul22 05)

## Teaching Notes and Tips

Instructor notes for entire activity (Microsoft Word 24kB Jun29 05)
Instructor notes for Lab 1 lecture (Microsoft Word 860kB Jun29 05)
Photos of Activity in Action (Acrobat (PDF) 287kB Mar17 05)