Disclaimer: This contains a 20-minute lecture (google slides) + interactive model (Javascript) that I developed for GRAD 8101 (Teaching in Higher Education) during the Spring semester of 2023 at the University of Minnesota. It incorporates active learning techniques the probe the students knowledge on diffusion, mathematical equations, and hillslope processes. The Javascript model is an example of the type of interative models that I want to create to promote active learning as well as model-based learning.

Hillslope Processes

Hillslope processes in landscape evolution models are simulated using a hillslope diffusion model. $$\frac{\partial \eta}{\partial t} = D\nabla^2\eta,$$ where $\eta$ is elevation, $t$ is time, and $D$ is a hillslope diffusion coefficient. It models soil movement via:

• rainsplash
• bioturbation
• freeze-thaw processes
• creep
• agricultural tillage

What is $\nabla^2\eta$? It is a symbol that represents the sum of second derivatives in the x and y direction, i.e., $\nabla^2\eta = \left(\frac{\partial^2\eta}{\partial x^2}\right) + \left(\frac{\partial^2\eta}{\partial y^2}\right)$. Remember from your calculus class that the 2nd derivative represents the slope of slope? We call $\nabla^2\eta$, topographic curvature.

Local Hillslope Diffusion Model

Radius = m

Low $\eta$ High $\eta$

Instructions:

1. Move the circle and click to drive hillslope diffusion on the landscape.
2. Use the slider above to change the size of the circle.