Interim: The Cascade Failure Group

Project Idea
We plan to model erosion on a given piece of land per day. The model includes many factors, such as the area considered, the number of trees, the amount of rain it receives, the typical wind speed, and deforestation. If we have time, we will also model the economic costs this erosion in farms, lakes, rivers, and dams.

Model and Variables
Erosion is caused by many factors such as ice, wind, and rain. For our current model, we are only considering rain erosion, the main type of erosion, in a forested environment. The erosion is related to the energy of a given raindrop and the type of soil that it hits. The energy of a raindrop is related to its radius and its shape (which is fairly constant). The raindrop’s terminal velocity also factors into its energy, but if shape is constant, then its mass determines terminal velocity. Because a raindrop is mostly water, its density is constant, thus its mass depends on its radius. Therefore, the only variable affecting energy per raindrop is the radius of the raindrop. The total energy of the rainstorm includes raindrop radius, average rain rainfall time per day, and the average wind speed.
The next factor to consider is the area of the land that the rain hits. More area leads to more potential erosion. Because tree roots protect soil from being eroded, the number of trees in the given area, and the ratio of its crown size to the area its roots hold through. Our model also measures daily deforestation.

Simplifications of the Model:
• We are currently measuring soil displacement from rain, not true erosion.
• We are currently considering only a flat area.
• We assume wind is parallel to the ground.
• We over-count displacement because a given amount of soil can be “displaced” multiple times.
• Our model counts snow, ice, etc. as rain.
• The model only includes one type of tree and one type of soil.

Problems
One of our biggest problems is the lack of data. We had to mix data from many sources to create the right information, creating the risk of compounding estimation errors from different sources. Also, many current models measure yearly erosion, while ours measure daily erosion, allowing us to actually consider the reasons behind certain numbers, but causes complications. Lastly, the official data use different units, causing us to constantly have to convert units.

Team Members:

Sam Kester
Mi Deng

Sponsoring Teacher: Gregory Marez

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