Does deforestation effect erosion

Deforestation frequently causes erosion. Tree roots hold the soil in place and impede the flow of water from a rainstorm. As a result, they make the water run much slower. Slower water carries far less dirt. That causes far less erosion. When the material making water move slower is removed, water speeds up. It caries more stuff away. Try an experiment. If you have a garden hose, turn it on. Point it at a tree trunk. See what happens. Then point it at some bare dirt. See what happens. Notice the difference between what happens when something is there to hold back the water and something is not there. Now picture the difference when tree roots hold the soil in place and when they are not there.

In South America, the Incas terraced the mountains so they would not wash away. In Nicaragua, the mountains have washed away. Deforestation without making any adjustment has caused mudslides with the mud covering the villages below killing the inhabitants.