Why is soil erosion relatively less in dense forests as compared to barren, open fields?

Very large numbers of trees are grown in the dense forest. The trees have large number of leaves covering the ground. Even very less amount sunlight reaches to the ground. The leaves covering prevents rain water from directly falling on the ground. Besides roots of the trees bind the soil particles and hold them together. As a result soil erosion is minimised.

But in barren, open fields the soil is directly exposed to the falling rain. The soil particles become loose with the effects of the rain water. The water that carries away the soil causes erosion. Further the flowing water erodes the soil surface increases the amount of soil erosion.