Why is soil erosion relatively less in dense forest as compared to barren fields?

In dense forests, there is dense vegetation. The roots of these trees grow deep into the soil and firmly bind to it and prevent the soil from being eroded by wind and water. The topsoil remains bound to the roots of trees. Soil erosion is relatively less in dense forests as compared to barren lands because there is scarcely any vegetation in arid areas (barren lands). Hence the soil gets washed away easily by heavy rainfall. There are no plants or trees to prevent the soil from being eroded.