How does deforestation affect the water cycle?

Answer 1

The water cycle is movement of water through various forms and holding locations. The majority of the processes that move water are physical, but trees are a biotic (living) component of the water cycle. Trees contribute to the transition of water from an earth-bound liquid to a gas in the atmosphere by the process of transpiration. Transpiration is the evaporation of water from leaves. If trees are cut down, then they no longer promote evaporation, so water is less likely to evaporate. Water can't fall from the sky as precipitation unless it first evaporates, so deforestation will reduce rainfall. Deforestation will also increase temperature, because evaporation requires input of energy. No transpiration means that energy sits around on earth as heat.

Answer 2

To make it short and sweet:

Trees suck up water from the ground and release water vapor from their leaves into the atmosphere contributing to cloud formation. The clouds get more dense, it rains, then it starts over. Without trees, the water just erodes the earth beneath it, causing runoff, topsoil nutrient depletion, etc. and not as much water vapor can be contributed to cloud formation.