Do forests affect local rainfall and climate significantly?
For rain to fall, water vapour must exist in sufficient quantities in the atmosphere. The main source of atmospheric water vapour is evaporation from oceans. However, evaporation from large bodies of water such as lakes and dams also contributes. Another significant contributor, on a local level, is transpiration from forests.


  the Amazon alone creates 50-80 percent of its own rainfall through transpiration


Removing forests has 


  the biggest impact on cross-continental transport of water vapour


Removal of trees from an area of forest immediately stops transpiration in the that area. This causes less rain to fall in that area. It changes the way light is reflected from the Earth's surface, which changes the heating characteristics of the ground, which changes air movements. It will also have an influence on ground water levels and depending on local geology can bring salt to the surface causing salt scars and eventually desertification.