Yes they are! Thermoclimatical and ombrothermic belts describes very well what can happen to woodlands in situatuions of precipitation decrease and raising temperature...
Rivas-Martínez S., Rivas-Sáenz S. & Penas A. 2011. Worldwide bioclimatic classification system. Global Geobotany 1: 1-634 + 4 Maps.