Climate has an important role on desertification processes through its impacts on dryland soils and vegetation, on dryland hydrology, and on human land use. Research on precipitation dynamics is of major importance to understand desertification processes, especially at local scales. A large part of this book is dedicated to a literature review on the interactions of climate and desertification processes, on issues related to the homogenisation of climate data, on the analysis of extreme precipitation indices, and on the spatial interpolation of rainfall fields. This book provides a qualitative classification of 107 daily rainfall series, and an assessment of spatiotemporal patterns in extreme precipitation indices in the south of Portugal where large areas have high susceptibility to desertification. Trends and other temporal patterns in the precipitation indices are analysed, and geostatistical simulation methods are used to produce space-time scenarios. This book opens perspectives for new approaches on the analysis of extreme climate events, particularly in the context of impact studies, and should be especially useful to climatologists, hydrologists and environmental engineers.