In this thesis, a formal mathematical definition will be established for the empirical mode decomposition (EMD). This definition is then used to establish a probabilistic framework for EMD. In the applications section, EMD will be applied to reconstructed global precipitation datasets for the period 1900-2008 to diagnose differences with climate model simulations. Also, precipitation gauge data will be analyzed using EMD to extract a high temporal resolution, nonlinear and nonstationary annual cycle (NAC). The NAC will be assessed as a candidate for an alternative climate normal and the concept of climate normal and anomaly will be explored in general.
