**SDSU**

presents a thesis defense for

Master of Science degree in**
**Applied Mathematics

**David New**

*Advances in the Empirical Mode Decomposition and Applications to Analysis of Precipitation Data*

Abstract

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, for when it is applied to random data. In the applications section, EMD will first be applied to reconstructed global precipitation datasets for the period 1900-2008 to diagnose differences with climate model simulations. Also, precipitation gauge data also 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.

Thesis Committee

Sam Shen, Thesis Chair, Department of Mathematics & Statistics

Barbara Bailey, Department of Mathematics & Statistics

Trent Biggs, Department of Geography