Fast Multidimensional Ensemble Empirical Mode Decomposition Using a Data Compression Technique

Abstract

Abstract The process of obtaining key information on climate variability and change from large climate datasets often involves large computational costs and removal of noise from the data. In this study, the authors accelerate the computation of a newly developed, multidimensional temporal–spatial analysis method, namely multidimensional ensemble empirical mode decomposition (MEEMD), for climate studies. The original MEEMD uses ensemble empirical mode decomposition (EEMD) to decompose the time series at each grid point and then pieces together the temporal–spatial evolution of climate variability and change on naturally separated time scales, which is computationally expensive. To accelerate the algorithm, the original MEEMD is modified by 1) using principal component analysis (PCA) to transform the original temporal–spatial multidimensional climate data into principal components (PCs) and corresponding empirical orthogonal functions (EOFs); 2) retaining only a small fraction of PCs and EOFs that contain spatially and temporally coherent structures; 3) decomposing PCs into oscillatory components on naturally separated time scales; and 4) obtaining the original MEEMD components on naturally separated time scales by summing the contributions of the similar time scales from different pairs of EOFs and PCs. The study analyzes extended reconstructed sea surface temperature (ERSST) to validate the accelerated (fast) MEEMD. It is demonstrated that, for ERSST climate data, the fast MEEMD can 1) compress data with a compression rate of one to two orders and 2) increase the speed of the original MEEMD algorithm by one to two orders.