Empirical mode decomposition using rational splines: an application to rainfall time series

Abstract

Empirical mode decomposition ( EMD), a relatively new form of time-series decomposition, has the feature of not assuming that a time series is linear or stationary, as is implicitly done in Fourier analysis. In natural time series such as records of rainfall, streamflow, temperature, etc., where most variables exhibit nonlinear and nonstationary behaviour, this feature is particularly useful, allowing more meaningful quantification of the proportion of variance in a time series due to fluctuations at different time scales, than previous spectral analysis techniques. However, in its original form, the EMD algorithm relies on cubic spline interpolation of the extrema, which often inflate the variance of the resultant components (intrinsic mode functions) and residual. In this paper, a suggested improvement to the EMD algorithm, using rational splines and flexible treatment of the end conditions, is outlined and the consequent effect on three exemplary annual rainfall time series is assessed as a proof of concept. It is recognized that many more examples are needed for the fine tuning of the ideas before it can be widely recommended and this work is currently underway.

Empirical Mode Decomposition on the sphere: application to the spatial scales of surface temperature variations

“…Fourier analysis concentrates on orthogonal "East-West" and "North-South" directions (e.g. Press et al, 1992). Wavelet analysis can, in general, consider any direction of the wavelet relative to the data, however a typical 2-D Wavelet analysis examines only horizontal, vertical and diagonal orthonormal wavelet basis functions (Daubechies, 1992, pp.…”

“…One of the difficulties associated with 1-D EMD is the treatment of the ends of the bounding functions, requiring some (non-objective) decisions to be made in order to proceed Pegram et al, 2008). In the application of 2-D EMD in radar fields, the edges of the wet areas are well defined, so the ending problem is solved, since the envelopes of the extrema at any stage of the decomposition process are set implicitly to zero.…”

“…For example, Empirical Orthogonal Functions (EOFs) and their derivatives have been widely used in climatology/meteorology (e.g. Preisendorfer, 1988). They seek to maximise the variance in time, associated with a set of hierarchical EOF (spatial patterns) to Principal Components (time-series) that describe the variations in sign and amplitude of these patterns, but as such EOFs potentially mix different scales of variations in both in time and space.…”

Signal analysis of electrostatic gas-solid two-phase flow probe with Hilbert-Huang transform

“…The EMD of a one-dimensional dataset z(k) given on a sequence of points {k} is obtained using the following procedure [6]. c i before each iteration) until this is achieved.…”

Assessing the performance of rational spline-based empirical mode decomposition using a global annual precipitation dataset

“…Recently, in this journal, Pegram et al (2008), expanding on Peel et al (2007), proposed a modification to the EMD algorithm, whereby rational splines replaced cubic splines in the extrema envelope-fitting procedure. The rational spline modification was designed to reduce the variance inflation frequently observed in cubic spline-based EMD components, primarily due to spline overshooting, by introducing a spline tension parameter.…”