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

Abstract

Empirical mode decomposition (EMD), an adaptive data analysis methodology, has the attractive feature of robustness in the presence of nonlinear and non-stationary time series. Recently, in this journal, Pegram and co-authors Proc. R. Soc. A 464, 1483-1501, proposed a modification to the EMD algorithm whereby rational splines replaced cubic splines in the extrema envelope-fitting procedure. The modification was designed to reduce variance inflation, a feature frequently observed in cubic spline-based EMD components primarily due to spline overshooting, by introducing a spline tension parameter. Preliminary results there demonstrated the proof of concept that increasing the spline tension parameter reduces the variance of the resultant EMD components. Here, we assess the performance of rational spline-based EMD for a range of tension parameters and two end condition treatments, using a global dataset of 8135 annual precipitation time series. We found that traditional cubic spline-based EMD can produce decompositions that experience variance inflation and have orthogonality concerns. A tension parameter value of between 0 and 2 is found to be a good starting point for obtaining decomposition components that tend towards orthogonality, as measured by an orthogonality index (OI ) metric. Increasing the tension parameter generally results in: (i) a decrease in the range of the OI, which is offset by slight increases in (ii) the median value of OI, (iii) the number of intrinsic mode function components, (iv) the average number of sifts per component, and (v) the degree of amplitude smoothing in the components. The two end conditions tested had little influence on the results, with the reflective case being slightly better than the natural spline case as indicated by the OI. The ability to vary the tension parameter to find an orthogonal set of components, without changing any sifting parameters, is a powerful feature of rational spline-based EMD, which we suggest is a significant improvement over cubic spline-based EMD.

Sea level rise around Korea: Analysis of tide gauge station data with the ensemble empirical mode decomposition method

“…It is also applicable to nonlinear and nonstationary processes, because it is based on the local characteristic timescale of the data. Since its development by Hunag (1998), it has been used to analyze and model various geophysical data such as sea level, precipitation, radiation and runoff (e.g., Duffy, 2004;Peel et al, 2009;Kuo et al, 2013;Di et al, 2014). For example, Kuo et al (2013) used the ensemble EMD (EEMD Q1 ), a successor of EMD, to derived regional intensity-duration-frequency (IDF) curve for Edmonton, Canada based on the scaling property of precipitation, and Di et al (2014) used the EEMD in combination with artificial neural network models to develop a hydrological forecasting model of precipitation and runoff.…”

Stochastic simulation of nonstationary oscillation hydroclimatic processes using empirical mode decomposition

“…Motivated by the requirements of purely oscillatory functions, the EMD method was developed by Huang et al [1998]. The HSA and EMD have been applied in the field of hydroclimatology during the last few years [ Xie et al , 2002; Chiew et al , 2005; Huang and Wu , 2008; McMahon et al , 2008; Pegram et al , 2008; Peel et al , 2009; Lee and Ouarda , 2010, 2011]. Barnes [2007] showed that the instantaneous frequency has the disadvantage of not being robust in the presence of noise and fluctuations.…”

Prediction of climate nonstationary oscillation processes with empirical mode decomposition

“…The value of 0.2 is employed in the current study. Pegram et al [2008] and Peel et al [2009] advocated employing rational splines instead of cubic splines to improve the end effects and to decrease the number of siftings. In the current study, rational splines are not used mainly because their use requires additional adjusting procedures which are time consuming and need some additional work.…”

“…The advantage of the rational spline method is that it allows for an interplay between spline tension and IMF characteristics, whereas the original cubic method provides a single output [ Pegram et al , 2008]. Peel et al [2009] carried out additional work to assess the performance of rational spline‐based EMD for a global annual precipitation data set. Future research efforts on the use of EMD in the prediction of nonstationary hydroclimatological oscillation processes should integrate the use of rational splines.…”