My research focuses on the subject of time series analysis and its application to environmental data sets, particularly those relating to natural hazards. Specifically, my research involves methods of time series analysis that are applicable to non-stationary and nonlinear data.  Such methods have advantages over classical time series analysis methods, such as Fourier or wavelet analysis, due to their more adaptable nature and their ability to provide more physically meaningful results.

The primary method I am examining in my research is the Empirical Mode Decomposition (EMD) (Huang et al. 1998). Essentially the EMD method relies on interpolation of extreme points in the time series to successively filter the data into various intrinsic mode functions (IMFs). Each IMF represents a sub-signal that can be analysed in relation to environmental drivers, which may act over varying time scales.

Although  EMD  has  been  applied  in  various  areas  of  environmental  science,  and  has produced some promising results, there are a number of known technical issues that can affect the performance of EMD. These include effects due to problems with interpolation near the boundaries,  mode mixing due to the presence of noise and determination of stoppage criteria. Less well understood are the sensitivities of the method to things like changes in the method of interpolation employed within the EMD procedure and its suitability to data possessing different types of non-stationarity. In my research I address this knowledge gap by systematically investigating the performance of the EMD procedure employing different  interpolation methods, and by investigating the effects of different types of data non-stationarity, namely time dependent trend, time dependent variance, or a combination of the two.

This research will provide important information on the limitations of the EMD procedure, and thus on the limits to which it can be used to infer temporal trends in environmental data. In particular, my research will focus on application of the EMD method to sea-level, temperature and fire danger rating time series. My research findings will provide enhanced information on the key climatic drivers of these variables, and the uncertainty associated with them, and will thus have implications for the management of natural hazards into the future.

References:

Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C. and Liu, H.H., 1998, March. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 454, No. 1971, pp. 903-995). The Royal Society.