10. Discussion 987 11. Conclusions 991 References 993A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the 'empirical mode decomposition' method with which any complicated data set can be decomposed into a finite and often small number of 'intrinsic mode functions' that admit well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. With the Hilbert transform, the 'instrinic mode functions' yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert spectrum.In this method, the main conceptual innovations are the introduction of 'intrinsic mode functions' based on local properties of the signal, which makes the instantaneous frequency meaningful; and the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need for spurious harmonics to represent nonlinear and non-stationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. Classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and non-stationary effects in the energy-frequency-time distribution.

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SUMMARYA new method, the Hilbert-Huang Transform (HHT), developed initially for natural and engineering sciences has now been applied to financial data. The HHT method is specially developed for analysing nonlinear and non-stationary data. The method consists of two parts: (1) the empirical mode decomposition (EMD), and (2) the Hilbert spectral analysis. The key part of the method is the first step, the EMD, with which any complicated data set can be decomposed into a finite and often small number of intrinsic mode functions (IMF). An IMF is defined here as any function having the same number of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima, and minima respectively. The IMF also thus admits well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to non-linear and non-stationary processes. With the Hilbert transform, the IMF yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, which we designate as the Hilbert Spectrum. Comparisons with Wavelet and Fourier analyses show the new method offers much better temporal and frequency resolutions. The EMD is also useful as a filter to extract variability of different scales. In the present application, HHT has been used to examine the changeability of the market, as a measure of volatility of the market. Published in

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This paper briefly presents the West African Monsoon (WAM) Modeling and Evaluation Project (WAMME) and evaluates WAMME general circulation models' (GCM) performances in simulating variability of WAM precipitation, surface temperature, and major circulation features at seasonal and intraseasonal scales in the first WAMME experiment. The analyses indicate that models with specified sea surface temperature generally have reasonable simulations of the pattern of spatial distribution of WAM seasonal mean precipitation and surface temperature as well as the averaged zonal wind in latitudeheight cross-section and low level circulation. But there are large differences among models in simulating spatial correlation, intensity, and variance of precipitation compared with observations. Furthermore, the majority of models fail 123Clim Dyn (2010) 35:3-27 DOI 10.1007 to produce proper intensities of the African Easterly Jet (AEJ) and the tropical easterly jet. AMMA Land Surface Model Intercomparison Project (ALMIP) data are used to analyze the association between simulated surface processes and the WAM and to investigate the WAM mechanism. It has been identified that the spatial distributions of surface sensible heat flux, surface temperature, and moisture convergence are closely associated with the simulated spatial distribution of precipitation; while surface latent heat flux is closely associated with the AEJ and contributes to divergence in AEJ simulation. Common empirical orthogonal functions (CEOF) analysis is applied to characterize the WAM precipitation evolution and has identified a major WAM precipitation mode and two temperature modes (Sahara mode and Sahel mode). Results indicate that the WAMME models produce reasonable temporal evolutions of major CEOF modes but have deficiencies/ uncertainties in producing variances explained by major modes. Furthermore, the CEOF analysis shows that WAM precipitation evolution is closely related to the enhanced Sahara mode and the weakened Sahel mode, supporting the evidence revealed in the analysis using ALMIP data. An analysis of variability of CEOF modes suggests that the Sahara mode leads the WAM evolution, and divergence in simulating this mode contributes to discrepancies in the precipitation simulation.