Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 12 3 2008 10.5194/hess-12-933-2008 http://www.hydrol-earth-syst-sci.net/12/933/2008/ http://www.hydrol-earth-syst-sci.net/12/933/2008/hess-12-933-2008.html http://www.hydrol-earth-syst-sci.net/12/933/2008/hess-12-933-2008.pdf 933 941 2008-06-20 Empirical Mode Decomposition on the sphere: application to the spatial scales of surface temperature variations N. Fauchereau G. G. S. Pegram S. Sinclair Department of Oceanography, University of Cape-Town, Cape Town, South Africa Civil Engineering, University of KwaZulu-Natal, Durban, South Africa Empirical Mode Decomposition (EMD) is applied here in two dimensions over the sphere to demonstrate its potential as a data-adaptive method of separating the different scales of spatial variability in a geophysical (climatological/meteorological) field. After a brief description of the basics of the EMD in 1 then 2 dimensions, the principles of its application on the sphere are explained, in particular via the use of a zonal equal area partitioning. EMD is first applied to an artificial dataset, demonstrating its capability in extracting the different (known) scales embedded in the field. The decomposition is then applied to a global mean surface temperature dataset, and we show qualitatively that it extracts successively larger scales of temperature variations related, for example, to topographic and large-scale, solar radiation forcing. We propose that EMD can be used as a global data-adaptive filter, which will be useful in analysing geophysical phenomena that arise as the result of forcings at multiple spatial scales. Balocchi, R., Menicucci, D., Santarcangelo, E., Sebastiani, L., Gemignani, A., Gellarducci, B., and Varanini, M.: Deriving the respiratory sinus arrhythmia from the heartbeat time series using Empirical Mode Decomposition, Chaos Soliton. Fract., 20, 171–177, 2004. Chiew, F. H. S., Peel, M. C., Amirthanathan, G. E., and Pegram, G. G. S.: Identification of oscillations in historical global streamflow data using Empirical Mode Decomposition, in: Regional Hydrological Impacts of Climatic Change Hydroclimatic Variability, Proceedings of Symposium S6 held during the Seventh IAHS Scientific Assembly at Foz do Iguaçu, Brazil, IAHS Publ., 296, p 5362, 2005. Cressie, N.: Statistics for Spatial Data, Wiley, New York, 1991. Daubechies, I.: Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1992. Delechelle, E., Nunes, J., and Lemoine, J.: Empirical mode decomposition synthesis of fractional processes in 1D and 2D space, Image Vision Comput., 23, 799–806, 2005. Elsner, J. and Tsonis, A.: Singular Spectrum Analysis. A New Tool in Time Series Analysis, Plenum Press, New York, 1996. Gloersen, P. and Huang, N. E.: Comparison of Interannual Intrinsic Modes in Hemispheric Sea Ice Covers and Other Geophysical Parameters, IEEE T. Geosci. Remote, 41, 1062–1074, 2003. Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N., Tung, C. C., and Liu, H. H.: The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and NonStationary Time Series Analysis, Proceedings of the Royal Society London A, 454(1971), 903–995, 1998. Huang, N. E., Shen, Z., and Long, S. R.: A new view of Nonlinear water waves: the Hilbert Spectrum, Annu. Rev. Fluid Mech., 31, 417–457, 1999. Hwang, P. A., Huang, N. E., and Wang, D. W.: A note on analyzing nonlinear and nonstationary ocean wave data, Appl. Ocean Res., 25, 187–193, 1999. Kumar, P. and Foufoula-Georgiou, E.: A Multicomponent Decomposition of Spatial Rainfall Fields 1. Segregation of Large- and Small-Scale Features Using Wavelet Transforms, Water Resour. Res., 29(8), 2515–2532, 1993. Leopardi, P.: A partition of the unit sphere into regions of equal area and small diameter, Electron. T. Numer. Ana., 55, 309–327, 2006. Linderhed, A.: 2D empirical mode decompositions in the spirit of image compression, Proceedings of SPIE, Wavelet and Independent Component Analysis Applications IXI, 4738, 2002. Linderhed, A.: Adaptive Image Compression with Wavelet Packets and Empirical Mode Decomposition, Linkoping Studies in Science and Technology, Dissertation No 909, ISBN 91-85295-81-7, 2004. Nunes, J. C., Bouaoune, Y., Delechelle, E., Niang, O., and Bunel, Ph.: Image analysis by bidimensional empirical mode decomposition, Image Vision Comput., 21, 1019–1026, 2003. Peel, M. C., Amirthanathan, G. E., Pegram, G. G. S., McMahon, T. A., and Chiew, F. H. S.: Issues with the application of Empirical Mode Decomposition Analysis, in: MODSIM 2005 International Congress on Modelling and Simulation, Modelling and Simulation Society of Australia and New Zealand, edited by: Zerger, A. and Argent, R. M., December 2005, 1681–1687, ISBN 0975840029, 2005. Pegram, G. G. S., Peel, M. C., and McMahon, T. A.: Empirical mode decomposition using rational splines: an application to rainfall time series, Proc. Royal Soc. A, 464, 1483–1501, 2008. Preisendorfer, R. W.: Principal Component Analysis in Meteorology and Oceanography, Elsevier, Oxford, New York, Tokyo, 1988. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes in C The art of scientific computing, Second Edition, Cambridge University Press, 1992. Sinclair, S. and Pegram, G. G. S.: Empirical Mode Decomposition in 2D space and time: a tool for spacetime rainfall analysis and nowcasting, Hydrol. Earth Syst. Sci., 9, 127–137, 2005. Zhang, R. R., Ma, S., and Hartzell, S.: Signatures of the seismic source in EMD-based characterization of the 1994 Northridge, California, earthquake recordings, B. Seismol. Soc. Am., 93, 501–518, 2003.