Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 14 1 2007 10.5194/npg-14-73-2007 http://www.nonlin-processes-geophys.net/14/73/2007/ http://www.nonlin-processes-geophys.net/14/73/2007/npg-14-73-2007.html http://www.nonlin-processes-geophys.net/14/73/2007/npg-14-73-2007.pdf 73 77 2007-02-01 Expectation-maximization analysis of spatial time series K. W. Smith alfredo@whoi.edu A. L. Aretxabaleta Woods Hole Oceanographic Institution, Woods Hole, MA, USA Expectation maximization (EM) is used to estimate the parameters of a Gaussian Mixture Model for spatial time series data. The method is presented as an alternative and complement to Empirical Orthogonal Function (EOF) analysis. The resulting weights, associating time points with component distributions, are used to distinguish physical regimes. The method is applied to equatorial Pacific sea surface temperature data from the TAO/TRITON mooring time series. Effectively, the EM algorithm partitions the time series into El Niño, La Niña and normal conditions. The EM method leads to a clearer interpretation of the variability associated with each regime than the basic EOF analysis. Belamari, S., Redelsperger, J.-L., and Pontaud, M.: Dynamic Role of a Westerly Burst in Triggering an Equatorial Pacific Warm Event, J. Climate, 16, 1869–1890, 2003. Emery, W J. and Thomson, R E.: Data Analysis Methods in Physical Oceanography, Pergamon, pp 634, 1997. Fraley, C. and Raftery, A.: Model Based Clustering, Discriminant Analysis, and Density Estimation., J. American Statistical Assoc., 97, 611–631, 2002. Houseago-Stokes, R E. and Challenor, P G.: Using PPCA to Estimate EOFs in the Presence of Msing Values, J. Atmos. Oceanic Technol., 21, 1471–1480, 2004. Keeler, W S.: EOF Representation of the Madden-Julian Oscillation and its Connection with ENSO, J. Climate, 14, 3055–3061, 2001. Kondrashov, D. and Ghil, M.: Spatio-temporal filling of missing points in geophysical data sets, Nonlin. Processes Geophys., 13, 151–159, 2006. McPhaden, M J.: Genesis and Evolution of the 1997–1998 El Niño, Science, 283, 950–954, 1999. McPhaden, M J., Busalacchi, A J., Donguy, R. C. J R., Gage, K S., Halpern, D., Ji, M., Julian, P., Meyers, G., Mitchum, G T., Niiler, P P., Picaut, J., Reynolds, R W., Smith, N., and Takeuchi, K.: The Tropical Ocean-Global Atmosphere observing system: A decade of progress, J. Geophys. Res., 103, 14 169–14 240, 1998. Tangang, F T., Tang, B., Monahan, A H., and Hsieh, W W.: Forecasting ENSO Events: A Neural Network-Extended EOF approach, J. Climate, 11, 29–41, 1998. Tipping, M E. and Bishop, C M.: Probabilistic principal component analysis, J. R. Statist. Soc. B, 61, 611–622, 1999. Tourre, Y M. and White, W B.: ENSO Signals in Global Upper-Ocean Temperature, J. Phys. Oceanogr., 25, 1317–1332, 1995. Wolter, K. and Timlin, M S.: Measuring the strength of ENSO – how does 1997/98 rank?, Weather, 53, 315–324, 1998.