Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 13 3 2006 10.5194/npg-13-321-2006 http://www.nonlin-processes-geophys.net/13/321/2006/ http://www.nonlin-processes-geophys.net/13/321/2006/npg-13-321-2006.html http://www.nonlin-processes-geophys.net/13/321/2006/npg-13-321-2006.pdf 321 328 2006-07-26 A Stochastic Iterative Amplitude Adjusted Fourier Transform algorithm with improved accuracy V. Venema victor.venema@uni-bonn.de F. Ament C. Simmer Meteorologisches Institut, Universität Bonn, Germany A stochastic version of the Iterative Amplitude Adjusted Fourier Transform (IAAFT) algorithm is presented. This algorithm is able to generate so-called surrogate time series, which have the amplitude distribution and the power spectrum of measured time series or fields. The key difference between the new algorithm and the original IAAFT method is the treatment of the amplitude adjustment: it is not performed for all values in each iterative step, but only for a fraction of the values. This new algorithm achieves a better accuracy, i.e. the power spectra of the measurement and its surrogate are more similar. We demonstrate the improvement by applying the IAAFT algorithm and the new one to 13 different test signals ranging from rain time series and 3-dimensional clouds to fractal time series and theoretical input. The improved accuracy can be important for generating high-quality geophysical time series and fields. The traditional application of the IAAFT algorithm is statistical nonlinearity testing. Reassuringly, we found that in most cases the accuracy of the original IAAFT algorithm is sufficient for this application. Andrzejak, R. G., Lehnertz, K., Rieke, C., Mormann, F., David, P., and Elger, C. E.: Indications of nonlinear deterministic and finite dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state, Phys. Rev. E., 64, 061907, 2001. Brown, A. R., Cederwall, R. T., Chlond, A., Duynkerke, P. G., Golaz, J. C., Khairoutdinov, M., Lewellen, D. C., Lock, A. P., MacVean, M. K., Moeng, C. H., Neggers, R. A. J., Siebesma, A. P., and Stevens, B.: Large-eddy simulation of the diurnal cycle of shallow cumulus convection over land, Quart. J. Roy. Meteorol. Soc., 128, 582, 1075–1093, 2002. Kantz, H. and Schreiber, T.: Nonlinear time series analysis, Cambridge Univ. Press, 0-521-55144-7, 1999. Kugiumtzis, D.: Test your surrogate data before you test for nonlinearity, Phys. Rev. E, 60(3), 2808–2816, 1999. Lewis, G. M. and Austin, P. H.: An iterative method for generating scaling log-normal simulations, in Proc. of the 11th conf. on Atmospheric Radiation, 3–7 June, Odgen UT, USA, 2002. Masters, F. and Gurley, K. R.: Non-Gaussian simulation: cumulative distribution function map-based spectral correction, J Eng. Mech., 1418–1428, doi:10.1061/(ASCE)0733-9399(2003)129:12(1418), 2003. Pincus, R., Hannay, C., and Evans, K. F.: The accuracy of determining three-dimensional radiative transfer effects in cumulus clouds using ground-based profiling instruments, J. Atmos. Sci., 62, 2284–2293, 2005. Popescu, R., Deodatis, G., and Prevost, J. H.: Simulation of homogeneous non-Gaussian stochastic vector fields, Prob. Eng. Mech., 13, 1–13, 1998. Scheirer, R. and Macke, A.: On the accuracy of the independent column approximation in calculating the downward fluxes in the UVA, UVB and PAR spectral ranges, J. Geophys. Res., 106, 14 301–14 312, 2001. Schreiber, T.: Constrained randomization of time series data, Phys. Rev. Lett., 80, pp. 2105, 1998. Schreiber, T. and Schmitz, A.: Improved surrogate data for nonlinearity tests, Phys. Rev. Lett, 77, 635–638, 1996. Schreiber, T. and Schmitz, A.: Surrogate time series, Physica D, 142(3–4), 346–382, 2000. Small, M.: Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance, 981-256-117-X, World Scientific, 2005. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J. D.: Testing for nonlinearity in time series: the method of surrogate data, Physica D, 58, 77–94, 1992. Theiler, J. and Prichard, D.: Constrained-realization Monte-Carlo method for hypothesis testing, Physica D, 94(4), 221–235, 1996. Venema, V., Meyer, S., Gimeno García, S., Kniffka, A., Simmer, C., Crewell, S., Löhnert, U., Trautmann, T., and Macke, A.: Surrogate cloud fields generated with the Iterative Amplitude Adapted Fourier Transform algorithm, Tellus 58A, 1, 104–120, 2006. Vidal, R. V. V. (Ed.): Applied simulated annealing, ISBN: 3-540-56229-X, Springer, Berlin, Germany, 1993.