Nonlinear time series analysis of the fluctuations of the geomagnetic horizontal field

Abstract

Abstract.A detailed nonlinear time series analysis of the hourly data of the geomagnetic horizontal intensity H measured at Kodaikanal (10.2 • N; 77.5 • E; mag: dip 3.5 • N) has been carried out to investigate the dynamical behaviour of the fluctuations of H . The recurrence plots, spatiotemporal entropy and the result of the surrogate data test show the deterministic nature of the fluctuations, rejecting the hypothesis that H belong to the family of linear stochastic signals. The low dimensional character of the dynamics is evident from the estimated value of the correlation dimension and the fraction of false neighbours calculated for various embedding dimensions. The exponential decay of the power spectrum and the positive Lyapunov exponent indicate chaotic behaviour of the underlying dynamics of H. This is also supported by the results of the comparison of the chaotic characteristics of the time series of H with the pseudo-chaotic characteristics of coloured noise time series. We have also shown that the error involved in the short-term prediction of successive values of H , using a simple but robust, zero-order nonlinear prediction method, increases exponentially. It has also been suggested that there exists the possibility of characterizing the geomagnetic fluctuations in terms of the invariants in chaos theory, such as Lyapunov exponents and correlation dimension. The results of the analysis could also have implications in the development of a suitable model for the daily fluctuations of geomagnetic horizontal intensity.

A study on chaotic behaviour of equatorial/low latitude ionosphere over Indian subcontinent, using GPS-TEC time series

“…Since ionosphere is a complex system, it exhibits both deterministic and stochastic behaviours, whose influences vary with physical conditions. To check the stationarity, probability density of the time series of TEC was calculated, by dividing the range of values of TEC into short intervals, and then by counting the values of the series fall in each interval (George et al, 2001;Kumar et al, 2004;Unnikrishnan et al, 2006aUnnikrishnan et al, , 2006bUnnikrishnan, 2008). The probability density for the first half of detrended TEC time series (continuous line) and that of the second half of the series (dashed line) was calculated and shown in Fig.…”

Deterministic nature of the underlying dynamics of surface wind fluctuations

“…However, many authors have argued that the solar radiations are stochastic in nature and hence the underlying dynamics of the surface wind should be governed by both deterministic as well as stochastic factors. On the other hand, our previous analysis of the data of total electron content (TEC), which is strongly influenced by the solar radiation, shows strong evidence of deterministic low-dimensional character of the underlying dynamics (George et al, 2002;Kumar et al, 2004). The surface wind speed is a similar atmospheric parameter to solar influence but its dynamics is further complicated by the local conditions such as topography.…”

Chaos analysis of groundwater depth time series using surrogate data method

“…Among them, the correlation dimension values for the original and corresponding surrogate data were determined by the correlation dimension method, which is described in section 2.4. Based on the results presented from Table 1 to Table 3, the values of "sigmas" S for all three types of data selected in the present study was computed according to Equation (5). The values of "sigmas" S for them are 2.96077, 0.42633 and 3.43467 respectively.…”

“…In regard to the surrogate method, some statistic characteristics of the data are compared with those of signals which have the same Fourier amplitudes and the same distribution values. If the index of the surrogate data and the original one are significantly different in such characteristics, then it may be safely concluded that the series under study cannot be described by a stationary, linear stochastic model (George et al, 2001).…”