Dagmar Novotná

Non-linear dependence and teleconnections in climate data: sources, relevance, nonstationarity

Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The choice of dependence measure is key for the results of the subsequent analysis and interpretation. The use of linear Pearson’s correlation coefficient is widespread and convenient. On the other side, as the climate is widely acknowledged to be a nonlinear system, nonlinear dependence quantification methods, such as those based on information-theoretical concepts, are increasingly used for this purpose. In this paper we outline an approach that enables well informed choice of dependence measure for a given type of data, improving the subsequent interpretation of the results. The presented multi-step approach includes statistical testing, quantification of the specific non-linear contribution to the interaction information, localization of areas with strongest nonlinear contribution and assessment of the role of specific temporal patterns, including signal nonstationarities. In detail we study the consequences of the choice of a general nonlinear dependence measure, namely mutual information, focusing on its relevance and potential alterations in the discovered dependence structure. We document the method by applying it to monthly mean temperature data from the NCEP/NCAR reanalysis dataset as well as the ERA dataset. We have been able to identify main sources of observed non-linearity in inter-node couplings. Detailed analysis suggested an important role of several sources of nonstationarity within the climate data. The quantitative role of genuine nonlinear coupling at monthly scale has proven to be almost negligible, providing quantitative support for the use of linear methods for monthly temperature data.

Testing for nonlinearity in weather records

Daily records of atmospheric surface pressure, temperture and geopotential heights of 500 hPa ispbaric level were tested for nonlinearity, the necessary condition for deterministic chaos, using redundancy and surrogate data techniques. While the time series of the temperature and the geopotential heights were found indiscernible from correspondent isospectral linear stochastic processes, a significant nonlinear component was detected in the dynamics of the presure recording, however, no specific signatures of low-dimensional chaos were manifest.

Detecting modes with nontrivial dynamics embedded in colored noise: enhanced Monte Carlo SSA and the case of climate oscillations

Abstract Singular spectrum analysis (SSA) is a useful tool for identification and extraction of oscillatory or other signals from a noisy background. Its basic form, however, is reliable when a signal is embedded in white noise, while the presence of “colored” noises could lead to spurious results. Recently, Monte Carlo SSA, based on a so-called surrogate data technique, has been introduced in order to increase the reliability of detecting signals embedded in colored noises, which are usually present in geophysical data. We propose to enhance the Monte Carlo SSA by evaluating and testing the regularity of dynamics (quantified by so-called coarse-grained entropy rates) of the SSA modes against the colored noise null hypothesis, in addition to the test based on variance (eigenvalues). We demonstrate that such an approach can improve the test reliability in detection of relatively more regular dynamical modes than those obtained by decomposition of colored noises, in particular, in the identification of irregular oscillations embedded in red noise. The method is illustrated in the detection of oscillations with a period of eight years in historical temperature records obtained from several European locations, as well as in the detection of approximately five-year cycles in the global temperature series.

IS THE SOLAR ACTIVITY CYCLE SYNCHRONIZED WITH THE SOLAR INERTIAL MOTION

The 300 year record of the yearly sunspot numbers and numerically generated trajectory of the solar inertial motion (SIM) were subjects of a synchronization analysis. Phase synchronization of the sunspot cycle and a fast component of the SIM have been found and confirmed with statistical significance in three epochs (1727–1757, 1802–1832 and 1863–1922) of the entire 1700–1997 record. This result can be considered as a quantitative support for the hypothesis that there is a weak interaction of gravity and solar activity.

Detecting Oscillations Hidden in Noise: Common Cycles in Atmospheric, Geomagnetic and Solar Data

In this chapter we present a nonlinear enhancement of a linear method, the singular system analysis (SSA), which can identify potentially predictable or relatively regular processes, such as cycles and oscillations, in a background of colored noise. The first step in the distinction of a signal from noise is a linear transformation of the data provided by the SSA. In the second step, the dynamics of the SSA modes is quantified in a general, non-linear way, so that dynamical modes are identified which are more regular, or better predictable than linearly filtered noise. A number of oscillatory modes are identified in data reflecting solar and geomagnetic activity and climate variability, some of them sharing common periods.

Nonlinear Science issues in the dynamics of unstable rock slopes: new tools for rock fall risk assessment and early warnings

Abstract Time series of displacement data from unstable rock slopes contain ‘hidden’ information about the dynamics of slope failure. This information cannot be found when using the current linearly causal paradigm based on analytical methods, but is revealed when numerical and graphical methods from the toolbox of the Nonlinear Sciences are applied. The occurrence of fractal patterns, which suggests a qualitative difference between intrinsic slope movement dynamics of time series from the near-to-equilibrium and the far-from-equilibrium dynamical states of slope failure systems, is an example of such a ‘hidden’, diagnostically important indicator. It helps to identify the stage of immediate danger of rock fall occurrence, just in time to launch an efficient early warning. Phase portrait and correlograms of time series proved to be suitable for earlier revelation of transitions from the near-to-equilibrium to the far-from-equilibrium dynamical states, as well as for helping to distinguish between intrinsic slope movement dynamics and climatically driven reversible deformation activity.