A. M. Feigin

Toward an understanding of the nonlinear nature of atmospheric photochemistry: Essential dynamic model of the mesospheric photochemical system

We present the essential dynamic model of the mesospheric photochemical system (PCS) and suggest a step-by-step procedure for elaborating such a model of an arbitrary atmospheric PCS. The model demonstrates the same possibilities of nonlinear dynamic behavior and qualitatively the same dynamic characteristics as the corresponding original model, but is much simpler than the latter. We show the adequacy of the essential model compared with the original one in bifurcation diagrams, equilibrium states, and such new characteristics as correlation dimension and minimum embedding dimension of a chaotic attractor. The model can be used both for identifying and studying the mechanisms of the nonlinear dynamic behavior of the mesospheric PCS, as well as for solving a number of problems aimed at revealing nonlinear photochemical phenomena in the actual mesosphere.

On the possibility of complicated dynamic behavior of atmospheric photochemical systems : Instability of the Antarctic photochemistry during the ozone hole formation

We suggest a new approach to studying atmospheric photochemical processes by analyzing an atmospheric photochemical system as a dynamic system possessing many degrees of freedom and demonstrate a good agreement between the Antarctic photochemical system (APCS) behavior described by a three-order set of ordinary differential equations and ozone variations taking place during ozone hole phenomenon. We investigate the dynamic properties of this set under the parameter values corresponding to the Antarctic stratosphere conditions during the last decade and show that APCS may become unstable as a result of the loss of equilibrium state stability and/or as a result of the self-oscillations appearance. We present some arguments in favor of close connection between the APCS instability and anomalous deep depletion of Antarctic ozone concentration in spring observed since the mid-1980s.

Structure, Energy, and Vibrational Frequencies of Oxygen Allotropes On (n ≤ 6) in the Covalently Bound and van der Waals Forms: Ab Initio Study at the CCSD(T) Level.

Recent experiments on the UV and electron beam irradiation of solid O2 reveals a series of IR features near the valence antisymmetric vibration band of O3 which are frequently interpreted as the formation of unusual On allotropes in the forms of weak complexes or covalently bound molecules. In order to elucidate the question of the nature of the irradiation products, the structure, relative energies, and vibrational frequencies of various forms of On (n = 1-6) in the singlet, triplet, and, in some cases, quintet states were studied using the CCSD(T) method up to the CCSD(T,full)/cc-pCVTZ and CCSD(T,FC)/aug-cc-pVTZ levels. The results of calculations demonstrate the existence of stable highly symmetric structures O4 (D3h), O4 (D2d), and O6 (D3d) as well as the intermolecular complexes O2·O2, O2·O3, and O3·O3 in different conformations. The calculations show that the local minimum corresponding to the O3···O complex is quite shallow and cannot explain the ν3 band features close to 1040 cm(-1), as was proposed previously. For the ozone dimer, a new conformer was found which is more stable than the structure known to date. The effect of the ozone dimer on the registered IR spectra is discussed.

Principal nonlinear dynamical modes of climate variability.

We suggest a new nonlinear expansion of space-distributed observational time series. The expansion allows constructing principal nonlinear manifolds holding essential part of observed variability. It yields low-dimensional hidden time series interpreted as internal modes driving observed multivariate dynamics as well as their mapping to a geographic grid. Bayesian optimality is used for selecting relevant structure of nonlinear transformation, including both the number of principal modes and degree of nonlinearity. Furthermore, the optimal characteristic time scale of the reconstructed modes is also found. The technique is applied to monthly sea surface temperature (SST) time series having a duration of 33 years and covering the globe. Three dominant nonlinear modes were extracted from the time series: the first efficiently separates the annual cycle, the second is responsible for ENSO variability, and combinations of the second and the third modes explain substantial parts of Pacific and Atlantic dynamics. A relation of the obtained modes to decadal natural climate variability including current hiatus in global warming is exhibited and discussed.

On the influence of diffusion upon the nonlinear behavior of the photochemistry of the mesopause region

The photochemical system of the mesopause region is a nonlinear driven oscillator enforced by the diurnal-periodic solar radiation. Under idealized conditions this oscillator can display nonlinear effects such as period doubling cascades or chaos. We investigate what happens if this system is subjected to atmospheric diffusion. A high-resolution one-dimensional chemical system of the mesopause region has been established in order to answer this question. Strong diffusion destroys nonlinear effects, but for the lower values of the diffusion coefficient which are still of the order of magnitude of real values, different nonlinear effects occur. The most important effect consisted of the creation of a 2-day subharmonic oscillation. Such a 2-day oscillation of the concentration of chemical active species entails a corresponding oscillation of the chemical heating rates which feeds back to the dynamics of this region. The zonal wind influences the period of the oscillation so that the periods differ from the exact 48-hour value by a few hours depending on the wind velocity and its direction. We call this phenomenon the photochemical Doppler effect.

Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models

AbstractThe present paper is the second part of a two-part study on empirical modeling and prediction of climate variability. This paper deals with spatially distributed data, as opposed to the univariate data of Part I. The choice of a basis for effective data compression becomes of the essence. In many applications, it is the set of spatial empirical orthogonal functions that provides the uncorrelated time series of principal components (PCs) used in the learning set. In this paper, the basis of the learning set is obtained instead by applying multichannel singular-spectrum analysis to climatic time series and using the leading spatiotemporal PCs to construct a reduced stochastic model. The effectiveness of this approach is illustrated by predicting the behavior of the Jin–Neelin–Ghil (JNG) hybrid seasonally forced coupled ocean–atmosphere model of El Nino–Southern Oscillation. The JNG model produces spatially distributed and weakly nonstationary time series to which the model reduction and prediction m...

Toward understanding of the nonlinear nature of atmospheric photochemistry: Multiple equilibrium states in the high‐latitude lower stratospheric photochemical system

We investigate the qualitative nonlinear dynamic properties of the high-latitude stratospheric (HLS) photochemical system (PCS). For the investigation we use the model of HLS PCS, which includes all the most significant processes of chemical nature, taking place in the high-latitude (both Arctic and Antarctic) lower stratosphere in winter-spring period, and adequately simulates the evolution of the Antarctic ozone hole. We analyze the photochemistry in the stratospheric region at 17–18 km altitude and 70–80 degrees latitude and reveal that HLS PCS may possess simultaneously several equilibrium states (multistability) under conditions, which differ from the conditions of the actual present-day atmosphere only by smaller total mixing ratio of inorganic chlorine species. The required conditions were typical for the atmosphere in recent past and are expected in future. Through a graphical-analytical consideration we reveal the origin of multistability of HLS PCS and in doing so we insure that multistability is not a consequence of any approximation used in the model but is a property inherent in nature of HLS PCS. We demonstrate that when the multistability of HLS PCS is present, it may considerably influence the spring evolution of the Antarctic photochemistry.

Prognosis of Qualitative Behavior of a Dynamic System by the Observed Chaotic Time Series

An approach to the long-term prognosis of qualitative behavior of a dynamic system (DS) is proposed, which is based on the nonlinear-dynamical analysis of a weakly nonstationary chaotic time series (TS). A method for constructing prognostic models using the observed evolution of a single dynamic variable is described, which employs the proposed approach for prediction of bifurcations of low-dimensional DSs. The method is applied to analyze the TS generated by the Roessler system and the system of equations modeling photochemical processes in the mesosphere. The analysis is performed for a TS calculated in the case of a slow variation in the control parameter of the system. The duration of the “observed” TS is limited such that the system demonstrates only one, chaotic, type of behavior without any bifurcations during the observed TS. The proposed algorithm allows us to predict correctly the bifurcation sequences for both systems at times much longer than the duration of the observed TS, to point out the expected instants of specific bifurcation transitions and accuracy of determining these instants, as well as to calculate the probabilities to observe the predicted regimes of the systems behavior at the time of interest.

Method for reconstructing nonlinear modes with adaptive structure from multidimensional data

We present a detailed description of a new approach for the extraction of principal nonlinear dynamical modes (NDMs) from high-dimensional data. The method of NDMs allows the joint reconstruction of hidden scalar time series underlying the observational variability together with a transformation mapping these time series to the physical space. Special Bayesian prior restrictions on the solution properties provide an efficient recognition of spatial patterns evolving in time and characterized by clearly separated time scales. In particular, we focus on adaptive properties of the NDMs and demonstrate for model examples of different complexities that, depending on the data properties, the obtained NDMs may have either substantially nonlinear or linear structures. It is shown that even linear NDMs give us more information about the internal system dynamics than the traditional empirical orthogonal function decomposition. The performance of the method is demonstrated on two examples. First, this approach is successfully tested on a low-dimensional problem to decode a chaotic signal from nonlinearly entangled time series with noise. Then, it is applied to the analysis of 250-year preindustrial control run of the INMCM4.0 global climate model. There, a set of principal modes of different nonlinearities is found capturing the internal model variability on the time scales from annual to multidecadal.

Predicting Critical Transitions in ENSO Models. Part I: Methodology and Simple Models with Memory

AbstractA new empirical approach is proposed for predicting critical transitions in the climate system based on a time series alone. This approach relies on nonlinear stochastic modeling of the system’s time-dependent evolution operator by the analysis of observed behavior. Empirical models that take the form of a discrete random dynamical system are constructed using artificial neural networks; these models include state-dependent stochastic components. To demonstrate the usefulness of such models in predicting critical climate transitions, they are applied here to time series generated by a number of delay-differential equation (DDE) models of sea surface temperature anomalies. These DDE models take into account the main conceptual elements responsible for the El Nino–Southern Oscillation phenomenon. The DDE models used here have been modified to include slow trends in the control parameters in such a way that critical transitions occur beyond the learning interval in the time series. Numerical results ...