Properties Of Oscillation Modes Research Articles

Manifestation of characteristic periods of oscillations of the Earth’s orbital parameters in the paleoclimatic data

We performed a joint analysis of the fluctuations of the Earth's orbital parameters: eccentricity of the orbit, inclination of the Earth's axis to the plane of its orbit, and precession with variations in the indicators of the climate variations, such as reconstructions of temperature variations, CO2 and CH4 concentrations based on the drilling data of glaciers in Antarctica, and relative concentration of oxygen�18 in the benthic deposits on the sea floor (series LR04). The wavelet analysis of various paleoclimatic parameters demon� strated the existence and inphase properties of oscil� lation modes with periods of 100, 41, and 20 ky in the last 800 ka. Oscillations with a period of 41 ky distin� guished in the LR04 series are inphase with the fluc� tuations of the inclination of the Earth's axis in the last 2 Ma, and the oscillations with a period of 20 ky are correlated with the precession fluctuations in the last 1.25 Ma (at high amplitude values). In the last 700- 750 ka, synchronization is observed between the modes of 100 ky fluctuations in δ 18 O (and phase corre� lation of this mode with the other indicators of the cli� mate variations based on the Antarctic data) and eccentricity of the orbit. The transition to the regime of 100-120 ky glacialinterglacial cycles in the last 700 ka may be caused by the existence of such a corre� lation between the fluctuations of the climatic and orbital parameters. In the major part of the works related to studies of the Milankovitch cycles, the authors use calculated data on the solar irradiance flux that is incident at a specific latitude, in a specific season, and even on a specific day. Such data can be found for example, in (1). The calculated data on the variations in the Earth's orbital parameters can also be found there: eccentricity of the Earth's orbit, inclination of the Earth's axis, and precession during the last 5 Ma with a step of 1000 years. Time series LR04 was constructed in (2) on the basis of the composition data of sea floor drilling. The time series consists of δ 18 O in the fossil residuals of benthic marine organisms in the last 5.3 Ma with a step from 1 to 5 ky. To reach consistency between the evolution of largescale variations in the LR04 time series and the Earth's temperature varia� tions, we inverted the sign of variable δ 18 O. Then we calculated and excluded the nonlinear trend from the data and denoted the obtained time series as Δδ 18 O. The trend (Fig. 1) provides evidence that the Earth was cooling, which slowed down in the Middle Pleistocene and later. We used in this work the reconstructions of variations in the climatic parameters obtained from the analysis of ice cores at Antarctic stations Concor� dia, Dome C (3), and Vostok (4) including temperature T, carbon dioxide CO2, methane CH4, etc. The data from Dome C obtained within the EPICA project are for 800 ky, the other data from Vostok are for 415 ky with a time step of 500 years. We used the wavelet analysis with a real wavelet function of the Morlet type to study the amplitudes and phases of the data. This function uses a zero order discrete spheroid wave function instead of a Gaussian (5): , where the parameter is β = 3.5. We note that such choice of β, in particular, allows us to decrease the interval of distortions at the edges in the wavelet trans� form by a factor of 1.57-1.77 compared with the selection of the Morlet wavelet function where the selection of β is recommended within 5.5-6.2. The method of real wavelet analysis is described in (5). In this work it is adjusted for the analysis of data with gaps and uses the amplitude normalizing of the obtained modes. We note that distortions at the edges cover an interval equal to 1.75P, where P is the corresponding period. The range of periods in the wavelet analysis of data from Dome C is 5-115 ky. It is limited by the duration of the glacier data. The step over the period is 1000 years. The wavelet analysis applied to the Δδ 18 O time series (LR04), which covers an interval of 0 () ut

Numerical Simulations of Oscillation Modes of the Solar Convection Zone.

We use the three-dimensional hydrodynamic code of Stein & Nordlund to realistically simulate the upper layers of the solar convection zone in order to study physical characteristics of solar oscillations. Our first result is that the properties of oscillation modes in the simulation closely match the observed properties. Recent observations from the Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) and Global Oscillations Network Group have confirmed the asymmetry of solar oscillation line profiles, initially discovered by Duvall et al. In this Letter, we compare the line profiles in the power spectra of the Doppler velocity and continuum intensity oscillations from the SOHO/MDI observations with the simulation. We also compare the phase differences between the velocity and intensity data. We have found that the simulated line profiles are asymmetric and have the same asymmetry reversal between velocity and intensity as observed. The phase difference between the velocity and intensity signals is negative at low frequencies, and phase jumps in the vicinity of modes are also observed. Thus, our numerical model reproduces the basic observed properties of solar oscillations and allows us to study the physical properties which are not observed.