N. G. Makarenko

Comparison of the dynamics of active regions by methods of computational topology

This work analyzes the temporal evolution for three active regions (ARs) (AR 2034, AR 2035, and AR 2036). In terms of complexity, these are objects with high a priori probability of flares. However, their actual flare scenarios proved to be very different. The temporal evolution of ARs is analyzed with modern prognostic parameters and descriptors obtained by methods of computational topology. We show that these methods are more suitable for describing the actual situation. We note that the change in complexity descriptors for prognostic problems is more important than the set of characteristics themselves.

On the Prognostic Efficiency of Topological Descriptors for Magnetograms of Active Regions

Solar flare prediction remains an important practical task of space weather. An increase in the amount and quality of observational data and the development of machine-learning methods has led to an improvement in prediction techniques. Additional information has been retrieved from the vector magnetograms; these have been recently supplemented by traditional line-of-sight (LOS) magnetograms. In this work, the problem of the comparative prognostic efficiency of features obtained on the basis of vector data and LOS magnetograms is discussed. Invariants obtained from a topological analysis of LOS magnetograms are used as complexity characteristics of magnetic patterns. Alternatively, the so-called SHARP parameters were used; they were calculated by the data analysis group of the Stanford University Laboratory on the basis of HMI/SDO vector magnetograms and are available online at the website (http://jsoc.stanford.edu/) with the solar dynamics observatory (SDO) database for the entire history of SDO observations. It has been found that the efficiency of large-flare prediction based on topological descriptors of LOS magnetograms in epignosis mode is at least s no worse than the results of prognostic schemes based on vector features. The advantages of the use of topological invariants based on LOS data are discussed.

The dynamic relation between activities in the Northern and Southern solar hemispheres

The north–south (N/S) asymmetry of solar activity is the most pronounced phenomenon during 11-year cycle minimums. The goal of this work is to try to interpret the asymmetry as a result of the generalized synchronization of two dynamic systems. It is assumed that these systems are localized in two solar hemispheres. The evolution of these systems is considered in the topological embeddings of a sunspot area time series obtained with the use of the Takens algorithm. We determine the coupling measure and estimate it on the time series of daily sunspot areas. The measurement made it possible to interpret the asymmetry as an exchangeable dynamic equation, in which the roles of the driver–slave components change in time for two hemispheres.

Radiocarbon version of 11-year variations in the interplanetary magnetic field since 1250

It is known that the interplanetary magnetic field (IMF), which is controlled by solar activity, modulates the flux of galactic cosmic rays (GCRs). Because GCRs are the only source of the 14C isotope in the atmosphere before the era of atmospheric nuclear tests, the formation rate of this isotope in the atmosphere is one of the few reliable sources of information on solar activity before the initiation of regular telescopic observations. In this study, we solve the inverse problem for the equation of radiocarbon diffusion from the atmosphere into the ocean by calibrating the radiocarbon content in tree rings from 1510 to 1950. We obtain an approximation of 11-year IMF cycles represented by the IDV index from 1872 to 1950. The model extrapolation to the calibration curve for the Korean Peninsula over the time period from 1250 to 1650 makes it possible to calculate the sequence of minima of quasi-11-year cycles since 1250.

Millennial reconstruction of the global terrestrial climate: New approaches to the available data

The main aim of the work was to reliably reconstruct the change in global temperature for the last 1000 years using new methods. We have considered two approaches to obtaining composite series based on symbolic analysis and on the so-called “principle of witnesses,” respectively. Based on the first approach, it has been indicated that the known reconstruction proposed by Moberg et al. is preferable in the scope of the accepted symbolic analysis variant among the available reconstructions. An approach based on the eyewitness principle made it possible to reveal the years when five different reconstructions give coordinated data on a 1000-year scale. The obtained new reconstructions are in good agreement with instrumental series data on the consistent time interval of their existence.

Topological diagnostics of the cyclic component of the time series associated with helium

Detection of the deterministic component from noised time series is a common procedure in the solar–terrestrial coupling problem when climate is modeled, solar activity is analyzed, or a signal associated with helium is extracted. Such series are mostly generated by the superposition of different processes for which the concept of a noise component cannot be determined formally. A method based on the combination of time-series topological embedding in Euclidean space and the identification of a persistent cycle by homology theory methods is proposed. The method application is demonstrated based on actual data.

Evolution of the Bochner Laplacian for magnetograms of solar active regions

A search for powerful flare predictors remains a problem of current interest in solar—terrestrial physics. The magnetograms (LOS SDO/HMI instrument) for active regions (ARs) 1158, 1166, 1283, and 1520, which produced an X-ray flare located near the central meridian, are analyzed. АR 1654, which was rather complex but generated only M flares near western limb, remaining quiet during the passage over the disk, has been analyzed in a similar manner for comparison. The combinatorial Bochner Laplacian was used as a complexity descriptor. We calculate it for each magnetogram, which was converted into the magnetic energy density of the longitudinal field component, and analyze its maximal spatial variation. It has been shown that the maximal spatial Laplacian values trace the neutral line during AR evolution, demonstrating sharp peaks before and after the flare in this case. Although this signature has no established statistical reliability, it can be interesting as an effective parameter when flares are predicted.

Global correlation between surface heat fluxes and insolation in the 11-year solar cycle: The latitudinal effect

Because of the small amplitude of insolation variations (1365.2–1366.6 W m−2 or 0.1%) from the 11-year solar cycle minimum to the cycle maximum and the structural complexity of the climatic dynamics, it is difficult to directly observe a solar signal in the surface temperature. The main difficulty is reduced to two factors: (1) a delay in the temperature response to external action due to thermal inertia, and (2) powerful internal fluctuations of the climatic dynamics suppressing the solar-driven component. In this work we take into account the first factor, solving the inverse problem of thermal conductivity in order to calculate the vertical heat flux from the measured temperature near the Earth’s surface. The main model parameter—apparent thermal inertia—is calculated from the local seasonal extremums of temperature and albedo. We level the second factor by averaging mean annual heat fluxes in a latitudinal belt. The obtained mean heat fluxes significantly correlate with a difference between the insolation and optical depth of volcanic aerosol in the atmosphere, converted into a hindered heat flux. The calculated correlation smoothly increases with increasing latitude to 0.4–0.6, and the revealed latitudinal dependence is explained by the known effect of polar amplification.

Regional instrumental series in reconstructions of global changes in the Earth’s climate

The possibility to apply long-term regional series to reconstruct the Earth’s global temperature in the past is considered. It is shown using symbolic analysis methods that significant (on the so-called order patterns) are relations of time series of St. Petersburg temperature with certain regional and global series. New sets of global temperature reconstructions, starting from the mid-18th century, are constructed on the basis of the previously proposed MSR and DPS methods.

SDO in Pulkovo Observatory

We discuss effective applications of data obtained by both instruments of the Solar Dynamics Observatory: The Helioseismic & Magnetic Imager (HMI) and The Atmospheric Imaging Assembly (AIA). The purpose of this presentation is to show the most important problems of solar activity which are the main subjects in Pulkovo Observatory of the Russian Academy of Science. For these investigations uniform data sets of magnetic fields and coronal emissions in extreme ultra-violet bands are needed. Thus, we are planning to create SDO center in Pulkovo Observatory, which will help us in collaboration with existing SDO centers and provide more effective way of access to data for studies of the Sun.