Wolf, Rudolf (1816-1893), and Wolf number

2011 ◽  
Keyword(s):  
Wolf Number

scholarly journals The mean tilt of sunspot bipolar regions: theory, simulations and comparison with observations

2020 ◽  
Vol 495 (1) ◽  
pp. 238-248
Author(s):  
N Kleeorin ◽  
N Safiullin ◽  
K Kuzanyan ◽  
I Rogachevskii ◽  
A Tlatov ◽  
...  
Keyword(s):  
Coriolis Force ◽  
Large Scale ◽  
Mean Field ◽  
Wolf Number ◽  
Additional Contribution ◽  
Solar Cycles ◽  
Dynamo Theory ◽  
Large Scale Magnetic Field ◽  
Budget Equation ◽  
The Mean

ABSTRACT A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. A mechanism of formation of the mean tilt is related to the effect of the Coriolis force on meso-scale motions of super-granular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the solar differential rotation affects the mean tilt, which can explain deviations from Joy’s law for the sunspot bipolar regions at high latitudes. The theoretical results obtained and the results from numerical simulations based on the non-linear mean-field dynamo theory, which takes into account conservation of the total magnetic helicity and the budget equation for the evolution of the Wolf number density, are in agreement with observational data of the mean tilt of sunspot bipolar regions over individual solar cycles 15–24.

scholarly journals Large-Scale Patterns of Prominences in the Global Solar Cycles During 1880–1995

1998 ◽  
Vol 167 ◽  
pp. 442-445
Author(s):  
Dirk K. Callebaut ◽  
Valentine I. Makarov ◽  
Ksenia S. Tavastsherna
Keyword(s):  
Large Scale ◽  
Wolf Number ◽  
Solar Cycles ◽  
Zonal Distribution ◽  
Periodic Oscillations ◽  
Period 1880 ◽  
Latitude Distribution ◽  
The Mean ◽  
Long Term Variations

AbstractThe zonal distribution of prominences, their poleward migration from the sunspot zone to the poles, the polar magnetic field reversals and a correlation of the mean latitude of filament bands at minimum activity with the maximum of Wolf number in the next cycle are briefly discussed for the period 1880–1995. The need for research on the longterm latitude distribution of the prominences is emphasized. New results concerning long-term variations of the torsional oscillations of the Sun and quasi-periodic oscillations of the latitude zonal boundaries from an analysis of Hα charts (1915–1990) are given.

scholarly journals Statistical Effects in the Solar Activity Cycles during AD 1823–1996

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Maxim Ogurtsov ◽  
Markus Lindholm
Keyword(s):  
Solar Activity ◽  
Wolf Number ◽  
Sunspot Area ◽  
Period Effect ◽  
Group Sunspot Number ◽  
Activity Cycles ◽  
General Statistical ◽  
Odd Cycles ◽  
Solar Activity Cycles ◽  
Selection Of

General statistical properties of solar activity cycles during the period AD 1823–1996—including the Gnevyshev-Ohl and Waldmeier effects as well as an amplitude-period effect—were analyzed using Wolf number, group sunspot number, and extended total sunspot area series. It was found out that the Gnevyshev-Ohl effect GO2 (the positive correlation between intensity of the even cycles 2N and intensity of the odd cycles 2N+1) and the Waldmeier effect W2 (the anticorrelation between rise times of sunspot cycles and their amplitudes) are the most universal and robust features of the solar cycle. Other statistical relations were found appreciably sensitive to the selection of solar index, the interval of analysis, and the way of the cycle feature determination.

The Large-Scale Magnetic Field and Sunspot Cycles

2000 ◽  
Vol 179 ◽  
pp. 161-162
Author(s):  
V. I. Makarov ◽  
A. G. Tlatov
Keyword(s):  
Magnetic Field ◽  
Spherical Harmonics ◽  
Legendre Polynomials ◽  
Large Scale ◽  
Magnetic Moments ◽  
Radial Component ◽  
Wolf Number ◽  
Spherical Functions ◽  
Large Scale Magnetic Field ◽  
The Magnetic Field

Extended abstractWe report on the correlation between the large scale magnetic field and sunspot cycles during the last 80 years that was found by Makarovet al. (1999) and Makarov & Tlatov (2000) in H-αspherical harmonics of the large scale magnetic field for 1915–1999. The sum of intensities of the low modes 1 = 1 and 3, A(t), was used for comparison with the Wolf number, W(t). It was shown that the large scale magnetic field cycles, A(t), precede the sunspot cycles, W(t), by 5.5 years.Let us consider the behaviour in time of the harmonics with low numbers 1 = 1 and 1 = 3. The radial component B(r) of the magnetic field may be expanded in terms of the spherical harmonicswhereθandϕare the latitude and longitude,are Legendre polynomials andandare coefficients of expansion on the spherical functions.The magnetic moments of a dipole (1 = 1) and an octopole (1 = 3) are determined by the following equations:Let us enter the parameter describing their intensity,

SPECTRAL ANALYSIS AND FORECASTING OF THE 25TH SOLAR CYCLES

2021 ◽  
Vol 44 ◽  
pp. 96-99
Author(s):  
D.B. Rozhdestvensky ◽  
◽  
V.I. Rozhdestvenskaya ◽  
V.A. Telegin ◽  
◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Fourier Series ◽  
Solar Activity ◽  
Digital Filtering ◽  
Frequency Component ◽  
Wolf Number ◽  
Complex Signal ◽  
Data Set ◽  
Processing Scheme ◽  
Spectral Ranges

In the present work, we propose an extrapolation method, developed on the basis of spectral analysis, digital filtering, and the principle of demodulation of a complex signal, for predicting the beginning of cycle 25 of solar activity. The Wolf number and other measured characteristics of solar activity have a very complex spectral composition. The Sun, by the nature of its radiation, contributes a significant stochastic component to the observational data. The experimental data are known only up to the present, and the prediction is about bridging the gap in our data set. Mathematically, the prediction problem boils down to extrapolation of discontinuous functions, which leads to a Gibbs phenomenon that occurs at the point of discontinuity and makes prediction into the future impossible. To overcome this discontinuity, additional physical models describing a continuous process are most often used. This paper uses only the Wolf series of numbers from 1818 to 2020. The authors developed an original forecasting technique using Fourier series, digital filtering and representation of the complex process as modulated and subsequent demodulation. As a result of decomposing the complex signal by Fourier series into separate components, the spectral ranges characteristic of the Wolf number were singled out. Taylor's series was used for construction of prediction or extrapolation algorithms. The extraction of spectral ranges, characteristic for the investigated process, is carried out by means of sequential digital filtering methods and information compression in accordance with the cut-off frequency of the digital filter. For example, when selecting eleven-year cycles of solar activity, we have to compress the information by a factor of 160. With such a processing scheme, the forecasting starts with the ultralow-frequency component with a period of more than 11 years, successively moving to the ranges of higher frequencies. The use of spectral analysis and Chebyshev filtering showed the possibility to predict the low-frequency component for the full cycle period. The eleven-year component forecast obtained by the authors is in good agreement with the data of the Brussels Royal Center.

scholarly journals On variations of <i>fo</i>F2 and F-spread before strong earthquakes in Japan

2006 ◽  
Vol 6 (5) ◽  
pp. 735-739 ◽  
Author(s):  
E. V. Liperovskaya ◽  
M. Parrot ◽  
V. V. Bogdanov ◽  
C.-V. Meister ◽  
M. V. Rodkin ◽  
...  
Keyword(s):  
Analysis Data ◽  
Wolf Number ◽  
Study Data ◽  
Occurrence Probability ◽  
Ionospheric Electron Density ◽  
Strong Earthquakes ◽  
Mean Frequency ◽  
Ionospheric Effects ◽  
Statistical Reliability ◽  
Better Than

Abstract. The statistical analysis of the variations of the dayly-mean frequency of the maximum ionospheric electron density foF2 is performed in connection with the occurrence of (more than 60) earthquakes with magnitudes M>6.0, depths h<80 km and distances from the vertical sounding station R<1000 km. For the study, data of the Tokyo sounding station are used, which were registered every hour in the years 1957–1990. It is shown that, on the average, foF2 decreases before the earthquakes. One day before the shock the decrease amounts to about 5%. The statistical reliability of this phenomenon is obtained to be better than 0.95. Further, the variations of the occurrence probability of the turbulization of the F-layer (F spread) are investigated for (more than 260) earthquakes with M>5.5, h<80 km, R<1000 km. For the analysis, data of the Japanese station Akita from 1969–1990 are used, which were obtained every hour. It is found that before the earthquakes the occurrence probability of F spread decreases. In the week before the event, the decrease has values of more than 10%. The statistical reliability of this phenomenon is also larger than 0.95. Examining the seismo-ionospheric effects, here periods of time with weak heliogeomagnetic disturbances are considered. For the foF2 analysis, the Wolf number is less than 100 and the index ΣKp is smaller than 30, and in case of the F-spread study a Wolf number less than 80 and ΣKp smaller than 17 are chosen.

scholarly journals Day-time variations of foF2 connected to strong earthquakes

2009 ◽  
Vol 9 (1) ◽  
pp. 53-59 ◽  
Author(s):  
E. V. Liperovskaya ◽  
V. V. Bogdanov ◽  
P.-F. Biagi ◽  
C.-V. Meister ◽  
V. A. Liperovsky ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Characteristic Frequency ◽  
Wolf Number ◽  
Temporal Dependence ◽  
Strong Earthquakes ◽  
Time Variations

Abstract. The statistical analysis of the characteristic frequency foF2 of the Earth's ionosphere averaged over mid-day hours – from 11:00 till 17:00 h LT – is carried out. Disturbances of foF2 connected to earthquakes are considered on the background of seasonal, geomagnetic, 11-years and 27-days solar variations. A special normalized parameter F is introduced, which represents the almost seasonal-independent part of foF2. Days with high solar (Wolf number >100) and geomagnetic (∑Kp>30) activity are excluded from the analysis. Events with magnitude M>5, distance from the sounding station R<500 km and depth h<70 km are taken into account. The superimposed epoches' method is used to determine the temporal dependence of F. It is found that F increases about 3–6 days before the earthquakes and then decreases one day – two days before the shock. The decreased values of F continue to exist two-three days after events with M>5.5. The obtained phenomenon depends on the magnitude of the earthquake. For events with M>5.5, the reliability of the effect is larger than 95%. For data of more than 80 earthquakes in the vicinity of Petropavlovsk-Kamchatsky and more than 200 earthquakes in the vicinity of Tokyo analogous results are obtained.

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