Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.gao.spb.ru/personal/ivanov/papers/nimv_en1.pdf Дата изменения: Fri Nov 8 18:02:20 2013 Дата индексирования: Sun Apr 10 00:05:19 2016 Кодировка: Поисковые слова: total solar eclipse

SOLAR ACTIVITY RECONSTRUCTION FROM PROXY DATA
Yu.A.Nagovitsyn1,2, V.G.Ivanov1, E.V.Miletsky1 and D.M.Volobuev 1 Central astronomical observatory at Pulkovo, Russian Academy of Science, Saint-Petersburg, Russia; 2 nag@gao.spb.ru
1

Abstract
In this paper an approach to investigation of the long-term behaviour of solar activity (SA) is discussed. Specifically, we discuss questions of construction of satisfactory database of SA variability on long-time ranges, and also present the original results of our investigations of SA and links between the solar activity and the terrestrial climate.

Keywords: solar activity, solar-climate links, long-time variability. Whatever natural process we study, our knowledge about it always has such a feature that the deeper in the past we go the less volume of factual material we have, because natural loss of information takes place. Hence, if a process under investigation has a reach frequency structure, we can presume, at first glance, that we should inevitably obtain worse description of its longer variation as compared with the shorter ones. However, on the other hand, for description of the longer variations we a priori need less information than for the shorter ones. For understanding of this fact the following analogy is helpful: in practice of wavelet transformation (or another transformation of such a kind) after two times increasing of the wavelet scale the required density of measurement of the investigated series can be two times less. Therefore, for a principal description of a process on whole range of time scales we can use series of different quality: more detailed and high-quality ones for small scales and more rough, for large scales. Such a "logarithmic logic" is determinative for our approach to the task of adequate description of the solar activity (SA): we explore this process separately on individual scales, with different (and based on available data) requirements for quality of the used series on different scales. Below we conventionally shall use a term "multi-scale approach" to designate such an ideology. Our investigation includes three time scales (and time ranges): 1. A scale from 102 to some hundred years (we use notation SC+2 for it). This time range, since beginning of the XIX century, is supplied, in one or another degree, by regular observations of the Sun (as well as by physical characteristics of the Earth and its atmosphere). Our requirement to these observational data is their adequacy and maximal complexity from the viewpoint of physical description of the process. The time series must be uniform, regular and have a maximal duration. 2. A scale ~103 years (SC+3). On this time interval we cannot rely on regular data with a direct physical interpretation. However, for this interval various sets of indirect data are available, and their accurate and combined interpretation can help us, probably, both to depicture time behavior of the main (sunspots, low-latitude) component of SA and to evaluate a confidence of this representation. This time scale is of fundamental interest for understanding of the physics of solar activity, because on this scale we have a good chance to study extreme manifestations of SA, such as the Maunder minimum, the Late Medieval minimum and so on. 3. A scale ~104 years (SC+4). For this time interval we have available only so called "decade" Stuiver series of radiocarbon concentrations, which indirectly reflect variations of SA through the process of the galaxy cosmic rays modulation by the solar magnetic field (possibility to use long series of berriluim-10 is so far questionable). But if we learn "rules of play" for radiocarbon on the scale SC+3, we shall construct certain estimates of SA behaviour on time scales of approximately 10000 years. This interval is important for us since in this case we


operate with times close to the duration of Holocene, i.e. to time scale of typical large variations of the terrestrial climate. Here we are to make note about the general strategy: in addition to the abovementioned scales SC+2, SC+3, SC+4 for sufficiently full description of SA one should study another scales as well. For example, the scale SC+1 (i.e. ~10 years) is perfectly supplied by observational data (including data of SOHO, TRACE etc.), and for the scales SC-0 and SC-1 there are series of more unique observations. But appealing to such short-term scales qualitatively increases requirements for the observational materials and greatly broadens its volume. Therefore, we restrict ourselves with interpretation of mainly long-term SA dynamics, i.e. with scale > 100 years. Let us regard some of the available data on behaviour of SA on various time scales, not pretending, however, to a completeness of this review. Scale SC+2. Archives that describe SA on this timescale consist of SA data obtained from direct observations of the Sun. These data represent, generally speaking, different space components of the solar magnetic field and, consequently, sufficiently well describe its evolution. It is these data on which various "laws" and "rules" of solar activity are based, such as ones of Schwabe-Wolf, SpЖrer, Gnevyshev-Ohl, Weber, etc. Recently we made attempts to prolong some indices of SA on longer time ranges (up to 150-200 years), which is necessary both for control and for generalization of the today's conceptions of SA. In this connection we can mention our reconstructions of the polar faculae numbers, the total sunspot areas, the average sunspot latitudes, the indices of N-S asymmetry of solar hemispheres. This data are now sited on the server of Pulkovo observatory (http://www.gao.spb.ru/database/esai/), and their description is presented in Appendix. Scale SC+3. This scale, in some sense, is crucial for our consideration. We regard a problem to widen the described above data SC+2 to their characteristic time scale, i.e. 300-1000 years, as one of our main targets. One of ways to solve this problem is construction of mathematical models. In [1] we proposed a nonlinear "Duffing" model of the solar cyclicity and presented a version of Wolf numbers since 11 century AD. In [2] an analogous model for the polar faculae number, since 1700, was proposed (see Appendix). In Fig.1 the last results of modeling of the alternating-sign polar faculae numbers by our Multi-Scale Regression (MSR-) method are presented [3]. In Fig.2 a model series for the average sunspot latitudes, obtained by the same method, are shown. The MSR-method allows uncovering and accounting for possible links between time series that have different correlation for different time scales. It is based on construction of multi-dimensional regression models in the space of wavelet-coefficients, which is followed by a subsequent invert wavelet transform. In short, the idea of the method is as follows. The wavelet-transform of an original series f (t ) is

[Wf ](a, b) = 1 a

-



t -b f (t ) dt a
q

(1)

It produces its expansion in a basis formed by orthogonal stretching and shifts of a base wavelet, which is a function localized both in time and space. A set of values a = 2 , q = 1,2,.., p allows "splitting" of f (t ) into p components, which present various scales and cover the whole frequency range. Let us suppose that we aim to investigate relations between a function Y (t ) and a set of functions X i (t ), i = 1,2,..., m . In accordance with the idea of the MSRmethod, we make wavelet transforms of all these functions (1) and for each of the scales (i.e.


of the components of the wavelet transform) regard the MLS-approximation of possible functional relations

[WY ]( [WY ](

2 q , t ) = F [WX 1 ]( 2 q , t ), [WX 2 ]( 2 q , t ),..., [WX

(

m

](

2q , t ) ,

)

(2)

for example, in this work, in the form of multi-dimensional regression model
q q q 2 q , t ) = c0 + c1q [WX 1 ]( 2 q , t ) + c2 [WX 2 ]( 2 q , t ) + ... + cm [WX q m

Having found the MLS-approximation [WY ] ( 2 , t ), q = 1,2,..., p , we can make the inverse wavelet transform, thereby obtaining a representation of Y (t ) behaviour by means of "factors" X i (t ) , which make, generally speaking, different contributions to the regression for different scales. The rules of construction of multi-dimensional regression models allow estimating the differences of this contribution, and we can tell about confidence of conditionality q of variations of Y (t ) with a scale 2 by variations of X i (t ) . The correlation coefficient between the obtained series Y (t ) and the original one Y (t ) will indicate a success of the approximation (or its failure). The second way to describe SA on the time scale SC+3 is generalization of various indirect data. Let us note that while earlier investigators used for reconstruction of the SA behaviour in the past separate sources of data about it (carbon-14, berrilium-10, aurorae, observed by naked eye sunspots, etc), we believe that only synthesis of these heterogeneous data can provide reliability of the reconstructions. Fig.3 can serve as an illustration of our optimism. In Fig.4 data on variation of long cycles periods (from 70 to 350 years) are brought together (grey areas). These data are obtained by application of the wavelet transformation (Morlet wavelet of sixth order was used) to the radiocarbon series of Stuiver, the aurora series of Kivsky, the observed by naked eye sunspot series [4] and the nonlinear model [1]. The black circles correspond to variations of the corresponding periods for global terrestrial temperatures by Mann [5]. One can see quite good similarity between behaviour of the solar and temperature parameters. Therefore, this picture confirms our belief in conditionality of climatic changes by the solar activity (at least, on large time scales). Scale SC+4. On this time scale, as it was mentioned above, we have available mainly the "decade" series of Stuiver. This series (and its predecessor, a series with the 20-year step) was repeatedly studied. In our study the main attention was focused on the correction of the data for variations of the geomagnetic field and the CO2 concentration (which cause a global trend of the series), as well as on the correction for the reservoir effect by the MSR-method. In Fig.5 the resulting decade Wolf number estimates by the Stuiver series is presented. In Fig.6 these estimates are compared with the observed by naked eye sunspot series [4]. We can see that the agreement of the data is good enough. Therefore, in this paper we applied the "multi-scale" approach to study of the solar activity in the past and presented some recently obtained results. The work was supported by grants of INTAS No. 00-0752, 01-0550, 00-543 (in part), by grant "Astronomy" No. 1105 of Science and Industry Ministry of Russian Federation, by the grant of Russian fund for Basic Researches No. 01-07-90289 (in part), by Program of Presidium of Russian Academy of Sciences "Non-stationary phenomena in astronomy" and by Program of Division for Physical Sciences of RAS No. 16 "Solar Wind".


](

2q , t ) .

(3)


References [1] Yu.A. Nagovitsyn, A Nonlinear Mathematical Model for the Solar Cyclicity and Prospects for Reconstruction the Solar Activity in the Past, Astron. Lett., 23(11), p.742 (1997). [2] Yu.A. Nagovitsyn, Solar activity on the long time scale, in: Proc. of conference "New cycle of solar activity: observational and theoretical aspects", Saint-Petersburg, Pulkovo, 1998, p.321 (in Russian). [3] Yu.A. Nagovitsyn, On relation between geomagnetic AA-index and indices of solar activity (multi-scale regression method), in: Proc. of conference "Solar activity and cosmic rays after solar magnetic filed reversal", Saint-Petersburg, Pulkovo, 2002, p.397 (in Russian). [4] Yu.A. Nagovitsyn, Solar Activity during the Last Two Millennia: Solar Patrol in Ancient and Medieval China, Geomagnetism and Aeronomy, 41(5), p.711 (2001). [5] M.E. Mann, R.S. Bradley, and M.K. Hughes, Northern Hemisphere Temperatures During the Past Millennium: Inferences, Uncertainties, and Limitations, Geophys. Res. Lett., 26(6), 759 (1999). [6] Krivsky L., ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/AURORAE/; Silverman S., ftp://nssdcftp.gsfc.nasa.gov/miscellaneous/aurora/.

Appendix. Description of ESAI database sited on http://www.gao.spb.ru/database/esai/ Extended time series of Solar Activity Indices (ESAI) is a database including observational, synthetic and simulated sets to study solar magnetic field variations and their influence on the Earth. ESAI extend the ordinary lengths of some traditional indices of the solar activity: sunspot areas, Wolf numbers (the equatorial component of magnetic field of the Sun), the polar faculae numbers (the polar component), the mean latitudes and the North-South asymmetry of hemispheres (the location of activity). Series Monthly sunspot areas (Greenwich general system) Yearly sunspot areas (Greenwich general system) for N- and S- hemispheres Yearly mean latitudes of sunspots for N- and Shemispheres Yearly polar faculae numbers (Mt.Wilson general system) for N- and S- hemispheres Yearly Wolf numbers (International general system) Yearly polar faculae numbers (Mt.Wilson general system) Table 1 ESAI monthly sunspot areas (1821-1989), yearly sunspot areas (1821-1994) and yearly mean latitudes of sunspots (1854-1985) were created by compilation of the pre-Greenwich observational data sets (by Schwabe, Carrington, De La Rue, Sporer) and the post-Greenwich Conventional time interval 1874-1976 1874-1976 1874-1976 1906-1991 1700-2002 1906-1991 ESAI time interval 1821-1989 1821-1994 1854-1985 1837-1999 1090-2002 1705-1999


observations (Gnevysheva) to Greenwich general system. Ref: Nagovitsyn Yu. A. The series of total sunspot area index in the Greenwich general system (1821-1989). // "Solnechnye dannye. 1995-1996" Bulletin. PP.38-48. 1997. (in Russian). Yearly polar faculae numbers were constructed by synthesis of different data series: Mt.Wilson, Greenwich, Lyon, Kodaykanal, Tokyo, Zurich, Kislovodsk observations of polar facula and observations of polar coronal structures during solar eclipses. Ref: Nagovitsyn Yu.A. A synthetic series of yearly means of polar faculae numbers for 18471979. // "Solnechnye dannye" Bulletin. No 8. PP. 88-95. 1988. (in Russian). Series of yearly Wolf numbers for 1090-2002. Based on Krylov-Bogolyubov's approach to the description of weakly nonlinear oscillatory processes, the nonstationary frequencyamplitude structure of the Wolf numbers (1700-1995) was analysed. Using the nonlinear description and the well-known Schove's data on epochs of extrema of the 11-yr solar cycles in the past, the yearly average Wolf numbers in 1090-1699 were reconstructed. Ref. Nagovitsyn Yu.A. A nonlinear mathematical model for the Solar cyclicity and prospects for reconstructing the Solar activity in the Past.// Astronomy Letters. Vol. 23. No. 6. PP. 742748. 1997. Yearly polar faculae numbers for 1705-1999 were created by a procedure similar to one used for the Wolf numbers reconstruction (in assumption that 11-yr cycles of the polar faculae develop in exact anti-phase to sunspot cycles). Ref. Nagovitsyn Yu.A. The Solar cyclicity on the large time scale. // Proceedings of conference "New cycle of Solar activity: observational and theoretical aspects". Pulkovo. 1998. PP.321-324 (in Russian). GRAPHICS: Figure 7 shows variations of the mentioned above indices. Time intervals of ESAI-extension of solar activity parameters are marked by the gray colour.


1700
100 50 0

1750

1800

1850

1900

1950

2000

MS R - m o d e l
100 50

- 100
100 50 0 -5 0 - 100 1700 1750

= 0. 92

= 0. 95

Original set

-5 0

0 -50

NP F - s e r ie s

-100 -100 -50 0 50 100

MSR - model

1800

1850

1900

1950

2000

Fig.1. The alternating-sign series of polar faculae numbers and its MSR-model. The reference interval for construction of the model relations is marked by a dashed rectangle.

1100 25

1200

1300

1400

1500

1600

1700

1800

1900

2000

Mean latitudes,

O

20 15 10 5

W
0 200 150 100 50 0 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Fig.2. The MSR-model of the annual average sunspot latitudes (top) and the "Duffing" model of Wolf numbers [1] (bottom).


0

200

400

600

800

1000 1200 1400 1600

SONE

CARS

AURA NOMO

0

200

400

600

800

1000 1200 1400 1600 Years

Fig.3. Comparison of data about SA in the last two millennia obtained from different sources. SONE -- sunspots observed by naked eye [4]; CARS -- variations of the radiocarbon concentration by Stuiver; AURA -- observations of aurorae by Silverman and Kivsky [6]; NOMO -- the nonlinear model [1].

40 0 35 0 30 0 25 0

PERIOD, YRS

20 0 15 0 10 0 50 0

120 0

1400 1 600 Y EARS

1 800

Fig. 4. Variations of periods of long cycles of the solar activity (gray areas) and the global terrestrial temperature (black circles).


100 80 60 40 20 0 -3000

W olf's number

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

Years

Fig.5. The decade estimates of Wolf numbers for the last 5000 years.

0

200

400

600

800 1000 1200 1400 1600 1800 2000 80 60 40

20 15 10 5 0 0 200 400 600

20 0

800 1000 1200 1400 1600 1800 2000

Years

Fig.6. The decade Wolf number estimates by the Stuiver series and the observed by naked eye sunspot series from [4].


Fig.7. Extended time series of Solar Activity Indices (ESAI). Time intervals of ESAIextension of solar activity parameters are marked by the gray colour