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George C. Mdrshdll Spuce Flzght Center, Hmts Vzlle, a Id Bdma .’ NASA TECHNICAL NASA TM X-53593 MEMORANDUM March 30, 1967 SURVEY OF SOLAR CYCLE PREDICTION MODELS By Jeanette A. Scissum Aero-Astrodynamics Laboratory (CODE) .?a (NASA C~ORTMX OR AD NUMBER) (CATEGORY) NASA I George C. Mdrshdll Spuce Flzght Center, Hmtsvzlle, A Id bdma TECHNICAL MEMORANDUM x-53593 *IA, SURVEY OF SOLAR CYCLE PREDICTION MODELS .* BY Jeanette A. Scissum George C. Marshall Space Flight Center Huntsville, Alabama ABSTRACT As scientists make greater strides toward unfolding the secrets of the activities of the sun, we become more aware of its influence on the activities of the earth. In recent years, a more definite correlation has been found between the number of spots on the sun and the density of the upper atmosphere. Since the lifetimes of satellites in orbit depend upon this density, future plans for space research on these satellites depend upon an adequate forecasting of the sunspot cycle. Some prediction techniques now in existence are presented in this report. Although much literature is available on the solar cycle, the literature on solar cycle prediction is limited. Since many of the techniques are essentially duplicates, an effort is made to present the basic types in terms of procedures and results. As an evaluation of the techniques becomes necessary, the need for greater prediction reliability becomes obvious. The ultimate means to this end is the formulation of an adequate theory on the reason and formation of sunspots. As we try to achieve this, an immediate objective is the synthesis of current ideas and theories on solar activity into a comprehensive theory having a statistically I’ acceptable degree of reliability when applied to prediction. NASA - GEORGE C. MARSHALL SPACE FLIGHT CENTER ." Technical Memorandum X-53593 March 30, 1967 SURVEY OF SOLAR CYCLE PREDICTION MODELS by Jeanette A. Scissum SPACE ENVIRONMENT BRANCH AEROSPACE ENVIRONMENT DIVISION AERO-ASTRODYNAMICS LABORATORY RESEARCH AND DEVELOPMENT OPERATIONS l. TABLE OF CONTENTS Page .. I . INTRODUCTION ........................................... 1 I 11. SUNSPOTS ............................................... 2 2.1 General Characteristics ........................... 2.2 Cyclic Characteristics ............................ 2.3 Fundamental Activity Indices ...................... t 2.4 Theories of Formation ............................. 111 . PREDICTION TECHNIQUES .................................. 5 3.1 Data Analysis ..................................... 5 3.1.1 King Hele's Method ......................... 5 3.1.2 Gleissberg's Method ........................ 8 3.1.3 Superposition Method ....................... 11 3.1.4 Waldmeier's Method ......................... 11 3.1.5 Mayot's Method.. ........................... 16 3.1.6 Lincoln-McNish Method ...................... 16 I 3.1.7 Schove's Method ............................ 17 3.1.8 Mihnis' Method ............................. 19 3.1.9 Shapley' s Method., ......................... 20 3.1.10 Linder's Method ............................ 22 3.1.11 Yule's Method.. ............................ 23 3.1.12 Herrinck's Method. ......................... 24 3.2 Causal Methods.... ............................... 25 3.2.1 Jose's Method .............................. 25 3.2.2 Suda's Method .............................. 30 3.2.3 Bell and Wolbach's Method ................... 30 IV . S.RY ................................................ 31 iii TECHNICAL MEMORANDUM X-53593 SURVEY OF SOLAR CYCLE PREDICTION MODELS SUMMARY 1 .. i As scientists make greater strides toward unfolding the secrets of the activities of the sun, we become more aware of its influence 1 on the activities of the earth. In recent years, a more definite correlation has been found between the riumber of spots on the sun and the density of the upper atmosphere. Since the lifetimes of satel- lites in orbit depend upon this density, future plans for space research on these satellites depend upon an adequate forecasting of the sunspot cycle. Some prediction techniques now in existence are presented in this report. Although much literature is available on the solar cycle, the literature on solar cycle prediction is limited. Since many of the techniques are essentially duplicates, an effort is made to present the basic types in terms of procedures and results. As an evaluation of the techniquns hecomes necessary, the need for greater prediction reliability becomes obvious. The ultimate means to this end is the formulation of an adequate theory on the reason and formation of sunspots. As we try to achieve this, an immediate objective is the synthesis of current ideas and theories on solar activity into a comprehensive theory having a statistically acceptable degree of reliability when applied to prediction. I. INTRODUCTION Mankind has been attracted by the phenomenal activity of the sun since ancient times. The earliest observations were made with the naked eye. Since the invention of the telescope, the sun has been under regular observation with accurate records being kept from the middle of the nineteenth century to the present. Our daily life is influenced greatly by the effects of solar activity. Some of these effects are variations in radio-communication conditions, changes in climatic conditions, polar auroras, and geo- magnetic storms. The effect of sunspots on upper atmosphere density is pronounced. Since the lifetime of orbiting satellites is directly related to the density of the upper atmosphere, experiments with these satellites make it necessary to predict long range solar activity. This is complicated by the limited amount of basic knowledge of solar activity. Within the framework of this restriction, many methods have been derived for predicting the sunspot cycle. This report is a survey of some typical solar cycle prediction techniques found in a search of the literature. 11. SUNSPOTS 2.1 General Characteris tics Sometimes in a particular region on the sun, granulation motions are replaced by more intense motions, setting up a magnetic field in this area on the solar surface. This is known as the birth of an active region. In the photosphere there comes into being a bright compact formation known as a solar facula, which gradually increases in area and brilliance. About 24 hours after the facula forms, a few dark dots called "pores" are observed in the facula. One or more pores then develop into dark regions with dimensions as great as or greater than the earth's diameter. These are called "sunspots,," the characteristic attribute of an active region [l]. The beginning of a new solar cycle is usually marked by the appearance of new spots at high latitudes (30" approximately) on the sun's surface. As the cycle progresses, the spot zone descends toward the equator, reaching about 16" at the cycle maximum and about 8" at the next minimum. Sunspots are encountered in groups in which there are usually two prominent spots - a leading (western) spot and a trailing (eastern) spot. The line joining this pair of spots is generally slightly inclined to the equator. The magnetic fields associated with these spots are often of different polarity. During a cycle, all the leader spots in one hemisphere have one polarity, while the leader spots in the other hemisphere have the opposite polarity. 2.2 Cyclic Characteristics The variation of sunspots with time is well known. On the basis of observations between 1761-1769, Horrebow, a Danish astronomer, was first to discover this phenomenon. Schwabe, on the basis of twenty years of observations, established that solar activity varies with a period of about 10 years. This enabled the director of the Zurich Observatory, 2 Rudolph Wolfe, to set up systematic observ,ations of the variations in sunspot activity. These observations resulted in the discovery of the 11-year sunspot cycle. Wolfe showed that the number of sunspots, the Wolfe number, fluctuates with an average cycle duration of 11.1 years. The length of a cycle can be determined by the interval of time between successive minima or by the interval of time between successive maxima. It has varied from 8 to 15 years in the first case and from 7 to 17 years in the second case. There is a variation also in the heights of the cycles at minimum and maximum. The minima have varied from 0.0 to 11.2 and the maxima have varied from 48.7 to 189.9. Here, the numbers quoted are smoothed mean annual sunspot numbers. This regularity is given much consideration in references 2 and 3. 2.3 Fundamental Activity Indices The number of spots on the sun is not the same at all times. The need for a universal method of measuring the number of spots visible on the solar surface resulted in an introduction by Wolfe in 1849 of the "relative sunspot number," R = K(1Og + f), (1) where f is the number of individual spots and g is the number of groups. The factor K is a number assigned to each individual observer and/or his equipment to reduce the individual sunspot numbers to a cons is tent scale. The relative sunspot number, commonly called the Wolfe number, depends on the visibility conditions, the apparatus used, and the method of observation, as well as on such subjective factors as observer's fatigue and the way in which the sunspots are arranged into groups. It is obvious then, that this index is not entirely objective. How- ever, this is the longest existing series with acceptable results dating back to 1749. This perhaps is the reason, along with high correlation with other geophysical indexes, this index has been preserved. Daily Wolfe numbers are not very significant
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