FINAL REPORT

Application of Solar Max ACRIM Data to Analyze

Solar-Driven Climatic Variability on Earth

Martin I. Hoffert

Principal Investigator

NYU/86-146

NASA Grant NAG 5-503

January 1986

{H&SA-CR-176483) APPLICATION OF SOLAR HAX H86-18890

ACRIM DATA TO AKAIYZE SOLAB-DBIVEN CLIHAI1C

VARIABILITY ON IAB1H Final fie port (New York

Ouiv., New York.) 13 p HC A02/8F AOI Unclas

CSCL 04B G3/47 05305

NEW YORK UNIVERSITY

FACULTY OF ARTS AND SCIENCE

DEPARTMENT OF APPLIED SCIENCE

3
FINAL REPORT

Application of Solar Max ACRIM Data to Analyze

Solar-Driven Climatic Variability on Earth

Martin I. Hoffert

Principal Investigator

NYU/86-146

NASA Grant NAG 5-503

January 1986

NEW YORK UNIVERSITY

FACULTY OF ARTS AND SCIENCE

DEPARTMENT OF APPLIED SCIENCE
THE CORRELATION BETWEEN SUNSPOTS

AND SOLAR IRRADIANCE

Allan Frei

Dr. Martin Hoffert

Zun-Yan Wang

Principal Investigator: Dr. M. Hoffert

NASA contract NAG-5-503

January, 1986
-1-

I. INTRODUCTION

HistoricalIv, associations have been observed between sunspots

and solar activity, and between sunspots and climate. The most

obvious example o-f a possible correlation is the coincidence of

the Maunder minimum EEddy 19763, which was an approximately seventy year period (1645-1715) with scarcely any sunspots, and the

"little ice age", a relatively cold period in Europe (-for historic sunspot data, see CEddy 19SO3). Although the positive

correlation is harder to quanti-fy than the actual existence of

the Maunder minimum itself, other evidence support the idea.

Greenland ice core temperature data CSchove 19833, auroral

numbers CSchove 19833, carbon fourteen data in trees, and historic accounts of coronal activity during eclipses all reinforce

the conclusion that: <1) periods of increased sunspot observations correspond to increased solar activity and increased terrestrial temperatures <ie. the "Medieval Climatic optimum" of the

eleventh to thirteenth centuries); and (2) periods of fewer sunspot observations correspond to decreased solar activity and

lower terrestrial temperatures <ie. the "little ice age",, the

early twentieth century). Eddy C19763 gives a very interesting

discussion of the historical evidence.

Langley Csee Newkirk 19833, in .the late nineteenth century,

attempted to measure solar irradiance over an extended period of

time in order to detect changes. The problem with this and other

early attempts was that ground based measurements are not sufficiently accurate to measure solar irradiance fluctuations, which

are on the order of O.IX. It was not until the Active Cavity

Radiometer Irradiance Monitor (ACRIM) experiment on the NASA

Solar Maximum Mission (SMM) was launched in 198O that continuous

data with precision 0.1% was available CWillson, et al 19813.

Will son CWillson et al. 19813 and Hoyt and Eddy C19833 concluded

that over timescales of days, solar irradiance is inversely correlated to sunspot activity: an increase in daily sunspot activity caused a decrease in solar irradiance. Their observations
-2-

are consistant with current theories, in which energy blocked by

sunspots is temporarily stored in the convective zone.

Energy, temporarily blocked, should eventually be radiated by the

sun. According to mixing length theory the properties of convec—

tive cells at a given depth are characterized by the parameter

a=w/H, where w is the mixing length and H is the pressure scale

height. Current theories predict a thermal relaxation time in

the convective zone of about 1OS years Csee Newkirk 19833. If

this is true, then the inverse correlation between sunspots and

solar irradiance may carry over into yearly timescales.

However, perturbations of solar thermal and magnetic structures

associated with sunspots are still relatively poorly understood.

The depth of temperature perturbations due to sunspots, and the

propagation rate of these perterbations are unknown. If large

scale eddies exist, the convective thermal relaxation time might

be much shorter than 1OS years. If the blocked energy is re—radiated over yearly timescales, then, over this timescale, no

correlation would exist. Historical terrestrial temperatures,

however, and recent solar irradiance data, suggest the possibility of a positive correlation. In any case, the long term relationship between sunspots and solar irradiance is unknown.

Here, we consider the correlation between the number of sunspot

groups and solar irradiance over monthly timescales. At the

outset of these calculations, we believed that we might find a

positive correlation between these two time series, which would

add weight to the theory that turbulence—induced sunspots, over

timescales greater than days, increase solar irradiance. We

found no correlation at all between the number of sunspot groups

and solar irradiance over monthly timescales.
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II. DATA

Monthly averaged sunspot data (covering the period -from January,

198O until December, 1984) was obtained from the High Altitude

Observatory at the National Center for Atmospheric Research in

Colorado. In fig 1 we have plotted the monthly averaged number

of daily sunspot groups. Daily ACRIM/SMM data (covering the same

period), which we converted to monthly averages, was obtained

from Professor Will son at JPL (see fig 2).
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III. DATA ANALYSIS

In -fig 3 we plotted the monthly averaged solar irradiance against

the monthly averaged number of daily sunspots. The data appears

to be randomly scattered. In -fact, we calculated a regression

line through the data using the least squares best fit method.

The standard deviation about the regression line was SD = O.556

(quite large considering that the entire interval o-f irradiance

is 3.0), and the percent o-f variation in irradiance which could

be predicted by a linear -fit was only R2 = 16. IX. This suggests

that, over monthly timescalesT irradiance is not a linear function o-f the number of daily sunspot groups.

We also calculated cross correlation coefficients, R, which compare the deviations about the means in the two time series. A

value of R = +1 implies that the relative magnitudes and the

signs of deviations in one time series about its mean value can

be used to exactly predict the behavior of the second time

series; a value of R = -1 implies that deviations in one data set

correspond in relative magnitude, but are apposite in sign, to

deviations in the other data set. One can predict the behavior

of one time series according to the behavior of the second time

series with a confidence level of <RZX100)2. We introduce the

variable k, which is a time lag. CR(k)D2 is the confidence level

with which we can predict the behavior of one time series at time

t according to the behavior of a second time series at time t+k.

In fig 4 we see correlation coefficients of our two time series

for various time lags. We can predict the fluctuation in solar

irradiance by the number of daily sunspots with a confidence of

only <R=X10O) <= 25%. This is a low correlation. Yet, one interesting feature of the figure is immediately apparent: correlation coefficients for all lag times are positive, and form a very

smooth function. This suggests some similarity between the two

data sets. Actually, this occurs as a result of similarities in

the long term, or yearly, trends, not in the monthly fluctua-
-5-

tions. The yearly trends are important, and we shall discuss

them. For now, though, we shall eliminate the yearly trend from

the data in order to more accurately correlate the monthly fluctuations.

To eliminate the yearly trend, we subtracted the five month running mean from both time series, and correlated, in effect, deviations from the local five month running means. The results,

plotted in fig 5, substantiate our previous result. Monthly

fluctuations in solar irradiance can be predicted by monthly

fluctuations in sunspot—group freguency with a confidence level

of only (R^XIOO) <= Q.O4JC. The two time series do not seem to be

correlated over monthly timescales.

Over yearly timescales, however, there seem to be similarities.

It is important to realize that with only five years of data, no

conclusions can be drawn. However, if yearly averages are considered, then from 198O through 1984: (1) both the solar irradiance

and the average number of daily sunspot—group time series are

monotonically decreasing; (2) the 198O and 1981 values are above

the mean, and the 1983 and 1984 values are below the mean in both

cases. The long term trends appear to be similar. Again, we

emphasize that too few data points are available to make a yearly

correlations we mention these issues for purely speculative pur—

poses.
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V. CONCLUSION

From Will son C19813, and Hoyt and Eddy C19833 we know that over

daily timescales solar irradiance and sunspot activity are inversely correlated. By this we mean that sunspots cause a decrease in solar irradiance.

We investigated the relationship between irradiance and sunspot

groups over monthly timescales. Simple statistical methods (ie.

linear regression, and correlation coefficients) reveal no correlation between the monthly averaged data sets. This leads us to

conclude that over monthly timescales, the number of sunspot

groups and the solar constant seem to be unrelated phenomenon.

The problem of correlating sunspots and irradiance over longer

timescales has yet to be resolved. Although five data points

are insufficient to make a statistical correlation, the trend

seems to show a positive correlation. Woodard and Noyes C19853

point out activity—related changes in the solar radius, possibly

due to variations in the convective zone <ie. the shrinkage of

granulations cells, and dynamo generation of magnetic fields),

which would affect luminosity and explain the correlation. If

the trend continues over the next sunspot cycle, and the physical

mechanism is understood more thoroughly, we might conclude that

over yearly timescales increased sunspot activity is associated

with increased solar irradiance.

This work was supported by NASA contract NAG-5-503.
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REFERENCES

-1- Eddy, J. A. , "The Historical Record of Solar Activity", -from

"The Ancient Sun: Fossil Record in the Earth, Moon, and Meteorites", Pepin, R.O., Eddy J.A., and Merrill, R.B. (ed), Pergamon

Press, 198O

-2- Eddy,J.A.,"The Maunder Minimum", Science, 192:1189-1202, 1976

—3— Hoyt, D.V. , and Eddy, J.A., "Solar Irradiance Modulation by

Active Regions -from 1969 through 1981", Geophysical Researh

Letters, Vol. 1O, No. 7, pp.5O9-512, July, 1983

-4— Newkirk Jr., Gordon, "Variations in Solar Luminosity", Anu

Rev. Astron. Astrophys., 1983, 21:429-67

-5— Schove, D.J. (ed), "Sunspot Cycles", Hutchinson Ross Publishing Company, Stroudsberg, Pennsylvania, 1983

-6— Willson, R.C., et al, "Observations of Solar Irradiance Variability", Science, 211:7OO-7O2, 1981

-7— Woodard, M.F., and R.W. Noyes, "Change of solar oscillation

eigenfrequencies with the solar cycle", Nature, 318:449—450
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