Pure and Applied Geophysics (PAGEOPH) Vol. 106-108 (1973/V-VII) Birkhguser Verlag, Basel

Further Studies of Ozone and Sunspots

By JULIUS LONDON and SAMUEL OLTMANS 1)

The primary mechanism for the production of ozone in the atmosphere is through

solar ultraviolet radiation. It has always seemed logical, therefore, to search for evidence of a direct or indirect relationship between variations of indicators of solar activity and of ozone. Suggestions for such relationships date back at least to HuMPImZYS [1] who

reasoned that increased sunspots should result in a decrease of ultraviolet radiation and a corresponding decrease in the production of ozone in the upper atmosphere. At that

time, however, there was very little information about the distribution of ozone in the upper atmosphere and certainly no knowledge of its variations that could be used to test Humphreys' ideas.

Observations of total ozone were made as early as 1905 and by 1925 sufficient routine data had become available so that some preliminary studies could be undertaken of possible relationships between total ozone and sunspots and/or geomagnetic activity

(e.g., DOBSON and HARRlSON [2], CABANNES and DUFAY [3], FOWLE [4]). The statistical results of these investigations were ambiguous and, in some ways, contradictory.

The possibility that variations in total atmospheric ozone follow the sunspot cycle

was also considered by WILLETT [5] who had available to him a set of mean monthly ozone data from a large number of stations throughout the world covering various time intervals during the 26-year period 1933-1959. From his study Willett concluded that a highly negative correlation existed between relative sunspot number and the world- wide average of total ozone with a lag of 1�89 years of the sunspots relative to ozone. (Actually, a higher, positive correlation was computed by him for a lag of 3-4 years, sunspots coming before ozone.) It was found by LONDON and HAURWITZ [6], however, that the results derived by Willett were without statistical significance and could have arisen from a biased treatment of the data.

When two series of data are correlated and one or both of the individual series has a pronounced harmonic variation, it is necessary to remove this :variation from the original series to preclude a spuriously high correlation resulting from the statistical analysis. (Or, alternatively, to evaluate the statistical significance of the results by suitable reduction in the number of degrees of freedom.) An interesting and appropriate

~) Department of Astro-Geophysics, University of Colorado, Boulder, Colorado 80302~ USA. Samuel Oltmans now at ERL, NOAA, Boulder, Colorado, USA.

Further Studies of Ozone and Sunspots 1303

example of such a possible fallacious result can be derived from the data published by

CAMPBELL [7] on the lag correlation of annual sunspot numbers with the annual numbers of publications by S. Chapman (1910-1967). The maximum correlation coefficient for this series is +0.52 (standard error • l ag -1 years (publications follow sunspots). Each series, however, is highly autocorrelated and if the harmonic trend is removed from each series the cross-correlation coefficients at lag -1 is reduced

to -0.074 • and the maximum correlation is now found at a lag o f - 6 years (0.54 • 0.1). This last result, although statistically significant at better than the 1% level, is certainly highly suspect since it is very unlikely that Professor Chapman would

have published related papers with a lapse of 6 years! It is helpful to have some guideline in evaluating the parameters to be used in

considering a statistical analysis o f the probability of an anomalous solar-ozone relationship. These guidelines make use of some assumptions, however tentative, of the physical mechanisms involved in the relationship, and the availability of appropriate

data for the analysis. Solar activity is specifically manifested in characteristic changes in emitted electro-

magnetic radiation (particularly in the extreme shortwave and longwave regions of the solar spectrum) and particle radiation with energies varying from less than 10 KeV to

more than 10 a MeV. The immediate and direct influence of enhancement of EM radiation should be at the sub-solar region in the upper atmosphere, whereas particle streams generally have a delay time of a few hours to severat days and affect the upper

atmosphere, chiefly in polar magnetic latitudes. If sufficient ozone data were available, it would be most reasonable to relate ozone variations above 30 km with various pertinent indices of solar activity. At the same time the data should be grouped geo- graphically to reflect dominant EM or particle influence. These ozone data, however, have not been continuously observed over a long period of time. Indeed, a representative world-wide distribution of total ozone observing stations did not get started until the beginning of the IGY in July, 1957. The only two stations having continuous total ozone observations for more than 20 years are Arosa, Switzerland (since 1932), and Oxford, U.K. (since 1951). Observations of ozone above 30 km are even more sparse.

The following statistical analyses are based on the mean annual total ozone at Arosa and Oxford along with the relative sunspot number since the latter (sunspot number) is the most general indication of solar activity which tends to combine the two physical processes discussed above.

Cross-correlations were computed between the mean annual total ozone at Arosa and annual relative sunspot number for the period 1932-1969 with lags of from -1 0 to +10 years. Similar computations were made for Oxford for the period 1951-1969. An earlier preliminary analysis of the cross-correlation between Arosa ozone and sunspots (1933-1959) resulted in a relatively high coefficient of +0.48 (+0.15) at a lag o f - 3 years. When the series was extended to cover the full period (1932-!,969) the coefficient was reduced somewhat (0.42 • 0.13). If the data pairs were assumed independent (which they were certainly not - as shown below), the correlation between Arosa ozone and

1304 Julius London and Samuel Oltmans (Pageoph,

sunspots for the full period would still be significant at about the 1% level. It was

decided, therefore, to break up the Arosa series into two 18-year subsets to see if there was any statistical difference between the two periods. The computed correlation

coefficients are shown in Fig. 1 as a function of annual lag. In all cases the lag is defined

as the year of sunspots minus the year of ozone.

In the case of the full Arosa series (1932-1969) maximum correlation coefficients are

found at lags - 3 (+0.42) lag +3 (-0.40) and lag +7 (0.42). When the series is broken into

two subsets, (1932-1950) and (1951-1969), the maximum correlation coefficients are

shifted slightly and only positive lags show any statistical significance even at the 5 %

level. Even if the statistical analyses were to hold up, it is difficult to understand the

o.8! - - AROSA ( 1 9 5 2 - 1 9 6 9 ) x ' ' ' •

. . . . . . . . AROSA ( 1952 - 1950) i 0.6 A.----,L AROSA ( 1 9 5 1 - 1 9 6 9 ) z"* 'x !

x - - - - x OXFORD (195~-1969) ..~Z ~X x,... ." t : [ 4 "x ..... ~ :' " /

0 4 ,

\ -7"i "- ~, ,, ' , , "".%

0 .2 ~ " ~ ' ~ "... ~'

o

-o . z ~ " " / ~ \~ " ' "".. ~ ~"'. x' k % x , ~- /

"" ~ / - \ x - ' " ", ". : x �9 ~.. ~... ' , ' k , \ / , : / - 0 . 4 ~.'-: " " ~\ ."':~'.~;~, _ v - "

_ ' % j ~ •

-0 .6

-0 .8

- I 0 - 8 - 6 - 4 - 2 0 2 4 6 8 I0

L A G ( Y E A R S )

Figure 1 Cross-correlation between annual total ozone and annual relative sunspot number

physical meaning of a high correlation with a positive lag since this would imply that sunspot variations somehow follow variations in ozone!

For Oxford the correlation coefficients between total ozone and sunspots are smaller than those computed for Arosa for all lags except +9 and +10 years. Again, it is difficult to assess the physical meaning of strong correlation for positive lags of the data.

The Arosa and Oxford data were also divided into three seasonal groups: winter-spring, summer and fall. There was no obvious pattern in the distribution of correlation

coefficients between seasonal mean total ozone and average sunspots either as a function of season or of serial lag. That is, high and low, positive and negative coefficients were

found during each season with no pronounced cluster of statistically significant correlation coefficients about any particular lag.

As mentioned earlier, a spurious cross-correlation could arise between two sets of data if one or both have a significant autocorrelation. Autocorrelations were computed

Vol. 106-108, 1973/V-VII) Further Studies of Ozone and Sunspots 1305

for lags up to l0 years and are shown in Fig. 2 for annual total ozone at Arosa (a), and

annual relative sunspot number (b), for the entire interval (1932-1969) and for the two sub-intervals (1932-1950) and (1951 1969). For these time intervals, the autocorrelation for sunspots shows a strong 10-year period (slightly shorter than the long time average period &approximately 11 years). The data for Arosa, however, show no such persistent harmonic relationships. Similar analyses for Oxford (not shown here) also indicate no pronounced peak in the autocorrelation curve.

0 . 9 1 , I I f I ~ I I

: : AROSA (1952-1969) 0.8 ........ AROSA (1952-1950)

,~--& AROSA (1951-1969) 0.6

o ~ ,"', --.

I \ \ ' I I ,, I

o ;~.A ...... l r -~'.k k' "~t '., A: r . . 'V ." ~"~4" .f ~ t l : .,' �9 q . : : :

-0.2 "....; 4 �9 : : .'

- 0 . 4 , , t

- 0 . 6

- 0 . 8 (a)

i I ~ l l L L l l 2 4 6 8

0_9 i

0 . 8 ~

06

o41

o zl

r OI

-0"2 1 - 0 . 4

- 0 . 6

- 0 . 8

I , I I 0 0

LAG (YEARS)

F i g u r e 2

."A -" ~-]932-1969 i t

........ ~93z-,9~o / / , , ~ - - ~ , I 9 5 1 - 1 9 6 9 : / f

" l

l

- / : I

. /

( b ) " " "

I L I , I ~ I 4 6 8 I0

Autocorrelation of annual total ozone (a); annual relative sunspot number (b)

Cross-correlations were recomputed, with a harmonic filter applied to the sunspot data. The annual relative sunspot data for the entire period was approximated by the relationship

[2~(t + 4)7 Y(t) = 64.9 + 60cos [ ~ J,

where t = 0 at 1921. The new sunspot series used for the computations was the function Y(t) as given above subtracted from the original series�9 The results of the computed cross-correlation with the harmonic trend removed from the sunspot data are shown in Fig. 3 for Arosa (a) and Oxford (b).

It can be seen that in the case of Arosa, the correlation coefficients are now smaller and the high correlation originally found at a lag of - 3 years has fallen to a value of r = 0.18 4- 0.16 and has no statistical significance. For Oxford, the only correlations for the filtered series that have statistical significance at better than the 5 % level are those for lags - 8 and - 9 years. Curiously, there are some similarities between the curves

1306 Julius London and Samuel Oltmans (Pageoph,

shown in (a) and those in (b) (i.e., the remnant oscillation and the phase lag of the curves involving the original and filtered series). It is difficult to attach any meaning to these

similarities. The results discussed above confirm the view that evidence for the existence of a

significant relationship between mean annual total ozone and annual relative sunspot

number tends to disappear in the noise of the data as more care is taken with the

statistical analysis. This is, of course, not surprising. I f there were some direct relation-

ship, we should expect to find, because of the relatively short time constants involved,

0.8

0.6

0.4

0.2

r o

0.2

-0 .4

-0.6

-0 .8

I t I ' I ~ I ~ I ' I ~ I ' I ~ I ' I i I

: -'~ CROSS-CORRELATION (ORIG, DATA)

,~--i GROSS-CORRELATION WITH A HARMONIC TREND REMOVED FROM THE SUNSPOT SERIES

1 , 1 , 1 , 1 IO - 8 - 6 - 4

�9 i ~ , ~

"., ,,/ \ /

(o)

-2 2 4 6 8 I0

LAG ( Y E A R S )

I i I ~ I b I L I ' ] ' I ' I I ' I i I

OB - : : CROSS-CORRELATION (ORIG. DATA) . ~ - ~ . - - i CROSS-CORRELATION WiTH A HARMONIC

TREND REMOVED FROM THE SUNSPOT / 0.6 ~ . SERIES

\ \ / ! - o.2 p " " i . \

-0 .4 ~ ,,

-0 .6

(b) -0.8

- I 0 - 8 -6 -4 -2 0 2 4 6 8 I0

LAG ( Y E A R S )

Figure 3 Cross-correlation between annual total ozone and filtered annual relative sunspot number (a) Arosa

(1932-1969); (b) Oxford (1951-1969)

Vol. 106-108, 1973/v-vii) Further Studies of Ozone and Sunspots 1307

variations of ozone in the upper atmosphere (above about 30 kin) responding to some

specific aspect o f solar activity. Some such studies relating solar flares to changes in

ozone concentrat ion have been reported in the literature (e.g., STEBLOVA [8],

SCHUURMAN [9]) without definitive results. Variations in total ozone, however, reflect

the important intervention of related stratospheric and tropospheric circulation

processes, thus obscuring any direct link between ozone and solar variability. I f long-

term effects are to be seen (i.e., over many years) then these effects should probably be

much more noticeable in variations in circulation patterns than in total ozone. Short-

period responses, if they existed, could perhaps be detected. Continued observations,

both ground-based and satellite, o f the ozone distribution are providing data for a more

direct approach to the analysis of ozone-solar activity relations. Much more information

on the solar spectrum is needed, however, before any substantial progress is made in

understanding the mechanism of these relationships.

It is well to remember the sound suggestion made by HUMPI-IREYS [1] more than 60

years ago: ' . . . In addition to a careful determination of the solar constant and terrestrial

temperatures during one or more sunspot cycle, it would be well to measure, at the same

time, the accompanying changes in the ultra-violet port ion o f the radiation . . . and to note,

i f possible, the amount Of ozone in the upper atmosphere. ' (Emphasis ours.)

Acknowledgemen t s

Support for the research discussed above came from the Atmospheric Sciences

Section, Nat ional Science Foundat ion, through NSF Grant GA-28688X.

REFERENCES

[1] W. J. HUMPHREYS, Solar disturbances and terrestrial temperatures, The Astrophys. J. X X X l l (2) (1910), 97-111.

[2] Go M. B. DOBSON and D. N. HARRISON, Measurements of the amount of ozone in the earth's atmosphere and its relation to other geophysical condition~, Proc. Roy. Soc. Lond. 110 (1926), 660-693.

[3] J. CABANNES and J. DUFAY, Les variations de la quantit~ d'ozone contenue dans l'atmosphOre, J. de Physique 8 (1927), 353-364.

[4] F. E. FOWLE, Atmospheric ozone: Its relation to some solar and terrestrial phenomena, Smithsonian Misc. Collections 81 (11) (1929), 1-27.

[5] H. C. WILLETT, The relationship of total atmospheric ozone to the sunspot cycle, J. Geophys. Res. 67 (2) (1962), 661-670.

[6] J. LONDON and M. W. HAURWlYZ, Ozone and sunspots, J. Geophys. Res. 68 (3) (1963), 795-801. [7] W. H. CAMPBELL, Correlation of sunspot numbers with the quantity of S. Chapman publications,

Trans. Amer. Geophys. Union 49 (4) (1968), 609-610. [8] R. S. SYEBLOVA, Solar flare effects in the ozonosphere, Geomagnetism and Aeronomy VIII (2)

(1968), 299-301. [9] C.J.E. SCr~UURMANS, The influence of solar flares on the trophospheric circulation, Mededelingen en

Verhandelingen 92 (1969), 1-112.