Journalof Atmospheric and Terresrrrul Physics, Vol. 50, No. 3, pp. 197-206, 1988. 0021-9169188 $3.00+ .OO

Printed in Great Britain. Pergamon Press plc

Associations between the 11-year solar cycle, the QBO and the atmosphere. Part I : the troposphere and stratosphere in the

northern hemisphere in winter*

KARIN LABITZKE

Institute of Meteorology, Freie Universitlt Berlin, F.R.G

and

HARRY VAN LOON?

NCARf, Boulder, CO, U.S.A.

(Received in$nalform 25 September 1987)

Abstract-Linear correlations between the three solar cycles in the period 19561987 and high-latitude stratospheric temperatures and geopotential heights show no associations. However, when the data are stratified according to the east or west phase of the quasi-biennial-oscillation (QBO) in the equatorial stratosphere significant correlations result: when the QBO was in its west phase the polar data were positively correlated with the solar cycle while those in middle and low latitudes were negatively correlated. The converse holds for the east phase of the QBO. Marked relationships existed throughout the troposphere too.

No major mid-winter warming occurred in the west phase of the QBO during a minimum in the three solar cycles. In the east phase major warmings tended to take place in the minima of the cycle. Thus the signal of the quasi-biennial-oscillation in the extratropical stratosphere tends to be strengthened in solar minima, and weakened in solar maxima.

INTRODUCTION

Many attempts to prove an association between solar activity and weather and climate on Earth have all too often not survived statistical tests or additional

observations (PITTOCK, 1983). We have made an approach to this controversial subject which yields results that we believe can be related to features of the

circulation in the troposphere and stratosphere and thus open the possibility of physical and dynamical explanation. For this approach, which depends on the quasi-biennial-oscillation in the equatorial strato- sphere (QBO), we can use only the last three solar cycles as the QBO has been defined only since 1952. We shall show that within these three cycles it is prob- able that there was a connection between solar varia- bility and the state of the atmosphere.

HOLTON and TAN (1980) presented compelling evi- dence that the equatorial QBO modulates the mean zonal wind and planetary wave components of the

* This paper is dedicated to the memory of the late Pro- fessor Richard Scherhag, who would have been 80 this year.

7 Visitor at the Freie Universitlt Berlin. $NCAR is sponsored by the National Science Foun-

dation.

geopotential field in the stratosphere in the northern hemisphere in winter. The effect of this modulation is

that the polar vortex in the stratosphere is stronger and colder in the west than in the east phase of the QBO. LABITZKE (1982) examined the temperature of the stratospheric winter vortex in the two opposites of the QBO, using Holton and Tan’s definition of the

phase of the oscillation. In addition to corroborating their results, she pointed out that major mid-winter warmings in the westerly phase of the QBO occurred only during sunspot maxima. LABITZKE (1987) con- firmed this observation for three solar maxima by means of the 30 mb temperature at the North Pole during 17 winters in the west phase of the QBO. In the same paper she showed that the north polar tem- perature at 30 mb is positively correlated with the 11 year sunspot cycle when the QBO is in its west phase, and negatively correlated in the east phase. Therefore, the polar vortex responds during maxima in the solar cycle opposite to what one would expect from Holton and Tan’s study.

In the following we expand LABITZKE’S (1987) paper, and use the classification of the winters given in her table 1, including 1977/1978 which was omitted in her table. Labitzke used the months November-

197

19x K. LABU7.W and H. VAX Lowi

February but further work showed that the largest contribution to the correlation comes from the

months of January and February. We have therefore used only those two months, considering also that Holton and Tan found a marked difference between early and late winter in the response of the planetary waves to the QBO.

DATA

The material analysed below consists of the fol- lowing :

(1) monthly mean temperatures and geopotential heights of the 100, 50 and 30 mbar levels from the maps analysed in the Stratospheric Research Group, Freie Universitat Berlin:

(2) sea level pressure and gcopotcntial heights of the 500 mbar level from the U.S. National Mctcorological Center.

Both sets of data are available at the National

Center for Atmospheric Research, Boulder, Color- ado, and the stratospheric data also at the Metcoro- logical Institute, F.U. Berlin. The observations of the 10.7 cm solar flux are from the World Data Center A, Boulder. Colorado. WC obtained the phase of the QBO from a paper by NAIJJOKA~ (1986), in which the analysis of the oscillation is brought up-to-date until April 1985. The direction of the wind in the levels near 50 mbar was used to determine the phase of the QBO. in line with Holton and Tan.

TEMPERATURE IN TIIE STRATOSPI?ERE

Figure I a shows time scrics of the 30 mbar January-

February average temperature at the North Pole and of the solar flux during the three solar cycles between 1956 and 1987. Thccorrelation coefficient between the 32 winter temperatures and the solar flux in Fig. la is

0.14. However. if one correlates the I7 winters in the west phase of the QBO with the solar flux in the same winters the correlation cocfficicnt is 0.76. Thus, thcs: winters are in phase with the solar cycle as may be seen in Fig. I b. The correlation between the i 5 winters when the QBO was in its east phase is -0.45. These winters arc thus out of phase with the solar cycle (Fig. Ic). The correlation between the 32 winter tem- peratures in Fig. la and the solar cycle is then low because the winters in the cast phase arc out of phase with the solar cycle. in contrast to those in the west phase.

Since the three series in Figs. la-c are the foun- dation upon which we base this study we must cstab- lish the statistical significance of the associations in

Figs. lb and c. The series in Fig. la contains data for 32 winters. We make the null hypothesis (i.c. no correlation exists between the 30 mbar temperature

and the solar cycle) and test for significance at the 95% level using

(see PAMWSKY and BRIER, 1958, p. 92), where N,. is the number of indepcrident samples.. This number was determined through an approach discussed by DAVIS

(I 976) and LIVEZEY and CHL% (1983). which takes into account the autocorrelations in both the tcmpcraturc and solar flux series. Applying this method to the 32 winters in Fig. la, the number of independent samples is reduced to 23. Thus ro5 = 0.43 and WC cannot reject the null hypothesis as r is only 0.14. Even if II, = 32. the null hypothesis could not be rcjccted at the 95% level. The same approach cannot be used for the data in Figs. I b and c because the sampling interval varies. We ask instead the question: how likely is it that a series such as the 30 mb temperatures in Fig. la by being split into two series according to the state of the QBO will follow the solar cycle in the manner of Figs.

lb and c? To answer this question we employ the following Monte Carlo tcchniquc: tirst. the lag-one- year autocorrelation of the tempcraturc series in Fig. la was detcrmincd to be -0.35. Second. 10,000 first- order autorcgressivc series (Markov process) of length 32 were gcneratcd by

7”, = -0.3ST,, , fe,,.

where e is a random number. Third. 17 (I 5) clemcnts were chosen, as in the observed pattern, from each of the 10,000 series to simulate the west (cast) phase of the QBO. Finally, correlations between the solar flux and these chosen elements were calculated. The resulting distribution of these correlations is shownin Fig 2. The circle has a radius of length J(O.76)’ + ( - 0.45) I. Points lying outside this circle are pair correlations which exceed the observed ones

of 0.76 and -0.45. In the simulation of 10.000 scrics shown in Fig. 2 only 25 wcrc outside the circle. In four additional, similar tests at most 40 of the 10,000 series fell outside the circle. This is convincing evidence that our original correlations of 0.76 and -0.45 did not occur by change and it justifcs the approach that we have taken at other atmospheric levels of separating the data according to the phase of the QBO.

WC should like to draw attention to Fig. I b. The

correlation of 0.76 between the west phase and the solar cycle is quite large. If wc assume that each of the winter tcmpcratures arc indcpcndent (i.c. ~1, = 17) this

The I 1 -year solar cycle, the QBO and the atmosphere 1

Solar Flux and 30-mbar NorthPole

P ‘7-------I ’ g ’ T--

bl WEST 250

,= 2501 , u. /

,E 2001-

2

tii 150. z 0

loo-

70 '.

_I ,*, * / !X”cd :** j j , * x , Ai 1956 1960 1970 1980 1990

pci

58

62

66

-58

-62

.78

Fig. I. (a) Time series of the 10.7 cm solar Aux (u&s are IO-” W m ’ 11~ ‘) for (Jan. t Feb.)!2 and of the mean 30 mhar temperature ( C) at the North Pole for (Jan. + Feb.)!?. The squares on the lempcrature curve denote winters in the west phase of the QBO. The asterisks a1 the bottom are the years with major mid-winter warming,. The number of years, the correlation coeetficient between the two series, and the confidence lcvcf are shown too. (b) The solar flux as in Fig. la. The 30 mbar temperature curve at the North Pole for (Jan. + Feb.)/?. is drawn only for the winters m the west phase of the QBO. The asterisks denoto the major mid-winter warmings which occurr4 in the west phase. (c) As (b), hut for the winters in the cast phase of the QBO. The asterisks show the major mid-winter warmings which occurred in the

east phase.

199

200 K. LABITZKE and H. VAN LOON

SCRTTERGRRM: NTRY= I Rl,R2= -0.350 0.000 1.0 , 1 I 1

.8

-1.0 -1.0 -.8 -.6 -.4 -.Z 0 .2 .4 .6 .8 1.0

RI4

Fig. 2. Scatter~am showing the results of one Monte Carlo run as described in the text. The abscissa and ordinate refer to pair correlations corresponding to the west and east phase, respectively. The location of

the observed pair correlation, r, = +0.76 and r, = -0.45 is circled.

correlation is significant above the 99% level. Even if one reduces the number of independent samples by 50% (i.e. np = 9) it is significant at the 95% level.

To determine the variability of this correlation coefficient (0.76) a method called ‘boot-strapping’ (EFRON, 1982) was employed. Briefly, in this approach a series is randomly sampled (with resampling allowed) a large number of times. This information is then used to establish the bounds at a specified confidence limit. After 1000 simulations of the 17

years, 95% of the boot-strapped correlations fell between 0.54 and 0.9 1.

The asterisks in Fig. la denote the occurrence of major mid-winter warmings in January and February. In Fig. lb only those mid-winter warmings are included which took place in the west phase of the QBO, and it is clear that in this phase such warmings happened only during maxima in the solar cycle. No major mid-winter warming was observed in the west phase between 1952 and 1987 when the solar flux

was below about 150x 10m2’ [W mm2 Hz-‘]. The warmings in the east phase (Fig. lc) took place more often during low than during high solar flux: out of

ten major warmings which occurred in the east phase between 1952 and 1987, eight were in solar minima.

Daily maps of the 50 mbar temperature have been analysed in the Stratospheric Research Group since July 1964. In this series of maps are 11 winters in the

west phase of the QBO and nine in the east phase. We have correlated the two-monthly (Jan. + Feb.) mean temperatures at 50 mbar with the solar flux in the same months at points IO” latitude by 10” longitude apart. Figure 3a shows lines of equal correlation coefficient for the west phase and Fig. 3b for the east phase. The areas where the correlation coefficient is significant above the 95% confidence level are hatched, and those above the 99% level are cross- hatched. In the maps to follow we show no isopleths of correlation coefficient but only the areas where the statistical significance exceeds the level indicated.

The 11 -year solar cycle, the QBO and the atmosphere-1 201

50-mbar Temperatures

Fig. 3a. Lines of equal correlation coefficient between 50 mbar temperature and solar flux (10.7 cm) for (Jan. + Feb.)/2 in the years of the west phase of the QBO. Dashed lines are negative correlations. In the hatched areas the statistical significance is above the 95% confidence level (Y = I.961 ,/(n-2)), in the cross-hatch areas above the 99% level (r = 2.58/j@-2)). The number of years is shown in the lower right hand corner. .4 is the position of the station Alert.

Figures 3a and 3b demonstrate that the opposite signs in the east and west phase of the QBO in Figs. 1 b and c are not limited to the region near the North Pole but cover large areas from North America to Siberia. In middle and low latitudes the sign of the

Fig. 3b. As Fig. 3a, but for the east phase of the QBO.

% B ‘-

2 G1

d $ 250.

zoo-

150

100

70

-58-436

* * x, III,,/, ,I!,/lIl~ 1956 1960 1970 1960 1990

Fig. 4. Time series of solar flux (10.7 cm) as in Fig. la and of temperatures for (Jan. + Feb.)/2 in the west phase of the QBO for 100 mbar, 200 mbar and 300 mbar, observed at Alert (position at A in Fig. 3a). The asterisks show the years of major mid-winter warmings in the west phase. At 100 mbar there is only a February value in 1956 and no values

in 1983.

correlation is the opposite of that in higher latitudes, which is also the stratosphere’s pattern of response to, e.g. the southern oscillation and the QBO (VAN

LOON and LABITZKE, 1987). Figure 3a contains only two solar cycles so we sup-

plement the maps with data from a polar station (Alert, 82S”N. 62.3”W) to show that the association extends through one more solar cycle and down into the low stratosphere (Fig. 4). This extension of the relationship into one more cycle is corroborated by the geopotential heights in the following.

GEOPOTENTIAL HEIGHTSIN THE WEST PHASE OF THE QBO

The pattern of correlation between geopotentiai height in the stratosphere and the solar cycle (Figs. 5a-c) is similar to that of the temperature correlations in the same phase of the QBO (cf. Fig. 3a). The height analyses began in 1958 and thus cover one solar cycle more than the temperature analyses. All three strato- spheric levels in Fig. 5 have substantial correlations with the solar cycle over wide areas, and the levels are vertically consistent.

The association with the solar cycle is not limited to the stratosphere. If one groups 500 mbar height and sea level pressure according to the phase of the QBO one also obtains correlation patterns which are

202 K. LABITZKE and H. VAN LOON

Pig. 5a. Lines of equal confidence level for correlations between 30 mbar geopotential height and IO.7 cm solar flux in Jan.-Feb. in the west phase of the QBO, e.g. r for the 99% CL. = 2.58/J(n-2). The number of years in the cor- relations is shown in the lower right hand corner. Dashed

lines are negative correlations.

coherent over large areas and which by their shape hint at connection with the quasi-stationary long waves (Figs. 5d and e). One can recognise the main

traits of the correlation pattern in the stratosphere at the tropospheric level: a region of positive cor- relations almost surrounded by negative correlations. This pattern is, however, not s~rnet~~al about the pole in the troposphere but is offset toward North

50-mbar Heights J+F-West ATT--~.

Fig. 5b. As Fig. 5a, but for 50 mbar.

America. The alternating positive and negative cor- relations in Figs. 5d and e have the shape of a wave train from the eastern Pacific Ocean across North America to the southwestern parts of the Atlantic Ocean.

We add an observed time series from Resolute in the Canadian Arctic where the correlation coefficient in Figs. 5a and e is high. In the station data (Fig. 6) the m-phase relationship with the solar cycle is clear at all three levels.

500-mbar Heights

J+F - West -7---y. ‘;“’

Fig. 5d. AS Fig. 5a, but for 500 mbar. R is the position of the station Resolute.

The 1 l-year solar cycle, the QBQ and the atmosphere--l 203

and temperature and pressure in the troposphere and stratosphere during those northern winters when the phase of the QBU was westerly. In the easterly phase there is a similar association in the stratosphere (Figs. 7a and b) but the sign is the opposite of that in the westerly phase : negative at higher latitudes sur- rounded by positive in middle and low latitudes (cf. Figs. Sa and b). At 100 mbar (not shown) the pattern is the same.

In the troposphere (not shown) the pattern in the east phase is also opposite to that in the west phase.

-Q-L/ +__L-~~ 19

Fig, 5e. As Fig. Sa, but for sea level pressure.

GEOPCYI’ENI’IAL HEIGHTS IN THE EAST PHASE

OF THE QBU

It is thus probable that from the 1950s till the mid- 1980s an association existed between the solar cycle

Fig. 6.

SPECULATION

In this section we speculate on a possible tink in the association between pressure and temperature and the solar cycle. Since the QBO plays a necessary part in the association, and as this oscillation is forced in the equatorial zone, it is natural to examine radiosonde data from the equatorial zone for possible clues.

We use data from Singapore (I .4”N, I039”Ef which has a continuous record over the last two solar cycles that regularly reaches into the lower stratosphere, sup- plemented during the first of the three cycles with data

I-$

+! H E %

“0 ::

++L_% 132

130

S.L.l? I28 1016 - 126

- 124

1012 - 122

1008.

I, I,, I I I& f t I L e I *tf 1956 1960 1970 1980 1990

Time series of s&r fiux f10.7 cm) as in Fig. la and of geopotcntial heighht at 500 mbar mbar and pressure at station Ievei for Resolute (position at R in Fig. 5d).

and 850

204 K. LABITZKE and H. VAN LOON

Fig. 7a. As I&. 5a, but for the east phase of the QBO. Dashed lines are negative correlations.

from Canton Island (2.8%. 171.7”W). It is a question

how much importance one can attach to observations from two stations and for a limited period, but we note that this part is only speculation-intended as a basis for discussion and further probing.

The curve of 50 mbar temperature at Singapore in the northern winter has a strong high-frequency component which we have smoothed by running 3- year means (Fig. Sa); the corresponding curve for Canton Island (2.85, 171.7”W) appears in the early years of the diagram. The smoothed curves are both out of phase with the solar cycle. As the temperature

Fig. 7b. As Fig. 5b, but for the east phase of the QBO.

Temperatures near Equator I, I I I I, I I I I, 4 I I( al SO-mbar Temperatures

i

$7 -66

-67

-68

'200

250

--53

;200

f c: 0150

;a

3 loo

Fig. 8. (a) For (Jan.+Feb&) time series of solar flux (10.7 cm) and of the 50 mbar temperature at Singapore (1.4”N, 103.9”E) and Canton Island (2.8”s. 171.7”W). The temperatures are smoothed by (a+ h + c);3. The parts of the curves which are dashed are likely affected by the eruptions of Agung (1963) and el Chichbn (1982). (b) As (a), but

for 200 mbar temperatures.

at 50 mbar and the height of the tropopause vary inversely, one should expect a higher tropopause in the maxima of the solar cycle and a lower one in the minima, judging by the time series in Fig. 8a. Such a behaviour of the tropopause has in fact been observed by COLE (1975) and GAGE and REID (19811, among others, with data going back to 1951. As the height of the tropopause is related to convection, the tem- perature in the upper half of the troposphere should be out of phase with that in the lower stratosphere- warmed in the troposphere by the release of latent heat in the areas of convection and by the sinking in the regions around the convection. The smoothed time series of 200 mbar temperature from Canton Island and Singapore in Fig. 8 suggest that the tem- perature of the upper troposphere during the 29 years was indeed out of phase with that in the lower strato- sphere on the time scale of the solar cycle.

The 11 -year solar cycle, the QBO and the atmosphere-I 205

The signal in the temperature of the upper tro- posphere-lower stratosphere near the equator in the northern winter may then be that of the solar cycle itself, without regard to the phase of the QBO. In the regions north of 10”N which we show in our analyses, the QBO is clearly part of the signal as the sign of the correlations changes from the west to the east phase of the quasi-biennial-oscillation. A direct effect of the solar cycle on the convection near the equator must therefore be transformed and transmitted out of the tropics by the circulation in the QBO.

From mid-December till the beginning of April the main tropical convection is much nearer the equator than during the corresponding months of the northern summer. Therefore, if convection near the equator is a necessary part of those sunclimate relationships that we have described, the signal in the northern summer, if any, need not be the same as in winter.

CONCLUSION

Our analyses show that during the last three solar cycles the troposphere and stratosphere in the north- ern hemisphere in winter, as high as we have been able to analyse (30 mbar), may have been influenced by solar variability on the time scale of the 11 year solar cycle. One must arrange the data according to the phase of the quasi-biennial-oscillation to be able to discern the association between solar and atmospheric variability. When that is done, one observes that the stratospheric temperatures and geopotential heights in the west phase of the QBO are positively correlated with the solar cycle at higher latitudes and negatively correlated in middle and low latitudes; and conversely in the east phase of the QBO. Statistical tests indicate that these results are unlikely to be owing to sampling. Because the correlation coefficients change from the east to the west phase of the QBO, little or no associ- ation is found with the 11 year solar cycle when one correlates a complete series with it.

Large correlation coefficients are found in the troposphere as well. The correlations are especially marked in the west phase over North America and the adjacent ocean areas.

As mentioned in the Introduction, the signal in the extratropical stratosphere of the QBO proper is a deeper and colder polar vortex in the west than in the east phase of the oscillation (HOLTON and TAN, 1980; VAN LOON and LABITZKE, 1987). This signal is modi- fied by the 11 year solar cycle in the following way. Owing to the lack of major midwinter warmings dur- ing solar minima in the west phase of the QBO, the signal of the QBO is enhanced (Fig. 9, top). It is, however, suppressed during solar maxima in the u’est

I ’ 1

Sotar Maximum (J+F)/2 i

2oo

19591 EAST I / I

SON BO 70 60 5 40 30 20 10

Deviations of SO-mbar Heights from Mean (1958-86)

Pig. 9. Meridional profiles for selected years of the zonally averaged deviations of 30 mbar geopotential height (geopot. m) from the mean of 19581986 for (Jan.+Feb.)/Z. (Top) During minimum of solar flux. (Bottom) During maximum of solar flux. Solid lines are for a year in the east phase of

the QBO and dashed lines for the west phase.

phase of the QBO (Fig. 9, bottom) because of the major warmings in this phase (Fig. lb). In the east phase of the QBO during solar maxima (Fig. 9, bottom), the vortex is colder and stronger than during solar minima (Fig. 9, top).

In other words, the solar cycle at its maximum tends to suppress the extratropical signal of the QBO in the stratosphere whereas it tends to enhance it during solar minima. The response of the QBO in the extra- tropical stratosphere to the solar cycle is expressed schematically in Table 1.

Table 1. The stratospheric polar vortex in winter in the northern hemisphere in the two phases of the QBO. (1) Unmodi~ed; (2) in solar maxima; (3) in solar minima (c$

Figs. 1 b and c)

East phase West phase

(1) Signal of QBO Warm, weak Cold, strong

(2) During solar maxima Cold, strong Warm, weak

(3) During solar minima Warm, weak Cold, strong

206 K. LABITZ~CE and H. VAN LOON

The second part of this study will examine sea ~c~owledgemen~s-We thank D. J. SHEA for ingeniously level pressure, surface air temperature, and the designing and performing the statistical tests and R. A.

long waves in the troposphere and stratosphere in MADDEN for illuminating discussions. W. SPANGLER at

winter. NCAR helped in handling the data and computations and Mrs B. MITSCHKE, FUB, drafted the figures.

REFERENCES

COLE H. P. DAVIS R. E. EFRON B. GAGE K. S. and REID G. C. HOLTON J. R. and TAN H.-C. LABITZKE K. LABITZKE K. LIVEZEY R. A. and CHEN W. Y. NAUJOKAT B PANOFSKY H. A. and BRIER G. W.

PITTOCK A. B. VAN LOON H. and LABITZKE K.

1975 .I. atmos. Sci. 32,998. 1976 J. Phys. Oceanogr. 6,249. 1982 SIAM Monogr. 92 pp. 1981 Geophys. Res. Lea. 8, 187. 1980 J. atmos. Sci. 37,220. 1982 J. met. Sot. Japan 60, 124. 1987 Geoph,s. Res. Lett. 14, 535. 1983 Mon. Weath. Rev. Am. met. Sot. 111,46. 1986 J. atmos. Sci. 43, 1873. 1963 Some Applications of Statistics to Meteorology. 224 pp.

1983 1987

Pennsylvania State University. Q. 3. R. met. Sot. 109,23. Mon. Weath. Rev. Am. met. Sot. 115, 357.