Influences of ozone depletion, the solar cycle and the QBO on the Southern Annular Mode

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 133: 1855 1864 (2007) Published online in Wiley InterScience (www.interscience.wiley.com).153 Influences of ozone depletion, the solar cycle and the QBO on the Southern Annular Mode Howard K. Roscoe a * and Joanna D. Haigh b a British Antarctic Survey, Cambridge, UK b Imperial College, London, UK ABSTRACT: We present results of multiple regressions of the leading mode of atmospheric variability at southern high latitudes: the Southern Annular Mode (SAM). It is regressed against indices with large interannual variability, and one of several trend indices in order to determine which trend term gives the optimum fit. We use SAM in sea-level pressure from station data in order to provide a long time series, from 1957 to 2005. The regression indices are stratospheric volcanic aerosol, solar activity, the quasi-biennial oscillation (QBO), the El Niño Southern Oscillation, together with either a linear trend, or the effective equivalent stratospheric chlorine (EESC) that depletes polar ozone, or ozone mass deficit (OMD) in the Antarctic vortex. We find a statistically significant signal for volcanic aerosol, and, when the solar and QBO indices are represented by their product, a highly significant response to the product. We find a significant linear trend in SAM, but there is a major increase in significance using EESC 2 and a further increase using OMD. We make no direct attempt to identify cause and effect, but if the trend is due to human influence then ozone loss is at least 9 times more likely the principle cause of the trend in SAM than greenhouse gases, although we do not exclude greenhouse gases making a smaller contribution. Monthly and seasonal regressions show a maximum correlation with OMD between December and May (summer and autumn), consistent with previous work on stratospheric change as a cause of change in the troposphere. Copyright 2007 Royal Meteorological Society KEY WORDS SAM; stratosphere; troposphere; ozone hole; Antarctic Received 27 December 2006; Revised 26 July 2007; Accepted 27 July 2007 1. Introduction At extratropical latitudes in the southern hemisphere, the leading empirical orthogonal function (EOF) of variability in geopotential height and zonal winds, throughout the troposphere and stratosphere, is the Southern Annular Mode (SAM) (Limpasuvan and Hartmann, 1999; Thompson and Wallace, 2000), so-called because it takes the form of a pair of near-concentric rings (Gong and Wang, 1999). Over several decades the SAM has shown biases towards more positive values, representing greater latitudinal pressure gradients and stronger zonal winds. The stronger winds are now thought to be responsible for increased summer temperatures in the eastern Antarctic Peninsula, which have led to widespread collapse of ice sheets (Marshall et al., 2006). The trend in SAM has led to speculation that it is responding to changed temperatures and heights in the stratosphere, caused by the ozone hole and propagating downwards to the surface (Thompson and Solomon, 2002), and to increased greenhouse gases (Marshall et al., 2004). Perturbations to temperatures and heights in the stratosphere may also be influenced by natural factors such as * Correspondence to: Howard K. Roscoe, British Antarctic Survey, High Cross, Madingley Road, Cambridge, CB3 0ET, UK. E-mail: h.roscoe@bas.ac.uk volcanic aerosol or solar variability. Possible solar influences were reviewed by van Loon and Labitzke (1994). They concluded that an oscillation in geopotential height, in phase with the 11-year solar cycle, occurs over much of the Northern Hemisphere in both the stratosphere and troposphere. In winter they found that the quasi-biennial oscillation (QBO) modulates the solar signal: by grouping the data according to the phase of the QBO they showed that when it is easterly (QBO-E) the Arctic lower stratosphere is colder when the sun is more active, implying a stronger polar vortex and more positive Northern Annular Mode (NAM), but that the opposite holds during the westerly phase QBO-W. Labitzke (2004) showed that the Antarctic polar vortex is similarly influenced by the solar cycle modulated by the QBO. Other studies of the polar annular modes have suggested that in both northern (Baldwin and Dunkerton, 1999, 2001) and southern (Thompson et al., 2005) high latitudes, anomalies in the stratospheric polar vortex are often followed by similarly signed anomalies in the troposphere. In the southern hemisphere, these events seem robust in their decadal changes in both measurements (Thompson and Solomon, 2002) and models (Gillett and Thompson, 2003), plus in the sole example in 2002 of a sudden warming in Antarctica other than the final warming (Charlton et al., 2005). Although the cause of the mechanisms involved has yet to be established, the Copyright 2007 Royal Meteorological Society

1856 H. K. ROSCOE AND J. D. HAIGH evidence suggests an important route whereby factors affecting the stratosphere might have an impact at the surface. In this paper, we present results of multiple regression analyses of SAM time series from station data against indices that are possible influences. Indices with significant interannual variability are the solar cycle, volcanic aerosol, the QBO and the El Niño Southern Oscillation (ENSO). Factors with longer term trends include changes in well-mixed greenhouse gases and polar ozone loss, possibly represented by stratospheric chlorine loading. The statistical significance of each result is examined in detail, including whether we can attribute trends to ozone loss as opposed to increased greenhouse gases, and whether we can define the seasonality of the trends. 2. Regression models Our approach is the same as that used by Haigh (2003). The regression code (Myles Allen, University of Oxford, UK, personal communication) includes a red-noise model in order to take account of autocorrelation. This is particularly important with monthly as opposed to annual data, as data from adjacent months are often strongly correlated. If so, the number of independent data points is reduced, thereby reducing the number of degrees of freedom, increasing the standard error of the fitted coefficients and reducing the significance of the fit. The regression can be represented by y = X β + u where: y is a rank-n vector containing the series of monthly values of the annular mode X is an n m matrix containing the series of m indices which are thought to influence the data, one of which is a constant term β is a rank-m vector containing the solution the fitted amplitudes of the indices u is a noise term, representing observational error plus variability due to factors other than our chosen indices. The variance and autocorrelation of the noise are estimated from the residual (y X ˆβ, where ˆβ is an estimate of β). A red-noise function (here assumed to be of order 1) is fitted to the residual, then the values of ˆβ and the noise parameters are iterated until the noise model fits within a pre-specified threshold. This process minimises the possibility of noise being interpreted as signal. It also produces the confidence intervals of the resultant β values from a two-sided Student s t-test, taking account of any covariance between the indices. Significance is further assessed using the F test, which examines the sum of squares of residuals explained and unexplained in the regression. For the regression as a whole the value is defined as (see e.g. von Storch and Zwiers, 1999): F = SSR/df R SSE/df E, (1) where: SSR is the regression sum of squares df R is the number of degrees of freedom in the regression (i.e. the number of independent explaining indices, m) SSE is the residual (error) sum of squares, and df E is the number of degrees of freedom in the residual (n m 1) The significance level can be assessed by referring to tables of the F distribution, which depends strongly on m, and on df E at small df E. The significance of an additional index in the regression may be assessed from (von Storch and Zwiers,1999): F add = SSR (regression with m indices) SSR (regression with m 1 indices) SSE (regression with m indices)/df E. (2) By analogy with Equation (2) we assess the significance of replacing one index by another using: F replace = SSR (regression with one index replaced) SSR (regression with original indices) SSE (regression with one index replaced)/df E. (3) A different approach that gives a method to rank regressions with replacement indices is to use the Akaike Infor mation Criterion (AIC). This quantity is based on information theory, and includes the concept of parsimony so that a fit with fewer indices with the same SSE is more highly ranked. Standard textbook treatments derive AIC that can be used to give only a qualitative ranking of possible alternative regression models. Advanced treatments of AIC calculate the relative likelihood of regressions in a formal quantitative way, including replacing one index by another, by means of so-called AIC weights. Following Burnham and Anderson (1998, p.48 and pp.122 124), for any one regression model i, (i.e. set of indices i), wehave AIC = n ln (SSE/n) + 2 (k + 1) i = AIC i 1/2 {min(aic i )} w i = exp ( 1/2 i )/{ r = 1 R exp ( 1/2 r)}, (4) where w i are the AIC weights and R is the number of alternative regression models r considered. The denominator in Equation (4) is a constant for a given suite of regression models, so the AIC weights for the suite sum to unity. Each AIC weight is then the probability of that regression model being the best of the given suite of models.

INFLUENCES ON THE SOUTHERN ANNULAR MODE 1857 3. Regression indices and data sources Here, we discuss the input data, then describe the explaining indices shown graphically in Figure 1. Values of the explaining indices are scaled so that the maximum range of each is unity over the time period of the data, 1957 2005. This allows direct intercomparison of the magnitudes of the derived β values to help assess their relative importance. (1) SAM data Meteorological analyses are used to determine EOFs, but in the data-sparse Southern Hemisphere these are unreliable in the pre-satellite era. However, Gong and Wang (1999) showed that a time series of the difference in sea-level pressure between 40 S and 65 S was highly correlated with a time series of the EOF of sealevel pressure. Hence to derive a surface SAM index back to 1958, Marshall (2003) examined anomalies in sealevel pressure from direct observations, averaged over six locations at about 40 S and six locations at about 65 S. Again, the post-satellite time series was highly correlated with that of the EOF. We use values updated to 2005 and including 1957 (Marshall, private communication). In order to retain seasonal effects, we use the absolute differences in sea-level pressure without monthly normalisation. (2) Long-term trends We use several alternate trend parameters. To represent the long-term increase in greenhouse gases, we use a linear trend. To represent ozone depletion due to chlorofluorocarbons (CFCs) and halons, assumed to be the main cause of stratospheric temperature change in the Antarctic polar vortex, we use an index based on the effective equivalent stratospheric chlorine (EESC, from the European Environment Agency at http://dataservice.eea.eu.int/dataservice/viewdata/view pvt.asp?id=9). Because polar ozone depletion progresses via a reaction involving ClO + ClO, we actually use EESC 2, which is close to the empirical fit by Huck et al. (2005) of (EESC 2 + 0.258 EESC). Ozone depletion can also be represented by directly observed ozone values. In the ozone hole, unlike the smoothly varying EESC, observed ozone has significant interannual variability in the marginal ozone loss conditions of the late 1980s. Then, dynamical effects associated with the QBO modulated the downward supply of chlorine gases to altitudes where they give rise to ozone loss. Using observed ozone therefore has the advantage of separating effects of dynamics on ozone directly, from effects of dynamics on ozone-loss chemistry. Hence it might remove an otherwise false signal from regressions against dynamical parameters such as QBO. We use the mean annual Ozone Mass Deficit (OMD) below 220 Figure 1. Indices used in the regressions. Values were scaled so that the maximum range of each is unity over the time period of the data, to allow direct intercomparison of the magnitudes of their regression slopes (β values).

1858 H. K. ROSCOE AND J. D. HAIGH Dobson units (DU) (updated from Bodeker et al., 2005). OMD is derived from Total Ozone Mapping Spectrometer (TOMS) measurements, with seasonal, latitudinal and trend corrections to fit the available Dobson measurements. OMD cannot be derived before TOMS data started in 1979, and is negligibly small in 1980 and 1981, so we have set it to zero before 1979. True ozone mass deficit is unlikely to be zero then, as examination of EESC 2 shows, but the low value in 1981 is an inevitable result of the choice of the low value of 220 DU as the baseline. (3) Solar activity is represented by the 10.7 cm solar flux from the National Geophysical Data Center, USA at ftp://ftp.ngdc.noaa.gov/stp/solar DATA/. (4) The QBO signal is the zonal wind at 40 hpa over Singapore (Barbara Naujokat, Free University of Berlin, personal communication). (5) The ENSO index is the cold tongue index from the University of Washington at Seattle at http://tao. atmos.washington.edu/data sets/cti/. (6) The stratospheric aerosol loading was constructed by Sato et al. (1993), updated to 2004 at his website http://data.giss.nasa.gov/modelforce/strataer/; here we used a tropical average. (7) We make no assumptions about the seasonal variation of SAM. Our regressions include subtractions of monthly means of the whole time series, which avoids any requirement to use harmonic functions to represent annual and semi-annual cycles (see below). 4. The mixed solar QBO index Labitzke (2004) showed that winter polar stratospheric temperatures in the Southern Hemisphere vary from being in-phase with solar activity (solar activity anti-correlated with annular modes) when the QBO is westerly, but antiphase (solar activity correlated with annular modes) when the QBO is easterly. Hence Haigh and Roscoe (2006) defined a new regression index, composed of the product of the solar and QBO indices, to be used in place of the separate solar and QBO indices: solar QBO = (solar S m ) (QBO Q m ), (5) where S m and Q m were the midpoints of the range of each index, as in Figure 1. This index is similar to the LvL portion of fits to Northern Hemisphere stratospheric meteorology used by Dunkerton and Baldwin (1992). The offsets S m and Q m are arbitrary but the choice of their values influences the compound index. Thus we explored the impact on the regression results of all possible combinations of S m and Q m. We found that the best response (i.e. the maximum value of β) resulted from retaining Q m as the mid-range value, but using the mean valueofsfors m. Although using the mid-range value for S m had resulted in a significant β, usingthemean value increased β by over 50%. The combined index in Figure 1 is the resulting product, rescaled to unity amplitude, and it is this index that has been used in the work discussed below. To investigate the sensitivity of our results to the choices of Q m and S m, we carried out the optimisation of the offsets independently on the two halves of the time series and used the resulting values for regression of the whole data period. We find that use of either of these gives high (t >2.4) significance, and that the β- value is always of greater magnitude than when using the mid-range offsets, so that the choice is not artificially enhancing our results. 5. Results and discussion The regression slopes (β values) and significances for the indices are presented in the Tables. Note that the significances using the t-test are calculated within the regression code, which includes autocorrelation via the noise model. The numbers of degrees of freedom of the F-function, df E, are overestimates because of autocorrelation, which leads to an overestimate of the significances from values of F. However, from standard tables of F, the significance is a very weak function of df E when df E is as large as here, so the overestimate is very small. Unsurprisingly, in each case the largest signal is in the seasonal cycle, represented by the monthly means. Table I shows very high significance for EESC 2, good significance for volcanic aerosol, but poor correlation with solar or QBO indices. When the independent solar and QBO indices are replaced by our multiplicative solar QBO index (Table II), its significance becomes very high. A similar conclusion about the usefulness of a mixed solar QBO index was reached by Dunkerton and Baldwin (1992) for Northern Hemisphere stratospheric data. The timing of the QBO varies with height, so the lack of significance for QBO alone and the good significance of the solar QBO index might depend on the choice of height. To investigate, we repeated the regressions using the Naujokat QBO values as defined at 13 pressure levels between 10 and 90 hpa. For QBO alone, the t-value of the coefficient never exceeds 1.1 the fit is poor for all Table I. Results of multiple regression of SAM (difference in sea-level pressure, 40 S 65 S) from 1957 to 2005, against all indices (see text) plus monthly means of the whole SAM data set. EESC 2c ENSO Volcanic aerosol Solar QBO Regression 2.24 2.14 3.12 0.66 0.53 slope a Significance level (%) b 99.9 87.9 94.9 47.9 42.0 a Indices were normalised to unity amplitude, so regression slope is in units of hpa (as SAM) and the magnitudes of values corresponding to different indices may be compared. b From a 2-sided Student s t-test. c Effective equivalent stratospheric chlorine, associated with ozone depletion caused by halocarbons (see text).

INFLUENCES ON THE SOUTHERN ANNULAR MODE 1859 Table II. As Table I, but replacing separate Solar and QBO indices by our mixed Solar QBO index. Table IV. As Table III, but adding our mixed Solar QBO index, showing its very high significance. Regression slope Significance level (%) EESC 2 ENSO Volcanic aerosol Solar QBO 2.23 1.66 3.72 5.00 99.9 77.7 98.1 99.6 Indices m F add Monthly means, EESC 2, ENSO, Volcanic aerosol Monthly means, EESC 2, ENSO, Volcanic aerosol, Solar QBO 15 16 85.2 choices of height. For the solar QBO index, all data in the range 35 60 hpa give significant results (t >2) our conclusion is not particularly dependent on height, but 40 hpa remains a good choice. Furthermore, Crooks and Gray (2005) derived dual QBO indices from different heights to improve their fit, use of which might give significance to the QBO indices alone, so we repeated regressions using all possible pairing combinations from the 14 levels available, but the t-values never exceed 1.2. The additional significance of including each index sequentially in the regression is explored in Tables III and IV, where once again there is negligible significance for solar or QBO terms independently but very high significance for our mixed solar QBO index. The large significance for adding ENSO without volcanic aerosol in Table III, compared to the modest significance for ENSO in Table I when volcanic aerosol is also included, is probably because of correlation between ENSO and volcanic aerosol indices. Haigh et al. (2005) show correlations between various indices, by far the largest being that between ENSO and volcanic indices with correlation coefficient of 0.326. Tables I III show that SAM has a strong correlation with stratospheric chlorine. Table V gives the results of regressions using various trend-like terms. These have increasing significance going down the Table a linear trend is the poorest, EESC 2 is better, OMD is best. Table III. Values of m a and F add b when adding each index of Table I in turn to our multiple regression of SAM. Standard tables of F for large df E b and this range of m show significance of 90% and 99% if F>1.5 and 2 respectively, so adding each of ENSO, EESC 2 and Volcanic aerosol is highly significant, but adding Solar and QBO indices has negligible significance. Indices m F add Monthly means 12 Monthly means, EESC 2 13 17.2 Monthly means, EESC 2,ENSO 14 6.58 Monthly means, EESC 2, ENSO, Volcanic 15 5.20 aerosol Monthly means, EESC 2, ENSO, Volcanic 16 0.55 aerosol, Solar Monthly means, EESC 2, ENSO, Volcanic aerosol, Solar,QBO 17 0.48 a Number of independent explaining indices, df R = m b See Equation (2), df E = n m 1 exceeds 500. However it is hard to quantify the significance of a direct replacement from this table all significances from t values are high. Hence in Table VI, we show the results using the F replace function defined in Equation (3), and the AIC weights defined in Equation (4). We see that each replacement in turn gives an improvement of high significance, and of much larger AIC weights. Hence we adopt OMD for the trend-like term in the remaining Tables and Figures. In model runs with a variety of external forcings, Arblaster and Meehl (2006) found that changes in stratospheric ozone only gave a trend in SAM of about half the magnitude of that observed from 1958 to1999, while greenhouse gases only also produced about half of the observed trend. We infer from Tables V and VI that if Table V. Regression slopes and significance values of the trend-like index, when also fitting ENSO, Volcanic aerosol and Solar QBO indices as in Table II. Regression slope t-value b Significance level (%) b linear 2.54 3.00 99.72 EESC 2 2.23 3.49 99.95 OMD a 2.75 3.92 99.99 a Ozone mass deficit over the whole of the ozone-hole period, see text. b From a 2-sided Student s t-test. Table VI. As Table IV, but showing the effect of replacing the trend-like index, where values of F replace refer to replacement of the row above (i.e. F replace for OMD refers to replacement of EESC 2 by OMD). Indices m F replace b AIC weights c linear EESC 2 OMD a 16 0.0110 16 4.35 0.1022 16 4.08 0.827 a Ozone mass deficit over the whole of the ozone-hole period, see text. b See Equation (3). c See Equation (4); total is not unity because relative likelihoods from Tables III and IV are included in the suite of possible regression models.

1860 H. K. ROSCOE AND J. D. HAIGH we were to explain the SAM trend as exclusively a result of either greenhouse gas increases or the stratospheric ozone hole, then the ozone hole is much more likely. The ratio of AIC weights shows that it is at least 9 times more likely that it is due to the action of chlorine from CFCs, if they were exclusive alternatives. Unfortunately, we cannot explore the more realistic case of the two effects simultaneously in our regressions because the high correlation between a linear trend and ozone loss produced unrealistically large signals of opposite sign, but we surmise that greenhouse gases make a significantly smaller contribution. Figure 2 shows the fitted terms and the reconstruction of the regression. This reconstruction explains over 30% of the variance, but much of this is due to the seasonal cycle represented by the monthly means, as is clear from Figure 2(b). In some preliminary regressions (not shown), we represented the seasonal cycle by annual and semi-annual cycles. This led to a similarly large variance explained, but necessarily included arbitrary restrictions on symmetry of the seasonal cycle, so on grounds of generality we adopt monthly means. By smoothing the reconstruction and data in Figure 2(c), almost all of this seasonal cycle is removed, so the quality of the fit to (a) (b) remaining terms can be assessed by eye. Formally, all except ENSO have significance exceeding 98%. The dip in SAM in 2002, coincident with much smaller OMD when the ozone hole split in mid-season, is well captured. This probably explains much of the high significance of replacing EESC 2 by OMD. It also indicates the value of separating the effects of stratospheric dynamics alone from that of dynamics on chemistry, discussed above the 2002 ozone hole split was caused by an increase in planetary waves originating in the extra-polar troposphere, not originating in the stratosphere (Newman and Nash, 2005). However, it is clear from the figure that the dip in SAM in the mid 1960s, coincident with the eruption of Agung, is not well represented, whereas that in 1992 from Pinatubo agrees well. Because there was rather more aerosol in the Southern than Northern Hemisphere following Agung, we ran the regression with various latitudinal averages of volcanic aerosol. The results in Table VII show that tropical aerosol has the best significance, but southern hemisphere is an improvement over global aerosol. As shown in Figure 3, the dip in the 1960s is best represented by southern hemisphere aerosol, but the dip in the representation is still of much smaller amplitude than that in the measured SAM. We speculate that tropical aerosol has the best significance because it is the most important for the poleward gradient of heating in the stratosphere, and so of geopotential height, which dominates the strength of the polar stratospheric vortex. Note that the correlation of SAM with volcanic aerosol is negative, unlike that of NAM with volcanic aerosol (e.g. Haigh and Roscoe, 2006). Figure 4 shows the residuals from the fits, with various degrees of smoothing to allow us to search for signs of (c) Figure 2. (a) Regression components due to OMD (black, thick solid), ENSO (blue, thick dashed), volcanic aerosol (purple, thin dashed) and Solar-QBO (red, thin solid) monthly mean values are not shown. (b) Raw data (black, thin line) and value reconstructed from regression (without noise model) (red, faint line). (c) As (b) but smoothed by a triangular filter with FWHM 13 months, and reconstructed data is red, thick line. Units of pressure difference (SAM) are hpa. Note the accuracy of the reconstruction of the monthly mean (seasonal) cycle in (b), whereas the accuracy of reconstruction of the longer-term variability in (c) is less good, though the trend is well reproduced, as are the dip in 1992 due to the eruption of Mt Pinatubo and the dip in 2002 when the ozone hole split. This figure is available in colour online at www.interscience.wiley.com/qj Figure 3. SAM (black, thin line) and reconstructions (red, thick lines) from multiple regressions to monthly mean values, OMD, ENSO and Solar-QBO indices, plus differing latitudinal averages of volcanic aerosol index, each smoothed by a triangular filter with FWHM 13 months. Upper using tropical volcanic aerosol, as in Figure 2(c). Lower using volcanic aerosol in the southern hemisphere only. Units of pressure difference (SAM) are hpa. Note the slight improvement of the fit to the 1960s dip using southern hemisphere aerosol, despite its reduced significance in the regression as a whole (Table 7), though neither reconstruction properly represent the dip. This figure is available in colour online at www.interscience.wiley.com/qj

INFLUENCES ON THE SOUTHERN ANNULAR MODE 1861 Table VII. Multiple regressions of SAM against monthly means, ENSO, Volcanic aerosol, Solar QBO and EESC 2, where the latitudinal averaging of the volcanic aerosol index is changed. Latitudinal average m F replace a Global 16 Tropical (between 15 N and 15 S) 16 2.4 Southern Hemisphere 16 1.7 South of 30 S 16 0 South of 60 S 16 0 a See Equation (3). A value of 2.4 indicates 99% significance to the replacement, 1.7 indicates 95%. other cyclic behaviour, missing from our chosen indices. For example, the Ap index of cosmic ray activity has a similar period to the solar cycle but different phase, and many tropospheric components might have multi-annual cyclic behaviour. No cycles are obvious, although each has variability of period a little longer than the smoothing function, as would be expected from smoothing data with random components. In order to shed light on possible cause and effect, we examine the seasonal variation of the regression fits. We define a separate index for each month from each original index, so that a regression against monthly means plus four indices had 60 parameters instead of the original 16. Comfortingly, the earlier results, of high significance for our mixed solar QBO index, and of the superiority (a) (b) (c) (d) Figure 4. (a) Difference between raw data and reconstruction from the regression indices (as in Figure 2). (b) (d) Residual smoothed by triangular filters of FWHM 7, 13 and 31 months (about 0.6, 1.1 and 2.6 years) respectively. Units of pressure difference (SAM) are hpa. Note there are no obvious cycles in the smoothed residuals.

1862 H. K. ROSCOE AND J. D. HAIGH of the fit with ozone-related trends to the fit with a linear trend, are reinforced in these monthly regressions (Tables VIII and IX). The process was repeated with independent indices for each season (DJF etc.) as well as for each month. Figure 5 explores the monthly and seasonal variation of the β values in detail. The figure reveals that: (1) Monthly means are dominated by something akin to a semi-annual cycle (the semi-annual oscillation of van Loon, 1967), but show seasonal asymmetry hence our earlier decision to avoid the use of harmonic seasonal functions in the fits. (2) Ozone mass deficit has large positive signals in all summer and autumn months, most of >95% significance. This proves the hypothesis of Thompson Figure 5. Monthly (upper panels) and seasonal (lower panels) regression slopes (β values) for each index (solid line), together with ± one standard error (dashed lines). Units of pressure difference (SAM) are hpa. Despite the large variability in the monthly slopes for the ozone mass deficiency (OMD), they clearly maximise between December and May, as reflected in its seasonal slopes.

INFLUENCES ON THE SOUTHERN ANNULAR MODE 1863 Table VIII. As Table IV, but where regression values were found for each month for each index. Tables of F for large df E and m = 60 show significance of 99% if F>1.5, so again addition of the Solar QBO index is highly significant. Indices m F add Monthly means, EESC 2, ENSO, Volcanic aerosol Monthly means, EESC 2, ENSO, Volcanic aerosol, Solar QBO 48 60 18.2 Table IX. As Table VI, but where regression values were found for each month for each index. Note that F replace for OMD refers to replacement of EESC 2 by OMD. For AIC weights, the suite of possible regression models includes those of Tables III, IV and VI, hence the small values here. Indices m F replace AIC weights linear EESC 2 OMD 60 0.8 10 5 60 7.72 0.6 10 3 60 6.67 0.0227 and Solomon (2002), and extends it to a longer period (1957 2005, rather than 1969 2000), to a more complete definition of SAM (pressure differences between 40 S and 65 S, rather than heights south of 65 S), and to a better measure of ozone loss (OMD, rather than geopotential height during the ozone hole). (3) The solar QBO index shows something of an annual cycle with largest effect in autumn. (4) The volcanic aerosol signal is significant only in midwinter. (5) ENSO shows a clear annual cycle but of small amplitude and not statistically robust. It might be supposed that the volcanic aerosol and solar QBO indices should have a stratospheric origin and thus a similar seasonality to OMD. This is not apparent from our results, although detection of these signals is clearly at the limit of what is achievable given the intrinsic noise, due to atmospheric variability, in the SAM dataset. 6. Conclusions We have performed multiple regressions of SAM against possible climate forcing factors, to explore their significance. In order to have an accurate long-term dataset for trend examination in the pre-satellite era, we used a SAM derived from station data of sea-level pressure at 40 S and 65 S. In order to retain seasonal effects, we used un-normalised differences in sea-level pressure. The results of Haigh and Roscoe (2006), that independent solar and QBO indices have negligible correlation with annular modes from meteorological analyses, but a multiplicative solar QBO index has major significance, is confirmed for the SAM station data. When the solar QBO index is optimised, its significance exceeds 99%. Again, this further places the findings of Labitzke and co-workers, concerning the combined influence of solar activity and phase of QBO on polar meteorology, in a statistically robust framework. In the regressions, the signals of stratospheric chlorine and volcanic aerosol have high significance. The ENSO signal is modest, unless ENSO alone is included in the regression because of its correlation with volcanic index. Residuals show no obvious signs of a missing index. Although the significance of a linear trend in the regressions is high, the regressions show that the trendlike term is better represented by the square of effective stratospheric chlorine than a linear trend. The fit is significantly improved again if stratospheric chlorine is replaced by observed Antarctic ozone loss. Although we do not directly address cause and effect by means of model predictions, these results suggest that although it is possible that the trend in SAM could be caused by increased greenhouse gases as represented by a linear trend, it is at least 9 times more likely that it is due to the action of chlorine from CFCs via the stratospheric ozone hole, if we assume that the trend is a result of one of these influences exclusively. We cannot exclude a combination of increased greenhouse gases plus ozone changes as the cause of the trend in SAM, and naturally we cannot distinguish the effects of ozone from any nonlinear effects due to greenhouse gases. Monthly and seasonal regressions show a strong signal of OMD throughout most of the summer and autumn. This is consistent with the findings of Thompson and Solomon (2002), but using data over a longer period, and with more complete definitions of SAM and ozone loss. This seasonal dependence strengthens the case for the stratospheric cause of tropospheric effect as seen in the model predictions of Gillett and Thompson (2003). Acknowledgements We thank Myles Allen for access to the multiple regression code, Gareth Marshall for provision of SAM data from station measurements, and Greg Bodeker for provision of OMD data. Some of the work at Imperial College was supported by the European Space Agency under contract number 18453/04/NL/AR. References Arblaster JM, Meehl GA. 2006. Contribution of external forcings to Southern Annular Mode trends. J. Climate 19: 2896 2905. Baldwin MP, Dunkerton TJ. 1999. Propagation of the Arctic Oscillation from the stratosphere to the troposphere. J. Geophys. Res. 104: 30937 30946.

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