• Introduction
• Data and spectral decomposition
• Preliminary analysis
• Interannual variability study
• Conclusions
• Acknowledgements
• References

FIGURES

• Figure 1
• Figure 2
• Figure 3
• Figure 4
• Figure 5
• Figure 6
• Figure 7
• Figure 8
• Figure 9
• Figure 10
• Figure 11
• Figure 12
• Figure 13
• Figure 14
• Figure 15
• Figure 16
• Figure 17
• Figure 18
• Figure 19

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To give an objective characteristics of circulation patterns the spectral structure of stratospheric fields is analyzed to compare the long-term behaviour and connections to some extra-terrestrial influence and circulation patterns. Two sources of data became available for this study, reanalyses of geopotential and temperature from Free University in Berlin available in 50, 30 and 10 hPa levels covering unregularly the period of 1976-96 that we have analysed in terms of spherical harmonics and huge database of reanalyses from NCEP, where appropriate spectral coefficients are available for period 1948-now four times per day in 28 levels for vorticity, divergence, temperature, etc. Temporal analysis of significant spherical harmonics is introduced as well as the comparison of their changes with respect to the changes of different sets of solar, geomagnetic and global circulation indices. Quite strong connections to a set of 3extraterrestrial" parameters appear for four trough shape of polar vortex. The natural variability connected to the extraterrestrial influence is studied as well as interannual variability with the emphasis to the QBO and ENSO. The systematic review of the appropriate correlations is presented and attempt to find some special case study is discussed. The influence on the tropospheric circulation is also discussed in terms of coefficients of spherical harmonics.

Introduction

Atmospheric circulation of different scales, as well as the distribution of some trace gases (ozone) is believed to be influenced by solar and geomagnetic activity (van Loon and Labitzke, 1993; Kodera, 1991; Bucha, 1993; BochnÌcek et al., 1993). Many more or less probable explanations of the observed correlations were also given by Tinsley and Dean (1991), Hood (1995) and Hood et al. (1995). These extra-terrestrial factors are often correlated with the parameters describing the oscillations of global atmospheric system such as QBO and ENSO with very impressive results (Baldwin and Dunkerton, 1997, Salby,1995, Labitzke and van Loon, 1988, van Loon and Labitzke, 1993).

As many attempts were made in dealing with connections between the changes in circulation of different scales and interannual factors, such as solar and geomagnetic activity parameters, internal oscillations of the atmospheric system (QBO, ENSO, North Atlantic Oscillations - NAO or others), as many approaches were introduced in these attempts. The standard approach in describing stratospheric fields is the use of the amplitude of the principal zonal wave numbers and their variability, mainly during winter and spring (Naujokat and Labitzke,1993). These parameters are able to reflect polar vortex distorsion or breakdown, and allow us to inspect changes in large-scale stratospheric circulation quickly. But this approach does not include processes of synoptic and sub-synoptic scales whose origins are at lower latitudes. In our previous studies (e.g., Halenka and Mlch, 1996) we analysed the connections between the ozone profile structure and circulation patterns characterized in terms of the standard classification of synoptic types (Gerstengarbe et al.,1993). Even though this approach (based on a subjective classification of tropospheric circulation) does not seem to be convenient for such purposes concerning mainly lower stratosphere circulation, it is capable of providing new insights into this problem through the very close connection between the winter upper troposphere and the lower stratosphere (Petzoldt et al., 1994; Holton and Tan, 1980, 1982). Interesting results concerning changes in synoptic variability have also been presented by Goeber and Hense (1995). Therefore, the need for parameters which are able to encompass a wide range of scales leads to the application of complex decomposition of stratospheric fields by spectral method as shown in Halenka and Mlch (1998). This technique is more complicated in the sense of interpretation, however, it provides a very comprehensive survey of circulation characteristics. Being quite smooth and regular without larger small-scale disturbances, stratospheric fields could be spectrally represented in terms of only a very few significant wave components of low wave numbers. Simple characteristics of the circumpolar vortex might thus become available, which would provide us good possibility of further analysis.

Data and spectral decomposition

We have used the 50, 30 and 10 hPa level of stratospheric geopotential and temperature data of the 21-year period 1976 to 1996 from the Free University Berlin. As daily values were not available regularly every day during whole year, we finally used the monthly means of spectral coefficients. We analyzed all the midnight data in the northern hemisphere at 64 gridpoints on each of 32 Gaussian latitudes. Using the standard algorithm of the spectral method, we applied Fourier decomposition along the Gaussian latitudes and transformation in terms of associated Legendre's polynomials in meridional direction obtaining the spectral coefficients which are generally complex (for detailes see, e.g., Bourke et al., 1977, Haltiner and Williams, 1980, Machenhauer, 1979). It should be pointed out that the decomposition is good enough to provide substantial information about the circulation patterns. For the rhomboidal truncation by wavenumber 7 the comparison of the original field and the field reconstructed from the truncated spectral domain is under 1% of difference for the geopotential and slightly worse for the temperature. Even for truncation by wave number 5 only a very limited area displays a higher error, the difference generally remaining very low.

Most of results presented here is based on this data analysis. Moreover, we used for the analysis a huge database of reanalyses from NCEP as well , where just appropriate spectral coefficients are available for period 1948-now four times per day in 28 levels for vorticity, divergence, temperature, etc. in triangular truncation by wavenumber 64.

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Preliminary analysis

Fig. 1 and Fig. 2 display the annual cycles of some significant wave numbers for geopotential and temperature, respectively. There are some wave numbers where the analog between the field and the spectral representation is straightforward, however, for the other numbers it is rather cumbersome. The behaviour of the ''absolute'' component 1-1 is analogous to the general seasonal cycle of pressure surfaces and temperature in the stratosphere. Further components m-n describe the variation of the polar vortex parameters, m reffering to the number of troughs and ridges (waves) and n to the intensity of the polar vortex. Fig. 3 and Fig. 4 show the interannual variability for the annual mean values of significant wave numbers again for geopotential and temperature, respectively. Here we can clearly see, e.g., the influence of the Mt. Pinatubo eruption in 1991 on some of them, especially as regards temperature (1992 – T 1-3, …, T 2-5, T 3-5, G 2-5 …). The absence of the absolute component 1-1 in both figures is due to appropriate scaling; these wave numbers are presented in Fig. 5 and Fig. 6 for geopotential and temperature, respectively. Typical courses of component 1-1 both for the geopotential and temperature appear to be quite stable, being a little more variable during the warm seasons (northern hemisphere). The double cycle seems to be typical for the other component, e.g. 1-3, apparently with higher variability during the cold seasons (see Fig. 7). This also applies to component 3-3 with its usual maximum in winter and minimum in summer (see Fig. 8, both for geopotential). For NCEP reanalysis we present just simple figures of the courses of wavenumbers of the zeroth and first order in longitude during whole period, i.e. from 1948 to 1997 (see Fig. 9 and Fig. 10). For some of them the well expressed trends can be seen as well as the oscillations which can display QBO, for some of them two regimes seems to be acceptable splitted by around the year 1973.

Figure 1. Annual cycle of significant spherical harmonics components (except wave number 1-1) of spectral decomposition of geopotential height on 30 hPa level.

Figure 2. Annual cycle of significant spherical harmonics components (except wave number 1-1) of spectral decomposition of temperature on 30 hPa level.

Figure 3. Annual means of significant spherical harmonics components (except wave number 1-1) of spectral decomposition of geopotential height on 30 hPa level.

Figure 4. Annual means of significant spherical harmonics components (except wave number 1-1) of spectral decomposition of temperature on 30 hPa level.

Figure 5. Interannual variability of 1-1 spherical harmonics component of spectral decomposition of geopotential height on 30 hPa level.

Figure 6. Interannual variability of 1-1 spherical harmonics components of spectral decomposition of temperature on 30 hPa level.

Figure 7. Interannual variability of 1-3 spherical harmonics component of spectral decomposition of geopotential height on 30 hPa level.

Figure 8. Interannual variability of 3-3 spherical harmonics component of spectral decomposition of geopotential height on 30 hPa level.

Figure 9. Interannual variability of spherical harmonics components based on NCEP reanalysis of vorticity on 50 hPa level (1-1 to 1-6 adequate to previous notation).

Figure 10. Interannual variability of spherical harmonics components based on NCEP reanalysis of vorticity on 50 hPa level (2-1 to 2-6 adequate to previous notation).

Interannual variability study

Based on the monthly values of all spectral coefficients obtained from the reanalyses of Free University in Berlin we tested the variability of the data by means of normalized standard deviations of the coefficients, both for geopotential and temperature. It is plotted in Fig. 11 and Fig. 12, respectively, as a ratio of the standard deviation and the mean for all data from available levels. The high variability can be seen just for low significant wavenumbers, in accordance with the main principles and objections of the method. We also present on similar figures for geopotential the sensitivity of the spherical harmonics components to quasi-biennial oscillations for 30 and 50 hPa levels by means of the ratio between the values for westerly and easterly phase of QBO (see Fig. 13) as well as for variability of these phases by means of the ratio of standard deviations (see Fig. 14).

Figure 11. The variability of the data of FUB by means of normalized standard deviations of the coefficients for geopotential.

Figure 12. The variability of the data of FUB by means of normalized standard deviations of the coefficients for temperature.

Figure 13. The sensitivity of the data of FUB for westerly and easterly phase of QBO for geopotential.

Figure 14. The sensitivity of the data of FUB for variability during the westerly and easterly phase of QBO for geopotential .

Based on the monthly values of some spectral coefficients we analyzed the interannual variability with respect to other available factors as well. We have used both extraterrestrial characteristics and the parameters developed from long-term atmospheric observations. Solar activity in terms of the F10.7 index was available from the National Goddard Data Center, as well as geomagnetic activity data in terms of the AP index. The latter group of factors was created by ENSO – standardized monthly values of the Southern Oscillations index – and QBO characteristics mentioned previously based on standardized monthly Singapore winds at the 30 and 50 hPa levels. Some comparisons, using cross-correlation analysis for geopotential wave number 5-1, are shown in Fig. 15 for solar activity and in Fig. 16 for geomagnetic activity. This served mainly to find some similarities between some coefficients and indices and to estimate the time scale of the potential response of the spectral coefficients to the individual parameters. To avoid the periodicity of the annual cycle, we worked with moving averages with a 12-month span which makes sense mainly for the spectral coefficients, for the series of extraterrestrial indices it yields better results due to lower dispersion. In the further analysis of the regression relations, we have used shifted series regarding the causality of the potential influence, i.e., extraterrestrial parameters as lagged independent variables unlike the other "circulation parameters" like ENSO or QBO, where the "causality" does not seem to have the physical meanings and only criterion of the better correlation may be accepted.

Figure 15. Cross-correlations analysis of geopotential component of wave number 5-1 against solar activity parameter (F10.7) with lag in months.

Figure 16. Cross-correlations analysis of geopotential component of wave number 5-1 against geomagnetic activity index (AP) with lag in months.

We have run numerous experiments with the linear regression model with the significant geopotential and temperature components used as dependent variables, series of extraterrestrial indices and other circulation parameters with the appropriate shifts being independent variables. In some cases it seems to be convenient to test the influence of appropriate temperature component in geopotential regression and vice versa. We have obtained quite good results for some of them although for other wave numbers it seems to be impossible to find any reliable connections. Anyway, the method of the spectral decomposition appears to be useful seeking possible effects in global scale. The systematic analysis will be a subject of further studies, here we will limit ourselves to present quite interesting results of the experiment with the component of wave number 5-1, which corresponds to four trough shape of polar vortex and which manifests very strong dependence.

Table 1 describes the first attempt to estimate parameters of the linear regression model with solar and geomagnetic activity as the only independent variables. It can be seen quite high correlation of such a model with the smoothed data. It is evident the dominant influence of solar activity comparing to geomagnetic activity, which can be confirmed also in Tab. 2, where temperature component of wave number 5-1 is included as well. It should be mentioned that temperature actually is not independent variable with regard to the geopotential and, moreover, our temperature record in data is not complete in 1992, but solar activity still remains the dominant factor of our regression analysis. The results of these experiments are presented in Fig. 17 and Fig. 18 for both modifications of the model, together with standardized residua comparison (see Fig. 19). It should be mentioned here that other circulation parameters do not help to fit better our model to the data, although it seems that some strong events of ENSO could result in higher departures, as well as, e.g., stratospheric warmings. Moreover, concerning the QBO, we have tested the model for QBO positive and negative, i.e., west and east phases, respectively. The results are even better for the first case, the similar model gives correlation 0.967.

Table 1. Linear regression model results for geopotential component of wave number 5-1 (Z51 smoothed by moving average – MA with 12 months span) against solar activity (represented by F10.7 index also smoothed – F10.7_1 and lagged by 45 months) and geomagnetic activity (represented by AP index also smoothed – AP_1 and lagged by 42 months).

Model Summary

Model	R	R Square	Adjusted R Square
a	.878	.771	.770
b	.895	.801	.798

Coefficients

Model	Variable	B	Std. Error	Sig.
a	(Constant)	.113	.002	.000
Ý	LAGS(F10.7_1,45)	-3.349E-05	.000	.000
b	(Constant)	.101	.003	.000
Ý	LAGS(F10.7_1,45)	-3.753E-05	.000	.000
Ý	LAGS(AP_1,42)	1.092E-03	.000	.000

a Predictors: (Constant), LAGS(F10.7_1,45)

b Predictors: (Constant), LAGS(F10.7_1,45), LAGS(AP_1,42)

Dependent Variable: MA(Z51,12,12)

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Table 2. Linear regression model results for geopotential component of wave number 5-1 (Z51) against solar activity (represented by F10.7 measurement), geomagnetic activity (represented by AP index) – similarly as in Tab.1. and temperature component of wave number 5-1 (TZ51 also smoothed by moving average – MA with 12 months span).

Model Summary

Model	R	R Square	Adjusted R Square
a	.884	.782	.781
b	.938	.881	.879
c	.948	.899	.897

Coefficients

Model	Variable	B	Std. Error	Sig.
a	(Constant)	.112	.002	.000
Ý	LAGS(F10.7_1,45)	-3.351E-05	.000	.000
b	(Constant)	7.661E-02	.003	.000
Ý	LAGS(F10.7_1,45)	-2.509E-05	.000	.000
Ý	MA(TZ51,12,12)	.719	.061	.000
c	(Constant)	7.080E-02	.003	.000
Ý	LAGS(F10.7_1,45)	-2.891E-05	.000	.000
Ý	MA(TZ51,12,12)	.651	.058	.000
Ý	LAGS(AP_1,42)	8.470E-04	.000	.000

a Predictors: (Constant), LAGS(F10.7_1,45)

b Predictors: (Constant), LAGS(F10.7_1,45), MA(TZ51,12,12)

c Predictors: (Constant), LAGS(F10.7_1,45), MA(TZ51,12,12), LAGS(AP_1,42)

Dependent Variable: MA(Z51,12,12)

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Figure 17. Linear regression analysis of the geopotential height of 30hPa level, spectral component with wave number 5-1.

Figure 18. Linear regression analysis of the geopotential height of 30hPa level, spectral component with wave number 5-1, improvement by inclusion of appropriate temperature component.

Figure 19. Linear regression analysis of the geopotential height of 30hPa level, spectral component with wave number 5-1, plots of residuals for both the models.

Conclusions

The method presented here seems to be able to describe basic circulation characteristics with a good possibility of further analysis. It can help with evaluation of the effects of phenomena involved in long term analysis in global scale, the responsibility of solar activity on partial circulation pattern, i.e., tendency to 4-trough structure appears to be very strong. The reasons of this dependence are not clear at this moment, the results for other wave numbers do not display such connections, even though some of them are still in quite good correlation. Hopefully the method could be good enough even for daily data to serve as a tool for case study analyses which will be able to investigate the potential of real physical connections better. Both this kind of studies and previous mentioned systematic presentation of long term analyses of all significant wave numbers, as well as for other levels, might move us from this preliminary study to the more detailed analysis with more important conclusions. It should be mentioned here, that NCEP reanalys provides more data, but maybe either with respect to more not even solar cycles or the preference of significance of conection between the solar activity and circulation on northern hemisphere, or both of features, the analysis of the data has not provided us better insight to the problem.

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Acknowledgements

Our thanks for the stratospheric data used in this study go to the Free University Berlin and NCEP. We wish also to express our thanks to the SC&C Company for the support of SPSS software used in the Dept. of Meteorology and Environment Protection. Finally, part of the work was done under support of the project of Charles University Grant Agency B-GEO-97/3. The work was partly supported in framework of research project CEZ: J13/98:113200004 as well.

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