• Baldwin, M., , and T. Dunkerton, 1998: Biennial, quasi-biennial, and decadal oscillations of potential vorticity in the northern stratosphere. J. Geophys. Res., 103 , 39193928.

    • Search Google Scholar
    • Export Citation
  • Båth, M., 1976: Spectral Analysis in Geophysics. Elsevier, 563 pp.

  • Bruhwiler, L., , and K. Hamilton, 1999: A numerical simulation of the stratospheric ozone quasi-biennial oscillation using a comprehensive general circulation model. J. Geophys. Res., 104 , 30;th52530;th557.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T., , and M. Baldwin, 1992: Modes of interannual variability in the stratosphere. Geophys. Res. Lett., 19 , 4952.

  • Fusco, A., , and M. Salby, 1999: Interannual variations of total ozone and their relationship to variations of planetary wave activity. J. Climate, 12 , 16191629.

    • Search Google Scholar
    • Export Citation
  • Gray, L., , S. Phipps, , T. Dunkerton, , M. Baldwin, , E. Drysdale, , and M. Allen, 2001: A data study of the influence of the equatorial upper stratosphere on Northern Hemisphere stratospheric warmings. Quart. J. Roy. Meteor. Soc., 127 , 19852003.

    • Search Google Scholar
    • Export Citation
  • Hadjinicolaou, P., , A. Jrrar, , J. Pyle, , and L. Bishop, 2002: The dynamically-driven trend in stratospheric ozone over northern middle latitudes. Quart. J. Roy. Meteor. Soc., 128 , 13931412.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R., , and H-C. Tan, 1980: The influence of the equatorial quasi-biennial oscillation on the global circulation at 50 mb. J. Atmos. Sci., 37 , 22002208.

    • Search Google Scholar
    • Export Citation
  • Hu, Y., , and K. K. Tung, 2002: Interannual and decadal variations of planetary wave activity and stratospheric cooling. J. Climate, 15 , 16591673.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Kodera, K., , M. Chiba, , and K. Shibata, 1991: A general circulation model study of the solar and QBO modulation of the stratospheric circulation during the Northern Hemisphere winter. Geophys. Res. Lett., 18 , 12091212.

    • Search Google Scholar
    • Export Citation
  • Labitzke, K., 1982: On the interannual variability of the middle stratosphere during the northern winters. J. Meteor. Soc. Japan, 60 , 124139.

    • Search Google Scholar
    • Export Citation
  • Labitzke, K., , and H. van Loon, 1988: Association between the 11-year solar cycle, the QBO, and the atmosphere, I, The troposphere and stratosphere on the Northern Hemisphere winter. J. Atmos. Terr. Phys., 50 , 197206.

    • Search Google Scholar
    • Export Citation
  • Labitzke, K., , and H. van Loon, 1996: On the stratosphere, the QBO, and the sun. Meteor. Z., 5 , 166169.

  • Lean, J., 2000: Evolution of the sun's spectral irradiance since the Maunder Minimum. Geophys. Res. Lett., 27 , 24252428.

  • Naito, Y., , and I. Hirota, 1997: Interannual variability of the northern winter stratosphere circulation related to the QBO and solar cycle. J. Meteor. Soc. Japan, 75 , 925937.

    • Search Google Scholar
    • Export Citation
  • Newman, P., , E. Nash, , and J. Rosenfeld, 2001: What controls the temperature of the Arctic stratosphere during the spring? J. Geophys. Res., 106 , 1999920010.

    • Search Google Scholar
    • Export Citation
  • O'Sullivan, D., , and M. L. Salby, 1990: Coupling of the quasi-biennial oscillation and the extratropical circulation in the stratosphere through planetary wave transport. J. Atmos. Sci., 47 , 650673.

    • Search Google Scholar
    • Export Citation
  • O'Sullivan, D., , and R. Young, 1992: Modeling the quasi-biennial oscillation's effect on the winter stratospheric circulation. J. Atmos. Sci., 49 , 24372448.

    • Search Google Scholar
    • Export Citation
  • Quiroz, R., 1981: Period modulation of the stratospheric quasi-biennial oscillation. Mon. Wea. Rev., 109 , 665674.

  • Salby, M., , and P. Callaghan, 2000: Connection between the solar cycle and the QBO: The missing link. J. Climate, 13 , 26522662.

  • Salby, M., , and P. Callaghan, 2002: Interannual changes of the stratospheric circulation: Relationship to ozone and tropospheric structure. J. Climate, 15 , 36733685.

    • Search Google Scholar
    • Export Citation
  • Salby, M., , P. Callaghan, , and D. Shea, 1997: Interdependence of the tropical and extratropical QBO: Relationship to the solar cycle versus a biennial oscillation in the stratosphere. J. Geophys. Res., 102 , 2978927798.

    • Search Google Scholar
    • Export Citation
  • Soukharev, B., , and L. Hood, 2001: Possible solar modulation of the quasi-biennial oscillation: Additional statistical evidence. J. Geophys. Res., 106 , 1485514868.

    • Search Google Scholar
    • Export Citation
  • Tung, K., , and H. Yang, 1994: Global QBO in circulation and ozone. Part II: A simple mechanistic model. J. Atmos. Sci., 51 , 27082721.

  • van Loon, H., , and K. Labitzke, 1994: The 10–12 year atmospheric oscillation. Meteor. Z., 3 , 259266.

  • WMO, 1987: Atmospheric ozone: Assessment of our understanding of the processes controlling its present distribution and change. World Meteorological Organization Rep. K., 648 pp. [Available from NASA, Office of Mission to Planet Earth, Two Independence Square, 300 E. Street SW, Washington, DC 20546.].

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Number of months between Nov and Feb during which 30;chmb uEQ is westerly and easterly, as a function of year. Adapted from the RAOB analysis of Salby and Callaghan (2000)

  • View in gallery

    Anomalous wintertime tendency (Sep–Feb) of 70-mb temperature at 90°N (solid), as a function of year. Superposed is the wintertime-mean 50-mb equatorial wind uEQ (dashed), averaged over the same months

  • View in gallery

    Running 3-yr cross correlation between the records in Fig. 2 (solid). Superposed is the 10.7-cm solar flux Fs (dashed), lagged by 1 yr; cTFeb–Sep, uEQ] in year n then corresponds to Fs one year earlier in year n − 1

  • View in gallery

    As in Fig. 3 but for the wintertime tendency of 100-mb temperature at 45°N

  • View in gallery

    Anomalous wintertime tendency of temperature (contoured), as a function of latitude and pressure, operating coherently with 50-mb uEQ and Fs. Shaded are significance levels of 99% and higher. Anomalous temperature during individual winters follows by scaling values by the product of anomalous Fs and anomalous uEQ during those winters (each normalized); see text

  • View in gallery

    As in Fig. 5 but for anomalous wintertime tendency of zonal wind

  • View in gallery

    Anomalous wintertime tendency of 30-mb height operating coherently with 50-mb uEQ and Fs

  • View in gallery

    Wintertime tendency of 30-mb height (mean + anomaly) for equatorial easterlies and extrema of Fs. (Note: the wintertime tendency is negative throughout)

  • View in gallery

    As in Fig. 3 but for the instantaneous cross-correlation between the wintertime tendency of 70-mb temperature at 65°N, lagged by 15 yr, and 50-mb temperature over the North Pole

  • View in gallery

    Instantaneous cross-correlation between the wintertime tendency of 20-mb height at 90°N, lagged by 7 yr, and 100-mb height over the equator (solid). Superposed is the record of Fs lagged by 4 yr (dashed)

  • View in gallery

    Anomalous wintertime tendency of height (contoured), as a function of latitude and pressure, operating coherently with the 100-mb height over the equator and Fs

  • View in gallery

    Instantaneous autocorrelation, for a lag of 21 yr, of the wintertime tendency of 30-mb height at 32°N (solid). Superposed is the record of Fs lagged by 5 yr (dashed).

  • View in gallery

    Instantaneous power of 20-mb height tendency at 78°N, ‖ΔZFeb–Sep202 (solid). Superposed is the record of Fs lagged by 6 yr (dashed)

  • View in gallery

    Anomalous wintertime tendency of height (contoured), as a function of latitude and pressure, associated with amplitude modulation that operates coherently with Fs

  • View in gallery

    Fraction of the stochastic ensemble that produces correlations to Fs exceeding 0.40 (solid), as a function of lag between the field variable and the reference time series. The net probability, integrated over lag, is less than 10%. Superposed is the fraction of the stochastic ensemble that produces correlations to Fs exceeding 0.40 jointly under all shifts of the 4-decadal records by 1, 2, 3, 4, and 5 yr (dashed); see text. The net probability, integrated over lag, is then less than 0.001%

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 155 155 3
PDF Downloads 12 12 1

Evidence of the Solar Cycle in the General Circulation of the Stratosphere

View More View Less
  • 1 University of Colorado, Boulder, Colorado
  • | 2 Atmospheric Systems and Analysis, Broomfield, Colorado
© Get Permissions
Full access

Abstract

NCEP reanalyses are used to isolate systematic variations in the stratosphere that operated coherently over the last four decades with the 11-yr variation of UV irradiance. Only a small systematic variation is visible at low frequency, which would reflect a simple linear response that drifts with solar flux, Fs. However, a systematic variation manifests itself prominently at high frequency, which involves changes between neighboring years. Corresponding to interannual variability, the systematic variation at high frequency reflects a more complex, nonlinear response to the 11-yr variation of UV irradiance. It is analogous to a similar variation found earlier in the quasi-biennial oscillation (QBO) of equatorial wind, uEQ.

Interannual variability undergoes a frequency modulation that systematically alters its phase during winter, when planetary waves couple the polar and equatorial stratosphere. The polar-night vortex is then sensitive to equatorial wind, which itself varies systematically with Fs. Monte Carlo simulations indicate that the systematic variation of wintertime phase is highly significant.

The systematic variation appears prominently in the wintertime tendency of temperature, which is coupled directly to the residual mean circulation. In fact, the anomalous wintertime tendency operating coherently with Fs has the same basic structure as that operating coherently with anomalous forcing of the residual circulation. Each reflects anomalous downwelling over the Arctic that is compensated at lower latitude by anomalous upwelling. The resemblance of these anomalous structures suggests that the systematic variation at high frequency enters through changes of the residual circulation.

Accompanying the variation of zonal-mean structure is a systematic amplification and decay of wavenumber 1 at high latitude. It represents a poleward advance and retreat of the critical region, or surf zone, where planetary waves experience strong absorption that forces residual motion. This variation of wave structure, along with the anomalous residual motion it forces, parallels the systematic variation of equatorial wind. Wintertime-mean uEQ suggests a reversal of anomalous downwelling between solar min and solar max, one broadly consistent with the observed reversal of anomalous temperature.

Corresponding author address: Dr. Murry Salby, University of Colorado, Campus Box 311, Boulder, CO 80309

Abstract

NCEP reanalyses are used to isolate systematic variations in the stratosphere that operated coherently over the last four decades with the 11-yr variation of UV irradiance. Only a small systematic variation is visible at low frequency, which would reflect a simple linear response that drifts with solar flux, Fs. However, a systematic variation manifests itself prominently at high frequency, which involves changes between neighboring years. Corresponding to interannual variability, the systematic variation at high frequency reflects a more complex, nonlinear response to the 11-yr variation of UV irradiance. It is analogous to a similar variation found earlier in the quasi-biennial oscillation (QBO) of equatorial wind, uEQ.

Interannual variability undergoes a frequency modulation that systematically alters its phase during winter, when planetary waves couple the polar and equatorial stratosphere. The polar-night vortex is then sensitive to equatorial wind, which itself varies systematically with Fs. Monte Carlo simulations indicate that the systematic variation of wintertime phase is highly significant.

The systematic variation appears prominently in the wintertime tendency of temperature, which is coupled directly to the residual mean circulation. In fact, the anomalous wintertime tendency operating coherently with Fs has the same basic structure as that operating coherently with anomalous forcing of the residual circulation. Each reflects anomalous downwelling over the Arctic that is compensated at lower latitude by anomalous upwelling. The resemblance of these anomalous structures suggests that the systematic variation at high frequency enters through changes of the residual circulation.

Accompanying the variation of zonal-mean structure is a systematic amplification and decay of wavenumber 1 at high latitude. It represents a poleward advance and retreat of the critical region, or surf zone, where planetary waves experience strong absorption that forces residual motion. This variation of wave structure, along with the anomalous residual motion it forces, parallels the systematic variation of equatorial wind. Wintertime-mean uEQ suggests a reversal of anomalous downwelling between solar min and solar max, one broadly consistent with the observed reversal of anomalous temperature.

Corresponding author address: Dr. Murry Salby, University of Colorado, Campus Box 311, Boulder, CO 80309

1. Introduction

The circulation of the stratosphere varies from one year to the next. The interannual anomaly (deviation from the climatological average) is closely related to changes of the residual mean circulation (Fusco and Salby 1999; Newman et al. 2001; Hu and Tung 2002). Forced by planetary waves, the residual circulation regulates wintertime temperature through downwelling and adiabatic warming. It also regulates wintertime ozone through poleward transport from its chemical source in the Tropics. Interannual changes of North Polar temperature TNP and Northern Hemisphere ozone are, in fact, strongly coherent with anomalous forcing of the residual circulation (ibid.; Salby and Callaghan 2002; Hadjinicolaou et al. 2002). The latter is characterized by the change of upward Eliassen–Palm (EP) flux from the troposphere, which measures the anomalous momentum transmitted upward by planetary waves.

An analogous influence is exerted by the quasi-biennial oscillation (QBO) of equatorial wind uEQ (Holton and Tan 1980; Labitzke 1982). It too operates coherently with interannual changes of TNP. The QBO determines the position of the critical line (u = 0), where planetary waves experience strong absorption that forces residual motion. Inside the “critical region” or so-called surf zone (found poleward of the critical line), planetary waves become nonlinear, producing horizontal mixing that limits the size and strength of the vortex. By displacing the critical line, the QBO modulates the residual circulation, along with properties that it controls (O'Sullivan and Salby 1990; O'Sullivan and Young 1992; Tung and Yang 1994; Bruhwiler and Hamilton 1999). Equatorial westerlies remove the critical line into the summer hemisphere, favoring a polar-night vortex that is anomalously cold and strong. Conversely, equatorial easterlies advance the critical line into the winter hemisphere, favoring a vortex that is anomalously warm and weak and one that is routinely disrupted by stratospheric warmings (Labitzke and van Loon 1996; Naito and Hirota 1997).

Jointly, changes of upward EP flux from the troposphere and of equatorial wind represent anomalous forcing of the residual circulation. These two influences account for much of the interannual variance of wintertime temperature and ozone (Salby and Callaghan 2002). In fact, the structure of anomalous temperature bears the imprint of the residual circulation: a signature of anomalous downwelling and adiabatic warming over the winter pole, compensated at lower latitudes by a signature of anomalous upwelling and adiabatic cooling.

The involvement of the QBO opens the door to an auxiliary influence. The 11-yr variation of solar irradiance assumes increased importance in the upper stratosphere, where ozone heating involves wavelengths shorter than 200 nm. Unlike longer wavelengths, UV irradiance at short wavelengths changes significantly between solar min and solar max (e.g., WMO 1987; Lean 2000). Implied are analogous changes of ozone heating, which shapes thermal structure and the global circulation. A signature of such changes is, in fact, inherent in wintertime polar temperature (Labitzke and van Loon 1988, 1996). An 11-yr variation emerges conspicuously when TNP is stratified against the equatorial QBO—even though no systematic variation is evident in the raw record of polar temperature.

A clue to the origin of such changes comes from the equatorial QBO, which itself varies with solar activity (Quiroz 1981; Salby and Callaghan 2000; Soukharev and Hood 2001). Equatorial wind in the lower stratosphere undergoes a systematic modulation of frequency, one that tracks the 11-yr variation of UV irradiance. Near solar min, the downward migration of westerlies and easterlies, characteristic of the QBO, stalls. This prolongs the duration of westerlies below 30 mb and easterlies overhead, reducing the QBO's frequency. The systematic modulation of frequency influences how long uEQ of one sign is maintained during winter, when planetary waves disturb the polar-night vorted and make it sensitive to equatorial wind.

During winter, midlatitude westerlies support planetary wave propagation, which couples the polar and equatorial stratosphere. Those months comprise the “disturbed season,” when the vortex is weakened by stratospheric warmings. Figure 1 plots, as a function of year, the number of winter months during which 30-mb uEQ is westerly and easterly [adapted from the RAOB, analysis of Salby and Callaghan (2000)]. Near solar min (in the middle of the decades), uEQ of one sign persists throughout the winter season: It occupies all four months of the disturbed season; uEQ then persists with opposite sign throughout the next winter season. Wintertime-mean uEQ thus alternates between opposite extremes—biennially. However, near solar max (near the beginning of each decade), equatorial wind changes sign during the winter season: uEQ of one sign occupies only part of the disturbed season. Equatorial wind is thus both westerly and easterly during one winter season and likewise during the next. Wintertime-mean uEQ is then weak and it changes only gradually between consecutive years.

The polar vortex during late winter is shaped by planetary waves and their interaction with equatorial wind throughout the preceding months of winter. The systematic variation of uEQ between solar min and solar max should then produce an analogous variation of the polar-night vortex. According to Fig. 1, wintertime-mean uEQ favors a biennial swing in the state of the vortex near solar min, but a more gradual variation near solar max.

Interannual changes of the polar-night vortex are, in fact, punctuated by a biennial oscillation (BO). Corresponding to a frequency of 0.50 cpy, the BO is manifested in TNP, as well as in potential vorticity (PV) (Salby et al. 1997; Baldwin and Dunkerton 1998). Both reveal a component that alternates between consecutive winters. The BO, in fact, accounts for almost as much interannual variance of TNP as the QBO. It is separated in frequency from the QBO (which has a mean frequency of 0.41 cpy) by 0.09 ≅ 11 yr−1. The BO is closely related to signatures of the solar cycle. If it is filtered out, evidence of a systematic 11-yr variation disappears.

Below, we employ a long record of National Centers for Environmental Prediction (NCEP) reanalyses to isolate systematic variations of the stratospheric circulation and determine what relationship they have to the 11-yr variation of UV irradiance. Following a description of the data and various analyses, sections 3 and 4 identify systematic variations that operated coherently over the last four decades with solar activity. Section 5 then validates those variations against Monte Carlo simulations.

2. Data and analysis

a. The atmospheric record

Daily reanalyses from NCEP between 1955 and 2000 provide records of the global circulation upward to 10 mb (Kalnay et al. 1996). Those records describe behavior over four complete decades, plus additional years that are used to bolster statistical confidence (section 5). They have been consolidated into monthly mean records of temperature, height, and wind. The resulting 3D distributions are used to isolate changes that varied systematically over four decades.

The analyzed fields derive from a wide range of operational measurements. They are based initially on ground-based RAOBs that are distributed nonuniformly over the earth. In later decades, they also include satellite measurements, which have complete horizontal coverage but limited vertical resolution. The observations are married with a forecast model, from which the analyzed 3D distributions are produced.

Analysis error (e.g., introduced by changes in the operational network and the introduction of satellites) limits the accuracy of the NCEP record. However, such error can only interfere with systematic variations. It cannot produce them. A definitive assessment of analysis error is made difficult by the heterogeneous nature of the data and analysis procedure. Instead, we appeal to the deterministic nature of UV irradiance, which varies predictably over the four decades. In tandem with Monte Carlo simulations, this feature is used to establish the reliability of systematic variations that operate coherently with solar flux Fs. The deterministic nature of UV irradiance enables the confidence in such variations to be increased dramatically (section 5).

b. Analysis for systematic variations

A systematic variation can manifest itself at low frequency (LF), where it appears as a gradual drift of a field property ψ(t) that simply tracks Fs(t). This represents a direct or linear response to the 11-yr variation of UV irradiance. A systematic variation can also manifest itself at high frequency (HF). Involving changes between neighboring years, the high-frequency component will be treated synonymously with “interannual variability.” The dependence on Fs is then more complex, representing a generally nonlinear response to the 11-yr variation of UV irradiance (e.g., Dunkerton and Baldwin 1992). It can occur through interaction with the annual cycle, for example, through a mechanism that is restricted to winter months (Salby et al. 1997). At high frequency, a systematic variation can assume the form of an amplitude modulation and/or a frequency modulation of interannual variability (e.g., like the one in Fig. 1 manifested by the equatorial QBO).

Such changes are considered separately by decomposing the 3D record of the property ψ into low- and high-frequency components:
ψtψLFtψHFt
The decomposition is achieved by applying a 3-yr running mean 〈 〉 to annual records of ψ(t). It constitutes a low-pass filter that discriminates to periods longer than about 5 yr (see, e.g., Båth 1976), which defines
ψLFtψt
The deviation from the 3-yr running mean then represents the rest of the variance. It constitutes a high-pass filter that discriminates to periods shorter than about 5 yr, which defines
ψHFtψtψt
When added, ψLF and ψHF account for all of the variance. Consequently, they decompose ψ into changes operating on long and short time scales.
Each of these components is subjected to a variational analysis that isolates systematic variations and relates them to the 11-yr variation of UV irradiance. The analysis is applied to diagnostics χ of low- and high-frequency variance. A diagnostic of LF variance is provided directly by ψLF(t). For HF variance, diagnostics are considered for both amplitude modulation and frequency modulation. Amplitude modulation is described by the 3-yr running deviation
i1520-0442-17-1-34-e2
where Δt = 1 yr and extrema refer to values over the three neighboring years. Then ‖ψHF‖(t) measures the instantaneous amplitude of interannual variability. Frequency modulation is described by the running cross-correlation between ψHF(t) and a reference time series Γ(t): c[ψHF, Γ](t). The reference time series is chosen to reveal how ψHF depends upon another field property, for example, how temperature depends upon equatorial wind, which influences the residual circulation. In this capacity, Γ(t) serves as an interannual clock, against which the phase of ψHF(t) is measured. Then c[ψHF, Γ](t) represents the cosine of the instantaneous phase between the two records. Like the amplitude of interannual variability, it varies over the four decades.

Collectively, the diagnostics χ(t) = ψLF(t), ‖ψHF‖(t), and c[ψHF, Γ](t) account for the major forms of systematic variation through which the 11-yr variation of UV irradiance can manifest itself: a linear response at low frequency, as well as a nonlinear response at high frequency. Each has been subjected to a variational analysis that isolates, in the 3D NCEP record, interannual changes which operate coherently over the four decades with solar activity. For an individual diagnostic χ(t), the analysis first evaluates the corresponding time series at each longitude, latitude, and pressure, and likewise over all possible seasons. It then calculates, over all possible lags, the correlation between χ(t) and the record of solar flux Fs(t). The analysis isolates those locations, seasons, and lags for which the diagnostic χ(t) is strongly correlated to Fs(t).

The structure of changes operating coherently with Fs over four decades is composited by renormalizing the correlation between the diagnostic χ and Fs:
ψ̂xcχ,Fsxψ21/2x
where x refers to position and 〈ψ21/2 to the corresponding variance of either ψLF or ψHF. In (3), c[χ, Fs] represents the projection of χ(t) onto Fs(t). If χ equals the running correlation c[ψHF, Γ](t), which measures the instantaneous phase of ψHF(t) relative to the reference time series Γ(t), then c[χ, Fs] represents a double projection of ψHF: first onto the reference time series Γ(t) and then onto the solar time series Fs(t).

The composite structure defined by (3) describes changes of ψ for which the diagnostic χ(t) = ψLF(t) or ‖ψHF‖(t) or c[ψHF, Γ](t) tracks the 11-yr variation of Fs. For LF variability, the composite structure describes the change of ψ that simply drifts with the systematic variation of Fs. For HF variability, it describes the change of ψ associated with an amplitude or a frequency modulation of interannual variability, one that likewise varies systematically with Fs.

A signature of the 11-yr variation of UV irradiance emerges prominently in the HF component. The LF component also evidences a systematic variation. However, it is comparatively weak, limited chiefly to the highest levels in the analyses. For this reason, the presentation here concentrates on interannual variability, represented in the HF component.

3. Frequency modulation of interannual variability

Operating on periods shorter than 5 yr, the HF component includes variance associated with the QBO and BO. It therefore describes dynamical changes that alternate between neighboring years. A systematic modulation of such changes is particularly noticeable in the “wintertime tendency” of dynamical structure, for example, in
TFeb–SepTFebTSep
Unlike temperature itself, ΔTFeb–Sep is coupled directly to the residual circulation through adiabatic warming, which forces the tendency of temperature in the thermodynamic equation. The wintertime tendency, in turn, determines TNP during late winter (often used as a proxy for the vortex during individual years).

a. Relationship to equatorial wind

Figure 2 plots, as a function of year, the wintertime tendency of 70-mb temperature over the Arctic, ΔTFeb–Sep (solid). The raw annual record exhibits no systematic drift or modulation of amplitude. However, its power spectrum (not shown) contains a peak at 0.50 cpy. It is analogous to the signature of the BO in the monthly record of temperature (Salby et al. 1997). Superposed in Fig. 2 is the annual record of 50-mb uEQ (dashed), averaged over the same months. It alternates sign between neighboring years, reflecting the QBO. Like ΔTFeb–Sep, uEQ exhibits little evidence of a systematic long-term variation.

Consider now the instantaneous phase of ΔTFeb–Sep relative to uEQ, which then serves as the reference time series. Figure 3 plots the running correlation between the records in Fig. 2 (solid). Despite the apparent absence of long-term changes in the individual records, their instantaneous correlation varies systematically on the time scale of a decade: cTFeb–Sep, uEQ](t) swings from −1.0 in the middle of the decades (ΔTFeb–Sep out of phase with uEQ) towards +1.0 around solar max (ΔTFeb–Sep in phase with uEQ), in each of the 4 decades. In fact, cTFeb–Sep, uEQ](t) tracks the record of 10.7-cm flux (dashed). For a lag of 1 yr, it has a correlation to Fs of 0.84, which is highly significant.

Near solar min, the correlation between ΔTFeb–Sep and uEQ is negative. It reflects a polar-night vortex that is anomalously warm (ΔTFeb–Sep > 0) during QBO easterlies (uEQ < 0), but one that is anomalously cold (ΔTFeb–Sep < 0) during QBO westerlies (uEQ > 0). The relationship between ΔTFeb–Sep and uEQ during those years is consistent with the dependence of the vortex on the critical line. However, near solar max, the relationship reverses, as first reported by Labitzke and van Loon (1988). During those years, the correlation between ΔTFeb–Sep and uEQ is positive. It reflects a polar-night vortex that is anomalously warm (ΔTFeb–Sep > 0) during QBO westerlies (uEQ > 0), but one that is anomalously cold (ΔTFeb–Sep < 0) during QBO easterlies (uEQ < 0). The relationship between ΔTFeb–Sep and uEQ during those years is inconsistent with the dependence of the vortex on the critical line.

The origin of the systematic variation in Fig. 3 can be traced back to the raw time series (Fig. 2). In the middle of the decades, ΔTFeb–Sep varies out of phase with uEQ. However, in the late 1950s, it misses a beat. Then ΔTFeb–Sep becomes temporarily in phase with uEQ. A similar phase transition occurs in the late 1960s–early 1970s, in the late 1970s–early 1980s, and again in the late 1980s–early 1990s. Notice that, at certain times, ΔTFeb–Sep alternates between consecutive years. It changes almost biennially in the middle 1960s, in the middle 1970s, and again in the middle to late 1980s. Those are the same years when the correlation between ΔTFeb–Sep and uEQ approaches −1.0 (i.e., near solar min).

The relationship between ΔTFeb–Sep and uEQ is consistent with the expected dependence on the critical line near solar min, when equatorial wind of one sign persists throughout the winter season (Fig. 1). Wintertime-mean uEQ is then strong and positive during one year, but strong and negative during the next. The swing between extreme values produces a large quasi-biennial displacement of the critical line about its climatological-mean position.

On the other hand, the relationship between ΔTFeb–Sep and uEQ is inconsistent with the expected dependence near solar max, when the equatorial wind reverses during the winter season. Wintertime-mean uEQ is then weak. In particular, it is shifted towards an equatorial wind of opposite sign: Wintertime-mean easterlies near solar max are thus westerly relative to conditions near solar min, when easterlies persist throughout the disturbed season. Accordingly, the wintertime-mean critical line is removed equatorward of its extreme poleward position, found during easterly winters near solar min. Analogous reasoning applies to wintertime-mean westerlies. Near solar max, the critical line is advanced poleward of its extreme equatorward position, found during westerly winters near solar min.

The systematic variation of uEQ favors a vortex during easterly winters that is colder near solar max than near solar min. Likewise, it favors a vortex during westerly winters that is warmer near solar max than near solar min. The reversed dependence is implied by a weakening of wintertime-mean uEQ near solar max when the equatorial wind changes sign during the disturbed season (Fig. 1). In fact, near solar max, wintertime-mean uEQ, integrated upward over 30–10 mb, actually reverses: Column-integrated uEQ then assumes sign opposite to uEQ at 50 mb (see Salby and Callaghan 2000, Fig. 9). It is on uEQ inside a deep overlying layer that the 70-mb ΔTFeb–Sep depends (through the so-called downward control principle). Formally, this dependence also involves altitudes above 10 mb (e.g., Gray et al. 2001), which lie beyond the range of conventional measurements and NCEP reanalyses. Nonetheless, the reversal of uEQ at 30–10 mb suggests that anomalous ΔTFeb–Sep at 70 mb should also reverse near solar max: ΔTFeb–Sep should then become anomalously cold when the 50-mb uEQ is easterly and anomalously warm when the 50-mb uEQ is westerly. Polar temperature, which changes out of phase with 50-mb uEQ near solar min, should then change in phase with 50-mb uEQ near solar max.

Behavior analogous to that in Fig. 3 is found at lower latitude. Figure 4 plots the instantaneous correlation between the wintertime tendency of the 100-mb temperature at 45°N and 50-mb uEQ averaged over the same months. At this latitude, cTFeb–Sep, uEQ](t) also varies coherently with solar activity—but out of phase. It has a correlation to Fs of −0.74, likewise highly significant. As cTFeb–Sep, uEQ](t) over the Arctic is positively correlated to Fs (Fig. 3), the systematic variation of ΔTFeb–Sep at high latitude is compensated at lower latitude by a systematic variation of opposite sign.

At both high and low latitudes, cTFeb–Sep, uEQ](t) undergoes a decadal swing between −1.0 and +1.0. This systematic variation leads to a cancellation in the overall correlation between temperature and equatorial wind. When calculated over all four decades, the correlation between ΔTFeb–Sep and uEQ is close to 0.

Figure 5 plots the structure of anomalous ΔTFeb–Sep (contoured) operating coherently with 50-mb uEQ and Fs, along with the corresponding significance (shaded). It has been composited according to (3) with χ = cTFeb–Sep, uEQ]. Anomalous temperature during individual years then follows by scaling values in Fig. 5 by the product of anomalous Fs and anomalous uEQ during those years (each normalized).

Anomalous temperature over the Arctic is highly coherent with uEQ and Fs (significant at the 99.99% level). According to the above scaling, it is strong and positive during winters when Fs < 0 and uEQ < 0 (which leaves the sign of ΔTFeb–Sep in Fig. 5 unchanged). Then ΔTFeb–Sep reflects a warmer vortex during easterly winters near solar min when uEQ < 0 persists throughout the disturbed season (Fig. 1). Wintertime-mean easterlies are therefore strong. The critical region, which limits the size and strength of the vortex, is then advanced deep into the winter hemisphere. Implied is intensified downwelling and adiabatic warming at high latitudes, consistent with anomalous temperature.

The same behavior, however, is also implied during winters when Fs > 0 and uEQ > 0 (which likewise leaves the sign of ΔTFeb–Sep in Fig. 5 unchanged). Then ΔTFeb–Sep reflects a warmer vortex during westerly winters near solar max, when uEQ reverses during the disturbed season. Wintertime-mean westerlies are therefore weak, in fact, reversed at higher levels. The critical region is then advanced poleward of its position during westerly winters near solar min. Implied is intensified downwelling and adiabatic warming at high latitudes, likewise consistent with anomalous temperature.

At subpolar latitudes is anomalous temperature of opposite sign. Although weaker, it too is highly coherent with uEQ and Fs. Anomalous temperature is negative from midlatitudes of the winter hemisphere, across the Tropics, and into the subtropics of the summer hemisphere. There, ΔTFeb–Sep reflects intensified upwelling and adiabatic cooling during winters when Fs < 0 and uEQ < 0. Corresponding to easterly winters near solar min, the intensified upwelling compensates intensified downwelling over the Arctic that is found during those winters. The same behavior is also implied during winters when Fs > 0 and uEQ > 0. They correspond to westerly winters near solar max, when uEQ reverses during the disturbed season.

Anomalous temperature in the Arctic stratosphere exceeds 6 K. This is comparable to the systematic variation of temperature that is recovered when TNP is stratified against the QBO (Labitzke and van Loon 1988). Both are almost as large as the full rms variation of wintertime temperature. They can be understood from the systematic phase shift of interannual variability represented in Fig. 3. Interannual variability includes variance from the QBO. It undergoes a systematic modulation of phase that tracks the 11-yr variation of Fs (e.g., Fig. 1). When windowed to winter months, the QBO's phase then drifts with Fs: gradually passing from the westerly extremum to the easterly extremum. In this manner, the QBO can introduce a systematic variation in wintertime TNP that is as large as the full rms variation—even though no systematic variation in amplitude or baseline is evident.

Anomalous ΔTFeb–Sep in Fig. 5 has the same basic structure as that found to operate coherently with anomalous forcing of the residual circulation (see Salby and Callaghan 2002). For each, anomalous temperature is strong and positive over the Arctic, where it reflects intensified downwelling and adiabatic warming. Compensating it at subpolar latitudes is negative anomalous temperature, which reflects intensified upwelling and adiabatic cooling. Although weaker, that structure is consistent with the residual circulation and the wider area over which upwelling occurs. The resemblance between these anomalous structures suggests that the systematic variation of ΔTFeb–Sep, which operates coherently with both uEQ and Fs, enters through a modulation of the residual circulation.

Changes of thermal structure in Fig. 5 are, through thermal wind balance, related to changes of zonal wind. Undergoing a similar systematic variation is the wintertime tendency of zonal wind ΔuFeb–Sep. The correlation cuFeb–Sep, uEQ](t) varies coherently with Fs, but out of phase at high latitude. This makes it out of phase with cTFeb–Sep, uEQ](t) at high latitude. Hence, cuFeb–Sep, uEQ] ≅ +1.0 near solar min and ≅−1.0 near solar max, just opposite to the variation in Fig. 3.

Figure 6 plots the anomalous wintertime tendency of zonal wind operating coherently with the 50-mb uEQ and Fs. As before, anomalous wind during individual years follows by scaling values by the product of anomalous Fs and uEQ during those years. Anomalous wind at polar latitudes is highly coherent with uEQ and Fs (significant at the 99.99% level). It is strong and negative during winters when Fs < 0 and uEQ < 0. Then ΔuFeb–Sep reflects a weakening of the polar-night jet during easterly winters near solar min when uEQ < 0 persists throughout the disturbed season (Fig. 1). The behavior is consistent with warmer temperature over the Arctic during those winters (Fig. 5). The same behavior, however, is also implied during winters when Fs > 0 and uEQ > 0. Then ΔuFeb–Sep reflects a weakening of the jet during westerly winters near solar max when uEQ reverses during the disturbed season. Wintertime-mean equatorial westerlies are therefore weak, in fact, reversed at higher levels. The critical region is then advanced poleward, implying intensified downwelling and adiabatic warming at high latitudes.

At subpolar latitudes, the wind anomaly is also highly coherent, but reversed. Positive anomalous wind reflects a weakening of easterlies that lie equatorward of the Aleutian high; it plays a key role in the dynamics of the polar-night vortex. Anomalous westerlies lie equatorward of the Aleutian high, whereas anomalous easterlies lie poleward of it. These opposing changes of zonal wind flatten its gradient at middle and high latitudes. They reflect a poleward shift of the critical region where the PV gradient is weak and planetary waves experience strong absorption, which in turn forces residual mean motion.

Figure 7 plots, as a function of longitude and latitude, the anomalous wintertime tendency of the 30-mb height operating coherently with the 50-mb uEQ and Fs. The correlation cZFeb–Sep30, uEQ](t) varies coherently and in phase with Fs at high latitude, making it in phase with cTFeb–Sep, uEQ](t). Hence, cZFeb–Sep30, uEQ](t) ≅ −1.0 near solar min and ≅+1.0 near solar max, as in Fig. 3. As for the zonal-mean structure, anomalous height during individual years follows by scaling values in Fig. 7 by the product of anomalous Fs and uEQ during those years.

Anomalous ΔZFeb–Sep30 is strong and positive over the Arctic, approaching 350 m, during winters when Fs < 0 and uEQ < 0. These conditions correspond to easterly winters near solar min when uEQ < 0 persists throughout the disturbed season (Fig. 1). Wintertime-mean easterlies are then strong, producing a wintertime-mean critical region that is advanced deep into the winter hemisphere. Positive anomalous ΔZFeb–Sep30 over the Arctic during those years opposes the wintertime deepening of the polar trough, favoring a vortex during late winter that is anomalously weak. Similar structure is recovered by grouping winters according to uEQ and Fs (van Loon and Labitzke 1994).

The same behavior, however, is also implied during winters when Fs > 0 and uEQ > 0. These conditions correspond to westerly winters near solar max when uEQ reverses during the disturbed season. Wintertime-mean westerlies are therefore weak, in fact, reversed at higher levels. The critical region is then advanced poleward, implying intensified downwelling and adiabatic warming at high latitudes.

Flanking the vortex over the date line is a negative wave anomaly. It opposes the wintertime amplification of the Aleutian high, at least at midlatitudes. However, north of the Arctic Circle, the Aleutian high is reinforced by positive ΔZFeb–Sep30. Jointly, the opposing anomalies in Fig. 7 favor an Aleutian high that is weakened at midlatitudes and amplified at high latitudes. They represent a poleward shift of wavenumber 1. The behavior is analogous to a poleward shift of wave activity found in a GCM (Kodera et al. 1991), albeit under exaggerated radiative forcing. Here, the observed displacement appears to be related to a systematic variation of the annual cycle and its influence on the critical region.

Wavenumber 1 is shifted poleward during winters when Fs < 0 and uEQ < 0. Found near solar min, those are winters when uEQ < 0 persists throughout the disturbed season (Fig. 1). This produces wintertime-mean easterlies that are strong and a critical region that is advanced deep into the winter hemisphere. Nonlinear mixing then damps wavenumber 1 at midlatitudes. Conversely, the poleward advance of wave activity inside the critical region amplifies wavenumber 1 at high latitudes.

The same behavior is also implied during winters of Fs > 0 and uEQ > 0. Found near solar max, those are winters when uEQ reverses during the disturbed season (Fig. 1). They produce wintertime-mean westerlies that are weak, in fact, reversed at higher levels, and a critical region that is likewise advanced poleward. The Aleutian high should then also experience a poleward shift, with wavenumber 1 weakened at midlatitudes and amplified at high latitudes.

The wintertime reversal of uEQ near solar max implies different behavior during early and late winter. Even though uEQ during late winter is westerly, behavior during early winter should resemble that of easterly years. This is just what is found for winters grouped near solar max (van Loon and Labitzke 1994, their Fig. 10).

Surrounding the vortex in Fig. 7 is a collar of negative anomalous height. It modifies the meridional gradient, which characterizes the edge of the vortex. Bounding the vortex to its south is the critical region, where nonlinear mixing flattens the height gradient and limits the size of the vortex. According to Fig. 7, the meridional gradient is steepened near 30°N, where anomalous ΔZFeb–Sep30 decreases northward. However, the gradient is flattened near 60°N, where anomalous ΔZFeb–Sep30 increases northward. These changes imply a critical region that is advanced poleward during winters of Fs < 0 and uEQ < 0, when equatorial easterlies persist throughout the disturbed season. The same behavior is implied during winters of Fs > 0 and uEQ > 0, when equatorial wind reverses during the disturbed season. During both winters, the poleward shift of the critical region should be accompanied by a weakening of planetary waves at midlatitude and an amplification at high latitude.

Figure 8 compares the full tendency (mean + anomaly) of the 30-mb height during easterly winters at extrema of Fs. (Note: the wintertime tendency is negative throughout.) Years when Fs < 0 and uEQ < 0 (Fig. 8a) correspond to easterly winters near solar min when uEQ < 0 persists throughout the disturbed season. The vortex is then anomalously weak. It is displaced out of polar symmetry by an Aleutian high that invades the Arctic. Analogous structure is represented in PV (not shown), wherein the vortex is small, weak, and distorted. Straddling the pole in Fig. 8a are opposing height anomalies. Low and high values of ΔZFeb–Sep30 represent an amplification of wavenumber 1 at high latitude, accompanied by a poleward advance of the critical region.

Years when Fs > 0 and uEQ < 0 (Fig. 8b) correspond to easterly winters near solar max when uEQ reverses during the disturbed season. The vortex is then anomalously strong. It is left nearly in polar symmetry by an Aleutian high that, while amplified at midlatitudes, scarcely crosses the Arctic circle. Increased zonal symmetry over the Arctic represents a weakening of wavenumber 1 at high latitude, accompanied by an equatorward retreat of the critical region.

b. Relationship to other field variables

The systematic modulation of interannual variability reappears at particular lags of the field property (e.g., ΔTFeb–Sep) relative to the reference time series uEQ: at lags of 5–6 yr, 10–12 yr, etc. Reflecting multiples of half a solar cycle, those lags also recover a systematic variation of phase. Like the variation in Fig. 3, it operates coherently with Fs. That phase variation is associated with dynamical structure very similar to the structure in Figs. 58.

Analogous behavior emerges if the phase of interannual variability is referenced against time series other than uEQ. Figure 9 plots, for a lag of one and a half solar cycles, the running correlation between ΔTFeb–Sep at 50 mb over the Arctic and North-Polar temperature at 50 mb, which then serves as the reference time series. Here, cTFeb–Sep, TNP] (solid) swings systematically from −1.0 towards +1.0 in each of the four decades. It operates coherently with Fs (dashed). The behavior in Fig. 9 does not explicitly involve uEQ. Consequently, it represents a systematic variation within temperature itself. Analogous behavior is recovered by high-pass filtering TNP to the QBO and BO, which likewise reveals an 11-yr modulation (Salby and Callaghan 2000).

Anomalous ΔTFeb–Sep operating coherently with TNP and Fs has the same basic structure (not shown) as that operating coherently with uEQ and Fs (Fig. 5). In each, anomalous temperature is strong and positive over the Arctic during easterly winters near solar min, but also during westerly winters near solar max. Compensating it at subpolar latitudes is negative anomalous temperature, consistent with the structure of the residual circulation.

A systematic modulation emerges even if interannual variability is referenced against properties at the tropical tropopause. Figure 10 plots the running correlation between the wintertime tendency of the 20-mb height over the Arctic, lagged by half a solar cycle, and 100-mb height over the equator. Here cZFeb–Sep20, ZEQ] (solid) swings systematically from −1.0 towards +1.0 in each of the Four decades. It has an overall correlation to Fs (dashed) of 0.80, which is highly significant.

Figure 11 plots the anomalous wintertime tendency of height operating coherently with ZEQ and Fs. Anomalous height (contoured) is highly significant (shaded) and positive over the Arctic, where it reflects anomalous downwelling. Here ΔZFeb–Sep intensifies upward through the roof of the NCEP analyses, to levels where the variation of UV absorption between solar min and solar max becomes substantial. The upward intensification may also reflect the dependence on uEQ in the upper stratosphere and mesosphere, which influences polar temperature at lower levels (Gray et al. 2001). Compensating positive ΔZFeb–Sep over the Arctic is negative anomalous height at subpolar latitudes. Although weaker, it too is highly significant. Reflecting anomalous upwelling, negative ΔZFeb–Sep coincides with the collar of negative anomalous height surrounding the vortex that was seen earlier (Fig. 7).

A systematic modulation of interannual variability is evident even if phase is referenced against the local field property itself. Setting the interannual clock Γ equal to ψHF references changes at each location against those at the same location, but lagged in time. The running cross-correlation is then replaced by the running autocorrelation. The latter measures the cosine of the phase at one time relative to the phase at another time. Figure 12 plots, for a lag of two solar cycles, the running autocorrelation of ΔZFeb–Sep30 (solid). Like the cross-correlation, cZFeb–Sep30, ΔZFeb–Sep30] swings systematically between −1.0 and +1.0 in each of the four decades. It varies coherently with Fs, producing a correlation of −0.83.

The behavior in Fig. 12 describes a systematic variation of phase within the height record itself. The phase of interannual variability changes rapidly in some years, but slowly in others. This systematic variation reflects a frequency modulation, one that determines the phase of interannual variability during winter months. The corresponding structure of anomalous height (not shown) is similar to that presented earlier, when height is referenced against other field properties.

4. Amplitude modulation of interannual variability

The variational analysis also isolates a systematic modulation in the amplitude of interannual variability. However, relative to frequency modulation, the signature of amplitude modulation is weak. Figure 13 plots the instantaneous power of the 20-mb height tendency over the Arctic, ‖ΔZFeb–Sep202 (solid). It describes interannual variance, inclusive of the QBO and BO. Superposed is the record of Fs, lagged by half a solar cycle (dashed). Instantaneous height power in Fig. 13 has an overall correlation to Fs of 0.72. This is smaller than the correlation to Fs of frequency modulation, which tracks UV irradiance closely. Nonetheless, the implied variation of amplitude is still highly significant according to Monte Carlo tests (section 5).

With the lag accounted for, interannual power amplifies near solar min in each of the four decades. Those are the years when wintertime-mean uEQ alternates between consecutive years—biennially (Fig. 1). During the same years, Arctic temperature changes almost biennially (Fig. 2). An analogous amplitude modulation results if TNP is filtered about the QBO and BO (Salby and Callaghan 2000, their Fig. 6).

The corresponding structure of anomalous height is plotted in Fig. 14. It has been composited according to (3), now with χ = ‖ψHF‖. Anomalous ΔZFeb–Sep has much the same form as that associated with frequency modulation (Fig. 11). Anomalous height maximizes over the Arctic. It increases upward through the roof of the NCEP analyses, where the change of UV absorption between solar min and solar max becomes substantial.

5. Reliability of systematic variations

The variational analysis isolates systematic variations in a diagnostic χ that operate coherently over four decades with Fs. For a record of any fixed length, however, there is a small but finite probability that χ will track Fs simply through chance. Isolating systematic variations that are truly related to the variation of UV irradiance thus requires us to discriminate to those which will maintain their relationship to Fs as the atmospheric record is extended. The challenge then is to separate the wheat from the chaff.

We define a null hypothesis that the correspondence between the diagnostic χ and Fs (e.g., measured by their overall correlation) actually occurred through chance. The probability that χ track Fs over four decades is then required to be small. Under these circumstances, the null hypothesis can be rejected with a high level of confidence.

a. Monte Carlo simulation

To evaluate the reliability of systematic variations, the same operations used to define χ and its relationship to Fs are now performed on field properties that are generated randomly. The individual NCEP record is then replaced by a large stochastic ensemble of such records. Each represents one realization of a stochastic process—unrelated to solar activity. The diagnostic χ(t) is calculated over the stochastic ensemble, producing many realizations of the corresponding time series. From them, we evaluate the probability that a systematic variation operating coherently with Fs over four decades occurs through chance.

The running correlation is based on a field property (e.g., ψHF = ΔTFeb–Sep) and a reference time series (e.g., Γ = uEQ). Each is now represented as a stochastic process. The process is defined from a Gaussian spectrum, with a correlation time of about 2 yr (representative of observed variability). The null hypothesis then holds that the correspondence between χ = c[ψHF, Γ] and Fs follows randomly via this red spectrum.

From the stochastic process, some 400 000 realizations are generated—each four decades long. They are used to produce the running correlation between the stochastic field property and reference time series. Of some 400 000 realizations, less than 10% yield an overall correlation to Fs exceeding 0.40. Realizations satisfying this criterion are collected in Fig. 15 into a histogram, as a function of lag between the field property and the reference time series (solid). Notice that realizations satisfying the above criterion are distributed over lag almost uniformly.1 A correlation to Fs of 0.40 is therefore exceeded randomly with respect to lag. This contrasts with behavior in the observed records, wherein the criterion is satisfied at preferred lags: A strong correlation to Fs reappears at lags of 5–6 yr, 10–12 yr, and so forth.

b. Shifted records

The ensemble of records is randomized further by shifting each by an integral number of years. One set of 400 000 records begins in 1955, extending forward for four decades. Another set begins in 1956, and so forth. Systematic variations that are genuinely related to Fs (e.g., in the observed record) are then modified only through a phase shift because new data introduced at the tail of the record maintain a consistent relationship to Fs. On the other hand, systematic variations over four decades that occur through chance (e.g., in the stochastic records) quickly deteriorate with increasing shift because new data introduced have only a small probability of maintaining the existing relationship to Fs. Requiring the diagnostic χ to vary coherently with Fs under all shifts of the 4-decadal record: by 1, 2, 3, 4, and 5 yr (i.e., jointly in records over 1955–96, 1956–97, and so forth) reduces the chance correlation to Fs dramatically.

Superposed in Fig. 15 are realizations that yield an overall correlation to Fs exceeding 0.40 in all of the shifted records (dashed). The probability of satisfying the null hypothesis through chance is sharply reduced. Of 400 000 realizations, each shifted successively by an integral number of years, less than 0.001% yield an overall correlation to Fs exceeding 0.40 under all shifts of the 4-decadal record. Observed records that satisfy this more restrictive criterion are therefore significant at the 99.999% level.

c. Referenced against observed uEQ

The picture is unchanged even if the reference time series is not stochastic. If the observed record of uEQ is employed, then the reference time series includes a frequency modulation that varies systematically with Fs (Fig. 1). Still generated stochastically, however, is the field property. For an unshifted 4-decadal record, realizations yielding an overall correlation to Fs greater than 0.40 still comprise less than 10% of the ensemble. The histogram of those realizations resembles the solid curve in Fig. 15. As when the field property and reference time series are both stochastic, those realizations are distributed over lag almost uniformly. Therefore, a correlation to Fs of 0.40 is still exceeded randomly with respect to lag, even though the reference time series now includes a systematic variation that favors preferred lags.

Requiring the same criterion to be satisfied jointly under shifts of the 4-decadal record again reduces the chance correlation to Fs dramatically. The correlation to Fs must now exceed 0.40 in all of the shifted records. The probability of satisfying the null hypothesis through chance is then sharply reduced. Of some 400 000 realizations, each one shifted successively by an integral number of years, less than 0.1% satisfy this condition. Observed records that satisfy the more restrictive criterion (shaded in preceding figures) are then significant at the 99.9% level.

6. Conclusions

The circulation of the wintertime stratosphere includes a component that varies systematically with the 11-yr variation of UV irradiance. Only a small systematic variation is visible in the LF component, which represents a simple linear response that drifts with Fs. However, the 11-yr variation manifests itself prominently in the HF component, which corresponds to interannual variability. The systematic variation at high frequency represents a more complex, nonlinear response to the variation of UV irradiance.

Involving periods shorter than 5 yr, interannual variability includes the QBO and BO. Collectively, those components account for an 11-yr modulation in the frequency of interannual variability. It modifies the phase of interannual variability during winter when planetary waves couple the polar and equatorial stratosphere. The polar-night vortex is then sensitive to equatorial wind, which itself varies systematically with UV irradiance.

The frequency modulation of interannual variability surfaces when wintertime structure is referenced against any of several field properties. It is visible even when a property is referenced against itself. Monte Carlo simulations indicate that the systematic variation of frequency is highly significant. It intensifies upward through the roof of NCEP analyses, where the variation of ozone heating between solar min and solar max becomes substantial.

A signature of the 11-yr variation also surfaces as an amplitude modulation of interannual variability. It is magnified in each of the four decades near solar min, when polar temperature and wintertime-mean uEQ change almost biennially. However, the signature of amplitude modulation is comparatively weak. It becomes substantial only at the highest levels of the NCEP analyses. A similar conclusion applies to the LF component of the circulation, which simply drifts with UV irradiance.

The systematic variation is prominent in the wintertime tendency of temperature, which is coupled directly to the residual mean circulation. In fact, the anomalous wintertime tendency operating coherently with Fs has the same basic structure as that operating coherently with anomalous forcing of the residual circulation. The resemblance of these anomalous structures suggests that the systematic modulation of interannual variability enters through changes of the residual circulation.

Accompanying the systematic variation of zonal-mean structure is an amplification and decay of wavenumber 1 at high latitude. It represents a poleward advance and retreat of the critical region where planetary waves experience strong absorption that forces residual motion. The critical region is advanced poleward during easterly winters near solar min, but during westerly winters near solar max.

Exactly how these changes are introduced remains uncertain. However, the upward intensification of anomalous structure suggests that they are somehow imprinted at higher levels where the variation of UV absorption becomes substantial. A likely vehicle is wind at low latitude. Influencing the critical line and thus planetary wave absorption, equatorial wind can change significantly with only a minor change of temperature.

Observed variations of wave structure and implied residual motion, in fact, parallel the systematic variation of equatorial wind. The behavior of wintertime-mean uEQ suggests a reversal in anomalous downwelling between solar min and solar max. Establishing this connection, however, will require observations above the altitude range of meteorological analyses, altitudes that also influence polar temperature in the lower stratosphere. Although other factors cannot be ruled out, the behavior implied by wintertime-mean uEQ at and below 10 mb is broadly consistent with the observed reversal of anomalous temperature.

The signature of anomalous downwelling over the Arctic is visible as low as 100 mb. Implied are systematic changes in the transfer of stratospheric air to the troposphere. Compensating those changes at lower latitudes is a signature of anomalous upwelling. Visible even at the tropical tropopause, the signature of anomalous upwelling implies systematic changes in the return of tropospheric air to the stratosphere. Through these transfers, a systematic variation in the stratosphere's residual circulation can influence the tropospheric circulation.

Acknowledgments

The authors are grateful for constructive remarks provided during review. This work was supported by ASF Grant ATM.0127671.

REFERENCES

  • Baldwin, M., , and T. Dunkerton, 1998: Biennial, quasi-biennial, and decadal oscillations of potential vorticity in the northern stratosphere. J. Geophys. Res., 103 , 39193928.

    • Search Google Scholar
    • Export Citation
  • Båth, M., 1976: Spectral Analysis in Geophysics. Elsevier, 563 pp.

  • Bruhwiler, L., , and K. Hamilton, 1999: A numerical simulation of the stratospheric ozone quasi-biennial oscillation using a comprehensive general circulation model. J. Geophys. Res., 104 , 30;th52530;th557.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T., , and M. Baldwin, 1992: Modes of interannual variability in the stratosphere. Geophys. Res. Lett., 19 , 4952.

  • Fusco, A., , and M. Salby, 1999: Interannual variations of total ozone and their relationship to variations of planetary wave activity. J. Climate, 12 , 16191629.

    • Search Google Scholar
    • Export Citation
  • Gray, L., , S. Phipps, , T. Dunkerton, , M. Baldwin, , E. Drysdale, , and M. Allen, 2001: A data study of the influence of the equatorial upper stratosphere on Northern Hemisphere stratospheric warmings. Quart. J. Roy. Meteor. Soc., 127 , 19852003.

    • Search Google Scholar
    • Export Citation
  • Hadjinicolaou, P., , A. Jrrar, , J. Pyle, , and L. Bishop, 2002: The dynamically-driven trend in stratospheric ozone over northern middle latitudes. Quart. J. Roy. Meteor. Soc., 128 , 13931412.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R., , and H-C. Tan, 1980: The influence of the equatorial quasi-biennial oscillation on the global circulation at 50 mb. J. Atmos. Sci., 37 , 22002208.

    • Search Google Scholar
    • Export Citation
  • Hu, Y., , and K. K. Tung, 2002: Interannual and decadal variations of planetary wave activity and stratospheric cooling. J. Climate, 15 , 16591673.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Kodera, K., , M. Chiba, , and K. Shibata, 1991: A general circulation model study of the solar and QBO modulation of the stratospheric circulation during the Northern Hemisphere winter. Geophys. Res. Lett., 18 , 12091212.

    • Search Google Scholar
    • Export Citation
  • Labitzke, K., 1982: On the interannual variability of the middle stratosphere during the northern winters. J. Meteor. Soc. Japan, 60 , 124139.

    • Search Google Scholar
    • Export Citation
  • Labitzke, K., , and H. van Loon, 1988: Association between the 11-year solar cycle, the QBO, and the atmosphere, I, The troposphere and stratosphere on the Northern Hemisphere winter. J. Atmos. Terr. Phys., 50 , 197206.

    • Search Google Scholar
    • Export Citation
  • Labitzke, K., , and H. van Loon, 1996: On the stratosphere, the QBO, and the sun. Meteor. Z., 5 , 166169.

  • Lean, J., 2000: Evolution of the sun's spectral irradiance since the Maunder Minimum. Geophys. Res. Lett., 27 , 24252428.

  • Naito, Y., , and I. Hirota, 1997: Interannual variability of the northern winter stratosphere circulation related to the QBO and solar cycle. J. Meteor. Soc. Japan, 75 , 925937.

    • Search Google Scholar
    • Export Citation
  • Newman, P., , E. Nash, , and J. Rosenfeld, 2001: What controls the temperature of the Arctic stratosphere during the spring? J. Geophys. Res., 106 , 1999920010.

    • Search Google Scholar
    • Export Citation
  • O'Sullivan, D., , and M. L. Salby, 1990: Coupling of the quasi-biennial oscillation and the extratropical circulation in the stratosphere through planetary wave transport. J. Atmos. Sci., 47 , 650673.

    • Search Google Scholar
    • Export Citation
  • O'Sullivan, D., , and R. Young, 1992: Modeling the quasi-biennial oscillation's effect on the winter stratospheric circulation. J. Atmos. Sci., 49 , 24372448.

    • Search Google Scholar
    • Export Citation
  • Quiroz, R., 1981: Period modulation of the stratospheric quasi-biennial oscillation. Mon. Wea. Rev., 109 , 665674.

  • Salby, M., , and P. Callaghan, 2000: Connection between the solar cycle and the QBO: The missing link. J. Climate, 13 , 26522662.

  • Salby, M., , and P. Callaghan, 2002: Interannual changes of the stratospheric circulation: Relationship to ozone and tropospheric structure. J. Climate, 15 , 36733685.

    • Search Google Scholar
    • Export Citation
  • Salby, M., , P. Callaghan, , and D. Shea, 1997: Interdependence of the tropical and extratropical QBO: Relationship to the solar cycle versus a biennial oscillation in the stratosphere. J. Geophys. Res., 102 , 2978927798.

    • Search Google Scholar
    • Export Citation
  • Soukharev, B., , and L. Hood, 2001: Possible solar modulation of the quasi-biennial oscillation: Additional statistical evidence. J. Geophys. Res., 106 , 1485514868.

    • Search Google Scholar
    • Export Citation
  • Tung, K., , and H. Yang, 1994: Global QBO in circulation and ozone. Part II: A simple mechanistic model. J. Atmos. Sci., 51 , 27082721.

  • van Loon, H., , and K. Labitzke, 1994: The 10–12 year atmospheric oscillation. Meteor. Z., 3 , 259266.

  • WMO, 1987: Atmospheric ozone: Assessment of our understanding of the processes controlling its present distribution and change. World Meteorological Organization Rep. K., 648 pp. [Available from NASA, Office of Mission to Planet Earth, Two Independence Square, 300 E. Street SW, Washington, DC 20546.].

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Number of months between Nov and Feb during which 30;chmb uEQ is westerly and easterly, as a function of year. Adapted from the RAOB analysis of Salby and Callaghan (2000)

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 2.
Fig. 2.

Anomalous wintertime tendency (Sep–Feb) of 70-mb temperature at 90°N (solid), as a function of year. Superposed is the wintertime-mean 50-mb equatorial wind uEQ (dashed), averaged over the same months

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 3.
Fig. 3.

Running 3-yr cross correlation between the records in Fig. 2 (solid). Superposed is the 10.7-cm solar flux Fs (dashed), lagged by 1 yr; cTFeb–Sep, uEQ] in year n then corresponds to Fs one year earlier in year n − 1

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 4.
Fig. 4.

As in Fig. 3 but for the wintertime tendency of 100-mb temperature at 45°N

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 5.
Fig. 5.

Anomalous wintertime tendency of temperature (contoured), as a function of latitude and pressure, operating coherently with 50-mb uEQ and Fs. Shaded are significance levels of 99% and higher. Anomalous temperature during individual winters follows by scaling values by the product of anomalous Fs and anomalous uEQ during those winters (each normalized); see text

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 6.
Fig. 6.

As in Fig. 5 but for anomalous wintertime tendency of zonal wind

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 7.
Fig. 7.

Anomalous wintertime tendency of 30-mb height operating coherently with 50-mb uEQ and Fs

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 8.
Fig. 8.

Wintertime tendency of 30-mb height (mean + anomaly) for equatorial easterlies and extrema of Fs. (Note: the wintertime tendency is negative throughout)

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 9.
Fig. 9.

As in Fig. 3 but for the instantaneous cross-correlation between the wintertime tendency of 70-mb temperature at 65°N, lagged by 15 yr, and 50-mb temperature over the North Pole

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 10.
Fig. 10.

Instantaneous cross-correlation between the wintertime tendency of 20-mb height at 90°N, lagged by 7 yr, and 100-mb height over the equator (solid). Superposed is the record of Fs lagged by 4 yr (dashed)

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 11.
Fig. 11.

Anomalous wintertime tendency of height (contoured), as a function of latitude and pressure, operating coherently with the 100-mb height over the equator and Fs

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 12.
Fig. 12.

Instantaneous autocorrelation, for a lag of 21 yr, of the wintertime tendency of 30-mb height at 32°N (solid). Superposed is the record of Fs lagged by 5 yr (dashed).

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 13.
Fig. 13.

Instantaneous power of 20-mb height tendency at 78°N, ‖ΔZFeb–Sep202 (solid). Superposed is the record of Fs lagged by 6 yr (dashed)

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 14.
Fig. 14.

Anomalous wintertime tendency of height (contoured), as a function of latitude and pressure, associated with amplitude modulation that operates coherently with Fs

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

Fig. 15.
Fig. 15.

Fraction of the stochastic ensemble that produces correlations to Fs exceeding 0.40 (solid), as a function of lag between the field variable and the reference time series. The net probability, integrated over lag, is less than 10%. Superposed is the fraction of the stochastic ensemble that produces correlations to Fs exceeding 0.40 jointly under all shifts of the 4-decadal records by 1, 2, 3, 4, and 5 yr (dashed); see text. The net probability, integrated over lag, is then less than 0.001%

Citation: Journal of Climate 17, 1; 10.1175/1520-0442(2004)017<0034:EOTSCI>2.0.CO;2

1

Minor deviations with lag converge to zero as the ensemble size is increased.

Save