Observational Zonal Mean Flow Anomalies: Vacillation or Poleward

ATMOSPHERIC AND OCEANIC SCIENCE LETTERS, 2013, VOL. 6, NO. 1, 1 7 Observational Zonal Mean Flow Anomalies: Vacillation or Poleward Propagation? SONG Jie The State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China Received 17 May 2012; revised 24 May 2012; accepted 28 May 2012; published 16 January 2013 Abstract North-south displacements and meridional vacillations of the eddy-driven jet are widely accepted as the dominant cause of variability of the observational zonal-mean zonal wind anomalies (denoted [u] ). In this study, a new idea regarding the primary variability of the observational [u] in the middle latitude troposphere is presented. It is hypothesized that there are two different classes of primary variability of the observational [u] : the poleward propagation of the [u] (abbreviated as PP) and meridional vacillations. To validate this hypothesis, one-point correlation maps of [u] at 200-hPa during the boreal cold season (November April) of every year from 1957 2002 are used as a criterion. Twelve PP years, in which the PP events are dominant in the variability of [u], and 15 no_pp years, in which the PP events are recessive and the meridional vacillations are dominant in the variability of [u], are examined. The results show that the variabilities of [u] are different in the chosen PP and no_pp years. In the PP years, the PP events dominate the variability of [u] ; however, the meridional vacillations are prevalent in the no_pp years. Keywords: zonal-mean zonal wind, zonal index, poleward propagation Citation: Song, J., 2013: Observational zonal mean flow anomalies: Vacillation or poleward propagation? Atmos. Oceanic Sci. Lett., 6, 1 7. 1 Introduction For a long time, meteorologists have sought to understand the characteristics of the variability of zonal-mean zonal. The zonal index, first proposed by Rossby (1939), is an innovative attempt to depict the dominant low-frequency variability of the zonal-mean zonal wind. Namias (1950) noted that the differing intensity of the zonal index is associated with the north-south vacillation of the middle latitude jet. Since this study, the low-frequency variability in zonal-mean zonal wind anomalies (denoted [u] in this paper) has attracted a great deal of attention from atmospheric scientists. Numerous studies have indicated that the primary variability of [u] is the north-south displacement, i.e., the meridional vacillations of the middle latitude jet, whether in observations (e.g., Trenberth, 1984; Kidson, 1988; Thompson and Wallace, 2000; Lorenz and Hartmann, 2001, 2003) or in simulations of the general circulation models (e.g., Robinson, 1991, 1994, 1996; Yu Corresponding author: SONG Jie, song_jie@mail.iap.ac.cn and Hartmann, 1993; Lee and Feldstein, 1996). In the last decade, the poleward propagation of [u] from the tropics to approximately 70 latitude in both hemispheres and an unnoticed low frequency variability of zonal-mean zonal wind has aroused the interest of a few atmospheric scientists. The poleward propagation of zonal-mean zonal wind anomalies (hereafter abbreviated as PP) is not a new finding. In 1950, Riehl et al. (1950) first reported the existence of this phenomenon in the atmosphere; however, the data that they analyzed only covered a seven-month period. Since then, few published papers focused on the PP, until James et al. (1994) found ultra-low frequencies, an equivalent barotropic system, and the poleward propagation phenomena of [u] in an ideal model. Later, Feldstein (1998) confirmed the existence of this type of unusual atmospheric event through observations. Recently, Son and Lee (2006, SL hereafter) and Lee et al. (2007) examined the PP using a global spectral primitive equation model (Son and Lee, 2005). They added small-scale tropical heating (referred to as H) and high latitude cooling (referred to as C) into an idealized radiative equilibrium temperature profile. In this way, the model s basic flow (the basic flow means the long-term mean zonal-mean zonal wind) is modified. Interestingly, they found that in the large-c and small-h region of the parameter space, where the basic flow has double jets and the associated potential vorticity (PV) gradient is relatively smooth, a distinct and stable PP phenomenon occurs; in contrast, in the small-c and large-h region of the parameter space, where the basic flow has a single jet and the PV gradient is relatively sharp, the jet meridional meander is dominant (Fig. 2 in Lee et al. (2007) gives a convincing and impressive illustration). Based on the results of their model, SL argued that the variability of [u] in their ideal model can be divided into two classes: the well-known meridional vacillations of the middle latitude jet and the poleward propagation of [u]. From daily observations of the latitude-time plots of 200-hPa [u] from 1957 2002, it was found that in some years, the PP phenomenon dominated the variability of the [u]. These PP events are so robust and stable that they can be identified through simple inspection; in contrast, in other years, it is hard to ascertain the occurrence of the PP events. Rather, the meridional vacillations of the middle latitude jet are clearer (not shown). Combining the insights gained from the latitude-time plots and the SL

2 ATMOSPHERIC AND OCEANIC SCIENCE LETTERS VOL. 6 findings from the ideal numerical model, it is hypothesized that the observed variability of [u] can be characterized into two classes: PP and zonal index/meridional vacillation. The primary objective of this study is to validate this hypothesis. It is found that the observational extratropical variability of [u] can be separated into two classes. In certain years (named PP years), the poleward propagation characteristics of [u] are very distinct, while in other years (named no_pp years), the poleward propagation of [u] is recessive and the primary variability of [u] is the meridional vacillation. The remaining parts of this paper in support of this hypothesis are organized as follows. Section 2 provides the observational data used in this study. The method for choosing the PP and no_pp years and the chosen PP and no_pp years are listed in section 3. Three pieces of evidence are also presented to validate the assertion that the poleward propagation characteristic of [u] is indeed distinct in the chosen PP years and recessive in the chosen no_pp years. Finally, section 4 gives the conclusions of this study. 2 Data For this study, the daily fields of the European Centre for Medium-Range Weather Forecasts (ECMWF) 40 year re-analysis (ERA-40) (Uppala et al., 2005) from September 1957 to August 2002 are used. The horizontal resolution of the ECMWF data is 2.5 2.5 and archived for 23 pressure levels spanning from 1000 hpa to 1hPa. In this study, the term anomaly refers to a deviation from the seasonal cycle, which is defined by each calendar date s climatic average. Cold season is defined as the period of time from November to April. Because the PP or jet meridional meander events are more distinct in cold seasons, except where otherwise noted, only data from the cold season is used in this study. Because data from the Northern Hemisphere (NH) are more reliable than the data from the Southern Hemisphere (SH), and considering the daily time-resolution of the data used here, only the NH is analyzed in this study. 3 The PP and no_pp years 3.1 Picking up the PP and no_pp years To validate the hypothesis, the 45 cold seasons from 1957 to 2002 are separated into the so-called PP and no_pp years. Following the method of SL, one-point lag correlation maps of cold seasons [u] are used to select the PP and no_pp years. The one-point lag correlation maps of cold season [u] at 200hPa with a basic latitude of 30 N are calculated for every year. If the one-point lag correlation map of a certain year has a regular and obvious poleward propagating characteristic, similar to the characteristic for 1976 1977 (top panel of Fig. 1) in which the PP events are dominant, that year will be chosen as a PP year. On the other hand, if the one-point lag correlation map is disordered and without a visible poleward propa gating characteristic, as in the pattern for 1983 1984 (bottom panel of Fig. 1), that year is chosen as a no_pp year. In this way, 12 PP years and 15 no_pp years are identified from the 45-year period spanning from 1957 2002. The intervenient years are discarded (the PP and no_pp years are listed in Table 1). Figure 2 shows the daily evolution of [u] at 200hPa during the so-called PP and no_pp years. The characteristics of the variability of [u] at 200hPa during the PP and no_pp years are clearly very different. In the PP years, the variability of [u] is clearly dominated by well-regulated PP phenomena. In many PP years, even one PP event can persist throughout almost the whole cold season. For the no_pp years, the variability of [u] is more disordered, and the meridional vacillation is prevalent. Although the PP events in Fig. 2 are not as regular as in the results of the ideal model (see Fig. 2 of SL), these data still strongly support the hypothesis that the dominant variability of observational [u] can be characterized into two classes: the PP and the meridional vacillation. 3.2 Validation The chosen PP and no_pp years listed in Table 1 are somewhat subjective. Although one can identify distinct differences in the characteristics of the variability of [u] through quick inspection (see Fig. 2), objective and convincing evidence is still needed to validate this point. In this subsection, three pieces of evidence, obtained in three distinct ways, are presented to demonstrate that the characteristics of the variability of [u] in the chosen PP and no_pp years are different. The averaged space-time spectrums (Hayashi, 1982) of the PP and no_pp years are shown in Fig. 3. The spacetime spectrum analysis can distinguish the statistical spacetime structure of the eastward- and westward-moving components for a given wavenumber and period and is widely used in the study of tropical intraseasonal oscillations (e.g., Hayashi and Golder, 1993). Conventionally, because of the earth s bounded spherical condition, the space-time spectrum analysis is carried out along a full latitudinal circle. To examine the poleward propagation of [u], in this study, wavenumber-frequency analyses are carried out along the meridional direction, similar to the study by Teng and Wang (2003). First, throughout each year for the 45 years of this study, the daily tropospheric [u] from 10 N 80 N is weighted by the square root of cosine of the latitude and the square root of the pressure interval represented by that level. The daily tropospheric [u] is then vertically (1000hPa to 100hPa) integrated (the stratospheric parts are neglected here because the mass of the stratosphere is sufficiently small so that the results are essentially identical regardless of whether the vertical integral includes the stratosphere). As a result, 45 twoimensional matrices of weighted zonal- and vertical-mean zonal wind anomalies are acquired, where one dimension is latitude and the other is time. Then, the space-time spectrum analysis is applied to these 45 two-dimensional matrices. The composite space-time spectrums of the PP (top panel of Fig. 3) and no_pp (middle panel of Fig. 3) years are shown in Fig. 3. In the composite space-time

NO. 1 SONG: OBSERVATIONAL ZONAL MEAN FLOW ANOMALIES 3 Figure 1 One-point lag correlations maps of zonal-mean zonal wind anomalies at 200hPa during November April of 1976 1977 (top) and 1983 1984 (bottom). Shading denotes correlations exceeding the 95% confidence level based on the t-statistic. Contour intervals are 0.1, zero contours are omitted, and negative contours are dashed. Table 1 The chosen PP and no_pp years. Year PP (12) 1957/58, 1962/63, 1963/64, 1966/67, 1976/77, 1979/80, 1982/83, 1984/85, 1989/90, 1991/92, 1995/96, 1996/97 no_pp (15) 1958/59, 1960/61, 1964/65, 1971/72, 1972/73, 1973/74, 1974/75, 1980/81, 1983/84, 1986/87, 1990/91, 1993/94, 1994/95, 1997/98, 1998/99 spectrum of the PP years, the northward variance is very strong, and there is an independent peak at wavenumber one with a northward period of 121 days. However, for the no_pp years, the northward variance is faint and the peak at wavenumber one with the northward period of 121 days has completely disappeared. The main differ- ences in the space-time spectrum between the PP years and the no_pp years are located in the northward part (bottom panel of Fig. 3). These results indicate that, in the NH, the [u] has a prominent poleward propagation characteristic with a typical period of approximately 121 days during the PP years. On the contrary, the poleward propagating characteristic of [u] is inconspicuous during the no_pp years. The one-point lag correlation maps for the 200-hPa [u] with the basic latitude of 30 N for all of the cold seasons in the PP and no_pp years are shown in Fig. 4. The lag correlation map for the PP years clearly shows that, during the PP years, [u] has a distinct poleward propagating characteristic (top panel of Fig. 4). Additionally, [u]

4 ATMOSPHERIC AND OCEANIC SCIENCE LETTERS VOL. 6 Figure 2 Evolution of anomalous daily zonal-mean zonal wind (m s 1) at 200-hPa during the cold season of the PP (left panel) and no_pp (right panel) years. shows the meridional vacillation characteristic during the no_pp years (bottom panel of Fig. 4). Furthermore, the empirical orthogonal functions (EOFs) analysis on the 45 cold seasons daily [u] over the merid- ional pressure-latitude cross-section (1000hPa 100hPa over 10 N 80 N) is performed. For the EOFs analysis, the data fields are properly weighted by the square root of cosine of the latitude and the square root of the pres-

NO. 1 SONG: OBSERVATIONAL ZONAL MEAN FLOW ANOMALIES 5 Figure 4 The one-point lag correlation maps for the 200-hPa zonal-mean zonal wind anomalies with the base latitude of 30 N for the PP and the no_pp years. Shading denotes correlations exceeding the 95% confidence level based on the t-statistic. Contour intervals are 0.1, zero contours are omitted, and negative contours are dashed. Figure 3 Composite space-time spectrums of the PP (top) and the no_pp years (middle) and the differences (bottom) between them. sure interval represented by that level. The spatial distributions of the first two principal modes are shown in Figs. 5a and 5b. They are very similar to the results of previous studies (e.g., Lorenz and Hartmann, 2003), and the explained variances are 26.9% (EOF1) and 20.1% (EOF2), respectively. The lag correlations between the first Principal Component (PC1) and the second Principal Component (PC2) of the PP (Fig. 5c) and no_pp years (Fig. 5d) are calculated. In Figs. 5c and 5d, every thin curve represents one year s lag correlations, and the thick curve denotes the averaged results of the all PP and no_pp years. It is obvious that, as a whole, the lagcorrelations between the two PCs of the PP years are more regular, which strongly implies that low-frequency PP events indeed exist in those years. However, for the no_pp years, the correlations between PC1 and PC2 are more disordered, suggesting that the PP events are unapparent and that the primary variability of [u] is dominated by the jet s meridional meander (SL). These three pieces of evidences strongly suggest that the characteristics of the variability of [u] in the PP and no_pp years are distinct, validating the hypotheses on the variability of the observational [u] proposed in section 1. 4 Conclusions In contrast to the traditional viewpoint that the dominant variability of the observational [u] is the meridional vacillations, the results of this study indicate that there are two different classes of the dominant variability of [u] : the PP and the meridional vacillations. This idea is moti-

6 ATMOSPHERIC AND OCEANIC SCIENCE LETTERS VOL. 6 Figure 5 The (a) first and (b) second EOF modes of the zonal-mean zonal wind anomalies on the meridional pressure-latitude cross-section (1000 hpa 100hPa over 10 N 80 N) and the lag correlations between the first Principal Component (PC1) and the second Principal Component (PC2) of (c) every PP and the no_pp (d) year. The thick curve represents the averaged results.

NO. 1 SONG: OBSERVATIONAL ZONAL MEAN FLOW ANOMALIES 7 vated by the findings reported by Son and Lee (2006) and Lee et al. (2007). These authors found that, in their ideal model, the variability of [u] is completely different in different parameter spaces. Using one-point lag correlation maps of [u] at 200hPa during boreal cold seasons as a criterion, the variabilities of [u] over a 45 year period (from 1957 to 2002) are separated into two different classes: the PP and no_pp years. The PP years are those in which the PP events are dominant in the primary variability of [u]. On the contrary, the no_pp years denote years when the PP events are recessive and the meridional vacillations dominate the primary variability of [u]. Although the method for selecting the PP and no_pp years is simple, three pieces of evidence are presented to demonstrate that the variabilities of [u] are indeed completely different in the PP and no_pp years. In the PP years, [u] is prone to be well organized and poleward propagating; in contrast, in the no_pp years, the north-south displacement of the middle latitude jet is prevalent. Acknowledgements. This work is sponsored by the National Key Technologies R&D Program of China (Grant No. 2009BAC51B02), the National Basic Research Program of China (973 Program, Grant No. 2010CB950401), the National Nature Science Foundation of China (Grant Nos. U0833602 and 40805023), and the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Free Exploration Fund. References Feldstein, S. B., 1998: An observational study of the intraseasonal poleward propagation of zonal mean flow anomalies, J. Atmos. Sci., 55, 2516 2529. Hayashi, Y., 1982: Space-time spectral analysis and its applications to atmospheric waves, J. Meteor. Soc. Japan, 60, 156 171. Hayashi, Y., and D. G. Golder., 1993: Tropical 40 50- and 25 30-day oscillations appearing in realistic and idealized GFDL climate models and the ECMWF dataset, J. Atmos. Sci., 50, 464 494. James, P. M., K. Fraedrich, and I. N. James, 1994: Wave-zonal-flow interaction and ultra-low-frequency variability in a simplified global circulation model, Quart. J. Roy. Meteor. Soc., 120, 1045 1067. Kidson, J. W., 1988: Indices of the Southern Hemisphere zonal wind, J. Climate, 1, 183 194. Lee, S., and S. Feldstein, 1996: Mechanism of zonal index evolution in a two-layer model, J. Atmos. Sci., 53, 2232 2246. Lee, S., S. W. Son, K. Grise, et al., 2007: A mechanism for the poleward propagation of zonal mean flow anomalies, J. Atmos. Sci., 64, 849 868. Lorenz, D. J., and D. L. Harmann, 2001: Eddy-zonal flow feedback in the Southern Hemisphere, J. Atmos. Sci., 58, 3312 3327. Lorenz, D. J., and D. L. Hartmann, 2003: Eddy-zonal flow feedback in the Northern Hemisphere winter, J. Climate, 16, 1212 1227. Namias, J., 1950: The index cycle and its role in the general circulation, J. Meteor., 7, 130 139. Riehl, H., T. C. Yeh, and N. E. La seur, 1950: A study of variations of the general circulation, J. Meteor., 7, 181 194. Robinson, W. A., 1991: The dynamics of the zonal index in a simple model of atmosphere, Tellus, 43A, 295 305. Robinson, W. A., 1994: Eddy feedback on the zonal index and eddy-zonal flow interactions induced by zonal flow transience, J. Atmos. Sci., 51, 2553 2562. Robinson, W. A., 1996: Does eddy feedback sustain variability in the zonal index? J. Atmos. Sci., 53, 3556 3569. Rossby, C. G., 1939: Relation between variations in intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action, J. Mar. Res., 2, 38 55. Son, S-W., and S. Lee., 2005: The response of westerly jets to thermal driving in a primitive equation model, J. Atmos. Sci., 62, 3741 3757. Son, S-W., and S. Lee., 2006: Preferred modes of variability and their relationship with climate change, J. Climate, 19, 2063 2075. Teng, H., and B. Wang, 2003: Interannual variations of the boreal summer intraseasonal oscillation in the Asian-Pacific region, J. Climate, 16, 3572 3584. Thompson, D. W. J., and J. M. Wallace, 2000: Annular modes in the extratropical circulation. Part I: Month-to-month variability, J. Climate, 13, 1000 1016. Trenberth, K. E., 1984: Interannual variability of the Southem Hemisphere circulation: Representativeness of the year of the global weather experiment, Mon. Wea. Rev., 112, 108 123. Uppala, S. M., P. W. KÅllberg, A. J. Simmons, et al., 2005: The ERA-40 reanalysis, Quart. J. Roy. Meteor. Soc., 131, 2961 3012. Yu, J. J., and D. L. Hartmann, 1993: Zonal flow vacillation and eddy forcing in a simple GCM of the atmosphere, J. Atmos. Sci., 50, 3244 3259.