Regional Features of the 20–30 Day Periodic Behavior in the Southern Hemisphere Summer Circulation

The Southern Hemispheric storm tracks exhibit a robust intraseasonal periodicity of 20–30 days as the leading mode of zonal‐mean eddy kinetic energy. To what extent this hemispheric‐scale mode of variability translates to smaller scales remains debated. This work studies the regional features of Southern Hemisphere storm tracks through a filtered variance analysis of local finite‐amplitude wave activity. While the synoptic variance is zonally elongated over the storm track, we find a strong enhancement of intraseasonal variability within the South Pacific. With a minimum strength of the storm track, this region is marked with 20–30 day periodic behavior of local wave activity and precipitation and is driven by enhanced variability of low‐level eddy heat flux on the same timescale. The local nature of 20–30 day periodicity offers a potential source of subseasonal to seasonal predictability for weather analysts and forecasters.


Introduction
High-quality societal applications for decision-makers for optimizing resource management and preventing disaster require accurate sub-seasonal to seasonal (S2S, intraseasonal) predictions, because high-impact extreme weather events, such as long-lasting heatwaves and extreme cold spells, often occur on this timescale.Recent research has identified multiple sources of S2S predictability, such as the Madden-Julian oscillation (MJO), the basic state of the ENSO, soil moisture, tropical-extratropical teleconnections, etc (see the review in Vitart et al. (2017)).However, nearly all of these sources are outside of the midlatitude internal dynamics.This is due to the conventional understanding that the large-scale midlatitude variability is typically consistent with Gaussian red noise rather than periodic behaviors (Feldstein, 2000;Lorenz & Hartmann, 2001).As a "null hypothesis," regional intraseasonal variability in the midlatitudes can be considered as a response to stochastic forcing by higher-frequency synoptic system's disturbances (Green, 1977;Hasselmann, 1976;Leith, 1973).Assuming synoptic disturbances as Gaussian white noise forcing, this "null hypothesis" suggests the intraseasonal variability should be a Gaussian red noise process.Hence, no unique source of predictability on regional scales has been identified within the midlatitude atmosphere beyond the synoptic weather range.Baroclinic Annular Mode (BAM), however, a recently discovered large-scale midlatitude variability over the Southern Hemisphere, is characterized by a robust intraseasonal periodicity about 20-30 day (Thompson & Barnes, 2014;Thompson & Woodworth, 2014).BAM is defined by the leading empirical orthogonal function (EOF) of the zonal-mean eddy kinetic energy, representing the intraseasonal oscillation of eddy activity on a hemispheric scale.Such large-scale mode of variability has important implications for shaping the extratropical circulation and associated hydrological cycle (Marshall et al., 2017).

Abstract
The Southern Hemispheric storm tracks exhibit a robust intraseasonal periodicity of 20-30 days as the leading mode of zonal-mean eddy kinetic energy.To what extent this hemispheric-scale mode of variability translates to smaller scales remains debated.This work studies the regional features of Southern Hemisphere storm tracks through a filtered variance analysis of local finite-amplitude wave activity.While the synoptic variance is zonally elongated over the storm track, we find a strong enhancement of intraseasonal variability within the South Pacific.With a minimum strength of the storm track, this region is marked with 20-30 day periodic behavior of local wave activity and precipitation and is driven by enhanced variability of low-level eddy heat flux on the same timescale.The local nature of 20-30 day periodicity offers a potential source of subseasonal to seasonal predictability for weather analysts and forecasters.
Plain Language Summary Storms and precipitations in the Southern Hemisphere overall experience a regular pulsing every 20-30 days that we call Baroclinic Annular Mode.We don't understand what physical process drives this regular pulsing but we hypothesize that a regional analysis would be helpful to investigate this open question.Further, if such periodic pulsing of storms and precipitations can be identified within a specific region, it would have important implications for understanding and predicting the medium-range weather system, especially for extreme events.In this work, we pin down the regional features of the 20-30 day pulsing by demonstrating the spatial distribution of storms and precipitations in terms of their variance and periodicity within different time scales.We found that while the short-time storm activity (2-7 days) exhibits a similar strength across the Southern Ocean, the storm activity within the time scale of Baroclinic Annular Mode (20-30 days) exhibits a localized periodicity concentrated in the South Pacific.The local nature of this 20-30 day periodicity indicates a potential utility for weather analysts and forecasters.

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2 of 8 A high BAM state may indicate an overall strong wave activity on hemispheric-scale.This calls for a regional analysis which would enable us to pinpoint the most sensitive region(s) that may contribute to a high BAM state.Specifically, a regional analysis of the BAM's periodicity may reveal the linkage between BAM and serial clustering of extreme weather events in the mid-latitudes, including atmospheric blocking, heat waves, or cold spells, all of which are largely characterized by intraseasonal variability rather than synoptic timescale.Thus if such periodic nature were to translate to smaller scales at certain regions, it could serve as a new source of S2S predictability.Further, since BAM refers to a zonally symmetric annular structure, to what extent such annular pattern has a high degree of zonal symmetry is an important open question (see Gerber and Thompson (2017) for a relevant discussion in the context of Annular Mode).In a regional scale study of BAM, Thompson et al. (2017) find that the periodicity in the upper troposphere eddy kinetic energy is not apparent at a fixed location.As the averaging windows reduce from the entire global circle to 30-degree wide regions, the power spectra reduce from a robust quasi-periodic shape to a red noise without any major enhancement of the variance on the 20-30 day frequency range.The discovery of the lack of local periodicity for regions smaller than 30° is explained through a conceptual model featuring out-of-phase anomalies between the upper and lower troposphere (Thompson et al., 2017).A similar finding was also confirmed in Xue et al. (2021), that the domain should be wide enough to accommodate a wave packet so that the intraseasonal periodicity can be identified.Therefore, as the averaging domain size reduces to smaller scales, previous work suggested that periodic behavior at a fixed region is not expected, which is consistent with the above "null hypothesis."To what extent such a leading mode of variability is translated to regional scale intraseasonal variability-and thus modulating serial clustering of extreme weather events-remains an open question.
To address this question, we adopt a filtered variance approach, which has been well-developed to identify the geographic distributions of the storm tracks (Blackmon et al., 1977).Typically, a scalar quantity combining multiple variables is preferred, such as the 500 hPa geopotential height field (Z500), which is related to both the wind and temperature.Blackmon et al. (1977) developed this filtered variance framework using the Northern Hemisphere Z500, with the spectral domains separated into synoptic and intraseasonal bands, respectively (also see Blackmon et al. (1984)).Through a similar filtered variance analysis, Trenberth (1981Trenberth ( , 1991) ) studied the Southern Hemisphere circulation within synoptic time scales and found that the Southern Hemisphere storm tracks exhibit strong zonal symmetry along with a maximum located at the Southern Indian Ocean and a minimum at the South Pacific.Kidson (1991) found a zonal-symmetric pattern for the intraseasonal variability in the Southern Hemisphere (see also Hartmann (2015)).Therefore, we aim to make progress on deepening the understanding of the regional features of the intraseasonal variability-a less explored territory, especially on timescales relevant to the recently discovered Baroclinic Annualar Mode.Specifically, we ask: are these regions with enhanced intraseasonal variance mainly characterized by a Gaussian red-noise spectrum as expected from the "null hypothesis," or have certain quasi-periodic behaviors that may be connected with the hemispheric-scale 20-30 day periodic mode of variability?
To answer this question, we start with the surface precipitation analysis, a directly measured quantity as a surrogate for the local behavior of storm activities.Next we quantify the regional variability pattern by applying the filtered variance approach (Blackmon et al., 1977) to key representative variables including a newly developed diagnostics local wave activity (LWA).This work focuses on austral summer season (DJF) since the periodic behavior is much more significant in austral summer than other seasons (Wang & Nakamura, 2015).Comparisons to the Northern Hemisphere and with different seasons will be addressed in follow-up studies.The paper is organized as follows.In Section 2, we introduce data and key methodologies such as LWA and filtered variance framework.In Section 3, we first discuss the regional features of surface precipitation and then demonstrate the synoptic and intraseasonal variability patterns of local wave activity associated with spectral analysis.Section 4 concludes with a summary with discussions.

Data and Method
We use ERA-Interim reanalysis data set to produce all the eddy quantities related to filtered variance approach, with a horizontal resolution 1.5° × 1.5° and daily resolution from 1979 to 2018.Additionally, the daily precipitation is obtained from the Advanced Microwave Scanning Radiometer (AMSR) -E from 2003 to 2010 processed by a three-day moving average.AMSR-E measures the surface rain rate covering from 70°N to 70°S.
The key methodology in this work is to adopt the filtered variance approach of Blackmon et al. (1977) to quantify the regional features of eddy activity in different time scales.The filtered variability is calculated as the standard deviation of eddy quantities in the 2-7 day band for synoptic analysis and the 10-45 day band for intraseasonal analysis.The temporal filter is based on Fast Fourier Transform (FFT) with Hanning window from 1 December to 28 February between 1979 and 2018.The framework is mainly applied to local wave activity (LWA), but the result for conventionally used variables including Z500, eddy kinetic energy and 850 hPa eddy heat flux will also be shown to make a comparison.Eddy kinetic energy is defined as  ( ( * ) 2 + ( * ) 2 ) ∕2 and is averaged with density weighting along the vertical column.Eddy heat flux is defined as v*T*.In both cases the asterisks represent the departures from the zonal mean.Note that, all the eddy quantities are first calculated from the raw data with daily resolution, then the filtered variance framework is used to separate the variables into synoptic and intraseasonal bands.In the associated power spectral analysis, we use the original eddy quantities without any filtering processes.
LWA emphasizes on coherent meandering of the contours of a quasi-conserved quantity.Conserving flow circulation through Kelvin's circulation theorem, the area bounded by the reference quantity contour is the same as the one bounded by the latitude circle.Finite-amplitude wave activity (FAWA, see Nakamura and Zhu (2010)) focuses on the total displacement over the entire longitudes, while LWA (see Huang and Nakamura (2016); Chen et al. ( 2015)) measures the displacement for each longitude, so that a full two-dimensional longitude-latitude pattern of wave activity can be quantified.For example, the field of Z500 can be used to define the local wave activity (Chen et al., 2015): where a is the earth radius, ϕ, λ, represents the latitude and longitude respectively, z′ = z − Z(ϕ e ) is the deviation from the reference Z500 contour Z(ϕ e ) at its equivalent latitude ϕ e .The relation between Z(ϕ e ) and ϕ e is connected by the same bounded area ] .
We choose LWA for filtered variance analysis as it provides an objective diagnostics of eddy activity and can capture both coherent spatial and temporal feature.Please see Supporting Information S1 for the discussion on using conventional approaches (e.g., Z500 or eddy kinetic energy) which meet challenges on revealing key regional features of large-scale Rossby wave packets.LWA can capture the breaking waves as part of an underlying coherent pattern, and the zonal-mean version of the wave activity framework (FAWA) has been shown to capture a robust 20-30 day periodicity (Wang & Nakamura, 2015), consistent with features of BAM defined by the EOF-based eddy kinetic energy framework.Both the quasi-geostrophic potential vorticity (QGPV) and Z500 fields can be used to calculate the LWA.QGPV-based LWA is a conserved quantity and driven by eddy flux terms-each bearing clear physical interpretations, directly representing the pseudo-momentum carried by eddy.Z500-based LWA shares many features of the QGPV-based LWA, and it is more straightforward to calculate.Our analysis confirms that both approaches yield qualitatively consistent results.

Results
We start with analyzing the temporal and spatial features of precipitation, since surface rain rate is a directly measured quantity by space-based meteorological satellites, and is highly correlated with the variability of storm activity.Thompson and Barnes (2014) found that the hemispheric-averaged mid-latitude mean precipitation can also exhibit a significant intraseasonal periodicity around 20-30 days as a key feature of BAM.Is there any localization of such periodic behavior in the precipitation?
To illustrate the regional feature, we calculated the power spectra of surface rain rate retrieved from AMSR-E in four separated regions as shown in Figure 1c: 0°-90°E, 90°E-180°, 180°-90°W, 90°W-0°, all of which are averaged between 40°S and 50°S, and we find that the most significant 20-30 day periodicity is located at the South Pacific (180°-90°W with 95% confidence level) resembling that from the hemispheric-averaged midlatitude precipitation (Figure 1b).On the other hand, spectra features in other three regions are mainly characterized by enhanced synoptic variability (0°-180°E) or similar to a red-noise (90°W-0°) less similar to that robust periodicity from the hemispheric-averaged midlatitude precipitation.Thus, there is a localization of the surface rain rate's 20-30 day periodic behavior.Since surface rain rate is a direct measured variable through remote-sensing, this localization of periodicity motivates us to investigate deeper into this problem through a more advanced diagnostic approach to evaluate the associated large-scale atmospheric circulation patterns.Is this localization of rain rate periodicity a coincidence?Or does it imply a strong localization of the 20-30 day periodic behavior for the underlying large-scale atmospheric circulation?
Figure 2 shows the synoptic and intraseasonal variability pattern of LWA in austral summer based on filtered variance approach.The synoptic variability still exhibits a zonally symmetric pattern, with the maximum variance concentrated in the Southeast Indian Ocean as well as in the Southeast Atlantic, and the minimum variance in the Southeast Pacific close to South America.This result is qualitatively consistent with the pattern shown by the filtered variance of the Z500 field, but the filtered-variance pattern of LWA further captures a more detailed and coherent structure clearly emphasizing the maximum region.Such intensified synoptic variability at the Southeast Indian Ocean and Atlantic can be largely attributed to the downstream development of baroclinic waves  ( Berbery & Vera, 1996), and therefore the largest synoptic variance is expected to occur closely downstream to the regions of maximum observed baroclinicity, which is located at the Southwest Indian Ocean and Atlantic (the sea surface temperature frontal zones, see H. Nakamura and Shimpo (2004)).The weakened synoptic signal at the South Pacific is associated with the decaying process of extratropical cyclones' lifecycles.
With an ability to capture larger-scale meandering, the filtered variance of LWA captures the corresponding intraseasonal variability more efficiently than that of the Z500 and eddy kinetic energy field.As shown in Figure 2b, the intraseasonal variance of LWA is nearly twice its synoptic counterpart.Besides, the intraseasonal pattern is not as zonally-elongated as the synoptic variance or the pattern captured by Z500.In contrast, a strong local enhancement is found confined at the South Pacific, largely within 180°-150°W and 50°S-60°S.This region is right at the center between the two branches in the intraseasonal pattern of eddy kinetic energy, which demonstrates the advantage of LWA in capturing coherent patterns for large-scale eddies.Thus, when it comes to studying regional patterns, the conventional approach to study BAM using eddy kinetic energy meets a challenge on capturing coherent and localized Rossby wave structures well, because the two branches as revealed by the eddy kinetic energy pattern may actually belong to one coherent Rossby wave packet.Further, instead of considering the averaged power spectra across multiple regional bands which may dilute important contributions of periodicity from certain key regions, the filtered-variance of LWA approach can explicitly reveal the two-dimensional latitude-longitude distribution of the periodic variability to highlight key regions with significant intraseasonal variance.
With the region of enhanced intraseasonal variance pinned down, we next investigate whether the enhanced frequencies are related to the 20-30 day periodic mode of variability.To zoom into the crucial latitudes where such periodicity is concentrated, Figure 3 shows the power spectra of LWA as the function of longitudes and frequencies at 45°S and 55°S, since Wang and Nakamura (2015) found that the 20-30 day periodic variability mainly dominates the midlatitudes from 40°S to 60°S.Within the intraseasonal domain, the 20-30 day periodicity (0.03-0.05 cpd, bounded by two blue lines in Figure 3) exhibits a strong localization as suggested by the filtered variance approach.At 45°S for example, the strongest 20-30 day frequency band is largely confined between 180° and 150°W, overlapping the region where the intraseasonal variance reaches its maximum (shown in Figure 2b).This regional feature of periodicity may slightly vary with different latitudes, for example, the most significant 20-30 day periodicity at 55°S exhibits an elongated range covering 180°-100°W.By and large, all 10.1029/2023GL104256 6 of 8 cross sections within midlatitudes demonstrate that the 20-30 day periodicity has a strong regional preference located at the South Pacific.A similar result can be observed if the LWA is meridionally averaged between 40°S and 60°S (see Figure S5 in Supporting Information S1), the 20-30 day periodicity is still strongly localized at the South Pacific, resembling the pattern at individual latitudes.Note that, in this case, the influence from the budget term of meridional eddy momentum flux is eliminated by construction due to the meridional average, and therefore it suggests that, the meridional eddy momentum flux plays a non-dominant role in the intraseasonal variability.The zonal wave flux convergence, as another important budget term of LWA, will not directly impact LWA's intraseasonal variability either, as the zonal wave flux convergence primarily populates the synoptic variability of wave activity (Huang & Nakamura, 2017).
What would be a key factor that drives such locally confined intraseasonal variability including the 20-30 day periodicity?Wang andNakamura (2015, 2016) find that eddy forcing due to the low-level eddy heat flux drives the 20-30 day periodicity in zonal-mean of LWA (i.e., FAWA).A local enhanced variance of eddy heat flux should be expected if this can also translate into regional scales.Figure 4 confirmed this expectation by showing that the intraseasonal variance of 850 hPa eddy heat flux is also localized between 180° and 150°W, largely overlapping the region where the intraseasonal variance of LWA is strongly enhanced, as shown in Figures 2  and 3.The cross-section power spectra of 850 hPa eddy heat flux further indicates that the low-level eddy heat flux also exhibits enhanced 20-30 day periodicity at fixed locations, largely confined within the South Pacific as well (see Figure S8 in Supporting Information S1).This locally enhanced intraseasonal variability of 850 hPa eddy heat flux is marked with a strong r.m.s.eddy streamfunction as a surrogate of eddy diffusivity for estimating the horizontal eddy heat flux (Held, 1999;Kushner & Held, 1998).Strong thermal damping over this area reduces linear baroclinic eddy growth rates (Swanson & Pierrehumbert, 1997).Thus, this sufficient temperature homogenization in the lower troposphere sustains states neutral to the growth of synoptic eddies but favorable to intraseasonal variability and the associated periodic behavior.

Conclusion and Discussion
We study the regional features of storm tracks' 20-30 day periodic variability in austral summer by applying the filtered variance approach to local wave activity.While the synoptic variance is largely zonally elongated over the storm tracks, we find a strong local enhancement of intraseasonal variability within the South Pacific with a minimum strength of the storm track.We find that this enhanced region is marked with local 20-30 day periodic behavior of precipitation and local wave activity whereby rejecting the "null hypothesis" that regional intraseasonal variability in the midlatitudes is nothing more than a red-noise response to stochastic forcing by synoptic transients.The 20-30 day periodicity becomes practically useful for predicting extreme weather events when the periodicity can be identified on a regional scale and can be pinpointed at a particular location.The local periodicity is driven by enhanced variability of low-level eddy heat flux on the same timescale.Although the robustness of such localized 20-30 day periodicity is reduced compared to the BAM index (Thompson & Barnes, 2014) or zonal-mean LWA (Wang & Nakamura, 2015) both of which define the periodicity on a hemispheric scale, the filtered variance and spectral analysis of local wave activity offers insights into the regional features of the coherent and slowly meandering structures of the circulation.
Internal modes of variability, such as BAM, result from the deterministic dynamics of the atmosphere.Thus a translation into regional scales may indicate unique predictability beyond the typical weather range and provide insights into BAM's physical mechanisms and whether there is any specific regional pattern from which BAM originates.This regional pattern may be related to downstream suppression of baroclinic eddies (Boljka et al., 2021) or BAM-associated systematic modulations in the presence of midlatitude oceanic frontal zone (Nakayama et al., 2021).While the fundamental dynamics of BAM remain an open question, it is clear that cross-scale interactions between the synoptic and intraseasonal scales set the regional structure of this internal mode.The local nature of the 20-30 day periodicity identified by local wave activity provides a potential source of intraseasonal predictability for weather analysts and forecasters.As an internal mode that has yet to be tapped for extending the forecast beyond the typical weather range, more work is needed to connect this intraseasonal mode of variability with serial clustering of extreme weather events, including atmospheric blocking, heat waves, and cold spells, to quantify this potential regional predictability.Besides, since this work focuses on the austral summer, whether similar regional features can be identified in the Northern Hemisphere midlatitudes remains unexplored and worth future investigations.In a warming climate, BAM is projected to increase its strength (Wang et al., 2018).A further implication of this work is the question of how the intraseasonal mode of variability and the associated regional impacts will evolve as climate changes.With the rapid development of high-resolution Earth system modeling, we are at a crucial era to deepen our understanding of the synoptic-intraseasonal interactions and the associated Earth system's regional variability and predictability.

Figure 3 .
Figure 3. Power spectra of QGPV-based LWA as functions of longitude and frequency at two representative latitudes 45°S (upper panel) and 55°S (lower panel), respectively.