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In other words, the spectra in Figure 1 include available potential energy and the whole model depth. Furthermore, the application of spherical harmonics allows the decomposition of kinetic energy into rotational and divergent components, whereas the Hough harmonics provide an energy decomposition into balanced or vorticity-dominated Rossby and unbalanced or IG, mainly divergent components.

The divergent energy spectra are often regarded as synonymous with IG spectra in mid-latitude mesoscale conditions. On large scales and in the tropics, such an assumption is not valid.

For example, the equatorial Kelvin wave is a half-rotational and half-divergent mode and as such difficult to extract from IFS data.

By contrast, the computation of rotational and divergent energy for the wavenumber k from spherical harmonics involves derivatives and thus depends on velocities in neighbouring wavenumbers.

For example, the planetary scales were significantly more energetic in January than in July not shown. Comparing these with the analyses suggests that HRES tended to somewhat underpredict the variability at most scales, especially at zonal wavenumber 2.

The modal decomposition can be used to filter any mode and spatial scale back to physical space. For example, Figure 2 presents balanced and unbalanced flow in January and July for a level at the tropical tropopause.

In this region, the unbalanced winds were of the same direction, whereas over the central Pacific they were stronger and with the opposite sign compared to the balanced flow Figure 2b,c.

In July, the unbalanced winds were strongest over the Indian Ocean region in relation to the summer monsoon. Overall, Figure 2 shows that a significant component of large-scale tropical circulation is unbalanced in both months.

In the lower tropical troposphere, unbalanced winds tend to be stronger than balanced winds, especially in the cross-equatorial component not shown.

Figure 2 Average horizontal winds and geopotential height shading at model level 60 approximately hPa in the tropics in January showing a total average flow, b balanced average flow and c unbalanced average flow; and in July showing d total average flow, e balanced average flow and f unbalanced average flow.

Averaging is performed for analyses at 00 UTC. Note that here the presented levels are sigma levels and geopotential height is a modified geopotential variable that includes surface pressure.

As a result, circulation follows the terrain throughout the model depth. Geopotential height is visualised by five contours between the maximal and minimal value in each panel.

Figure 3 shows that, on average, the equatorial Kelvin wave signal is dominated by the zonal wavenumber 1 and has the largest amplitude over the Indian ocean in July.

The propagation of Kelvin waves in the model forecasts is illustrated in Figure 4. Here, we put together results of the modal decomposition every 12 hours and show both zonal wind and temperature perturbations, computed from geopotential perturbations using the hydrostatic relationship.

Although the decomposition is performed independently for each time step, when the outputs for successive times are put together, they naturally connect and show propagation properties known from linear theory and studies based on frequency filtering.

This is a strong justification for the assumptions made for the derivation of normal modes used for the decomposition. It should be noted that the presented wave properties are the result of a summation over 70 vertical modes.

Figure 3 Kelvin wave winds arrows and geopotential height perturbations shading in January at a model level 68 approx.

Averaging is performed for analyses from 00 UTC. Figure 4 The evolution of Kelvin waves in the day forecast started on 20 July , 00 UTC, showing zonal wind speed perturbations shading and Kelvin wave temperature perturbations isolines every 2 K , with positive perturbations drawn in solid lines and negative perturbations in dashed lines, for a level 29 approx.

The verification can also be performed in physical space for any mode of interest. The growth of RMSEs in Figure 5 is associated with the variability of the tropical stratosphere, which is driven by vertically propagating equatorial waves associated with convection.

In July, convection is most intense over the maritime continent and the errors in stratospheric circulation first develop here.

By contrast, the RMSEs of the stratospheric unbalanced zonal wind component propagate eastward in forecasts in both July Figure 5b and January not shown , but the error amplitudes are greater and develop earlier in the forecasts in July.

The location of the maximal stratospheric RMSE is not the same in January and July as the most intense convection, which generates vertically propagating IG waves, moves along the equator not shown.

The fact that RMSEs for balanced flow along the equator in Figure 5a,b appear smoother than RMSEs for unbalanced flow can possibly be explained by the dynamical properties of IG waves and their generation by physical processes.

The growth of zonally averaged tropical forecast errors in the zonal wind component is largest in the balanced component in the upper troposphere.

In the day range, the balanced error at level hPa is nearly twice as large as the error in the unbalanced component Figure 5c,d.

The two components initially have similar amplitudes, which indicates that the analysis errors relative to the variability of the wind is higher in the unbalanced component compared to the balanced component, or possibly that the error growth is much higher during the first forecast day.

In the stratosphere level 50 the unbalanced component of error dominates in both January and July but the error growth is greatest in July, when convection is stronger.

In the next section we are going to discuss short-range errors by presenting average analysis increments. Another useful error decomposition is presented in Figure 6, which shows zonal wind analysis increments in autumn as the mean absolute differences between the analysis and the first-guess forecast.

The average increments are small if the short-range forecast first-guess agrees with the available observations.

The increments are also small if there was no significant error growth in the short-range forecast. In general, one expects the increments to be larger in dynamically active regions with faster intrinsic error growth e.

To understand the nature of errors, the decomposition of the increments into balanced and unbalanced components could be valuable.

Figure 6 Mean analysis increments of zonal wind from September to November showing a total increments at model level approx.

Increments are computed as mean absolute differences between hour forecasts and analyses valid at 18 UTC. Global analysis increments for all modes, split into balanced and unbalanced modes, are shown in Figure 6 at two model levels.

The level close to hPa represents the flow in the upper troposphere in the tropics and in the lower stratosphere in the mid-latitudes. The increments are largest at the hPa level in the tropics.

Lower in the troposphere, the increments are distributed more evenly and appear smoother, especially for the balanced component in the mid-latitudes.

Note also that smaller increments at the hPa level in the extra-tropics are above the tropopause, where variability is significantly smaller.

In the tropics, a larger part of increments is associated with unbalanced modes than with balanced modes at both levels.

The largest increments are found over tropical Africa. A further diagnostic into various modes reveals that some of the increments over Africa are associated with the Kelvin modes not shown.

Furthermore, these increments, which are believed to be connected to convection over Africa, are strongest during daytime 18 UTC analysis. There are also big increments in unbalanced flow over eastern Africa, which is related to very localised and unrealistic convection in the model over Ethiopia.

This feature has been improved in the new IFS model cycle 41r2. Overall, Figure 6 suggests that data assimilation is most difficult in the tropics, where forecast errors grow fastest and where a lack of direct wind observations makes it difficult to constrain circulation in the analyses.

Figure 6 also shows that in high-resolution forecasts a significant part of tropospheric analysis increments projects onto unbalanced modes in the extra-tropics too.

We have presented a new diagnostic technique that can usefully be applied to ECMWF forecasts in the tropics and that complements other methods to validate model performance.

Based on a decomposition into balanced and unbalanced IG modes, the technique enables balanced flow features, such as individual equatorial Rossby waves, and unbalanced waves, such as Kelvin waves, to be evaluated separately.

In this way, we can more easily relate errors in forecasts to initial-state uncertainties and model errors. Bechtold , P. Koehler , T.

Jung , F. Doblas-Reyes , M. Leutbecher , M. The temporal evolution of SAM in DJF can be divided subjectively into two epochs —93 and — that have the largest contrast.

For JJA, the entire period can be divided into —89 and — To illustrate the spatial patterns of the trends in winter and summer, based on the corresponding seasonal SAM index, the — period of record can be divided subjectively into the two epochs that exhibit the largest contrast.

The Z epochal differences in Fig. In DJF a pronounced zonally symmetric dipole dominates the circulation difference Fig. Similar changes are observed in the middle troposphere and at the surface, as shown in Ding et al.

On the interannual time scales, the positive SST anomalies over these two regions corresponds to the negative polarity of the SAM, Thus, the sign of the SST trends in these regions matches the sign of the SH circulation trends, consistent with the relationships for the year-to-year variability discussed in the previous section.

The upper-tropospheric circulation is more sensitive to the subtle change in the tropics than the flow at lower levels; hence the upper-level divergence associated with the tropical forcing plays a key role in driving tropical—extratropical teleconnections Hoskins and Karoly ; Sardeshmukh and Hoskins ; Trenberth et al.

The changes in tropical outgoing longwave radiation OLR and velocity potential that are coincident with the trend in the SAM are plotted in Figs. These long-term changes in upper-level divergence, which appears to be directly driven by the forcing at the lower boundary, may play a key role in forcing the extratropical trends.

The choice of which two periods to use in making epochal difference, while subjective, is useful in illustrating the patterns associated with the largest changes in high-latitude circulation.

Results obtained from the MCA consist of modes comprising paired spatial patterns of SST and Z and the corresponding expansion coefficient time series.

The leading mode indicates the pattern of tropical SST anomalies that is most strongly coupled with the SH circulation and the SH circulation anomalies associated with that pattern.

The corresponding time series are dominated by interannual variability and exhibit negligible linear trends over the yr record.

Hence, the canonical eastern Pacific ENSO-related variability does not contribute at least not directly to the observed long-term changes in the SH circulation.

In contrast, the second MCA modes in both seasons capture the long term trends in the circulation and the related trends in tropical SST.

The associated time series exhibit significant long term trends very similar to those in the respective time series of the seasonal SAM index shown in Fig.

The MCA thus captures the salient features of the covariability between the SH circulation trend and concurrent changes in the tropical SST and further supports our interpretation of their statistical relationship.

We note that, because the strong interannual variability associated with ENSO is captured in the first mode of the maximum covariance analysis, the trend of SH circulation associated with the second mode has greater statistical significance than the SAM index.

Principal modes of covarying tropical sea surface temperature and Southern Hemisphere circulation in austral summer DJF. Spatial patterns of tropical SST shading and hPa geopotential heights Z , contour interval 10 m associated with a mode 1 and b mode 2.

Time series of SST and Z for c mode 1 and d mode 2. Amplitudes in a , b are scaled by one standard deviation of the corresponding time series in c , d.

As in Fig. Figure from Ding et al. The empirical evidence presented in sections 3 and 4 shows that the low frequency variability in SAM pattern—as conventionally defined based on the leading EOF of SH circulation —is partly tropically forced.

In all seasons except summer, the SH upper troposphere exhibits a double split jet structure Fig. In summer the subtropical jet in the Pacific is severely weakened and a prominent jet is only present over the Indian Ocean.

The tight vorticity gradient associated with the jet and the strong variability of upper-level divergent flow over the warm pool should combine to form an active source of Rossby waves over the jet core region Renwick and Revell ; Lachlan-Cope and Connolley Indeed, as shown in Fig.

The most active and spatially extensive subtropical Rossby wave source occurs in JJA when the jet itself is strongest Fig.

Thus, the location and seasonality of RWS activity appears to be mainly determined by the seasonal evolution of the intensity and shape of the jet stream, rather than by the strength of the variability of tropical SST.

This is additional evidence that the interannual variability of the high-latitude SH circulation in the Pacific sector is more directly related to conditions in the tropics than to eddy—mean flow interactions or high-latitude orographic effects.

Because the circulation response to tropical SST forcing yields a pair of Rossby wave gyres residing to the west and poleward of the forcing, whose divergent wind field has a much larger meridional width and a stronger intensity than that associated with Kelvin waves Gill , the tropical SST anomalies to the east of Australia are efficient in triggering an active RWS in the core region of the subtropical jet.

This is consistent with the correlation analysis in section 3b , which shows that Z variations over the Amundsen Sea are more strongly correlated with SST anomalies over the central and eastern Pacific than with SST anomalies over the Indian Ocean and Western Pacific.

Considering the very active RWS along the core of subtropical jet, tropical internal instability largely unrelated to tropical SST anomalies could also excite fluctuations resembling the PSA wave train if it were able to generate a strong wave source over the jet core region.

If this were the case, then one would expect the PSA signature to be prominent in the SH circulation variability, not only on interannual time scales but also intraseasonally.

To explore this possibility, EOF analysis was performed on pentad-mean SH Z anomalies separately for each season and for the year as a whole.

Because tropical SST fluctuations should be very small on the intraseasonal time scale, this suggests that the PSA-like pattern obtained from pentad data reflects an extratropical response to tropical internal variability rather than a SST-forced response.

It thus appears that the PSA pattern is a preferred mode of the extratropical basic state that is very sensitive to small variations in the tropical convection: tropical SST forcing is one way to force such variations, but it is not a requirement.

In Fig. Circulation variability associated with a meridional shift of the eddy-driven midlatitude jet favors eddy feedback that tends to sustain a meridional seasaw mode between the Indian Ocean and East Antarctica Barnes and Hartmann The subtropical jet driven by the Hadley circulation inhibits eddy feedback Eichelberger and Hartmann but favors the generation of a Rossby wave source over its core region on a broad frequency band.

Thus, a Rossby wave train emanating from subtropical Australia to West Antarctica is the preferred circulation mode of the basic state in the Pacific sector.

In all seasons but summer, two different leading oscillation modes in the India Ocean and Pacific sector work together to establish the annular SAM pattern that exhibits strong zonal mean structure and out of phase action between the midlatitude and the high latitude.

In austral summer, the basic state of the SH is dominated by a single jet structure in the midlatitude.

The eddy feedback is thus the main dynamical source to maintain an annular SAM in that season Lorenz and Hartmann This is also the season when ENSO tends to reach its peak.

The extratropical response to a mature ENSO also exhibits a PSA type wave train but with stronger meridional orientation and zonal mean structure, which may further strengthen the variability of the annular character of SAM in austral summer Seager et al.

Schematic showing the role of subtropical jet and midlatitude jet in shaping the SAM during nonsummer season when the basic state is characterized by the double jet structure.

See discussion section for further details. The summer DJF trend in the SAM over the past 30 years has been most commonly attributed to the direct influence of radiative forcing from both greenhouse gases and ozone depletion Thompson and Solomon ; Gillett and Thompson ; Marshall et al.

The abrupt rise in the summertime SAM index in the mids may have also been at least partly due to the abrupt change of DJF SST in the tropical Pacific, which occurred around the same time.

Ding et al. Given the strong projection of the Pacific—South American pattern upon the SAM, we suggest that the forcing attributable to SST warming in the tropical central Pacific explains a substantial part of the observed trend in the SAM in winter.

Similarly, the DJF SST warming over most of the tropics along with cooling in the eastern Pacific also has the potential to excite a zonally symmetric response in the extratropics by changing the Hadley cell and the midlatitude jet stream Seager et al.

The focus of this study is to examine the relationship between the southern annular mode and SST variability in the tropics.

Analyses based on EOF1 of monthly geopotential height at hPa show that the SAM pattern contains strong zonally asymmetric variability and that in the Pacific sector it projects strongly upon the PSA wave train that is mainly forced by SST anomalies in the equatorial central-eastern Pacific.

The intensity of this Rossby wave source is mainly determined by the strength and sharpness of the subtropical jet in the basic state flow.

This geographically fixed wave source may play an important role in anchoring the PSA wave train and favoring the recurrence of the PSA, with its primary center of action off the West Antarctic coast, even in the absence of a spatially coherent pattern of SST variability over the central Pacific.

When circulation variability associated with the PSA in the SH circulation is regressed out of the hemispheric hPa height field, the leading EOF exhibits a zonal dipole structure confined to the Indian Ocean sector, suggesting that the behavior of the SAM over the Indian Ocean sector and Pacific sector is different.

In combination, these results indicate that the SAM, which has conventionally been regarded as the leading EOF mode of SH circulation variability, in fact represents the superposition of a PSA type wave train in the Pacific sector and a meridional dipole pattern in the Indian Ocean sector.

Although eddy—mean flow interaction in the extratropics is widely believed to be the primary source of SAM variability, our study shows that planetary waves emanating from the tropical Pacific also strongly contribute to the variability of the SAM.

The long-term trend in the SAM over the past three decades is also examined with emphasis on its connection with tropical SST. The SAM trend in summer is well known and has already been extensively discussed in previous work.

The SAM index also exhibits a detectable downward trend in winter and the associated upper-tropospheric geopotential height pattern in the Pacific sector projects strongly onto the PSA wave train.

The interdecadal changes in the SAM in winter and summer are of opposing sign, and their time history is different.

The summer SAM index exhibited an abrupt shift in the mids, whereas the main shift in the winter SAM began a decade earlier and was more gradual.

In both winter and summer, a close association is observed between the change in the SAM index and tropical SST changes. The Plumb wave activity analysis is used to reveal stationary Rossby wave energy propagation.

In spherical coordinates,. The Plumb flux provides direct information on the flux of wave activity, which is parallel to the group velocity of quasi-stationary Rossby waves.

This diagnostic tool is well suited for detection of propagation characteristics of large scale quasi-stationary Rossby waves.

For the correlation of monthly data in Fig. The corrected sample size for the month 31 years time series is about We use maximum covariance analysis MCA to capture the dominant coupled modes between Southern Hemisphere Z equator to MCA between the Z and SST field is achieved by performing singular value decomposition on the temporal covariance matrix Bretherton et al.

The pairs of singular vectors describe the spatial patterns of the respective fields. The corresponding squared singular value divided by the sum of the squares of the singular values represents the squared covariance fraction SCF and thus indicates the relative importance of that pair of vectors in relationship to the total squared covariance between the two fields.

The expansion coefficients obtained by projecting the singular vectors onto the original data fields depict the temporal variations in amplitude and polarity of the spatial patterns.

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Interannual variability of the SAM. Dynamical interpretation. Summary and conclusions. Research Article 16 April E-mail: qinghua uw.

This Site. Google Scholar. Eric J. Steig ; Eric J. David S. Battisti ; David S. John M. Wallace John M. Climate 25 18 : — Article history Received:.

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View large Download slide. Table 1. Table 2. Table 3. One-month-lag autocorrelation of monthly Z in the SH. Search ADS.

The wintertime Southern Hemisphere split jet: Structure variability and evolution. An intercomparison of methods for finding coupled patterns in climate data.

The effective number of spatial degrees of freedom of a time-varying field. Observed relationships between the southern annular mode and atmospheric carbon dioxide.

The structure and composition of the annular modes in an aquaplanet general circulation model. Observations of large-scale ocean—atmosphere interaction in the Southern Hemisphere.

Relation between annular modes and the mean state: Southern Hemisphere summer. Winter warming in West Antarctica caused by central tropical Pacific warming.

Decadal variability of the ENSO teleconnection to the high-latitude South Pacific governed by coupling with the southern annular mode.

ParkY. If this were the case, then one would expect the PSA signature to be prominent in the SH circulation variability, not only on interannual time scales but also intraseasonally. Global analysis increments for all modes, split into balanced and unbalanced modes, are shown in Figure 6 Beste Spielothek in Horperath finden two model levels. The energy is summed over all meridional and vertical scales. Clash Forum positive feedback of the stationary waves upon zonal-mean flow, as suggested by DeWeaver and Nigamis one mechanism that might cause these two separate patterns to occasionally vary in tandem. The associated time series exhibit significant long term trends very similar to those in the respective time series of the seasonal SAM index shown in Fig.

In other words, the spectra in Figure 1 include available potential energy and the whole model depth. Furthermore, the application of spherical harmonics allows the decomposition of kinetic energy into rotational and divergent components, whereas the Hough harmonics provide an energy decomposition into balanced or vorticity-dominated Rossby and unbalanced or IG, mainly divergent components.

The divergent energy spectra are often regarded as synonymous with IG spectra in mid-latitude mesoscale conditions. On large scales and in the tropics, such an assumption is not valid.

For example, the equatorial Kelvin wave is a half-rotational and half-divergent mode and as such difficult to extract from IFS data.

By contrast, the computation of rotational and divergent energy for the wavenumber k from spherical harmonics involves derivatives and thus depends on velocities in neighbouring wavenumbers.

For example, the planetary scales were significantly more energetic in January than in July not shown. Comparing these with the analyses suggests that HRES tended to somewhat underpredict the variability at most scales, especially at zonal wavenumber 2.

The modal decomposition can be used to filter any mode and spatial scale back to physical space. For example, Figure 2 presents balanced and unbalanced flow in January and July for a level at the tropical tropopause.

In this region, the unbalanced winds were of the same direction, whereas over the central Pacific they were stronger and with the opposite sign compared to the balanced flow Figure 2b,c.

In July, the unbalanced winds were strongest over the Indian Ocean region in relation to the summer monsoon. Overall, Figure 2 shows that a significant component of large-scale tropical circulation is unbalanced in both months.

In the lower tropical troposphere, unbalanced winds tend to be stronger than balanced winds, especially in the cross-equatorial component not shown.

Figure 2 Average horizontal winds and geopotential height shading at model level 60 approximately hPa in the tropics in January showing a total average flow, b balanced average flow and c unbalanced average flow; and in July showing d total average flow, e balanced average flow and f unbalanced average flow.

Averaging is performed for analyses at 00 UTC. Note that here the presented levels are sigma levels and geopotential height is a modified geopotential variable that includes surface pressure.

As a result, circulation follows the terrain throughout the model depth. Geopotential height is visualised by five contours between the maximal and minimal value in each panel.

Figure 3 shows that, on average, the equatorial Kelvin wave signal is dominated by the zonal wavenumber 1 and has the largest amplitude over the Indian ocean in July.

The propagation of Kelvin waves in the model forecasts is illustrated in Figure 4. Here, we put together results of the modal decomposition every 12 hours and show both zonal wind and temperature perturbations, computed from geopotential perturbations using the hydrostatic relationship.

Although the decomposition is performed independently for each time step, when the outputs for successive times are put together, they naturally connect and show propagation properties known from linear theory and studies based on frequency filtering.

This is a strong justification for the assumptions made for the derivation of normal modes used for the decomposition. It should be noted that the presented wave properties are the result of a summation over 70 vertical modes.

Figure 3 Kelvin wave winds arrows and geopotential height perturbations shading in January at a model level 68 approx. Averaging is performed for analyses from 00 UTC.

Figure 4 The evolution of Kelvin waves in the day forecast started on 20 July , 00 UTC, showing zonal wind speed perturbations shading and Kelvin wave temperature perturbations isolines every 2 K , with positive perturbations drawn in solid lines and negative perturbations in dashed lines, for a level 29 approx.

The verification can also be performed in physical space for any mode of interest. The growth of RMSEs in Figure 5 is associated with the variability of the tropical stratosphere, which is driven by vertically propagating equatorial waves associated with convection.

In July, convection is most intense over the maritime continent and the errors in stratospheric circulation first develop here. By contrast, the RMSEs of the stratospheric unbalanced zonal wind component propagate eastward in forecasts in both July Figure 5b and January not shown , but the error amplitudes are greater and develop earlier in the forecasts in July.

The location of the maximal stratospheric RMSE is not the same in January and July as the most intense convection, which generates vertically propagating IG waves, moves along the equator not shown.

The fact that RMSEs for balanced flow along the equator in Figure 5a,b appear smoother than RMSEs for unbalanced flow can possibly be explained by the dynamical properties of IG waves and their generation by physical processes.

The growth of zonally averaged tropical forecast errors in the zonal wind component is largest in the balanced component in the upper troposphere.

In the day range, the balanced error at level hPa is nearly twice as large as the error in the unbalanced component Figure 5c,d.

The two components initially have similar amplitudes, which indicates that the analysis errors relative to the variability of the wind is higher in the unbalanced component compared to the balanced component, or possibly that the error growth is much higher during the first forecast day.

In the stratosphere level 50 the unbalanced component of error dominates in both January and July but the error growth is greatest in July, when convection is stronger.

In the next section we are going to discuss short-range errors by presenting average analysis increments. Another useful error decomposition is presented in Figure 6, which shows zonal wind analysis increments in autumn as the mean absolute differences between the analysis and the first-guess forecast.

The average increments are small if the short-range forecast first-guess agrees with the available observations.

The increments are also small if there was no significant error growth in the short-range forecast.

In general, one expects the increments to be larger in dynamically active regions with faster intrinsic error growth e. To understand the nature of errors, the decomposition of the increments into balanced and unbalanced components could be valuable.

Figure 6 Mean analysis increments of zonal wind from September to November showing a total increments at model level approx.

Increments are computed as mean absolute differences between hour forecasts and analyses valid at 18 UTC.

Global analysis increments for all modes, split into balanced and unbalanced modes, are shown in Figure 6 at two model levels. The level close to hPa represents the flow in the upper troposphere in the tropics and in the lower stratosphere in the mid-latitudes.

The increments are largest at the hPa level in the tropics. Lower in the troposphere, the increments are distributed more evenly and appear smoother, especially for the balanced component in the mid-latitudes.

Note also that smaller increments at the hPa level in the extra-tropics are above the tropopause, where variability is significantly smaller. In the tropics, a larger part of increments is associated with unbalanced modes than with balanced modes at both levels.

The largest increments are found over tropical Africa. A further diagnostic into various modes reveals that some of the increments over Africa are associated with the Kelvin modes not shown.

Furthermore, these increments, which are believed to be connected to convection over Africa, are strongest during daytime 18 UTC analysis.

There are also big increments in unbalanced flow over eastern Africa, which is related to very localised and unrealistic convection in the model over Ethiopia.

This feature has been improved in the new IFS model cycle 41r2. Overall, Figure 6 suggests that data assimilation is most difficult in the tropics, where forecast errors grow fastest and where a lack of direct wind observations makes it difficult to constrain circulation in the analyses.

Figure 6 also shows that in high-resolution forecasts a significant part of tropospheric analysis increments projects onto unbalanced modes in the extra-tropics too.

We have presented a new diagnostic technique that can usefully be applied to ECMWF forecasts in the tropics and that complements other methods to validate model performance.

Based on a decomposition into balanced and unbalanced IG modes, the technique enables balanced flow features, such as individual equatorial Rossby waves, and unbalanced waves, such as Kelvin waves, to be evaluated separately.

In this way, we can more easily relate errors in forecasts to initial-state uncertainties and model errors. Bechtold , P.

Koehler , T. Jung , F. Doblas-Reyes , M. Leutbecher , M. The inset shows the annual cycle of the amplitude of PC1 defined as the yr average of the absolute value of PC1 for each month.

The solid line denotes the mean of the annual cycle. It is approximately zonally symmetric, but the zonal asymmetries are notable, and their configuration differs between the high and midlatitudes.

The high-latitude band consists of two centers of variability: one over East Antarctica and one over West Antarctica, while the midlatitude outer ring is dominated by a zonal wavenumber 3 structure.

A wavenumber 3 pattern is also prominent at midlatitude in the climatology Van Loon and Jenne The strongest loading occurs over the Amundsen Sea, where the month-to-month variability is also greatest.

Prominent features of the Z SAM pattern are the occurrence of two anomalous highs over the South Pacific and South Atlantic, with an anomalous low between them near the Amundsen Sea.

As shown in Fig. The most significant correlations between the SAM and tropical SST occur during austral winter and summer, although the specific tropical region with which the SAM is most strongly correlated varies from season to season Fig.

In the monthly mean data for all calendar months Fig. We estimate the significance of the correlations in Figs. The seasonality of the amplitude and structure of the SAM can be assessed by calculating EOFs for each season individually.

The annual cycle of the absolute value of the conventional monthly SAM index inset in Fig. In all seasons except summer DJF , the pattern of EOF1 exhibits strong zonal asymmetries with the largest loading over the Amundsen Sea and neighboring regions, where the largest monthly and seasonal variability in Z is observed Fig.

EOF1 has been scaled by one standard deviation of the corresponding principal component. The percentage of the total variance explained by EOF1 is indicated on the top of each panel.

Let us consider how the Z variability over this region of high variability is linked with the SH circulation as a whole. These one-point regression maps strongly resemble the corresponding leading EOF for the respective seasons, thus suggesting that the EOFs are dominated by the circulation variability over the Amundsen Sea.

The region of maximum correlation in the SST field appears in each season to be directly associated with the wave-train-like pattern in Z In each of those seasons, the maximum correlation with SST is also located in the tropical central Pacific.

Regression of Z over the AS point This relationship is further illustrated in Fig. The correlation between those tropical SST anomalies and the low-level circulation exhibits a PSA-like wave train structure in the extratropics, with a phase reversal between the upper and lower troposphere over the tropical Pacific, indicative of a stationary Rossby wave response to tropical SST forcing.

Regression of tropical SST over the key region denoted as the box in Fig. Previous work has shown that the North Hemisphere annular mode may represent a superposition of regional patterns Cash et al.

This is equivalent to removing a PSA-shaped wave train from each monthly Z field. By construction, the variability over the AS point and the neighboring region is almost entirely eliminated, while the variability over remote areas that is unrelated to the AS point is retained.

EOF1 of the residual monthly data exhibits a pattern that is distinct from EOF1 of the raw data, with a zonal dipole pattern that is well defined only in the Eastern Hemisphere Fig.

Dashed line denotes the mean of the annual cycle. The time-varying index of the pattern in Fig. The correlation between the seasonal-mean index of this pattern and simultaneous SST anomalies Fig.

In the other two seasons the connection with the tropics is very weak. As shown in Table 2 , the correlation between the indices for the Eastern and Western Hemispheres is weak and varies erratically from one calendar month to the next.

Analogous tables not shown were constructed using other longitudes for partitioning the two hemispheres. The weakest interhemispheric correlations are obtained when the Pacific sector is separated from the Indian Ocean sector.

Thus, the zonal homogeneity and coherence of the SAM are not robust throughout the year. The SAM-related fluctuations over the Pacific and Indian Ocean sector have a stronger tendency to behave independently in the upper troposphere than at lower levels.

Analogous calculations based on the Z field indicate that the regional SAM indices exhibit similar independence in the midtroposphere. At the surface the zonal coupling is somewhat stronger.

At midlatitudes e. Figure 9 shows the 1-month-lag autocorrelation of the monthly Z in the SH. The tropical Z shows large autocorrelation, indicating strong month-to-month persistence of tropical circulation resulting from slowly varying tropical SSTs.

In the midlatitudes of the Indian Ocean, Z shows very little persistence. In contrast, Z over the Pacific show relatively large persistence at midlatitudes.

The largest autocorrelation of Z is observed adjacent to and over West Antarctica, and this high autocorrelation appears to connect to the tropics through the South Pacific.

These results offer additional evidence that high-latitude circulation variability over the Pacific sector and Indian Ocean sector have quite different origins, with a strong tropically related process prevailing in the Pacific and a midlatitude-related processes dominating in the Indian sector.

This is consistent with the results of Barnes and Hartmann , who found that in JJA a positive eddy feedback that acts to sustain the SAM is observed over the Indo-Atlantic sector but not over the Pacific sector.

Barnes and Hartmann further suggested that the lack of wintertime eddy feedback over the South Pacific is due to the absence of the midlatitude jet in that region.

The results presented above indicate that the leading EOF mode of SH circulation variability, conventionally defined as the SAM, owes its existence to a superposition of two largely independent patterns: a PSA wave train over the Pacific sector that projects upon the zonally symmetric SAM signature and a north—south shifting of the jet stream and storm track over the Indian Ocean sector that is a reflection of extratropical eddy—mean flow interaction.

A positive feedback of the stationary waves upon zonal-mean flow, as suggested by DeWeaver and Nigam , is one mechanism that might cause these two separate patterns to occasionally vary in tandem.

Most research on the trend in the SAM has focused on the observed positive trend during austral summer and its association with both global tropospheric greenhouse gas forcing and high-latitude SH stratospheric ozone forcing Thompson and Solomon ; Gillett and Thompson ; Marshall et al.

In view of the close connection between variations in tropical SST and the SAM discussed above, it is of interest to explore the possible role of trends in tropical SST in contributing to the observed trend in the SAM.

However, a positive trend is clearly discernible in the seasonal index for DJF Fig. The shift in the SAM index mainly occurs in the mids. In contrast, a decreasing trend is observed in JJA that has not previously been discussed in the literature Fig.

Much of the decrease in the index in JJA occurred around During spring and fall, there is no apparent trend in the SAM index. The temporal evolution of SAM in DJF can be divided subjectively into two epochs —93 and — that have the largest contrast.

For JJA, the entire period can be divided into —89 and — To illustrate the spatial patterns of the trends in winter and summer, based on the corresponding seasonal SAM index, the — period of record can be divided subjectively into the two epochs that exhibit the largest contrast.

The Z epochal differences in Fig. In DJF a pronounced zonally symmetric dipole dominates the circulation difference Fig.

Similar changes are observed in the middle troposphere and at the surface, as shown in Ding et al. On the interannual time scales, the positive SST anomalies over these two regions corresponds to the negative polarity of the SAM, Thus, the sign of the SST trends in these regions matches the sign of the SH circulation trends, consistent with the relationships for the year-to-year variability discussed in the previous section.

The upper-tropospheric circulation is more sensitive to the subtle change in the tropics than the flow at lower levels; hence the upper-level divergence associated with the tropical forcing plays a key role in driving tropical—extratropical teleconnections Hoskins and Karoly ; Sardeshmukh and Hoskins ; Trenberth et al.

The changes in tropical outgoing longwave radiation OLR and velocity potential that are coincident with the trend in the SAM are plotted in Figs.

These long-term changes in upper-level divergence, which appears to be directly driven by the forcing at the lower boundary, may play a key role in forcing the extratropical trends.

The choice of which two periods to use in making epochal difference, while subjective, is useful in illustrating the patterns associated with the largest changes in high-latitude circulation.

Results obtained from the MCA consist of modes comprising paired spatial patterns of SST and Z and the corresponding expansion coefficient time series.

The leading mode indicates the pattern of tropical SST anomalies that is most strongly coupled with the SH circulation and the SH circulation anomalies associated with that pattern.

The corresponding time series are dominated by interannual variability and exhibit negligible linear trends over the yr record.

Hence, the canonical eastern Pacific ENSO-related variability does not contribute at least not directly to the observed long-term changes in the SH circulation.

In contrast, the second MCA modes in both seasons capture the long term trends in the circulation and the related trends in tropical SST.

The associated time series exhibit significant long term trends very similar to those in the respective time series of the seasonal SAM index shown in Fig.

The MCA thus captures the salient features of the covariability between the SH circulation trend and concurrent changes in the tropical SST and further supports our interpretation of their statistical relationship.

We note that, because the strong interannual variability associated with ENSO is captured in the first mode of the maximum covariance analysis, the trend of SH circulation associated with the second mode has greater statistical significance than the SAM index.

Principal modes of covarying tropical sea surface temperature and Southern Hemisphere circulation in austral summer DJF.

Spatial patterns of tropical SST shading and hPa geopotential heights Z , contour interval 10 m associated with a mode 1 and b mode 2.

Time series of SST and Z for c mode 1 and d mode 2. Amplitudes in a , b are scaled by one standard deviation of the corresponding time series in c , d.

As in Fig. Figure from Ding et al. The empirical evidence presented in sections 3 and 4 shows that the low frequency variability in SAM pattern—as conventionally defined based on the leading EOF of SH circulation —is partly tropically forced.

In all seasons except summer, the SH upper troposphere exhibits a double split jet structure Fig. In summer the subtropical jet in the Pacific is severely weakened and a prominent jet is only present over the Indian Ocean.

The tight vorticity gradient associated with the jet and the strong variability of upper-level divergent flow over the warm pool should combine to form an active source of Rossby waves over the jet core region Renwick and Revell ; Lachlan-Cope and Connolley Indeed, as shown in Fig.

The most active and spatially extensive subtropical Rossby wave source occurs in JJA when the jet itself is strongest Fig.

Thus, the location and seasonality of RWS activity appears to be mainly determined by the seasonal evolution of the intensity and shape of the jet stream, rather than by the strength of the variability of tropical SST.

This is additional evidence that the interannual variability of the high-latitude SH circulation in the Pacific sector is more directly related to conditions in the tropics than to eddy—mean flow interactions or high-latitude orographic effects.

Because the circulation response to tropical SST forcing yields a pair of Rossby wave gyres residing to the west and poleward of the forcing, whose divergent wind field has a much larger meridional width and a stronger intensity than that associated with Kelvin waves Gill , the tropical SST anomalies to the east of Australia are efficient in triggering an active RWS in the core region of the subtropical jet.

This is consistent with the correlation analysis in section 3b , which shows that Z variations over the Amundsen Sea are more strongly correlated with SST anomalies over the central and eastern Pacific than with SST anomalies over the Indian Ocean and Western Pacific.

Considering the very active RWS along the core of subtropical jet, tropical internal instability largely unrelated to tropical SST anomalies could also excite fluctuations resembling the PSA wave train if it were able to generate a strong wave source over the jet core region.

If this were the case, then one would expect the PSA signature to be prominent in the SH circulation variability, not only on interannual time scales but also intraseasonally.

To explore this possibility, EOF analysis was performed on pentad-mean SH Z anomalies separately for each season and for the year as a whole.

Because tropical SST fluctuations should be very small on the intraseasonal time scale, this suggests that the PSA-like pattern obtained from pentad data reflects an extratropical response to tropical internal variability rather than a SST-forced response.

It thus appears that the PSA pattern is a preferred mode of the extratropical basic state that is very sensitive to small variations in the tropical convection: tropical SST forcing is one way to force such variations, but it is not a requirement.

In Fig. Circulation variability associated with a meridional shift of the eddy-driven midlatitude jet favors eddy feedback that tends to sustain a meridional seasaw mode between the Indian Ocean and East Antarctica Barnes and Hartmann The subtropical jet driven by the Hadley circulation inhibits eddy feedback Eichelberger and Hartmann but favors the generation of a Rossby wave source over its core region on a broad frequency band.

Thus, a Rossby wave train emanating from subtropical Australia to West Antarctica is the preferred circulation mode of the basic state in the Pacific sector.

In all seasons but summer, two different leading oscillation modes in the India Ocean and Pacific sector work together to establish the annular SAM pattern that exhibits strong zonal mean structure and out of phase action between the midlatitude and the high latitude.

In austral summer, the basic state of the SH is dominated by a single jet structure in the midlatitude. The eddy feedback is thus the main dynamical source to maintain an annular SAM in that season Lorenz and Hartmann This is also the season when ENSO tends to reach its peak.

The extratropical response to a mature ENSO also exhibits a PSA type wave train but with stronger meridional orientation and zonal mean structure, which may further strengthen the variability of the annular character of SAM in austral summer Seager et al.

Schematic showing the role of subtropical jet and midlatitude jet in shaping the SAM during nonsummer season when the basic state is characterized by the double jet structure.

See discussion section for further details. The summer DJF trend in the SAM over the past 30 years has been most commonly attributed to the direct influence of radiative forcing from both greenhouse gases and ozone depletion Thompson and Solomon ; Gillett and Thompson ; Marshall et al.

The abrupt rise in the summertime SAM index in the mids may have also been at least partly due to the abrupt change of DJF SST in the tropical Pacific, which occurred around the same time.

Ding et al. Given the strong projection of the Pacific—South American pattern upon the SAM, we suggest that the forcing attributable to SST warming in the tropical central Pacific explains a substantial part of the observed trend in the SAM in winter.

Similarly, the DJF SST warming over most of the tropics along with cooling in the eastern Pacific also has the potential to excite a zonally symmetric response in the extratropics by changing the Hadley cell and the midlatitude jet stream Seager et al.

The focus of this study is to examine the relationship between the southern annular mode and SST variability in the tropics.

Analyses based on EOF1 of monthly geopotential height at hPa show that the SAM pattern contains strong zonally asymmetric variability and that in the Pacific sector it projects strongly upon the PSA wave train that is mainly forced by SST anomalies in the equatorial central-eastern Pacific.

The intensity of this Rossby wave source is mainly determined by the strength and sharpness of the subtropical jet in the basic state flow.

This geographically fixed wave source may play an important role in anchoring the PSA wave train and favoring the recurrence of the PSA, with its primary center of action off the West Antarctic coast, even in the absence of a spatially coherent pattern of SST variability over the central Pacific.

When circulation variability associated with the PSA in the SH circulation is regressed out of the hemispheric hPa height field, the leading EOF exhibits a zonal dipole structure confined to the Indian Ocean sector, suggesting that the behavior of the SAM over the Indian Ocean sector and Pacific sector is different.

In combination, these results indicate that the SAM, which has conventionally been regarded as the leading EOF mode of SH circulation variability, in fact represents the superposition of a PSA type wave train in the Pacific sector and a meridional dipole pattern in the Indian Ocean sector.

Although eddy—mean flow interaction in the extratropics is widely believed to be the primary source of SAM variability, our study shows that planetary waves emanating from the tropical Pacific also strongly contribute to the variability of the SAM.

The long-term trend in the SAM over the past three decades is also examined with emphasis on its connection with tropical SST.

The SAM trend in summer is well known and has already been extensively discussed in previous work. The SAM index also exhibits a detectable downward trend in winter and the associated upper-tropospheric geopotential height pattern in the Pacific sector projects strongly onto the PSA wave train.

The interdecadal changes in the SAM in winter and summer are of opposing sign, and their time history is different. The summer SAM index exhibited an abrupt shift in the mids, whereas the main shift in the winter SAM began a decade earlier and was more gradual.

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