Abstract

A moist static energy (MSE) framework for zonal-mean storm-track intensity, defined as the extremum of zonal-mean transient eddy MSE flux, is derived and applied across a range of time scales. According to the framework, storm-track intensity can be decomposed into contributions from net energy input [sum of shortwave absorption and surface heat fluxes into the atmosphere minus outgoing longwave radiation (OLR) and atmospheric storage] integrated poleward of the storm-track position and MSE flux by the mean meridional circulation or stationary eddies at the storm-track position. The framework predicts storm-track decay in spring and amplification in fall in response to seasonal insolation. When applied diagnostically the framework shows shortwave absorption and land turbulent surface heat fluxes account for the seasonal evolution of Northern Hemisphere (NH) intensity; however, they are partially compensated by OLR (Planck feedback) and stationary eddy MSE flux. The negligible amplitude of Southern Hemisphere (SH) seasonal intensity is consistent with the compensation of shortwave absorption by OLR and oceanic turbulent surface heat fluxes (ocean energy storage). On interannual time scales, El Niño minus La Niña conditions amplify the NH storm track, consistent with decreased subtropical stationary eddy MSE flux. Finally, on centennial time scales, the CO2 indirect effect (sea surface temperature warming) amplifies the NH summertime storm track whereas the direct effect (increased CO2 over land) weakens it, consistent with opposing turbulent surface heat flux responses over land and ocean.

1. Introduction

Extratropical storm tracks, which reflect the dynamics of extratropical cyclones, are important for Earth’s climate because their poleward moist static energy (MSE) flux moderates the equator-to-pole energy gradient (Peixoto and Oort 1992; Trenberth and Stepaniak 2003; Shaw et al. 2016). Understanding and predicting storm-track position and intensity in response to climate change is one of the grand challenges of climate science (Bony et al. 2015; Shaw et al. 2016).

Barpanda and Shaw (2017, hereafter BS17), used the MSE budget to develop a framework for zonal-mean storm-track position defined as the latitude of the zonal-mean transient eddy MSE flux extremum. The BS17 framework was motivated by the MSE framework for shifts of the intertropical convergence zone (Schneider et al. 2014). According to the BS17 framework a storm-track shift can be decomposed into contributions from changes in net energy input (energy input to the atmosphere minus atmospheric storage) and meridional MSE flux divergence by the mean meridional circulation and stationary eddies. The framework was used to predict storm-track shifts in response to seasonal insolation assuming no change of meridional MSE flux divergence by the mean meridional circulation and stationary eddies. While the prediction was an overestimate of the observed storm-track shift, the BS17 framework was the first to make a seasonal prediction.

When applied diagnostically, the BS17 framework revealed net energy input was not a dominant contributor to seasonal, interannual, and centennial storm-track shifts. Instead the shifts across time scales were connected to compensation between circulation components. The stationary eddy contribution dominated shifts in response to seasonal insolation, El Niño minus La Niña conditions, and the CO2 direct effect [increased CO2 with fixed sea surface temperature (SST)] in the Northern Hemisphere (NH). The mean meridional circulation contribution dominated in response to the CO2 indirect effect (increased SST with fixed CO2) in the NH and Southern Hemisphere (SH). While the results did not provide causal explanations for the shifts, they motivated idealized model experiments to test causality.

Storm-track intensity also changes across a range of time scales. Seasonally, storm tracks generally reach maximum intensity during winter and minimum intensity during summer (Chang et al. 2002; Shaw et al. 2016). On longer time scales, El Niño conditions increase the NH storm-track intensity (Chang et al. 2002) whereas anthropogenic aerosol changes and Last Glacial Maximum conditions weaken it (Ming et al. 2011; Li and Battisti 2008). Reducing topography in atmospheric general circulation models (AGCMs) amplifies the NH storm track (Manabe and Terpstra 1974; Park et al. 2013). Future projections of storm-track intensity in response to increased CO2 suggest intensity changes are seasonally and hemispherically dependent (O’Gorman 2010).

Existing frameworks for storm-track intensity focus on eddy kinetic energy (EKE) and its connection to mean-state stratification and baroclinicity via the mean available potential energy (MAPE) or Eady growth rate (Lorenz 1955; Green 1970). The frameworks have been used to interpret intensity changes in response to climate change (e.g., Caballero and Langen 2005; Li and Battisti 2008; O’Gorman and Schneider 2008; O’Gorman 2010). While existing intensity frameworks represent an important step forward, they cannot be easily connected to energetic perturbations that are known to affect intensity. For example, seasonal insolation drives changes in the storm track; however, the EKE and MAPE frameworks cannot easily be used to predict storm-track intensity given seasonal insolation. Furthermore, they cannot easily be used to diagnose the importance of seasonal insolation for storm-track intensity because insolation must be first converted into mean-state changes that are, in part, a consequence of the moderation of the equator-to-pole energy gradient by the storm-track MSE flux.

While there exist many storm-track intensity metrics, including high-pass-filtered standard deviation of sea level pressure, EKE, and eddy heat flux [see Fig. 2 of Chang et al. (2002)], here we build on the results of BS17 and derive an energetic framework that connects zonal-mean storm-track intensity, defined as the extremum of transient eddy MSE flux, to energetic perturbations. The framework predicts seasonal intensity given insolation, assuming fixed planetary albedo and no change in the MSE flux by the mean meridional circulation and stationary eddies. The framework is used to diagnose the factors affecting storm-track intensity in response to seasonal insolation, El Niño minus La Niña conditions, and the direct and indirect effects of increased CO2.

2. MSE framework and datasets

a. MSE framework

We derive an energetic framework for zonal-mean storm-track intensity based on the atmospheric MSE budget:

 
formula

where , , and are the MSE flux divergence by the mean meridional circulation, stationary, and transient eddies, respectively; υ is meridional wind; m is MSE (, where is specific heat at constant pressure, T is temperature, L is latent heat of vaporization, q is specific humidity, and is geopotential); the overbar and the square brackets denote monthly and zonal averages, respectively, with the prime and the asterisk representing deviations from those averages, respectively; angle brackets denote a mass-weighted vertical integration; is the meridional divergence in spherical coordinates, where ϕ is latitude and a is the radius of Earth; t is time; and h is thermal energy . The net energy input is the difference between energy input to the atmosphere [EIA = top-of-the-atmosphere (TOA) radiative minus surface fluxes] and atmospheric storage .

Here storm-track intensity is defined as the zonal-mean transient eddy MSE flux at the storm-track position , that is, , where is defined as the latitude where transient eddy MSE flux divergence is zero (i.e., ) or where the transient eddy MSE flux reaches an extremum following BS17. According to this definition, storm-track intensity is negative in the SH and thus indicates a weakening of the SH storm track. The energetic definition of storm-track intensity, which includes all submonthly transients, represents an overestimate when compared to the 10-day bandpass-filtered MSE flux ( appendix A).

An equation for storm-track intensity is obtained after multiplying the MSE budget by and integrating between the pole and :

 
formula

where , , and for the NH. Thus, storm-track intensity changes are connected to changes in net energy input integrated poleward of and zonal-mean MSE flux by the mean meridional circulation and stationary eddies at :

 
formula

where the subscripts 0 and 1 indicate the climatology and changed climate, respectively.

Across the time scales considered net energy input is dominated by energy input to the atmosphere. We decompose energy input to the atmosphere into contributions from shortwave absorption (, where SW is shortwave), surface heat fluxes into the atmosphere [, where SH + LH is the turbulent surface heat flux (sensible plus latent heat flux) and LW is longwave], and outgoing longwave radiation (OLR) (i.e., ), following Donohoe and Battisti (2013). Thus, the net energy input change can be decomposed as since atmospheric storage is small.

We note that the storm-track intensity framework in (2) and (3) provides a physical interpretation of storm-track intensity changes; that is, they are related to changes in (i) net energy input poleward of the storm track, which affects the equator-to-pole energy gradient and/or (ii) MSE flux by the mean meridional circulation and stationary eddies at the storm-track position caused by circulation compensation. However, the framework is diagnostic, and thus it cannot be used to infer causality; that is, the right-hand-side terms are not necessarily causal and can exhibit symbiotic relationships with the storm track. Nevertheless, the framework can be used to formulate hypotheses regarding causality as discussed in section 4.

The MSE framework derived above uses an energetic metric of storm-track intensity (extremum of transient eddy MSE flux) following BS17. Other storm-track metrics include the high-pass-filtered standard deviation of sea level pressure, EKE, and eddy heat flux [see Fig. 2 of Chang et al. (2002)]. These metrics are complementary. The transient eddy MSE flux and EKE reflect different regions of the atmosphere (eddy MSE flux reaches extremum in the lower troposphere and EKE reaches extremum in the upper troposphere). Furthermore, the transient eddy MSE flux is affected by dynamic and thermodynamic factors. Seasonally, the transient eddy MSE flux is correlated with the 10-day high-pass-filtered EKE in the NH reflecting the importance of dynamic changes ( appendix A). The seasonal variations are too small in the SH for a meaningful comparison. On interannual time scales, the transient eddy MSE flux and EKE response to El Niño minus La Niña conditions are also consistent. However, on centennial time scales the energetic storm-track intensity exhibits some differences with EKE in response to increased CO2, particularly in the SH, reflecting the importance of thermodynamic changes ( appendix A).

b. Datasets

Observed storm-track intensity is quantified using atmospheric MSE flux from the NCEP (Kalnay et al. 1996) and ERA-Interim (Dee et al. 2011) reanalyses for 1979 to 2015. The data were processed and decomposed into transient eddy, stationary eddy, and mean meridional circulation contributions consistent with the averaging described in section 2a and following Marshall et al. (2014). The data were also interpolated onto a 0.1° grid.

The seasonal climatology of storm-track intensity in the ERA-Interim is 10% larger than in NCEP in the SH; however, the month-to-month seasonal tendency in both hemispheres is in reasonable agreement ( appendix B). The response to El Niño minus La Niña conditions in the NCEP reanalysis and ERA-Interim is only robust in the NH (cf. Tables 1 and 2). The maximum absolute difference between the NCEP reanalysis and ERA-Interim for all terms in (3) is used as an error estimate for the observed storm-track intensity. The error estimate for seasonal month-to-month tendency is 0.3 PW whereas the error estimate for the response to El Niño minus La Niña conditions is 0.1 PW. Results below the estimated error are not discussed.

Table 1.

The DJF storm-track intensity response (PW) to El Niño minus La Niña conditions from the NCEP reanalysis data for 1979–2015. The error estimate is 0.1 PW (see section 2b for more information).

The DJF storm-track intensity response (PW) to El Niño minus La Niña conditions from the NCEP reanalysis data for 1979–2015. The error estimate is 0.1 PW (see section 2b for more information).
The DJF storm-track intensity response (PW) to El Niño minus La Niña conditions from the NCEP reanalysis data for 1979–2015. The error estimate is 0.1 PW (see section 2b for more information).
Table 2.

As in Table 1, but for the ERA-Interim.

As in Table 1, but for the ERA-Interim.
As in Table 1, but for the ERA-Interim.

The observed shortwave absorption and OLR contributions to the net energy input are quantified using radiation fluxes (top-of-atmosphere LW and SW and surface SW) from three different sources: 1) NCEP reanalysis from 1979 to 2015, 2) ERA-Interim from 1979 to 2015, and 3) CERES energy balanced and filled (EBAF) from 2000 to 2015. When computing the contributions to (i.e., , , and ), the global mean of each term is subtracted prior to computing the spatial integral over the polar cap to ensure the implied energy transport at is independent of whether the integral is computed from the South Pole to or the North Pole to . The removal of the global mean is equivalent to balancing the global-mean MSE budget with a spatially invariant adjustment and is consistent with previous work (Trenberth and Caron 2001; Lucarini and Ragone 2011; Donohoe and Battisti 2013). It is also consistent with (1) being interpreted as an equation for deviations from the global mean.

The results presented in section 3 show the difference between the different radiation datasets is fairly small in terms of the impact on storm-track intensity. This is consistent with 1) the dominance of SWABS, which is constrained by the Earth–sun geometry and atmospheric constituents (water vapor and ozone) and 2) the removal of the global mean from net energy input contributions, which likely removes radiation biases in reanalysis data. The small impact of the different radiation datasets also suggests the spatially invariant adjustment does not have a significant impact on the results.

The observed SHF contribution to the net energy input is quantified as the residual of the atmospheric MSE budget following previous work (Donohoe and Battisti 2013). We obtain four different estimates of SHF: 1) NCEP radiation and NCEP MSE flux divergence from 1979 to 2015, 2) ERA-Interim radiation and ERA-Interim MSE flux divergence from 1979 to 2015, 3) CERES EBAF radiation and NCEP MSE flux divergence from 2000 to 2015, and 4) CERES EBAF radiation and ERA-Interim MSE flux divergence from 2000 to 2015. The results presented in section 3 show all four estimates of SHF are in qualitative agreement.

The response of storm-track intensity to El Niño–Southern Oscillation is quantified by the difference between El Niño and La Niña years during December–February (DJF) following BS17. El Niño years were defined by a DJF-averaged Niño-3.4 index value ≥0.5°C (1979, 1982, 1986, 1987, 1991, 1994, 1997, 2002, 2004, 2006, and 2009) and La Niña years were defined by a DJF index value ≤−0.5°C (1984, 1988, 1998, 1999, 2000, 2007, 2010, and 2011).1

c. AGCM experiments

Following BS17 we quantify the storm-track response to the CO2 direct and indirect effects using the MPI-ESM-LR AGCM (MPI AGCM; Stevens et al. 2013). BS17 showed the MPI AGCM reproduces the observed seasonal cycle of MSE flux. Shaw and Voigt (2015, 2016) showed the CO2 direct and indirect effect responses in the MPI AGCM agree with the CMIP5 multimodel mean.

The CO2 direct effect involves increasing CO2 by 4 times its climatological value with fixed SST. Following Shaw and Voigt (2016) the CO2 direct effect is quantified as the response to increased CO2 over land since it dominates the storm-track shift. The CO2 indirect effect is quantified as the response to SST warming by 4 K with fixed CO2. The MPI AGCM simulations used here are the same as those in Shaw and Voigt (2016), and the data are interpolated onto a 0.1° grid. A spatial invariant adjustment is applied to the MPI AGCM energy input data.

3. Results

The MSE framework connects storm-track intensity to energetic perturbations. This connection can be used to make a falsifiable prediction of month-to-month seasonal storm-track intensity. Given the storm-track intensity I, position , and planetary albedo α from NCEP during month m, the MSE framework in (3) predicts the storm-track intensity change between months m and m + 1 given the TOA insolation change assuming no change in the MSE flux by the mean meridional circulation and stationary eddies [i.e., ]. The framework predicts that if insolation dominated intensity then the storm tracks would amplify in fall and decay in spring (Fig. 1a).

Fig. 1.

Month-to-month seasonal storm-track intensity (a) predicted from the MSE framework given seasonal insolation, assuming fixed planetary albedo from NCEP and no change in MSE flux by the mean meridional circulation and stationary eddies and (b) diagnosed from the NCEP reanalysis. Dashed lines show the intensity evaluated at the storm-track position in the opposite hemisphere.

Fig. 1.

Month-to-month seasonal storm-track intensity (a) predicted from the MSE framework given seasonal insolation, assuming fixed planetary albedo from NCEP and no change in MSE flux by the mean meridional circulation and stationary eddies and (b) diagnosed from the NCEP reanalysis. Dashed lines show the intensity evaluated at the storm-track position in the opposite hemisphere.

The observed amplitude of the storm-track intensity tendency in both hemispheres is smaller than that predicted from insolation changes (Figs. 1a and 1b). The discrepancy is largest in the SH where the predicted amplitude exhibits a clear sinusoidal evolution whereas the observed intensity does not (cf. blue lines in Figs. 1a and 1b). The large difference in seasonal storm-track position in each hemisphere documented by BS17 does not account for the amplitude discrepancy (dashed lines in Fig. 1).

The predicted and observed timing of maximum tendency or intensification of the NH storm track occurs in fall (September minus August) whereas the timing of minimum intensity or weakening occurs in spring (April minus March). In the SH, the predicted minimum tendency or intensification also occurs in fall (March minus February) whereas the maximum tendency or weakening occurs in spring (October minus September). The predicted magnitude and timing of seasonal intensification relative to the solstices is nearly equal in the two hemispheres except for small differences resulting from the impact of precessional phasing and planetary albedo. However, the seasonal cycle of predicted intensification is not antisymmetric about the solstices (time of zero tendency). Clearly, month-to-month changes in TOA insolation with fixed planetary albedo do not dominate the seasonal evolution of storm-track intensity.

The discrepancy between the insolation-predicted and observed seasonal evolution of storm-track intensity may result from the compensation of TOA insolation changes poleward of the storm track by 1) surface heat fluxes and/or OLR poleward of the storm track or 2) MSE flux by the mean meridional circulation and/or stationary eddies at the storm-track position. In the following subsections, the MSE framework is applied diagnostically across time scales (seasonal, interannual, and centennial) to determine the dominant contributions in (3).

a. Seasonal intensity changes

The observed NH seasonal storm-track intensity weakens in spring and strengthens in fall, exceeding the error estimate (gray shading in Fig. 2a). In addition, there is a midwinter intensity minimum relative to the insolation-predicted intensity. Nakamura (1992) first reported the midwinter minimum, which is strongest in the Pacific basin. The SH seasonal storm-track intensity is negligible (i.e., it does not generally exceed the error estimate) (gray shading in Fig. 2b). According to the MSE framework, the net energy input contribution dominates the seasonal storm-track intensity in both hemispheres (magenta line in Figs. 2a,b) and is consistent with weakening in spring and strengthening in fall. The NH seasonal intensity amplitude is smaller than the net energy input contribution because stationary eddies oppose it. In particular, NH stationary eddy MSE flux damps storm-track intensification during early winter (December minus November) and storm-track weakening during midwinter (February minus January; blue line in Fig. 2a). Thus, stationary eddies dominate the midwinter minimum. The mean meridional circulation contribution in the NH does not exceed the error estimate (green line in Fig. 2a). In the SH, the net energy input contribution is very different from the predicted intensity (cf. magenta line in Fig. 2b and blue line in Fig. 1a) suggesting seasonal insolation is compensated by other net energy input contributions.

Fig. 2.

Decomposition of seasonal intensity into contributions from net energy input , mean meridional circulation , and stationary eddies following the MSE framework in (3) for the (a) NH and (b) SH diagnosed from the NCEP reanalysis. Decomposition of seasonal net energy input into contributions from shortwave absorption , surface heat fluxes into the atmosphere , and outgoing longwave radiation for the (c) NH and (d) SH using NCEP radiation and MSE flux divergence (solid lines) and CERES radiation and NCEP MSE flux divergence (dashed lines). The shaded region represents the error estimate (±0.3 PW); see section 2b for more information.

Fig. 2.

Decomposition of seasonal intensity into contributions from net energy input , mean meridional circulation , and stationary eddies following the MSE framework in (3) for the (a) NH and (b) SH diagnosed from the NCEP reanalysis. Decomposition of seasonal net energy input into contributions from shortwave absorption , surface heat fluxes into the atmosphere , and outgoing longwave radiation for the (c) NH and (d) SH using NCEP radiation and MSE flux divergence (solid lines) and CERES radiation and NCEP MSE flux divergence (dashed lines). The shaded region represents the error estimate (±0.3 PW); see section 2b for more information.

The decomposition of net energy input into contributions from shortwave absorption, surface heat fluxes into the atmosphere, and OLR is shown in Figs. 2c and 2d. In the NH, shortwave absorption dominates (red line in Fig. 2c) and accounts for the overall seasonal evolution; however, it is partially compensated by OLR (green line in Fig. 2c) consistent with the Planck feedback. The different amplitudes of the predicted seasonal intensity and diagnosed shortwave absorption contribution shows surface shortwave is important (cf. red lines in Figs. 1a and 2c). Surface heat fluxes lead to a delay in the net energy input evolution relative to the shortwave absorption during summer and midwinter (blue line in Fig. 2c). In the SH shortwave absorption also dominates (red line in Fig. 2d) but is almost entirely compensated by OLR and surface heat fluxes (green and blue lines in Fig. 2d) leading to negligible net energy input and seasonal intensity.

The latitudinal structure of net energy input during periods of large intensity tendency in the NH (May minus April and September minus August) reveals changes in shortwave absorption and turbulent surface heat flux are in phase where land dominates the zonal mean (50°–70°N; Fig. 3) but out-of-phase where ocean dominates the zonal mean (20°–50°S and 20°–40°N; Fig. 3). Accordingly, during the period of increasing insolation in the NH (May minus April) land is a source of turbulent surface heat fluxes into the atmosphere, consistent with increased net energy input poleward of the storm track, decreased equator-to-pole energy gradient, and decreased storm-track intensity (Figs. 3a,b). During the period of decreasing insolation in the NH (September minus August) land is a sink of turbulent surface heat fluxes into the atmosphere, consistent with decreased net energy input poleward of the storm track, an increased equator-to-pole energy gradient, and increased storm-track intensity (Figs. 3c,d). Over the ocean, changes in insolation are almost entirely compensated by turbulent surface heat fluxes (ocean energy storage), leading to small intensity changes in the SH.

Fig. 3.

(left) Net energy input (NE) decomposed into shortwave absorption (SWABS), surface heat fluxes into the atmosphere (SHF), and outgoing longwave radiation (OLR) contributions for (a) May minus April and (c) September minus August in the NCEP reanalysis. (right) Response of surface longwave radiation (SFCLW), sensible and latent heat flux over land (HFL), and ocean (HFO) contributions to surface heat flux into the atmosphere for (a) May minus April and (c) September minus August in the NCEP reanalysis. The dashed vertical black lines indicate the storm-track position during (top) April and (bottom) August whereas the solid vertical black lines indicate the position during (top) May and (bottom) September. The global mean is removed from all contributions.

Fig. 3.

(left) Net energy input (NE) decomposed into shortwave absorption (SWABS), surface heat fluxes into the atmosphere (SHF), and outgoing longwave radiation (OLR) contributions for (a) May minus April and (c) September minus August in the NCEP reanalysis. (right) Response of surface longwave radiation (SFCLW), sensible and latent heat flux over land (HFL), and ocean (HFO) contributions to surface heat flux into the atmosphere for (a) May minus April and (c) September minus August in the NCEP reanalysis. The dashed vertical black lines indicate the storm-track position during (top) April and (bottom) August whereas the solid vertical black lines indicate the position during (top) May and (bottom) September. The global mean is removed from all contributions.

b. Interannual intensity changes

On interannual time scales, the DJF NH storm track strengthens in response to El Niño minus La Niña conditions; however, the SH storm-track response is not robust (NCEP suggests a weakening whereas ERA-Interim suggests no change; see Tables 1 and 2 and Figs. 4a and B4a). According to the MSE framework, the strengthening of the NH storm track is consistent with stationary eddy MSE flux changes at the storm-track position and opposed by changes in the mean meridional circulation MSE flux (Tables 1 and 2). More specifically, the strengthening of the NH storm track is consistent with a weakening of the subtropical stationary eddy MSE flux but opposed by a weakening of the Ferrel circulation MSE flux (Fig. 4). The net energy input change in response to El Niño minus La Niña conditions does not exceed the error.

Fig. 4.

The DJF (a) transient eddy, (b) mean meridional circulation, and (c) stationary eddy MSE flux for El Niño (colored, solid), La Niña (colored, dashed), and their difference (black) in the NCEP reanalysis. The El Niño and La Niña MSE fluxes are divided by 10. The vertical solid (dashed) black line indicates the El Niño (La Niña) storm-track position.

Fig. 4.

The DJF (a) transient eddy, (b) mean meridional circulation, and (c) stationary eddy MSE flux for El Niño (colored, solid), La Niña (colored, dashed), and their difference (black) in the NCEP reanalysis. The El Niño and La Niña MSE fluxes are divided by 10. The vertical solid (dashed) black line indicates the El Niño (La Niña) storm-track position.

c. Centennial intensity changes

On centennial time scales, the CO2 direct effect weakens the NH storm track from June to September and strengthens it from December to February (red line in Fig. 5a). The CO2 direct effect does not significantly impact the SH storm track (red line in Fig. 5b). According to the MSE framework, the strengthening of the NH wintertime storm track is consistent with net energy input changes poleward of the storm track and stationary eddy MSE flux changes at the storm-track position (magenta and blue lines in Fig. 5a). More specifically, the storm-track intensification in January is consistent with a weakening of midlatitude stationary eddy MSE flux (Fig. 6). The net energy input change during January is dominated by the change in OLR (Fig. 7a).

Fig. 5.

Response of storm-track intensity to the CO2 (a),(b) direct and (c),(d) indirect effects in the (left) NH and (right) SH in the MPI AGCM decomposed into contributions from net energy input , mean meridional circulation , and stationary eddies following the MSE framework in (3).

Fig. 5.

Response of storm-track intensity to the CO2 (a),(b) direct and (c),(d) indirect effects in the (left) NH and (right) SH in the MPI AGCM decomposed into contributions from net energy input , mean meridional circulation , and stationary eddies following the MSE framework in (3).

Fig. 6.

The January (a) transient eddy, (b) mean meridional circulation, and (c) stationary eddy MSE flux for the CO2 direct effect (colored, solid), climatology (colored, dashed), and their difference (black) in the MPI AGCM. The climatology and CO2 direct effect MSE flux are divided by 10. The vertical dashed (solid) black line indicates the climatological (CO2 direct effect) storm-track position during January.

Fig. 6.

The January (a) transient eddy, (b) mean meridional circulation, and (c) stationary eddy MSE flux for the CO2 direct effect (colored, solid), climatology (colored, dashed), and their difference (black) in the MPI AGCM. The climatology and CO2 direct effect MSE flux are divided by 10. The vertical dashed (solid) black line indicates the climatological (CO2 direct effect) storm-track position during January.

Fig. 7.

Response of net energy input to the CO2 (a),(b) direct and (c),(d) indirect effects in the (left) NH and (right) SH in the MPI AGCM decomposed into contributions from shortwave absorption , surface heat fluxes into the atmosphere , and outgoing longwave radiation .

Fig. 7.

Response of net energy input to the CO2 (a),(b) direct and (c),(d) indirect effects in the (left) NH and (right) SH in the MPI AGCM decomposed into contributions from shortwave absorption , surface heat fluxes into the atmosphere , and outgoing longwave radiation .

According to the MSE framework, the weakening of the NH summertime storm track is consistent with net energy input changes poleward of the storm track (magenta line in Fig. 5a). The net energy input change is dominated by surface heat flux changes (blue line in Fig. 7a) and opposed by changes in OLR (green line in Fig. 7a). The surface heat flux changes poleward of the NH storm track during August (blue lines in Figs. 8a,b) are consistent with (i) increased surface LW over land (black line in Fig. 8b) and (ii) increased turbulent surface heat flux over land (brown line in Fig. 8b). In response to the CO2 direct effect land warms more than the atmosphere and ocean (ocean temperature is fixed).

Fig. 8.

As in Fig. 3, but for the response to the CO2 (a),(b) direct effect during August and (c),(d) indirect effect during June in the MPI AGCM. The dashed vertical black lines indicate the climatological storm-track position during (top) August and (bottom) June whereas the solid vertical black lines indicate the position in response to CO2 (top) direct and (bottom) indirect effect. The global mean is removed from all contributions.

Fig. 8.

As in Fig. 3, but for the response to the CO2 (a),(b) direct effect during August and (c),(d) indirect effect during June in the MPI AGCM. The dashed vertical black lines indicate the climatological storm-track position during (top) August and (bottom) June whereas the solid vertical black lines indicate the position in response to CO2 (top) direct and (bottom) indirect effect. The global mean is removed from all contributions.

The CO2 indirect effect strengthens the storm track in both hemispheres (red lines in Figs. 5c,d). According to the MSE framework, the strengthening is mostly consistent with net energy input changes poleward of the storm track (magenta lines in Fig. 5c,d), with the exception of July–September in the SH when the mean meridional circulation MSE flux at the storm-track position dominates (green line in Fig. 5d). The mean meridional circulation MSE flux response during July is consistent with a strengthening of the MSE flux by the SH Ferrel circulation (Fig. 9).

Fig. 9.

The July (a) transient eddy, (b) mean meridional circulation, and (c) stationary eddy MSE flux for the CO2 indirect effect (colored, solid), climatology (colored, dashed), and their difference (black) in the MPI AGCM. The climatology and CO2 indirect effect MSE flux are divided by 10. The vertical dashed (solid) black line indicates the climatological (CO2 indirect effect) storm-track position during July.

Fig. 9.

The July (a) transient eddy, (b) mean meridional circulation, and (c) stationary eddy MSE flux for the CO2 indirect effect (colored, solid), climatology (colored, dashed), and their difference (black) in the MPI AGCM. The climatology and CO2 indirect effect MSE flux are divided by 10. The vertical dashed (solid) black line indicates the climatological (CO2 indirect effect) storm-track position during July.

The net energy input change in response to the CO2 indirect effect is dominated by surface heat flux and shortwave absorption (blue and red lines in Figs. 7c,d) and opposed by OLR (green lines in Figs. 7c,d). Increased shortwave absorption is dominated by clear-sky radiative fluxes, suggesting increased water vapor dominates the storm-track response rather than cloud changes (not shown). The strengthening of the NH storm track during June is consistent with decreased turbulent surface heat fluxes over land and ocean poleward of the storm track (Figs. 8c,d). The surface latent heat flux increases everywhere in response to the indirect effect. Upon removal of the global mean there is increased surface latent heat fluxes in the tropics and decreased heat flux poleward of the storm track, consistent with an increased equator-to-pole energy gradient.

4. Conclusions and discussion

Storm-track intensity responds to energetic perturbations across a range of time scales. Here we formulate an MSE framework for storm-track intensity and apply it to seasonal (month to month), interannual (El Niño minus La Niña conditions) and centennial (direct and indirect effect of increased CO2) time scales.

The MSE framework defines storm-track intensity as the extremum of transient eddy MSE flux. According to the MSE framework, storm-track intensity changes can be decomposed into contributions from net energy input (energy input to the atmosphere minus atmospheric storage) poleward of the storm-track position and MSE flux by the mean meridional circulation and stationary eddies at the storm-track position. The energy input to the atmosphere contribution can be further decomposed into shortwave absorption, surface heat fluxes into the atmosphere, and OLR components. The surface heat flux contribution is the sum of turbulent surface heat fluxes (sensible plus latent heat flux) and surface longwave radiation.

The MSE framework for storm-track intensity connects intensity to energetic perturbations. This connection can be used to predict seasonal intensity changes given seasonal insolation, assuming fixed planetary albedo and no change in MSE flux by the mean meridional circulation and stationary eddies. The predicted intensity exhibits phase and amplitude discrepancies with the observed intensity in both hemispheres, suggesting seasonal insolation alone does not determine seasonal intensity.

When applied diagnostically, the MSE framework suggests the large seasonal intensity in the NH is consistent with seasonal heating of the atmosphere by shortwave absorption amplified by land turbulent surface heat fluxes. In particular, the increased seasonal heating and land turbulent surface heat fluxes poleward of the storm track during spring weakens the storm-track intensity, consistent with a reduced equator-to-pole energy gradient. Decreased seasonal heating and land turbulent surface heat fluxes poleward of the storm track during fall strengthens intensity, consistent with a stronger equator-to-pole energy gradient. The seasonal intensity evolution is compensated by OLR (Planck feedback), oceanic turbulent surface heat fluxes, and stationary eddy MSE flux. The stationary eddy changes are associated with a midwinter minimum of intensity. In the SH, seasonal intensity is negligible because shortwave absorption is almost entirely compensated by OLR and oceanic turbulent surface heat fluxes. The results highlight the buffering of seasonal storm-track intensity in the SH by ocean energy storage. Donohoe and Battisti (2013) previously noted the damping of shortwave absorption by surface heat fluxes into the atmosphere in the SH extratropics.

On interannual time scales, the framework suggests the intensification of the NH storm track in response to El Niño minus La Niña conditions is consistent with decreased subtropical stationary eddy MSE flux but opposed by increased MSE flux by the Ferrel circulation. The decreased MSE flux by subtropical stationary eddies could occur through a thermodynamic (water vapor or temperature) and/or dynamic (stationary eddy amplitude) response. The subtropical stationary eddy amplitude in the eastern Pacific weakens in response to El Niño minus La Niña conditions [see Fig. 6 of Spencer and Slingo (2003)], suggesting dynamic changes play a role. The response of the Ferrel circulation has been connected to changes in eddy momentum fluxes (Seager et al. 2003). The SH storm-track intensity and net energy input response to El Niño minus La Niña conditions are not robust.

Finally, on centennial time scales, the framework suggests the weakening of the NH summertime storm track in response to the CO2 direct effect is consistent with increased surface longwave and turbulent surface heat flux over land poleward of the storm track as a result of land warming more than the atmosphere and ocean. In contrast, the intensification of the NH wintertime storm track in response to the direct effect is consistent with decreased midlatitude stationary eddy MSE flux. The CO2 indirect effect strengthens the storm track in both hemispheres in all seasons, consistent with 1) increased shortwave absorption, most likely caused by increased water vapor (cf. Takahashi 2009), which peaks equatorward of the storm track, increasing the energy gradient across the storm track; and 2) decreased oceanic turbulent surface heat fluxes poleward of the storm track. The decreased oceanic turbulent surface heat flux poleward of the storm track is relative to the global-mean increase (global mean is removed), which is dominated by the tropics and consistent with an increased equator-to-pole energy gradient. The increased turbulent surface heat flux follows surface energy balance constraints (Boer 1993; Held and Soden 2000). The strengthening of intensity during NH summer in response to the CO2 indirect effect is opposite to the weakening in response to CO2 direct effect and is consistent with opposing turbulent surface heat flux changes over land and ocean. The mean meridional circulation MSE flux response to the CO2 indirect effect strengthens the SH storm-track intensity from July to September, which reflects an increase of MSE flux by the Ferrel circulation rather than an expansion of the Hadley circulation. Understanding the factors affecting intensity on decadal and millennial time scales is a work in progress.

The energetic metric of storm-track intensity used in the MSE framework and by BS17 is complementary to existing metrics (e.g., high-pass-filtered standard deviation of sea level pressure, EKE, and eddy heat flux; Chang et al. 2002). The energetic metric correlates with EKE when dynamic processes dominate (e.g., in response to seasonal insolation). However, the two metrics differ during some months in response to increased CO2 when thermodynamic processes dominate (e.g., increased saturation specific humidity following the Clausius–Clapeyron relation). Thus, the energetic metric of storm-track intensity is connected to both dynamic (EKE) and thermodynamic (precipitation) processes.

The MSE framework provides a physical interpretation of storm-track intensity changes; that is, they are related to changes in net energy input poleward of the storm track, which affects the equator-to-pole energy gradient, and MSE flux by the mean meridional circulation and stationary eddies at the storm-track position, which involves circulation compensation. However, the MSE framework is diagnostic and based on the MSE budget, and thus it does not provide causal explanations of storm-track intensity changes across time scales. In particular, the terms in the framework (net energy input poleward of storm track, MSE flux by the mean meridional circulation, and stationary eddies at the storm-track position) can exhibit symbiotic relationships with the storm track. For example, stationary eddies, which were shown here to play a key role in the seasonal evolution of NH storm-track intensity, have previously been shown to exhibit a symbiotic relationship with transient eddies during NH winter (e.g., Wang and Ting 1999; Held et al. 2002). Nevertheless, the framework motivates hypotheses regarding causality that can be tested using idealized models. For example, the results suggest surface heat fluxes over land and ocean have an impact on seasonal storm-track intensity (ocean energy storage buffers seasonal insolation leading to small seasonal intensity whereas zero storage over land is consistent with large seasonal intensity). This hypothesis is currently being tested using idealized simulations.

The results provide a new interpretation of storm-track intensity changes and can be compared to existing frameworks. O’Gorman (2010) showed NH EKE weakens and SH EKE strengthens during June–August (JJA) in response to increased CO2 in CMIP3 simulations. The EKE changes were connected to MAPE changes, highlighting a competition between changes in baroclinicity and stratification. Our results highlight a competition for JJA NH storm-track intensity between the CO2 direct and indirect effects, which exhibit opposing surface heat flux responses. The outcome of this competition in coupled climate models depends on the exact amount of CO2 and SST increase. According to the energetic framework, the NH wintertime storm track strengthens in response to the CO2 direct and indirect effects. However, previous work has highlighted a tug of war between upper- and lower-level changes in NH wintertime EKE (Chang et al. 2012). An assessment of the vertical structure of wintertime transient eddy MSE flux changes, including the role of thermodynamic versus dynamic changes, is needed. Finally, our results show the factors related to storm-track intensity changes, that is, net energy input poleward of the storm track, are generally different than those for storm-track position, that is, circulation compensation as shown by BS17.

Finally, using the MSE framework to accurately predict storm-track intensity requires closures for shortwave absorption, OLR, surface heat fluxes into the atmosphere, and circulation MSE fluxes. Furthermore, storm tracks are mostly confined to ocean basins, and thus the framework needs to be extended to include zonally asymmetric effects, which is work in progress. Ultimately the MSE framework for storm-track intensity provides a step toward understanding energetic intensity across a range of time scales.

Acknowledgments

TAS and PB acknowledge support from the National Science Foundation (AGS-1538944 and AGS-1742944). TAS is also supported by the David and Lucile Packard Foundation. The MPI simulations in this paper were completed with resources provided by the University of Chicago Research Computing Center. The authors thank Isla Simpson for providing the high-pass-filtered reanalysis data and three anonymous reviewers for their helpful comments. The model data in this study are available from TAS upon request.

APPENDIX A

Comparison of Storm-Track Intensity Metrics

Chang et al. (2002) discuss the different storm-track intensity metrics used in the literature (see their Fig. 2). One of the most common metrics is EKE. The energetic storm-track metric used here, which is based on the vertically integrated transient eddy MSE flux and includes all submonthly transients, is in qualitative agreement with vertically integrated 10-day high-pass-filtered EKE in terms of its seasonal evolution especially in the NH (Figs. A1 and A2). The seasonal correlation at each latitude is shown in Fig. A1d (solid black line). The two metrics also agree in terms of their interannual response to El Niño minus La Niña conditions. However, on centennial time scales in response to increased CO2 the EKE and transient eddy MSE flux differ during some months, especially in the SH (Fig. A3). These results suggest the transient eddy MSE flux can differ from the EKE because it is sensitive to both dynamic and thermodynamic factors.

Fig. A1.

Seasonal evolution of vertically integrated (a) transient eddy MSE flux calculated using a monthly average (PW), (b) MSE flux calculated using a 10-day high-pass filter (PW), and (c) EKE calculated using a 10-day high-pass filter (MJ m−2). (d) Correlation of transient eddy MSE flux calculated using a monthly average and 10-day high-pass-filtered EKE (solid) and 10-day high-pass-filtered MSE flux and EKE (dashed).

Fig. A1.

Seasonal evolution of vertically integrated (a) transient eddy MSE flux calculated using a monthly average (PW), (b) MSE flux calculated using a 10-day high-pass filter (PW), and (c) EKE calculated using a 10-day high-pass filter (MJ m−2). (d) Correlation of transient eddy MSE flux calculated using a monthly average and 10-day high-pass-filtered EKE (solid) and 10-day high-pass-filtered MSE flux and EKE (dashed).

Fig. A2.

Month-to-month seasonal storm-track intensity as measured by vertically integrated transient eddy MSE flux calculated using a monthly average (solid red), 10-day high-pass-filtered MSE flux (dashed red) and 10-day high-pass-filtered EKE (black) in the (a) NH and (b) SH.

Fig. A2.

Month-to-month seasonal storm-track intensity as measured by vertically integrated transient eddy MSE flux calculated using a monthly average (solid red), 10-day high-pass-filtered MSE flux (dashed red) and 10-day high-pass-filtered EKE (black) in the (a) NH and (b) SH.

Fig. A3.

Response of (a),(b) vertically integrated transient eddy MSE flux calculated using a monthly average; (c),(d) 10-day high-pass-filtered MSE flux; and (e),(f) 10-day high-pass-filtered EKE to the CO2 (left) direct and (right) indirect effect in the MPI AGCM.

Fig. A3.

Response of (a),(b) vertically integrated transient eddy MSE flux calculated using a monthly average; (c),(d) 10-day high-pass-filtered MSE flux; and (e),(f) 10-day high-pass-filtered EKE to the CO2 (left) direct and (right) indirect effect in the MPI AGCM.

Storm-track metrics typically involve a high-pass filter. The MSE framework for storm-track intensity uses a monthly average instead of a bandpass filter. A monthly average tends to overestimate the storm-track intensity but does not qualitatively change the results (cf. Figs. A1a and A1b). In particular, the correlations over the seasonal cycle between the transient eddy MSE flux defined using a monthly average or a 10-day high-pass filter and the 10-day high-pass-filtered EKE are similar (cf. solid and dashed lines in Fig. A1d). The transient eddy MSE flux response to the direct and indirect effects of increased CO2 is in qualitative agreement with the response of 10-day high-pass-filtered MSE flux (Fig. A3).

APPENDIX B

ERA-Interim

The transient eddy MSE flux in the ERA-Interim is approximately 10% larger than in the NCEP reanalysis in the SH (Fig. B1). The larger transient eddy MSE flux in the ERA-Interim is consistent with the larger bandpass-filtered EKE in the ERA-Interim (Guo et al. 2009). However, the ERA-Interim month-to-month seasonal tendency is in agreement with NCEP (cf. red lines in Figs. 2a,b and B2a,b).

Fig. B1.

The difference of vertically integrated transient eddy MSE flux calculated using a monthly average for the ERA-Interim and NCEP reanalysis from 1979 to 2015. Contour interval is 0.2 PW.

Fig. B1.

The difference of vertically integrated transient eddy MSE flux calculated using a monthly average for the ERA-Interim and NCEP reanalysis from 1979 to 2015. Contour interval is 0.2 PW.

Fig. B2.

As in Fig. 2, but for the ERA-Interim.

Fig. B2.

As in Fig. 2, but for the ERA-Interim.

The seasonal decomposition of storm-track intensity in the ERA-Interim is consistent with NCEP; in particular, net energy input dominates the NH intensity, and stationary eddy MSE flux leads to a midwinter minimum (cf. Figs. 2c,d and B2c,d). Furthermore, the ERA-Interim net energy input in both hemispheres is dominated by shortwave absorption and opposed by OLR in the NH and OLR and surface heat fluxes in the SH, consistent with the NCEP reanalysis (cf. Figs. 2c,d and B2c,d). Finally, during the period of increasing seasonal intensity tendency land is a source of turbulent surface heat flux whereas during the period of decreasing intensity tendency it is a sink consistent with NCEP (cf. Figs. 3 and B3).

Fig. B3.

As in Fig. 3, but for the ERA-Interim.

Fig. B3.

As in Fig. 3, but for the ERA-Interim.

The response of the DJF NH storm-track intensity to El Niño minus La Niña conditions in the ERA-Interim is also in agreement with NCEP reanalysis (cf. Tables 1 and 2). The NH storm track strengthens, consistent with decreased MSE flux by stationary eddies, which is opposed by increased MSE flux by the Ferrel circulation (cf. Figs. 4 and B4). However, the SH storm-track response is not robust (the NCEP reanalysis suggests weakening and the ERA-Interim shows no change), and the net energy response does not exceed the error estimate.

Fig. B4.

As in Fig. 4, but for the ERA-Interim.

Fig. B4.

As in Fig. 4, but for the ERA-Interim.

REFERENCES

REFERENCES
Barpanda
,
P.
, and
T. A.
Shaw
,
2017
:
Using the moist static energy budget to understand storm-track shifts across a range of time scales
.
J. Atmos. Sci.
,
74
,
2427
2446
, https://doi.org/10.1175/JAS-D-17-0022.1.
Boer
,
G. J.
,
1993
:
Climate change and the regulation of the surface moisture and energy budgets
.
Climate Dyn.
,
8
,
225
239
, https://doi.org/10.1007/BF00198617.
Bony
,
S.
, and Coauthors
,
2015
:
Clouds, circulation and climate sensitivity
.
Nat. Geosci.
,
8
,
261
268
, https://doi.org/10.1038/ngeo2398.
Caballero
,
R.
, and
P. L.
Langen
,
2005
:
The dynamic range of poleward energy transport in an atmospheric general circulation model
.
Geophys. Res. Lett.
,
32
,
L02705
, https://doi.org/10.1029/2004GL021581.
Chang
,
E. K. M.
,
S.
Lee
, and
K. K.
Swanson
,
2002
:
Storm track dynamics
.
J. Climate
,
15
,
2163
2183
, https://doi.org/10.1175/1520-0442(2002)015<02163:STD>2.0.CO;2.
Chang
,
E. K. M.
,
Y.
Guo
, and
X.
Xia
,
2012
:
CMIP5 multimodel ensemble projection of storm track change under global warming
.
J. Geophys. Res.
,
117
,
D23118
, https://doi.org/10.1029/2012JD018578.
Dee
,
D. P.
, and Coauthors
,
2011
:
The ERA-Interim reanalysis: Configuration and performance of the data assimilation system
.
Quart. J. Roy. Meteor. Soc.
,
137
,
553
597
, https://doi.org/10.1002/qj.828.
Donohoe
,
A.
, and
D. S.
Battisti
,
2013
:
The seasonal cycle of atmospheric heating and temperature
.
J. Climate
,
26
,
4962
4980
, https://doi.org/10.1175/JCLI-D-12-00713.1.
Green
,
J. S. A.
,
1970
:
Transfer properties of the large-scale eddies and the general circulation of the atmosphere
.
Quart. J. Roy. Meteor. Soc.
,
96
,
157
185
, https://doi.org/10.1002/qj.49709640802.
Guo
,
Y.
,
E. K. M.
Chang
, and
S. S.
Leroy
,
2009
:
How strong are the Southern Hemisphere storm tracks?
Geophys. Res. Lett.
,
36
,
L22806
, https://doi.org/10.1029/2009GL040733.
Held
,
I. M.
, and
B. J.
Soden
,
2000
:
Water vapor feedback and global warming
.
Annu. Rev. Energy Environ.
,
25
,
441
475
, https://doi.org/10.1146/annurev.energy.25.1.441.
Held
,
I. M.
,
M.
Ting
, and
H.
Wang
,
2002
:
Northern winter stationary waves: Theory and modeling
.
J. Climate
,
15
,
2125
2144
, https://doi.org/10.1175/1520-0442(2002)015<2125:NWSWTA>2.0.CO;2.
Kalnay
,
E.
, and Coauthors
,
1996
:
The NCEP/NCAR 40-Year Reanalysis Project
.
Bull. Amer. Meteor. Soc.
,
77
,
437
472
, https://doi.org/10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2.
Li
,
C.
, and
D. S.
Battisti
,
2008
:
Reduced Atlantic storminess during Last Glacial Maximum: Evidence from a coupled climate model
.
J. Climate
,
21
,
3561
3579
, https://doi.org/10.1175/2007JCLI2166.1.
Lorenz
,
E. N.
,
1955
:
Available potential energy and the maintenance of the general circulation
.
Tellus
,
7
,
157
167
, https://doi.org/10.3402/tellusa.v7i2.8796.
Lucarini
,
V.
, and
F.
Ragone
,
2011
:
Energetics of climate models: Net energy balance and meridional enthalpy transport
.
Rev. Geophys.
,
49
,
RG1001
, https://doi.org/10.1029/2009RG000323.
Manabe
,
S.
, and
T. B.
Terpstra
,
1974
:
The effects of mountains on the general circulation of the atmosphere as identified by numerical experiments
.
J. Atmos. Sci.
,
31
,
3
42
, https://doi.org/10.1175/1520-0469(1974)031<0003:TEOMOT>2.0.CO;2.
Marshall
,
J.
,
A.
Donohoe
,
D.
Ferreira
, and
D.
McGee
,
2014
:
The ocean’s role in setting the mean position of the Inter-Tropical Convergence Zone
.
Climate Dyn.
,
42
,
1967
1979
, https://doi.org/10.1007/s00382-013-1767-z.
Ming
,
Y.
,
V.
Ramaswamy
, and
G.
Chen
,
2011
:
A model investigation of aerosol-induced changes in boreal winter extratropical circulation
.
J. Climate
,
24
,
6077
6091
, https://doi.org/10.1175/2011JCLI4111.1.
Nakamura
,
H.
,
1992
:
Midwinter suppression of baroclinic wave activity in the Pacific
.
J. Atmos. Sci.
,
49
,
1629
1642
, https://doi.org/10.1175/1520-0469(1992)049<1629:MSOBWA>2.0.CO;2.
O’Gorman
,
P. A.
,
2010
:
Understanding the varied response of the extratropical storm tracks to climate change
.
Proc. Natl. Acad. Sci. USA
,
107
,
19 176
19 180
, https://doi.org/10.1073/pnas.1011547107.
O’Gorman
,
P. A.
, and
T.
Schneider
,
2008
:
Energy of midlatitude transient eddies in idealized simulations of changed climates
.
J. Climate
,
21
,
5797
5806
, https://doi.org/10.1175/2008JCLI2099.1.
Park
,
H.-S.
,
S.-P.
Xie
, and
S.-W.
Son
,
2013
:
Poleward stationary eddy heat transport by the Tibetan plateau and equatorward shift of westerlies during northern winter
.
J. Atmos. Sci.
,
70
,
3288
3301
, https://doi.org/10.1175/JAS-D-13-039.1.
Peixoto
,
J. P.
, and
A. H.
Oort
,
1992
: Physics of Climate. American Institute of Physics, 520 pp.
Schneider
,
T.
,
T.
Bischoff
, and
G. H.
Haug
,
2014
:
Migrations and dynamics of the intertropical convergence zone
.
Nature
,
513
,
45
53
, https://doi.org/10.1038/nature13636.
Seager
,
R.
,
N.
Harnik
,
Y.
Kushnir
,
W.
Robinson
, and
J.
Miller
,
2003
:
Mechanisms of hemispherically symmetric climate variability
.
J. Climate
,
16
,
2960
2978
, https://doi.org/10.1175/1520-0442(2003)016<2960:MOHSCV>2.0.CO;2.
Shaw
,
T. A.
, and
A.
Voigt
,
2015
:
Tug of war on summertime circulation between radiative forcing and sea surface warming
.
Nat. Geosci.
,
8
,
560
566
, https://doi.org/10.1038/ngeo2449.
Shaw
,
T. A.
, and
A.
Voigt
,
2016
:
Land dominates the regional response to CO2 direct radiative forcing
.
Geophys. Res. Lett.
,
43
,
11 383
11 391
, https://doi.org/10.1002/2016GL071368.
Shaw
,
T. A.
, and Coauthors
,
2016
:
Storm track processes and the opposing influences of climate change
.
Nat. Geosci.
,
9
,
656
664
, https://doi.org/10.1038/ngeo2783.
Spencer
,
H.
, and
J. M.
Slingo
,
2003
:
The simulation of peak and delayed ENSO teleconnections
.
J. Climate
,
16
,
1757
1774
, https://doi.org/10.1175/1520-0442(2003)016<1757:TSOPAD>2.0.CO;2.
Stevens
,
B.
, and Coauthors
,
2013
:
Atmospheric component of the MPI-M Earth System Model: ECHAM6
.
J. Adv. Model. Earth Syst.
,
5
,
146
172
, https://doi.org/10.1002/jame.20015.
Takahashi
,
K.
,
2009
:
The global hydrological cycle and atmospheric shortwave absorption in climate models under CO2 forcing
.
J. Climate
,
22
,
5667
5675
, https://doi.org/10.1175/2009JCLI2674.1.
Trenberth
,
K. E.
, and
J. M.
Caron
,
2001
:
Estimates of meridional atmosphere and ocean heat transports
.
J. Climate
,
14
,
3433
3443
, https://doi.org/10.1175/1520-0442(2001)014<3433:EOMAAO>2.0.CO;2.
Trenberth
,
K. E.
, and
D. P.
Stepaniak
,
2003
:
Covariability of components of poleward atmospheric energy transports on seasonal and interannual timescales
.
J. Climate
,
16
,
3691
3705
, https://doi.org/10.1175/1520-0442(2003)016<3691:COCOPA>2.0.CO;2.
Wang
,
H.
, and
M.
Ting
,
1999
:
Seasonal cycle of the climatological stationary waves in the NCEP–NCAR reanalysis
.
J. Atmos. Sci.
,
56
,
3892
3919
, https://doi.org/10.1175/1520-0469(1999)056<3892:SCOTCS>2.0.CO;2.

Footnotes

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