Climate Dynamics

, Volume 39, Issue 7, pp 1905–1912

Co-variability of poleward propagating atmospheric energy with tropical and higher-latitude climate oscillations


    • Department of Geological and Atmospheric SciencesIowa State University
    • Guy Carpenter Asia–Pacific Climate Impact Centre, School of Energy and EnvironmentCity University of Hong Kong
  • Tsing-Chang Chen
    • Department of Geological and Atmospheric SciencesIowa State University
  • Shih-Yu Wang
    • Utah Climate Center and Department of Plants, Soils and ClimateUtah State University

DOI: 10.1007/s00382-011-1238-3

Cite this article as:
Huang, W., Chen, T. & Wang, S. Clim Dyn (2012) 39: 1905. doi:10.1007/s00382-011-1238-3


One may infer from the poleward propagation of angular momentum that energy change in tropical regions may be manifested in polar regions through a poleward propagation. This idea does not seem to be extensively addressed in the literature. It has been found that the poleward propagation of total atmospheric energy appears to connect the tropics and the polar regions on the interannual timescale. The present study explores how this poleward propagation may be linked to prominent climate oscillations such as ENSO, PNA, NAO, AO, AAO, and PSA. Analysis suggests that the poleward propagation of energy is likely a result of the atmospheric circulation change modulated by the climate patterns of ENSO, PNA, NAO, AO from tropical to Arctic regions and by the climate patterns of ENSO, PSA, AAO from tropical to Antarctic regions. The existence of the poleward energy propagation may shed light on studies exploring the linkage between topical climate and polar climate.


Atmospheric energyPoleward propagationClimate oscillations

1 Introduction

Dickey et al. (1992) and subsequent studies (e.g., Chen et al. 1996; Mo et al. 1997; Dickey et al. 1999) have uncovered a distinct poleward propagation of the atmospheric angular momentum (AAM) which originates from the tropics and is closely linked to the El Niño-Southern Oscillation (ENSO). The alternation of AAM appears to be forced by the ENSO cycle affecting the subtropical, zonal flows. By observing a poleward propagation signal in both the interannual and decadal variabilities of sea surface temperature (SST), Dickey et al. (2003) proposed that these low-frequency variabilities of SST may be the forcing mechanisms of AAM. These studies also noted that the maximum AAM variations around 60° latitude in both hemispheres tend to lag the ENSO cycle by about three to 4 years—a feature coincident with other studies (e.g., Derome et al. 2005; Tang et al. 2007; Sobolowski and Frei 2007; Jia et al. 2009) that proposed a teleconnected, yet lagged, correspondence between ENSO and various high-latitude climate oscillations, such as NAO, AO and AAO (acronyms given in Table 1). It is therefore reasonable to hypothesize that the poleward propagation of AAM may play a role in connecting these tropical and higher-latitude climate oscillations.
Table 1

References for the definition of climate modes


Full name

References for definition


El Niño Southern Oscillation

Webster (1983); Webster and Chang (1988)


Pacific-North American pattern

Wallace and Gutzler (1981); Kushnir and Wallace (1989)


Pacific-South American pattern

Mo and White (1985); Ghil and Mo (1991)


North Atlantic Oscillation

Barnston and Livezey (1987); Kushnir and Wallace (1989)


Arctic Oscillation

Thompson and Wallace (1998); Thompson and Wallace (2000)


Antarctic Oscillation

Thompson and Wallace (2000); Thompson and Solomon (2002)

A disadvantage of using AAM, however, is that its zonal average expression (as it has been used in the previously cited studies) is unable to reflect changes in the thermodynamic parameters (e.g. as heating) that often are the driving mechanisms for changes in the atmospheric circulations. This situation can be remedied through the computation of the atmosphere’s total energy (TE) that consists of a tropical source and a polar sink. AAM is mainly driven by zonal wind (i.e. a component related to kinetic energy), which is equivalent to the meridional gradient of geopotential height (i.e. a component related to internal energy), whose vertical gradient is proportional to temperature (i.e. a component related to potential energy). Such a linkage suggests that TE—a variable that comprises internal, potential, latent, and kinetic energy (Peixoto and Oort 1992)—should exhibit a poleward propagation similar to that of AAM. In such a case, the poleward propagating TE may be more directly linked to the various climate oscillations on its way from the tropics to higher latitudes. The objective of this study is to examine whether a poleward propagation of TE does exist, and, if so, how it may be connected to prominent climate oscillations such as PNA, NAO, AO, AAO, and PSA (acronyms given in Table 1). The analysis is carried out using data and methodology as described in Sect. “2”. Possible poleward propagation of TE and its linkage with climate oscillations is discussed in Sect. “3”. A summary and some conclusions are provided in Sect. “4”.

2 Methodology and data sources

2.1 Atmospheric energy budget equation

The atmospheric energy budget equation can be expressed as:
$$ \frac{{\partial {\text{TE}}}}{{\partial {\text{t}}}} + \nabla \cdot{\text{F}}_{\text{A}} = {\text{F}}_{\text{SFC}} ( {\text{upward}}\,{\text{positive)}} - {\text{F}}_{\text{TOA}} ( {\text{upward}}\,{\text{positive),}} $$
where TE is the vertically integrated total atmospheric energy, expressed as
$$ {\text{TE }} = {\text{g}}^{ - 1} \int\limits_{0}^{{{\text{P}}_{\text{S}} }} { [ {\text{CpT}} + {\text{gZ}} + {\text{Lq}} + {\text{KE]dp}}} , $$
where ps, Cp, T, g, Z, L, and q are respectively surface pressure, specific heat capacity, temperature, gravity, geopotential height, latent heat, and specific humidity. The flux form of TE, denoted as FA, is expressed as
$$ {\text{F}}_{\text{A}} = {\text{g}}^{ - 1} \int\limits_{0}^{{{\text{P}}_{\text{S}} }} {{\mathbf{V}} [ {\text{CpT}} + {\text{gZ}} + {\text{Lq}} + {\text{KE]dp}}} . $$
In Eq. 1, FSFC is a combination of sensible heat flux, latent heat flux, net shortwave and net longwave radiation flux at the surface. FTOA is the difference between incoming shortwave radiation and outgoing long wave radiation at the top of the atmosphere (Nakamura and Oort 1988; Peixoto and Oort 1992).
To examine the relationship between atmospheric circulation change and atmospheric energy change, Eq. 3 can be further decomposed into a rotational component (FR) and a divergent component (FD):
$$ {\text{F}}_{\text{A}} = {\text{ F}}_{\text{R}} + {\text{ F}}_{\text{D}} = {\text{ k}} \times \nabla \psi \left( {{\text{F}}_{\text{A}} } \right) \, + \nabla {{\upchi}}\left( {{\text{F}}_{\text{A}} } \right), $$
where ψ(FA) = ∇−2(k·∇ × FA) is the streamfunction of FA and χ(FA) = ∇−2(∇·FA) is the potential function of FA, introduced by Boer and Sargent (1985). The analysis here uses monthly data. Because our focus is on the interannual variation, periods shorter than 18 months are filtered out through a second-order Butterworth filter. Any filtered variable is denoted as Δ().

2.2 Data sources

The ECMWF 40-year Reanalysis (ERA-40; Uppala et al. 2005) offers an improved representation of high-latitude circulation variability, especially in the Southern Hemisphere, compared to earlier-generation reanalyses, such as NCEP1 and NCEP2 (Marshall 2003; Manney et al. 2005). Thus, the atmospheric energy transport involving wind speed, air humidity, air temperature, geopotential height, and surface latent and sensible heat fluxes are derived from ERA-40. The spatial resolution of ERA-40 is 2.5° × 2.5°. The time period used in this study is from 1960 to 2002. The monthly indices of NINO3.41 (for ENSO), AO, AAO, NAO, and PNA are obtained from the NOAA Climate Prediction Center. For the PSA index, we adopt the Empirical Orthogonal Function (EOF) analysis on the geopotential height field as was used in Kidson (1988).

3 Results

To examine whether or not TE features a poleward propagation in correspondence to AAM, we constructed the latitude-time evolution of zonally-averaged, 18-month, lowpass filtered TE, denoted as ΔTE. The result (Fig. 1a) reveals a clear poleward propagation associated with robust tropical anomalies and pronounced polar region “responses” connected through subtle, yet discernable, extratropical anomalies. Compared with earlier studies (e.g., Dickey et al. 1992; Chen et al. 1996), this propagation pattern is broadly similar with that of the AAM propagation. A lagged correlation analysis of ΔTE (Fig. 2) depicts the poleward propagating ΔTE with a quasi-four year cycle consistent with Dickey et al. (1992) and subsequent studies.
Fig. 1

a The latitude-time diagram of 18-months lowpass filtered zonally-averaged total atmospheric energy (i.e. ΔTE) during the time period from January 1960 to December 2001. The contour interval is 5 × 106 J kg−1. Thick dashed lines indicate the poleward propagation. b Time series of area-averaged ΔTE at different latitude (shadings) versus index of climate oscillations (lines). The corresponding correlation coefficients σ are given in the left panel of (b). All variables in (b) are normalized
Fig. 2

The time-lagged correlation between index of tropical ΔTE (area-averaged between 0° and 360°, 25°S–25°N) and the zonally averaged ΔTE (ΔTEz) for the time period of 1960–2001. The correlation coefficients significant at the 95% confidence level are shaded

For the possible relationship between the propagating ΔTE and climate oscillations, as is revealed in Fig. 1b, time series of area-averaged TE at the tropics (25°S-25°N), mid-latitudes (40°–50°N/45°–55°S), higher-latitudes (55°N–65°N), and polar regions (70°N–80°N/65°S–75°S) appear to be coherent with the indices of ENSO, PNA/PSA, NAO, and AO/AAO, respectively. The correlation coefficients between ΔTE and the various climate indices are shown to the left within Fig. 1b. Even though the degree of freedom (dof) is conservatively reduced due to the filtering (i.e. dof = 33 here instead of 504 with monthly data), the correlation coefficients are significant at the 95% confidence level. Combined with the poleward propagating feature of ΔTE as well as the well-documented poleward propagating AAM, these significant correlations suggest the possibility that the poleward transport of atmospheric energy originating from tropical (ENSO) forcing may connect to higher-latitude modes. This inference echoes some previous observations on the tropical-polar region linkage (e.g., Kang and Lau 1994; Chen et al. 1996; Lin et al. 2002; Li et al. 2006; Jia et al. 2009).

The horizontal distribution of the variance in ΔTE (Fig. 3) depicts several “centers of action” coincident with the known variance centers of the different climate oscillations. These centers correspond well with the numbered climate patterns: (1) ENSO, (2) PNA, (3) NAO, (4) AO, (5) PSA, and (6) AAO. Combined with the propagation feature as in Fig. 1, this variance distribution suggests that the poleward propagation of ΔTE is modulated by, or at least co-existed with, various climate oscillations at different latitudes. This is possible because such climate oscillations are determined by planetary-scale atmospheric circulation anomalies. For example, warm ENSO years intensify the Hadley circulation (Oort and Yienger 1996) which subsequently transports more heat from the tropics into higher latitudes than normal, as opposed to cold ENSO years (Moore and Haar 2001; Held 2001). Positive PNA phases transport more sensible heat across 50°N than normal (Rogers and Raphael 1992). Positive-phase NAO or AO enhances the atmospheric heat transport toward the Arctic region (Carleton 1988) which then modulates the Arctic heat budget (Adams et al. 2000; Semmler et al. 2005). In the Southern Hemisphere, the PSA pattern dominates the heat transport variations across the mid-latitudes (Christoph et al. 1998) increasing poleward heat transport during positive phases (Hall and Visbeck 2002). All these documented features indicate a direct response in ΔTE.
Fig. 3

The variance of 18-month lowpass filtered total atmospheric energy (TE) during the time period from 1979 to 2001. The contour interval is 3 × 1013 J2 kg−2. See text for the meaning of numbers

To further examine the relationship between ΔTE and the major climate oscillations, we next conduct the Empirical Orthogonal Function (EOF) analysis on the streamfunction of FA, Δψ(FA), using Eq. 4. The EOF analysis has been a conventional approach in the identification of climatic loading patterns (e.g., Kidson 1988). As was shown in Fig. 1, the maximum variability of ΔTE often occurs during the winter season (December-February for the Northern Hemisphere and June–August for the Southern Hemisphere). Focusing on the winter season, the first four principal modes of Δψ(FA) over the areas north of 20°N (south of 20°S) are illustrated in Fig. 4a, b.
Fig. 4

The first four EOFs of Δψ(FA) over a 20°N–90°N, and b 20°S–90°S in the winter season [DJF (JJA) for northern (southern) hemisphere] during the time period from 1979 to 2001. The contour interval of Δψ(FA) is 1015 J s−1. The spatial correlation coefficients (scorr) between the loading patterns (EOF1-4) and the spatial pattern of the respective climate oscillations are given in the right bottom of Fig. 4ab. In addition, the temporal correlation coefficients (tcorr) between the principal components (PC1-4) and the indices of the respective climate oscillations are also given in the right bottom of Fig. 4ab

In the Northern Hemisphere, the percentages of the first four principal modes of Δψ(FA) with a sum of the variance contributions larger than 95% depict the variabilities of ENSO, AO, NAO, and PNA, respectively, as is substantiated by the correlation coefficients between the principal components (PCs) and the indices of ENSO, AO, NAO, and PNA (bottom right of Fig. 4a). This observation is strengthened by the spatial correlation coefficients between the loading patterns (EOF1-4) and the spatial pattern of the respective climate oscillations. Here, the spatial pattern of ENSO, PNA, NAO, AO (also PSA and AAO) are derived from the composites of the 200-hPa streamfunction anomalies based upon maximum phases that are greater than one standard deviation of their respective indices—an approach following that of the NOAA Climate Prediction Center.2 For example, EOF2 reveals an annular structure similar to that during the positive-phase AO. EOF3 depicts the dipole between Iceland and the Azores resembling the positive-phase NAO. In the Southern Hemisphere, the linkages of ENSO, PSA and AAO with Δψ(FA) are also suggested (Fig. 4b) by the temporal and spatial correlation coefficients that are both significant within the four leading modes. Table 2 shows the correlation coefficients of the aforementioned climate indices with the NINO3.4 index at various lags. By arranging those climate oscillations in a way similar to Fig. 1b, it appears that the significant correlations also depict a propagation pattern with a repeating cycle of 4 years. This, together with the propagating ΔTE pattern as shown in Fig. 1a, supports the possibility that ENSO, AO, NAO, and PNA (PSA and AAO) play major roles in modulating the poleward propagation of ΔTE.
Table 2

The correlation coefficients of various climate indices with the NINO3.4 index at various lags for the time period of 1960–2001


Lag_0 months

Lag_12 months

Lag_24 months

Lag_36 months

Lag_48 months

Lag_60 months

Climate index



























–, |σ| < 0.3

The propagation characteristics and possible dynamics of ΔTE are shown in Fig. 5 in terms of lagged composites of the annual mean of the ΔTE budget: (a) \( \Updelta \left( {\frac{{\partial {\text{TE}}}}{{\partial {\text{t}}}}} \right) \), (b) Δ(∇·FA), (c) \( \Updelta \left( {\frac{{\partial {\text{TE}}}}{{\partial {\text{t}}}} + \nabla \cdot{\text{F}}_{\text{A}} } \right) \), (d) ΔFSFC, (e) ΔFTOA, and (f) Δ(FSFC + FTOA). Here, the maximum phase (i.e. year zero) is determined by the years with the tropical ΔTE magnitude larger than one standard deviation through the 1960–2002 time period. The term \( \Updelta \left( {\frac{{\partial {\text{TE}}}}{{\partial {\text{t}}}}} \right) \) is weak because of the fact that the tendency term usually diminishes while reaching the maximum stage, although some residual tendency exists in polar regions. Poleward propagation features are visible in Δ(∇·FA) and its residual with \( \Updelta \left( {\frac{{\partial {\text{TE}}}}{{\partial {\text{t}}}}} \right) \) indicating an increase in energy diverging out of the tropics (year 0). This feature appears to balance the negative Δ(∇·FA) in the polar regions which suggests an increase in energy converging into the region. Based on Eq. 1, the change of Δ(∇·FA) is determined by changes in ΔFSFC and ΔFTOA through the (supposed) progression of ΔTE from the tropics to the poles. However, the lagged composites of ΔFSFC and ΔFTOA do not reveal such a poleward propagation. Rather, Figs. 5d, e show near instantaneous changes associated with the ΔTE maxima around the globe except for discernable migrations of both ΔFSFC and ΔFTOA emanating from the equator towards the midlatitudes (~45°N) within a year.3 On the other hand, the sum of ΔFSFC and ΔFTOA (Fig. 5f) again reveals a poleward propagation pattern spanning about 4–6 years (see Footnote 3), consistent with the residual of \( \Updelta \left( {\frac{{\partial {\text{TE}}}}{{\partial {\text{t}}}}} \right) \) and Δ(∇·FA) (Fig. 5c). It appears that changes in radiative forcing (ΔFSFC and ΔFTOA) are not balanced. This imbalance drives the atmospheric circulation change which, in turn, affects the distribution of energy through Δ(∇·FA), whose changes may reflect the poleward propagation behavior of ΔTE as shown in Fig. 1a (e.g. Rogers and Raphael 1992; Carleton 1988; Hall and Visbeck 2002).
Fig. 5

The lagged composites of the annual mean of ΔTE budget: a\( \Updelta \left( {\frac{{\partial {\text{TE}}}}{{\partial {\text{t}}}}} \right) \), b Δ(∇·FA), c\( \Updelta \left( {\frac{{\partial {\text{TE}}}}{{\partial {\text{t}}}} + \nabla \cdot{\text{F}}_{\text{A}} } \right) \), d ΔFSFC, e ΔFTOA, and f Δ(FSFC + FTOA). The contour interval of af is 0.1 Wm−2. Solid (dashed) arrow lines added in b, c and f indicate the direction of poleward propagation of positive (negative) phase of represented variable

4 Summary and Discussion

The poleward propagation of both AAM (Dickey et al. 1992) and TE (this study) poses a strong potential in improving climate prediction but also a challenge in the realization of the physical mechanism. In terms of the atmospheric circulations, the challenge lies in a simple question regarding the relatively short atmospheric “memory”. It is known that the response of the extratropical atmosphere to the tropical forcing, normally through the equivalent barotropic Rossby wave trains, takes only about 2 weeks (Jin and Hoskins 1995). It is also known that the time-dependent total northward transport of energy fluxes, consisting of the transport by stationary eddies and transport by the transient eddies (e.g. Peixoto and Oort 1992), also occurs at a submonthly timescale (e.g. Jin and Hoskins 1995). The quasi-four year cycle as revealed from the AAM and TE propagation contradict the known physical process linking to the Rossby wave propagation. As a result, Dickey et al. (2003) proposed that the memory lies not in the atmosphere but, rather, in the ocean.

Here we present evidence of the co-variabilities between the TE propagation and the major climate oscillatory modes, including ENSO, PNA, AO, and NAO in the Northern Hemisphere and PSA and AAO in the Southern Hemisphere. We offer no physical explanation as to how these seemingly independent modes, as was inferred from their depiction computed through the EOF analysis (i.e., all modes are orthogonal), appear to be connected, as was suggested from Fig. 1 through the poleward propagating ΔTE (i.e. that ΔTE is correlated with different modes at their specific latitudes). Our course has been to document these connections through diagnosis, and we present these results to call attention to this potentially useful information.


NINO3.4 is the area-averaged sea surface temperature in the region bounded by 5°N–5°S, from 170°W to 120°W.


Similar characteristics of the stationary ΔFSFC, ΔFTOA, as well as the propagating behavior in their differences, also appear from the analysis using the data of ISCCP-FD (International Satellite Cloud Climatology Project; Rossow and Zhang 1995) (not shown).



We thank anonymous reviewers for their comments and suggestions which greatly improved the manuscript. This research was partially supported by the Cheney Research Foundation. SYW was supported by the Utah Agricultural Experiment Station, Utah State University.

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