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    Lag composites of anomalous values of the Northern Hemisphere energetics during DJFM. (a) Anomalous shortwave EKE, anomalous shortwave EAPE, anomalous ZAPE, anomalous shortwave BC, and anomalous shortwave BT composited against shortwave EKE (n = 125 cases). (b) Anomalous longwave EKE, anomalous longwave EAPE, anomalous ZAPE, anomalous longwave BC, and anomalous longwave BT composited against longwave EKE (n = 97 cases). Red, orange, black, dark blue, and light blue lines correspond to EKE, EAPE, ZAPE, BC, and BT, respectively. By convention, we have multiplied BT by −1 before plotting it. Therefore, negative values of BT represent an anomalously large conversion from EKE to zonal kinetic energy. Each variable has been divided by the surface area of the NH. Thick lines indicate statistical significance at the 5% level, evaluated with a two-sided Student’s t test. Derived from ERA-Interim (1979–2012) data.

  • View in gallery

    Pentad averages of anomalous OLR composited against NH longwave EKE (n = 97 cases) during DJFM corresponding to lag days (a) −12 to −8, (b) −7 to −3, (c) −2 to +2, (d) +3 to +7, and (e) +8 to +12. Positive (negative) values indicate that OLR is enhanced (suppressed). Dotted areas indicate statistical significance at the 5% level, evaluated via a Monte Carlo simulation with 1000 random samples. Derived from ERA-Interim (1979–2012) data.

  • View in gallery

    Pentad averages of anomalous 300-hPa streamfunction composited against NH longwave EKE (n = 97 cases) during DJFM corresponding to lag days (a) −12 to −8, (b) −7 to −3, (c) −2 to +2, (d) +3 to +7, and (e) +8 to +12. Black contours represent the climatological 300-hPa streamfunction during DJFM. The contour interval is 15 × 106 m2 s−1. The thick line is zero, and solid (dashed) lines represent negative (positive) values. Dotted areas indicate statistical significance at the 5% level, evaluated via a Monte Carlo simulation with 1000 random samples. Derived from ERA-Interim (1979–2012) data.

  • View in gallery

    Composites (latitude vs lag day) of the zonal mean of the anomalous 2MT against (a) longwave EKE (n = 97 cases) and (b) shortwave EKE (n = 125 cases) during DJFM. Dotted areas indicate statistical significance at the 5% level, evaluated via a Monte Carlo simulation with 1000 random samples. Derived from ERA-Interim (1979–2012) data.

  • View in gallery

    DJFM climatological zonal means of the shortwave and longwave components of (a) latent heat flux convergence and (b) sensible heat flux convergence. Red (blue) lines correspond to the longwave (shortwave) components. Each series is smoothed twice with a 1–2–1 smoothing filter. Derived from ERA-Interim (1979–2012) data.

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Arctic Warming Induced by Tropically Forced Tapping of Available Potential Energy and the Role of the Planetary-Scale Waves

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  • 1 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania
  • | 2 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania, and School of Earth and Environmental Sciences, Seoul National University, Seoul, South Korea
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Abstract

One of the challenging tasks in climate science is to understand the equator-to-pole temperature gradient. The poleward heat flux generated by baroclinic waves is known to be central in reducing the equator-to-pole temperature gradient from a state of radiative–convective equilibrium. However, invoking this relationship to explain the wide range of equator-to-pole temperature gradients observed in past climates is challenging because baroclinic waves tend to follow the flux–gradient relationship such that their poleward heat flux is proportional to the equator-to-pole temperature gradient and zonal available potential energy (ZAPE). With reanalysis data, the authors show the existence of poleward heat transport by planetary-scale waves that are independent of the flux–gradient relationship and baroclinic instability. This process arises from a forced tapping of atmospheric ZAPE by planetary-scale waves that are triggered by enhanced tropical convection over the Pacific warm pool region. The Rossby waves excited by this tropical convection propagate northeastward over the Pacific Ocean and constructively interfere with the climatological stationary waves at higher latitudes. During polar night, when the current warming is most rapid, the forced tapping of ZAPE by planetary-scale waves produces a substantially greater warming than that by the synoptic-scale eddy fluxes that presumably arise from baroclinic instability.

Corresponding author address: Cory Baggett, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: cfb128@psu.edu

Abstract

One of the challenging tasks in climate science is to understand the equator-to-pole temperature gradient. The poleward heat flux generated by baroclinic waves is known to be central in reducing the equator-to-pole temperature gradient from a state of radiative–convective equilibrium. However, invoking this relationship to explain the wide range of equator-to-pole temperature gradients observed in past climates is challenging because baroclinic waves tend to follow the flux–gradient relationship such that their poleward heat flux is proportional to the equator-to-pole temperature gradient and zonal available potential energy (ZAPE). With reanalysis data, the authors show the existence of poleward heat transport by planetary-scale waves that are independent of the flux–gradient relationship and baroclinic instability. This process arises from a forced tapping of atmospheric ZAPE by planetary-scale waves that are triggered by enhanced tropical convection over the Pacific warm pool region. The Rossby waves excited by this tropical convection propagate northeastward over the Pacific Ocean and constructively interfere with the climatological stationary waves at higher latitudes. During polar night, when the current warming is most rapid, the forced tapping of ZAPE by planetary-scale waves produces a substantially greater warming than that by the synoptic-scale eddy fluxes that presumably arise from baroclinic instability.

Corresponding author address: Cory Baggett, Department of Meteorology, The Pennsylvania State University, 503 Walker Building, University Park, PA 16802. E-mail: cfb128@psu.edu

1. Introduction

A defining feature of warm equable paleoclimates is a reduction in their surface equator-to-pole temperature gradient (Budyko and Izrael 1991; Hoffert and Covey 1992; Miller et al. 2010; Lee 2014). Similarly, a muted warming in the tropics and much greater warming in the Arctic characterize the present climate and observed twentieth-century trends (Serreze and Barry 2011). Thus, when the Arctic receives little solar radiation, the Stefan–Boltzmann law implies (under the assumptions that there are no changes in lapse rate or the distribution of clouds and water vapor) that poleward heat flux into the Arctic is greater during warm periods. Consistent with this, model simulations of twenty-first-century warming show enhanced poleward heat flux (Held and Soden 2006; Wu et al. 2011; Zelinka and Hartmann 2012). However, when considering only dry dynamics, the flux–gradient relationship (Charney 1947; Eady 1949; Green 1970) states that the strength of the poleward heat flux by baroclinic waves is proportional to the equator-to-pole temperature gradient. Hence, the question arises as to how this increased heat flux into the Arctic is accomplished during equable climates, in light of the flux–gradient relationship of the baroclinic waves.

Energetically, baroclinic waves gain amplitude as they convert zonal available potential energy (ZAPE), which is highly correlated to the equator-to-pole temperature gradient, into eddy kinetic energy (EKE) through unstable baroclinic processes (Charney 1947; Eady 1949; Lorenz 1955). However, a shortage of ZAPE is not the cause of baroclinic wave saturation. During Northern Hemisphere (NH) winter, the average value of ZAPE is about 10 times larger than the energy found in the waves (Peixóto and Oort 1992). Therefore, there is a large quantity of ZAPE that remains untapped by unstable baroclinic waves and is available to be tapped by other means. In light of the recent finding that tropically forced planetary-scale waves can warm the Arctic (Lee et al. 2011a,b; Yoo et al. 2012; Lee 2012; Ding et al. 2014), we ask the following: Do these planetary-scale waves tap this vast reservoir of ZAPE without relying on the flux–gradient relationship? This was conjectured previously (Lee 2014), but its validity has not been tested. In this study, we address this question by comparing the life cycles of planetary-scale and synoptic-scale waves. Because Rossby waves propagate from the tropics to polar regions in about 10 days (Hoskins and Karoly 1981) and not over climate time scales, it is appropriate to examine the life cycles of these waves in order to understand the underlying mechanism that contributes to climates with Arctic warming.

2. Data and methods

For the purposes of this study, we examine the longwave EKE life cycle (zonal wavenumbers 1–3) to investigate planetary-scale waves and the shortwave EKE life cycle (zonal wavenumbers 4–72) to investigate synoptic-scale waves. For each life cycle, we perform a composite analysis of the time evolution of EKE, ZAPE, eddy available potential energy (EAPE), baroclinic energy conversion from ZAPE to EAPE (BC), barotropic energy conversion from EKE to zonal kinetic energy (BT), outgoing longwave radiation (OLR), 300-hPa streamfunction, and 2-m temperature (2MT). Moreover, we calculate the climatological values of latent and sensible heat flux convergence associated with planetary- and synoptic-scale waves.

To perform these calculations, we acquire from the European Centre for Medium Range Weather Forecasting (ECMWF) interim reanalysis (ERA-Interim) project (Dee et al. 2011) the following data: zonal wind u, meridional wind υ, vertical velocity ω (Pa s−1), specific humidity q, temperature T, surface pressure ps, 2MT, and OLR. Our analysis spans the years from 1979 to 2012. We interpolate the data to a horizontal resolution of 2.5° × 2.5°, employ 23 pressure levels in the vertical, and use the 0000 UTC time step.

Longwave (shortwave) contributions to EKE, EAPE, BC, BT, and energy flux convergence are calculated by performing a Fourier analysis of u, υ, ω, q, and T and retaining zonal wavenumbers 1–3 (4–72). We integrate daily over the entire NH values of EKE, EAPE, ZAPE, BC, and BT using only the spatial eddy component (deviation from the zonal mean) of the equations found in Peixóto and Oort (1974). An exact formulation of the equations used may be found in Baggett and Lee (2014). Integration over the NH results in one-dimensional time series of EKE, EAPE, ZAPE, BC, and BT, each spanning daily from 1979 to 2012. We calculate daily horizontal fields of energy flux convergence according to for latent heat and for sensible heat, where v = ui + υj, dp is the difference between ERA-Interim pressure levels (bounded by ps), g is the acceleration of gravity, Lυ is the latent heat of vaporization, and cp is the specific heat of gas at constant pressure. We calculate daily 300-hPa streamfunction using the velocity components u and υ and employing the National Center for Atmospheric Research (NCAR) Command Language (NCL) function “uv2sfvpF” (NCAR Command Language 2013).

Variables are composited based on days during December–March (DJFM) when the values of shortwave EKE and longwave EKE deviate by more than one standard deviation from their climatological daily means (n = 125 and 97 cases, respectively). To isolate events, only peak values within a 14-day time period are chosen. We do not isolate the 125 shortwave events from the 97 longwave events. However, we calculate (not shown here) that the magnitudes of the shortwave (longwave) components are much smaller than their longwave (shortwave) counterparts during the longwave (shortwave) life cycles. Moreover, we do not feel that it is necessary to isolate the life cycles, as the two scales often interact. For example, it is well established that synoptic-scale wave breaking can build planetary-scale waves (e.g., Franzke et al. 2011). Anomalous values of EKE, EAPE, ZAPE, BC, BT, OLR, 300-hPa streamfunction, and 2MT are determined by subtracting from the daily value of each variable its climatological daily mean. The climatological daily means have had their high-frequency variability removed by retaining only the first two harmonics of their raw annual cycles.

3. Results

Figure 1 displays the life cycles of the anomalous values of the energetics that are integrated over the NH during December–March (DJFM) and composited against shortwave EKE and longwave EKE. For events with large shortwave EKE (Fig. 1a), we find that the maximum in shortwave EAPE and EKE at lag 0 days follows a maximum in ZAPE at lag −5 days and precedes a minimum in ZAPE at lag +1 days. The reduction in ZAPE coincides with a peak in shortwave BC from ZAPE to EAPE at lag −1 days. Furthermore, EKE is decreasing most rapidly as a result of shortwave BT at lag +1 days. This evolution in ZAPE is consistent with the theoretical framework of the Lorenz energy cycle where energy flows from ZAPE to EAPE to EKE before undergoing barotropic decay (Lorenz 1955) and with observations of the NH (Peixóto and Oort 1992). Furthermore, it is consistent with the flux–gradient relationship, whereby an enhanced equator-to-pole temperature gradient associated with large ZAPE is followed within a few days by an increase in the poleward heat flux by unstable baroclinic waves. Although the flux–gradient relationship is mathematically a diagnostic relationship, from the perspective that this is a first-order closure for the eddy flux, a causal relationship is implicit in that the eddy flux responds to the equator-to-pole temperature gradient. This poleward heat flux subsequently diminishes the equator-to-pole temperature gradient and results in an atmosphere with reduced ZAPE.

Fig. 1.
Fig. 1.

Lag composites of anomalous values of the Northern Hemisphere energetics during DJFM. (a) Anomalous shortwave EKE, anomalous shortwave EAPE, anomalous ZAPE, anomalous shortwave BC, and anomalous shortwave BT composited against shortwave EKE (n = 125 cases). (b) Anomalous longwave EKE, anomalous longwave EAPE, anomalous ZAPE, anomalous longwave BC, and anomalous longwave BT composited against longwave EKE (n = 97 cases). Red, orange, black, dark blue, and light blue lines correspond to EKE, EAPE, ZAPE, BC, and BT, respectively. By convention, we have multiplied BT by −1 before plotting it. Therefore, negative values of BT represent an anomalously large conversion from EKE to zonal kinetic energy. Each variable has been divided by the surface area of the NH. Thick lines indicate statistical significance at the 5% level, evaluated with a two-sided Student’s t test. Derived from ERA-Interim (1979–2012) data.

Citation: Journal of the Atmospheric Sciences 72, 4; 10.1175/JAS-D-14-0334.1

Similar to the shortwave EKE life cycle, the longwave EKE life cycle (Fig. 1b) also follows the Lorenz energy cycle with peaks in longwave EAPE and EKE preceded by longwave BC and followed by longwave BT. However, in contrast to the shortwave EKE life cycle, there is no distinct maximum in ZAPE during the longwave EKE life cycle. Rather, there is only a sharp minimum in ZAPE at lag 0 days. The absence of a sharp maximum in ZAPE indicates that the flux–gradient relationship plays less of a role, if any, in the growth of longwave EKE.

Is this tapping of ZAPE forced by tropical convection? This question is addressed by examining lag composite maps of anomalous OLR versus anomalously positive longwave EKE at lag 0 days during DJFM (Fig. 2). The first two pentads (Figs. 2a,b) reveal significant negative OLR anomalies over the Pacific warm pool region, indicative of cold cloud tops resulting from enhanced tropical convection. The second pentad (Fig. 2b) alludes to the presence of a Rossby wave train propagating eastward and poleward across the Pacific, emanating from the region of warm pool convection. To support this interpretation of the OLR anomalies in midlatitudes, we construct a composite of the 300-hPa streamfunction anomaly versus longwave EKE, which reveals a Rossby wave train exiting the tropics and propagating northeastward over the Pacific (Fig. 3). This is consistent with the modeling results of Yoo et al. 2012. Using the spectral dynamical core from the Geophysical Fluid Dynamics Laboratory, they showed that when the model is initialized with warm pool convective heating superimposed on a climatological December–February background flow, a Rossby wave train similar to our Fig. 3 is excited [see Figs. 1 and 2 of Yoo et al. (2012)]. However, we wish to note that the communication of the divergence associated with the enhanced tropical convection and its subsequent initiation of a Rossby wave train is likely contingent upon the background state at higher latitudes: namely, the strength and position of the subtropical jet (Sardeshmukh and Hoskins 1988). Furthermore, since our analysis is based on composites, it is entirely possible that some of the longwave EKE events are not preceded by enhanced convection over the Pacific warm pool. We plan to test the importance of the background state versus warm pool convection in a future idealized modeling study in a manner similar to Yoo et al. (2012).

Fig. 2.
Fig. 2.

Pentad averages of anomalous OLR composited against NH longwave EKE (n = 97 cases) during DJFM corresponding to lag days (a) −12 to −8, (b) −7 to −3, (c) −2 to +2, (d) +3 to +7, and (e) +8 to +12. Positive (negative) values indicate that OLR is enhanced (suppressed). Dotted areas indicate statistical significance at the 5% level, evaluated via a Monte Carlo simulation with 1000 random samples. Derived from ERA-Interim (1979–2012) data.

Citation: Journal of the Atmospheric Sciences 72, 4; 10.1175/JAS-D-14-0334.1

Fig. 3.
Fig. 3.

Pentad averages of anomalous 300-hPa streamfunction composited against NH longwave EKE (n = 97 cases) during DJFM corresponding to lag days (a) −12 to −8, (b) −7 to −3, (c) −2 to +2, (d) +3 to +7, and (e) +8 to +12. Black contours represent the climatological 300-hPa streamfunction during DJFM. The contour interval is 15 × 106 m2 s−1. The thick line is zero, and solid (dashed) lines represent negative (positive) values. Dotted areas indicate statistical significance at the 5% level, evaluated via a Monte Carlo simulation with 1000 random samples. Derived from ERA-Interim (1979–2012) data.

Citation: Journal of the Atmospheric Sciences 72, 4; 10.1175/JAS-D-14-0334.1

Returning to our Fig. 3, the third pentad shows this Rossby wave train turning and propagating southeastward over the Atlantic. This transient Rossby wave train constructively interferes with the climatological stationary waves over the high latitudes that, by spherical geometry, have roughly the same wavelength as the midlatitude Rossby waves forced by the tropical convection (Fig. 3c). This constructive interference amplifies the planetary-scale waves, which ostensibly leads to an effective tapping of ZAPE (Fig. 1b) and poleward heat transport. This is consistent with Lee (2014), where it was proposed that the Rossby waves excited by warm pool tropical convection could forcefully tap ZAPE through a constructive interference with the climatological stationary waves. At the same time, there are significant positive OLR anomalies developing over much of the Arctic, with centers located over the Barents and Beaufort Seas (Fig. 2c). These positive OLR anomalies in the Arctic persist through the fourth pentad before dissipating during the fifth pentad (Figs. 2d,e).

We interpret these positive OLR anomalies in the Arctic that are associated with increased longwave EKE as being caused by either anomalously warm surface skin temperatures or enhanced cloud cover. Either case would be consistent with anomalously warm 2-m temperatures in the Arctic during its polar night, which is in fact confirmed in Fig. 4a. We find that the Arctic is anomalously warm beginning near lag −6 days and persisting through approximately lag +12 days. It can also be seen in Fig. 4a that the tropics are anomalously cold. In fact, throughout the entire 41-day period displayed in Fig. 4a, the equator-to-pole 2MT gradient is reduced. This reduced gradient is not conducive to enhanced poleward heat flux through the flux–gradient relationship; nevertheless, the Arctic is warmed during the longwave EKE life cycle. This result contrasts sharply with the shortwave EKE life cycle (Fig. 4b) where unstable baroclinic waves play a dominant role. As can be seen for the shortwave EKE life cycle, an enhanced equator-to-pole temperature gradient at negative lags is followed by anomalously warm temperatures north of 60°N at positive lags. However, the warm anomalies in the Arctic are larger and persist longer in time for the longwave EKE life cycle.

Fig. 4.
Fig. 4.

Composites (latitude vs lag day) of the zonal mean of the anomalous 2MT against (a) longwave EKE (n = 97 cases) and (b) shortwave EKE (n = 125 cases) during DJFM. Dotted areas indicate statistical significance at the 5% level, evaluated via a Monte Carlo simulation with 1000 random samples. Derived from ERA-Interim (1979–2012) data.

Citation: Journal of the Atmospheric Sciences 72, 4; 10.1175/JAS-D-14-0334.1

The time-dependent nature of the above life cycle analyses reveals important physical processes, yet because the quantities examined are deviations from their mean states, the question arises as to what is the relative importance of the forced tapping process in warming the Arctic for a time-mean state. To address this question, we calculate the climatological values of shortwave and longwave sensible and latent heat flux convergence during DJFM. The result (Fig. 5) indicates that over the Arctic, the contribution by the planetary-scale waves overwhelms that by the synoptic-scale waves in both sensible and latent heat fluxes. In fact, we find (not shown here) that during the longwave EKE life cycle, there is a significant convergence of longwave sensible and latent heat fluxes in the high latitudes, which is consistent with the climatology depicted in Fig. 5. Under the assumption that the planetary-scale-wave life cycle captures the typical process of the time-mean state, the implication is that the forced tapping of ZAPE excited by tropical convection plays a dominant role in transporting heat into the Arctic. However, the warming in the Arctic as depicted by the 2MT evolution for each life cycle (Fig. 4) likely involves a complex combination of sensible and latent heat fluxes, Arctic clouds, and downward infrared radiation by the clouds (Lee 2014). While determining the exact warming mechanisms is beyond the scope of this study, we do plan to discern them for both the planetary-scale and synoptic-scale-wave life cycles in future research.

Fig. 5.
Fig. 5.

DJFM climatological zonal means of the shortwave and longwave components of (a) latent heat flux convergence and (b) sensible heat flux convergence. Red (blue) lines correspond to the longwave (shortwave) components. Each series is smoothed twice with a 1–2–1 smoothing filter. Derived from ERA-Interim (1979–2012) data.

Citation: Journal of the Atmospheric Sciences 72, 4; 10.1175/JAS-D-14-0334.1

With respect to the latent heat fluxes, it is interesting to note that we find both anomalously low values of total column water vapor over the tropics and a reduced meridional gradient in total column water vapor in advance of the longwave EKE life cycle (not shown here). Therefore, at least for the mechanism that we describe in this study, we do not find evidence of a large low-latitude moisture supply that would increase the eddy diffusivity constant within the flux–gradient relationship (Langen and Alexeev 2007).

4. Summary and conclusions

We now make a summary of the key findings in this study. 1) Unlike synoptic-scale waves, we find planetary-scale waves are not reliant on the flux–gradient relationship because they are not preceded by an enhanced surface equator-to-pole temperature gradient and ZAPE. 2) Preceding the planetary-scale-wave life cycle, we see enhanced tropical convection over the Pacific warm pool region, which excites a Rossby wave train. This Rossby wave train constructively interferes with the climatological stationary wave as it propagates northeastward over the Pacific Ocean, reaches the high latitudes, and turns southeastward over the Atlantic Ocean. 3) The planetary-scale waves efficiently tap ZAPE and are associated with Arctic warming that is greater and persists longer in time than the warming produced by the unstable synoptic-scale waves.

The findings here bear a couple of implications in atmospheric dynamics and climate. First, at least for the NH winter, we need to reevaluate the traditional view that the flux–gradient relationship of the baroclinic waves plays the major role in establishing the equilibrium equator-to-pole temperature gradient in the atmosphere. It had been shown previously that during the NH winter, stationary and quasi-stationary waves play an important role in transporting moist static energy poleward (Peixóto and Oort 1992; Trenberth and Stepaniak 2003). Since the propagation speeds of the planetary-scale waves are small, our finding is consistent with the previous result. However, neither the forced tapping of ZAPE nor its importance on Arctic surface air is apparent in those earlier studies.

Second, given that most of the ZAPE in the atmosphere is left untapped, the operation of the forced tapping mechanism provides a theoretical framework for explaining a wide range of equator-to-pole temperature gradients in past and future climates. There are certainly other probable mechanisms for equable climates (Farrell 1990; Barron et al. 1993; Korty et al. 2008; Abbot and Tziperman 2008; Cai 2006; Langen and Alexeev 2007); hence, the forced tapping mechanism identified here is only one of many mechanisms that may be operating. That said, the coincidence between past warm climates and La Niña–like tropical conditions (Stott et al. 2002; Rickaby and Halloran 2005; Zhang et al. 2014) corroborates the forced tapping process as a viable mechanism. In fact, we find that the planetary-scale wave events identified in this study preferentially occur during La Niña over El Niño at an approximate ratio of 2:1. In the same vein, climate models are known to have cold biases in the Arctic (Koenigk et al. 2013), while they also simulate more El Niño–like conditions than observations. As the climate continues to warm, would tropical convection become more La Niña–like? Would more ZAPE be forcefully tapped to warm the Arctic? It remains to be seen, but the finding here provides a theoretical framework for how tropical and polar climates can be knotted together without being constrained by the flux–gradient relationship.

Acknowledgments

This study was supported by the National Science Foundation under Grant ATM-1139970 and by Seoul National University, South Korea. Valuable comments from Steven Feldstein and several anonymous reviewers helped to improve this manuscript.

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