Eddy Activity Response to Global Warming–Like Temperature Changes

1. Introduction

Due to the increase in greenhouse gas concentration in the atmosphere, atmospheric temperatures are predicted to increase. Climate models project an increase in temperatures that is not spatially uniform, and both meridional and vertical temperature gradients are expected to change in a global warming scenario. Changes in temperatures and especially in temperature gradients lead to changes in atmospheric stability and may lead to large-scale changes in atmospheric circulation. Global warming simulations show anomalous and robust temperature trends in three main regions of the atmosphere (Fig. 1a): 1) an enhanced warming aloft in the tropics, 2) a surface polar amplification in the Northern Hemisphere (NH), and 3) stratospheric cooling. These temperature trends occur in all climate models used for the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC), though the exact temperature amplitude change varies between models (Vallis et al. 2015). The tropical warming aloft can be attributed to the decrease in the saturated lapse rate with increased water vapor following warming (Manabe and Wetherald 1980), combined with the fact that in the tropics the moist static stability stays close to zero. The large warming in the Arctic has been attributed to different factors such as the ice albedo feedback (Manabe and Stouffer 1980), increased heat transport (Cai 2005, 2006), and changes in longwave radiation (Bintanja et al. 2011). The cooling of the stratosphere is caused by the large increase in emission compared to the small increase in absorption when CO₂ concentration in the stratosphere increases (Ramaswamy et al. 2001; Vallis et al. 2015).

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Global warming temperature trends. The mean difference between December–February (DJF) of the last 20 years of the twenty-first century (2081–2100) to the last 20 years of the twentieth century (1981–2000) for the RCP8.5 scenario taken from 10 CMIP5 models (the models that were used for this figure are MRI CGCM3, MPI-ESM-LR, MIROC-ESM, MIROC5, IPSL-CM5A-MR, IPSL-CM5A-LR, HadGEM2-ES, HadGEM2-CC, CSIRO-Mk3.6.0, and CMCC-CM; expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList) for (a) temperature (K), (b) the meridional temperature gradient (Km⁻¹ × 10⁻⁶, ∂T/a∂ϕ, where ϕ is the latitude and a is Earth’s radius), and (c) the Brunt–Väisälä frequency [s⁻¹ × 10⁻³, N = (g∂_zθ/θ)^1/2, where g is Earth’s gravity, θ is the potential temperature, and ∂_z is the derivative with respect to height].

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0190.1

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Global warming–like temperature changes might lead to large-scale changes in the atmospheric circulation. For example, models show a robust poleward shift in storm tracks and change in their intensity in the Southern Hemisphere (SH; e.g., Held 1993; Stephenson and Held 1993; Hall et al. 1994; Bengtsson and Hodges 2006; Yin 2005; O’Gorman and Schneider 2008; Wu et al. 2010; O’Gorman 2010; Chang et al. 2012; Tamarin-Brodsky and Kaspi 2017). Storm tracks play a fundamental part in the global circulation (e.g., Chang et al. 2002), and therefore it is crucial to understand future changes in their position and intensity.

Several mechanisms were suggested to explain the poleward shift of the storm tracks. Lorenz and DeWeaver (2007) showed in idealized simulations that an increase of the tropopause height, which is a robust result of global warming simulations (Vallis et al. 2015), leads to a poleward shift. Lu et al. (2008) and Lim and Simmonds (2009) suggested that the increase in the subtropical static stability pushes the baroclinic zone poleward, and leads to a poleward shift. Chen et al. (2008) suggested that the shift can be caused by increased phase speed of midlatitude eddies in a climate change scenario (see also Lorenz 2014). Kidston et al. (2011) suggested that increased eddy length scale will lead to a poleward shift. Tamarin-Brodsky and Kaspi (2017) suggested that a more tilted and poleward path of the storms themselves leads to an overall poleward shift of the zonal mean storm track. Voigt and Shaw (2016) and Li et al. (2019) used idealized GCM and showed that changes in cloud radiative effects in global warming simulations contribute to the poleward shift of the extratropical jet. These mechanisms provided the theoretical framework to understand how climate change temperature projections might affect the storm tracks in the SH.

The changes in the position and intensity of the NH storm track are less clear (Chang et al. 2012; Vallis et al. 2015). Besides the more complicated orography in the NH, which leads to large zonal asymmetries, the projected temperature trends in the NH are more complex. For example, the meridional temperature gradients at the lower and upper troposphere have opposite trends. At the lower troposphere, the temperature gradient reduces due to polar amplification, but in the upper troposphere the gradient increases due to the upper tropical heating (Fig. 1b). Motivated by the projected trends, Held and O’Brien (1992), Pavan (1996), Lunkeit et al. (1998), Wu et al. (2012), and Yuval and Kaspi (2016) have studied whether the upper or lower temperature gradient plays a more important role in affecting eddy activity in various complexity of models. These studies have mainly focused on the changes in meridional gradient at different levels.

In this study we emphasize that it is not possible to modify the meridional temperature gradient at specific vertical levels (nonuniformly with height) without affecting the lapse rate.¹ The baroclinicity is affected by both the static stability (which is proportional to the lapse rate) and the meridional temperature gradient. For example, the Eady growth rate (Eady 1949), which is commonly used as a measure of baroclinicity, is proportional to ∂_yT/N, where N is the Brunt–Väisälä frequency and ∂_yT is the meridional temperature gradient. Therefore, changes in both the meridional temperature gradient and the Brunt–Väisälä frequency (which is proportional to the square root of the static stability) should be taken into account when studying the response of eddy activity to temperature changes. For example, when the meridional temperature gradient decreases at the lower levels due to the Arctic amplification (Fig. 1b), the Brunt–Väisälä frequency decreases at the same time (Fig. 1c). Therefore, the decreased temperature gradient and decreased Brunt–Väisälä frequency have an opposite effect on the baroclinicity. Since both the meridional temperature gradient and the static stability affect baroclinicity, it is not straightforward to determine whether the Arctic amplification leads to increase or decrease in baroclinicity. As we show in this study, decreasing the lower-level temperature gradient via an increase in lower-level Arctic temperatures could lead to an increase or decrease in eddy activity, depending on the exact temperature modifications.² In the case of upper tropospheric tropical heating, the meridional temperature gradient changes and the (dry) static stability changes have an opposite effect on the baroclinicity in the subtropics. While the meridional temperature gradient increases and tends to enhance baroclinicity, the Brunt–Väisälä frequency (and static stability) increases and tends to decrease baroclinicity (Fig. 1).

In this study we use an idealized general circulation model (GCM) with a modified Newtonian relaxation scheme to study the effect of zonally symmetric increased lower-level Arctic temperatures, and zonally symmetric increased upper tropical tropospheric temperatures on eddy activity. Many previous studies used idealized GCMs to investigate the effects of global warming–like temperature changes on the atmospheric circulation. These studies focused on inducing diabatic heating changes that resemble the change in the temperature trends predicted by the IPCC report (e.g., Polvani and Kushner 2002; Kushner and Polvani 2004; Lorenz and DeWeaver 2007; Lim and Simmonds 2009; Butler et al. 2010; Lu et al. 2014). These studies have contributed to our understanding of how global warming–like temperature trends could affect the circulation. For example, Butler et al. (2010) used an idealized GCM with a Newtonian cooling scheme, and modified the relaxation temperature such that it will represent upper tropospheric tropical warming and low-level polar heating. They found that upper tropospheric tropical warming tends to shift storm track poleward while low-level polar heating leads to an opposite tendency (and hence there is a competition between the two effects).

One limitation of these studies is that instead of reproducing the projected global warming–like temperature changes, these studies prescribe an increased (or decreased) diabatic heating in regions that are projected to have anomalous temperature changes. However, inducing diabatic warming at a certain region may lead to temperature changes also in other regions due to temperature advection [e.g., see Fig. 2 in Butler et al. (2010), where the polar lower stratosphere is cooled when the upper tropics are warmed]. Therefore, it is not straightforward to obtain temperature changes that resemble a global warming–like temperature changes by adding diabatic heating terms, and to systematically investigate the effect of different temperature changes on atmospheric circulation. Nevertheless, controlling changes in diabatic heating or controlling temperature changes (by simulating a specified temperature field) could be both useful methods to study the circulation response to global warming–like changes. Since most of the theoretical explanations to the response of eddy fields in a climate change scenario rely on the projected temperature field changes, and not on the diabatic heating changes, and since most idealized studies focus on controlling the diabatic heating, we find it important to study the response of eddy activity to global warming–like changes in idealized framework where the mean temperature can be prescribed in simulations.

It is found in this study that the details of the exact temperature changes could lead to very different responses of eddy activity. Therefore, it is important to understand the eddy sensitivity to the shape of temperature changes, and be able to represent accurately the projected temperatures from a global warming scenario. We note that the response of dynamic variables is very sensitive to the specific details of warming even in comprehensive GCMs, and not unique to idealized GCMs. For example, Liu et al. (2012) and Screen et al. (2014) used two identical models and almost identical forcings and yet the response of sea level pressure due to Arctic amplification in their models was different.

The paper is organized as follows. The idealized GCM and the modified Newtonian relaxation scheme are presented in section 2a. The modified temperature profiles used to simulate global warming–like temperature trends in the idealized GCM are discussed in sections 2b and 2c. The simulations results using a hemispherically symmetric reference state with enhanced upper tropospheric temperature gradient and reduced lower-level temperature gradient are discussed in sections 3a and 3b. In these sections, the competing effects of static stability changes and meridional temperature gradient are investigated. In section 3c idealized simulations with simultaneous temperature changes in the upper tropical troposphere and the polar surface are discussed. Next, using a more “realistic” zonally symmetric reference state with temperature modifications taken directly from the representative concentration pathway 8.5 (RCP8.5) simulations, the circulation response to Arctic amplification and tropical upper tropospheric temperature increase are studied (section 4). The results are discussed and summarized in section 5.

2. Methods

A dry version of an idealized GCM based on the spectral dynamical core of the GFDL Flexible Modeling System (FMS) is used. The model is driven by a Newtonian cooling scheme that is described in section 2a. The simulations do not include orography or ocean, and dissipation in the boundary layer is represented by linear damping of near-surface winds (below σ = 0.7) with a relaxation time of 1 day at the surface [see Held and Suarez (1994) for details]. All simulations have 60 vertical sigma levels with a T42 (2.8° × 2.8°) horizontal resolution. What distinguishes our simulations from Held and Suarez (1994) is the relaxation temperature distribution and the different relaxation time used for the zonal mean and the eddies in the temperature equation (see section 2a). Throughout this study, unless stated explicitly otherwise, eddy fields are defined as a deviation from the zonal and time mean.

All simulations except the reference simulations are integrated over 3000 days, where the first 500 days of each simulation are treated as spinup, and the results are averaged over the last 2500 days. The reference simulations were integrated over 9000 days and results are averaged over the last 8500. In section 3 all the simulations are hemispherically symmetric and results are presented after averaging over both hemispheres. In section 4 the simulations are not hemispherically symmetric and we present results from both hemispheres or only for the NH, depending on the context.

b. Relaxation temperature profiles—Hemispherically symmetric simulations

In this study we focus on the effect of the anomalous temperature increase at the tropical upper troposphere and at the polar surface. To consider a global warming–like temperature changes in the upper troposphere, the reference temperature was modified as follows:

$\delta T_{\text{tropical}}=-A^{\text{upper}}\times e^{\left[-{\left(\sigma -{\sigma }_c^{\text{upper}}\right)}^2/{\left(2{\sigma }_w^{\text{upper}}\right)}^2\right]}\times \left[\tanh \left({\displaystyle \frac{\left|\varphi \right|-{\varphi }_{\mathit{c}}^{\text{upper}}}{{\varphi }_{\mathit{w}}^{\text{upper}}}}\right)-1\right],$(2)

where 2 × A^upper is the amplitude of the temperature change, ϕ is the latitudinal coordinate, ${\varphi }_c^{\text{upper}}$ determines the latitude where the temperature gradient is centered, ${\varphi }_w^{\text{upper}}$ determines the temperature gradient width, σ is the vertical coordinate, ${\sigma }_c^{\text{upper}}$ is the vertical level with maximal temperature changes, and ${\sigma }_w^{\text{upper}}$ determines the vertical width of the temperature changes. The relaxation temperature in simulations with tropical upper tropospheric temperature changes is $T_R=T_{\text{ref}}^{\text{HS}}+\delta T_{\text{tropical}}$, where $T_{\text{ref}}^{\text{HS}}$ is the reference temperature. The reference temperature was chosen to be the mean temperature of a simulation with the Held and Suarez (1994) forcing. The Newtonian cooling scheme presented in Eq. (1) was used with this reference temperature $\left(T_{\text{ref}}^{\text{HS}}\right)$ as its relaxation temperature to determine the reference simulation for all the simulations presented in section 3. The tanh function, which parameterizes the latitudinal shape of the heating, is preferred over an exponential dependence because it produces a sharper meridional gradient, which is similar to the projected gradient changes in global warming simulations (where the gradient change is concentrated in subtropics/midlatitudes and not inside the tropics; Fig. 1a).

The temperature differences between the reference simulation and simulations with increased tropical upper tropospheric temperature field with the parameters A = 2 K, ${\sigma }_w^{\text{upper}}=0.11$, ${\varphi }_c^{\text{upper}}=35\mathrm{°},40\mathrm{°},45\mathrm{°},50\mathrm{°},{\sigma }_c^{\text{upper}}=0.3$, and ${\varphi }_w^{\text{upper}}=10\mathrm{°}$ are shown in Figs. 2a–d. The modifications of ${\varphi }_c^{\text{upper}}$ allows us to investigate the interplay between the effect of the static stability and the meridional temperature gradient on the eddy fields. Larger ${\varphi }_c^{\text{upper}}$ values tend to modify the static stability in a broader region, while shifting the latitudinal location of the meridional temperature gradient but keeping its magnitude unaffected (appendix A). To investigate the sensitivity of eddy activity to changes in the center level of warming (σ_c) simulations with all the combinations of A^upper = 2 K, ${\sigma }_w^{\text{upper}}=0.11,{\varphi }_c^{\text{upper}}=30\mathrm{°},35\mathrm{°},40\mathrm{°},45\mathrm{°},50\mathrm{°},55\mathrm{°},{\sigma }_c^{\text{upper}}=0.2,0.3,0.4$, and ϕ_w = 10° were conducted (18 simulations). Since the results presented in section 3a are qualitatively robust to these changes, these simulations are not shown.

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The zonal wind and eddy fields response to temperature increase at low latitudes of the upper troposphere in an idealized GCM: (a)–(d) temperature, (e)–(h) zonal wind, (i)–(l) EKE, (m)–(p) EMFC × 10⁶, and (q)–(t) EHF for simulations that the upper troposphere was modified with tropical upper tropospheric temperature increase as in Eq. (2) using the parameters A^upper = 2 K, ${\varphi }_c^{\text{upper}}=35°,40\mathrm{°},45\mathrm{°},50\mathrm{°},{\varphi }_w^{\text{upper}}=10\mathrm{°},{\sigma }_c^{\text{upper}}=0.3,\text{and}{\sigma }_w^{\text{upper}}=0.11$. Colors indicate the deviation from the reference simulation and contours show the reference simulation fields. The contour intervals are 15 K (temperature), 5ms⁻¹ (zonal wind), 50 m² s⁻² (EKE), 5ms⁻² (EMFC), and 2Kms⁻² (EHF). Colors have the same units as contours.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0190.1

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To consider Arctic amplification–like temperature changes, the target temperature was modified as follows:

$T_{\text{arctic}}=A^{\text{lower}}\left\{1+\tanh \left[2{\displaystyle \frac{\text{abs}\left(\varphi \right)-{\varphi }_c^{\text{lower}}}{{\varphi }_{\mathit{w}}^{\text{lower}}}}\right]\right\}{e}^{-{\left(\sigma -1\right)}^2/{\left(2{\sigma }_w^{\text{lower}}\right)}^2},$(3)

where the parameters have similar meaning as in Eq. (2) (superscripts changed from upper to lower), but the temperature modification is concentrated at the polar surface. The temperature differences between the reference simulation and simulations with Arctic amplification–like temperature changes [using Eq. (3)] with the parameters $A^{\text{lower}}=2\text{K},{\sigma }_w^{\text{lower}}=0.2$, ${\varphi }_w^{\text{lower}}=30\mathrm{°}$, and ${\varphi }_c^{\text{lower}}=40°,50°,70°,80°$ are shown in Figs. 3a–d. Similarly to the case of upper tropospheric temperature gradient modifications, changes in ${\varphi }_c^{\text{lower}}$ allow the investigation of the interplay between the effect of the static stability and of the meridional temperature gradient on eddy fields.

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The zonal wind and eddy fields response to polar surface temperature increase in an idealized GCM: (a)–(d) temperature, (e)–(h) zonal wind, (i)–(l) EKE, (m)–(p) EMFC × 10⁶, and (q)–(t) EHF for Arctic amplification–like simulations. The temperature modifications are calculated from Eq. (3), using the parameters $A^{\text{lower}}=2\text{K},{\varphi }_c^{\text{lower}}=40\mathrm{°},50\mathrm{°},60\mathrm{°},80\mathrm{°},{\varphi }_w^{\text{lower}}=30\mathrm{°},\text{and}{\sigma }_w^{\text{lower}}=0.2$. Colors indicate the deviation from the reference simulation and contours show the reference simulation fields. The contour intervals are 15 K (temperature), 5ms⁻¹ (zonal wind), 50 m² s⁻² (EKE), 5ms⁻² (EMFC), and 2Kms⁻² (EHF). Colors have same units as contours.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0190.1

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To verify the robustness of the results presented in section 3b, we conducted simulations with the parameters $A^{\text{lower}}=2\text{K},{\sigma }_w^{\text{lower}}=0.1,0.2$, and ${\varphi }_w^{\text{lower}}=10\mathrm{°},20\mathrm{°},30\mathrm{°}$ and all the combinations with ${\varphi }_c^{\text{lower}}=10°,20°,30°,40°,50°,60°,70°,80°$ (48 simulations). The modifications in ${\varphi }_w^{\text{lower}}$ and ${\sigma }_w^{\text{lower}}$ are used to test the robustness of the qualitative conclusions when ${\varphi }_c^{\text{lower}}$ is modified. Since the qualitative results of the additional simulations are similar to the results presented in section 3b, these simulations are not shown.

3. Results with hemispherically symmetric simulations

In this section, the results of idealized hemispherically and zonally symmetric simulations with global warming–like temperature modifications are presented. We focus on the response of eddy fields to two robust anomalous temperature changes occurring in global warming simulations: low-latitude upper tropospheric temperature increase (section 3a) and Arctic amplification (section 3b).

c. Combined experiments

In this section, the eddy fields’ response to a simultaneous lower-latitude upper troposphere and surface polar region temperature increase $\left(T_{\text{combined}}=T_{\text{ref}}^{\text{HS}}+\delta T_{\text{tropical}}+\delta T_{\text{arctic}}\right)$ is investigated. There are many different parameter combinations that could be chosen to simulate a simultaneous changes at the polar surface region and at the upper troposphere. In Fig. 4 only two such choices are shown. The parameter combinations that are used lead to temperature changes that have some resemblance to global warming–like temperature gradients obtained in projections. Namely, the positions of the meridional temperature gradients, both in the upper troposphere and in the lower troposphere, are located at the same regions as in the projections, and their relative positions are similar to the projections (Fig. 1b). The simulations shown in Fig. 4 have a relatively similar temperature changes but nevertheless show a qualitatively different EKE response (Figs. 4i,j), indicating that the EKE response is sensitive to the exact details of the temperature modifications (seen also in Fig. 2).

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Comparison between the zonal wind and eddy fields response to simultaneous temperature increase at the low latitudes of the upper troposphere and polar surface to the response from a linear sum of similar temperature changes done in separate simulations: (a)–(d) temperature, (e)–(h) zonal wind, (i)–(l) EKE, (m)–(p) EMFC × 10⁶, and (q)–(t) EHF for (two left columns) combined simulations of upper tropospheric tropical warming and Arctic amplification–like simulations and (two right panels) the linear sum of simulations that the tropical upper tropospheric and polar surface are modified separately. The parameter combinations that are chosen for the first and third columns are A^lower = 2 K, ${\varphi }_c^{\text{lower}}=60\mathrm{°},{\varphi }_w^{\text{lower}}=30\mathrm{°},\text{and}{\sigma }_w^{\text{lower}}=0.2$ and $A^{\text{upper}}=2\text{K},{\varphi }_c^{\text{upper}}=40\mathrm{°},{\varphi }_w^{\text{upper}}=10\mathrm{°},{\sigma }_w^{\text{upper}}=0.11$, and ${\sigma }_c^{\text{upper}}=0.3$ (for the upper tropical warming). For the second and fourth rows the parameters the parameters are similar except that ${\varphi }_c^{\text{lower}}=70\mathrm{°}$ and ${\varphi }_c^{\text{upper}}=50\mathrm{°}$ (tropical warming). Colors indicate the deviation from the reference simulation and contours show the reference simulation fields. The contour intervals are 15 K (temperature), 5 ms⁻¹ (zonal wind), 50 m² s⁻² (EKE), 5ms⁻² (EMFC), and 2Kms⁻² (EHF). Colors have same units as contours.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0190.1

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The eddy activity and zonal wind response in the combined simulations is almost identical to the linear sum responses of simulations where the lower-latitude upper troposphere and the polar surface are warmed separately (Fig. 4).⁴ This implies that the simulated temperature modifications affect the circulation such that it is in the linear response regime, and the changes in the circulation due to the different temperature changes interact very weakly. Since the response of eddy activity to upper tropospheric changes is larger (cf. Figs. 2 and 3), eddy activity changes are dominated by the upper tropospheric temperature changes in the combined simulations. For example, the response in the first (second) column of Fig. 4 is similar to the response shown in the second (fourth) column of Fig. 2 (where the two simulations have the same upper tropospheric temperature change).

We note that there are many parameters other than the latitudinal extent of the temperature modification, such as the vertical width, the latitudinal width, amplitude, and so on that should be taken into account when considering the similarity of the temperature modifications in the idealized simulation and projections. Therefore, more realistic temperature modifications are considered in section 4, and we do not extend the discussion of whether the results presented in this section necessarily indicates that the upper tropospheric tropical warming modification will affect eddy fields more than the Arctic warming, and discuss this question in more detail in section 4.

4. Results with an ECMWF-like reference state

The results of section 3 highlighted the interplay between changes in the static stability and meridional temperature gradient. Building on the results of section 3, in this section, the eddy fields and zonal wind response to global warming–like temperature changes are studied using a more “realistic” zonally symmetric reference temperature taken from the ECMWF (section 2c). Since the eddy response to a specific temperature modification might be affected from the reference state, it is important to study the response using a reference state that is similar to Earth. This point is demonstrated in appendix C1, where it is shown that when the Held and Suarez (1994) reference $\left(T_{\text{ref}}^{\text{HS}}\right)$ is modified using the temperature trends from the RCP8.5 scenario $\left(T_{\text{RCP}85}^{\mathrm{mod}}\right)$, the eddy response is qualitatively different compared to similar changes applied to the ECMWF zonally symmetric reference ($T_{\text{ref}}^{\text{ECMWF}}$, Fig. 5).⁵

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The zonal wind and eddy fields response in the ECMWF reference simulation to temperature changes taken from projections of the RCP8.5 scenario. Contours show the (a) temperature, (b) zonal wind, (c) EKE, (d) EMFC × 10⁶, and (e) EHF for the ECMWF reference temperature ($T_{\text{ref}}^{\text{ECMWF}}$, details in section 2). Colors show the difference between a simulation with the simulated RCP8.5 trends $\left(T_{\text{RCP}85}^{\mathrm{mod}}\right)$ and the ECMWF reference. The contour intervals are 15 K (temperature), 5ms⁻¹ (zonal wind), 40 m² s⁻² (EKE), 5ms⁻² (EMFC), and 2 Kms⁻² (EHF). Colors have same units as contours.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0190.1

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The temperature, zonal wind, EKE, EMFC, and EHF of the ECMWF zonally symmetric reference simulation are plotted in Fig. 5 (contours). This simulation is hemispherically asymmetric, and since the reference temperature is taken from the NH winter, the temperature gradients as well as the EHF are larger in the NH (Figs. 5a,e). The differences between the ECMWF reanalysis data and the zonally symmetric reference simulation used in this section are discussed in section b of appendix C. In the NH, the simulation has some resemblance to the zonally average reanalysis data, while in the SH there are large differences in EKE and in surface winds (section b of appendix C). Despite the differences between the ECMWF reference and the reanalysis data in the NH, we find it important to study the response of global warming–like temperature changes in the ECMWF reference, as it still represents an Earth-like circulation better than the Held and Suarez (1994) reference (see section b of appendix C) in the NH.

When the RCP8.5 temperature changes are simulated with the idealized model, the zonal wind in the SH tends to intensify at the poleward flank of the jet, both at the surface and in the upper troposphere (Fig. 5b, colors). A similar poleward jet shift in the SH during DJF is a robust trend in a global warming scenario (e.g., Wu et al. 2010; Vallis et al. 2015). Furthermore, the EKE in the SH is enhanced at the EKE maximal region and slightly poleward to this region, and reduced at the equatorward flank of the jet (Fig. 5c), which is qualitatively similar to projections from CMIP5 simulations (Chang et al. 2012). The reduction of EKE at high latitudes in the SH (Fig. 5c) is not projected in global simulations and could be a result of the lack of orography (i.e., Antarctica) in the idealized model. In the NH the jet tends to intensify in the upper troposphere at midlatitudes, which is projected in some comprehensive models (Lorenz and DeWeaver 2007), and tends to weaken at higher latitudes (Fig. 5b), which is not projected in models. The weakening of the zonal winds at high latitude is related to the increased eddy momentum flux divergence at high latitudes in the simulation (Fig. 5d). The EKE response in the RCP8.5 idealized simulation in the NH is a general weakening at the mid- to lower troposphere, and an increase in the upper troposphere at lower latitudes. This result is with reasonable qualitative agreement with the CMIP5 ensemble mean modifications, which shows an overall decrease (with low certainty) in the lower troposphere, and an increase in the upper troposphere/lower stratosphere (Chang et al. 2012). Furthermore, the idealized model is missing a lot of the physical processes and does not include important components (clouds, orography, moisture etc.), and therefore it is not expected that the idealized model could simulate accurately the projected changes. Nevertheless, the idealized model is used to understand the direct effect of the zonally symmetric temperature changes on the circulation. In the next subsections (sections 4a and 4b), the idealized model is used with the ECMWF reference to isolate the direct effect of low-latitude upper tropospheric temperature increase and Arctic amplification trends in the RCP8.5 scenario on the atmospheric circulation in the NH in the idealized GCM.

a. Upper tropospheric tropical heating using the ECMWF reference

To consider the effect of the projected low-latitude upper tropospheric temperature changes on eddy activity, the ECMWF reference temperature was modified as in Eq. (5). The simulated modified temperatures mimic the upper tropospheric tropical meridional gradient temperature changes as in an RCP8.5 scenario. As in section 3a we find that the response of the EKE and EHF in the NH is dependent on the exact details of the temperature changes [see the work of Tandon et al. (2013) and Sun et al. (2013), who show that the circulation response to tropical warming is dependent on the width of the warming]. When the meridional temperature gradient modifications are constrained to lower latitudes, the EKE and EHF amplitude tend to increase (Fig. 6, left column). When the temperature gradient increase extends deep into the subtropics, as in CMIP5 temperature projections (Fig. 1a), eddy activity decreases, and the jet tends to shift poleward (Fig. 6, right column). These results are in agreement with the conclusion of section 3 that the increase in the meridional temperature gradient and the static stability have a competing and opposite effect on the eddy activity when the upper troposphere is warmed at lower latitudes. Specifically, the qualitative responses shown in Fig. 6 are in agreement with the results of Fig. 2.⁶

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The zonal wind and eddy fields response in the ECMWF reference state to low-latitude upper tropospheric meridional temperature gradient increase taken from RCP8.5 scenario. Contours show the (a),(b) temperature, (c),(d) zonal wind, (e),(f) EKE, (g),(h) EMFC × 10⁶, and (i),(j) EHF for the ECMWF reference temperature $\left(T_{\text{ref}}^{\text{ECMWF}}\right)$. Colors show the difference between RCP8.5 tropical upper troposphere temperature modifications, as in Eq. (5) with parameters (left) ${\varphi }_c^{\text{tropical}}=30\mathrm{°}$ and (right) ${\varphi }_c^{\text{tropical}}=60\mathrm{°}$ and the ECMWF idealized reference. The contour intervals are 15 K (temperature), 5ms⁻¹ (zonal wind), 40 m² s⁻² (EKE), 5ms⁻² (EMFC), and 2 Kms⁻² (EHF). Colors have the same units as contours.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0190.1

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When mimicking the meridional temperature gradient RCP8.5 trends in the upper troposphere also at higher latitudes (Fig. 6, right column), the EKE response is similar to the one obtained from the RCP8.5 idealized simulation (Fig. 5) in the upper troposphere. This implies that the changes in the low-latitude upper troposphere temperature plays an important role in affecting the EKE in the upper troposphere. On the other hand, the zonal wind, EMFC, and EHF changes are significantly different from the RCP8.5 idealized simulation, indicating that temperature changes in other regions play an important role in the zonal wind and eddy fields response. Furthermore, we note that according to the results presented here, it is not clear whether the increased upper tropospheric temperature gradient (Fig. 6) will necessarily lead to increased eddy activity.

b. Arctic amplification

To consider the effect of the projected Arctic amplification on eddy activity, the ECMWF reference temperature was modified as in Eq. (6). The simulated modified temperatures mimic the lower-level meridional gradient temperature changes as in the RCP8.5 scenario. As in section 3, when the extent of the temperature gradient increases, the EKE response is shifting from a negative sign (Fig. 7e), to a mixed response (Fig. 7f, also cf. Fig. 3k). Since in the NH surface the meridional temperature gradient is constrained to relatively high latitudes (Fig. 1b), the overall response is mostly negative due to the reduction in the meridional temperature gradient, with the reduction in static stability playing a smaller role. Consequently, the qualitative circulation changes due to RCP8.5-like Arctic amplification have relatively small sensitivity to changes of the parameter ${\varphi }_c^{\text{Arctic}}$ [Eq. (6)], and the two simulations presented in Fig. 7 show similar results (though their amplitude is different). The jet tends to weaken at high latitudes and increase at the jet center (Figs. 7a,b), which tends to sharpen the jet. The EHF decreases at lower levels where the gradient is reduced, indicating that the reduction in the EHF at lower levels seen in the idealized RCP8.5 idealized simulation (Fig. 5e) is caused by the meridional temperature reduction at the lower levels.⁷

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The zonal wind and eddy fields response in the ECMWF reference state to polar surface meridional temperature gradient decrease taken from RCP8.5 scenario. As in Fig. 6, but for Arctic amplification simulations [Eq. (6)] with the parameters (left) ${\varphi }_c^{\text{Arctic}}=60\mathrm{°}$ and (right) ${\varphi }_c^{\text{Arctic}}=30\mathrm{°}$. The contour intervals are 15 K (temperature), 5ms⁻¹ (zonal wind), 50 m² s⁻² (EKE), 5ms⁻² (EMFC), and 2Kms⁻² (EHF). Colors have the same units as contours.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0190.1

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The zonal wind, EKE, EMFC, and EHF changes due to tropical upper troposphere temperature increase and due to Arctic amplification are on the same order of magnitude. This implies that in order to understand the circulation changes in a global warming scenario that are caused by temperature modifications, it is necessary to consider both changes. This is different from the results of section 3, where the upper tropospheric changes lead to larger changes. Since both the reference and the temperature trends were not taken from a more realistic scenario in section 3, we find the results in this section more relevant when considering the effect of global warming–like temperature trends on the zonal wind and eddy fields.

c. Combined Arctic and upper tropospheric warming

In this section we investigate whether the main response in the NH in the RCP8.5 idealized simulation (Fig. 5) can be explained by these two observed temperature trends. Furthermore, it is demonstrated that the linear sum of simulations with low-latitude upper tropospheric heating and Arctic amplification gives similar eddy response as in a simulation with the combined temperature trends. The temperature modifications in the combined experiments can be expressed as

$T_{\text{combined}}^{\text{ECMWF}}=T_{\text{ref}}^{\text{ECMWF}}+\delta T_{\text{tropical}}^{\text{ECMWF}}+\delta T_{\text{Arctic}}^{\text{ECMWF}}.$(7)

It is found that the combined simulation (Fig. 8, middle column) and the linear sum of the separated simulation (Fig. 8, right column) give very similar results.⁸ Nevertheless, small differences between the combined simulation and the linear sum of separate simulation occur in certain regions (e.g., the amplitude of the EKE changes at higher latitudes is smaller in the combined simulations). This implies that in order to understand the eddy activity changes in the idealized simulations of the combined scenario, there is no need to consider interactions between the changes caused by low-latitude upper tropospheric warming and the Arctic amplification. Furthermore, it is found that the combined simulation (Fig. 8, middle column) and the full scenario (Fig. 8, left column) simulate very similar zonal wind, EKE, and EHF changes. This implies that the two anomalous temperature trends in the low-latitude upper troposphere and the polar surface have a large effect on the circulation changes, and in the idealized simulations conducted in this study most of the zonally symmetric circulation changes are induced by these changes. Nevertheless, the combined simulation does not produce the changes in the EMFC correctly at latitudes 40°–60°N. Whereas in the idealized RCP8.5 simulation there is a weaker convergence in this region, both in the combined and in the sum of the linear simulation there is stronger convergence. Overall these results imply that in order to understand the eddy activity response due to temperature changes as in the RCP8.5 scenario, it is enough to consider the low-latitude upper tropospheric temperature increase and the Arctic amplifications, though there are some exceptions when it is not enough to consider these changes (changes in the EMFC).

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Comparison between the zonal wind and eddy fields response in the ECMWF reference to (left) temperature modifications as in the RCP8.5 scenario, (middle) with combined temperature increase at the low latitudes of the upper troposphere and at the polar surface, and (right) to the response from a linear sum from separate simulations with similar temperature changes. (a)–(d) Temperature, (e)–(h) zonal wind, (i)–(l) EKE, (m)–(p) EMFC × 10⁶, and (q)–(t) EHF for the (left) full RCP8.5 changes, (middle) the combined simulation [Eq. (7)] with the parameters ${\varphi }_c^{\text{tropical}}=60\mathrm{°}$ and ${\varphi }_c^{\text{Arctic}}=30\mathrm{°}$, and (right) the linear sum of a simulation upper tropospheric tropical temperature increase $\left({\varphi }_c^{\text{tropical}}=60\mathrm{°}\right)$ and Arctic amplification (${\varphi }_c^{\text{Arctic}}=30\mathrm{°}$). The contour intervals are 15 K (temperature), 5ms⁻¹ (zonal wind), 40 m² s⁻² (EKE), 5ms⁻² (EMFC), and 2Kms⁻² (EHF). Colors have same units as contours.

Citation: Journal of Climate 33, 4; 10.1175/JCLI-D-19-0190.1

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5. Conclusions

In this study, the zonal wind and eddy fields response to global warming–like temperature variations are investigated using an idealized GCM with a modified Newtonian cooling scheme. The modified Newtonian cooling scheme enables simulation of any chosen zonal mean temperature distribution. This allows us to systematically study how temperature changes in different regions and with different spatial structures affect the circulation. Many different studies have used idealized GCMs to investigate the circulation response to global warming–like heating profiles (e.g., Polvani and Kushner 2002; Kushner and Polvani 2004; Lorenz and DeWeaver 2007; Lim and Simmonds 2009; Butler et al. 2010; Lu et al. 2014). One limitation of these studies is that they prescribe a diabatic heating profile that resembles the projected temperature changes. For example, to study the effect of Arctic amplification on the circulation, heating at the polar surface is prescribed (Butler et al. 2010). However, inducing diabatic warming at a certain region may lead to temperature changes also in other regions due to temperature advection, and the resulting circulation will be affected by temperature changes in regions that were not intended to be modified. The method used in this study allows the investigation of the zonal mean wind and eddy fields response to global warming–like temperature trends.

The zonal wind and eddy fields responses to low-latitude upper tropospheric and polar surface temperature increase are investigated. It is found that the response to low-latitude upper tropospheric temperature increase and to polar surface temperature increase is dependent on the shape of the temperature changes (Figs. 2 and 3). Specifically, it is found that the latitudinal extent of these temperature changes has a large effect on the response of eddy fields. For example, it is shown that as the low-latitude upper tropospheric temperature increase penetrates deeper into midlatitudes, the responses of the EKE and EHF tend to shift from an increase to a decrease (Fig. 2). Similarly, it is found that when the high-latitude surface warming is extended toward the tropics, the response of the EKE changes from a decrease to an increase. These results are explained by the interplay between the meridional temperature gradient and the static stability. When the meridional temperature gradient is modified only at certain vertical levels, the Brunt–Väisälä frequency also changes (e.g., Figs. 1b,c and Fig. A1). Therefore, when the low-latitude upper troposphere is anomalously warmed, the meridional temperature gradient is increased, but at the same time the dry static stability increases. These two trends have an opposite effect on baroclinicity. Similarly, when the surface is warmed at high latitudes, the meridional temperature gradient decreases, but at the same time also the static stability decreases. When the latitudinal extent of the temperature changes increases (while keeping the meridional temperature gradient magnitude constant), the static stability tends to play a larger role since it is modified in a broader region (section 3 and appendix A). It is demonstrated that in order to understand the circulation response to global warming–like temperature changes, both the static stability changes and meridional temperature gradient need to be taken into account, and considering only the meridional temperature gradient changes is not sufficient to understand the circulation changes (section 3 and appendixes B and C).

As shown in this study, it is not trivial to determine whether the temperature gradient or the static stability changes affect more the eddy fields (e.g., Fig. 2). Hence, studies that considered only changes in the meridional temperature gradient might not be sufficient to give an indication whether the low-latitude upper troposphere warming or the Arctic amplification will have a larger effect on the circulation [e.g., Held and O’Brien (1992) used a three-layer quasigeostrophic model, and considered only a meridional temperature gradient modifications, while static stability was unchanged]. To put the topic of eddy sensitivity to upper or lower baroclinicity changes in the context of global warming, it is necessary to simulate temperature changes that are representing global warming projections and affect both the meridional temperature gradient and static stability.

Highlighting the importance of static stability changes in affecting the circulation in a global warming scenario, and focusing simultaneously on changes in the meridional temperature gradient and in the static stability, could shed light on the results of Lunkeit et al. (1998) and Yuval and Kaspi (2016). Lunkeit et al. (1998) used an idealized model with realistic temperature profiles to investigate the effects of global warming on atmospheric circulation. Lunkeit et al. (1998) modified the temperature field at the lower and upper levels separately, using the difference between the historical temperature field and a global warming scenario. They found that when only the lower levels are modified (decreasing the temperature gradient), eddy activity increases, and when only the upper levels are modified (increasing the temperature gradient), eddy activity decreases (see Fig. 9 in their paper). Lunkeit et al. (1998) found this result surprising, and explained their results by the domination of the local modes over the global modes (Pierrehumbert 1984). As shown here, a simpler interpretation to their results is that the static stability decreases (increases) when the temperature is increased only at the lower (upper) levels. Also, the results of Yuval and Kaspi (2016), which showed that eddy activity changes much more when the upper-level temperature gradient is modified compared to the lower-level temperature gradient, can be partly explained by the static stability changes. In those simulations the temperature gradient was modified by changing the temperature at higher latitudes and at different vertical levels. Therefore, modifying the temperature gradient at lower levels led to opposite effects of the meridional temperature gradient and static stability on baroclinicity (as in the case of Arctic amplification). Conversely, modifying the temperature in the upper levels led to static stability changes and meridional temperature gradient changes that both tended to increase or decrease the baroclinicity in the same direction. This observation could explain the larger changes in eddy fields when the upper levels were modified compared to the small response when the lower levels were modified. Furthermore, similarly to Lunkeit et al. (1998), Yuval and Kaspi’s (2016) simulations showed a decrease in eddy activity when the meridional temperature gradient was increased at the lower levels, which can be explained by an increase in the static stability.

Two different reference states are used in this study. One is taken from the Held and Suarez (1994) reference temperature, and the second is taken from the ECMWF reanalysis data (section 2). Using the Held and Suarez (1994) reference temperature with imposed prescribed temperatures modifications [Eqs. (2) and (3)] at low-latitude upper troposphere and polar surface, it is found that the eddy activity response is dominated by the tropical upper troposphere (section 3c). To investigate the effect of global warming–like temperature changes on the circulation in a more realistic reference state, the zonally mean DJF temperature taken from ECMWF data $\left(T_{\text{ref}}^{\text{ECMWF}}\right)$ is simulated. The use of a second reference state, which resembles Earth’s temperature and circulation (especially in the NH; see Fig. C2 in section b of appendix C), is necessary since different reference states have different circulation response when the same temperature changes are applied. For example, when the RCP8.5 temperature changes are imposed on the ECMWF reference state (Fig. 5), the response is different compared to the same changes imposed on the Held and Suarez (1994) reference state (Fig. C2).⁹ This result has broader implications, and it suggests that idealized studies should use several representing reference states to verify the robustness of the results.

The ECMWF reference is used to study the effect of RCP8.5 temperature trends in the NH winter on zonal wind and eddy activity. The RCP8.5 temperature gradient changes are imposed on the ECMWF reference at the low-latitude upper troposphere [Eq. (5)] and at the Arctic surface [Eq. (6)] separately (Figs. 6 and 7). Similarly to what is found using the Held and Suarez (1994) reference, it is found that the meridional temperature gradient latitudinal extent have a large effect on the circulation in these simulations. Furthermore, we find that gradient changes in both regions have a large effect on eddy fields (right columns in Figs. 6 and 7). For example, while the EKE changes are larger when the upper troposphere gradient is modified, the EHF changes are larger when the polar surface is warmed (right columns in Figs. 6 and 7). It is found that the low-latitude upper tropospheric temperature gradient and the Arctic amplification have an opposite effect (and with similar magnitude) on EMFC. The low-latitude upper tropospheric temperature gradient tends to shift poleward the EMFC (and the zonal wind, Figs. 6d and 6h), while the Arctic amplification has an opposite effect (Fig. 7h). This implies that the poleward shift of the storm tracks in the NH might have a large variability between models because of the competing effects of the two temperature trends (and the large variability in the polar amplification), whereas in the SH the poleward shift is more robust because there is no anomalous warming in Antarctica.

We find that the linear sum of simulations with upper tropospheric tropical heating and Arctic amplification gives very similar eddy response as in a single simulation with the combined (tropical upper troposphere and Arctic) temperature trends (Fig. 8). This implies that there is little interaction between the circulation changes due to the temperature changes in the tropical upper troposphere and polar surface in the idealized GCM. Furthermore, comparing the zonal wind and eddy fields response in the combined simulation to the full idealized RCP8.5 (where temperature trends are as in the RCP8.5 in all regions), we find that in most regions the zonal wind and eddy fields have similar changes and there is agreement between the two simulations. This implies that the temperature trends at the tropical upper troposphere and at the Arctic are the cause of most of the circulation changes in the idealized model when considering a global warming scenario (Fig. 8).