Previous studies have found that the most consistent response of the eddy-driven jet to sea ice loss and Arctic amplification in fully coupled general circulation models (GCMs) is a broad region of anomalous easterlies on the poleward flank. In this study, a similar response is noted in a dry dynamical core GCM with imposed surface heating at the pole, and it is shown that in both a fully coupled GCM’s North Atlantic basin and the dry dynamical core, the anomalous easterlies cause an asymmetrical narrowing of the jet on the poleward flank of the climatological jet. A suite of barotropic model simulations run with polar forcing shows decreased jet positional variability consistent with a narrowing of the jet profile, and it is proposed that this narrowing decreases the distance Rossby waves can propagate away from the jet core, which drives changes in jet variability. Since Rossby wave propagation and dissipation is intrinsic to the development and maintenance of the eddy-driven jet, and is tightly coupled to a jet’s variability, this acts as a meridional constraint on waves’ ability to propagate outside of the jet core, leading to the decreased variability in zonal-mean jet position. The results from all three models demonstrates that this relationship is present across a model hierarchy.
The eddy-driven jet stream has long been of interest to the scientific community because of its tight association with the storm tracks and synoptic weather (e.g., Hoskins and Valdes 1990; Cione et al. 1993; Hartmann 2007; Eichelberger and Hartmann 2007; Yoshiike and Kawamura 2009; Woollings et al. 2018). Because storm tracks gain energy from highly baroclinic regions, they are most often associated with warm ocean currents and land–sea contrast, placing them in proximity to heavily populated coastlines (e.g., Hoskins and Valdes 1990; Held 1993; Brayshaw et al. 2009). Many environmental factors are expected to impact the jet and, recently, great interest has been placed on the warming of the Arctic and associated sea ice loss (e.g., Magnusdottir et al. 2004; Deser et al. 2004, 2010; Francis and Vavrus 2012; Barnes 2013; Screen et al. 2013; Deser et al. 2015; Smith et al. 2017). Specifically, in recent decades the Arctic near-surface has warmed at an accelerated rate, almost double that of the globally averaged temperature (e.g., Holland and Bitz 2003; Serreze and Francis 2006; Screen and Simmonds 2010). This accelerated warming is commonly referred to as Arctic amplification, and is due, in part, to cryospheric feedbacks associated with changes in sea ice concentration and thickness (e.g., Serreze and Francis 2006; Winton 2006), and high-latitude cloud cover (e.g., Graversen and Wang 2009), to name a few. Recent studies examining the impact of Arctic amplification and sea ice loss on the eddy-driven jet have found the response to be a weakening due to thermal wind balance and an equatorward shift (e.g., Fletcher et al. 2009; Francis and Vavrus 2012; Liu et al. 2012; Peings and Magnusdottir 2014; Francis and Vavrus 2015; Petrie et al. 2015). These studies suggest that as a result of this weakening, the jet stream becomes “wavier,” though other studies have failed to find this relation in either observations or models (e.g., Barnes 2013; Screen 2014; Hassanzadeh et al. 2014; Hassanzadeh and Kuang 2015). Many of these studies focus on the North Atlantic jet stream, comparing its response to Arctic amplification to its leading mode of variability, commonly called the North Atlantic Oscillation (NAO; e.g., Deser et al. 2004; Screen et al. 2013; Petrie et al. 2015). The NAO is characterized by the north–south shifting of the jet: in its positive phase the jet is shifted farther poleward, and vice versa (e.g., Wittman et al. 2005). For the purposes of this work we refer to the meridional shifting of a relatively zonal jet as jet positional variability, using the zonal-mean jet position over time as a metric. In this study, we explicitly quantify the response of the jet positional variability to Arctic amplification and sea ice loss in a hierarchy of models and propose a barotropic mechanism explaining the resulting behavior. Our aim is to understand fundamental barotropic mechanisms that are applicable to zonal jets, and so this work inherently ignores mechanisms associated with zonal asymmetries, such as land–sea contrast and their associated stationary waves.
Jet stream dynamics research over the last decade suggests that an equatorward shift and weakening of the eddy-driven jet could result in an increase in jet positional variability (e.g., Kidston and Gerber 2010; Barnes et al. 2010; Woollings et al. 2018). Using a barotropic model with stirring representing eddy forcing, Barnes and Hartmann (2011) showed that jets closer to the equator have greater positional variability than jets placed closer to the pole. This is in keeping with research showing the sensitivity of jet stream dynamics to jet latitude (e.g., Kidston and Gerber 2010; Kidston and Vallis 2010, 2012; Garfinkel et al. 2013; Barnes and Polvani 2013; Burrows and Chen 2017). Additionally, Woollings et al. (2018) showed that a weaker jet is also related to higher positional variability. The mechanisms described in these papers are rooted in barotropic Rossby wave dynamics. Rossby waves are tightly coupled to the jet stream’s variability: Rossby wave breaking affects both jet position and speed through their eddy momentum transport (e.g., Thompson 1980; Robinson 2006). When a jet is farther poleward, wave breaking on the poleward flank is suppressed because of Earth’s sphericity, minimizing the deposition of momentum and thereby decreasing jet positional variability (e.g., Barnes et al. 2010). When a jet strengthens, Rossby waves can become trapped near the jet core, also decreasing Rossby wave breaking and associated jet variability (Hoskins and Ambrizzi 1993; Woollings et al. 2018). Given the simulated response of the eddy-driven jet to Arctic amplification and sea ice loss, we may expect the resulting jet to be closer to the equator and weaker, and thus have greater positional variability according to these mechanisms.
In this work, we first highlight results from a fully coupled general circulation model (GCM), namely, how both the mean state and, more importantly, the variability of the eddy-driven jet responds to sea ice loss. From there, we work down the model hierarchy to a barotropic model, which we use to examine one possible barotropic mechanism at play in the jet stream response to Arctic amplification and sea ice loss. Previous studies have shown that the atmospheric circulation can be recreated surprisingly well using only barotropic theory, and barotropic models have been used extensively in studies of the jet and its response to external forcing (e.g., Vallis et al. 2004; Kidston and Vallis 2010; Barnes et al. 2010; Kidston and Vallis 2012). Our results indicate that even when there is an apparent equatorward shift and weakening of the jet in response to sea ice loss and Arctic amplification, jet positional variability decreases, rather than increases, as one might expect from previous studies. We explain this decrease in jet positional variability via changes in Rossby wave propagation. We place this work in the context of past studies relating the response of the midlatitude circulation to sea ice loss and Arctic amplification to the annular modes. It is important to note that our chosen metric does not quantify the meandering of the jet stream over space, that is, the waviness of the flow, but rather, quantifies the zonal-mean jet position over time. Further, our idealized experiments contain no topography and therefore neglect stationary wave mechanisms, previously discussed in the literature as critical for the atmospheric response to sea ice loss (e.g., Petoukhov and Semenov 2010; Sun et al. 2015; Wu and Smith 2016). This highlights that the mechanism that we are proposing, which relies solely on the horizontal propagation of synoptic-scale waves, is one of many.
To assess how sea ice loss may impact eddy-driven jet variability, we first analyze experiments run with a fully coupled GCM. Monthly results from a set of sea ice loss experiments run by Deser et al. (2015, hereinafter D15) using the Community Climate System Model, version 4 (CCSM4), were made available. CCSM4 is a fully coupled GCM with a horizontal resolution of 0.90° latitude and 1.25° longitude, 26 vertical levels, and a full oceanic component. The specifics of the experiments can be found in D15, but we include relevant details here for reference. The seasonal cycle of Arctic sea ice is artificially controlled in order to match an ensemble mean of six CCSM4 historical runs over the period 1980–99 for the control simulation (CONTROL), and six CCSM4 representative concentration pathway 8.5 (RCP8.5) simulations for the period 2080–99 for the experiment simulation (LOWICE). The radiative forcing conditions for both simulations are constant, with values taken from the year 2000. What differentiates CONTROL and LOWICE, however, is that an additional longwave radiative flux is prescribed only to the ice model component in the LOWICE simulation, with values chosen so that the resulting sea ice loss is similar to that seen in the 2080–99 CCSM4 RCP8.5 ensemble mean. This flux is spatially invariant with a seasonal dependence (see appendix of D15 for more details). Both simulations are then run for 360 years, with the first 100 years removed for spinup of the Atlantic meridional overturning circulation. The data are saved at a monthly time resolution, giving us 260 years of monthly zonal wind data from each experiment.
b. Dry dynamical core model
Next, we step down the model hierarchy to a much simpler model, namely, a dry dynamical core with no topography. Here, we analyze the response of jet stream variability to an imposed polar thermal forcing, which mimics the Arctic amplification signal. We use the Geophysical Fluid Dynamics Laboratory (GFDL) spectral dry dynamical core model, which is run with the Held and Suarez (1994) physics, using spectral T63 resolution, 40 vertical levels, 900-s time steps, and no topography (Hassanzadeh and Kuang 2016). This basic-state setup comprises the control simulation (CTRL) and is run for 15 000 days under perpetual equinox conditions. The data are saved in zonal averages, and the first 500 days are discarded for spinup, giving us 14 500 days of 6-hourly measurements of zonal-mean wind fields for our analysis. To simulate the low-level polar warming associated with sea ice loss and Arctic amplification, a zonally symmetric Gaussian thermal forcing is applied at the 1000-hPa pressure level (standard deviation of 250 hPa) at both 90°N and 90°S (standard deviation of 16° latitude). The amplitude of the heating is equal to 1.0 K day−1. This forcing is identical to the one used in the POLAR experiment in McGraw and Barnes (2016), with the exception that the polar heating is applied here to both hemispheres. The Arctic amplification simulation (AAMP) branches off of the CTRL and is run for another 15 000 days, and again, the first 500 days are discarded. We calculate the daily mean values for the 14 500 days from both simulations, and consider the hemispheres to be independent, allowing for doubling of the data. This gives us 29 000 daily mean, zonal-mean, zonal wind values for each experiment.
c. Barotropic model
The barotropic model is one of the simplest in the atmospheric model hierarchy (Shaw et al. 2016), giving us an ideal framework in which to analyze Rossby wave dynamics and the eddy-driven jet. We use an initial model setup identical to that of Vallis et al. (2004), where the nondivergent vorticity equation is integrated on the sphere:
The LHS of Eq. (1) represents the Lagrangian change in absolute vorticity, defined as relative vorticity ζ plus the planetary vorticity f. It is balanced by a parameterized representation of the baroclinic eddies that stir the barotropic flow S plus a damping term rζ, with damping parameter r, and diffusion κ∇4ζ. Values for S, r, and κ are identical to those used in Barnes et al. (2010). Additionally, following Vallis et al. (2004), we impose a Gaussian spatial mask, that is, the global stirring field is multiplied by a Gaussian curve that damps the stirring away from a chosen central latitude with a specified standard deviation σs. For all simulations the value of σs remains unchanged at 12°. All other parameters of the model follow Vallis et al. (2004), with a resolution of spectral T42 and a time step of 3600 s. Each simulation is spun up for 100 days and runs an additional 32 000 days for analysis.
Previous studies, as well as our own analysis of the CCSM4 and dry dynamical core models discussed above, have shown that the most consistent response of the mean jet to sea ice loss and Arctic amplification is anomalous easterlies on the poleward flank of the jet, suggesting an easterly forcing. To approximate the results from this forcing in a barotropic model, we run a variety of simulations with an additional angular momentum forcing term applied on the poleward flank of the stirred jet, similar to that used by Ring and Plumb (2007), and later by Barnes and Thompson (2014). This angular momentum forcing acts as an easterly torque on the flow, approximating the influence of the change in temperature gradient by sea ice loss and Arctic amplification. The easterly torque is Gaussian in latitude, centered at latitude with a standard deviation of σf = 8°. By setting the amplitude of the forcing to be negative it acts as an easterly torque. We set to be poleward of , thus giving us a representation of the easterly forcing from both sea ice loss and Arctic amplification, as seen in the CCSM4 and the dry dynamical core results, respectively.
The first set of experiments consists of a control simulation (NoTRQ) with the forcing turned off and the stirring latitude placed at = 35°N. The experimental simulation, TRQ10, has stirring placed at the same latitude, and an easterly torque located at = 55°N, with an amplitude of −1.0 m s−1 day−1. The distance of 20° between and is motivated by the climatological jet profiles from the CCSM4 and the dry dynamical core, where it represents the distance from jet core to where the zonal wind goes to zero on the poleward flank. The changes in jet variability from this set of barotropic model experiments is used to compare directly to the results from the CCSM4 and the dry dynamical core. In addition, we also run another control simulation, NoTRQ33, with no easterly torque and the stirring placed at = 33°N. This is done to simulate a very small equatorward shift, found when comparing TRQ10 with NoTRQ, in order to isolate the impact of changing the latitude of wave generation.
The next two sets of barotropic model experiments are composed of a suite of simulations, one with varying torque amplitudes, with and held constant, and the other with varying stirring latitude , while the easterly torque remains constant and fixed in latitude.
VaryAmp: This set of simulations is run with varying torque amplitudes, with an easterly torque from −0.2 to −2.0 m s−1 day−1 and a westerly torque from 0.2 to 2.0 m s−1 day−1. Both the stirring and torque latitudes remain fixed, with = 35°N and = 55°N.
VaryStir: In this set of simulations, the torque latitude and amplitude are set at the same conditions as TRQ10, with = 55°N and a torque amplitude of −1.0 m s−1 day−1. However, the stirring latitude is increased by 5°N from the equator to 50°N. Thus, for each individual simulation, there is a new control run with the same and no forcing.
a. Defining the jet
The primary focus of this work is on the impacts of sea ice loss on eddy-driven jet variability. CCSM4 includes full topography; therefore the storm tracks occur primarily over the ocean basins, where the eddy-driven jets are strongest and have the greatest flow variability (e.g., Blackmon 1976; Hoskins and Valdes 1990; Woollings et al. 2010). Motivated by previous studies examining the response of the North Atlantic jet stream, we restrict our analysis to the North Atlantic basin (0°–70°W), whose leading mode of variability has been referred to as a “wobble” in meridional position (e.g., Wittman et al. 2005). Using the 850-hPa zonal winds as representative of the eddy-driven jet (Woollings et al. 2018), and looking only at boreal winter [January–March (JFM)], we take both a zonal and seasonal mean across the basin. The seasonal mean provides additional smoothing of the data, and results in 260 seasonal-mean jet profiles. Results and conclusions resulting from analysis of three definitions of the winter season (December–March, December–February, and January–March) were very similar; therefore we chose JFM so as to utilize all 260 years of data. The latitude and magnitude of the seasonal-mean maximum zonal-mean zonal winds, that is, jet position and speed, are identified for each year (Woollings et al. 2010; McGraw and Barnes 2016), with a northerly limit of 75°N. The climatological jet profiles from both simulations are plotted in Fig. 1.
In the dry dynamical core experiment, topography was not included in order to examine the zonally symmetric response to polar thermal forcing. Here, the 775-hPa zonal winds are considered to be representative of the eddy-driven jet (McGraw and Barnes 2016). Again, the zonal mean of the zonal winds is calculated, and the 29 000 daily mean jet positions and speeds are identified for CTRL and AAMP. (The climatological jet profiles for both simulations are shown in Fig. 4.)
Finally, in the barotropic model there is no topography and no vertical levels. Taking the zonal mean of the zonal winds, we again identify the 32 000 daily maximum wind latitudes and magnitudes for NoTRQ, TRQ10, and all of the simulations within the VaryAmp and VaryStir experiments. (The climatological jet profiles of NoTRQ and TRQ10 are plotted in Fig. 7.)
b. Quantifying jet variability
Our focus here is on quantifying changes in jet variability in response to sea ice loss and Arctic amplification. To do this, we plot the distributions of the jet speeds and positions identified in each of the following model experiments: CCSM4 CONTROL versus LOWICE (Fig. 2), dry dynamical core CTRL versus AAMP (see Fig. 5), and the barotropic model NoTRQ versus TRQ10 (see Fig. 8). We assess changes in variability by comparing the standard deviations of each simulation’s distribution to their respective control simulations. The distributions are smoothed for plotting using a Gaussian kernel function, where the bandwidth was chosen to be as small as possible in order to remove the noise while still retaining the important features of the distributions. The CCSM4 bandwidth is 0.4 for both jet speeds and positions, while the dry dynamical core and the barotropic models use 0.2 for the position distributions and 0.1 for the speed. The standard deviation of each distribution is included in the legends of each figure, and the value is boldfaced if it is significantly different from the control at a confidence level greater than 95% (one sided variance F test).
c. Refractive index
Interactions between the mean flow and synoptic-scale eddies greatly impact jet stream variability. This interaction is essentially rooted in Rossby wave propagation and the associated momentum fluxes, particularly with regards to the convergence of westerly momentum in the jet core via Rossby wave breaking on its flanks. We map out the wave breaking associated with a certain climatological jet profile using the refractive index K* [see Eq. (2) below; Hoskins and Karoly 1981]:
where k and l are the zonal and meridional wavenumbers, respectively; is the meridional gradient of absolute vorticity; is the zonal-mean zonal wind; and c is the phase speed (Hoskins and Karoly 1981; Barnes et al. 2010). The additional factor of cos() accounts for the fact that the specific wavelength associated with a zonal wavenumber k decreases with latitude (Barnes and Hartmann 2012). As long as the zonal wavenumber, k, is smaller than K* the waves may propagate freely. Once k = K* (i.e., l = 0; Hoskins and Karoly 1981), the waves are reflected, or if K* gets very large the waves break (Barnes et al. 2010; Barnes and Hartmann 2012). The refractive index in Eq. (2) can then be used to calculate the reflective and critical latitudes, which are the two distinct limits mentioned above (Lorenz 2014a,b, 2015). Rossby waves created within the jet core propagate away from their source region until they meet one of these two latitudes (e.g., Hoskins and Karoly 1981; Hartmann 2007; Barnes et al. 2010). When k = K*, the waves turn without breaking (reflective latitude). When K* instead goes to infinity, the waves break (critical latitude) and deposit easterly momentum. In the linear limit, both refractive latitudes (critical and reflective) depend upon the upper-level zonal winds and wave phase speeds; however, the reflective latitude has an additional dependence on wavelength and the vorticity gradient, as given by for midlatitude, tropospheric Rossby waves in Eq. (2) (e.g., Hoskins and Karoly 1981).
Both the reflective and the critical latitudes contribute to variability in jet position and speed through their impact on wave propagation (e.g., Benedict et al. 2004; Woollings et al. 2008; Lorenz 2014a; Woollings et al. 2018). These refractive latitudes depend on the zonal wind profile [see Eq. (2); Barnes et al. 2010], and therefore will be affected by changes in the zonal-mean zonal wind in response to an external forcing, such as sea ice loss and Arctic amplification. Changes in the refractive latitude profiles, in turn, impact jet variability by adjusting the local Rossby wave propagation (e.g., Kidston and Gerber 2010; Barnes et al. 2010).
It is important to note that K* is based on linear assumptions and does not distinguish between irreversible wave breaking and other processes (such as wave absorption and reversible wave breaking). However, it was demonstrated by Barnes and Hartmann (2012, see their Fig. 4) to be an approximate measurement of where waves preferentially break, as well as providing appropriate wave-breaking limits away from the jet core.
For the purposes of this work we analyze changes in both the critical and reflective latitudes in each model experiment. Tropospheric Rossby wave breaking occurs predominantly at upper levels, with the momentum transfer also impacting the lower-level eddy-driven jet (Robinson 2006; Hartmann 2007). Therefore, in order to calculate the two refractive latitude profiles derived from K*, we use the 300-hPa-level zonal-mean zonal winds for both the CCSM4 and dry dynamical core model, while for the barotropic model we continue to use the zonal-mean zonal wind field. For the reflective level, we look at a range of zonal wavenumbers within the Rossby wave spectrum, that is, synoptic wavenumbers (generally defined as k ≥ 4; Hoskins and Karoly 1981). To easily compare the simulations from each experiment we define a simple metric, the wave propagation width, which is the distance between the critical latitudes on either side of the jet core, that is, the maximum distance a wave may travel out of the jet core, both poleward and equatorward, before breaking. If one flank of the jet has a reflective latitude placed closer to the jet, then the waves are turned back and we calculate the wave propagation width as twice the distance to the critical latitude on the other flank. If, on both flanks, waves of a certain phase speed only encounter reflective latitudes then we define wave propagation width as being zero.
While the key insights of this study revolve around the barotropic model experiments, we initially motivate these results and model setup by analyzing changes in jet variability in CCSM4 and the dry dynamical core model.
Focusing on the boreal winter (JFM), we examine the impact of sea ice loss on the North Atlantic eddy-driven jet in the CCSM4, a fully coupled GCM. We start by looking at changes in the climatological zonal-mean zonal wind profile over the North Atlantic basin (Fig. 1). Figure 1a shows both the CONTROL (blue) and LOWICE (red) wind profiles, while Fig. 1b shows the anomalies, defined as LOWICE − CONTROL. While we do see the expected changes (a small decrease in wind speeds within the jet core and a very slight equatorward shift), the clearest response is in the anomalous easterlies on the poleward flank of the jet and little to no change on the equatorward flank, causing a narrowing of the jet profile and an enhancement of the preexisting easterlies.
The distributions of seasonal-mean jet position and speed give us an objective way to evaluate any changes in variability, as demonstrated in Fig. 2. The distributions have been centered around their respective means so as to make visual comparison easier between CONTROL (blue) and LOWICE (red) in Fig. 2. When sea ice declines, the jet position distributions narrows, with the biggest fractional changes occurring in the tails (Fig. 2a): in LOWICE, the seasonal-mean jet position remains relatively close to its climatological position, corresponding to lower jet positional variability. This decrease in variability is corroborated by the significant decrease in standard deviations of jet position in both basins (noted in the legends) at a confidence level of 95%. There is essentially no change in the distribution of jet speeds (Fig. 2b).
To summarize, in the fully coupled GCM the main change in the North Atlantic mean state is an asymmetrical narrowing of the jet caused by anomalous easterlies on the poleward flank and decreasing jet variability, as quantified by the jet position variance. These two results may both be explained by Rossby wave breaking (Lorenz 2015; Woollings et al. 2018). As stated previously in section 3, from linear theory, the determining factor for wave breaking is the latitude where the phase speed c is equal to the upper-level zonal wind , that is, the critical latitude [see Eq. (2)]. Therefore, if the mean zonal wind profile changes throughout the column, so too will the latitude of Rossby wave breaking. Additionally, if there are any changes in absolute vorticity, either through wind shear changes (relative vorticity) or changes in mean jet position (planetary vorticity) this can also lead to changes in K* and therefore changes in the reflective latitude, where k = K*.
In Fig. 3, we examine the zonal profiles of both critical and reflective latitudes for the upper-level jet for wavenumber k = 4 waves (in the range of synoptic wavenumbers; Hoskins and Karoly 1981) and measure the change in wave propagation width between LOWICE (red) and CONTROL (blue). This wavenumber was chosen as representative of the results for analyses conducted on a large range of k = 2–20. This range was based, in part, on Fig. 3 of Randel and Held (1991), which showed the power of the Northern Hemisphere December–March transient eddies as a function of both phase speed and wavenumber. They showed that hemisphere-wide power is concentrated in phase speed range c = 0–18 m s−1 and wavenumbers k = 3–9. The thin, vertical, black line included in our Fig. 3 is a visual representation of the wave propagation width for waves of k = 4 and c = 15 m s−1 for the CONTROL run. If the wave propagation width decreases in the LOWICE simulation, then the ability for waves to travel out of the jet core and influence the jet position via the depositing of easterly momentum on the flanks will be limited. That is, a narrowing of the jet can decrease the distance Rossby waves may propagate before breaking or reflecting. Similar to previous arguments of how Rossby wave propagation impacts jet speed and position (e.g., Barnes et al. 2010; Barnes and Hartmann 2011, 2012), the limitation on wave propagation distance means a decrease of eddy momentum flux convergence on the flanks of the jet, outside of the jet core. This would imply greater persistence of the jet at its current latitude, restricting its ability to shift, thus ultimately leading to a decreased latitude range of jet position. Upon examination of Fig. 3 we see a narrowing of the wave propagation width in response to sea ice loss.
The difference in wave propagation width from CONTROL to LOWICE was also measured for phase speeds c = 5–30 m s−1 at wavenumbers k = 2–20 (not shown). While there are a few wavenumber–phase speed combinations where the wave propagation width increases because of a switch from reflective to critical latitudes being felt, the general conclusion of decreased wave propagation width in the LOWICE simulation is consistent across most wavenumbers.
Based on previous studies linking changes in both the mean state and the variability of the eddy-driven jet with the barotropic mode of Rossby wave breaking (e.g., Barnes et al. 2010; Barnes and Hartmann 2011, 2012; Woollings et al. 2018), we propose a barotropic mechanism linking our two main results: the decreased wave propagation width and the decreased jet positional variability. This mechanism, which will be further explored and tested in subsequent sections, can be summarized by the following for the CCSM4 experiment results:
Anomalous easterlies on the poleward flank of the jet lead to a narrowing of the jet profile.
This narrowing results in a decrease in wave propagation width across most Rossby wavenumbers and phase speeds.
The decreased wave propagation width limits the jet’s positional variability, as Rossby waves break closer to the jet core, leading to the significantly decreased standard deviations seen in the jet position distributions.
This barotropic mechanism implies that the response will be felt by jet position variability rather than jet speed variability. It has been previously stated that jet speed variability is dependent on the mean jet speed itself (e.g., Klink 1999; May and Bourassa 2011), making it possible that any changes we see in jet speed variability may be entirely due to the change in mean jet speed. To that end, we will primarily focus on the jet positional variance for the rest of this article. However, we will continue to show the jet speed distributions for completeness as they result directly from our jet position calculations.
b. Dry dynamical core model
Our findings from the fully coupled GCM suggest a possible barotropic mechanism for decreased jet positional variability through changes in Rossby wave propagation. We next use the results from the GFDL dry dynamical core Arctic amplification experiment to further explore our hypothesis. We compare the 29 000 daily zonal-mean zonal wind data from the AAMP to that of CTRL.
Beginning once more with the climatological profiles (Fig. 4), we immediately see similarities to the CCSM4 North Atlantic jet results, with the biggest response being the anomalous easterlies on the poleward flank. This results in a narrowing of the jet profile and, therefore, our mechanism would suggest a decrease in jet position variability. In addition to the narrowing, however, the difference in the temporal-mean zonal-mean zonal wind profiles between AAMP (Fig. 4, red) and CTRL (Fig. 4, blue) also shows a clear equatorward shift and slowing down of the jet. An equatorward shift of the jet profile could be linked with increased jet position variability (Barnes et al. 2010; Barnes and Hartmann 2011), as could the decreased jet speed (Woollings et al. 2018). While this would indicate competing dynamical effects, it is important to note that the results from Barnes and Hartmann (2011) do not extend farther south than 35°N, and Woollings et al. (2018) are looking at internal variability, not changes in internal variability in response to an external forcing. Thus, the results from these two studies may not truly represent a dynamical competition to our proposed mechanism.
To quantify the change in jet variability, we again look at the change in standard deviation of the distributions of daily mean jet positions and speeds from CTRL to AAMP. Both jet speed and position distributions narrow and show significantly decreased variability, this time at over 99% confidence (Fig. 5). The decrease in jet position variance is consistent with the response seen in the CCSM4 results and suggests that the narrowing of the jet profile is of greater significance than the small equatorward shift. The significant decrease in jet speed variability could suggest that it is not only the jet position but also the jet speed that is impacted by a narrowing of the jet, or it could be as simple as weaker winds have less variance.
Since we see decreased jet positional variability between AAMP and CTRL, we next analyze the refractive latitudes from each simulation in order to determine if there is a decrease in the wave propagation width. Figure 6 shows the changes in the critical and reflective latitudes, where we plot results for wavenumbers k = 4 (Fig. 6a) and 8 (Fig. 6b) in order to demonstrate the robustness of our conclusions with the zonal wavenumber range of interest, k = 4–10. This specific range was found to have the most power in the barotropic model results, and was also chosen for the dry dynamical core, since neither contains topography and thus have little to no power at wavenumbers k < 4. Figure 6 also includes thin, vertical, black lines representing the wave propagation width of a wave of k = 4 and c = 12 m s−1 (Fig. 6a) and k = 8 and c = 15 m s−1 (Fig. 6b).
For wavenumber k = 4, we find decreased wave propagation width for all phase speeds, including those below 10 m s−1, which encounter a reflective latitude on the poleward flank. This is also true for wavenumber k = 8, except for phase speeds of less than about 8 m s−1 for AAMP or 10 m s−1 for CTRL. For slower-moving waves at synoptic scales it appears the waves cannot exit the jet core, essentially remaining trapped with a wave propagation width of zero.
The results from the dry dynamical core further support the hypothesis that an impact of sea ice loss and Arctic amplification on the eddy-driven jet may cause decreased variability as a result of a narrowing of the jet and restricted Rossby wave propagation.
c. Barotropic model
Using results from CCSM4 and the dry dynamical core model, we now explore and test this hypothesis in a barotropic model.
Based on the consistent anomalous easterly response on the poleward flank of the jet to sea ice loss (CCSM4) and polar heating (dry dynamical core), we represent the direct effect of sea ice loss and Arctic amplification as an easterly torque poleward of the jet core in the barotropic model. The set of experiments we show in Figs. 7, 8, and 9 use stirring placed at 35°N, and easterly torque placed at 55°N with an amplitude of −1.0 m s−1 day−1. A range of torque amplitudes will be explored further on.
The zonal-mean zonal wind response seen in Fig. 7 consists mainly of a narrowing of the jet resulting from the imposed easterly torque. This narrowing causes the position of maximum winds to shift slightly equatorward. However, there is no true displacement of the entire jet profile, since the shift of the maximum westerlies is caused by asymmetrical narrowing on the poleward flank. There is also a decrease in maximum wind speed, similar to the results seen in both the CCSM4 North Atlantic basin and the dry core experiment.
To quantify the change in jet variability we compare distributions of the 32 000 daily jet positions and speeds for TRQ10 (red) and NoTRQ (blue) in Fig. 8. These distributions show a similar story as the dry core, with significant decreases in the standard deviation of both jet speed and position at more than 99% confidence. The narrowing of the distributions is most evident at the tails. Therefore, we have very similar results to those seen in both the dry dynamical core model and CCSM4, with an asymmetrical narrowing of the jet on the poleward flank, very little change on the equatorward flank, and significantly decreased jet position variability in response to an easterly torque.
The transient eddy momentum flux has little power at planetary wave scales within the barotropic model; therefore, the range chosen for this portion of the analysis is k = 4–10, the same as in the dry dynamical-core model. For the barotropic model we chose wavenumbers k = 6 and k = 10 as our representative examples. Again, the conclusions are consistent across a range of wavenumbers (k = 4–10) and phase speeds (c = 0–10 m s−1). The critical (solid) and reflective (dashed) latitude profiles for waves of wavenumbers k = 6 and k = 10 are shown in Figs. 9a and 9b, respectively, for both NoTRQ (blue) and TRQ10 (red). The thin, vertical, black lines both represent the wave propagation width for the NoTRQ run for waves of phase speed c = 4 m s−1.
Figure 9a shows that for waves on the bigger end of the synoptic scale and stirring at 35°N, the reflective latitude is not seen by waves with a positive phase speed, and so the wave propagation width is dictated by the critical latitude alone. This is also true for most phase speeds in Fig. 9b, with a zonal wavenumber of k = 10. Recall that the critical latitude is defined as when the phase speed is equal to the zonal wind speed; thus, as the jet narrows, the wave propagation width decreases. Again, this is consistent with our proposed theory: the jet narrows because of anomalous easterlies on the poleward flank, which in turn decreases the wave propagation width, decreasing the jet’s ability to vary its position as effectively as it had previously.
When looking at the climatological jet profiles in Fig. 7, we do see a small equatorward shift of the jet. To determine whether this small shift alone may cause changes in jet positional variability, we include an additional control run, NoTRQ33, with stirring at 33°N and no easterly torque. This additional run allows us to analyze the change in jet position and speed distributions resulting from a pure shift of the zonal wind profile alone, that is, changing the latitude of wave generation, as compared to the changes resulting from the asymmetrical narrowing and subsequent modification of the wave-breaking dynamics. The jet positional and speed variability are shown as black dashed lines in Fig. 8. The mean jet position of NoTRQ is approximately 37.9°N, while both TRQ10 and NoTRQ33 are at about 35.5°N, giving us a comparison between simple changes in latitude of wave generation (NoTRQ33) versus the additional narrowing by the easterly torque (TRQ10). The variance in jet position for NoTRQ33 decreases slightly compared to NoTRQ; however, we note that the jet positional variability decreases even more in TRQ10.
To explain this small decrease in jet positional variability when the jet is shifted equatorward, we refer to results from Kidston and Vallis (2010), where it was found that as the stirring in the barotropic model is moved equatorward, the jet profile narrows. This would indicate a decreasing wave propagation width and is thus consistent with our proposed mechanism. We calculated the wave propagation widths for wavenumber k = 6 and phase speed c = 4 m s−1 for all three simulations and included them in Fig. 8: NoTRQ in blue (20.76°), TRQ10 in red (17.55°), and NoTRQ33 in black (20.45°). The wave propagation width in NoTRQ33 is slightly less than in NoTRQ, consistent with a narrower jet as described in Kidston and Vallis (2010). However, the values for both wave propagation width and standard deviation of jet position for the TRQ10 simulation are significantly smaller than in either NoTRQ or NoTRQ33. This indicates that the significant narrowing on the poleward flank of the jet resulting from the easterly torque appears to contribute to a larger decrease in jet positional variability than can be accounted for by a mere jet shift.
An advantage of studying a barotropic model is the ease at which a large variety of experiments can be run. We examine the impact of increasing the easterly torque amplitude from −0.2 to −2.0 m s−1 day−1 in a suite of simulations (VaryAmp), analyzing the changes in jet speed, position, positional standard deviation, and wave propagation width between VaryAmp and NoTRQ as a function of the easterly torque amplitude (Fig. 10). The wave propagation width is calculated for wavenumber k = 6 for two phase speeds, c = 0 and 4 m s−1, and is shown in Fig. 10b.
Figure 10a demonstrates that the mean jet speed (orange) is a weak function of torque amplitude, decreasing slightly with increasing easterly torque. Mean jet position (green) also decreases more as the torque amplitude increases; however, this does not represent a displacement of the entire jet profile (as previously discussed). The main impact of the easterly torque is felt on the poleward flanks, with very little to no change on the equatorward flank, meaning that the equatorward movement of the jet’s position is merely an artifact of the asymmetrical narrowing of the jet. This is demonstrated by the decreasing wave propagation widths seen in Fig. 10b, which are a strong function of torque amplitude. Consistent with our previous results, the standard deviation of the jet position (purple; Fig. 10a) also continues to decrease with increasing easterly torque.
Now we take this a step further: if the narrowing of the jet caused by the easterly torque decreases the wave propagation width, which then decreases jet position variability, does a widening of the jet caused by a westerly torque do the opposite? We run the same set of experiments as in VaryAmp but for a westerly torque on the poleward flank, with amplitudes 0.2 to 2.0 m s−1 day−1. The results are shown in Fig. 11, along with those for easterly torques, where we plot changes in jet position standard deviation and changes in wave propagation width for wavenumber k = 6 and phase speed c = 4 m s−1. The negative amplitudes (blue shades) represent the easterly torque simulations already discussed, and positive amplitudes (red shades) represent the westerly torque experiments. Figure 11 demonstrates that as a westerly torque is applied and the amplitude is increased, both the wave propagation width and the standard deviation of the jet position increase, opposite to what happened with the easterly torque. The relation between changes in wave propagation width and jet position standard deviation is relatively linear for torques of 2.0 m s−1 day−1 down to approximately −1.0 m s−1 day−1. From there, the increasing easterly torque amplitude results in a very large section of easterlies on the poleward flank of the jet. The wave propagation width continues to decrease, though not as strongly, as the easterlies become larger, and the jet positional variability also continues to decrease. Despite this limit on the wave propagation width decrease, the relationship between jet positional variance and wave propagation width appears consistent for both easterly and westerly torques, further strengthening the relationship between wave propagation width and jet variability.
Fully coupled models have a well-known bias with regards to the mean jet position, placing it farther equatorward than observations (e.g., Kidston and Gerber 2010; Barnes and Polvani 2013; Simpson and Polvani 2016). It has been argued that the response of the atmospheric circulation to various external forcings, including sea ice loss and Arctic amplification, could differ because of these biases (Barnes and Simpson 2017). To test the role of model bias, we run a set of experiments in the barotropic model with the easterly torque latitude and amplitude held fixed at 55°N and −1.0 m s−1 day−1, respectively, while the stirring latitude is moved north from the equator to simulate model biases in the position of the climatological jet. For each new stirring latitude there is a control run (NoTRQ) and an experimental run (TRQ10), and the differences between the two (TRQ10 − NoTRQ) are calculated. The resulting changes in mean jet position (green), speed (orange), positional standard deviation (purple), and wave propagation width (black solid and dashed) in response to the easterly torque are shown in Fig. 12. The location of the torque plus and minus one standard deviation is shown in gray shading. Note that all variables are plotted as a function of stirring latitude, and that the control jet position is generally consistently 2°–3° latitude north of the stirring for stirring south of 40°N. This was also noted in Barnes et al. (2010).
The mean jet position, represented in Fig. 12a by the green line, moves farther equatorward as the stirring moves north toward the torque and the asymmetrical narrowing becomes more pronounced. The response of the mean jet speed (Fig. 12a, orange) is initially an increase for stirring from 10° to 35°N, with seemingly no dependence on the stirring latitude within that range (i.e., the increase from control is generally by the same amount, even as the control itself is changing as it moves north), then plummets as the stirring gets closer to the torque. Figure 12a also shows the jet position standard deviation (purple) decreasing fairly steadily for all stirring north of the equator, with a dependence on the stirring latitude. The decrease of jet position variability becomes smaller at stirring at 40°N, showing a possible upward trend in the decrease of variability, though it still represents a decrease. We posit that this could be due to the jet being almost on top of the torque, at which point the likelihood of bimodality of the jet position increases, making our chosen metric for variability (standard deviation) no longer optimal (not shown). From Fig. 12b we see that the wave propagation width decreases very slightly for stirring at 10°N, then steadily decreases further as the stirring moves north (again, only shown for k = 6 and c = 0 and 4 m s−1). This decrease correlates highly with the apparent equatorward shift resulting from asymmetrical narrowing and the decrease in standard deviation, even for stirring as far south as 10°N.
These results demonstrate how differently the mean jet responds to the torque on the poleward flank due only to changes in the jet’s initial position, even in a simple barotropic model. While many of the responses are the same sign no matter the distance of the jet from the external forcing, their magnitudes are strongly dependent on jet proximity to the easterly torque. Interestingly, there is a range of latitudes across which jet speed increases, something which has previously been noted in the CMIP5 models by Barnes and Simpson (2017). In analyzing the seasonality of the jet response to Arctic amplification, Barnes and Simpson (2017) found that the wind anomalies forced by the changing Arctic temperatures remained fairly stationary annually, with the jet moving in and out of the region of anomalous easterlies throughout the seasonal cycle, especially in the North Pacific. This suggests that our approach of keeping the torque fixed and varying the stirring is not only realistic, but also potentially important for understanding the effect of the climatological jet position on the jet’s response to polar forcing.
5. Discussion and conclusions
Here, we explore a possible mechanism for why jet positional variability, defined as the variance in location of the maximum zonal-mean zonal winds, decreases with sea ice loss and Arctic amplification. The key insights from this work can be summarized as follows:
The response of the mean eddy-driven jet to sea ice loss and polar warming in both a fully coupled GCM and a dry dynamical core is an asymmetrical narrowing on the poleward flank of the zonal-mean eddy-driven jet (zonal mean taken over the North Atlantic in the GCM and hemisphere wide in the dry dynamical core). In both the CCSM4 and dry dynamical core experiments, the jet also exhibits decreased positional variability.
Using a barotropic model, we find very similar responses in both the mean jet and the jet variability when an easterly torque is placed on the poleward flank of the jet.
We propose and test a mechanism whereby the asymmetrical narrowing of the jet limits Rossby wave propagation out of the jet core, which in turn may be responsible for the decreased jet position variability.
We find decreased jet positional variability in all three models in response to polar forcing. Using a barotropic model we posit that decreased wave propagation width is a possible barotropic mechanism for this decreased variability, by acting to meridionally constrain the Rossby wave breaking and therefore the variability in zonal jet position. If the jet narrows in response to anomalous easterlies on the poleward flank, either because of sea ice loss, polar heating, or an easterly torque, Rossby waves will encounter a critical latitude closer to the jet core, which implies the deposition of easterly momentum is closer to the jet core and therefore the jet is less likely to shift. This, in turn, decreases the variability in the jet position. Our results suggest that this change in Rossby wave breaking may be present across a model hierarchy, including a fully coupled GCM. While we believe this mechanism to be present in the real atmosphere, it is likely one of many dynamical mechanisms at play. For example, our idealized experiments do not take into account the role of stationary waves, which have been identified as important players in determining the atmospheric response to Arctic amplification and sea ice loss.
Both the dry dynamical core and the barotropic models show a clear decrease in wind speeds within the climatological jet core (Figs. 4 and 7, respectively). Results from Woollings et al. (2018) suggested a clear link between slower jets and increased jet positional variability. However, we again note that while their study focused on internal variability, we looked at changes in internal variability in response to an external forcing. The fact that we noted decreased jet positional variability suggests that the wave propagation response resulting from an external forcing and the subsequent narrowing seen in all three model setups has a greater influence on the jet variability response than the decrease in mean jet speed (which is also a result of the external forcing and associated feedbacks).
Upon examining Fig. 8a, specifically comparing the NoTRQ and NoTRQ33 experiments in the barotropic model (stirring at 35° and 33°N, respectively), we found that a jet shifted slightly equatorward, with no easterly torque, has decreased jet positional variability. This appears contrary to what was found by Barnes and Hartmann (2011), where jets equatorward of approximately 55°N were shown to have similar jet positional variability (their Fig. 8c). There are two reasons for this apparent discrepancy. First, Barnes and Hartmann (2011) did not show results for jets farther south than 35°N, and when we expand their previous methodology to stirring at these lower latitudes we find a similar decrease in jet “wobbling” as was found in our study. Second, Barnes and Hartmann (2011) used empirical orthogonal functions in order to separate the variability into orthogonal modes of variability, with the leading mode generally being referred to as a “shift” unless the jet is placed too close to the pole. As such, any shifting of the jet position based upon this leading mode of variability may not capture all of the jet’s meridional movement, whereas our metric is exactly that: the change in the mean jet position as the stirring latitude is changed.
We also note a decrease in both the climatological jet core speeds and the jet speed variability in both the dry dynamical core and the barotropic models. We posit that as the jet narrows, more waves break within the jet core itself, depositing easterly momentum there, which leads to the decrease in mean speed. As the zonal wind speed decreases, the variance in speed also goes down (Klink 1999; May and Bourassa 2011). Thus, the decrease in jet speed variability may have more to do with the mean speed decrease, rather than our barotropic wave-breaking argument, though this too warrants further study.
The results of this study imply that when considering the impact of sea ice loss and/or Arctic amplification on the jet stream, it is important to consider changes in the width of the jet stream and associated Rossby wave propagation, and not just the jet position or speed. An apparent shift of jet position could either be a displacement of the entire jet profile, impacting both flanks of the jet, or it could be due to an asymmetrical narrowing of the jet, as is the case here. The resulting changes in jet stream variability are sensitive to this distinction.
Further, the precise nature and amplitude of the response of the zonal wind to sea ice loss and Arctic amplification likely depends on the position of the climatological jet relative to where the forcing is located. Ring and Plumb (2007, 2008) found in an idealized dry dynamical core GCM that the exact nature of the atmospheric response to an imposed torque was dependent on the location of the torque, particularly in regards to how well the response projected onto the annular modes. Barnes and Thompson (2014) also imposed torques at varying latitudes in both an idealized GCM and a barotropic model, with similar findings. The idea that the structure of the atmospheric response, as well as the magnitude of the response, are dependent on the initial position of the jet with respect to the position of the external forcing is crucial when discussing the differences in the responses from different climate models, as many have the jet placed farther equatorward than observed (Kidston and Gerber 2010; Bracegirdle et al. 2013).
Many studies define jet positional variability as a measurement of jet amplitude, or “waviness,” over space, and have argued that this variability increases with sea ice loss and Arctic amplification (e.g., Francis and Vavrus 2012; Liu et al. 2012; Peings and Magnusdottir 2014; Francis and Vavrus 2015). Here, we define jet positional variability as changes in the location of the zonal-mean zonal wind maximum over time, and, when we do so, we find the opposite response: a decrease in jet positional variability. Though the decrease in positional variability is small, it is consistent across a model hierarchy, leading us to believe that this response is robust. This suggests that further work examining the difference between spatial and temporal jet variability in response to external forcing is important for broader understanding of the mechanisms at play.
The authors thank Lantao Sun for providing the CCSM4 data, Ding Ma for his insightful discussions, and three anonymous reviewers for their constructive evaluations. BR and EAB are supported by the Climate and Large-Scale Dynamics Program of the National Science Foundation under Grant AGS-1545675. PH is supported by NASA Grant 80NSSC17K0266.
Current affiliation: Colorado State University, Fort Collins, Colorado.
Current affiliation: Rice University, Houston, Texas.