1. Introduction
Extratropical cyclones are the dominant synoptic-scale features of the midlatitude atmosphere, and trends in their behavior are of societal, economic, and scientific significance. Here we focus on the North Atlantic cyclones that affect the eastern United States and western Europe. The future behavior of these cyclones depends on competing effects of global warming. In general, the meridional temperature gradient in the lower troposphere is expected to decrease owing to the polar amplification of greenhouse warming (Meehl et al. 2007), and this has been shown to weaken cyclone activity, or eddy kinetic energy (EKE) (Geng and Sugi 2003; O’Gorman and Schneider 2008). Upper-tropospheric warming in the tropics increases subtropical static stability and the upper-level meridional temperature gradient, which drives the upper-level baroclinic zone poleward (Yin 2005; Lu et al. 2007). Meanwhile, lower-tropospheric specific humidity is expected to increase under global warming (e.g., Allen and Ingram 2002; Held and Soden 2006; Pall et al. 2007). The intensification of cyclones is often amplified by latent heating (Davis and Emanuel 1991; Reed et al. 1992; Stoelinga 1996; Posselt and Martin 2004; Watterson 2006; Booth et al. 2013), and this diabatic amplification should be enhanced in a moister atmosphere.
We suggest that the modeled response of the North Atlantic storm track to these competing dynamic and thermodynamic effects is further complicated by a strong sensitivity to horizontal resolution. Several studies have shown that cyclone intensity increases with horizontal resolution (Chang and Fu 2003; Jung et al. 2006; Champion et al. 2011; Jung et al. 2012; Colle et al. 2013; Eichler et al. 2013). Willison et al. (2013) linked resolution sensitivity to a positive feedback with condensation that occurs in mesoscale cyclone structures, and they showed how systematic underrepresentation of condensational heating can affect the larger-scale climatological storm track and mean flow. On the other hand, Li et al. (2011) found little resolution sensitivity for zonally averaged mean or extreme precipitation in the midlatitudes when using an aquaplanet model with idealized sea surface temperature (SST) perturbations. Here we use a less-idealized model configuration and focus on regional sensitivity to resolution with warming.
Climate models are roughly calibrated to the current climate, but the GCMs used in phase 3 of the Coupled Model Intercomparison Project (CMIP3) have been shown to have biases in North Atlantic storm-track position and amplitude (Chang et al. 2013). Recent findings from models of phase 5 of CMIP (CMIP5) show that the same CMIP3 biases persist, with storm tracks that are generally weaker in the western Atlantic, displaced toward the equator, and more zonally oriented than observed storm tracks (Chang et al. 2012; Mizuta 2012; Chang et al. 2013; Eichler et al. 2013). In the northeastern Atlantic, however, the models have excessive eddy activity—a bias that again persists in the newer CMIP5 models (Zappa et al. 2013). Higher horizontal resolution models, though, are often better able to simulate cyclone intensity and track density in both CMIP3 and CMIP5 (Chang et al. 2013; Colle et al. 2013).
Projected changes in cyclone behavior under climate warming vary by season and region, with studies often finding an increase in wintertime northeastern Atlantic cyclone activity (Geng and Sugi 2003; Bengtsson et al. 2009; Harvey et al. 2012) where large biases exist in simulations of current climate. We hypothesize that this signal is driven by lower-tropospheric temperature changes and amplified by a resolution-sensitive diabatic feedback. This hypothesis is supported by studies that show eastern North Atlantic cyclones to be more sensitive to latent heat release than are western North Atlantic cyclones (Plant et al. 2003; Dacre and Gray 2009, 2013) and by the results of Willison et al. (2013), which showed that high-resolution models are necessary for representing moist cyclone processes.
In this study, we present findings that reveal how the diabatic feedback that leads to resolution sensitivity in the current climate (Willison et al. 2013) can affect projected storm-track changes in a warmer climate. The primary purpose of this paper is not to provide a more accurate projection of storm-track changes but to investigate the potential for and mechanism of increased resolution sensitivity in a warmed climate. To the extent that resolution sensitivity is associated with the diabatic amplification of cyclones, we anticipate that it will increase in a warmer and more moist atmosphere.
2. Model and methods
We use the Weather Research and Forecast (WRF) Model, version 3.4.1, as described by Skamarock et al. (2008) to simulate 10 January–March (JFM) winters (2002–11). Our model domain extends from 15° to 72°N and from 96°W to 46°E. The model initial and lateral boundary conditions are provided by 1° × 1° 6-hourly National Centers for Environmental Prediction (NCEP) final operational global analysis (FNL). Sea surface temperatures are provided by 0.5° × 0.5° weekly NCEP real time global (RTG) SST updates. We use two nominal grid spacings to test the sensitivity to horizontal resolution. The first (120 km) is consistent with the higher resolutions used in current GCMs while the second (20 km) is adequate for demonstrating the resolution sensitivity of cyclones and the midlatitude storm tracks (Jung et al. 2006; Willison et al. 2013). We initialize each JFM season in late December and run into early April to compensate for the loss of 2 weeks of output that results from the high-pass filtering that we use to isolate disturbances with synoptic time scales.
The physics used include Zhang–McFarlane (ZM) convection, WRF single-moment 6-class microphysics, Community Atmospheric Model radiation, Noah land surface, and Mellor–Yamada–Janjić planetary boundary layer schemes. The only changes in parameterizations between the 120- and 20-km configurations are made to the resolution of static gravity wave drag fields. We perform no other manual tuning of physics parameterizations between low and high resolution. Scale-aware convective parameterizations may be of interest for future study, but we note that both resolutions used here are safely inside the range of resolutions that require convective parameterization. Using a different convection and planetary boundary layer pairing, Kain–Fritsch (KF) and Yonsei University (YSU) schemes, respectively, we found reduced agreement with reanalysis but qualitatively similar results when fully reproducing the experiments described below (not shown). Various other physics options were tested for individual seasons, and our current configuration was found to be most consistent with reanalyses. Microphysics and other parameterization sensitivities were also tested for a cyclone case study by Willison et al. (2013), who found the sensitivity to resolution to be the dominant effect.
To test the fidelity of the WRF configurations we compare output with the NCEP Climate Forecast System Reanalysis (CFSR). We use CFSR model output at a horizontal grid spacing of 0.5° × 0.5° with 6-hourly frequency, which is available for the 2002–10 JFM seasons. We omit the 2011 season because of the lack of 2011 CFSR output. All atmospheric fields are interpolated to the 120-km grid prior to any analysis in order to separate the dynamical consequences of higher resolution from signals that result merely from better spatial sampling. While it is uncertain whether models that are more skillful in the current climate produce more accurate climate projections [compare Stainforth et al. (2007) with Matsueda and Palmer (2011)], the primary intent of this study is not to provide an accurate projection of storm-track behavior. Nevertheless, comparison to observations is necessary to identify potential model biases.
The two pseudo global warming runs use the same 2002–11 FNL and RTG boundary and initial conditions as the two current-day runs but are perturbed using temperature changes taken from the mean of five CMIP5 models (Table 1). The CMIP5 models are chosen from the “Best7” group described in Colle et al. (2013). The Best7 models were those found to be the best at reproducing cyclone track density and central pressure distributions over the U.S. East Coast and western and central Atlantic. The RCP8.5 scenario changes in temperature from 2006–15 to 2090–99 are calculated to obtain twenty-first-century monthly average changes. These spatially and temporally varying changes are added to the FNL and RTG SST fields to make “future” initial and boundary conditions. The Community Atmosphere Model radiation scheme CO2 concentration is also adjusted to 936 ppm, which is consistent with levels projected by RCP8.5 for 2100 (Meinshausen et al. 2011). This pseudo global warming technique has been used previously (Schär et al. 1996; Kimura and Kitoh 2007; Sato et al. 2007; Mallard et al. 2013) and allows for a controlled sensitivity experiment that guarantees present-day synoptic variability at the boundaries. Another benefit of this method is a much lower computational cost than century-long global simulations at high resolution. We reproduced all analyses presented here with five CMIP3 models forced with the A2 emissions scenario and found qualitatively similar results (not shown).
CMIP5 models used.
There are two common methods for presenting cyclone and storm-track statistics. The first is a Lagrangian approach in which cyclone features are identified and tracked throughout their life cycle (Hodges 1994; Sinclair 1997). This method provides distributions of cyclone growth, intensity, and track density but is sensitive to scheme choice, background state changes, and grid resolution (Blender and Schubert 2000; Neu et al. 2013; Chang 2014). The other, simpler, method is to use Eulerain statistics to describe eddy activity in terms of filtered atmospheric variables. Variance and covariance statistics have a long history of use for characterizing storm-track activity and variations (Blackmon 1976; Chang et al. 2002). The Eulerian method results in undesirable conflation of extreme values and bulk eddy activity, as well as of cyclones and short-lived anticyclones, but avoids needless complication from tracking algorithm configuration and yields easily reproducible results. Despite its shortcomings, we find the Eulerian method to be adequate for the present study. We employ an 8-day Lanczos high-pass filter (Bloomfield 1976; Duchon 1979) with 57 points to restrict our analysis to perturbations that occur on the time scale of typical extratropical cyclones.
We use potential vorticity (PV) to quantify diabatic influence along the storm track. PV is a tool that has been widely applied for partitioning and isolating cyclone processes (Hoskins et al. 1985; Stoelinga 1996; Lackmann 2002). Model-output temperature tendencies from the microphysics and convective parameterization schemes are used to calculate diabatic PV generation, which we invert to obtain diabatic wind tendencies. We follow the quasigeostrophic potential vorticity tendency formulation and inversion method described in Willison et al. (2013).
3. Results
We compare seasonal WRF simulations to CFSR data in order to evaluate the ability of the WRF model to simulate the present-day storm track and to confirm that the 20-km configuration results in reduced bias relative to the 120-km configuration. Figure 1 shows 300-hPa EKE, 
EKE at 300 hPa for CFSR (contours, interval 30 m2 s−2) and WRF minus CFSR (shaded) for (a) 120-km grid spacing and (b) 20-km grid spacing.
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
a. Warming signal
Figure 2 shows the response of 300-hPa EKE to climate warming. We note that the warming technique reproduces the general response seen in the CMIP3 and CMIP5 models (e.g., Zappa et al. 2013) at the lower resolution, with increased activity particularly in the exit region of the storm track. This is significant because here, unlike in the GCMs, the storms that enter the model domain at its western boundary are taken from analyses and are thus consistent with the present-day climate. Similarly, the SST variability comes from the current climate. This result suggests that the modeled storm-track response to global warming at coarse resolution is primarily driven by large-scale thermal forcing. Comparison with the high-resolution simulations, however, reveals an enhanced response to warming in the northeastern Atlantic. Fractional changes in EKE are 13.3% over the storm-track exit region (30°–55°N, 45°W–0°; box on Fig. 2) at 120 km and 17.3% at 20 km. We find the resolution-enhanced response both in the 10-yr mean as well as for most individual seasons, suggesting that the signal is robust to interannual variability. Here we focus on the storm-track exit region where the EKE change is most dramatically sensitive to resolution. The storm-track exit region is also an area that is more likely to represent storms that affect Europe.
Change in EKE with warming at 300 hPa (shaded) for (a) 120-km grid spacing and (b) 20-km grid spacing. Current-day values shown in contours (interval 20 m2 s−2).
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
The magnitude of EKE energy is often associated with a change in the mean flow (Chang and Fu 2003). Figure 3 shows the changes in the mean zonal wind at the 850-hPa level (U850) and the 300-hPa level (U300). At both levels we see increases in the mean zonal wind around 40°N with warming. We find the same result for total wind magnitude (not shown). Once again an enhanced response to warming is visible at higher resolution, particularly in the storm-track middle and exit regions. The jet appears to extend zonally with little meridional shift. The lack of poleward shift may result from our upstream boundary condition being inconsistent with expected Hadley cell expansion. The limited ability of eddies to feed back on the large-scale energetics or surface temperature gradient may also prevent poleward shifting of baroclinicity, and this is a fundamental limitation of our experimental design. Nevertheless, it is reasonable to conclude that the general patterns of EKE and mean flow change at both resolutions are a first-order effect of the imposed large-scale thermodynamic forcing since they are consistent with the findings of CMIP3 and CMIP5 models (Zappa et al. 2013). The question, then, is why the warming signal amplifies at higher resolution for the same magnitude of thermal forcing.
Change in mean zonal wind speed with warming for (a) 300 hPa at 120-km grid spacing, (b) 300 hPa at 20-km grid spacing, (c) 850 hPa at 120-km grid spacing, and (d) 850 hPa at 20-km grid spacing. Current-day values are shown in brown contours (contour interval 2 and 5 m s−1 for 850 and 300 hPa, respectively).
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
Changes in the near-surface temperature structure and Eady growth rate reveal the aforementioned large-scale thermodynamic forcing from climate change. The JFM low-level temperature perturbation (925 hPa) and meridional temperature gradient (∂T/∂y) are shown in Fig. 4. Here we note that ∂T/∂y becomes less negative in the western Atlantic and north of the storm track. The meridional temperature gradient becomes slightly more negative in the northeastern Atlantic. From conventional views of baroclinic instability we expect that stronger temperature gradients will result in a downstream EKE increase. The temperature gradient change in the downstream portion of the storm track is consistent with the increase in EKE, but the change from Newfoundland to 45°W should accompany a decrease of EKE. Colle et al. (2013) find similar ambiguity along the U.S. East Coast and speculate that increased latent heating may compensate for changes in baroclinicity, particularly for relatively intense storms. We conclude that changes in low-level baroclinicity are only partly responsible for changes in EKE.
Change in season-averaged 925-hPa temperature with warming (shaded; K) and 925-hPa meridional temperature gradient [contours, interval 0.5 K (1000 km) −1].
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
Change in Eady growth rate with warming (shaded; day−1) at (a) 120-km grid spacing and (b) 20-km grid spacing. Current-day values are shown in brown contours (contour interval 0.15 day−1).
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
b. Diabatic influence
We seek to determine whether the enhanced increase in eddy activity at higher resolution is associated with moist processes, as discussed in Willison et al. (2013). Changes in the average precipitation rate for the 10 winters are presented in Fig. 6. The increases in EKE over the eastern Atlantic with warming and resolution are coincident with increased precipitation. The warming-induced response found at low resolution is again amplified at higher resolution along the U.S. East Coast as well as in the subtropical region in the middle of the storm track, where the EKE does not increase. The relatively small increase in precipitation in the western Atlantic, despite a much warmer SST, is likely due to the competition between decreased cyclone activity here (Colle et al. 2013; Lombardo et al. 2015) and a moister atmosphere. The change in precipitation in this region is, therefore, a less robust signal. This also suggests that the relationship between storm dynamics and latent heat release differs between the entrance and exit regions of the storm track, with the modification of cyclogenesis by condensation playing an important role in the exit region, consistent with the results of Dacre and Gray (2013). The area-averaged increase of precipitation with global warming over the northeastern Atlantic region at 120 km is 6.1%, while the increase with global warming over this region at 20 km is 6.7%, with absolute increases of 0.27 and 0.37 mm day−1, respectively. The increased precipitation response in the northeastern Atlantic at 20 km supports the hypothesis that diabatic processes are strongly influenced by and exert influence on the sensitivity of the warming signal to resolution.
Change in average JFM precipitation rate with warming (shaded; mm day−1) at (a) 120-km grid spacing and (b) 20-km grid spacing. Current-day values are shown in brown contours (contour interval 1 mm day−1).
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
Figure 7 shows 6-hourly precipitation intensity histograms for the northeastern Atlantic region. All of the distributions are dominated by light precipitation events [<1 mm (6 h)−1]. At both resolutions the number of dry periods and the number of heavy precipitation periods increase in the warming experiments, while the number of light precipitation periods decreases. At 20-km grid spacing there is a stronger percent change with warming for both dry periods and for heavily precipitating periods. This change represents a more dramatic flattening of the distribution at higher resolution and circumstantially suggests that the enhanced response of eddy activity and precipitation at higher resolution may be the result of strengthened mesoscale diabatic forcing.
Frequency of JFM 6-hourly precipitation rates with warming [shaded; mm (6 h) −1]. The 0 bin corresponds to 6-h periods without precipitation, and the light precipitation bin is shown separately at left.
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
We next seek to determine whether the increased heating directly contributes to EKE. We compute the generation of EKE by the diabatically induced wind through PV inversion. The diabatic PV tendency is computed from model-output temperature tendencies calculated by the convective and microphysics parameterizations. Diabatic PV tendency is inverted to yield diabatically induced tendencies in the geostrophic winds. The generation of EKE can be written as 
Change in 850-hPa generation of EKE by the diabatic wind tendency with warming (shaded; 10−5 m2 s−3) at (a) 120-km grid spacing and (b) 20-km grid spacing. Current-day values are shown in brown contours (contour interval 4 × 10−5 m2 s−3).
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
c. Eddy–mean flow interaction
Further support for the argument that enhanced mean flow response at higher resolution is tied to diabatically enhanced eddy–mean flow interaction comes from consideration of the components of Eliassen–Palm (EP) flux. EP flux is a well-known measure of wave propagation, and its divergence is a measure of interaction between eddies and the mean flow. Two important components for eddy–mean flow interaction are momentum flux and heat flux. Horizontal momentum flux convergence and vertically increasing poleward heat flux indicate eastward mean flow driving by eddies (Edmon et al. 1980).
Eddy momentum flux (
Change in 300-hPa eddy momentum flux with warming (shaded; m2 s−2) at (a) 120-km grid spacing and (b) 20-km grid spacing. Current-day values are shown in brown contours (contour interval 5 m2 s−2).
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
Change in 850-hPa eddy heat flux with warming (shaded; K m s−1) at (a) 120-km grid spacing and (b) 20-km grid spacing. Current-day values are shown in brown contours (contour interval 5 K m s−1).
Citation: Journal of Climate 28, 11; 10.1175/JCLI-D-14-00715.1
Table 2 summarizes the percentage and absolute changes in key storm-track quantities resulting from warming, averaged over a region of the northeastern Atlantic. For almost every quantity, percentage changes are enhanced at higher model resolution, while all quantities show enhanced absolute changes. In some cases, the change with warming is of the same order of magnitude as the sensitivity to resolution.
Absolute and percent changes, between future and current climates, over the region 45°W–0° and 30°–55°N.
4. Discussion
We have found that the response of the Atlantic storm track to projected climate warming is amplified, particularly in the northeastern Atlantic, at 20-km grid spacing relative to 120-km grid spacing. Increases in the mean zonal wind and eddy activity with warming are coincident with increased Eady growth rate and average precipitation rate. The amplification of the warming signal with resolution is, then, likely caused by an enhanced diabatic feedback. Increased eddy–mean flow interaction at high resolution is also consistent with a diabatic feedback mechanism.
The nonlinear diabatic feedback works as follows: Stronger precipitation in a warmer and moister climate allows for enhanced cyclone activity. Cyclones are able to release more latent heat at higher resolution. Additional latent heating strengthens cyclones directly by enhancing the low-level cyclonic circulation and indirectly by increasing the Eady growth rate. The resolution-enhanced cyclones work to alter the mean flow in a way that is favorable for additional cyclone development as evident in the Eady growth rate changes that result from increased shear.
Our results suggest that the simulated response of extratropical cyclones to global warming varies significantly with horizontal resolution. It follows that even if midlatitude storm tracks in GCMs are well calibrated for the current climate, their calibration might become less valid in a warmer climate. This finding has potential implications for model projections of midlatitude cyclone activity. Strong cyclones are often associated with strong precipitation and, therefore, diabatic forcing. Since extreme wind and precipitation events are of particular interest to society, future work using a Lagrangian framework with feature tracking is needed to determine the sensitivity of cyclone distributions to resolution.
The amplification of the signal in the eastern Atlantic raises the question of whether type C cyclones, as described by Plant et al. (2003), are especially sensitive to climate change. These cyclones rely heavily on latent heating owing to the general lack of low-level baroclinicity in this region, in comparison with the western Atlantic where type B cyclones are dominant (Dacre and Gray 2009, 2013). Since GCM resolutions typically underrepresent latent heating in cyclones in the present-day climate, they are likely to underestimate potential changes in type C cyclones with climate warming.
Increasing horizontal resolution is not a panacea for GCMs. Aside from the computational cost associated with increasing resolution, parameterizations that are not scale aware, namely the convective schemes, may require recalibration. As both CMIP3 and CMIP5 models overestimate eddy activity in the northeastern Atlantic (Zappa et al. 2013), diabatic enhancement of eddy activity at higher resolution would increase this bias. Doblas-Reyes et al. (1998) also found an excessively zonal storm track and excessive eddy activity with higher resolution. On the other hand, increased resolution tends to correct the general underrepresentation of eddy activity in the western Atlantic.
Our results may, in part, result from the one-way interaction with the surface and lateral boundaries in our model configuration. In a global model, increased eddy activity at higher resolution can be self-regulating, as more active eddies consume large-scale baroclinicity and ocean heat content more aggressively. Increased eddy heat flux into high latitudes could further reduce the low-level meridional temperature gradient. Subsequent papers will present results from WRF configured globally with a two-way high-resolution nest in the Northern Hemisphere midlatitudes. This will allow for identification of potential feedbacks outside of the storm-track region.
Acknowledgments
This material is based upon work supported by the National Science Foundation (NSF) under Grant AGS-1007606. WRF and NCAR Command Language (NCL) were developed by the National Center for Atmospheric Research (NCAR). NCAR is sponsored by NSF. FNL data for this study are from the Research Data Archive (RDA), which is maintained by the Computational and Information Systems Laboratory (CISL) at NCAR. The original data are available from the RDA (http://rda.ucar.edu) in dataset number ds083.2. SST data are from the National Centers for Environmental Prediction (NCEP; http://polar.ncep.noaa.gov/sst). We also thank the World Climate Research Programme’s Working Group on Coupled Modeling, which is responsible for CMIP, and we thank the climate modeling groups listed in Table 1 of this paper for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We also wish to thank Brian A. Colle and an anonymous reviewer for their valuable insights.
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