1. Introduction
The unprecedented loss of sea ice and associated amplified warming of the Arctic in recent years has spurred a flurry of research on how these changes at high latitudes may impact the jet streams, and thus weather, at lower latitudes [see Cohen et al. (2014) for a review]. While there is ample model evidence that future Arctic warming and sea ice loss will modulate the changes to the jet stream by 2100 under climate change (e.g., Barnes and Screen 2015; Deser et al. 2015), there is much disagreement on whether we have already witnessed substantial impacts. Some studies suggest that the year-to-year changes in sea ice over the observational record have driven changes in blocking anticyclones (e.g., Liu et al. 2012; Francis and Vavrus 2012), cold winters (e.g., Tang et al. 2013a; Chen et al. 2016), heat waves (Tang et al. 2013b), and even the occurrence of superstorm Sandy (Greene et al. 2013). However, many of these studies have been challenged in the literature, (e.g., Screen and Simmonds 2013a; Barnes 2013; Barnes et al. 2013; Woollings et al. 2014; Screen 2017a). For example, it is argued that any such signal may be small (e.g., Screen and Simmonds 2014; Barnes and Screen 2015; Chen et al. 2016) and thus swamped by midlatitude internal variability, suggesting that variations in the jet stream and midlatitude weather since around 1980 likely cannot yet be attributed to changes in Arctic climate.
One possible reason for the substantial disagreement in the literature is the issue of causality. Most observational studies employ some form of correlation analysis in an attempt to quantify the response of the midlatitude circulation to variations in sea ice loss and Arctic warming. However, as the saying goes, “correlation does not equal causation,” and thus, there is concern that any links identified are instead a reflection of the midlatitude circulation driving the Arctic warming and ice loss as has been demonstrated to occur in many previous studies (e.g., Graversen 2006; Screen and Simmonds 2013b; Wettstein and Deser 2014; Perlwitz et al. 2015; Woods and Caballero 2016; Baggett et al. 2016; Sorokina et al. 2016). Another approach is to simulate the circulation response using a climate model run under two scenarios: high sea ice concentrations and low sea ice concentrations (e.g., Deser et al. 2004; Peings and Magnusdottir 2014; Chen et al. 2016; Screen 2017b). By analyzing the changes in midlatitude weather between the two simulations, one can confidently attribute any changes to the loss of sea ice assuming the simulations are run for a suitably large number of years (e.g., Screen and Simmonds 2014; McCusker et al. 2016). This approach has been used extensively to improve our understanding of the mechanisms linking the Arctic and midlatitudes, and results of these past studies will be vital in interpreting the results shown here. However, this approach only considers changes in sea ice and does not include Arctic warming driven by other sources (e.g., Pithan and Mauritsen 2014; Yoo et al. 2014; Ding et al. 2017), it does not quantify the relative importance of sea ice in driving weather variability compared to other drivers (e.g., eddy–mean flow feedbacks, tropical forcing, decadal variability), the results appear to be highly sensitive to the model used for the simulations (e.g., Screen and Simmonds 2014), and the approach cannot be directly applied to the observations. Thus, there is need for additional methods of quantifying the midlatitude response to Arctic warming.
An alternative to analyzing trends in the reanalyses or running prescribed sea ice loss experiments is to approach the problem in terms of subseasonal forecasting. Jung et al. (2014) performed forecast experiments with the ECMWF forecast model both with (through relaxation to reanalysis) and without knowledge of the Arctic troposphere. They found a reduction (10%) in the root-mean-square error of the wintertime midlatitude 500-hPa geopotential heights for days 11–30 forecasts when the model included Arctic relaxation. That is, knowledge of the Arctic troposphere provided information on the evolution of the midlatitude circulation. Scaife et al. (2014) focused on seasonal prediction of the North Atlantic Oscillation (NAO), a mode of midlatitude jet stream variability, and found that model initialization of sea ice in the Kara Sea led to improved seasonal predictability of the NAO, with low sea ice leading to a negative NAO and vice versa. Thus, on subseasonal-to-seasonal time scales, there is evidence that Arctic near-surface temperature variations driven by sea ice may modulate the midlatitude jet stream in the present day.
Even with the disagreement in the literature on the magnitude of the effect of Arctic warming and sea ice loss on midlatitude weather, studies seem to agree that any circulation response will be a function of the season (e.g., Deser et al. 2010; Francis and Vavrus 2015; McGraw and Barnes 2016; Screen 2017b). This seasonality is in large part attributed to the seasonality of sea ice itself and how it impacts near-surface Arctic temperatures (e.g., Screen and Simmonds 2010; Deser et al. 2010). What has been largely neglected up until this point is how the seasonality of the midlatitude circulation itself may impact the seasonality of its response to Arctic warming. The seasonal progression of the jet streams (and thus storm tracks and weather systems) represents variations in the dynamics that ultimately dictate the position, strength, and variability of the flow. There are a number of ways in which this seasonality of the midlatitude flow could impact the response to Arctic warming. In winter, the midlatitude jet stream is strong and positioned closer to the tropics, while in summer, the jet stream is weak and positioned closer to the pole (e.g., Shaw 2014) (Figs. 1 and 2). This simple seasonality of the proximity of the jet stream flow to Arctic warming may impact its overall response. Another possibility is seasonality in eddy–mean flow feedback strengths. It has been shown in a number of idealized modeling studies that different climatological jet structures can be associated with different eddy–mean flow feedback strengths, ultimately leading to differences in the magnitude of response to an external forcing (e.g., Simpson et al. 2010; Barnes and Hartmann 2010). Arguments along these lines were put forward by Kidston and Gerber (2010) to explain the intermodel spread of the response of the Southern Hemisphere jet stream to global warming as a function of present-day climatological jet latitude. It is possible that such a mechanism could explain any seasonality in the jet stream response to Arctic warming, and such an argument was put forward by McGraw and Barnes (2016) to explain seasonal differences in the jet stream response to imposed polar warming in a dry dynamical core. Finally, if the jet stream response is quantified via metrics such as jet latitude and speed, it is possible that the seasonality in the jet structure could induce a seasonality in its response; for example, the same zonal wind anomalies in two seasons could induce very different jet shifts because of how they are positioned relative to the jet maximum. Indeed, Simpson and Polvani (2016) showed that such geometric arguments could explain a portion of the intermodel spread in the Southern Hemisphere jet stream response to global warming discussed by Kidston and Gerber (2010).
(a) December and (b) June zonal wind at 700 hPa from the Twentieth Century Reanalysis (1950–2004). The black lines denote the climatological position of the jet streams over the North Pacific and North Atlantic sectors. Dashed lines denote the regions used to define the Arctic temperature anomalies.
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
Climatological seasonal cycle of the (a) North Pacific and (b) North Atlantic midlatitude jet stream positions. Light purple lines denote individual CMIP5 ensemble members, and the thick purple line denotes the CMIP5 multimodel median.
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
The aim of this study is to quantify the sensitivity of the jet stream to regional Arctic warming on short (subseasonal) time scales and assess its seasonality. That is, we are interested in how weekly variations in Arctic temperatures, not long-term warming, may drive changes in the midlatitude jet stream. We decouple the seasonality of the circulation from that of the warming by quantifying the response of the jet stream to a 1-K warming of the Arctic lower troposphere using regression techniques. Since modeling evidence suggests any jet response will likely be small compared to internal variability (e.g., Screen et al. 2014; Chen et al. 2016), we make use of 4800 years of climate model simulations to extract the forced signal from the noise. Unlike most previous studies that employ instantaneous or lagged correlations, we take an approach from causality theory, namely, Granger causality (see discussion in section 2d), in an attempt to ensure we are capturing the jet response to Arctic warming and not the other way around. With this approach, we will demonstrate a clear seasonality in the jet stream sensitivity to Arctic warming and will discuss the implications for mean state climate model biases.
2. Methods
a. Data
The majority of the analysis is performed using model output from simulations performed for phase 5 of the Coupled Model Intercomparison Project (CMIP5) (Taylor et al. 2012). We make use of daily 700-hPa zonal wind and 850-hPa air temperature from simulations run under the historical (1950–2004) and RCP8.5 (2006–2100) emission scenarios (the period over which the majority of models provided daily data). All fields are interpolated to a common 2° × 2° grid before any analysis is performed. Table 1 shows the models analyzed and the number of ensemble members for each model. Given the unequal number of ensemble members across the models, for all multimodel analysis we average the final results across model ensemble members before computing the CMIP5 multimodel median.
The 24 CMIP5 models and the number of ensemble members analyzed from the historical and RCP8.5 simulations. (Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.)
The ensemble-mean monthly 700-hPa zonal wind from the Twentieth Century Reanalysis (Compo et al. 2011) for years 1950–2004 (to be consistent with the CMIP5 historical period analyzed here) is also analyzed for comparison of the jet stream climatology with that of the CMIP5 models. A detailed analysis of Granger causality in the reanalysis is left for a future study.
When relevant, anomalies are defined with respect to the seasonal cycle, where the seasonal cycle is computed as the first four Fourier harmonics of the calendar-day climatology. In addition, all time series are detrended for data within each month separately using a second-order polynomial before the regressions are performed. That is, the trend for daily data within a given month is calculated and then subtracted from each day in the month. While we have performed all of the analysis separately for the historical and RCP8.5 forcing scenarios, we make use of a combined time series (historical + RCP8.5), which is created by appending the detrended RCP8.5 time series to the detrended historical time series. This combined time series essentially doubles the degrees of freedom for the regression calculations and will be used throughout this work unless otherwise specified. We note, however, that the general results for each individual scenario are similar but noisier.
We make use of daily data from the CMIP5 archive and calculate nonoverlapping 10-day averages of zonal wind and air temperature. The data are chunked to remove high-frequency synoptic variability, and the chunks are nonoverlapping since our approach involves making “forecasts” of the future evolution of the winds, and thus, we wish to ensure the past has no knowledge of future events. These “chunks” are named according to the first date of the average (i.e., the 1–10 January average will be given the date 1 January, the average from 11 to 20 January given 11 January, and so on). Conclusions are robust to the choice of averaging length between 5 and 30 days. However, we show results using 10-day averages to strike a balance between noise reduction and resolving high-temporal interactions.
b. Defining the jet stream
Time series of jet latitude 
We have also performed the analysis defining the jet stream as the latitude of maximum zonal winds for each longitude individually within a sector (see, e.g., the black lines in Fig. 1) and find very similar conclusions. However, we ultimately chose to zonally average the winds over each sector first before locating the jet core in order to smooth the field further and ensure a robust maximum is identified. Following Kidston and Gerber (2010), we fit a quadratic around the zonal wind maximum to more precisely determine the jet latitude and speed.
Once the jet latitude and speed are defined for each 10-day chunk, we compute the anomalies with respect to the seasonal cycle and then detrend each month as described above.
c. Defining Arctic temperatures
Time series of regional Arctic temperature are defined as the area-weighted average 850-hPa air temperature over the polar cap (70°–90°N) in the sector of interest. The North Pacific analysis uses polar cap temperatures averaged over longitudes defined by our North Pacific sector, and the North Atlantic analysis uses polar cap temperatures averaged over longitudes defined by our North Atlantic sector. These polar domains are delineated by dashed lines in Fig. 1. We chose to divide the Arctic temperatures into regions, rather than take an average over the entire polar cap, because different regions might dominate the polar cap time series at different times of the year. This would introduce unwanted seasonality in the high-latitude warming structure. The majority of the discussion here is focused on the regional circulation response (i.e., North Pacific or North Atlantic) to Arctic warming in the same region, with remote responses (i.e., warming in one region impacting the other) left for future work.
Once the Arctic temperature time series are calculated, we compute the anomalies with respect to the seasonal cycle, average these anomalies into 10-day chunks, and then detrend each month as described above. For the hemispheric zonal wind analysis, the zonal wind anomalies are processed in a similar manner.
d. Granger causality approach
The main aim of this work is to quantify the sensitivity of the jet stream to lower-tropospheric Arctic warming, and to do this, we employ linear regression with a Granger definition of causality. Granger causality has previously been used in climate variability studies to quantify the links between the midlatitude circulation, quantified by the NAO, and surface drivers. For example, Wang et al. (2004) and Mosedale et al. (2006) took this approach to diagnose feedbacks between the NAO and sea surface temperatures while Strong et al. (2009) applied Granger causality to quantify the feedbacks between winter sea ice and the NAO on weekly time scales. A more advanced causality approach, graphical models (e.g., Ebert-Uphoff and Deng 2012), was also recently employed by Kretschmer et al. (2016) to analyze the connections and feedbacks between various Arctic actors on driving variability in the tropospheric annular mode and the stratospheric polar vortex. A more thorough discussion of the benefits of Granger causality in climate variability studies can be found in McGraw and Barnes (2017, manuscript submitted to J. Climate).
We reject the null hypothesis that T does not Granger cause 
C1: There exists at least one significant b according to a t test.
C2: All of the b terms collectively add power to the regression according to an F test.
This Granger causality approach captures the extent to which lagged Arctic temperatures provide additional information about the jet position beyond what is already provided by the memory in the jet position itself. That is, it tests whether Arctic temperatures provide unique information for predicting the future jet beyond what past values of the jet stream already provide. If Arctic warming provides no unique information, then we cannot reject the null hypothesis. If, on the other hand, Arctic temperatures do provide unique information, quantified as a significant increase in the variance explained of the jet stream position, T is said to Granger cause 
To illustrate our approach, an example calculation is shown in Fig. 3 for one ensemble member of the CanESM2 model. Specifically, the example shows the regression coefficients for predicting the North Pacific jet latitude in March: 
An example Granger causality calculation for the jet latitude 
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
Next, we apply the second regression [Eq. (3)], whereby we now include lagged values of Arctic near-surface temperature over the North Pacific domain. The regression coefficient for lagged values of 
Before moving on, we take a moment to explicitly discuss some of the limitations of this method. 1) Granger causality cannot determine whether there is some third driver causing both the jet stream and Arctic temperatures to change. 2) It does not account for instantaneous relationships (i.e., lag zero), as causality would be impossible to determine. 3) As employed here, it is a linear technique, and thus, nonlinear behavior may not be adequately captured. Finally, 4) Granger causality alone does not demonstrate true causality, as this requires theoretical and experimental understanding of the physical processes at work. While these caveats are certainly important to keep in mind, we note that all four also pertain to the standard lagged-regression approach often applied in climate science. In our case, however, Granger causality is viewed as desirable since it removes the possibility that the predictor (in this case, Arctic temperature) only contributes information already contained in the midlatitude jet stream anomalies from prior weeks.
Throughout this paper, we apply the Granger causality method to three predictands. The first is the anomalous jet latitude 
For this work, we use a maximum lag of 
3. Seasonal sensitivity of the jet stream
a. Jet latitude response
The goals of this work are to 1) determine whether the position and strength of the jet stream is sensitive to Arctic warming and 2) assess whether there is any seasonal variation in this sensitivity. To begin, we will discuss the seasonal sensitivity of the jet stream latitude and jet stream speed in the North Atlantic and North Pacific regions to Arctic warming in their respective regions. The Granger causality approach described in section 2 results in a single regression coefficient for each month of the year for each model simulation. We are interested in whether these regression coefficients are significant and whether their magnitudes vary over the annual cycle. Figure 4a shows results only for simulations that satisfy C1 and C2 for each month (i.e., those that exhibit Granger causality) and demonstrates a strong seasonality of the sensitivity of the North Pacific jet stream latitude to Arctic temperatures in the North Pacific region. Specifically, the black crosses denote 
The median CMIP5 jet latitude regression coefficients 
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
Figure 4b shows similar results but for the North Atlantic jet latitude and Arctic temperatures. Again, nearly all of the regression coefficients across the model simulations are negative, implying an equatorward jet shift in response to a 1-K Arctic warming. However, unlike the North Pacific, there is not as strong of a seasonality. Even so, the small seasonality that is present implies the largest sensitivity in summer, as is the case for the North Pacific.
Given that only model simulations that exhibit Granger causality are included in the above analysis, it is useful to know the fraction of simulations that actually showed a significant Granger causality relationship. Figure 5a shows that this percentage hovers between 40% and 70% for the North Pacific and the North Atlantic. There are multiple possible reasons why some models exhibit Granger causality but others do not. For example, the models may have different circulation responses to Arctic warming (e.g., Screen et al. 2014), or the time series length may not be long enough to significantly identify the signal from the noise in some models. We will return to this issue later when we discuss the role of mean circulation biases in explaining a portion of these model differences.
Percent of the CMIP5 simulations showing Arctic temperatures Granger cause changes in jet (a) latitude and (b) speed using the combined historical + RCP8.5 time series.
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
Now that we have established that the Granger causality signal is robust across many of the CMIP5 simulations, the question remains as to how much additional jet stream position variance is explained by Arctic warming in the prior weeks. That is, how much additional information is added by the lagged values of T in Eq. (3)? Figure 6a shows the median across the models exhibiting Granger causality of the percent variance explained 
Median CMIP5 variance explained by the two regressions as a function of month for the combined historical + RCP8.5 time series. Specifically plotted is the median variance explained across the CMIP5 simulations that show Arctic temperatures Granger cause changes in jet (a) latitude 
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
b. Jet speed response
We have performed a similar analysis for jet speed 
As in Fig. 4, but for jet speed 
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
Results for the North Atlantic jet speed are shown in Fig. 7b, and while the multimodel median suggests that the jet stream strengthens as a result of Arctic warming in the warm months and weakens in January and February, the spread is large and only 20%–40% of the simulations exhibit Granger causality at all (Fig. 5b). In the autumn, less than 10% of the simulations exhibit Granger causality (Fig. 5b), and so we have little confidence in the sign of the regression coefficients in these months. Possible reasons for this flip in sign of the jet speed response will be explored in the next section. The added variance explained by Arctic temperatures is similar to that for jet latitude (Fig. 6b compared to Fig. 6a).
4. Seasonal sensitivity of Northern Hemisphere zonal winds
Thus far, we have summarized the midlatitude circulation response to regional Arctic warming by two jet stream metrics: jet position and jet speed. We now perform the Granger causality regressions to predict anomalous zonal wind anomalies at every Northern Hemisphere grid point. The results from the detrended RCP8.5 data are plotted as maps of the CMIP5 median of 
CMIP5 multimodel median zonal wind regression coefficients 
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
Recall that we found the North Pacific jet position was most sensitive to regional Arctic warming in the summer months. Viewing the results in terms of the magnitudes of the zonal wind anomalies, as opposed to jet latitude, we see that the anomalies in March and July are shifted slightly relative to one another (Fig. 8); however, the bigger difference is the position of the climatological jet stream (black lines; defined over the 2006–35 period) relative to the zonal wind anomalies. In March, the jet stream sits within the region of positive anomalous winds but slightly poleward of the maximum. This positioning of the jet axis means that the anomalous zonal winds act to both increase the jet speed and shift the jet equatorward, consistent with our results from the previous section (see Fig. 4a and Fig. 7a). Note that consistent with the thermal wind balance, there is a substantial reduction in the zonal winds in the high latitudes (blue shading); however, the jet is positioned far equatorward of this region. In this way, a reduction in the winds at high latitudes in response to Arctic warming does not imply a reduction in the jet stream at its core.
To visualize results for the other months of the year, Fig. 9 shows the sector average of the regression coefficients for the detrended RCP8.5 scenario (i.e., sector average of Fig. 8), where now the black dashed line denotes the climatological jet position. We have split the historical and RCP8.5 time series apart for these plots since the jet stream is simulated to shift its position under the RCP8.5 forcing scenario, and thus, it is not straightforward how to define a climatological jet position. With that said, the results are very similar between the two forcing scenarios, and so we show only the RCP8.5 scenario here.
The CMIP5 model median sector-averaged zonal wind regression coefficients as a function of latitude and month. Thin gray lines denote each member’s mean jet position, and the black dashed line denotes the CMIP5 multimodel average. Results are from the RCP8.5 scenario.
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
For the North Pacific, as the jet shifts poleward in the summer months, so too do the zonal wind regression coefficients but to a much lesser extent. Furthermore, the negative (poleward) regression coefficients vary little in magnitude throughout the annual cycle, while the positive (equatorward) coefficients exhibit a modest seasonal cycle. In the winter months, the jet axis tends to lie within the region of anomalously positive zonal winds while in the summer the jet axis lies poleward. Thus, the jet latitude is most sensitive to Arctic warming in the summer because it is in these months that the positive zonal wind anomalies are on the jet flank and thus can most easily result in a shift of the jet. Put another way, the seasonality appears to be explained by the seasonal migration of the jet with respect to the wind anomalies as opposed to seasonal variations in the wind anomalies.
We defined the temperature anomaly for the above regression over a region between 70° and 90°N, and one could imagine seasonality being introduced via seasonality in the spatial structure of the temperature anomalies that this temperature index represents. Figure 10a shows the 850-hPa temperature regression coefficient associated with a 1-K warming over the polar cap. That is, it is similar to Fig. 9 except for temperature rather than zonal wind and using instantaneous regression rather than Granger causality. The point here is that the distribution of temperature anomalies across the polar cap (70°N–90°N) associated with our index varies little throughout the annual cycle.
The CMIP5 model median sector-averaged temperature regression coefficients as a function of latitude and month. Unlike Fig. 9, these coefficients are calculated at a lag of zero. Thin gray lines denote each member’s mean jet position, and the black dashed line denotes the CMIP5 multimodel average. Results are from the detrended RCP8.5 scenario.
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
The seasonality of the North Atlantic zonal wind response is more complex than that for the North Pacific. Figures 8 and 9 show that in March the zonal wind anomalies straddle the jet axis, implying an equatorward shift of the jet stream in response to a warmer Arctic. An additional consequence of this straddling is that there is no robust change in the jet speed as documented earlier (Fig. 7b). In July, however, the jet axis lies within the region of positive zonal wind anomalies indicative of a strengthening of the jet stream, again consistent with our earlier results. Looking at the sector-averaged regression coefficients for all 12 months (Fig. 9), we see that the jet axis lies within the region of positive zonal wind anomalies in the summer months and close to the zero or slightly within the negative zonal wind anomalies in the winter months, consistent with the flip in sign of the jet speed regression coefficient in Fig. 7b. Unlike for the North Pacific, the North Atlantic zonal wind anomalies themselves exhibit a strong seasonality, in terms of both their magnitude (largest in summer) and position (most poleward in summer). This seasonality in the magnitudes is not directly a result of differences in the distribution of polar cap temperature anomalies, as indicated by Fig. 10b.
5. Seasonality in sensitivity over the North Pacific
a. Contributions from the climatological seasonal cycle
We presented evidence in the previous section that the seasonality of the North Pacific jet position response to Arctic warming is due to the climatological jet stream moving into and out of the anomalies, rather than a function of the magnitude or location of the anomalies themselves. While it is possible that the explanation is complex, involving eddy–mean flow feedbacks (as discussed in the introduction), we will argue that the reason is likely much more straightforward and due simply to the climatological positioning of the jet stream relative to the zonal wind response. To demonstrate this quantitatively, we linearly decompose the seasonally varying CMIP5 multimodel median jet response into the contribution from the zonal-mean annual-mean zonal wind anomalies (denoted as 
Figure 11 shows the results of this decomposition for both sectors. The appropriateness of our linear approximation [Eq. (4)] is demonstrated by the similarity between 
The seasonal decomposition of the CMIP5 multimodel median jet shift over the (a) North Pacific and (b) North Atlantic. The 
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
For the North Pacific (Fig. 11), we see that the contribution of the seasonally varying climatological jet position (red line) largely explains the full jet position response (black line). This further supports our conclusion that the seasonality of the sensitivity of the North Pacific jet position seen in Fig. 4 is due to seasonality in the climatological jet position itself, rather than seasonality in the wind anomaly response to a 1-K Arctic warming.
For the North Atlantic, the decomposition is less enlightening. While the linear approximation appears to hold, both 
b. Implications for model biases in the North Pacific jet position
We have demonstrated that the seasonality in the North Pacific jet position and speed response appears to be due to the jet axis shifting into and out of the zonal wind anomalies throughout the annual cycle as opposed to seasonality in the zonal wind response. Given that many of the CMIP5 models exhibit biases in the placement of the jet axis (see Fig. 2), one might thus expect these biases to impact the jet position response to Arctic temperature anomalies assuming the induced zonal wind anomalies lie at roughly the same latitude in every model. To support this assumption, Fig. 12 shows similar fields to what is shown in Fig. 8 but for North Pacific warming in January and June. We divide the CMIP5 models into two groups: the half with more poleward jet streams (red lines) and the half with more equatorward jet streams (blue lines). Plotted on Fig. 12 is the median jet stream position in each of the two groups (solid lines) and the median position of the axis of maximum regression coefficient (dashed lines). The point is that the zonal wind anomalies in both groups tend to lie at the same latitude (cf. dashed lines), while the jet streams do not by construction (cf. solid lines); that is, the position of the zonal wind anomalies is independent of the position of the jet maximum (there are no significant correlations in any month; not shown).
As in Fig. 8, but for January and June for the North Pacific. Solid lines denote the climatological jet position, and dashed lines denote the axis of the maximum regression coefficient for the half of models with the most poleward jets (red) and half of models with the most equatorward jets (blue). Results are from the detrended RCP8.5 scenario.
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
To further demonstrate this behavior throughout the annual cycle, Fig. 13 shows the latitude of the maximum and minimum regression coefficients for each CMIP5 simulation as a function of the climatological jet position. The four different colors denote four different months, and the solid black curve is the one-to-one line and thus denotes the mean jet stream position. The two important features in this figure are that 1) the poleward (minimum) regression coefficients lie at roughly the same latitude throughout the year while the equatorward (maximum) regression coefficients lie at roughly the same latitude in summer and that 2) there is no systematic relationship between where a model places the climatological jet and where the regression coefficient maxima and minima are located.
The latitudes of the maximum (crosses) and minimum (circles) zonal wind regression coefficients as a function of the position of the climatological mean jet. Results are from the detrended RCP8.5 scenario. The solid black line denotes the one-to-one line, and the dashed lines envelop the maxima and minima. Colors signify one of four months (January, April, July, and October).
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
Based on the evidence presented in Figs. 12 and 13, we might expect models with more poleward jets to exhibit a larger equatorward jet shift for a 1-K warming of the Arctic, since the anomalies are more optimally positioned on the jet flank (e.g., Barnes and Thompson 2014). Figure 14 provides evidence of this, where for each month we correlate the climatological jet latitude in each simulation with the 
Spearman correlations across the CMIP5 models of the mean jet latitude regression coefficient and the climatological jet position from the RCP8.5 scenario. Dark blue denotes negative correlations significantly different from zero at the 90% confidence level using a one-sided test. Results are from the detrended RCP8.5 scenario.
Citation: Journal of Climate 30, 24; 10.1175/JCLI-D-17-0299.1
While we hypothesized that all months of the year would exhibit negative correlations, instead, only 9 of the 12 do, and only 4 of them are significant. However, based on bootstrap resampling we estimate that the probability by chance alone of getting nine or more negative correlations with at least four being significant to be 0.5%. This check adds confidence to the hypothesis that a model’s climatological location of the jet stream impacts its jet position sensitivity to Arctic warming at least in some months of the year.
For the North Atlantic, both the latitude and magnitude of the zonal wind anomalies change throughout the annual cycle (e.g., Fig. 9b), and thus, such an attribution of model bias to the jet stream sensitivity is not straightforward. It is only because the North Pacific zonal wind anomalies are relatively fixed in magnitude and latitude throughout the annual cycle that model bias in the placement of the climatological jet stream so cleanly falls out of the analysis.
6. Discussion and conclusions
The main aim of this work was to quantify the sensitivity of the Northern Hemisphere midlatitude jet streams to variations in regional Arctic temperatures on subseasonal time scales and explore its seasonality. We took a Granger causality approach applied to the North Pacific and North Atlantic jet streams using 4800 years of simulations of the CMIP5 models. Granger causality allowed us to quantify the extent to which regional Arctic warming provides additional information about the future evolution of the regional midlatitude circulation beyond what is provided by the circulation’s persistence. Our main conclusions are summarized below:
Arctic warming Granger causes changes in the jet latitude and jet speed on subseasonal time scales. The North Pacific and North Atlantic jet streams consistently shift equatorward but often also strengthen in response to a warmer Arctic rather than weaken.
Arctic temperatures explain an additional 3% of the variance of 10-day-averaged jet position and speed after accounting for the variance associated with the persistence of jet anomalies from previous weeks.
The sensitivity of the jet stream position and speed to subseasonal variations in regional Arctic warming is a function of season and region. For example, the North Pacific jet position is most sensitive to North Pacific Arctic warming in the summer months.
Stepping away from defining a jet stream, the zonal wind anomalies in the North Pacific have similar magnitude throughout the annual cycle, while those in the North Atlantic are strongest in summer.
The seasonal sensitivity of the North Pacific jet position to North Pacific Arctic warming can be understood by the jet shifting into and out of the anomalies. This is shown to have implications for the influence of mean state circulation biases across the CMIP5 models on the jet position response to Arctic warming.
In this work, we quantified seasonality in the midlatitude circulation response to a 1-K warming of the Arctic on subseasonal time scales. This was done deliberately to separate out the part of the circulation response due to seasonality of the circulation, rather than seasonality of the warming itself. However, recent trends in Arctic temperatures do in fact show a strong seasonality, with the largest trends found in the winter months (Cohen et al. 2014). Thus, the dynamical link between this longer-term trend in Arctic temperatures and midlatitude weather may differ from what is shown here since we have explicitly focused on subseasonal time scales. Furthermore, because of our explicit focus on subseasonal time scales, longer-time-scale processes connecting near-surface Arctic warming and the midlatitude circulation, for example, via a stratospheric pathway, may be missed. In fact, many previous studies have argued for a stratospheric pathway (Sun et al. 2014, 2015; Wu and Smith 2016) that takes 2–4 months to develop (e.g., Kim et al. 2014; Kretschmer et al. 2016) and only occurs in the winter months (e.g., Sun et al. 2015). In addition, this stratospheric pathway is believed to be most sensitive to ice loss and Arctic warming in the Barents and Kara Seas region (e.g., Screen 2017b), which was not included in our North Atlantic region. Thus, further investigation of the circulation’s seasonal sensitivity to regional Arctic warming at longer time scales is warranted.
With that said, our results are largely consistent with those from atmosphere-only GCM experiments simulating the circulation response to Arctic warming and/or sea ice loss (e.g., Deser et al. 2004, 2010; Butler et al. 2010; Screen et al. 2013; Peings and Magnusdottir 2014). Namely, the jet stream shifts equatorward in response to Arctic warming. One of the benefits of using our Granger causality methodology is that the same analysis can be directly applied to the observations; however, even with 150 years of simulation, some models do not exhibit a significant Granger causal relationship between Arctic temperatures and the jet stream. Thus, with the more limited satellite record over which we can trust the daily data, it may be challenging to find a signal in the observations, even if it is present. We do note that Strong et al. (2009) successfully applied Granger causality definitions to quantify the feedbacks between winter sea ice variability and the North Atlantic Oscillation in reanalyses on weekly time scales, suggesting that such a signal may emerge in some seasons in the observations.
A number of possible reasons why we might expect a seasonality in the sensitivity of the response of the jet stream to Arctic warming were discussed in the introduction. These include ideas related to seasonality in the jet structure influencing eddy–mean flow feedbacks and seasonality in the proximity of the jet stream to the localized Arctic warming. Ultimately, however, it appears that much of the seasonality in the North Pacific jet position and jet speed response to Arctic warming is associated with simple geometric effects. In this region, the wind anomalies associated with a 1-K warming of the Arctic are similar throughout the year. However, seasonality in how these wind anomalies are positioned relative to the climatological jet leads to seasonality in the jet position response, resulting in a larger equatorward shift of the jet stream maximum in summer months. This was not the case for the North Atlantic, where the zonal wind anomalies were significantly stronger in the summer months compared to those in winter.
Differences between the North Pacific and North Atlantic responses to regional Arctic warming highlight the importance of clearly defining the circulation metric of interest. If one is specifically interested in the position and strength of the midlatitude jet streams, as might be the case for dynamics related to, for example, Rossby wave propagation, wave resonance, storm-track intensity and position, or ocean forcing by surface westerly wind stress, then the relevant results are that the jet shifts equatorward most in the summer months and that the jet most often strengthens in response to a warmer Arctic. On the other hand, if one is interested in the zonal wind response at all latitudes, the North Pacific shows little seasonality while the North Atlantic still exhibits the strongest response in the summer months. Thus, the sensitivity and response of the jet stream to Arctic temperature variability is distinct from that of the zonal flow, and future studies should clearly make this distinction.
Acknowledgments
EAB is supported by the Climate and Large-Scale Dynamics Program of the National Science Foundation under Grant 1545675. IRS is supported by the National Science Foundation, which sponsors the National Center for Atmospheric Research.
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Since the calculation is performed at every grid point, different numbers of simulations may contribute to each grid point. We have confirmed that regions exhibiting larger regression coefficients tend to have larger numbers of contributing simulations (>15), signifying that one simulation is not dominating the response in a particular region.
The median zonal wind fields across all models are analyzed, rather than each simulation separately, because no simulation exhibits Granger causality at every grid point, and thus, the fields for each individual simulation are riddled with holes (NaNs) making our decomposition impossible.