1. Introduction
There is overwhelming evidence that climate and its extremes are changing (Bindoff et al. 2013). As extremes affect many aspects of our society (Easterling et al. 2000; Field et al. 2012; Peterson et al. 2013; Perkins 2015) and may bear a disproportionate impact on public perception of climate change (Hansen et al. 2012), reliable predictions of extremes on time scales from days to centuries are urgently needed (Field et al. 2012). Before such predictions can be reliably issued, however, an improved understanding of the processes leading up to extremes must be reached.
We focus on the factors and mechanisms that lead to extremely cold and warm temperatures in the troposphere and at the surface. Observed changes in midlatitude temperature extremes have largely been explained by changes in the probability distribution function (PDF) of temperature variability, and in particular of its moments. A shift toward higher mean temperatures entails a reduction in the frequency of temperatures below a fixed cold threshold and a corresponding increase in the frequency of temperatures above a fixed warm threshold (Easterling et al. 2000; Donat and Alexander 2012; Hansen et al. 2012; de Vries et al. 2012; Rhines and Huybers 2013; Peterson et al. 2013; Coumou et al. 2013). While the variance of the temperature distribution is clearly important for extreme events, there is no consensus as to how it will change. On the global scale, interannual temperature variability is now decreasing, and climate models strongly suggest that this decrease will continue in response to increases in atmospheric greenhouse gas concentrations (Kitoh and Mukano 2009; Huntingford et al. 2013). It has recently been argued that the amplified Arctic warming that accompanies global warming should increase the amplitude of large-scale eddies in the midlatitude Northern Hemisphere and thus cause more extreme events (Francis and Vavrus 2012; Liu et al. 2012). However, observational support for this hypothesis is limited, as neither the amplitude nor the phase speeds of midlatitude eddies nor the frequency of blocking has appreciably changed (Barnes 2013; Screen and Simmonds 2013; Barnes et al. 2014; Screen 2014). Temperature variance, if anything, has been slightly reduced on synoptic time scales in midlatitudes (Screen 2014; de Vries et al. 2012), in agreement with model projections for a warming climates (Kitoh and Mukano 2009; Hassanzadeh et al. 2014; Screen et al. 2015; Schneider et al. 2015). Such a combination of reduced temperature variance with a shift toward warmer mean temperatures will lead to less frequent cold outbreaks.
The nature of the third moment (i.e., the skewness) of the temperature distribution is controversial, let alone its future changes. While some suggest that, on synoptic time scales, moments higher than the second are not important for near-surface temperature such that the temperature PDF in midlatitudes is indistinguishable from a Gaussian (e.g., Newman et al. 2010; Schneider et al. 2015; there are also others who tacitly make this assumption by not even broaching skewness), others find substantial deviations from Gaussianity (e.g., Petoukhov et al. 2008). Before a comprehensive understanding can be reached of how the PDF of temperature variability is changing, an understanding of the deviations from Gaussianity in a fixed, stationary climate needs to be reached. This issue is important for climate change adaptation, as the degree to which future extreme warm events depart from anything hitherto experienced depends on whether the tails of the temperature PDF are Gaussian or non-Gaussian. Specifically, under a given fixed warming, a Gaussian-tailed region tends to be at greater risk of extreme heat events than a comparable long-tailed region (Ruff and Neelin 2012; Loikith and Neelin 2015; Sardeshmukh et al. 2015). Therefore, accurate projection of the effect of climate change on extremes requires understanding of the underlying physical processes shaping all moments of these distributions (Sardeshmukh et al. 2015).
Here, we relate the PDF of near-surface temperature anomalies to the synoptic evolution of extreme events. While processes relating to the ground cover and orography are certainly important (Schär et al. 2004; Seneviratne et al. 2006, 2010; Berg et al. 2014), we focus our attention on the synoptic causes of temperature extremes. We show that approximating temperature variability as a Gaussian is erroneous. In particular, the skewness changes sign on opposite sides of the midlatitude storm track axis such that warm and cold extremes are fundamentally asymmetric. These conclusions are true both on the submonthly time scales that are of primary importance for heat waves and cold outbreaks, and also on longer time scales. Similar results are also present in long model integrations of a dry primitive equation atmospheric model. We demonstrate that the cold/warm asymmetry is a consequence of the synoptic evolution necessary in order to generate temperature extremes of either sign.
We also explore how temperature extremes change as the jet stream and storm track moves poleward. Previous work suggests that vorticity extremes, Rossby wave breaking, and blocking all change with the jet latitude (Barnes and Hartmann 2012; Garfinkel and Waugh 2014; Harnik 2014; Harnik et al. 2016). As Rossby wave breaking and blocking are related to extremes as well (Buehler et al. 2011; Masato et al. 2012; Sprenger et al. 2013), it is natural to expect a sensitivity of temperature extremes to storm track location (Scaife et al. 2008; Mahlstein et al. 2012).
The structure of the paper is as follows. After introducing the data and methodology in section 2, we show that warm and cold extremes are distributed asymmetrically in both reanalysis data (section 3) and in a dry general circulation model (section 4). We then analyze the synoptic evolution leading up to warm and cold extremes in order to elucidate how fluid-dynamical processes lead to this asymmetry (sections 5a and 5b). Finally, many of the key ingredients of this synoptic evolution are distilled in a relatively simple model of quasilinear Lagrangian temperature advection (section 5c). We then discuss implications of this work.
2. Data and methods
a. Data and models
We examine daily output from the European Center for Medium-Range Weather Forecasts interim reanalysis dataset (ERA-Interim, hereinafter ERAI; Dee et al. 2011) and from NASA’s Modern-Era Retrospective Analysis for Research and Applications (MERRA; Rienecker et al. 2011) reanalysis dataset. All relevant data from the period January 1979 to December 2013 are included in this analysis. Results are similar for both reanalysis datasets, and for brevity we only show ERAI results. We focus on the Southern Hemisphere where zonal inhomogeneities are relatively small as compared to the Northern Hemisphere.
In summary, our approach is to create a continuum of experiments in which the tropospheric baroclinic forcing gradually moves the storm track from near 30° to near 55°. We then analyze the subsequent extreme events. The key point is that the extremes in the model integrations are not driven by surface asymmetries due to topography or surface moisture content, and thus the integrations allow us to focus on the forcing of temperature extremes by synoptic variability.
b. Methodology
We focus both on the PDF of temperature variability and also on the extreme events. The PDF is constructed by normalizing the histogram of the distribution without applying any smoothing of adjacent bins. The bins for the histogram are located 0.15 K apart. Note that all dry model experiments extend for at least 10 000 days in order to allow precise determination of the nature of the tails of the PDF. The similarity of the PDFs (specifically the skewness) among experiments with adjacent storm track latitudes attests to the precision of the PDF. We pool all anomalies on a given zonal band before estimating the PDF, although results for the skewness are similar if we consider the mean skewness of each longitudinal grid point on the zonal band. The kurtosis of the temperature PDF is between 2 and 4 for all cases and all latitudes, and does not appear to be important for explaining the location of extreme events (not shown). We therefore focus in this manuscript on the skewness and warm/cold asymmetries.
Recent examinations of surface temperature variations that include both synoptic and longer time scales found significant departures from Gaussian statistics (e.g., Ruff and Neelin 2012; Perron and Sura 2013; Loikith et al. 2015; Sardeshmukh et al. 2015; Loikith and Neelin 2015), although Schneider et al. (2015) argue that the PDF of midlatitude surface temperature in the present climate, as well as its anticipated future changes, is indistinguishable from Gaussian once low frequencies of longer than 15 days are filtered out. Hence, we compute the PDF both from the unfiltered temperatures and also after performing a high-pass filter of the temperature variations on time scales of less than 15 days.
We now introduce the methodology used for identifying extreme surface temperature events. We first compute anomalies with respect to each grid point’s climatological value. We then order the anomalies for all experiments across all grid points located in each hemisphere, and compute the threshold for the coldest and warmest 1% of days. For surface temperature extremes in the dry model, for example, these thresholds are −10.86°C and 11.70°C for cold and warm extremes, respectively. We have explored sensitivity to a 0.5% or a 2% threshold, to setting the threshold separately for each experiment, and also to adding an additional requirement that events persist for at least three or five days, and the systematic warm/cold asymmetries on either side of the storm track axis are similar (not shown). We have also looked at the frequency of 2-sigma events with respect to each grid point’s variability, and again we still find similar systematic differences between warm and cold extremes on either side of the storm track axis (not shown).
For events that last more than one day, we include only the day with the most extreme value. Specifically, we begin by sorting the temperature anomalies from largest to those that marginally exceed the threshold. Starting from the largest anomaly, we search for any additional anomalies that occurred within a 30° longitude or latitude box surrounding the largest anomaly on the day of the event and for two days preceding and following the event; such “duplicate�? events are removed from the list. The net effect is that we isolate the events spatially and temporally and thus minimize serial correlation for long-lasting events. Note that approximately 2% of the extreme events persist for more than 5 days, and the warm/cold asymmetry is similar for these events as well.
When analyzing the synoptic evolution leading up to surface temperature extremes, we adopt an even stricter threshold of −18°C for cold extremes and 22°C for warm extremes in order to highlight the key features leading up to these events. We then center the events around the peak longitude, so that events occurring at different longitudes can be composited together. Robustness is determined by evaluating the fraction of events which agree on the sign of the anomaly. Shading is indicated when more than 80% of the events agree on the sign of the anomaly, and a white line encloses the region where more than 90% of the events agree. A binomial-signs test indicates that the probability that 80% of events will be of one sign by chance is vanishingly small for the composite sizes we construct (e.g., <10−33 for 384 events). Note that a conventional t test is built on an assumption of Gaussianity, and so we urge caution in applying such a test to temperature. The composites are calculated both for full fields and for the anomalies, defined as the deviation from the mean of each integration. The robustness, however, is determined solely from the anomaly fields.
3. Observed temperature extremes
We first consider 850-hPa temperature variations for the December–February (DJF) season in the Southern Hemisphere for the period January 1979 through December 2013 in ERAI reanalysis data. Motivated in part by previous studies that find meridional structure in the skewness (Petoukhov et al. 2008; Loikith and Broccoli 2012; Perron and Sura 2013), we separately consider the equatorward and poleward flanks of the climatological storm track axis (i.e., at 38° and 60°S). The estimated PDF of temperature anomalies is shown in Fig. 1, with the poleward flank (60°S) shown in red and the equatorward flank shown in blue (38°S). Whether one applies a filter to isolate synoptic variability or not, extreme warm anomalies occur more often on the poleward flank than on the equatorward flank, while extreme cold anomalies occur more often on the equatorward flank than the poleward flank. For example, an 8°C warm anomaly is 2 times more likely on the poleward flank than the equatorward flank of the storm track, while an 8°C cold anomaly is 4 times more likely on the equatorward flank than the poleward flank of the storm track. These deviations from Gaussianity are present for relatively small temperature variations, and are not limited to the tails of the distribution. Quantitatively, this information can be summarized by calculating the skewness of the two PDFs, and hence the skewness is included in each panel: temperature variations are negatively skewed on the equatorward flank of the storm track and positively skewed on the poleward flank.1
PDF of 850-hPa temperature in the ERAI reanalysis. (a),(b) The raw PDF as described in section 2b. (c),(d) The standardized PDF, and (e),(f) the standardized PDF shown on a log-scale. To ease visual comparison, we include in black a Gaussian distribution in (c)–(f).
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
The importance of this effect for climate change is quantified in Fig. 2. Figure 2a shows the PDF of 850-hPa temperature in the ERAI reanalysis data on either flank of the storm track repeated from Fig. 1b, and the PDF displaced uniformly warmer by 3 K is indicated with dashed lines. It is self-evident that cold extremes occur less frequently and warm extremes occur more frequently under such a uniform warming, but the change in probabilities differ on either flank of the storm track. The increase in probability of a warm anomaly exceeding 7°C is far larger on the equatorward flank of the storm track (cf. blue and red curves in Fig. 2b). This effect arises because of the relative shortness of the warm tail for the present climate on the equatorward side of the storm track, in agreement with Ruff and Neelin (2012), Loikith and Neelin (2015), and Sardeshmukh et al. (2015).
PDF of 850-hPa temperature in the ERAI reanalysis (a) presently and under a 3-K uniform warming; (b) logarithm of the ratio of the frequency of temperature anomalies between a uniform 3-K warming and the present climate.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
The systematic deviations from Gaussianity are summarized in Fig. 3a, which shows the distribution of skewness with latitude and pressure throughout the troposphere. Near 60°–65°S, temperature variations are positively skewed down to 750 hPa (the proximity of the extremely cold and high Antarctica to the relatively warmer Southern Ocean complicates the dynamics in boundary layer), while they are negatively skewed near 40°S. These results are generally consistent with those of Petoukhov et al. (2008), Loikith and Broccoli (2012), and Perron and Sura (2013) for levels above the boundary layer. (Future work is needed to understand the observed distribution below 900 hPa.) The distribution of extreme temperature events (as defined in section 2) is shown in Fig. 3b. Extremes of either sign are concentrated near the maximum in variance of the temperature. But consistent with the nonzero skewness, cold extremes (shown in blue) tend to occur further equatorward than warm extremes (shown in red) in both hemispheres and at all levels above 850 hPa.
(left) Skewness of temperature variations and (right) frequency of temperature extremes (in units of events per 100 days) in the troposphere in (a),(b) ERAI data and (c),(d) a 30 200-day integration of the dry model in which jet latitude is near 45°. (e) As in (c), except that a bandpass filter has been utilized to isolate synoptic time scales. Contours of warm extremes and positive skewness are shown in red, while those of cold extremes and negative skewness are shown in blue. The skewness is computed at each level and latitude independently. Gray shading represents the variance of the temperature PDF, and its corresponding color bar is shown on the bottom right. Note that topography is present in the Northern Hemisphere of these dry model integrations as described in Garfinkel et al. (2013) and Garfinkel and Waugh (2014), but the focus of this paper is on the hemisphere without topography.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
4. Dry model: Simulated temperature extremes
To isolate the dynamical contribution to the temperature extremes, we now consider temperature variations is a dry model that explicitly does not include surface moisture or zonal inhomogeneities. We first consider the PDF of 850-hPa temperature variations for our longest experiment (i.e., 30 200 days with fixed external forcings). The estimated PDF of temperature anomalies is shown in Fig. 4. As in the ERAI data, extreme warm anomalies occur more often than extreme cold anomalies on the poleward flank (red curve), while extreme cold anomalies occur more often than warm extremes on the equatorward flank (blue curve). The deviations from Gaussianity are larger for the dry model as compared to ERAI, although the temperature variance is also larger as well in the lower troposphere (cf. the gray shading in Figs. 3a,c) and thus the processes to be discussed in section 5 are likely more capable of differentially modulating the temperature field on either flank of the storm track. Filtering the temperature anomalies to focus on synoptic time scales weakens the deviations from Gaussianity but does not remove them (cf. left and right panels of Fig. 4).
As in Fig. 1, but for a 30 200-day integration of the dry model in which jet latitude is near 45°.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
The systematic deviations from Gaussianity are summarized in Fig. 3c, which shows the skewness as a function of latitude and pressure. Near 60°S, surface temperature variations are positively skewed at all levels, while they are negatively skewed (or not skewed near the surface) near 40°S. The crossover from negative to positive skewness tends to occur farther equatorward closer to the surface, and this tendency is similar to that found in ERAI. All of these results are robust even if we bandpass filter the temperature variations to focus on synoptic time scales (cf. Figs. 3c and 3e).
We now generalize the results of Figs. 3 and 4 by analyzing the skewness in all of the dry model experiments performed. Figures 5a and 5c show the skewness as a function of latitude (on the ordinate) for mean storm track axes ranging from 30° to 54°S. For all experiments, the skewness is negative on the equatorward flank of the storm track and positive on the poleward flank. Note that the rich structure of the skewness evident for temperature variations is not evident for other surface diagnostics, for example the surface pressure (Fig. 5e). Rather, surface pressure skewness is weakly negative on both storm track flanks, reflecting the slightly stronger nature of surface lows as compared to surface highs. The transition latitude between negative and positive skewness near the storm track axis occurs farther equatorward at the surface as compared to 500 hPa, and this is consistent with a slightly poleward shifted region of maximum variance in Figs. 5b and 5d. This effect is driven by the differences in the location of the peak baroclinicity at each level. The temperature gradient in the dry model runs is shown in Figs. 6a and 6b. The peak temperature gradient is offset by 5° to 10° (depending on the specific experiment) farther poleward at 500 hPa compared to the surface. Hence, it is to be expected that the transition from negative to positive skewness occurs further poleward at 500 hPa as well.
Skewness and variance of temperature at surface and 500 hPa, and of surface pressure, for each experiment. The experiments are ordered by the latitude of their maximum in zonal winds at 850 hPa, and this latitude is shown with a dashed blue line. The jets and region of maximum variance (i.e., the storm tracks) are located slightly poleward at 500 hPa and equatorward at the surface. Black contours denote the 15 m s−1 isotach at 300 hPa.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
(a),(b) The meridional temperature in in the dry primitive equation GCM in the hemisphere without topography at the surface and 500 hPa in K (100 km)−1. (c)–(f) Summary of the extreme temperature events. The details of the definition of an extreme event are given in section 2b. The ordering of experiments and the dashed blue line are as in Fig. 5. The contour interval is 0.1 K (100 km)−1 in the top row and 0.01 events per day in the bottom row.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
Figures 6c–f show the distribution of extreme warm and cold events at 500 hPa and at the surface. Cold extremes occur farther equatorward than warm extremes, and the transition occurs farther poleward at 500 hPa than at the surface.2 All of these features are consistent with that seen in reanalysis data and with the distribution of skewness. (Note that there is a second, subpolar peak for the jets located farther equatorward; a thorough investigation of this is left for future work, and here we concentrate only the peak that is near the storm track axis.)
5. Dry model: Synoptic evolution
We now examine the synoptic evolution leading up to the temperature extremes, with the goal of explaining the asymmetry in the location between cold and warm extremes. We first document the synoptic evolution leading up to extremes for the experiment that has been integrated the longest (30 200 days), though results are similar for the other experiments as well. We then demonstrate that horizontal temperature advection, a key process evident in the dry model composites, can quantitatively account for the generation of temperature extremes and for their meridional displacement relative to the storm track axis.
All extreme surface cold (warm) events that occurred 12° south (2° north) of the jet axis are composited together, and centered with respect to the longitude of the extreme temperature anomaly. Only extremes in which the temperature anomalies exceed −18°C for cold extremes and 22°C for warm extremes are included. Figures 7 and 8 show the sea level pressure anomalies (top), surface isotherms (middle), and 500-hPa absolute vorticity contours (bottom), leading up to the extremes.
Synoptic evolution associated with extreme warm events at the surface in the Southern Hemisphere in the dry primitive equation GCM for the 30 200-day-long experiment in which the climatological jet latitude is near 45°. (a)–(c) Surface pressure leading up to the event. (d)–(f) Surface temperature leading up to the event. (g)–(i) 500-hPa absolute vorticity leading up to the event. The contour interval is indicated by each row. A gray line represents the climatological zonal mean zonal wind at 925 hPa multiplied by a factor of 5, such that the maximum in near-surface wind peaks at 8 m s−1. Extreme warm events are defined by temperature anomalies exceeding 22°C, and we composite the extremes that occurred at the latitude where extremes occur most often. The location of the center of the extreme temperature anomaly is indicated by a magenta star in all panels. Wind anomalies are indicated with vectors wherever the surface wind speed anomaly exceeds 5 m s−1 in (a)–(f); for (g)–(i), we show the raw wind vectors at 500-hPa wind wherever the wind speed exceeds 20 m s−1. Gray shading, and the white line within the gray shading, indicates that anomalies are robust as described in section 2b.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
As in Fig. 7, but for the extreme cold temperature events at the surface in which the cold anomaly is more extreme than −18°C.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
a. Warm extremes
We first focus on the synoptic buildup to the warm extremes. Opposite-signed sea level pressure anomalies straddle the location of the incipient extreme warm anomaly (Figs. 7a,b), such that the wind advects isotherms more characteristic of tropical latitudes toward the pole. The low–high couplet is part of a longer Rossby wave train that is propagating poleward. Each extremum in the wave train extends over more than 30° meridionally, and therefore can advect over the entire region in which there is a large temperature gradient in Fig. 6a (from deep in the subtropics near 20° to near 50°). The net effect is that the isotherms are already substantially distorted a day before the warm extreme.
By the day of the extreme itself, the sea level pressure couplet is of the same magnitude as on the previous day, but it is displaced even farther poleward. Continual warm air advection leads to further distortion of the isotherms, such that there is no temperature difference between ~25° and 50° at the longitude of the extreme. At upper levels, intense vorticity anomalies and Rossby wave breaking, followed by blocking, occurs [see Fig. 7i, consistent with Pfahl and Wernli (2012), Sprenger et al. (2013), and Harnik (2014)]. Synoptic situations remarkably similar to those shown here led to record-breaking heat waves over the United States in mid-April 1976, in the beginning of November 1980, and in the second half of March 2012 (Wagner 1976; Livezey 1981; Grumm et al. 2014) and are similar to composites shown by Loikith and Broccoli (2012). The importance of horizontal temperature advection for the generation of temperature extremes has also been stressed by Screen (2014) and Schneider et al. (2015).
The upper-level steering flow likely contributes to the poleward propagation of the low–high couplet. Figures 7g–i show the absolute vorticity at 500 hPa leading up to the warm extremes. Two days before the extreme, there is upper level support for the surface low (i.e., westward tilt with height). To the east of the upper-level low, directly overlying the surface low pressure anomaly (i.e., the more westward member of the sea level pressure couplet), there are strong midtropospheric winds which steer (or advect) the lower-level anomalies poleward. These strong midtropospheric winds intensify a day before the extreme. We suggest that this steering flow is partially responsible for the poleward motion of the more westward member of the sea level pressure couplet (the low), although a thorough quantitative investigation of the cause of the poleward propagation is left for future work.
In additional to meridional movement of the system, there is also eastward propagation with time. If the eastward phase propagation of the low–high couplet matches the zonal wind speed advecting individual near-surface air parcels, then there is no difference between trajectories and streamlines of the flow and a given air parcel can stay in the same phase of the larger-scale pattern. Such a configuration would maximize the magnitude of the warm extreme. We now evaluate whether this optimal alignment occurs. The phase speed of the low–high couplet can be deduced from the phase lines of the low and high in the couplet in Figs. 7a–c and is estimated at 7 m s−1. In contrast, the surface zonal wind at the location of the midpoint of the low–high couplet averaged over these three days is 5 m s−1. Hence, the individual air parcels will be partially “left behind,�? although the difference corresponds to a shift of 350 km over the two days and is less than half the width of the tongue of warm air that is advected poleward.3 Overall, both the meridional and zonal movement of the low–high couplet are in a nearly optimal configuration for enhancing the magnitude of the surface warm extreme.
b. Cold extremes
Cold extremes evolve largely as the opposite of warm extremes. Opposite-signed sea level pressure anomalies straddle the location of the incipient extreme cold anomaly (Figs. 8a,b), such that the wind advects isotherms more characteristic of subpolar latitudes toward the equator. The high–low couplet is part of a longer Rossby wave train that is propagating equatorward (recall that for warm extremes, the wave train propagated poleward). Each extremum in the wave train has a characteristic meridional extent of more than 30°, and therefore can advect over the entire region in which there is a large temperature gradient in Fig. 6a. As for warm extremes, the equatorward propagation is driven (at least in part) by the steering of the midtropospheric flow (Figs. 8g–i). Sea level pressure anomalies of broad meridional scale that propagate equatorward are also present for cold-air outbreaks over East Asia and the Midwest and eastern United States (Joung and Hitchman 1982; Konrad and Colucci 1989; Walsh et al. 2001).
On the day of the extreme, the sea level pressure couplet is of the same magnitude as on the previous day (the downstream low is slightly stronger, and the upstream high correspondingly weaker), but it is displaced even farther equatorward. Continual cold air advection leads to further distortion of the isotherms, such that there is no temperature difference between ~35° and 60° at the longitude of the extreme. At upper levels, Rossby wave breaking occurs followed by an intense cutoff low [Fig. 8i, consistent with Sprenger et al. (2013) and Harnik (2014)]. Finally, the eastward phase speed of the high–low couplet, as deduced from the phase lines of the high and low, is 5.2 m s−1. This phase speed matches the zonal wind at the midpoint of the high–low couplet averaged over these two days, and thus streamlines of the flow and particle displacements closely match. Hence, the meridional and zonal movement of the high–low couplet is optimum for generating cold extremes.
c. Isolating horizontal temperature advection in a simple Lagrangian model
Thus far, this section has shown that horizontal temperature advection is qualitatively associated with both warm and cold extremes. We now demonstrate that this process 1) can quantitatively account for the temperature extremes that are simulated and 2) can lead to temperature extremes far removed from the largest anomalies in, say, geopotential height. We suggest that this process also contributes to the nonzero skewness.
We use the temperature advection model introduced in section 2a. Recall that at the start of the integration, the temperature field is zonally uniform 
Figure 9 shows the evolution of the temperature field with time. After 6 h (Fig. 9a), advection begins to distort the isotherms such that a temperature anomaly is generated at the axis of the low–high couplet, though even at this early stage the meridional position of the warm and cold anomaly can be differentiated (Fig. 9b). After 25 h, 10-K cold (warm) anomalies develop 600 km to the north (south) of the y = 0 axis. After 36 h of continual advection, the peak temperature anomaly of 13 K is located 800 km off the y = 0 axis (Figs. 9c,d). The spatial pattern of the temperature anomalies and isotherms is reminiscent of those seen in nonlinear baroclinic waves (Hoskins and West 1979; Davies et al. 1991; Thorncroft et al. 1993). After 48 h, the temperature anomaly exceeds 15 K.
Simplified model in which temperature is advected like a passive tracer. The model is initialized with a zonally uniform temperature profile and a low–high couplet, and shown (top) 6 h and (bottom) 36 h after the start of the simulation. All of the conventions are Southern Hemisphere centric, with a low in the left side of the domain and a ridge in the right side of the domain. Arrows indicate the wind field specified by the streamfunction, and are only shown for wind speeds larger than 5 m s−1 and at every other grid point (for clarity). (e),(f) As in (c),(d), but for a linearized version of the model in which covariances of anomalous temperature and anomalous wind are neglected. The contour interval is 2 K.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
In nature and also in the dry model, geopotential height anomalies and wave trains (and their associated meridional wind anomalies) occur preferentially within the storm track due to the peaked baroclinicity in this region. Hence, there will be a systematic tendency for cold extremes equatorward and warm extremes poleward, and hence systematic deviations from zero skewness on either side of the baroclinic zone [as hypothesized by Ruff and Neelin (2012)]. This of course follows directly from the localization of the advecting systems within the storm track latitudes—for an advecting field exhibiting homogeneous turbulence, we might still get the above asymmetry from the temperature advection from the eddies at a given latitude, but this latitudinal separation of warm and cold extremes would be counteracted by a similar effect of eddies just to the north and south. In contrast, in nature, only at the storm track center will temperature advection yield an unskewed distribution, as only here are temperature anomalies of either sign equally strong.
Finally, we have linearized the model to only integrate the advection of the zonal mean temperature gradient 
To highlight the importance of the poleward movement of the sea level pressure anomalies for warm anomalies, we have modified the model to allow for time dependence for the y component of the equation describing the streamfunction. Specifically, y in Eq. (3) is replaced by 
Overall, the key point is that 1) temperature anomalies quantitatively similar to those in the dry general circulation model can be captured by the relatively simple temperature advection model, and 2) the temperature advection model can explain the meridional displacement of temperature anomalies relative to the storm track axis.
As in Fig. 9 but in which the streamfunction propagate southward at a constant rate of 34 km h−1, such that the total southward movement over the 36 h is 1224 km or 11°.
Citation: Journal of Climate 30, 2; 10.1175/JCLI-D-15-0806.1
It is important to note that the temperature advection model is missing several important processes for the generation (and weakening) of temperature extremes in nature. For example, diffusional and radiational processes present in reanalysis data and in the dry model but not in this simple advection model will slow the growth of the extreme. In addition, the advective field is entirely deterministic while there is subsynoptic stochastic variability in the advective field in nature, and this additional stochasticity could modulate the skewness. Furthermore, vertical motion in response to horizontal temperature advection will also act as a negative feedback in many cases as well (Konrad and Colucci 1989; Walsh et al. 2001; Bieli et al. 2015), and this process is also not included in the simple advection model. On a related note, we are assuming that the wind field is fixed in time and independent of the temperature anomalies, but temperature anomalies and potential vorticity anomalies are inextricably linked and hence the relative vorticity (i.e., the horizontal winds) must change in order to satisfy potential vorticity conservation. Finally, there is no zonal propagation of the ridge–trough couplet in this model while in reality the zonal wind field may lead to faster propagation of the couplet (depending on the steering level) than for the individual air parcels within the boundary layer. These caveats noted, the horizontal temperature advection model distills the synoptic evolution evident in the dry model into its (likely) essential components, and thus serves as a simple explanation for the behavior in reanalysis data and in the dry model. Specifically, two days of horizontal temperature advection is sufficient to generate temperature extremes displaced meridionally several hundreds of kilometers from the largest anomalies in, say, geopotential height, and thereby induce nonzero skewness.
d. Summary
In summary, a simple model of temperature advection can describe important features of the evolution of extreme events in the dry model, including the time over which they develop, the meridional extent of the temperature advection, and the magnitude of the extreme temperature anomaly. Specifically, 48 h of continual temperature advection over a long meridional fetch propagating equatorward (for cold anomalies) or poleward (for warm anomalies) can homogenize temperatures over 25° meridionally and lead to temperature anomalies of 20 K or more displaced off the storm track axis. The covariance of meridional wind anomalies with temperature anomalies at large spatial and long temporal scales, as well as the fact that the eddies are localized in latitude, is crucial.
6. Discussion
a. Mechanisms
This paper focuses on a specific pathway for the generation of skewed temperature distributions because this pathway is most closely motivated by our composites. However, (at least) three other pathways exist for the development of skewed PDFs, and we now briefly discuss them.
Geometric effects: One might argue that it is more difficult to get warm extremes of the same magnitude on the equatorward side of a given zonal band as on the poleward side simply because the difference in mean temperature between the subtropics and the equatorward flank of a given zonal band is smaller. The same follows for the poleward side with relation to cold extremes: if the area is already among the coldest in the hemisphere, advection or any other process simply cannot cause an extreme deviation from the mean to occur. While such a process is certainly important and contributes to the skewness, nonzero skewness is found less than 5° from the jet and storm track axis, and is not limited to polar or tropical latitudes. In addition, we still find meridional displacement of maximum temperature anomalies even with a uniform temperature gradient across the integrated domain in the simple Lagrangian advection model from section 5c. We focus on a subtly different effect: meridional displacements are localized to a latitude range, and so warm anomalies will be strongest at its poleward edge and cold anomalies will be strongest at its equatorward edge.
Nonuniform temperature gradients: An additional means to generate skewness is to have a nonuniform meridional temperature gradient: if advection is along a large enough distance to “see�? these nonuniformities, then it will matter if the advection to a given latitude originated from a more poleward or equatorward latitude, with the corresponding anomalies being larger for those air parcels crossing the region with the sharper meridional temperature gradient. However, a nonuniform temperature gradient is not a necessary condition for a skewed distribution, as even with a uniform meridional temperature gradient in the simple Lagrangian advection model cold and warm extremes still develop on opposite flanks of the region with largest variance.
Multiplicative noise: Sardeshmukh et al. (2015) argue that skewed distributions of daily weather anomalies can be accounted for if their evolution is perturbed by stochastic noise whose amplitude increases linearly with anomaly amplitude, but asymmetrically for positive and negative anomalies. While the mechanism of Sardeshmukh et al. (2015) is more general in that it can be applied to atmospheric variations other than temperature, we adopt a more synoptic perspective for surface temperature variations motivated by the evolution in Figs. 7 and 8.
Our interpretation—that meridional winds over several days that are consistent in magnitude and move in phase with a subtropical or subpolar air mass lead to asymmetric temperature extremes and skewness—differs from the mechanisms listed above; it relies upon the asymmetry between poleward and equatorward advection due to the localization of atmospheric turbulence in the storm tracks. Thus, theoretical derivations that assume a given spatially homogeneous (or near-homogeneous) turbulent flow field cannot capture this effect, as the length scale of our advection is comparable to the characteristic meridional length scale of the large-scale flow. Neelin et al. (2010) also noted the ability of advection to lead to skewed distributions of atmospheric trace gases.
It is important to emphasize that the estimated probability distribution function of temperature variations is skewed even if we bandpass filter to focus on time scales of 15 days or less. Consistent with this, the time scale over which temperature extremes develop is several days (Figs. 7 and 8), as the synoptic processes necessary to generate extreme temperatures must persist for several days or the resulting temperature anomaly will not be extreme. Hence, a statistical treatment of temperature extremes should explicitly represent the short-term persistence inherent in temperature variations (even though the serial autocorrelation of temperature variations is small; e.g., Newman et al. 2010) and not assume that temperature variations from one day to the next are independent.
It is interesting to note that in the reanalysis data, extremes of either sign on the equatorward flank of the storm track occur more often than would be expected from a Gaussian (Fig. 1) due to the leptokurtic nature of the distribution—the blue curve (equatorward flank of the storm track) lies above the black curve (a representative Gaussian) in Figs. 1c and 1e. However, this effect is not present higher in the troposphere (cf. Fig. 8 of Perron and Sura 2013) and is not simulated by the dry model (Fig. 4). The following simple reasoning might explain this behavior. The PDF of pooled anomalies will generally be non-Gaussian, typically with an exponential tail, if the PDFs at the individual points are Gaussian with different variances (Frisch and Sornette 1997). As the variance at individual longitude grid points differs in the reanalysis data but not in the dry model, it is reasonable to expect longer tails (in both directions) for reanalysis data. This explanation is bolstered by the fact that tails are shorter (and the excess kurtosis closer to zero) when we consider each grid point individually. However, the skewness behavior on which we focus is present regardless of whether we pool the anomalies in a given zonal band or consider each grid point individually (not shown). We therefore focused our attention on the third moment of the distribution—the skewness—in this work.
We intentionally limited our dry model integrations and our temperature advection model to cases in which there is no large-scale zonal temperature gradient (i.e., no imposed 
b. Climate change
We intentionally limited the scope of this study to the processes building the tails of the temperature PDF in a fixed climate, to allow for a focused examination of the impact of horizontal temperature advection on the temperature PDF. Thus, by design our study does not address this question: How will the tails of the temperature PDF change in the future with global warming? However, these findings have implications for changes in future extreme temperature events. The subpolar NH is expected to warm faster than the rest of the Northern Hemisphere and skewness is expected to increase in subpolar high latitudes as well (Ballester et al. 2010; Donat and Alexander 2012). As the distribution of near-surface temperature is already positively skewed in the present climate in these regions due to its location poleward of the midlatitude baroclinic zone, the impact of these changes in temperature on extreme events may be less than had such a change occurred elsewhere (cf. Fig. 2 and surrounding discussion).
A second implication for climate change is that storm tracks are projected to shift poleward under climate change in most regions and seasons (Barnes and Polvani 2013). Hence, a given region in the vicinity of the storm track might have a change in the skewness properties of its regional temperature variations due to the processes described above. For example, a region near the present-day storm track core might be equatorward of the storm track core in the future as storm tracks move poleward, and hence experience stronger cold extremes than warm extremes relative to its new (warmer) climatological mean.
A third implication relates to the future frequency of extreme events themselves. While our focus in this paper was on the third moment of the temperature distribution, our model experiments demonstrate that the magnitude of extremes (i.e., temperature variance) is sensitive to two factors: the horizontal temperature gradient and the nature of the wind field advecting the isotherms. The first of these factors—the surface meridional temperature gradient—is projected to weaken, and hence in isolation this factor would lead to fewer and/or weaker surface extremes (Schneider et al. 2015; Screen 2014). For the second factor (long-lasting, strong surface wind anomalies in phase with temperature anomalies), the sign of future changes is not yet clear. If eddies became stronger under climate change and hence prolonged strong surface wind anomalies become more common, the reduction in temperature extremes could be partially compensated. However, evidence for changes in eddy intensity is mixed due to the large number of competing processes (Booth et al. 2013; Seiler and Zwiers 2016; Pfahl et al. 2015) may be misrepresented in coarse-resolution global models (Li et al. 2014; Willison et al. 2015) and may be region-specific (Zappa et al. 2013; Colle et al. 2013; Seiler and Zwiers 2016). Processes that can lead to stronger and more prolonged blocks (Sillmann and Croci-Maspoli 2009; Barnes et al. 2012; Dunn-Sigouin and Son 2013), or specifically that can lead to the meridional advection of the synoptic systems as identified herein, are even less certain. As extreme events are associated with an optimization of the meridional displacement of air parcels, even if storms do not strengthen but rather become more efficient in creating large meridional displacements, the weakening of the meridional temperature gradient could be offset. Exploring these climate change implications more fully is beyond the scope of this work, but it is clear that the synoptic evolution leading up to temperature extremes needs to be more carefully studied for both the present and future climate.
7. Conclusions
Extreme temperature events impact human society in many ways. Hence, it is crucial 1) to understand the climatological distribution of extreme events, including the nature of the temperature probability distribution function, and 2) to assess quantitatively how the distribution of extreme events changes with respect to jet and storm-track meridional position. While surface moisture and topographic effects are clearly important for temperature extremes, the goal of this paper is to isolate the synoptic contribution to temperature extremes. In particular, we relate the nature of the PDF of near surface temperature anomalies to the synoptic evolution of extreme events.
These aims are investigated in reanalysis data, in long integrations of a dry general circulation model, and in a quasilinear temperature advection model. An ensemble of experiments is performed in which the latitude of the storm track axis is set by varying the location of the midlatitude tropospheric baroclinicity while keeping the total equator-to-pole temperature difference constant. Specifically, eddy-driven jets are created from 30° to 54° latitude, which spans the latitudinal range of eddy-driven jets in Earth’s atmosphere. The distribution of extreme temperature events and the skewness of the temperature distribution are computed for each experiment. Similar statistics are computed for reanalysis data. While the dry general circulation model and the quasilinear temperature advection model are limited in the range of processes they can represent (including processes important for temperature extremes in nature such as surface moisture or snow cover anomalies), they serve as a useful first step toward a mechanistic understanding of the processes governing the shape of the temperature PDF.
The following conclusions can be drawn from this analysis:
Surface temperature variations are distinguishable from a Gaussian. A corollary of this is that approximating surface temperature variations as a Gaussian is erroneous. There is a systematic difference between skewness on the poleward flank and equatorward flank of the storm track, with differences present less than 5° from the midlatitude storm track maximum.
Cold and warm temperature extremes tend to occur on the equatorward and poleward flanks of the storm track respectively. This effect is consistent with the difference between the skewness on the poleward and equatorward flanks of the storm track.
The apparent source of this behavior can be traced back to the synoptic evolution leading up to temperature extremes: extremes occur when air is meridionally advected over tens of degrees in a region with a large climatological temperature gradient (i.e., in the storm track). After an extreme event has developed there is no meridional temperature gradient over a region that extends ~25° straddling the region in which the temperature gradient is largest climatologically. Quasilinear horizontal temperature advection is of crucial importance for this homogenization, and is also responsible, along with the localization of eddies within the storm track, for the occurrence of warm extremes preferentially poleward of the storm track axis yet cold extremes preferentially equatorward of the storm track axis. The meridional movements of the systems accelerates the formation of the extremes and thus regulates the magnitude of the extreme; understanding (with the hope of predicting) this meridional movement merits future work.
Acknowledgments
Modeling runs were performed at NCAR. CIG was supported by the Israel Science Foundation (Grant 1558/14). NH was supported by the Israel Science Foundation (Grant 1537/12). Part of the work of NH was supported by a Rossby Visiting Fellowship from the International Meteorological Institute of Stockholm. We also acknowledge GOAT (Geophysical Observation Analysis Tool; http://www.goat-geo.org) for the visualization of data. The authors thank Jonas Nycander for insightful discussions and the three anonymous reviewers for their constructive comments.
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These properties of the skewness are evident whether we pool all longitudes together before calculating the skewness (as is done in Fig. 1) or whether we compute the skewness of each longitude grid point separately and compute the zonal mean [not shown, but see e.g., Fig. 3a of Petoukhov et al. (2008)].
There are two experiments, with storm track axis near 46° and 48°S, in which the skewness, surface temperature gradient, and distribution of extremes all jump discontinuously. For these experiments, 
Note that at 850 hPa the mean zonal wind is 7 m s−1, thus matching the phase speed and leading to optimal phasing between the large-scale flow and individual air parcels. Future work with a feature-tracking algorithm is needed to more closely assess the most relevant level, although we expect that adiabatic warming through descent contributes to the extreme, and thus the air parcel likely originated above the surface and therefore experienced stronger zonal winds. The focus in this work is on horizontal advection, rather than vertical motion, and thus quantifying this effect is deferred to a future study.
Note that our wind field is deterministic; adding a stochastic component to the wind field could lead to skewness even in this situation.