This study presents a detection scheme for upper-tropospheric jets. The scheme identifies locations on the dynamical tropopause where the wind shear perpendicular to the wind direction vanishes, and subsequently uses a masking criterion to filter out zero-shear locations that do not belong to jets. The scheme reliably detects jet axes in ERA-Interim data with instantaneous, weekly, or monthly averaged wind fields. The dynamical implications of the detected jet axes and their relation to objectively detected wave breaking and blocking are demonstrated for the synoptic evolution during the boreal winter 2013/14. This winter featured a remarkable episode with a stationary ridge–trough couplet over the American continent leading to anomalously cold conditions from central Canada to the eastern United States. The mean synoptic situation during this episode resembles the climatological winter mean, but featured a more spatially focused jet axis distribution in the northeastern Pacific. The tight distribution suggests that a sequence of similar weather events lead to the mean synoptic conditions. Although the distribution of jet axes and wave breaking events together with the persistence of the anomalous ridge over the northeastern Pacific indicate a blocked situation, the block is not detected with common conventional methods due to the lack of a persistent gradient reversal of potential temperature on the dynamical tropopause. In addition, the importance of subseasonal variations in this winter is demonstrated by pointing out a period in which the jet configuration deviated considerably from the seasonal mean.
Jet streams are often identified using a wind speed threshold that defines the perimeter and hence the body of a jet stream (e.g., Koch et al. 2006; Strong and Davis 2007). Such identification schemes often detect large coherent areas as one jet body, thereby obscuring the existence of multiple wind speed maxima within one body. For example, in the winter snapshots in Figs. 2b and 2c of Koch et al. (2006), almost all visible wind maxima are encompassed by only one jet body that covers considerable parts of the Northern Hemisphere. The detection of such comprehensive jet bodies contrasts with typical subjective analyses that would identify a number of distinct jets in these snapshots. Furthermore, the choice of a particular wind speed threshold is somewhat arbitrary because it does not correspond to a fundamental change in the flow characteristics. To alleviate these shortcomings, we follow and extend the idea of Berry et al. (2007) to identify jet streams based on their axes.
Jet axes are an important aspect of the wind structure within jet bodies, because they can be related to at least two dynamical concepts describing the interplay between jets, blocking, and wave breaking. First, the location of the jet axis separates areas of preferential cyclonic and anticyclonic wave breaking, because the type of shear shapes the development of baroclinic disturbances (e.g., Davies et al. 1991) and determines the dominant type of wave breaking (Thorncroft et al. 1993; Rivière 2009; Barnes and Hartmann 2012). Second, the jet axis marks the line of maximum wind speed and is hence associated with a steep gradient in relative and potential vorticity (PV). This gradient constitutes a waveguide that determines the propagation and interaction of Rossby waves (Hoskins and Ambrizzi 1993; Martius et al. 2010). Furthermore, the PV gradient across a jet axis can become so steep that it approaches a discontinuity, leading Dritschel and McIntyre (2008) to view the associated meridional PV profile as a step in a “PV staircase.” Dritschel and McIntyre (2008) show that these steps play an important role in jet stream dynamics, acting as a barrier that is largely resilient toward mixing by eddies.
We apply these concepts to shed new light on the development and decay of the pronounced ridge–trough couplet over the northeastern Pacific and the North American continent that dominated the winter 2013/14. This couplet led to severe drought conditions in California, while the eastern United States experienced record-breaking low temperatures (e.g., Wallace et al. 2014). Nevertheless, climate variability indices like the Pacific–North American pattern (PNA) or the West Pacific pattern (WP; Barnston and Livezey 1987) do not show significant deviations during the peak intensity of the couplet in January 2014.1 Baxter and Nigam (2015) point out strongly negative values for their combined North Pacific Oscillation–West Pacific pattern index (NPO–WP) during December 2013 and February 2014, months that are also significantly negative in the WP time series. While there is some indication that sea surface temperature (SST) anomalies in different parts of the North Pacific played a role in establishing the couplet, their relative importance compared to other influences, such as decreasing sea ice cover and atmospheric internal variability, is still under debate (Hartmann 2015; Seager et al. 2015; Lee et al. 2015; Seager and Henderson 2016; Sigmond and Fyfe 2016).
The discussion of the winter 2013/14 in the aforementioned papers is largely based on seasonal anomalies and thus disregards subseasonal variations. Davies (2015) bridges this gap by linking the synoptic evolution of individual weather systems during this winter with the seasonal anomaly. In establishing this link, Davies (2015) argues for an important role of the jet stream as a waveguide that steers the movement of the individual weather systems, and hence determines the location of the anomalies in the seasonal mean. The analysis infers the jet location from a seasonal mean, namely, the region of strongest geopotential gradients. We refine this analysis using instantaneous detections of the jet location and analyze the interaction between weather systems and the waveguide on shorter time scales.
Recent studies have proposed several potential diagnostics for the jet location. Gallego et al. (2005) track the meridional distance between pairs of contour lines of the circumpolar streamfunction at 200 hPa, and identify jets using the minimum average distance between all considered pairs of contour lines. The Gallego et al. (2005) scheme requires jets to be circumpolar and thus cannot account for their discontinuous nature. For zonal or temporal mean fields, Barnes and Hartmann (2010), Athanasiadis et al. (2010), and Woollings et al. (2010) infer mean jet axes using local maxima in the meridional profiles of the zonal wind. The latter approach works well for smooth mean fields. When applying it to instantaneous data (e.g., Manney et al. 2014), it tends to fail due to the more complex structure of the wind field. Furthermore, meridionally oriented sections of a jet cannot be detected with this approach.
Berry et al. (2007) introduced a scheme that does not suffer from any of these restrictions. Based on Hewson (1998), they detect finite-length jets of any orientation from instantaneous data to study African easterly jets. They use the fact that the wind shear changes sign across the jet axis, which is also reflected in a sharp gradient in the orientation of deformation across the jet axis (Spensberger and Spengler 2014). While the Berry et al. (2007) scheme performs well for African easterly jets, its value has not yet been demonstrated for upper-tropospheric jet streams. The main aim of this study is to adapt the Berry et al. (2007) scheme for upper-tropospheric jet detection and to demonstrate its value as a diagnostic for large-scale dynamics by pinpointing features in the synoptic evolution of the boreal winter 2013/14 that previously went unnoticed.
We use 6-hourly ERA-Interim data at resolution for the period 1979–2014 obtained directly from the European Centre for Medium-Range Weather Forecasts (ECMWF; Dee et al. 2011). For jet detection, we use the level of the dynamical tropopause, defined as the surface where PV is m2 s−1 K kg−1 = 2 PVU (1 PVU = 10−6 K kg−1 m2 s−1) (Hoskins and Berrisford 1988; Berrisford et al. 2007). We analyze the wind velocity components on the dynamical tropopause, because upper-tropospheric jet streams at all latitudes are most pronounced at this level, allowing us to detect both subtropical and eddy-driven jets (e.g., Peixoto and Oort 1992; Winters and Martin 2016).
We compare the detected jet axes with wave breaking and blocking measures. The wave breaking detection is based on the Rivière (2009) contour tracking algorithm, applied to isentropic contours on the 2-PVU surface between 280 and 380 K in 5-K intervals. The algorithm identifies wave breaking by locating sections of the given set of contours that are horizontally overturning, and determines the type of wave breaking by the orientation of the contour. For the blocking detection, we use the two-dimensional schemes of Schwierz et al. (2004) and Masato et al. (2012), which identify persistent PV anomalies in the upper troposphere, and persistent regions of reversed potential temperature gradients on the 2-PVU surface, respectively.
3. Jet axis detection
The jet detection scheme is based on wind shear σ in natural coordinates,
where the shear is the projection of the total wind speed gradient onto the direction perpendicular to the wind direction. Here where u and υ are the zonal and meridional wind components on the 2-PVU surface, respectively, and is the unit vector in the vertical. Hewson (1998) and Berry et al. (2007) refer to σ as shear vorticity. Following Berry et al. (2007), the location of the jet axes must fulfill the following criterion:
We identify these locations by first looking for neighboring grid points with opposing signs in σ and then using linear interpolation between the grid points to determine the exact location where the zero-shear criterion is fulfilled.
However, not all zero-shear locations belong to jet axes. Wind speed minima also fulfill the criterion, and not all wind speed maxima are part of a jet. Weak wind speed maxima or those occurring at low absolute wind speeds should not necessarily be considered part of a jet. To filter these out, an additional masking criterion is necessary.
To this end, Berry et al. (2007) imposed two separate masks: one to filter out wind speed minima by requiring and another to filter out low wind speed areas by requiring a minimum wind speed. An obvious way to revise their scheme for upper-tropospheric jets would be to adapt the wind speed threshold to a value commonly used for detecting jet bodies (e.g., 30 m s−1) (Koch et al. 2006).
This approach, however, leads to questionable jet detections in areas that exceed the wind speed threshold, but lack a well-defined internal structure, like over eastern Asia and the northwestern Pacific in Fig. 1c. The lack of a clear internal structure is also illustrated by the frequent small-scale meanders of the jet axes in these regions.
For this reason, we instead require the wind maximum to be both well defined and at comparatively high wind speeds. These requirements can be summarized by the criterion
using the negative threshold K. In essence, the criterion applies a threshold for the product of wind speed U and shear-gradient . The criterion allows wind speed maxima to become less well defined with increasing wind speed. For lower wind speeds, the threshold does not cut off the jet axes at a certain wind speed, but traces the zero-shear line for as long as it follows a well-defined wind speed maximum. The term in (3) does not change the overall effect of the criterion, but improves the detection for asymmetric jets. The minimum in does not coincide with the jet axis, but is offset from the wind speed maximum to the side of larger wind shear (Fig. 2a). The term improves the detection by reducing this offset.
An undesirable property of our masking criterion (3) is that it emphasizes small-scale structures, because it involves a second derivative. These small-scale structures impair the detection of large-scale jets as they result in a rather noisy mask field. As a remedy, we apply a triangular truncation at wavenumber 84 (T84) to the input wind velocity components before evaluating both (1) and (3). At this resolution, the overall shape of the jet bodies is largely retained compared to the full ERA-Interim resolution, but meso- and smaller-scale features are removed (see the synoptic situation at 1200 UTC 5 November 2013 in Figs. 1c and 1d).
The detection procedure generally also works for unfiltered wind data (Fig. 1d). However, the detection procedure becomes less robust because well-defined wind maxima on larger scales can be obscured by smaller-scale variations, such as tropopause folds. Tropopause folds lead to discontinuities in the wind and temperature distribution on the PV2-surface, which are considerably damped by the T84 filtering. Without filtering, the reduced robustness of the detection scheme leads to a reduced temporal coherence of the detected jet axes (not shown). The reduced robustness is also seen in the example in Figs. 1c and 1d, where the jet over Nova Scotia is only detected using filtered data. While this comparison indicates that T84 is an appropriate resolution for the purposes of this study, different spectral cutoffs might be appropriate for other applications.
Figures 1a and 1b illustrate the detection procedure. For instantaneous data, we identified s−2 as a suitable threshold by subjectively evaluating the scheme in many different weather situations and different seasons. Relaxing the threshold allows us to trace existing jet axes farther into weak wind areas, but also leads to new detections in the Arctic, increasingly picking out wind structures that would generally not be considered jets. Figure 1b highlights all areas fulfilling the masking criterion and marks zero-shear locations within and outside these areas with yellow and gray dots, respectively.
Figure 3 compares our mask definition to the Berry et al. (2007) scheme in a two-dimensional histogram over wind speed and shear gradient that is based on all grid points containing zero-shear locations in the T84-filtered dataset. With , our masking criterion is equivalent to such that our masking threshold takes the form of a hyperbola in this histogram. Regions A and B in Fig. 3 satisfy the criteria used by the Berry et al. (2007) scheme, whereas regions A and C satisfy our masking criterion. Region C corresponds to zero-shear locations at low wind speeds where we are able to detect weak jets with well-defined wind maxima using our scheme. Meanwhile, region B corresponds to zero-shear locations at comparatively high wind speeds where the Berry et al. (2007) scheme detects strong but diffuse jets, often with zero-shear lines that meander on small scales (e.g., Fig. 1c).
The zero-shear locations that fulfill the masking criterion, referred to as “likely jet locations,” must be connected to form continuous jet axis lines. First, we identify the neighbors of each likely jet location using a search radius of 1.5 grid points (i.e., 0.75°) for the ERA-Interim data used in this study. This yields connected neighborhoods of likely jet locations (two such neighborhoods are shown in Fig. 2b). Identifying the jet axis in each neighborhood is not straightforward because some likely jet locations have more than two neighbors, resulting in more than one possible path for the jet axis. We calculate the shortest path for all combinations of likely jet locations within each neighborhood using the Floyd–Warshall algorithm (Floyd 1962; Warshall 1962). Of these shortest paths, the longest is the one that most efficiently connects the two likely jet locations farthest away from each other. These locations are thus the start and end points of the jet axis within this neighborhood (Fig. 2b). As an alternative to this algorithm, the jet axis lines may be identified by tracking relevant parts of the zero-shear contour (Hewson 1998). Finally, as we are only interested in synoptic- and larger-scale features, we require a minimum jet axis length of km.
The outlined detection scheme can easily be adapted to time-averaged wind data. With longer time averages, wind maxima become increasingly broad. Therefore, we need to adapt the threshold K to reflect the decrease in . The threshold for the instantaneous data corresponds to the 87.5th percentile of . We use this percentile to generalize the threshold definition of K for the time-averaged wind data. Figure 4 shows the resulting climatological jet axis frequency distribution for winter (December–February) based on 6-hourly data, as well as weekly, monthly, and seasonally averaged data. The adapted threshold K based on the general percentile-based definition is indicated in the lower-right corner of each panel.
With this adaptation of the threshold, jet axes tend to become longer as the averaging period increases (not shown). This tendency reflects the reduced spatial variability of the jet on longer time scales, which is also apparent in the tighter distribution of jet axes frequency (Fig. 4). Thus, as the averaging period increases, we lose information on more transient excursions of the jet such as those that would occur during wave breaking. Despite this, the maximum jet axis frequency remains consistent with the jet axis location based on the multiyear winter average wind field in all panels (white line), demonstrating that the scheme works reliably on different types of input data up to seasonal averages.
4. Synoptic evolution during the winter 2013/14
In the following, we discuss the synoptic evolution in the Pacific–North American sector during the boreal winter 2013/14, which featured a stationary trough over the eastern United States leading to record-breaking cold temperatures and severe snowstorms in this region (Wallace et al. 2014; Davies 2015). From inspection of the synoptic evolution over the North Pacific and North American sectors from December 2013 to February 2014, we identify two distinct periods: 16 December 2013–28 January 2014 and 28 January–22 February 2014 (Fig. 5). Our period definitions are supported by the NPO–WP index in Baxter and Nigam (2015), which is close to zero during our first period, and strongly negative during the second (their Fig. 4a). The mean synoptic conditions during the first period are similar to the seasonal mean for the entire winter as shown in Davies (2015), whereas the second period clearly deviates from the seasonal average.
Figure 6a shows a snapshot for 0000 UTC 15 January 2014, where the pronounced trough that led to the anomalously cold conditions in large parts of the eastern United States is evident. To the west of the trough, an equally pronounced ridge is visible both through the anomalously warm tropopause temperatures in the northeastern Pacific and from the wind speed showing a diversion of the main jet far north, up to Alaska. The ridge marks the abrupt exit of an otherwise almost zonal jet over the Pacific (Fig. 6b). To the south of the ridge, a second jet is present at subtropical latitudes stretching from the Pacific coast of Mexico into the Gulf of Mexico.
The diversion of the Pacific jet toward Alaska and the double-jet structure over the American continent indicate blocked flow over the northeastern Pacific. For a more rigorous test for blocking in this region, we use criteria suggested by Rex (1950) to objectively define a block. They are
an abrupt diversion of the westerly flow upstream,
a split of the westerly flow into two about equal branches,
a minimum zonal extend of the two branches of 45° longitude, and
a minimum persistence of 10 days.
Our instantaneous jet detections allow us to directly test for the Rex (1950) criteria. Based on the Rex (1950) definition of blocking, we would expect an abrupt transition from one zonal maximum in the jet axis distribution to a double-jet structure with an appreciable longitudinal extent. We expect the entire structure to persist for at least 5 days, implying little variance between the individual instantaneous jet detections during the life cycle of the block.
All these expectations are fulfilled for our first period 16 December 2013–28 January 2014 (Figs. 7c and 7d). Therefore, we interpret this synoptic situation as a blocked structure. In fact, the comparatively tight jet axis distribution and well-defined transition to a double jet structure in this six-week average indicates that the block persisted throughout our first period, by far exceeding even the Rex (1950) persistence threshold.
Furthermore, the distribution of wave breaking events agrees with the results of Altenhoff et al. (2008), with cyclonic wave breaking dominating over the North Pacific and anticyclonic wave breaking dominating over the western United States (Fig. 7c). The symmetric distribution of cyclonic and anticyclonic wave breaking on either side of the stationary ridge indicates that the block might be classified as an -type block (e.g., Barriopedro et al. 2010, and references therein).
However, using the Masato et al. (2012) scheme, no actual blocking is detected during these six weeks at the location of the ridge (Fig. 7c). The problem is not limited to this particular scheme because the lack of detected blocking stems from the lack of a persistent gradient reversal. No blocking detection scheme that requires a gradient reversal, no matter if based on potential temperature on the 2-PVU surface, PV on the -K potential temperature surface, or geopotential at 500 hPa, would classify this stationary ridge as a block, despite most other factors pointing toward a blocked situation. In contrast, the Schwierz et al. (2004) scheme, which identifies blocking by persistent PV anomalies, detects a block for the most intense period around 15 January 2014 (not shown).
This disagreement raises the question of whether a persistent gradient reversal is a necessary ingredient for blocking. The mean situation for 16 December 2013–28 January 2014 shows that a stationary ridge can exhibit most of the dynamical features that are typically associated with blocking even without reversed gradients. Furthermore, such a ridge can lead to the buildup of temperature extremes comparable to those of blocking events. In contrast, in areas like eastern Siberia where the gradient is very weak in the DJF climatology (Fig. 7a), the Masato et al. (2012) scheme detects blocks that are neither associated with a characteristic double-jet structure nor accompanied by wave breaking events, suggesting that different dynamical mechanisms are responsible for these gradient reversals.
Generally, the six-week average for the period 16 December 2013–28 January 2014 resembles the winter climatology for this region (Figs. 7a–d). The reduced potential temperature gradient and the wave breaking detections indicate a preferred location for ridging and wave breaking in the northeastern Pacific. Assuming that wave breaking is crucial for the maintenance of blocks or stationary ridges (e.g., as suggested by Spensberger and Spengler 2014), the overall similarity suggests that the enhanced frequency of wave breaking in its climatological mean location played an important role in maintaining the ridge–trough structure that lead to the anomalously cold conditions over the eastern United States. Furthermore, the tight jet axes distribution suggests that a sequence of similar weather events lead to the mean synoptic conditions, supporting the Davies (2015) analysis of the 2013/14 winter.
The ridge–trough couplet decays due to a vigorous and large-scale wave breaking event on 28 January (not shown). In the course of this event, subtropical air masses are advected northeastward along the North American west coast and up to the Beaufort Sea. This warm air mass reduces the meridional temperature gradient on the tropopause throughout the Pacific sector. Consistent with Dritschel and McIntyre (2008), the reduced temperature gradient allows for eddies to mix more effectively through the weakened PV barriers, resulting in a sequence of further wave breaking events at all longitudes in the Pacific (Figs. 7e,f). The synoptic situation from 0000 UTC 8 February in Figs. 6c and 6d depicts a snapshot from the cascade of further wave breaking events via large-scale jet meanders over the North Pacific and Arctic Ocean, where at least two jet axes are detected for each longitude throughout most of the Pacific.
The reduced potential temperature gradients persisted for about four weeks from 28 January to 22 February 2014 (Figs. 5 and 7e,f). During this period, jet axes and wave breaking events are more or less evenly distributed north of the strongest potential temperature gradient, suggesting that a dynamically different sequence of events led to the period average. This result supports the findings of Lee et al. (2015), who argue that natural variability was more important than an SST anomaly in the northeastern Pacific in the formation and maintenance of the ridge–trough couplet in our first period. While the SST anomaly persisted throughout our second period, the synoptic evolution followed a different pattern. Furthermore, this change in weather pattern over the Pacific sector was not associated with downstream changes over the Atlantic sector (not shown), as might be expected from the mechanism of Drouard et al. (2015).
In addition, our second period demonstrates that it can be misleading to infer typical jet locations from the location of the strongest geopotential gradients in the seasonal average (Fig. 1c of Davies 2015). During our second period, the jet axis distribution (Fig. 7f) follows neither the seasonal mean geopotential gradient nor the strongest period average potential temperature gradients (Fig. 7e). This discrepancy emphasizes the value of the instantaneous jet detections. In contrast to average geopotential or potential temperature, jet axis frequency maps depict all individual weather events, thereby providing a more direct link between events and averages.
5. Summary and conclusions
We adapted the Berry et al. (2007) algorithm for detecting African easterly jets to identify upper-tropospheric jet axes. Compared to Berry et al. (2007), our scheme can also identify weaker but well-defined jets. We demonstrate that our scheme reliably detects jets for a variety of input data ranging from instantaneous to seasonally time-averaged wind fields, with jet axes frequency distributions becoming tighter when using data averaged over longer time periods. The tighter distribution shows the reduced amplitude of jet meanders, which in turn leads to a straighter and more zonal jet on longer time scales. For predominantly zonal jets, our detection yields similar results compared to those based on meridional wind profiles (e.g., Woollings et al. 2010). However, for jet axes distributions based on instantaneous or short-term-averaged winds, our scheme has the ability to detect meridionally overturning jets as they occur in wave breaking events.
Using the jet axes in conjunction with objectively detected wave breaking and blocking events, we examined the synoptic evolution during the boreal winter season of 2013/14 in the Pacific–North American sector. We identified two periods featuring distinct weather patterns during that winter: 16 December 2013–28 January 2014 (43 days) and 28 January–22 February 2014 (25 days). The synoptic conditions during the first period featured an amplified ridge–trough couplet centered over North America, leading to anomalously cold conditions in the eastern United States, whereas the second period was characterized by a weaker jet, which meandered over large parts of the North Pacific sector.
The ridge over the northeastern Pacific in the first period is accompanied by the jet axis and wave breaking patterns characteristic of a blocked situation (e.g., Rex 1950; Altenhoff et al. 2008), but the Masato et al. (2012) scheme does not detect the block due to the lack of a persistent gradient reversal. Instead, the scheme detects blocking over eastern Siberia, which is not accompanied by the expected jet axis and wave breaking patterns. This comparison suggests that gradient reversals might not be a suitable indicator for wintertime blocking over the North Pacific. A potentially more suitable way to define blocking could be based on the strength and geographical extent of an anomaly rather than a gradient reversal in a pertinent field (e.g., Dole and Gordon 1983; Schwierz et al. 2004; Barriopedro et al. 2010). Irrespective of the blocking definition, our scheme can provide an independent method to test and visualize the characteristic deviation of the jet around a block.
In contrast to the first period, the second period differs considerably from both the winter climatology (Figs. 7a,b) and the mean winter conditions for 2013/14 (presented in Davies 2015). The ubiquitous jet meanders and wave breaking events over the North Pacific during this period yield a weak period-mean potential temperature gradient and a therefore not well defined period-mean waveguide. The jet meanders follow neither the strongest period-mean potential temperature gradient, nor the strongest seasonal mean geopotential gradient in Davies (2015), which illustrates the limitations of discussing waveguides based on period-mean fields.
Overall, our results show that jet axis distributions offer a valuable measure of mean jet position and variability, where a tight jet axis distribution indicates a persistence or sequence of similar transient weather events. A diffuse jet axis distribution, on the other hand, characterizes periods without a dominant synoptic pattern. As the jet axis distribution depicts both the mean and variability of the waveguide, it provides a refined, physically meaningful link between specific weather events and the average flow (or gradient) conditions over a certain period.
On even shorter time scales, our jet axes detections might also prove useful to study the interplay between jet streams and the evolution of individual cyclones. Jet streaks produce an ageostrophic circulation that leads to favorable conditions for cyclogenesis in their equatorward entrance and poleward exit regions (e.g., Holton and Hakim 2012). In addition, cyclones have been shown to rapidly intensify if they cross the jet axis from the warm to the cold side (Baehr et al. 1999; Wernli et al. 2002; Rivière et al. 2013). Instantaneous jet detections could help assess the relative importance of such processes in cyclone evolution, both climatologically and for specific cases.
We thank Elizabeth Barnes, Gwendal Rivière, and Tim Woollings for interesting discussions. We thank three anonymous reviewers, of which two were particularly constructive, for comments that helped to considerably improve the manuscript. We thank David Klaftenegger for pointing us to the Floyd–Warshall algorithm and Gareth Berry for the routine to find zero locations by linear interpolation. Finally, we thank ECMWF for providing the ERA-Interim data. The ERA-Interim data used in this study have been obtained directly through the Meteorological Archival and Retrieval System. This work was supported by the Research Council of Norway project jetSTREAM 231716.
Based on the monthly time series provided by the Climate Prediction Center of NOAA.