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    (a) Illustration of the displacement of a wavy 500-hPa zc (thick solid black line) with respect to its ϕe (thick dashed black line). In this specific example the contour zc(ϕe = 50°N) is shown for 13 Feb 1983, one of the strongest ridges observed over the Atlantic. The wavy contour zc encloses an area z500zc that is equal to the area found to the north of the equivalent latitude. By definition, the regions shaded in red and blue, used for the computation of LWAA and LWAC components of LWA, respectively, are also of equal surface area. The areas are not necessarily equal in this figure since only a subset of the NH is shown. The z500 is shown with colored lines at a contour interval of 100 m. (c) Values of LWAA (red) and LWAC (blue) computed at all equivalent latitudes are contoured with a contour interval of 0.5 × 108 m2. The ϕe = 50°N is shown again for illustrative purposes. (b),(d) As in (a),(c), but for QGPV300 using contour intervals of 1 × 10−4 s−1 for QGPV and 50 m s−1 for the wave activity.

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    Probability distribution of (a),(b) LWA and (c),(d) latitudinal-maximum LWA for (a),(c) winter (DJF) and (b),(d) summer (JJA). The PDF of LWA (solid lines), LWAA (dashed lines), and LWAC (dotted lines) are shown separately. In (c),(d), the 50th percentile of the distribution of LWA, used in the detection of wave events, is illustrated with vertical lines.

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    Frequency of wave events as a function of the threshold and minimum-duration parameters. The frequency is reported as the number of individual events, regardless of their physical size. Statistics are repeated for (a) winter (DJF) and (b) summer (JJA) separately. The color shading indicates the yearly occurrence of wave event using a logarithmic scale. Horizontal dotted lines indicate percentiles of the distribution of daily latitude-maximum LWA values. The median value (50%) reported here and used throughout this study is the same as shown in Figs. 2c,d.

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    Annual cycle of local wave activity in function of (a),(c) longitude and (b),(d) latitude. In (a),(c), LWA is averaged between 35° and 80°N. (a),(b) LWAA and (c),(d) LWCC are shown separately. The shaded contour interval is 0.25 × 108 m2.

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    The climatologies of (a),(b) EKE at 500 hPa, (c),(d) LWAA, and (e),(f) LWAC are shown in (left) winter (DJF) and (right) summer (JJA). Contours of EKE are shown every 25 (12.5) m2 s−2 in winter (summer). For wave activity, color shading illustrates the mean wave activity while gray lines show its standard deviation. Winter and summer use shaded contour intervals of 0.25 × 108 m2 and 0.125 × 108 m2, respectively. The average latitude of local latitudinal-maximum LWA in the Northern Hemisphere is shown with a green contour encircling the globe.

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    Comparing the frequency of (a) reversal events, (b) wave events, (c) anticyclonic wave events, and (d) cyclonic wave events in winter (DJF). The frequency of events is computed as the fraction of the time that a grid point is affected by an event and is shown with a contour interval of 5%. The north–south-oriented black lines illustrate the reference longitudes used later to perform composites of wave events and compute statistics over four sectors representing peak wave event frequencies.

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    Cumulative frequency of (a) anticyclonic and (b) cyclonic wave events in function of the minimum duration in DJF. The frequency is computed by counting the number of events that last for at least a specific number of days. Events are classified according to their respective sectors as indicated in each panel. Events located within 80° longitude of the reference longitude (see Fig. 6) are counted as being part of a given sector. Linear regressions of the logarithmic distribution of frequency are illustrated for the short-duration regime (1–4 days) and long-duration regime (5–14 days) according to ln[N(τ)] = −τ/τ0 + ln[N(0)], where N(τ) is the number of events lasting τ days or longer. The parameter τ0 is shown in the legend.

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    Composite evolution of anticyclonic wave events crossing the 355°E meridian in DJF. (a),(c),(e) Color shading illustrates z500 anomalies with an interval of 50 m while gray contour lines illustrate the absolute z500 field with a contour interval of 100 m. The anomalous frequency of reversal events is illustrated with purple contour intervals every 10%. Zonally oriented dashed lines indicate the latitude used for the Hovmöller diagrams shown in Fig. 12. (b),(d),(f) The T850 anomalies are shown with color shading every 2 K. The increase in the likelihood of cold and warm temperature extremes is shown using green and red contours. Only doubling and quadrupling of the probability of extremes are contoured. Only the 50 strongest events are used in the composite to match the number of events found over Alaska (see Fig. 9). The total number of events found over the European region is shown in the bottom-left corner.

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    As in Fig. 8, but for anticyclonic wave events crossing the 215°E meridian.

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    As in Fig. 8, but for cyclonic wave events crossing the 150°E meridian.

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    As in Fig. 8, but for cyclonic wave events crossing the 285°E meridian.

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    (a)–(d) Hovmöller diagrams illustrating the composite of z500 anomalies (shading) and T850 anomalies (contours) as a function of longitude and time for wave events occurring over different sectors in DJF. Negative and positive anomalies are shown with blue and red shading for geopotential height at an interval of 20 m and black and gray contours for temperature at a contour interval of 1 K. Vertical and horizontal black lines denote the reference longitude and the central date of the events, respectively.

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    Difference in wave event frequency between the positive and negative phases of (top)–(bottom) major climate indices in DJF. Frequency differences are contoured every 2.5% using red and blue for positive and negative values, respectively. Shown separately are for (left) anticyclonic and (right) cyclonic wave events. Significant differences, using a bootstrap resampling method described in section 2, are stippled in regions where differences exceed 2.5%. Composite difference of z500 between positive and negative phases is shown with solid and dashed black lines every 20 m for positive and negative values, respectively.

  • View in gallery

    Interannual variability of wave event frequency using total LWA (see Fig. 6b) in DJF over (a)–(d) different sectors and (e) the Northern Hemisphere. The meridional extent of each sector is delimited as illustrated by the black lines in Fig. 6. The longitudinal extent is 50° wide, centered on the black lines shown in Fig. 6. The frequency is computed as the fraction of the area that is under the influence of a wave event for a given winter (DJF). The frequency is computed for wave events detected using various thresholds (colors; see also Fig. 3) and the threshold used throughout this paper (black; see Fig. 2). Recent trends (1990–2015) in wave event frequency are evaluated. The p value is reported at the bottom of each panel. Statistically significant trends are shown using solid lines (p ≤ 0.05).

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Wave Events: Climatology, Trends, and Relationship to Northern Hemisphere Winter Blocking and Weather Extremes

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  • 1 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California
  • 2 Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York
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Abstract

Diagnostics of finite-amplitude local wave activity (LWA) are applied to the 500-hPa geopotential height field to diagnose persistent synoptic weather events of anomalously large wave activity in the Northern Hemisphere. By considering the cyclonic and anticyclonic components of LWA separately, persistent weather systems associated with large-amplitude troughs and ridges are detected. While anticyclonic wave events are predominantly found over Europe and Alaska, cyclonic wave events usually occur over East Asia and northeastern Canada. Those preferred regions correspond to the location of planetary-scale ridges and troughs, which contribute, together with transient anomalies, to the formation of wave events. Although wave events are not blocking events per definition, they are typically associated with increased blocking in their vicinity. Their spatial relationship to blocking, however, varies depending on their cyclonic or anticyclonic nature and the type of wave-breaking signatures. Wave events are also shown to be accompanied by warm or cold temperature extremes, whose spatial pattern depends on the type of events, cyclonic or anticyclonic, and the sector affected. Trends in the frequency of wave events indicate that cyclonic wave events and the associated cold extremes affecting East Asia have become more frequent in recent decades and could be linked to recent trends toward La Niña–like conditions in the Pacific and trends toward the negative phase of Arctic Oscillation.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Patrick Martineau, pmartineau@atmos.ucla.edu

Abstract

Diagnostics of finite-amplitude local wave activity (LWA) are applied to the 500-hPa geopotential height field to diagnose persistent synoptic weather events of anomalously large wave activity in the Northern Hemisphere. By considering the cyclonic and anticyclonic components of LWA separately, persistent weather systems associated with large-amplitude troughs and ridges are detected. While anticyclonic wave events are predominantly found over Europe and Alaska, cyclonic wave events usually occur over East Asia and northeastern Canada. Those preferred regions correspond to the location of planetary-scale ridges and troughs, which contribute, together with transient anomalies, to the formation of wave events. Although wave events are not blocking events per definition, they are typically associated with increased blocking in their vicinity. Their spatial relationship to blocking, however, varies depending on their cyclonic or anticyclonic nature and the type of wave-breaking signatures. Wave events are also shown to be accompanied by warm or cold temperature extremes, whose spatial pattern depends on the type of events, cyclonic or anticyclonic, and the sector affected. Trends in the frequency of wave events indicate that cyclonic wave events and the associated cold extremes affecting East Asia have become more frequent in recent decades and could be linked to recent trends toward La Niña–like conditions in the Pacific and trends toward the negative phase of Arctic Oscillation.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Patrick Martineau, pmartineau@atmos.ucla.edu

1. Introduction

Midlatitude extreme weather events such as heat waves and cold spells have, without any doubt, large financial and societal impacts. A better knowledge of the preferred locations for the occurrence of weather extremes and their trends and a better understanding of their regional impact on weather is therefore of prime importance. A well-known circulation pattern that can lead to such extremes, the blocking event, is a synoptic-scale phenomenon that blocks the jet stream, resulting in unusually persistent weather. Atmospheric blocking has received attention for many decades (Rex 1951) and is still very much a topic of actuality because of its relationship to extreme weather such as heat waves (Black et al. 2004; Dole et al. 2011; Matsueda 2011; Pfahl and Wernli 2012) and cold spells (Sillmann and Croci-Maspoli 2009; Buehler et al. 2011). Pfahl and Wernli (2012), for instance, have noted that a substantial fraction of warm temperature extremes in the Northern Hemisphere summer are ascribed to the collocated presence of atmospheric blocking. On the opposite, Buehler et al. (2011) have shown European temperatures to be colder than usual in winters with enhanced blocking occurrence. This interest for blocking events has led to the development of many detection methods and their variations in the literature [see Barnes et al. (2012) and Barriopedro et al. (2010) for in-depth summaries of blocking detection methods]. They are often classified in two broad categories whether they rely on an absolute field, such as the meridional reversal of geopotential height or potential vorticity (PV) gradient, which is indicative of a reversal of the zonal flow (Tibaldi and Molteni 1990; Pelly and Hoskins 2003), or an anomalous field, such as geopotential height anomalies (Dole and Gordon 1983; Nakamura et al. 1997), which is used to identify flow configurations characterized by a large-amplitude anticyclonic anomalies. The advantages and inconveniences of these identification methods are still subject to debate, and new hybrid methods that rely both on the absolute and anomaly fields have also been designed to address deficiencies (Barriopedro et al. 2010; Dunn-Sigouin et al. 2012). Because of differences between definitions, blocking climatologies have nonnegligible differences among themselves (see Fig. 7 of Barriopedro et al. 2010), but there is a general tendency for blocking climatologies to present a dipole affecting the North Atlantic–Europe and North Pacific regions as well as Greenland in definitions using flow reversal (Woollings et al. 2008; Masato et al. 2013a).

Francis and Vavrus (2012) have recently hypothesized that a rise in the incidence of extreme weather in recent decades is due to an increase in the amplitude of the jet’s meanders and increased frequency of blocking events resulting from the Arctic amplification: the accelerated wintertime warming of the Arctic as a result of the melting of sea ice (Serreze et al. 2009). This study subsequently sparked a large interest toward the development of new measures to quantify the waviness of the jet stream. The original analysis of Francis and Vavrus (2012) made use of the northward extent of contours of geopotential height at 500 hPa within each season to suggest an increase in the amplitude of the jet’s meanders. However, it is shown that such a method is sensitive to artifacts related to the choice of isopleths and is affected by the poleward migration of isopleths with warming polar temperatures (Barnes 2013). With respect to the frequency of blocking events, blocking indices do not agree on a positive trend of their frequency (Barnes et al. 2014).

Other than quantifying waviness using the meridional extent of contours, the length of isopleths has also been examined. Röthlisberger et al. (2016a) have considered the meridional component of the length of contours of PV and shown that the variations in the jet waviness captured by this measure is related to local weather extremes (Röthlisberger et al. 2016b). While taking care of reducing artifacts associated with the choice of isopleth, Cattiaux et al. (2016) have proposed sinuosity, a measure of the length of isopleths, to quantify the waviness. Only a slight wintertime increase in waviness during recent decades is observed using this method and is mainly attributable to the Atlantic and Pacific sectors. Di Capua and Coumou (2016) have also investigated trends of a meandering index computed using the length of isopleths. They have observed the largest increase in meandering occurring in fall with the largest contribution from the Eurasian sector. About the prognostics, the sinuosity diagnostic of Cattiaux et al. (2016) suggests a reduction of the waviness simulated by CMIP5 models due to climate change, which is consistent with the projected decrease of the frequency of blocking events (Masato et al. 2013b; Lee and Ahn 2016) and the reduction of daily meridional wave extent (Barnes et al. 2014).

Besides trends in blocking and meandering of the jet due to anthropogenic forcing, interannual variability is also observed in connection with major modes of variability. Blocking events over the Atlantic have been linked to the North Atlantic Oscillation (NAO) (Croci-Maspoli et al. 2007; Woollings et al. 2008). Similarly, the Pacific–North American (PNA) pattern is also tied to blocking in the Pacific (Croci-Maspoli et al. 2007). The meandering index of Di Capua and Coumou (2016) exhibits a statistical relationship with the Arctic Oscillation (AO), with greater midlatitude waviness associated with the negative polarity of the AO. Slower modes of climate variability of oceanic origin are also linked with the frequency of blocking over a decadal time scale (Hakkinen et al. 2011).

Although the aforementioned methodologies that rely on the meridional extent or the elongation of isopleths are useful to evaluate global or regional changes in the meanders of the jet stream, they lack the ability to identify true local features. Also, they do not take into account the strength of the anomalies that are considered in Eulerian diagnostics of waviness (e.g., Screen and Simmonds 2013; Coumou et al. 2015). It could be potentially misleading to use measures that are based solely on contour elongation as proxies of extreme weather that depend on the intensity of local anomalies. In fact, Screen and Simmonds (2013) have shown that the two types of measures could disagree concerning trends. Recently, Huang and Nakamura (2016) have proposed local wave activity (LWA) as a potential diagnostic of local wave anomalies and blocking events. LWA is a generalization of the finite-amplitude wave activity (FAWA) theory (Nakamura and Zhu 2010; Nakamura and Solomon 2010, 2011; Chen and Plumb 2014) into its local counterpart, quantifying waviness as a function of latitude and longitude, and is capable of measuring regional disturbances in the atmospheric circulation. The LWA framework has the advantage of having a dynamical basis, as opposed to the aforementioned diagnostics of blocking or jet meandering. Also, as explained in detail later, this new diagnostic takes into account not only the meridional displacement of PV contours but also the enclosed anomalies, which are ignored in the diagnostics of waviness discussed earlier. A form of LWA based on 500-hPa geopotential height instead of PV has also been proposed by Chen et al. (2015) and shown to be a useful quantity for the diagnosis of midlatitude extreme weather, such as cold spells, heat waves, and blocking events, which may be triggered by atmospheric blocking. The use of 500-hPa geopotential heights over PV is motivated by the need of a simpler diagnostic comparable to previous metrics of flow waviness (Francis and Vavrus 2012; Barnes 2013; Di Capua and Coumou 2016) and easily applicable to models of various vertical and horizontal resolution for which the computation of PV is sensitive, and for climate model archives that may not provide all variables necessary to compute PV. Concerning trends in waviness, Chen et al. (2015) found significant positive trends of LWA in recent decades over the North Atlantic, East Asian, and Pacific sectors, all linked to a reduction of upper-tropospheric wind.

To further explore the relationship between the jet’s meanders, blocking events, and weather extremes, this work extends the methodology proposed in Chen et al. (2015) by carrying a comprehensive detection and climatology of extreme weather events using LWA. Here the anticyclonic and cyclonic components of LWA, which allow the identification of pronounced troughs and ridges disturbing the 500-hPa geopotential height field, are considered separately. The climatology of LWA is first shown in the winter and summer seasons using reanalysis data. Wave events are then defined as extreme values of the cyclonic and anticyclonic components of the LWA. We stress the fact that wave events, as they are defined here, do not necessarily block the flow per their definition and therefore represent a wider spectrum of extreme events than the widespread wind-reversal (or wave-breaking) definition of a blocking event. A tracking algorithm, inspired by Masato et al. (2012), is devised to track events in time and to produce a comprehensive climatological record. Using composite methodology, the evolution of wave events is investigated with an emphasis on their impact on the midtropospheric flow and lower-tropospheric temperature extremes. The link between atmospheric blocking and wave events is also investigated, with particular attention to their spatial relation and wave-breaking characteristics. Finally, the relationship between the incidence of wave events and major climate indices, as well as trends in the frequency of wave events over the recent decades, is investigated.

In section 2, the local wave activity and the detection of wave events are described. Climatologies of LWA and wave events are then presented in section 3. The life cycle of wave events is then presented in section 4. Section 5 analyzes recent trends of the occurrence of wave events and the relationship between wave events and major climate indices. Main conclusions are finally given in section 6.

2. Methodology

a. Data

This study uses the ERA-Interim (ECMWF 2009; Dee et al. 2011) data from 1979 to 2015. The variables used include geopotential height on the 500-hPa level z500 and the temperature on the 850-hPa level T850. Quasigeostrophic potential vorticity at 300-hPa QGPV300 is computed here as , where θ is potential temperature, f is the Coriolis parameter, ζ is the relative vorticity, and p is pressure. The tilde over a variable denotes hemispheric mean. The variables are available at a 1.5° × 1.5° horizontal resolution. All results shown are based on daily averages. All computations and figures are also performed using MERRA (NASA 2009; Rienecker et al. 2011) without discernible sensitivity (not shown).

b. Local wave activity

This work quantifies LWA using z500, which has been used extensively to diagnose weather extremes in the troposphere (Dole and Gordon 1983; Barriopedro et al. 2010; Masato et al. 2013b; Dunn-Sigouin et al. 2012; Hassanzadeh et al. 2014; Chen et al. 2015). The variable z500 is usually monotonically decreasing from the equator to the pole in the Northern Hemisphere, which allows the use of LWA diagnostics to quantify the deformation of the flow by wave activity. The computation of wave activity relies on the definition of the equivalent latitude, which provides a monotonic relationship between a given geopotential height contour zc and its reference equivalent latitude ϕe. The equivalent latitude is defined as
e1
where z is the geopotential height, λ is the longitude, and ϕ is the latitude. By definition, the latitude ϕe encloses an area extending from ϕe to the pole that is equivalent to the area over which z is smaller than the contour zc [see Fig. 1 of Nakamura and Solomon (2010) or Fig. 1 of Huang and Nakamura (2016)]. The relationship between ϕe and zc is illustrated in Fig. 1 for the contour zc that corresponds to an equivalent latitude of 50°N. The area to the north of ϕe is equal to the area where z is smaller than the wavy zc contour illustrated. This, by definition, divides the areas where to the north of ϕe and to the south of ϕe, illustrated in red and blue, respectively, into two equal areas when summed around the Northern Hemisphere. The relationship between zc and ϕe is evaluated at each time step, which means that wave activity evaluated at a given equivalent latitude is not affected by the northward migration of geopotential height contours associated with global warming or its seasonal variations.
Fig. 1.
Fig. 1.

(a) Illustration of the displacement of a wavy 500-hPa zc (thick solid black line) with respect to its ϕe (thick dashed black line). In this specific example the contour zc(ϕe = 50°N) is shown for 13 Feb 1983, one of the strongest ridges observed over the Atlantic. The wavy contour zc encloses an area z500zc that is equal to the area found to the north of the equivalent latitude. By definition, the regions shaded in red and blue, used for the computation of LWAA and LWAC components of LWA, respectively, are also of equal surface area. The areas are not necessarily equal in this figure since only a subset of the NH is shown. The z500 is shown with colored lines at a contour interval of 100 m. (c) Values of LWAA (red) and LWAC (blue) computed at all equivalent latitudes are contoured with a contour interval of 0.5 × 108 m2. The ϕe = 50°N is shown again for illustrative purposes. (b),(d) As in (a),(c), but for QGPV300 using contour intervals of 1 × 10−4 s−1 for QGPV and 50 m s−1 for the wave activity.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

The LWA is then defined as
e2
LWA consists of anticyclonic LWAA and cyclonic LWAC components that are summed together. They are described, respectively, as follows in the NH:
e3
where is an eddy quantity defined as = zzc. The line integrals of LWAA and LWAC, in Eq. (3), are delimited by contours of zc and ϕe (see areas shaded in red and blue in Fig. 1a). The total length of the line integrals of LWAA and LWAC are equal when integrated around the Northern Hemisphere (Huang and Nakamura 2016) since, as mentioned earlier, the red and blue areas shown in Fig. 1 are equal by the definition of equivalent latitude.

By definition, is positive and negative over the red and blue regions found to the north and south of ϕe, respectively. For instance, z > zc over the red region related to the prominent ridge over Europe seen in Fig. 1. Similarly, z < zc over the blue region associated to a cutoff cyclone over Spain. Therefore, LWAA and LWAC as defined here are positive quantities (note minus sign in the definition of LWAC) that quantify anticyclonic and cyclonic anomalies, respectively. Consequently, their sum [Eq. (1)], which represents the total wave activity, is always positive. Although LWA provides a comprehensive measure of local wave activity, it is useful to consider LWAA and LWAC separately to investigate the cyclonic or anticyclonic nature of local anomalies. The two quantities are illustrated in Fig. 1c. While prominent ridges correspond to large values of LWAA (see over Europe in Fig. 1 for instance), troughs are accompanied by large values of LWAC (see cutoff low over Spain in Fig. 1). Signatures of wave breaking, observed as a reversal of the meridional geopotential height gradient (overturning of the zc contour), are accompanied by collocated positive values of LWAA and LWAC. Despite the fact that the zc contour shown in Fig. 1a does not overturn, some contours to the south show a clear blocking signature over Europe. Although this feature could be used to detect blocking events that result in a reversal of the westerly flow, it is not investigated further in this work.

This form of LWA applied on geopotential height can be thought of as a hybrid method bridging the gap between wave amplitudes measured as departures from zonal symmetry (e.g., Screen and Simmonds 2013; Coumou et al. 2015) and methods that investigate the meridional displacement (Francis and Vavrus 2012; Barnes 2013) or elongation (Cattiaux et al. 2016; Di Capua and Coumou 2016) of geopotential height contours. In the computation of LWA, both the meridional displacement of contours and the strength of the zonal anomalies are taken into account, providing a more robust measure of waviness.

As mentioned earlier, this work quantifies LWA using geopotential height at 500 hPa instead of upper-tropospheric QGPV (Huang and Nakamura 2016). The use of z500 allows a better comparison with other measures of wave activity using the same variable (Francis and Vavrus 2012; Barnes 2013; Cattiaux et al. 2016; Di Capua and Coumou 2016). The computation of LWA using z500 and QGPV300 is contrasted in Figs. 1b,d. The contours of z500 and QGPV300 are associated with the same reference latitude (ϕe = 50°). Overall, the deformation of the contours has similar large-scale features between the two quantities, while QGPV300 tends to capture smaller-scale features in comparison to z500. The two contours show prominent anticyclonic areas over Europe and cyclonic areas over Spain. Comparing the resulting wave activity further reveals qualitatively similar large-scale features between the two methods (Figs. 1c,d). The prominent anticyclonic wave activity over the Atlantic and the presence of cyclonic wave activity over Spain resulting in the blocked flow configuration are found in both LWA applied on z500 and LWA applied on QGPV300. This supports the fact that the local wave activity applied on the geopotential height field can adequately capture large-amplitude troughs and ridges and may therefore be useful to quantify the waviness when an exact relationship between wave activity and wave activity fluxes is not of prime importance. As a matter of fact, the two quantities are relatively well correlated in the midlatitudes (r ≈ 0.6; not shown). The correlation may be limited by differences in the noise and amount of finescale structures between the geopotential height and potential vorticity fields and vertical tilts in the wave structures.

c. Detecting wave events

Chen et al. (2015) illustrated that midlatitude extreme weather events are associated with unusually large LWA, which suggests that this metric could potentially be used to identify these events. This approach is used here to define extreme wave events by looking for values of LWA that exceed a specific threshold. This threshold should ideally be based on the observed distribution of LWA in the Northern Hemisphere and should not be sensitive to the domain over which statistics are taken. Since LWA, as shown later in section 3, is typically maximized in the midlatitudes, a robust and domain-independent method to evaluate the distribution of LWA consists of identifying maximum LWA values at each longitude. Since the median value of the distribution of the meridional maximum of LWA is a robust climatological feature, it is used here as a threshold to define wave events.

The probability distribution of LWA is first illustrated in Fig. 2. It resembles an exponential function where the likelihood of observing a specific magnitude of wave activity decreases for larger values. This is due to the fact that large areas of weak wave activity are found at the pole and the subtropics (discussed in more detail in section 3). The distribution is very sensitive to the spatial domain as the extension of the boundary toward the equator adds a substantial amount of small LWA values to the distribution. Concerning the seasonality, there is a shift in the distribution from larger LWA to weaker LWA between winter and summer, reflecting the overall weaker summertime wave activity.

Fig. 2.
Fig. 2.

Probability distribution of (a),(b) LWA and (c),(d) latitudinal-maximum LWA for (a),(c) winter (DJF) and (b),(d) summer (JJA). The PDF of LWA (solid lines), LWAA (dashed lines), and LWAC (dotted lines) are shown separately. In (c),(d), the 50th percentile of the distribution of LWA, used in the detection of wave events, is illustrated with vertical lines.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

On the other hand, the distribution of the meridional maximum of LWA sampled at each longitude grid around the Northern Hemisphere shows a clear peak in the distribution. Small LWA magnitudes are infrequent since only the maximum values of LWA are picked at each longitude, thereby excluding the small LWA found over large sections of the Northern Hemisphere. An exception is found in the LWAC, which peaks at small wave activities in comparison to LWAA or the total LWA. This is partly explained by the existence of two regions, around 0° and 120°W, where the meridional maximum is typically very small (shown later in section 3). The distribution of summer LWA shifts to weaker wave activity in comparison to winter, reflecting the reduced summertime wave activity. The median value of LWA, denoted hereafter by , is larger than the median of the individual components LWAC and LWAA.

To identify events, a Boolean array WE of the same horizontal dimension as the LWA field is defined as WE = LWA ≥ (the sensitivity of the detection algorithm to the threshold is investigated later in this section and in section 5). The WE field is equal to 1 when LWA values are above the threshold and 0 when it is below. To identify individual wave events, a connected component-labeling algorithm is used to identify and connect contiguous grid points where WE = 1. Each isolated contiguous area is stored as an individual wave event. To identify the precise coordinates of the wave event, the local maximum of LWA over the event is identified. The maximum value and its geographical coordinates are stored for each event.

To track and investigate the evolution of wave events in time, the wave events detected at individual time steps have to be connected. To connect them, the distances between each set of events over two time steps t and t + 1 are evaluated and stored as an array Dn(tn(t+1), where n represents the number of events at a given time. An algorithm then seeks to minimize the distance between pairs of events. This process ensures that past events are connected to only one event in the future and vice versa. In addition, two events are connected only if the distance separating them is less than 13.5° of latitude and 18° of longitude (Masato et al. 2013b). This criterion ensures that connected events are spatially related to each other and imposes a maximum displacement between two time steps.

In this work, only events with a certain amount of stationarity, similar to blocking events, are considered. The displacement of an event from its inception to a given time step D(t, t + k) is therefore limited to 1.5 × 13.5° latitude and 1.5 × 18° longitude (Masato et al. 2013b). This criterion is evaluated for each time step after the onset (k = 1, 2, …, n). When the maximum displacement criterion is exceeded, the event at time step t + k is defined as a new event from time t + k and after.

Finally, the persistence of events is evaluated. Events whose duration d is shorter than a chosen threshold dmin are discarded, and the contiguous area of the array WE defining this event is set to 0, effectively excluding the short-lived events from the statistics. Similar to blocking events, a minimum duration of 5 days is used in this work. This algorithm can be applied to the total LWA, but, later in this work, it is applied to LWAA and LWAC separately in order to track and differentiate events of large anticyclonic and cyclonic wave activity. The algorithm is also applied to the B array of Masato et al. (2013b) to evaluate the occurrence of blocking events that result in a reversal of the zonal circulation.

The frequency of wave events in the Northern Hemisphere is shown in Fig. 3 by applying the aforementioned algorithm to the total LWA. Its sensitivity is evaluated by varying the threshold (instead of using ) and dmin. Over large thresholds, the frequency of wave events decreases with increasing threshold and duration. The summer frequency is smaller but shows similar decrease with respect to the two parameters. Interestingly, at the long-duration end of the spectrum, the frequency of events increases as the threshold diminishes until it peaks at around the median values of meridional maximum wave activity. Then, the number of events subsequently decreases as the threshold diminishes. This feature may be partly explained by the merging of individual small-scale events as the threshold is lowered. Computing the frequency of events using the total area covered by wave events does not exhibit this feature. Although the number of wave events may be reduced by merging as the threshold is lowered, the areal fraction of the Northern Hemisphere covered by LWA events keeps increasing (not shown). In both winter and summer, (50th percentile) corresponds approximately to the peak frequency of wave events in the long-duration regime, avoiding the merging of individual events.

Fig. 3.
Fig. 3.

Frequency of wave events as a function of the threshold and minimum-duration parameters. The frequency is reported as the number of individual events, regardless of their physical size. Statistics are repeated for (a) winter (DJF) and (b) summer (JJA) separately. The color shading indicates the yearly occurrence of wave event using a logarithmic scale. Horizontal dotted lines indicate percentiles of the distribution of daily latitude-maximum LWA values. The median value (50%) reported here and used throughout this study is the same as shown in Figs. 2c,d.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

d. Temperature extremes

To quantify the impact of wave events on near-surface temperatures, we will consider in section 4 not only the composite-mean temperature anomalies but also the effect of wave events on the incidence of temperature extremes. The impact on temperature extremes is quantified by comparing the probability of temperature extremes in the upper and lower tails of the T850 distribution. Reference values are first defined using the 5th and 95th percentiles of the DJF temperature ( and , respectively) distribution at each grid point. Once the reference values are identified, the probability of observing temperature anomalies below and above those extremes are evaluated for a given time step of the composites of wave events. Then, the ratio of the probability of temperature extremes during wave events is taken with respect to the wintertime (DJF) probability:
e4
e5
where denotes the probability of temperatures being colder than in the wave events selected for the composite and denotes the probability of temperatures being colder than on any given winter day (5% by definition).

e. Composites with respect to climate indices

The relationship between the frequency of wave events and major climate indices such as the AO, the NAO, El Niño–Southern Oscillation (ENSO), and the PNA pattern is investigated using monthly time series obtained from the Physical Sciences Division of the NOAA/Earth System Research Laboratory.

For all winter-mean (DJF) climate indices, the composited difference in the occurrence of wave events is taken between their positive and negative phases. Here the positive and negative phases are defined as the highest and lowest 33% of the wintertime mean of each climate index sampled from 1979 to 2015. To evaluate the robustness of the differences in frequency, a bootstrap resampling method is used. Two random samples of DJF dates having the same size as the samples used to compute the real differences are taken randomly 1000 times. Frequency differences below or above the 2.5th and 97.5th percentiles of the randomly generated differences are regarded here as significant.

3. Climatology of local wave activity and wave events

The seasonal evolution of wave activity is illustrated in Fig. 4. The anticyclonic component of wave activity is more important in winter with maximum values around 0° and 150°W. Those regions of large wave activity attain their maximum amplitude in February and reach their minimum around September, also accompanied by an eastward shift. Their latitudinal distribution also shows a maximum in winter, with a peak around 70°N. In summer, zonally averaged LWA falls to within one-third of its winter amplitude and is marked by a reduction of wave activity in the midlatitudes.

Fig. 4.
Fig. 4.

Annual cycle of local wave activity in function of (a),(c) longitude and (b),(d) latitude. In (a),(c), LWA is averaged between 35° and 80°N. (a),(b) LWAA and (c),(d) LWCC are shown separately. The shaded contour interval is 0.25 × 108 m2.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

On the other hand, cyclonic wave activity is largest around 90°W and 130°E. Maximum wave activity is also achieved in the beginning of February and a decline in amplitude accompanied again by a slight eastward shift in the maximum is seen in the transition to summer months. The winter peak in LWAC is found southward of its LWAA equivalent (60°N) and is also seen to weaken considerably during summer months.

The winter and summer mean LWA is illustrated in more detail in Fig. 5. In winter, while LWAA is predominantly found over the United Kingdom and Alaska, LWAC shows larger values over northern Canada and the Sea of Okhotsk. This distribution of LWA corresponds to the winter location of stationary waves (Garfinkel et al. 2010; Martineau and Son 2015). The cyclonic and anticyclonic components of the climatology of wave activity are thus located at longitudes that correspond to the jet entrance and exit regions, respectively. This is not surprising as the North Atlantic and North Pacific jets exhibit a positive tilt that is set by stationary waves, the same waves responsible for setting the large-scale LWA structure. The extrema of eddy kinetic energy (EKE) at 500 hPa (Figs. 5a,b) computed as 0.5(υ2 + u2), where the prime denotes anomalies with respect to the mean along a latitude circle, clearly reflect the jet maxima in the Atlantic and Pacific. In winter, the jet entrance regions are located south of the climatological maximum of cyclonic wave activity over northern Canada and East Asia. The jets then extend to the northeast toward anticyclonic centers over Europe and Alaska. Those maxima in EKE are collocated with storm tracks measured using bandpass-filtered eddy fields (Chang et al. 2002). The mismatch between storm-track proxies and peaks in LWA climatology suggests that LWA primarily captures the large-scale features of the midlatitude flow instead of high-frequency, synoptic-scale variability.

Fig. 5.
Fig. 5.

The climatologies of (a),(b) EKE at 500 hPa, (c),(d) LWAA, and (e),(f) LWAC are shown in (left) winter (DJF) and (right) summer (JJA). Contours of EKE are shown every 25 (12.5) m2 s−2 in winter (summer). For wave activity, color shading illustrates the mean wave activity while gray lines show its standard deviation. Winter and summer use shaded contour intervals of 0.25 × 108 m2 and 0.125 × 108 m2, respectively. The average latitude of local latitudinal-maximum LWA in the Northern Hemisphere is shown with a green contour encircling the globe.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

The variability of wave activity follows closely its climatology, indicating an enhanced likelihood of observing extreme LWA over those same regions. In winter, the average latitude of the daily anticyclonic LWA maximum tends to shift southward over the same regions where it is strongest. It is also located to the north of the climatological maxima, indicating that the daily maxima in LWA are usually of larger amplitude when located to the south. On the other hand, the average latitude of the daily cyclonic LWA maximum is collocated with the climatological mean over East Asia and slightly southward of the climatological mean over northeastern Canada.

In summer, LWAA is much fainter and presents an elongated band around the polar region extending from 40°E to 130°W. Although weaker than in winter, LWAC shows two distinct maxima located over the Bering Strait and northeastern Canada. The overall weaker wave activity found in summer can be in part explained by the reduced amplitude of planetary-scale waves (Randel 1988) or weaker baroclinicity. Further investigation of wave activity in summer is left for future work.

The climatology of wave events, measured as the percentage of time that a geographical grid point is under the influence of a wave event, is illustrated in Fig. 6. Anticyclonic wave events present two distinct preferred regions. They occur most frequently over the western edge of Europe (25% of the time) with a maximum at around 55°N. A second less frequent center (15% of the time) is also found over Alaska. Those two centers correspond, as expected, to the climatological maxima of LWAA seen in Fig. 5. On the other hand, the preferred regions for the occurrence of cyclonic wave events are longitudinally out of phase with the anticyclonic events. They occur most frequently over East Asia (30% of the time) and less frequently over northeastern Canada (20% of the time).

Fig. 6.
Fig. 6.

Comparing the frequency of (a) reversal events, (b) wave events, (c) anticyclonic wave events, and (d) cyclonic wave events in winter (DJF). The frequency of events is computed as the fraction of the time that a grid point is affected by an event and is shown with a contour interval of 5%. The north–south-oriented black lines illustrate the reference longitudes used later to perform composites of wave events and compute statistics over four sectors representing peak wave event frequencies.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

Wave events may also be detected using the total LWA without using the anticyclonic and cyclonic components separately (Fig. 6b). The frequency of those events is roughly similar to the sum of the frequency of LWAA and LWAC events, suggesting that wave events largely result from either prominent anticyclonic or cyclonic activity alone. However, the contribution of the two components is not excluded, especially when wave breaking occurs (see, e.g., Fig. 1). It is also interesting to note that cyclonic events over East Asia and the anticyclonic events over Alaska become indistinguishable when identifying events using the total LWA, thus losing important information on the nature of the events.

The relationships between cyclonic and anticyclonic wave events and reversal events, often used as an indicator of atmospheric blocking (Masato et al. 2013b), are also investigated. Regions where reversal events typically occur include a wide band of relatively low frequency over Europe and two centers in the high latitudes, over Baffin Island–Greenland and Siberia (Davini et al. 2012; Masato et al. 2013b). Although qualitatively similar, differences in frequency with respect to previous studies may be attributed to differences in the tracking methodology, which appears to be more stringent in this work. As noted in Chen et al. (2015), the spatial distribution of wave events bears strong similarity to the reversal events. Relationships between the different types of events will be discussed further in the next section.

Following Pelly and Hoskins (2003), the persistence of wave events occurring over different sectors is investigated. However, instead of using Eulerian statistics as is the case in the sector-blocking events of Pelly and Hoskins (2003), we consider the persistence of individual events, regardless of their physical extent or displacement. Anticyclonic and cyclonic wave events are first classified into different sectors. The centers (reference longitudes) of these sectors are shown using meridionally oriented black lines in Figs. 6c,d. Each sector spans all latitudes from the equator to the pole with a longitudinal extent of 160° centered on the reference longitudes. The number of individual wave events is shown on a log scale in function of minimum duration in Figs. 7a,b. The persistence of events is evaluated using the simple model of block persistence proposed in Pelly and Hoskins (2003). The characteristic time scale τ0 is computed for two different regimes: from 1–4 days and 5–14 days. The τ0 is obtained from a linear fit of the natural log of the probability distribution of events lasting longer than a minimum duration τ, denoted as N(τ), according to the linear model ln[N(τ)] = −τ/τ0 + ln[N(0)]. The τ0 is related to the proportion α of event lasting one more day [α = N(τ + 1)/N(τ)] by τ0 = −1/lnα. The larger τ0 is, the more likely it is that an event will persist. European events are characterized by a τ0 of 3.9 in the short-duration regime and 4.4 in the long-duration regime. In comparison, events over Alaska display a τ0 of 3.2 and 3.8 in the short- and long-time-scale regimes, respectively. Cyclonic events are characterized by a τ0 of 3.2 (2.4) over the East Asian (northeastern Canada) sector in the short range and 3.7 (3.3) in the long range. Those results differ from the blocking events considered in Pelly and Hoskins (2003), who show greater difference in persistence between the short-and long-lived events. Several factors may explain differences with respect to their analysis, including the Lagrangian approach used in our study and the characterization of events by a large amplitude of wave activity rather than a reversal of the meridional circulation. Nonetheless, wave events, similar to blocking events, are characterized by an enhanced persistence in the long-duration part of their probability distribution.

Fig. 7.
Fig. 7.

Cumulative frequency of (a) anticyclonic and (b) cyclonic wave events in function of the minimum duration in DJF. The frequency is computed by counting the number of events that last for at least a specific number of days. Events are classified according to their respective sectors as indicated in each panel. Events located within 80° longitude of the reference longitude (see Fig. 6) are counted as being part of a given sector. Linear regressions of the logarithmic distribution of frequency are illustrated for the short-duration regime (1–4 days) and long-duration regime (5–14 days) according to ln[N(τ)] = −τ/τ0 + ln[N(0)], where N(τ) is the number of events lasting τ days or longer. The parameter τ0 is shown in the legend.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

4. Life cycle of wave events

The detection algorithm of wave events described in section 2 provides statistics about events throughout their lifetime and allows one to characterize their motion in time. To classify events according to their location in the Northern Hemisphere and provide a reference for the composite analysis, we define the reference time t0 of an event as the date during which the center of the event crosses predefined reference longitudes for four sectors. Those longitudes are illustrated as meridionally oriented black lines in Fig. 6. The reference longitudes correspond approximately to the maxima in the frequency of wave events (Figs. 6c,d) and the maxima in the climatology and variance of LWA (Figs. 5c,e). As illustrated in Fig. 6, the reference longitudes are of finite meridional extent. The meridional extent is chosen to be approximately centered on the region where the tracks of LWA events are more frequent (not shown). We note that this latitude span is not perfectly collocated with the maximum in blocking frequency measured using Eulerian statistics: the local maxima of LWA used to define the center of wave events are not necessarily located at the centroid of the area defining the event. Limiting the range of latitudes over which wave events are sampled helps to preserve finer details in the composite averages. For the composites, only events of a minimum duration of 5 days are considered, similar to the minimum duration criteria used in the definition of blocking events (Pelly and Hoskins 2003; Tibaldi and Molteni 1990).

By using a reference time t0 that is defined when a wave event crosses the reference longitude of each sector, composites that are performed at t0 have a strong geographical identity since all events are aligned on the reference longitude. However, composites performed at negative or positive lags may suffer from a spread in the geographical location of the events. Despite this drawback, this composite method has the advantage of presenting the evolution of wave events relative to the climatological features of the atmospheric circulation and allows one to identify the regional impact that wave events have on weather.

The aforementioned procedure of selecting wave events yields 113 events over Europe, 50 events over Alaska, 198 events over East Asia, and 110 events over northeastern Canada. Those numbers reflect the different frequencies of wave events typically found over those sectors (Fig. 6). However, only the 50 strongest events of each sector are included in the composites, which allows the comparison of events of similar return frequency. Results are not overly sensitive to the number of events used in composites. As expected, signals are weaker, but qualitatively similar, when including all events detected.

We first proceed to illustrate the evolution of anticyclonic wave events. The European anticyclonic wave events (Fig. 8) initially display positive z500 anomaly over the Atlantic. The anomaly attains its maximum amplitude slightly northwest of the United Kingdom at t0. At this time, the frequency of reversal events is enhanced to the south and slightly upstream of the geopotential height anomaly, collocated with the meridional reversal of the z500 contours. After t0, the z500 anomaly keeps moving to the east together with the region of meridional gradient reversal. The anticyclonic character of the wave breaking seen in the European wave events is consistent with the predominance of the anticyclonic-type reversal events in this region (Davini et al. 2012; Masato et al. 2012). Here, it is important not to confound the terminology of anticyclonic wave breaking used in Masato et al. (2012), which results from clockwise intertwining of a ridge to the west and a trough to the east, and the anticyclonic nature of the event used in this work, which refers to the prominence of an anomalous ridge, regardless of the direction of wave breaking. The latter is analogous to the cold (trough) and warm (ridge) events of Masato et al. (2012). Over the European sector, wave events are anticyclonic as per our definition as they are characterized by transient ridges that enhance the planetary-scale ridge. Concerning their impact on temperature extremes, European wave events are characterized by temperature anomalies transiting eastward in time, similar to the geopotential height anomalies. In the course of the events, the likelihood of warm extremes is quadrupled over the United Kingdom and Scandinavia. These events are also marked by cold temperature anomalies and extremes over southern Europe with a twofold increase of their probability. This warm-over-cold pattern is similar to the signature of European blocking events (Rex 1951; Masato et al. 2014).

Fig. 8.
Fig. 8.

Composite evolution of anticyclonic wave events crossing the 355°E meridian in DJF. (a),(c),(e) Color shading illustrates z500 anomalies with an interval of 50 m while gray contour lines illustrate the absolute z500 field with a contour interval of 100 m. The anomalous frequency of reversal events is illustrated with purple contour intervals every 10%. Zonally oriented dashed lines indicate the latitude used for the Hovmöller diagrams shown in Fig. 12. (b),(d),(f) The T850 anomalies are shown with color shading every 2 K. The increase in the likelihood of cold and warm temperature extremes is shown using green and red contours. Only doubling and quadrupling of the probability of extremes are contoured. Only the 50 strongest events are used in the composite to match the number of events found over Alaska (see Fig. 9). The total number of events found over the European region is shown in the bottom-left corner.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

Anticyclonic wave events over Alaska (Fig. 9) are more stationary than the European events. In the composite, an anomalous ridge sits over Alaska. While a trough is present over eastern Siberia at the beginning of the event, another trough develops over continental North America after t0. Opposite to the European events, Alaskan events are accompanied with an enhancement of reversal-type events to the west at t0, where the reversal of the meridional gradient of z500 tends to occur. This results from a cyclonic intertwining of the ridge over Alaska and the trough over eastern Siberia. This cyclonic wave-breaking tendency is also consistent with blocking statistics over that region (Davini et al. 2012; Masato et al. 2012). The cyclonic wave-breaking signature is, however, short lived and is replaced by a weak increase of reversal-type events to the south of z500 anomalies at t3. Temperature anomalies that are associated with the wave events over Alaska are more stationary and again are well aligned with geopotential height anomalies. Warm anomalies are accompanied by a fourfold increase in the likelihood of warm temperature extremes over Alaska. The events over Alaska also have a broad impact on temperatures over the continental United States and Canada in the form of large cold temperature anomalies and up to a fourfold increase in the probability of cold extremes.

Fig. 9.
Fig. 9.

As in Fig. 8, but for anticyclonic wave events crossing the 215°E meridian.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

Moving to cyclonic events, the wave events occurring over East Asia (Fig. 10) are characterized by eastward-traveling anomalies over the jet region. When those anomalies reach about 150°W, the frequency of reversal events is enhanced over eastern Siberia, north of the negative geopotential height anomalies. Contrary to the anticyclonic events, the reversal region is located to the north of the jet. It is therefore analogous to the high-latitude blocking (Berrisford et al. 2007; Woollings et al. 2008). Those events, unlike the anticyclonic ones, are not characterized by strong wave-breaking signatures in our composites. The cyclonic wave events of East Asia are initially accompanied by cold weather over eastern China, moving progressively over Japan, enhancing the likelihood of cold temperature extremes.

Fig. 10.
Fig. 10.

As in Fig. 8, but for cyclonic wave events crossing the 150°E meridian.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

Cyclonic events occurring over northeastern Canada (Fig. 11) are more stationary than their East Asian counterparts. In the early stage of the events, a prominent ridge is present over the west coast of North America. A low z500 anomaly develops over northern Quebec and leads to enhanced high-latitude reversal event frequency over northern Canada and Greenland (Davini et al. 2012), although no clear wave-breaking signature is observed. The composite shows that the hemispheric minimum z500 is located over northeastern Canada at t0, suggesting that a southward displacement of the polar temperature minimum is frequent in these events. The cyclonic wave events that occur over northeastern Canada are characterized by a broad sector of cold anomalies and a fourfold increase in the likelihood of cold temperature extremes over eastern Canada. They also tend to be accompanied by warmer weather along the North American west coast, leading to a twofold increase in the frequency of warm extremes.

Fig. 11.
Fig. 11.

As in Fig. 8, but for cyclonic wave events crossing the 285°E meridian.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

The longitudinal motion of the geopotential height anomalies at 500 hPa and temperature anomalies at 850 hPa in the composites of selected wave events over each sector is summarized in Fig. 12. The anomalies are averaged over 10°-wide latitude bands centered on the latitude belts illustrated with dashed black lines in Figs. 811. Those latitudes represent approximately where the largest anomalies are found. The anticyclonic wave events over Europe show a rapid displacement of positive geopotential height anomalies toward the east over time from day −5 to 5. Longer-lasting and weaker anomalies are also found from day 5 to 10. This could suggest that the European wave events result from a combination of the strengthening of the planetary-scale waves and the passage of transient anomalous ridges due to Rossby wave propagation (Altenhoff et al. 2008), which align at around t0 to produce large positive z500 anomalies. The negative geopotential height anomalies surrounding the positive anomaly, moving eastward at a similar speed, are also indicative of the presence of a Rossby wave train.

Fig. 12.
Fig. 12.

(a)–(d) Hovmöller diagrams illustrating the composite of z500 anomalies (shading) and T850 anomalies (contours) as a function of longitude and time for wave events occurring over different sectors in DJF. Negative and positive anomalies are shown with blue and red shading for geopotential height at an interval of 20 m and black and gray contours for temperature at a contour interval of 1 K. Vertical and horizontal black lines denote the reference longitude and the central date of the events, respectively.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

The anticyclonic wave events over Alaska show opposite motion. The events appear to be initiated by a trough at around 160°E–170°W, which transits westward in time. Positive geopotential height anomalies do not form until day −5 and appear more or less stationary until day 5 when the anomaly center accelerates toward the west. Negative geopotential height anomalies are observed from day 0 and onward to the east of the positive anomalies and undergo a similar displacement.

The cyclonic wave events over East Asia are characterized by negative geopotential height anomalies with an eastward phase speed that is similar to the European events. On the other hand, the cyclonic wave events over northeastern Canada are more persistent than their Asian counterpart but nonetheless show a signature of eastward displacement. These events also show precursor positive height anomalies over Alaska, possibly indicative of the eastward propagation and amplification of a Rossby wave train.

From Figs. 812, we observe that temperature anomalies at 850 hPa are to a large extent collocated with z500 anomalies in all sectors suggesting that the events are largely barotropic in nature. Nonetheless, some amount of vertical tilting is observed and is especially evident in the events over Alaska, where lower-tropospheric warm anomalies are clearly located to the west of z500 anomalies at t0 (Fig. 12b).

Although the spatial relationship between wave events and reversal events depends on the type of event (anticyclonic or cyclonic) and on the geographical location of the events as discussed earlier (Figs. 811), all events are accompanied by enhanced blocking of the zonal flow in their vicinity. The anticyclonic events affecting Europe show the greatest enhancement in the frequency of reversal events (up to 30%, in addition to the climatology of about 5%). On the other hand, the anticyclonic events affecting Alaska enhance reversal events by about 10% (from a climatology of about 20%–25%). An asymmetry also exists between cyclonic events affecting sectors over East Asia and northeastern Canada. The earlier are more strongly linked with reversal events (30% anomaly) in comparison to the latter (20% anomaly). Those differences in the relationship between wave events and blocking amid the different sectors may result from a geographical dependence of the interaction between transient anomalies and the stationary features of the flow. It does not appear, however, that the strength of anomalies plays a major role. For instance, the events affecting East Asia have relatively weak geopotential height anomalies in comparison to the events affecting northeastern Canada and yet bring a larger increase in reversal frequency. The anomalies of events affecting Europe and Alaska are of similar magnitudes but have a very different impact on the incidence of blocking. This suggests that the alignment of the anomalies with respect to the stationary wave and the strength of stationary waves are important to produce a reversal of the zonal flow.

5. Interannual variability and trends

The dominant modes of variability are known to be linked to the frequency of blocking in the midlatitudes (Croci-Maspoli et al. 2007; Woollings et al. 2008; Davini et al. 2014). Here, we investigate how the frequency of wave events is modulated by the major climate indices such as the AO, the NAO, ENSO, and the PNA pattern.

A stronger AO is typically accompanied with enhanced anticyclonic wave event frequency over southern Europe and reduced frequency over Iceland, representing a southward shift of the typical latitude of wave events (Fig. 13). A small reduction in frequency is also seen over eastern Siberia. Cyclonic wave events experience reduced frequency over the northern part of their East Asian sector. On the other hand, an increase in the frequency of cyclonic events can be observed over northern Canada. Those changes are overall consistent with the regression pattern of local wave activity on the AO (Chen et al. 2015).

Fig. 13.
Fig. 13.

Difference in wave event frequency between the positive and negative phases of (top)–(bottom) major climate indices in DJF. Frequency differences are contoured every 2.5% using red and blue for positive and negative values, respectively. Shown separately are for (left) anticyclonic and (right) cyclonic wave events. Significant differences, using a bootstrap resampling method described in section 2, are stippled in regions where differences exceed 2.5%. Composite difference of z500 between positive and negative phases is shown with solid and dashed black lines every 20 m for positive and negative values, respectively.

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

The NAO’s impact on the frequency of wave events over the Atlantic is similar to the AO, although the dipole pattern is oriented more to the west in the former. Overall, the effect of the AO and/or NAO on the incidence of anticyclonic wave events bears resemblance to the effect of NAO on blocking events over the Atlantic (Croci-Maspoli et al. 2007; Woollings et al. 2008; Davini et al. 2014). This may be partly explained by the link between wave events and atmospheric blocking highlighted in this work. The increased frequency of wave events over southern Europe can be at least partly explained by the enhanced large-scale ridging over the region during a positive AO and/or NAO but could also result from changes in synoptic-scale activity associated with the NAO.

ENSO (multivariate index) has a comparatively weak impact on the incidence of anticyclonic wave events. In El Niño conditions, a weak reduction of anticyclonic events is observed over eastern Siberia and the Bering Sea in agreement with the reduced incidence of high-latitude ridging events during the warm phase of ENSO (Renwick and Wallace 1996). Differences in the frequency of wave events are more remarkable as a reduction of cyclonic wave events over East Asia. The signature of ENSO in the geopotential height around that region is positive, suggesting a reduction of cyclonic wave activity. The relatively low impact of the wintertime ENSO index on the frequency of wave events in comparison to the AO suggests that the impact of ENSO on midlatitude eddies may not be as important as climate variability in the high latitudes. This is in general agreement with Cohen (2016), who highlights that AO dominates the interannual zonal-mean variability in the midlatitudes, in comparison to ENSO.

Finally, a stronger PNA pattern is associated with reduced anticyclonic events over the Bering Strait region, similar to the effect of the PNA pattern on blocking events (Renwick and Wallace 1996; Croci-Maspoli et al. 2007), and slightly enhanced anticyclonic events over the northeastern Atlantic Ocean. While the positive phase of the PNA pattern is accompanied by positive geopotential height anomalies over North America, it features negative anomalies over Alaska, potentially acting to reduce (increase) the occurrence of extremes in anticyclonic (cyclonic) wave activity over the region. Our results indicate that the wave trains generated by variability in the tropical Pacific may play a role in modulating extreme events in Europe, manifest as an increase in anticyclonic events (Croci-Maspoli et al. 2007).

While changes in the frequency of wave events during the positive and negative phases of major teleconnections can be partly explained by large-scale geopotential height anomalies that intensify or weaken the stationary wave pattern, a more thorough explanation of the changes in their incidence needs to take into account the effect of transient weather systems on the geopotential height variance (e.g., Renwick and Wallace 1996). Relationships between teleconnection patterns and the high-frequency variability leading to wave events will be the topic of future work.

We then proceed to evaluate recent trends (1990–2015) in the frequency of wave events over the four sectors discussed in this work. Figure 14 illustrates the evolution of the DJF-mean frequency of wave events over five different sectors. Although the winter-mean frequency of wave events is shown for events detected using total LWA, interannual variability and trends over European–Alaskan sectors and East Asian–northeastern Canada sectors are dominated by anticyclonic and cyclonic wave events, respectively (not shown). To test the robustness of interannual variations and trends in the occurrence of wave events, four different thresholds for the detection of wave events, in addition to the threshold used throughout this work, are used. Overall, the interannual variability of the incidence of wave events is robust across the different thresholds. Most sectors, such as Europe, do not show any evidence of a recent trend. An exception is the East Asian sector, which presents an increased occurrence of wave events since the 1990s. This trend over East Asia is responsible for the weak positive trends in wave event frequency seen over the Northern Hemisphere and is consistent with the increased probability of extreme values of the meandering index of Di Capua and Coumou (2016), attributable to the Eurasian sector. Recent trends in the NAO/AO (Cohen et al. 2012) and ENSO (Kosaka and Xie 2013) may be responsible for the increased frequency of wave events over East Asia as hinted by the relationship between the AO/NAO and ENSO polarity and the incidence of wave events over that region. Wave events over Alaska and northeastern Canada, which were shown to increase the likelihood of cold extremes over central and eastern America, do not show any clear recent trend suggesting that the reduction of cold extremes over America (Screen et al. 2015) may not be associated with the wave events considered here. The absence of negative trends could result from the fact that LWA is a measure of zonal asymmetry, which does not account for changes in the global mean temperature. Another indicator of flow waviness based on the lengthening of z500 contours shows an increase in the Northern Hemisphere (Cattiaux et al. 2016) but is attributable to the Atlantic sector instead of East Asia. Such discrepancy may result from differences in our wave activity metric. As mentioned previously, LWA takes into account not only the contour deformations but also the enclosed anomalies (see Fig. 1). LWA tendencies do show positive trends over the western side of the North Atlantic and Greenland Sea in recent decades (Chen et al. 2015) but also a negative trend over Europe as a result of a decrease of the anticyclonic component of wave activity (Xue et al. 2017). The meridional dipole of LWA trend over European longitudes expresses a poleward shift of the wave activity peak, without any detectable change of the frequency of wave events when the whole region is considered as shown here. An increase in anticyclonic wave activity is also observed by Chen et al. (2015) and Xue et al. (2017) over central Eurasia but is located too far from the European maximum of wave events to have an impact on their frequency. Trends of LWA are by far the largest over East Asia (Chen et al. 2015), consistent with the increased frequency of cyclonic events reported here. A major difference between this work and others (e.g., Chen et al. 2015; Cattiaux et al. 2016) lies in the fact we have considered here only the most extreme events (see also Di Capua and Coumou 2016), which may be affected not only by trends in the mean wave activity but also by its intraseasonal variability.

Fig. 14.
Fig. 14.

Interannual variability of wave event frequency using total LWA (see Fig. 6b) in DJF over (a)–(d) different sectors and (e) the Northern Hemisphere. The meridional extent of each sector is delimited as illustrated by the black lines in Fig. 6. The longitudinal extent is 50° wide, centered on the black lines shown in Fig. 6. The frequency is computed as the fraction of the area that is under the influence of a wave event for a given winter (DJF). The frequency is computed for wave events detected using various thresholds (colors; see also Fig. 3) and the threshold used throughout this paper (black; see Fig. 2). Recent trends (1990–2015) in wave event frequency are evaluated. The p value is reported at the bottom of each panel. Statistically significant trends are shown using solid lines (p ≤ 0.05).

Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-16-0692.1

6. Discussion and conclusions

A measure of local wave activity (LWA) has recently been developed (Huang and Nakamura 2016) as a generalization of the finite-amplitude wave activity (Nakamura and Zhu 2010; Nakamura and Solomon 2010) and shown to capture persistent weather events such as atmospheric blocking. It is used in this work to detect and produce a climatology of events of extreme wave activity in the troposphere. Following Chen et al. (2015), the LWA algorithm is applied to the 500-hPa geopotential height field z500, instead of a conserved tracer, like quasigeostrophic PV, which simplifies the analysis and allows a better comparison to other recent studies using 500-hPa geopotential heights to evaluate the waviness of the midlatitude circulation (Francis and Vavrus 2012; Barnes 2013; Cattiaux et al. 2016; Di Capua and Coumou 2016). The LWA quantity is further divided into its anticyclonic and cyclonic components (LWAA and LWAC, respectively), allowing the classification of wave events whether they result from large-amplitude ridges or troughs.

Climatological features of LWA applied on z500 reveal a strong seasonality with maximum values of both LWAA and LWAC occurring in February. In winter, prominent LWA regions are found over northern Europe and Alaska for the anticyclonic component and over northeastern Canada and East Asia for the cyclonic component. Those locations correspond to the wintertime structure of planetary-scale waves (Garfinkel et al. 2010). Summertime wave activity is distributed as a single anticyclonic region over northern Eurasia and two cyclonic centers over northeastern Canada and the North Pacific. Its amplitude is much weaker, reflecting the reduced amplitude of large-scale stationary waves (Randel 1988) or weakened baroclinicity in summer.

Focusing thereafter on the winter season, wave events, defined as persistent events of unusually large wave activity, are detected. Similar to blocking events, the likelihood that a wave event persists increases as it lasts longer (Pelly and Hoskins 2003; Tyrlis and Hoskins 2008). As a matter of fact, the geographical distribution of wave events bears strong resemblance to the reversal-type definitions of blocking events (Woollings et al. 2008; Masato et al. 2013b), although they are not necessarily the same. Wave events are defined as large-amplitude troughs and ridges, regardless of whether they display a signature of wave breaking or not.

The relationship between wave events and blocking events is clarified through the use of composites. Both cyclonic and anticyclonic wave events are characterized by transient geopotential height anomalies that align with the stationary planetary-scale waves, leading to enhanced wave activity. Blocking frequency is in fact enhanced during wave events, but the centers of blocking and wave events are not geographically collocated. In anticyclonic events, blocking is found downstream of wave events over Europe or upstream of wave events over Alaska, reflecting the anticyclonic or cyclonic wave-breaking signatures found over Europe or Alaska (Davini et al. 2012; Masato et al. 2012). Cyclonic events, on the other hand, are typically associated with high-latitude blocking (Woollings et al. 2008) to the north of the negative geopotential height anomalies. Composites reveal eastward or westward transit of geopotential height and temperature anomalies over time, highlighting the role of transient Rossby waves in the evolution of large-amplitude wave events, a feature also seen in atmospheric blocking (Altenhoff et al. 2008).

It is shown here that during wave events, LWA is enhanced by the constructive interaction of transient anomalies with the stationary waves. Consequently, the events of large-amplitude geopotential height anomalies identified in Dole and Gordon (1983) are not identified here if the anomalies interact destructively with the stationary waves. This means that while our method adequately identifies extremes defined as large departures from the zonally symmetric state, methods based on temporal anomalies are more appropriate to detect cases when cyclonic anomalies affect stationary ridges (destructive interference) and vice versa. Those events can also bring unusual weather, and thus deserve attention. The identification of such events would in theory be possible by looking for LWA anomalies instead of absolutes, but this alternative approach is out of the scope of this study. We also note that LWA can be employed to detect reversal-type events (Woollings et al. 2008; Masato et al. 2013b). Inspection of Fig. 1 reveals collocated nonzero values of LWAA and LWAC in regions where overturning of z500 or QGPV300 contours occur. The climatology of events characterized by nonzero LWAA and LWAC (not shown here) recovers qualitatively the geographical distribution of blocking that is obtained by previous reversal-based definitions. This method was not investigated further in this work.

Wave events are further associated with regional temperature extremes in the lower troposphere, with cold and warm extremes being generally more likely under the large-amplitude troughs and ridges characterizing wave events, which is consistent with the warm extremes usually found in the vicinity of blocking ridges (Pfahl and Wernli 2012). While Garfinkel and Harnik (2016) have highlighted the role of synoptic-scale systems to generate temperature extremes, this work suggests that large-scale wave trains may also play an important role in setting the frequency of those extremes in the Northern Hemisphere.

It is found that major modes of climate variability are statistically related to the frequency of wave events. The differences in the frequency of wave events between the positive and negative polarities of climate indices were shown here to be consistent to a first order with the geopotential height signature associated with the AO, the NAO, ENSO, and the PNA pattern. The statistical relationship between atmospheric climate indices and the frequency of wave events is not necessarily an indicator of causality as it is not possible to state whether a given phase of a teleconnection favors wave events or that the increased occurrence of wave events projects onto a teleconnection pattern. For instance, high-latitude blocking over northeastern Canada is known to be reflected in the variability of the NAO (Woollings et al. 2008). Atmospheric teleconnections, after all, do express modes of atmospheric variability that describe flow configurations that are more or less zonal, thus being to some extent indicators of wave activity.

The negative trends of the AO/NAO (Cohen et al. 2012) or ENSO (Kosaka and Xie 2013) in recent decades may thus be partly associated to the increased frequency of wave events over East Asia. In fact, an enhanced incidence of cold surges affecting northeast Asia in the 2000s compared to the 1990s is shown in Woo et al. (2012) to be related to negative AO phase and is consistent with the increased frequency of cyclonic wave events affecting the region. None of the other sectors investigated here display significant trends in the frequency of wave events.

Given the link between wave events and weather extremes illustrated here and in previous work (Chen et al. 2015; Huang and Nakamura 2016), further investigation of the interannual to multidecadal variability of local wave activity and projected trends is important to improve climate projections. Not only trends in the mean LWA or frequency of wave events merit further attention; trends in amplitude, size, and duration of extreme wave events should be investigated in future work. Local wave activity could also serve as a diagnostic to evaluate whether the current generation of climate models represents well weather extremes associated with the meandering jet in the midlatitudes and to identify aspects of numerical models, such as numerical resolution, that favor a more realistic representation of wave activity and its variability.

Acknowledgments

We wish to thank Jian Lu, Stephen J. Colucci, and three anonymous reviewers for providing useful comments. Gang Chen is supported by DOE Grant DE-SC0016117 and NSF AGS-1349605.

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