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DOI:10.2151/jmsj.2019-037

J-STAGE Advance published date: February 15th, 2019

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preliminary version at the above DOI once it is available.

Troposphere-Stratosphere Dynamical

Coupling in Regard to the North Atlantic

Eddy-Driven Jet Variability

Waheed Iqbal, Abdel Hannachi

Department of Meteorology (MISU) and Bolin Centre forClimate Research, Stockholm University, Stockholm, Sweden

Toshihiko Hirooka

Department of Earth & Planetary Sciences, KyushuUniversity, Fukuoka, Japan

Leon Chafik

Department of Meteorology (MISU) and Bolin Centre forClimate Research, Stockholm University, Stockholm, Sweden

and Yayoi Harada

Climate Research Department, Meteorological ResearchInstitute, Tsukuba, Japan

February 9, 2019

Corresponding author: Waheed Iqbal, Department of Meteorology, Stockholm

Abstract

The interaction between the troposphere and the stratosphere has attracted

the attention of climate scientists for several decades not least for the ben-

efit it has on understanding dynamical processes and predictability. This

interaction has been revived recently in regard to downward disturbance

propagation effects on tropospheric circulations. The current study inves-

tigates such interactions over the North Atlantic region in relation to the

eddy-driven jet stream. The atmospheric low-frequency variability in the

winter over the North Atlantic sector is mainly associated with variations

in the latitudinal positions of the North Atlantic eddy-driven jet stream.

The Japanese Reanalysis JRA-55 data has been used to analyse the jet lat-

itude statistics. The results reveal robust trimodality of the North Atlantic

jet reflecting the latitudinal (i.e., northern, central and southern) positions

in agreement with other reanalysis products. Thirty major sudden strato-

spheric warming events were analysed in relation to the three modes or

regimes of the eddy-driven jet. The frequency of occurrence of the eddy-

driven jet to be in a specific latitudinal position is largely related to the wave

amplitude. The stratospheric polar vortex experiences significant changes

via upward wave propagation associated with the jet positions. It is found

that when the jet is close to its central mode the wave propagation of zonal

University, Sweden, 10691 Stockholm Sweden.E-mail: waheed.iqbal@misu.su.se

1

wave number 2 from the troposphere to the stratosphere is significantly

high. Eliassen-Palm fluxes from all waves and zonal wave number 1 de-

pict deceleration of the stratospheric polar vortex for the eddy-driven jet

with latitudinal position close to the northern mode. Plumb wave activity

variations originate mainly in the Atlantic sector depending on the North

Atlantic eddy-driven jet states. These significant associations between pre-

ferred latitudinal positions of the North Atlantic eddy-driven jet and the

stratospheric dynamics may be a source of predictability.

2

Keywords North Atlantic eddy-driven jet; sudden stratospheric warming;

JRA-55; jet latitude index; wave activity; troposphere-stratosphere coupling

1. Introduction

The “Sudden Stratospheric Warmings (SSWs)” are extraordinary man-

ifestation of the troposphere-stratosphere coupling. These stratospheric

warming events impact the extra-tropical weather systems (e.g., Baldwin

and Dunkerton 1999). Besides minor and major, the warmings are also clas-

sified as Canadian and final warmings. Early winter warmings associated

with the eastward shift of the Aleutian high are called Canadian warmings,

whereas in the final warmings the cyclonic stratospheric polar vortex does

not recover (Butler et al. 2015). The major SSWs events are defined by

rapid temperature increase (30 to 50 K) and reversal of the zonal wind

(poleward of 60) in mid-to-high latitude stratosphere, if the zonal wind

does not reverse then warming is a minor SSW. The major SSWs mainly

occur in the Northern Hemisphere, only one event has been reported in the

Southern Hemisphere (see Manney et al. 2005; Kruger et al. 2005, for de-

tails). The average rate of major SSWs in the Northern Hemisphere is 6

per decade (Charlton and Polvani 2007).

Major SSWs lead to strong planetary wave reflection or downward prop-

3

agation (e.g., Kodera et al. 2016). As a result, the cold air advection from

high latitudes brings much colder than usual surface weather. Over Europe,

Siberian winds result in deadly weather conditions. Stratospheric warming

events are known to be forced by upward propagating Rossby and gravity

waves from the upper troposphere. A number of recent studies (e.g., Martius

et al. 2009; Nath et al. 2016; Harada and Hirooka 2017) have demonstrated

the two-way coupling between the troposphere and the stratosphere. The

effects of stratospheric dynamics on tropospheric weather were not much

acknowledged until late 1990s (see Kidston et al. 2015 for a recent review).

Baldwin and Dunkerton (1999, 2001) demonstrated that the stratospheric

variability can impact the surface weather at large and may lead to longer

predictability time scale. For a detailed discussion on the coupling between

the troposphere and stratosphere, the reader is directed to Haynes (2005)

and Kidston et al. (2015).

Other critical factors that can influence the Northern Hemisphere mid-

latitude weather are the jet streams and the planetary wave activity (e.g.,

Cohen et al. 2007). Troposphere dynamically interacting with eddy-driven

jet streams and Rossby waves impacts the stratospheric polar vortex through

vertical wave propagation (Matsuno 1971). Subsequently, the downward

wave propagation affects surface temperature gradient which influences tro-

4

pospheric jet streams (e.g., Kodera et al. 2016, 2017; Mukougawa et al.

2017). In the North Atlantic sector, the atmospheric low-frequency vari-

ability in the winter is related to shifts in the preferred latitudinal positions

of the North Atlantic eddy-driven jet (e.g., Woollings et al. 2010a). The

North Atlantic eddy-driven jet has three preferred latitudinal positions sit-

uated respectively south, close to, and north of its climatological mean

position. They represent respectively the Greenland blocking, a low pres-

sure system over the Atlantic and a high pressure system over the Atlantic

region (Woollings et al. 2010b).

The major variability in the stratosphere is associated with the dynam-

ics of the polar vortex. The SSWs occur during the Northern Hemisphere

winter when planetary scale waves are excited by either topography, or non-

linear interactions of eddies in the troposphere (Haynes 2005). A strong

stratospheric polar vortex does not allow the planetary waves to propagate

upward (e.g., Scaife et al. 2000). However, a weaker stratospheric polar

vortex cannot resist the upward wave propagation from the troposphere

(e.g., Hartmann et al. 2000) resulting either in displacement or splitting of

the stratospheric polar vortex. These types of events are respectively called

vortex displacement and vortex split warmings. The vortex displacement

type of events are caused by zonal wave number 1 (WN1) activity whereas

5

the main contributions for the vortex split events are from zonal wave num-

ber 2 (WN2) (e.g., Kidston et al. 2015; Harada and Hirooka 2017). It has

been observed that the vortex displacement events are preceded by blocking

over the Atlantic only (e.g., Mitchell et al. 2013).

Woollings et al. (2010a) analysed the relationship between stratospheric

variability and tropospheric blocking events. They reported existence of sig-

nificant relationship between stratospheric variability and blocking over the

North Atlantic region. Using NCEP reanalysis, Colucci and Kelleher (2015)

revisited the same issue for the 1980–2012 period and found that SSW events

coincide with tropospheric blocking, but blocking is not a necessary condi-

tion for SSWs. In an idealized modelling study Garfinkel et al. (2013) found

that a jet stream in the troposphere close to 30 and 50 latitude results in

stronger stratospheric polar vortex whereas a jet stream close to 40 latitude

results in a weaker stratospheric polar vortex. Until now, there have been

no systematic studies on the position of the North Atlantic eddy-driven jet

and the relation between sudden stratospheric warmings using reanalysis

data sets.

The objective of the current study is two-fold; 1) the analysis of the

variability of the North Atlantic eddy-driven jet in Japanese Reanalysis

6

(JRA-55; Kobayashi et al. 2015) in comparison with European Reanalysis

(ERA-40; Uppala et al. 2005) and 2) the investigation of the relationship

between major warmings and preferred latitudinal positions of the North At-

lantic eddy-driven jet. The interactions between the eddy-driven jet stream

and the wave activity are complex and not fully understood, and in the

present study we attempt to explore one key aspect of this complex puzzle.

The data and methods are described in section 2, variability of the

North Atlantic jet using JRA-55 is presented in section 3 and troposphere-

stratosphere interactions are presented in section 4. A summary and con-

clusions are presented in the last section.

2. Data and Methods

2.1 Reanalysis Data

The analysis is based on daily reanalysis data for winter (December-

February; DJF). The daily data of zonal wind, temperature, geopotential

height and meridional wind have been taken from the Japanese Reanalysis

(JRA-55; Kobayashi et al. 2015) data for the period 1958–2014. In ad-

dition, the daily zonal wind data from the European Reanalysis (ERA-40;

7

Uppala et al. 2005) available for the period 1958–2001, has also been used

to compare the characteristics of the North Atlantic jet with that from JRA-

55. Both the reanalysis data sets are at a horizontal resolution of 1.125 x

1.125. It is worth to mention here that ERA-40 data is used only for section

3 for comparison with JRA-55. The information about the warming event

types (vortex displacement or vortex split) and the onset dates is inferred

from the SSW compendium data (Butler et al. 2017). In this compendium

the major warming onset date is the day when the daily zonal mean zonal

wind at 10 hPa and 60N changes from westerly to easterly (similar to the

criterion by Charlton and Polvani 2007). The classification of these SSWs

to vortex split and vortex displacement is done by analysing temperature

anomalies at 10 hPa and the potential vorticity at 550K (e.g., Butler et al.

2017).

2.2 Analysis Methods

The study of the jet variability is based on the computations of the jet

latitude index (JLI; Woollings et al. 2010b). Briefly, this method uses daily

zonal wind at low levels (925–700 hPa) averaged over the North Atlantic

sector (0–60W). This mean wind is then filtered using a low-pass filter

to avoid small scale disturbances. The latitude at which the maximum of

8

this filtered zonal wind occurs is called the jet latitude and the wind speed

is called the jet speed. For further details about the jet latitude index,

the reader is directed to Woollings et al. (2010b). The estimation of the

probability density functions (PDFs) is done by using the kernel method of

Silverman (1981). The standard smoothing parameter h = 1.06σn−15 has

been used, where σ is the standard deviation and n is the sample size.

In order to study the impact of the stratosphere on the troposphere and

vice versa, we have used the Eliassen-Palm (EP) fluxes. The calculation

of EP fluxes is made using the Transformed Eulerian Mean (TEM) equa-

tions (Andrews et al. 1987). The TEM equations provide a suitable tool

to diagnose the eddy forcing in the zonal mean circulation system. The use

of EP flux vectors is an important diagnostic tool in the meridional plane

to study the effect of the troposphere on the stratosphere. The direction

of EP flux pointing upward implies that the eddy-heat fluxes are dominant

and a meridional direction of EP fluxes implies momentum fluxes or forcing

dominance. The divergence (convergence) of EP flux is related to the accel-

eration (deceleration) of the associated zonal flow. For further details about

the relationship between EP flux divergence and the mean flow, the reader

is directed to Andrews and McIntyre (1976) and Andrews et al. (1987).

9

There are a few variants of the EP fluxes. In this study we make use of

the two most used fluxes; 1) EP flux (Edmon et al. 1980 for Figs. 9 and

10) and 2) Plumb flux (Plumb 1985). The first type of flux is a latitude-

height cross-section whereas the Plumb flux provides a latitude, longitude

and height view to study the wave activity. We have used the vertical

component of EP flux at 100 hPa (EPFZ100) averaged over 30–90N to

study the vertical wave propagation. It has been shown that EPFZ100 is

a good representative of the upward wave activity from the troposphere to

the stratosphere (e.g., Newman and Nash 2000). The data for EPFZ100

is obtained from Harada and Hirooka (2017) which is computed following

the definition of Andrews et al. (1987). The vertical component of EP flux

represents the eddy-heat forcing from the troposphere to the stratosphere.

The 3D wave activity flux (WAF) is computed using JRA-55 data fol-

lowing the definition of Plumb (1985). The components of WAF on the

sphere in log-pressure coordinates are given by:

Fs = p cosφ

1

2a2 cos2 φ

[(∂ψ′∂λ

)2 − ψ′∂2ψ′∂λ2

]1

2a2 cosφ

[∂ψ′∂λ

∂ψ′∂φ− ψ′ ∂2ψ′

∂φ∂λ

]2Ω2 sin2 φN2a cosφ

[∂ψ′∂λ

∂ψ′∂z− ψ′ ∂2ψ′

∂λ∂z

]

(1)

10

where p is pressure, and φ and λ are latitude and longitude, respectively.

A prime denotes small perturbation to zonal mean. The stream-function,

Earth’s rotation rate, radius of Earth and buoyancy frequency are respec-

tively given by ψ, Ω, a and N . The pressure p (hPa) is divided by 1000 hPa.

For two-dimensional latitude-height cross-sections we employed the EP

flux methodology of Edmon et al. (1980), which is given by:

Fφ, Fp = −a cosφ u′v′, f a cosφv′θ′

θp (2)

The terms Fφ and Fp refer respectively to the meridional and vertical com-

ponents of the EP flux. The wind components are denoted by u and v,

the primes denote the deviations from the zonal mean and over-bar shows

the zonal mean. The variable θ represents potential temperature and θp is

partial derivative of θ with respect to p .

Lead/lag relationship between the jet states and the major SSWs is

analysed by performing the Superposed Epoch Analysis (SEA; e.g., Adams

et al. 2003). SEA is a statistical technique used to find the correlation of a

time series with a lead/lag to key events. The key events here refer to onset

11

dates of the major SSWs (see Table 3).

The downward wave propagation from the stratosphere to the tropo-

sphere can be analysed using reflective index (Perlwitz and Harnik 2004).

The reflective index (RI) is difference of the zonal mean zonal wind averaged

over 58–74N, between 2 hPa and 10 hPa pressure surfaces.

RI = u2hPa − u10hPa (3)

The positive values of RI correspond to a non-reflective stratospheric basic

state whereas negative values of RI imply a reflective stratosphere. We com-

puted daily values of RI from JRA-55 to report variability of the wave re-

flection for three preferred latitudinal positions of the North Atlantic eddy-

driven jet.

3. Variability of the North Atlantic jet in JRA-55

In this section we analyse the North Atlantic eddy-driven jet variability

from JRA-55 data and compare results with that of ERA-40 for 1958–2001

winters. The use of the JLI is to explore the statistical characteristics

of the North Atlantic jet. Previously this has been done using ERA-40

12

reanalysis (e.g., Woollings et al. 2010b; Hannachi et al. 2012). Analysis

based on Coupled Model Inter-comparison Project (CMIP) has been done in

Hannachi et al. (2013) for CMIP3 and Iqbal et al. (2018) for CMIP5. JRA-

55 data are explored here for the first time to the best of our knowledge. The

comparison of the two reanalyses is shown in Fig. 1. The first 500 winter

days of JLI from the two reanalyses (Fig. 1a) depict similar variability of

the North Atlantic jet. Certainly the two reanalyses have a good match for

variability of the North Atlantic jet. The kernel estimation of PDFs of the

daily JLI time series shows three maxima which are well separated. These

maxima are located respectively close to 37, 46 and 57N. The location and

relative frequencies of these modes are very similar in the two reanalyses,

which demonstrate the robustness of the trimodal structure of the jet PDF

to the choice of analysis dataset.

Fig. 1

In order to develop a physical representation of these three modes, com-

posites were computed of 500 hPa geopotential height anomalies for 700

days closest to each mode. The obtained spatial patterns associated to

each of these modes are shown in Fig. 2. The southern mode represents

atmospheric conditions similar to the negative phase of the North Atlantic

Oscillation (NAO) and depicts Greenland blocking. The central and the

northern modes represent respectively a positive and a negative East At-

13

lantic pattern. These flow patterns obtained from JRA-55 are similar to

those from the ERA-40 (Woollings et al. 2010b). These spatial patterns

are quite robust for changes in the sample size used for the composites.

Composites of 20 hPa geopotential height anomalies for 700 days closest to

each state of the North Atlantic eddy-driven jet are presented in the sup-

plementary material. The spatial patterns for both northern and central

modes of the jet are similar to a WN1 pattern while southern mode of the

jet resembles a WN2 pattern (Fig. S1).

Fig. 2

4. Wave activity and the North Atlantic jet during

winter

Stratospheric variability corresponds to different strengths of the strato-

spheric polar vortex. An Empirical Orthogonal Function (EOF) analysis of

geopotential height anomalies in the stratosphere at 20 hPa level (Fig. 3),

shows that planetary scale waves are the main contributors to stratospheric

variability. The leading mode with 34% of explained variance reflects the

zero wave pattern, representing mainly the Arctic Oscillation (AO). The

next two EOFs represent the zonal wave number 1 (WN1) pattern, synony-

mous with a displaced vortex with centres of actions situated over north-

14

ern Canada and Scandinavia/northern Siberia for EOF2, and Iceland and

north-eastern Russia for EOF3. These two patterns explain altogether 37%

of total winter stratospheric variability. The fourth pattern with 8% vari-

ance is a zonal wave number 2 (WN2) pattern for split events. Note that

these leading four patterns explain altogether 79% of the variability, and

45% is explained by displaced and split events (Fig. 3). A similar spatial

structure of variability for EOF analysis of 100 hPa geopotential heights is

observed (not shown) but with less percentage of explained variance. The

EOF analysis for 700 days closest to each state of the jet also represent sim-

ilar spatial structures and the sum of explained variance by the first four

EOFs is more than 80% (see. Figs. S2 to S4).

Fig. 3

The use of EPFZ100 has been reported to be a good indicator of up-

ward wave activity from the troposphere to the stratosphere (Newman and

Nash 2000). The positive values of EPFZ100 imply an upward propagation

which can affect the stratospheric polar vortex. Since only the longest scale

waves can affect the stratospheric dynamics (Charney and Drazin 1961),

we consider contributions of all waves, WN1 and WN2 to EP fluxes. The

interannual variability of EPFZ100 shows the dominance of WN1 in general

but occasionally higher wave activity associated with WN2 is also observed

(Fig. 4).

15

Fig. 4

Fig. 5

Table 1

The upward wave propagation for each preferred latitudinal position of

the North Atlantic eddy-driven jet is analysed by composite analysis similar

to Fig. 2 but for EPFZ100. The composites of the EPFZ100 for 700 days

closest to each state of the jet are presented in Fig. 5. All three states of

the North Atlantic jet have some differences for the upward wave activity.

The averaged values of EPFZ100 for three modes: southern, central and

northern are shown in Table 1. Contributions to upward wave propagation

from the troposphere to the stratosphere from all waves are higher for the

northern latitudinal position of the North Atlantic eddy-driven jet. The

contributions of WN1 are relatively stronger for the case when the jet is

either in the southern state or the northern state. However, WN2 upward

fluxes are stronger for central position of the North Atlantic eddy-driven

jet. Reflective index values for the same 700 days closest to each state of

the North Atlantic eddy-driven jet are 11.3, 7.7 and 5.5 ms−1 respectively

for southern, central and northern position of the jet. In all these three

composites, the basic state in the stratosphere is non-reflective.

Kernel estimation of PDF of EPFZ100 for 700 days closest to each mode

of the North Atlantic jet is also shown in Fig. 5. EPFZ100 contributions

from all waves in all three cases are almost similar whereas there are signif-

16

icant differences between the EP fluxes associated with WN1 and WN2 for

the days when the North Atlantic eddy-driven jet is close to either southern

or northern latitudinal positions. The total wave activity is nearly symmet-

rical with a near Gaussian shape. However, WN1 and WN2 histograms are

quite asymmetric or skewed with a long tail towards large fluxes, reflecting

the high impact of planetary scale (WN1,WN2) waves in the stratosphere.

The results of two sample Kolmogorov–Smirnov (K–S) test performed to

assess interdependence of these samples are shown in Table 2. The time

series of EPFZ100 from all waves are not significantly different from each

other. However, EPFZ100 flux for the central position of the North Atlantic

jet are significantly different from that of the northern and the southern po-

sitions of the jet for both WN1 and WN2.

Table 2

Fig. 6The occurrence of positive EPFZ100 from all waves and decomposed

components are almost same for three preferred positions of the North

Atlantic eddy-driven jet (Fig. 5a). The frequency of weak WN1 upward

propagation associated with the central mode of the jet is higher than that

from the southern position of the jet. Relative frequency of WN1 EPFZ100

is higher for the northern position of the North Atlantic eddy-driven jet

as compared to the other two modes. EPFZ100 associated with WN2 are

stronger for the central mode as compared to both southern and northern

17

modes of the jet (Fig. 5c).

An alternative way to look at the wave activity effects on the jet can be

obtained by analysing the PDF structure of the jet for various strengths of

the vertical component of EP flux. This is presented in Fig. 6 where the

kernel estimation of the PDFs of low, medium and high fluxes when con-

sidering all waves, WN1 and WN2 are compared. The stronger EPFZ100

from WN2 impacts the central mode of the jet (with higher frequencies),

making the other two modes extremely less frequent. The trimodal feature

of the North Atlantic eddy-driven jet might undergo significant changes as-

sociated with extreme amplitudes of EP flux. This implies that given the

higher frequencies of stronger or weaker EP flux will result in less or more

frequent jet for southern, central and northern positions.

4.1 Major Sudden Stratospheric Warmings in relation to North

Atlantic eddy-driven jet

The list of major SSWs, their onset date and the stratospheric polar

vortex type for these events are shown in Table 3. There are 16 events with

vortex displacement type and 14 events are with vortex split type in the

analysis period. In this section we use different statistical approaches to

18

study the possible relationship between the jet states and the wave activity.

Table 3

Fig. 7 shows the average position of the jet conditioned on the types of

SSWs with vortex split and vortex displacement types with a time lead/lag

of one week. Here ‘All’ refers to total number of SSW events, i.e., 30. The

climatological value of JLI during DJF season is around 47.5N. It can be

observed that the jet is closest to its climatological position before and af-

ter of any displacement event whereas the jet is well below in south for the

vortex split events. In all these three categories in Fig. 7, the jet is always

southward of its climatological position. The split events have been reported

to impact the European climate whereas the displacement events are more

related to have impact over the North American region (e.g., Kidston et al.

2015; Bancala et al. 2012; Martius et al. 2009). It is worth to mention that

due to the small sample size of two types of events, we avoid the segregation

of events into displacement or vortex split for further analysis.

Fig. 7

The superposed Epoch Analysis (SEA) is performed over the DJF daily

JLI time series and EPFZ100 for WN1 and WN2 components (Fig. 8). The

North Atlantic eddy-driven jet is significantly poleward of its climatological

position two days before the onset of a SSW event. There is a lead-time of

about 20 days for the North Atlantic jet to be significantly on the equator

19

side for any SSW event. The wave activity from both WN1 and WN2 is

significantly above normal for 2-5 days before an event and then gradually

decreases until it reaches the negative anomalies around 3-5 days after the

on-set date of the SSW event.

Fig. 8

4.2 Meridional cross sections of EP flux

As pointed out by Birner and Albers (2017), the fluxes at 100 hPa

are not enough to study the upward propagation. Therefore, we use here

two-dimensional EP fluxes for latitude-height cross-sections. The winter

climatology of EP fluxes (Fig. 9) from all waves, WN1 and WN2 shows

a weaker upward wave propagation over the polar region as compared to

mid-latitudes in the stratosphere. The strong stratospheric polar vortex

during winter implies less vertical wave propagation over the polar region

from large-scale planetary waves. The differences of the EP fluxes for com-

posites of jet states from winter climatology show significant changes in the

associated stratospheric zonal circulation (i.e., divergence in Fig. 10). The

significant deceleration of the associated zonal flow over the stratospheric

polar region is observed for the southern mode of the jet associated with

both all waves and WN1 EP fluxes implying stronger upward wave prop-

agation. Similar stronger wave activity associated with WN2 can be seen

20

for the central mode of the jet (Fig. 10h). For the central mode of the jet,

both all waves and WN1 EP flux are lower than the winter mean upward

propagation. It is important to mention here that these results are in good

agreement with the EP flux analysis for only one level (Table 1). Fig. 9

Fig. 10

4.3 Plumb Wave Activity

Here we examine the three-dimensional Plumb wave activity. To simplify

interpretation, we focus on analysing the latitudinal averages of the fluxes

over the latitudinal band: 45–65N. The longitude-height cross-sections of

the horizontal and vertical components of the Plumb wave activity are

shown in Fig. 11. The upward wave activity from the troposphere to the

stratosphere is stronger over the Pacific as compared to the Atlantic sector.

Departures of the wave activity composites for each jet state from the mean

wave activity during the Northern Hemisphere winter are shown in Fig. 12.

In all three states the wave activity differences from the winter climatology

are mainly in the Atlantic sector and eastern Pacific. Stronger anomalous

upward wave activity over the North Atlantic sector is observed for the

northern position of the jet. The anomalous upward wave propagation over

the North Atlantic sector is reduced when the jet is either in the central or

southern positions.

Fig. 11

Fig. 12

21

5. Summary and Conclusions

In this study, we have analysed the characteristics of the North Atlantic

eddy-driven jet from JRA-55 during the winter time (DJF) for the pe-

riod 1958–2014. These characteristics of the North Atlantic eddy-driven jet

were compared to previous studies based on ERA-40 (e.g., Woollings et al.

2010b; Hannachi et al. 2012). The PDF trimodality of the North Atlantic

eddy-driven jet is found to be robust and the two reanalyses (ERA-40 and

JRA-55) demonstrate good agreement for the jet latitude index diagnostics.

The second part of the paper is devoted to explore the associations be-

tween the stratospheric variability and the North Atlantic jet variability

(tropospheric variability) through eddy-mean flow interactions using wave

activity fluxes. A total of thirty major sudden stratospheric warming events

have been examined for possible relation with the preferred latitudinal posi-

tions of the North Atlantic eddy-driven jet. We have used two-dimensional

EP fluxes as well as three-dimensional Plumb fluxes.

Considering the fact that only the planetary and large scale waves can

propagate from the troposphere to the stratosphere, we have used the EP

flux contributions from the leading two waves (WN1, WN2), in addition

to considering the all waves contributions. The vertical component of EP

22

fluxes at 100 hPa (EPFZ100) averaged over 30–90N is used as an indicator

of upward wave propagation. Contributions to upward wave propagation at

100 hPa from all waves are higher for the northern latitudinal position of

the North Atlantic eddy-driven jet. We have shown that the WN1 upward

propagation is significantly stronger when the North Atlantic eddy-driven

jet is either in the northern or southern positions compared to the central

jet positions.

EPFZ100 composite of 700 days closest to each latitudinal position of

the North Atlantic eddy-driven jet reveals stronger wave activity: 1) for

north position associated to all waves fluxes, 2) for south and north po-

sitions associated to WN1 fluxes and 3) for central position associated to

WN2 fluxes. By extending this one dimensional analysis to latitude-height

vertical cross-sections, we confirm the strong wave activity from WN2 for

central position of the North Atlantic eddy-driven jet. The stronger wave

activity and EP flux divergence are manifestations of a weakening strato-

spheric polar vortex. Composites of all waves and WN1 EP flux depict

significant deceleration for northern position of the jet.

A three dimensional view from the Plumb wave activity composites for

three latitudinal positions of the North Atlantic eddy-driven jet shows a

23

stronger upward wave propagation for the northern mode only over the

North Atlantic sector. In all three states of the North Atlantic eddy-driven

jet the wave activity differences from the winter climatology are mainly in

the Atlantic sector. We also show that the jet latitude PDF trimodality fea-

ture of the North Atlantic eddy-driven jet reduces to a unimodal shape for

higher WN2 EP fluxes. The position of the North Atlantic jet is reported

to be south of its climatological position about 20 days both prior and after

the onset of a major warming event.

The analysis performed here aims at improving understanding of the in-

teraction between the North Atlantic eddy-driven jet and the wave activity.

The results indicate strong relationships for different latitudinal positions of

the North Atlantic jet and the associated wave activity. The strong upward

wave activity associated with the central mode of the jet and weak upward

propagation from the other two modes of the North Atlantic eddy-driven

jet are found to be interesting features. Significant changes in stratospheric

dynamics for the eddy-driven jet latitudinal positions may be a useful source

of predictability for both stratosphere and troposphere.

Acknowledgements

24

The authors would like to thank Tim Woollings for useful discussions.

W. Iqbal is supplied by International Exchange Scholarship 2017 from Kyushu

University, Japan. T. Hirooka was funded by International Meteorological

Institute (IMI) of Stockholm University, Stockholm Sweden. The compu-

tations were performed on resources provided by the Swedish National In-

frastructure for Computing (SNIC) at the National Supercomputing Centre

(SNC). This work was partly supported by Grants-in-Aid for Scientific Re-

search (16H04052, 17H01159 and 18H01280) from Japan Society of Promo-

tion of Science. L. Chafik acknowledges support from the Swedish National

Space Board (SNSB; Dnr 133/17). We thank two anonymous reviewers for

their useful suggestions.

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32

List of Figures

1 Comparison of two reanalysis data sets: ERA-40 and JRA-55for the jet latitude index (in N) computed for winter during1958–2001. JLI for first 500 winter days (a); the probabilitydistribution function of daily JLI time series along with akernel estimation to PDF (in solid black line) and a Gaussian(blue dotted line) for ERA-40 (b); same as in (b) but for JRA-55 (c). The two kernels estimated to ERA-40 and JRA-55JLI PDFs are presented in panel (d). . . . . . . . . . . . . . 36

2 Spatial patterns of geopotential height anomaly (gpm) at 500hPa for the composite of 700 days closest to each mode inFig. 1. The anomaly is computed by removing a smooth sea-sonal cycle. Panels a to c respectively represent the spatialpattern associated with northern, central and southern modeof the North Atlantic jet. Stippling indicates the regionswhere the composites are different from the winter climatol-ogy at 5% significance level from Student’s t-test. . . . . . . 37

3 The spatial patterns of variability in the stratosphere. Firstfour Empirical Orthogonal Functions (EOFs) of winter geopo-tential height anomaly at 20 hPa for the period 1958–2014.The amount of explained variance is also shown above eachpanel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 (Harada and Hirooka 2017). Inter-annual variability of EPfluxes at the high troposphere. The distribution of EPFZ100(x104kgs−2) during 1958–2014 winters. The contributions ofEPFZ100 associated with all waves (grey bars), WN1 (redline) and WN2 (blue line) are plotted for each winter year.Note that there are two y-axes; on left for all waves and onthe right for the decomposed components (WN1,WN2). . . . 39

5 Histogram and kernel PDF of the DJF daily EPFZ100 (x104kgs−2)for all waves (a), WN1 (b) and WN2 (c). Kernel estimationof the PDF of the 700 days closest to each mode of the NorthAtlantic jet are also shown in each panel. . . . . . . . . . . 40

33

6 Kernel estimation to the PDF of daily JLI (N) time seriesfor low, medium and high values of EPFZ100 computed forall Waves (a), WN1 (b), and WN2 (c). The black line in eachpanel represents the kernel estimation to full time series (i.e.,DJF). The classification of low, medium and high EPFZ100is based on percentiles (i.e., Low: EPFZ100≤P25, Medium:P25 <EPFZ100≤ P75 and High: EPFZ100> P75). . . . . . . 41

7 Composites of SSW events and the mean position of theNorth Atlantic jet (in N ). The composites are analysed foronset, one week before (Pre) and one week after (Post) of anevent. The winter mean for the JLI over the analysis periodis represented by black dashed line. . . . . . . . . . . . . . . 42

8 The Superposed Epoch Analysis (SEA) performed for all30 selected events (inclusive Split and Displacement types)shown in Table reftable-ssw-list. The values on the y-axisshow the deviation from the mean values and the x-axis val-ues are the lead/lag days from an event. The black colourrepresents the zero lag whereas the red and blue colours re-spectively denote the post and pre composites. The 95%confidence limits are shown by the continuous and dashedcurves. The jet latitude deviation is in N (a), whereas theEPFZ100 anomalies (b and c) are expressed in x104kgs−2. . 43

9 The latitude-height cross-sections of EP flux winter climatol-ogy for all waves (a), WN1 (b) and WN2 (c). The arrowsrepresent EP flux and the divergence (ms−1day−1) is in shaded. 44

10 The latitude-height cross-sections of EP flux difference be-tween winter climatology and three states of the North At-lantic eddy-driven jet. The columns from left to right re-spectively represent the northern, central and southern jetwhereas rows from top to bottom respectively represent allwaves, WN1 and WN2. EP flux vectors are displayed onlywhere the EP flux divergence is different from the climatol-ogy at 5% significance level. The divergence (in ms−1day−1)is shaded. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

34

11 The longitude-height cross-sections of geopotential height de-viations (gpm) from the zonal mean (shading) and Wave Ac-tivity Fluxes (vectors) averaged over 45–65N. WAFs are inunits of m2s−2. Following Harada and Hirooka (2017), thevectors are scaled: e.g., above 200 hPa Fx and Fz are di-vided by 20.0 and 0.10 respectively; and below 200 hPa by100 and 0.60. . . . . . . . . . . . . . . . . . . . . . . . . . . 46

12 The longitude-height cross-sections of geopotential height de-viations (gpm) from the zonal mean (shading) and Wave Ac-tivity Fluxes (vectors) averaged over 45–65N. WAFs are inunits of m2s−2. Scaling of vectors is same as in Fig. 11. Pan-els a to c respectively represent the difference from the cli-matology, for the northern, central and southern latitudinalpositions of the North Atlantic eddy-driven jet. . . . . . . . 47

35

Day No.

0 100 200 300 400 500

Jet

lat

(°

N)

30

40

50

60

70

a) First 500 days of JLI

ERA-40

JRA-55

Jet lat (° N)

20 30 40 50 60 70

Fre

qu

en

cy

0.01

0.02

0.03

0.04

0.05

b) PDF ERA-40

Jet lat (° N)

20 30 40 50 60 70

Fre

qu

en

cy

0.01

0.02

0.03

0.04

0.05

c) PDF JRA-55

Jet lat (° N)

20 30 40 50 60 70

Fre

qu

en

cy

0.01

0.02

0.03

0.04

0.05

d) Kernel estimation to PDF

ERA-40

JRA-55

Fig. 1. Comparison of two reanalysis data sets: ERA-40 and JRA-55 forthe jet latitude index (in N) computed for winter during 1958–2001.JLI for first 500 winter days (a); the probability distribution functionof daily JLI time series along with a kernel estimation to PDF (in solidblack line) and a Gaussian (blue dotted line) for ERA-40 (b); same asin (b) but for JRA-55 (c). The two kernels estimated to ERA-40 andJRA-55 JLI PDFs are presented in panel (d).

36

20°N

40°N

60°N

80°N

120°W 60°W 0° 60°Ea)

20°N

40°N

60°N

80°N

120°W 60°W 0° 60°Eb)

20°N

40°N

60°N

80°N

120°W 60°W 0° 60°Ec)

−150

−100

−50

0

50

100

150

Fig. 2. Spatial patterns of geopotential height anomaly (gpm) at 500 hPafor the composite of 700 days closest to each mode in Fig. 1. Theanomaly is computed by removing a smooth seasonal cycle. Panels ato c respectively represent the spatial pattern associated with northern,central and southern mode of the North Atlantic jet. Stippling indi-cates the regions where the composites are different from the winterclimatology at 5% significance level from Student’s t-test.

37

EOF1 (34%)

−0.006 0.000 0.006 0.012 0.018

EOF2 (23%)

−0.02 −0.01 0.00 0.01 0.02

EOF3 (14%)

−0.02 −0.01 0.00 0.01 0.02

EOF4 (8%)

−0.030 −0.015 0.000 0.015

Fig. 3. The spatial patterns of variability in the stratosphere. First fourEmpirical Orthogonal Functions (EOFs) of winter geopotential heightanomaly at 20 hPa for the period 1958–2014. The amount of explainedvariance is also shown above each panel.

38

1

2

3

4

5

6

7

8

EP

FZ

10

0 f

or

WN

1,W

N2

1960 1970 1980 1990 2000 2010

Year

6

7

8

9

10

11

12

13

14

EP

FZ

10

0 f

or

all

Wa

es

all waves

WN1

WN2

Fig. 4. (Harada and Hirooka 2017). Inter-annual variability of EP fluxes atthe high troposphere. The distribution of EPFZ100 (x104kgs−2) during1958–2014 winters. The contributions of EPFZ100 associated with allwaves (grey bars), WN1 (red line) and WN2 (blue line) are plotted foreach winter year. Note that there are two y-axes; on left for all wavesand on the right for the decomposed components (WN1,WN2).

39

-10 -5 0 5 10 15 20 25 30 35

0

0.02

0.04

0.06

0.08

Re

lati

ve

fre

qu

en

cy

a)

All Waves

South

Center

North

-10 -5 0 5 10 15 20 25 30 35

0

0.05

0.1

0.15

Re

lati

ve

fre

qu

en

cy

b)

WN1

-10 -5 0 5 10 15 20 25 30 35

EPFZ100 (x 10 4 kg/s 2 )

0

0.05

0.1

0.15

0.2

Re

lati

ve

fre

qu

en

cy

c)

WN2

Fig. 5. Histogram and kernel PDF of the DJF daily EPFZ100 (x104kgs−2)for all waves (a), WN1 (b) and WN2 (c). Kernel estimation of the PDFof the 700 days closest to each mode of the North Atlantic jet are alsoshown in each panel.

40

Jet lat (° N)

20 30 40 50 60 70

Fre

qu

en

cy

0.01

0.02

0.03

0.04

0.05

0.06

a) JLI given All Waves

Low

Medium

High

Jet lat (° N)

20 30 40 50 60 70

Fre

qu

en

cy

0.01

0.02

0.03

0.04

0.05

0.06

b) JLI given WN1

Jet lat (° N)

20 30 40 50 60 70

Fre

qu

en

cy

0.01

0.02

0.03

0.04

0.05

0.06

c) JLI given WN2

Fig. 6. Kernel estimation to the PDF of daily JLI (N) time series forlow, medium and high values of EPFZ100 computed for all Waves (a),WN1 (b), and WN2 (c). The black line in each panel represents thekernel estimation to full time series (i.e., DJF). The classification oflow, medium and high EPFZ100 is based on percentiles (i.e., Low:EPFZ100≤P25, Medium: P25 <EPFZ100≤ P75 and High: EPFZ100>P75).

41

Pre Onset Post424344454647484950

Mea

n JL

I (∘ N

∘

46.08

46.87

45.71

46.5146.96 46.88

45.70

46.79

44.68

AllD_even sS_even s

Fig. 7. Composites of SSW events and the mean position of the NorthAtlantic jet (in N ). The composites are analysed for onset, one weekbefore (Pre) and one week after (Post) of an event. The winter meanfor the JLI over the analysis period is represented by black dashed line.

42

Je

t L

ati

tud

e D

ev

iati

on

-2

-1

0

1

2

a)

WN

1 D

ev

iati

on

-2

-1

0

1

2

b)

Lag Days from key event

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

WN

2 D

ev

iati

on

-2

-1

0

1

2

c)

Fig. 8. The Superposed Epoch Analysis (SEA) performed for all 30 selectedevents (inclusive Split and Displacement types) shown in Table reftable-ssw-list. The values on the y-axis show the deviation from the meanvalues and the x-axis values are the lead/lag days from an event. Theblack colour represents the zero lag whereas the red and blue coloursrespectively denote the post and pre composites. The 95% confidencelimits are shown by the continuous and dashed curves. The jet latitudedeviation is in N (a), whereas the EPFZ100 anomalies (b and c) areexpressed in x104kgs−2.

43

Fig. 9. The latitude-height cross-sections of EP flux winter climatology forall waves (a), WN1 (b) and WN2 (c). The arrows represent EP fluxand the divergence (ms−1day−1) is in shaded.

44

Fig. 10. The latitude-height cross-sections of EP flux difference betweenwinter climatology and three states of the North Atlantic eddy-drivenjet. The columns from left to right respectively represent the northern,central and southern jet whereas rows from top to bottom respectivelyrepresent all waves, WN1 and WN2. EP flux vectors are displayed onlywhere the EP flux divergence is different from the climatology at 5%significance level. The divergence (in ms−1day−1) is shaded.

45

Fig. 11. The longitude-height cross-sections of geopotential height devia-tions (gpm) from the zonal mean (shading) and Wave Activity Fluxes(vectors) averaged over 45–65N. WAFs are in units of m2s−2. Follow-ing Harada and Hirooka (2017), the vectors are scaled: e.g., above 200hPa Fx and Fz are divided by 20.0 and 0.10 respectively; and below200 hPa by 100 and 0.60.

46

Fig. 12. The longitude-height cross-sections of geopotential height devia-tions (gpm) from the zonal mean (shading) and Wave Activity Fluxes(vectors) averaged over 45–65N. WAFs are in units of m2s−2. Scalingof vectors is same as in Fig. 11. Panels a to c respectively represent thedifference from the climatology, for the northern, central and southernlatitudinal positions of the North Atlantic eddy-driven jet.

47

List of Tables

1 The mean value of EPFZ100 (x104kgs−2) for 700 days clos-est to each mode of the North Atlantic eddy-driven jet fordifferent wave components. . . . . . . . . . . . . . . . . . . . 49

2 A two sampled Kolmogorov–Smirnov test (K–S test) per-formed to assess interdependence of data samples in Fig. 5.Here N, C and S respectively represent EPFZ100 samplesfor the northern, central and southern jet positions. In eachcolumn the value of H0, null hypothesis (the two samplescome from the same population) is presented at 5% signifi-cance value. A value of 1 indicates that the two samples arestatistically different. . . . . . . . . . . . . . . . . . . . . . . 50

3 List of SSWs in JRA-55 from 1958–2014 and their type. Sand D respectively represent the vortex splitting and the vor-tex displacement type events. . . . . . . . . . . . . . . . . . 51

48

Table 1. The mean value of EPFZ100 (x104kgs−2) for 700 days closestto each mode of the North Atlantic eddy-driven jet for different wavecomponents.

North Centre South

All Waves 10.7433 10.52 93 10.5889WN1 5.1559 3.5199 4.4935WN2 2.4763 4.0923 2.7631

49

Table 2. A two sampled Kolmogorov–Smirnov test (K–S test) performedto assess interdependence of data samples in Fig. 5. Here N, C and Srespectively represent EPFZ100 samples for the northern, central andsouthern jet positions. In each column the value of H0, null hypothesis(the two samples come from the same population) is presented at 5%significance value. A value of 1 indicates that the two samples arestatistically different.

All Waves WN1 WN2

N C S N C S N C SN – 0 0 – 1 1 – 1 0C 0 – 0 1 – 1 1 – 1S 0 0 – 1 1 – 0 1 –

50

Table 3. List of SSWs in JRA-55 from 1958–2014 and their type. S and Drespectively represent the vortex splitting and the vortex displacementtype events.

Sr No. Date Type Sr No. Date Type1 17-Jan-1960 D 16 23-Jan-1987 D2 30-Jan-1963 S 17 08-Dec-1987 S3 18-Dec-1965 D 18 21-Feb-1989 S4 23-Feb-1966 S 19 15-Dec-1998 D5 07-Jan-1968 S 20 26-Feb-1999 S6 02-Jan-1970 D 21 11-Feb-2001 D7 18-Jan-1971 S 22 31-Dec-2001 D8 31-Jan-1973 S 23 18-Jan-2003 S9 09-Jan-1977 S 24 05-Jan-2004 D10 22-Feb-1979 S 25 21-Jan-2006 S11 29-Feb-1980 D 26 24-Feb-2007 D12 06-Feb-1981 D 27 22-Feb-2008 D13 04-Dec-1981 D 28 24-Jan-2009 S14 24-Feb-1984 D 29 09-Feb-2010 S15 01-Jan-1985 S 30 07-Jan-2013 S

51