su.diva-portal.orgsu.diva-portal.org/smash/get/diva2:1266172/FULLTEXT01.pdf · GCMs. However, the existence of three preferred latitudinal positions remains a challenge for these

On atmospheric low frequency variability,teleconnections and link to jet variabilityWaheed Iqbal (وحید اقبال )

Academic dissertation for the Degree of Doctor of Philosophy in Atmospheric Sciences andOceanography at Stockholm University to be publicly defended on Thursday 10 January 2019 at10.00 in Nordenskiöldsalen, Geovetenskapens hus, Svante Arrhenius väg 12.

AbstractThe atmosphere is a complex system with an infinite number of independent variables. The best approximations of theatmosphere are made using numerical models. The use of such models provides an invaluable tool for studying theatmospheric system. In the atmosphere, narrow bands of strong winds at upper levels, called jet streams, impact theunderlying large-scale weather conditions. In this Ph.D. thesis, I have studied jet stream variability from reanalyses andclimate models. The regional climate model RCA4 simulations over South Asia reveal a good agreement between modelresults and reanalysis for jet stream representation. Lateral boundary data sources are believed to contribute to discrepanciesover the mountainous regions.

Currently, the weather forecasts have an upper limit of around 10 days. The atmospheric variability between 10 to 40days is known as low frequency variability (LFV). This Ph.D. thesis also examined the LFV from a non-linear perspective,which indicated the existence of multiple recurring atmospheric conditions. The North Atlantic eddy-driven jet, whichexplains a major part of the winter variability over the North Atlantic region, has three preferred latitudinal positionssituated south, closest to, and north of its climatological mean position. These positions represent, respectively, Greenlandblocking, a low-pressure system over the North Atlantic, and a high-pressure system over the North Atlantic. An improvedrepresentation of this jet is reported from CMIP5 GCMs. However, the existence of three preferred latitudinal positionsremains a challenge for these models.

The statistical properties of recurring atmospheric conditions can potentially enhance current weather and climatepredictions. Techniques from dynamical system theory, like unstable periodic orbits, can be employed to reconstruct suchstatistical properties. This has been demonstrated, for the first time, in a three-level baroclinic model, of intermediatecomplexity, for the Northern Hemisphere winter.

In the Northern Hemisphere winter, there are times when the stratosphere gets warmer due to upward propagation ofheat fluxes from the troposphere. This type of situation triggers a major sudden stratospheric warming, resulting in theequatorward shift of the jet streams and yielding much colder than usual surface conditions over the extratropics. I havestudied thirty such events from the Japanese reanalysis data in relation to the three preferred latitudinal positions of theNorth Atlantic eddy-driven jet. The probability of strong upward propagation from the troposphere is significantly higherfor the central position of the North Atlantic eddy-driven jet. These findings can potentially improve the troposphere-stratosphere predictions.

Stockholm 2019http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-162321

ISBN 978-91-7797-518-2ISBN 978-91-7797-519-9

Department of Meteorology

Stockholm University, 106 91 Stockholm

ON ATMOSPHERIC LOW FREQUENCY VARIABILITY,TELECONNECTIONS AND LINK TO JET VARIABILITY 

Waheed Iqbal

On atmospheric low frequencyvariability, teleconnections andlink to jet variability 

Waheed Iqbal

©Waheed Iqbal, Stockholm University 2019 ISBN print 978-91-7797-518-2ISBN PDF 978-91-7797-519-9 Cover image: A view of the polar jet stream over Europe.Credit to: NASA's Scientific Visualization StudioThe Blue Marble data is courtesy of Reto Stockli (NASA/GSFC).  Printed in Sweden by Universitetsservice US-AB, Stockholm 2018Distributor: Department of Meteorology, Stockholm University

To my beloved Familyریمے ایپرے ےبنک ےک انم

Abstract

The atmosphere is a complex system with an infinite number of independentvariables. The best approximations of the atmosphere are made using numer-ical models. The use of such models provides an invaluable tool for studyingthe atmospheric system. In the atmosphere, narrow bands of strong windsat upper levels, called jet streams, impact the underlying large-scale weatherconditions. In this Ph.D. thesis, I have studied jet stream variability from re-analyses and climate models. The regional climate model RCA4 simulationsover South Asia reveal a good agreement between model results and reanaly-sis for jet stream representation. Lateral boundary data sources are believed tocontribute to discrepancies over the mountainous regions.

Currently, the weather forecasts have an upper limit of around 10 days.The atmospheric variability between 10 to 40 days is known as low frequencyvariability (LFV). This Ph.D. thesis also examined the LFV from a non-linearperspective, which indicated the existence of multiple recurring atmosphericconditions. The North Atlantic eddy-driven jet, which explains a major part ofthe winter variability over the North Atlantic region, has three preferred latitu-dinal positions situated south, closest to, and north of its climatological meanposition. These positions represent, respectively, Greenland blocking, a low-pressure system over the North Atlantic, and a high-pressure system over theNorth Atlantic. An improved representation of this jet is reported from CMIP5GCMs. However, the existence of three preferred latitudinal positions remainsa challenge for these models.

The statistical properties of recurring atmospheric conditions can poten-tially enhance current weather and climate predictions. Techniques from dy-namical system theory, like unstable periodic orbits, can be employed to recon-struct such statistical properties. This has been demonstrated, for the first time,in a three-level baroclinic model, of intermediate complexity, for the NorthernHemisphere winter.

In the Northern Hemisphere winter, there are times when the stratospheregets warmer due to upward propagation of heat fluxes from the troposphere.This type of situation triggers a major sudden stratospheric warming, resulting

in the equatorward shift of the jet streams and yielding much colder than usualsurface conditions over the extratropics. I have studied thirty such events fromthe Japanese reanalysis data in relation to the three preferred latitudinal posi-tions of the North Atlantic eddy-driven jet. The probability of strong upwardpropagation from the troposphere is significantly higher for the central positionof the North Atlantic eddy-driven jet. These findings can potentially improvethe troposphere-stratosphere predictions.

Sammanfattning

Numeriska modeller är det bästa verktyget vi har för att beskriva atmosfärenoch studera atmosfäriska skeenden. Atmosfären är ett komplext system ochmodeller av denna är därför känsliga för valet av initialvillkor. I atmosfärenfinns “floder” av kraftiga vindar, så kallade jetströmmar, som påverkar de stor-skaliga vädersystemen. I denna avhandling har jag studerat jetströmmarnasvariabilitet med hjälp av reanalys- och modelldata. Simuleringar med regiona-la klimatmodeller visar på god överenstämmelse med reanalysen. De störstaskillnaderna, som kan ses över bergiga områden, härstammar från den regio-nala modellens randvillkor.

Tillförlitliga väderprognoser är idag begränsade till ungefär 10 dagar. At-mosfärens variabilitet på längre tidsskalor, men kortare än en säsong, kallas förlågfrekvent variabilitet (LFV). I denna avhandling har LFV undersökts från etticke-linjärt perspektiv, vilket indikerade förekomsten av flera återkommandeatmosfäriska tillstånd. Den virveldrivna nordatlantiska jetströmmen har visatsig kunna förklara en stor del av variabiliteten under vintersäsongen i området.Jetströmmen har tre typiska latitudinella lägen; ett söder om, ett nära och ettnorr om dess klimatologiska position. De är kopplade till var sitt storskaligt at-mosfäriskt tillstånd; Grönlandsblockeringen samt ett högtryckssystem respek-tive ett lågtryckssystem över Nordatlanten. Klimatmodeller i CMIP5 uppvi-sar en förbättrad representation av den nordatlantiska jetströmmen, men det ärfortfarande en utmaning att simulera dess tre typiska lägen.

Under norra hemisfärens vinter föreligger tillfällen då stratosfären värmsupp av storskaliga vågor som rör sig uppåt och transporterar energi från tro-posfären. Detta kan utlösa en kraftig plötslig stratosfärisk uppvärmning (majorsudden stratospheric warming) som resulterar i en sydlig förflyttning av jet-strömmen och ovanligt kallt väder på mellanlatituderna. Jag har studerat trettiosådana tillfällen i relation till variabiliteten hos den nordatlantiska jetströmmeni den japanska reanalysen. Sannolikheten för vågor som rör sig uppåt är högreom den nordatlantiska jetströmmen är nära sitt mellersta läge. Dessa resultathar potentialen att förbättra våra förutsägelser rörande förhållandena i tropo-sfären och stratosfären. Atmosfärens förutsägbarhet är större om denna befin-ner sig i ett ihållande, regelbundet återkommande tillstånd, men övergången

mellan tillstånden är fortfarande svår att prognostisera. Jag har använt en teo-retisk baroklin atmosfärsmodell för att studera detta. Resultaten indikerar attdynamiken kan beskrivas genom att tillämpa teorin för dynamiska system påinstabila periodiska trajektorior (unstable periodic orbits technique).

الخہص

رکہ وہایئ اکی دیچیپہ اظنم ےہ سج ںیم ال انتمیہ ریغ اتعب ریغتمات ںیہ -رکہ وہایئ اک رتہبنیادنازہ دعدی ومنونں ےک ذرےعی ایک اجات ےہ - ہی دعدی ومنےن اظنم رکہ وہایئ ےک اطمہعل ےکےیل اومنل وہلیس ںیہ - رکہ وہایئ ںیم حطس زنیم ےس دنلبی رپ زیت راتفر وہاؤں ےک گنت اہبؤ وک

ٹیج رٹسمی اہک اجات ےہ وج زینیم وممس رپ ارث ادناز وہیت ںیہ - اس اقمےل ںیم ںیم ےن ایسی یہ زیتوہاؤں اور ان ےک ریغت وک اموخذ وماد اور دعدی ومنونں یک دمد ےس رپاھک ےہ - ونجیب اایشی ےک ےیل

ںیم زیت وہاؤں یک امندنئیگ ایھچ دیھکی یئگ۴است̀معا\ل ےیک ۓگY دعدی ومنےن آر-یس -اے- ےہ - اہپڑی العوقں ںیم اموخز وماد اور دعدی ومنےن ےک امنیب رفتقی وک سپ رظنم ںیم است̀معا\ل

وہے وماد ےس ایبن ایک اج اتکس ےہ

وموجدہ دور ںیم ومیمس وگشیپیئ یک ابالیئ دح دس روز ےس زایدہ ںیہن ےہ - رکہ وہایئ ںیم دس ےساچسیل روزہ ومایمسیت رگدوشں ےک ریغت وک مک دعتد ریغت زپریی اہک اجات ےہ - اس اقمےل ںیم ںیم

ےن ایسی رگدوشں اک ریغ کی دریج رظنےی ےک سپ رظنم ںیم اجزئہ ایل ےہ- اس رظنےی ےکتحت رکہ وہایئ ںیم ابر ابر آےن وایل رگدوشں اک ووجد وتمعق ےہ - امشیل اوایقونس ںیم ٹیج رٹسمی

اےسی یہ وخاص یک احلم ےہ- رعیض اینبدوں رپ اس ٹیج رٹسمی ںیم نیت ہنکمم اقمامت یک دصتقییتلم ےہ- ہی ونیتں اقمامت ہن رصف امشیل اوایقونس ہکلب دوررس العوقں یک ومایمسیت وگشیپیئ ےکےیل اخص اتیمہ رےتھک ںیہ- ہی ہنکمم اقمامت ابرتلبیت رگنی ڈنیل البگنک ،امشیل اوایقونس ںیم وہاےک مک اور امشیل اوایقونس ںیم وہا ےک زایدہ دابؤ وک اظرہ رکےت ںیہ- ومعیم رگدیش دعدی ومنونں

ںیم اس ٹیج رٹسمی یک امندنئیگ اسہقب ومعیم رگدیش دعدی ومنونں٥ےک ومجمہع یس امی آئ یپ ےک ومجمہع ےک اقمےلب ںیم رتہب وہیئ ےہ- رہبفیک نیت ہنکمم اقمامت یک وموجدیگ ایھب یھب زمدی

وتہج بلط ےہ

راییض یک اکی اشخ رحتمک اظنم یک ویھتری وک ابر ابر اظرہ وہےن وایل ومایمسیت رگدوشں یکانبوٹ اور وگشیپیئ ےک ےیل است̀معا\ل ایک اج اتکس ےہ- ایسی یہ اکی کینکت سج وک "ریغ ینیقی اعیمدی

دمار" ای البیٹسن ریپویڈک اورٹیب ےتہک ںیہ- اےس است̀معا\ل رکےت وہے ںیم ےن یلہپ ابر اسکینکت اک یلمع اظمرہہ اکی دعتمل ومعیم رگدیش دعدی ومنےن ےس ایک ےہ

فصن رکہ امشیل ےک وممس رسام ںیم یھبک یھبک ریغ ومعمیل وتاانیئ رکہ ریغتمہ ےس رکہ اقہمئ ںیم لقتنموہیت ےہ- اس لمع ےک ےجیتن ںیم رکہ اقہمئ ےک درہج رحارت ںیم ااچکن ااضہف وبضمط رغمیب

رگدوشں وک زمکور رک ےک رشمیق رگدوشں ںیم دبل داتی ےہ- ہی وعالم دنچ یہ روز ںیم حطس زنیم رپدشدی رسدی اک ببس ےتنب ںیہ- ںیم ےن اےسی یہ سیت وااعقت وک اجاپین اموخذ وماد ںیم امشیل

اوایقونیس ٹیج رٹسمی ےک نیت ہنکمم اقمامت ےک انترظ ںیم داھکی ےہ- امہرے اجزئے ےکاطمقب اس ٹیج رٹسمی ےک درایمین ہنکمم اقمم ںیم رکہ ریغتمہ ےس ریغ ومعمیل وتاانیئ ےک ااکمانت

زایدہ ںیہ - ہی اتنجئ رکہ ریغتمہ اور رکہ اقہمئ دوونں یک ومایمسیت وگشیپویئں وک رتہب انبےن ںیم امہرکدار ادا رک ےتکس ںیہ

List of Papers

The following papers, referred to in the text by their Roman numerals, areincluded in this thesis.

PAPER I: Iqbal, W., F. S. Syed, H. Sajjad, G. Nikulin, E. Kjellströmand A. Hannachi (2017), Mean climate and representation of jetstreams in the CORDEX South Asia simulations by the regionalclimate model RCA4; Theor. Appl. Climatol., 129: 1–19.DOI: 10.1007/s00704-016-1755-4

PAPER II: Iqbal, W., WN. Leung and A. Hannachi (2018), Analysis ofthe variability of the North Atlantic eddy-driven jet stream inCMIP5; Clim Dyn., 51: 235–247 DOI: 10.1007/s00382-017-3917-1

PAPER III: Iqbal, W., A. Hannachi, T. Hirooka, L. Chafik and Y. Harada(2018), Troposphere-stratosphere dynamical coupling in regardto the North Atlantic eddy-driven jet variability; under review inJournal of Meteorological Society of Japan

PAPER IV: Iqbal, W., A. Hannachi, A. Gritsun, C. L. Franzke (2018), Dy-namical behavior of T21QGL3 model and unstable periodic or-bits; manuscript

Reprints of Papers were made with permission from the publishers.

Author’s contribution

The idea of this PhD project is proposed by my main supervisor A Hannachi.

The idea of paper I was developed by myself and FS Syed. I did all the analysisand wrote the paper. Paper II is a continuation of a previous study (Hannachiet al., 2013). WN Leung did his master thesis with A Hannachi on jet variabil-ity from CMIP5 GCMs. I extended this work to evaluate the performance ofCMIP3 and CMIP5 GCMs. I did all data downloading, analysis and write-up.

Paper III is a collaboration work with Prof. Toshihiko Hirooka. He visitedMISU as an IMI guest and presented work on sudden stratospheric warmingswhich lead to the starting point of this study. I performed all analysis and wrotethe manuscript. Paper IV is a collaboration with A Gritsun and CL Franzke.The original idea was proposed by A Hannachi and was further developed in ameeting with myself and the co-authors. UPOs were computed by A Gritsun.I performed simulations from QG model and analyzed the dynamical behaviorof the model and wrote the initial draft.

The following papers are not included in this thesis:

• Hannachi, A. and W. Iqbal (2018), On the nonlinearity of winter north-ern hemisphere atmospheric variability; Journal of the Atmospheric Sci-ences; in press

• Hannachi, A. and W. Iqbal (2018), Signature of tropospheric nonlinearregime behavior in Northern Hemisphere winter via flow tendencies andkernel empirical orthogonal functions; under review in Tellus

• Hassan, M. P. Du, S. Jia, W. Iqbal, R. Mahmood and W. Ba (2015) Anassessment of the South Asian summer monsoon variability for presentand future climatologies using a high resolution regional climate model(RegCM4. 3) under the AR5 scenarios; Atmosphere, 6(11):1833–1857

Contents

Abstract iii

Sammanfattning v

List of Papers vii

Author’s contribution ix

Abbreviations xiii

List of Figures xv

1 Introduction 17

2 Atmospheric Circulation and Variability 192.1 General circulation of the atmosphere . . . . . . . . . . . . . 192.2 Tropospheric Variability . . . . . . . . . . . . . . . . . . . . 212.3 Stratospheric Variability . . . . . . . . . . . . . . . . . . . . 21

3 Weather Regime Detection 253.1 Flow regime methods . . . . . . . . . . . . . . . . . . . . . . 253.2 Regimes in North Atlantic eddy-driven jet . . . . . . . . . . . 253.3 Example from flow tendencies . . . . . . . . . . . . . . . . . 26

4 Dynamical Systems Theory 29

5 Summary of Papers 31

Acknowledgements xxxv

References xxxvii

Abbreviations

AO Arctic Oscillation

CEOF Complex Empirical Orthogonal Function

CMIP3 Coupled Model Inter-comparison Project phase–3

CMIP5 Coupled Model Inter-comparison Project phase–5

CORDEX Coordinated Regional climate Downscaling Experiments

d.o.f degree of freedom

DJF December–January–February

EOF Empirical Orthogonal Function

EP-flux Eliassen–Palm flux

ERA European Reanalysis

GCM General Circulation Model

gpm geopotential meter

hPa hectopascal

IMI International Meteorological Institute

IPCC Inter-governmental Panel on Climate Change

JLI Jet Latitude Index

JRA Japanese Reanalysis

KPC Kernel Principal Component

LFV Low Frequency Variability

MISU Department of Meteorology, Stockholm University

NAM Northern Annular Mode

NAO North Atlantic Oscillation

NH Northern Hemisphere

PCA Principal Component Analysis

PDF Probability Distribution Function

PNA Pacific North America

QG Quasi-Geostrophic

RCA Rossby Center Atmospheric model

RCM Regional Circulation Model

SASM South Asian Summer Monsoon

SLP Seal Level Pressure

SMHI Swedish Meteorological Hydrological Institute

SSW Sudden Stratospheric Warming

UPO Unstable Periodic Orbit

WCRP World Climate Research Programme

z-20 Geopotential height at 20 hPa

z-500 Geopotential height at 500 hPa

List of Figures

2.1 An illustration of zonal (a) and blocked (b) flows. The contourplots show 10-day mean geopotential height (gpm) at 700 hPafrom JRA-55 reanalysis. 3050 gmp contour is highlighted forvisualization purpose. . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Patterns of variability in the Northern Hemisphere winter (December–February). Leading three Empirical Orthogonal Functions (EOFs)regressed to Mean Sea Level Pressure anomaly (in hPa) fromJRA-55 reanalysis data for the period 1958–2014. Contoursare at 1hPa interval, with positive contours in red and negativecontours in blue, and the zero contour omitted. . . . . . . . . . 21

2.3 An illustration of Troposphere-Stratosphere interactions for weakand strong stratospheric polar vortices. Composites for peri-ods of high and low Northern Annular Mode (NAM) indexat 100 hPa during December–January 1958–2014 from JRA-55 reanalysis. Panels a–b respectively show the zonal wind(in ms−1) composites for HIGH and LOW. Panels c–d showEliassen-Palm (EP) flux latitude–height cross sections for thesum of zonal wavenumbers 1 to 3. The divergence of EP fluxesis shown as contours with blue curves as convergence. . . . . . 23

3.1 Detection of regimes by means of PDF, for North Atlanticeddy-driven jet latitude index (JLI; Woollings et al., 2010) dur-ing winter 1958–2001. Blue curve represents a Gaussian andthe black line is a smooth kernel fitted to the daily Decemberto February jet latitude index time series. . . . . . . . . . . . . 26

3.2 Spatial patterns associated with three preferred latitudinal po-sitions of the North Atlantic eddy-driven jet. The shaded is theJRA-55 reanalysis 500 hPa geopotential height anomalies (ingmp) for the states close the northern mode (a), central mode(b) and southern mode and (c), of the North Atlantic eddy-driven jet. Stippling indicates the areas where the geopotentialheight anomalies are different from the climatological valuesat 5% significance level using a Student’s t-test. . . . . . . . . 27

3.3 Local mean phase space tendencies in EOF2–EOF3 plane, (a)Original tendencies, (b) Linear tendencies and (c) Non-lineartendencies. The magnitude expressed in 1 standard deviationday−1, is in shaded and arrows denote the direction of the ten-dencies. Non-linear tendencies are the difference between theoriginal and the linear tendencies (i.e. a-b). . . . . . . . . . . 28

4.1 A schematic for two types of dynamical behaviour in dynam-ical systems. An unstable dynamics where the neighboringtrajectories diverge after some time (a) and a stable dynamicswhere the two far-apart initial trajectories converge after sometime (b). Adapted from Kalnay (2003). . . . . . . . . . . . . . 30

1. Introduction

The atmosphere is a complex system with an infinite number of independentvariables or degrees of freedom (d.o.f). A small change in the atmosphericconditions could result in an entirely different outcome (Lorenz, 1963). Abun-dance of human-induced emissions have impacted the Earth’s weather and cli-mate at large. The number of extreme events (heat waves, floods, cyclones,droughts etc) has increased (Sobel & Tippett, 2018), posing a great challengeto adaptation for weather and climate change. Weather forecasts at the mo-ment are valid for up to 10 days and beyond this period the forecast qualityis poor. Atmospheric variations beyond the current forecast limits and lessthan a season are called the low frequency variability (LFV). Large-scale at-mospheric conditions related to LFV are described as persistent and recurrentatmospheric conditions – often called weather regimes and teleconnections.The strong zonal flow and blocking phenomena (e.g. Figure 2.1) are exam-ples of large-scale flow regimes. Since they are most frequent and probable,they provide important information to improve atmospheric predictability (e.g.Palmer & Zanna, 2013).

The importance of flow regimes was already recognized in 1940s (e.g.Berggren et al., 1949; Rex, 1950; Rossby, 1940). Weather forecasters in Eu-rope were using these flow regimes to improve forecasts. But these classifi-cations were subjective; from the late 1970s onward the scientific communitystudied weather regimes objectively. The nature of the LFV is still an on-goingdebate, some believe that changes in LFV can be described by linear theory,whereas others favor the non-linear nature of LFV. According to the linear the-ory, the atmospheric dynamics can be approximated as a stochastically drivenlinear system. The non-linear theory advocates the existence of more than onestationary solutions (e.g. Charney & DeVore, 1979; Reinhold & Pierrehumbert,1982) of the atmospheric system and multimodality (more than one peak) inthe probability distribution functions (PDF) (e.g. Corti et al., 1999; Woollingset al., 2010). This non-linear nature of LFV is mainly discussed in this thesis.

The interactions in the two lowest layers of the atmosphere (troposphereand stratosphere) with regard to weather forecasting were not acknowledgeduntil the late 1990s (e.g. Kidston et al., 2015). The two-way coupling between

17

these two atmospheric layers suggests that a better understanding can improvethe atmospheric predictability (Baldwin & Dunkerton, 1999, 2001). Changesin the surface weather together with planetary-scale waves transfer heat fluxesupward which can affect the stratospheric circulation. These stratospheric vari-ations alter the large-scale circulation in the troposphere via downward wavepropagation (Baldwin & Dunkerton, 2001). These important phenomena inone-way or the other result in changes of position and strength of the windfield in the troposphere. This leads to jet variability which is known to be ofparamount importance for surface weather and climate, and therefore affectsenvironment and society.

In this thesis we have investigated the non-linear paradigm of LFV by an-alyzing the Northern Hemisphere large-scale circulation. In particular, we ex-amine key aspects of the the tropospheric jet variability over the North Atlanticregion and South Asia, the formation to large-scale teleconnections as well asthe link to stratospheric variability. We use both conceptual and fully coupledclimate models 1 along with reanalyses2. The important questions addressedin this thesis are:

• How good are the Coupled Model Inter-comparison Project phase-5(CMIP5) models in representing the winter LFV of North Atlantic eddy3-driven jet?

• How is the North Atlantic eddy-driven jet variability related to the strato-spheric variability?

• Are high-resolution simulations from the Rossby Center Atmosphericmodel (RCA4) reasonable for analyzing the jet stream variability overSouth Asia?

• How can we apply dynamical system theory to explore atmospheric flowregimes?

The remainder of the thesis is organized as follows: Chapter 2 discusses theatmospheric circulation and variability; examples from the non-linear perspec-tive of Northern Hemisphere winter regimes are discussed in Chapter 3; theconcepts from dynamical system theory are presented in Chapter 4 as an aid tothe reader. The papers included in this thesis are summarized in Chapter 5.

1Mathematical representation of the physical laws.2Atmospheric data obtained by combining observations and weather forecasting model.3Fluid current whose flow direction differs from that of the general flow.

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2. Atmospheric Circulation andVariability

Weather is the actual status of the atmosphere whereas the average conditionsover a long time (usually 30 years) are called climate. Atmospheric predictabil-ity is achieved through a better understanding of the atmospheric large-scalecirculation. The vertical extent of the atmosphere from surface up to 10–15kilometers is termed the troposphere where most of the weather takes place.The large-scale circulation is symmetric around the equator, but we restrict ourdiscussion to the Northern Hemisphere (NH) as the papers included in the the-sis are focused on the NH. The atmosphere is a complex system and changesat different time scales ranging from minutes to decades. These changes arereferred as atmospheric variability. In this thesis we are interested in the intra-seasonal atmospheric variability over the NH i.e. with time-scale between 10to 40 days.

2.1 General circulation of the atmosphere

Atmospheric circulation is driven by equator-to-pole temperature gradients dueto differential solar heating at lower and higher latitudes. The atmosphericcirculation transports heat from the equator polewards to balance this temper-ature difference. In the higher atmosphere, there exist regions of very fastwinds called the jet streams. The two main jet streams are the subtropical andthe polar jet. The midlatitude eddies, via momentum and heat forcings, laythe ground for the polar jet stream, hence the name eddy-driven jet. The jetstreams play a crucial role for weather and climate variability. The equator-to-pole gradient is stronger in winter as compared to summer. Therefore thejet streams are stronger and located equatorwards during winter. Any changesin the location and strength can have an enormous impact on the underlyingsurface conditions. For example, the storm tracks over the Atlantic are linkedto the variability of the North Atlantic eddy-driven jet. An understanding ofthe jet variability will lead to an improved atmospheric predictability.

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Among these global "wind rivers", there are fast corridors of winds at re-gional levels as well. One example is the Somali jet which is a low-leveljet stream observed south of the Arabian Sea during the South Asian Sum-mer Monsoon (SASM) season. Moisture supply during the SASM is prettymuch dependant on the variability of the Somali jet (as discussed in Paper I).Over the North Atlantic region the North Atlantic eddy-driven jet has provento explain a significant amount of the winter variability (Hannachi et al., 2012;Woollings et al., 2010). We discuss the variability of this eddy-driven jet inCMIP5 GCMs and compare the results to those from CMIP3 GCMs (cf. PaperII).

Atmospheric conditions in the NH are dominated by strong westerly1 windsi.e. zonal flow, but occasionally the formation of high surface pressure condi-tions disrupts this zonal flow resulting in a more "wavy" flow. An exampleof such flows (e.g. blocked and zonal) is shown in Figure 2.1. The weatherregimes thus play a vital role in the atmospheric variability.

Figure 2.1: An illustration of zonal (a) and blocked (b) flows. The contour plotsshow 10-day mean geopotential height (gpm) at 700 hPa from JRA-55 reanalysis.3050 gmp contour is highlighted for visualization purpose.

1Coming from the west.

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2.2 Tropospheric Variability

Empirical Orthogonal Functions (EOFs) are frequently used in the field ofweather and climate to identify modes of variability, propagating signals andto facilitate dimension reduction (e.g. Hannachi et al., 2007). Major patternsof the NH winter variability in the troposphere are shown in Figure 2.2. Thesepatterns are also known as ‘teleconnections’ as they connect weather and cli-mate over great distances (Feldstein & Franzke, 2017; Hannachi et al., 2017).A dipole pattern with opposite Mean Sea Level Pressure (MSLP) daily anoma-lies over Iceland and the Azores is called the North Atlantic Oscillation (NAO;Hurrell et al., 2003). The Northern Annular Mode (NAM), also called theArctic Oscillation (AO), is similar to the NAO with opposite anomalies overthe polar and midlatitude North Atlantic regions. A wave train with oppositeanomalies in the Pacific and North America is termed the Pacific North Amer-ica (PNA) pattern. The beauty lies in the fact that these ‘teleconnections’ havelonger persistent times than synoptic scale phenomena. Also they explain asignificant amount of total winter variance. The first two EOFs for daily MSLPexplain 46% of the DJF variability.

90◦E

180◦

90◦W

(a) EOF1 (23%)

90◦E

180◦

90◦W

(b) EOF2 (13%)

90◦E

180◦

90◦W

(c) EOF3 (10%)

Figure 2.2: Patterns of variability in the Northern Hemisphere winter(December–February). Leading three Empirical Orthogonal Functions (EOFs)regressed to Mean Sea Level Pressure anomaly (in hPa) from JRA-55 reanaly-sis data for the period 1958–2014. Contours are at 1hPa interval, with positivecontours in red and negative contours in blue, and the zero contour omitted.

2.3 Stratospheric Variability

The stratosphere is the atmospheric layer where temperature increases withheight as opposed to conditions in the troposphere. It comprises only 15% ofthe atmospheric mass. The importance of the stratosphere in relation to day-to-day weather was not much acknowledged until the late 1990s (e.g. Kidston

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et al., 2015). Rather it was considered that only the troposphere can affect thestratosphere via vertical wave propagation but not the other way around. Thestratospheric variability is characterized by changes in the stratospheric polarvortex (strong westerly circulation at higher latitudes).

The stratospheric polar vortex owes its development in autumn to reducedsolar heating over higher latitudes (Waugh et al., 2017). The stratospheric po-lar vortex is strongest in the winter with westerly flow around the polar anticy-clone1 and in summer the mean flow around the polar anticyclone is easterly2

(e.g. Hartmann et al., 2000; Waugh et al., 2017). The stratospheric polar vor-tex because of anomalous planetary wave activity from the troposphere losesits strength and is displaced from its centre of action (viz. the pole) or splitinto two or more vortices. Such changes are related to a phenomenon knownas Sudden Stratospheric Warming (SSW). A SSW takes place when, due toanomalous planetary wave activity, temperatures in the stratosphere rise up to50 ◦C within few days and the zonal flow north of 60 ◦ latitude is reversed.Whenever such a scenario happens the effects on the surface weather, are ob-served later on in the form of extremely cold anomalies.

Figure 2.3 demonstrates the effects of the stratospheric polar vortex vari-ability on the surface heat fluxes from the troposphere in the NH winter viaEP fluxes3. Here the ‘HIGH’ refers to situations when there is a strong pres-sure gradient between higher and lower latitudes, indicating a stronger polarvortex in the stratosphere. The composites of stronger polar vortices implya very weak impact of vertical wave propagation from the planetary waves,whereas the situation is reversed in the case of a ‘LOW’ polar vortex (Hart-mann et al., 2000). In paper III we analyzed major SSWs in relation to theNorth Atlantic eddy-driven jet variability from reanalysis data. We found thatthe central mode of the jet has a higher probability of upward propagation.The latitudinal positions of the jet are south of its climatological mean posi-tion about three weeks before the onset of an SSW.

1High pressure.2Coming from the east.3A vector quantity with nonzero components in the latitude–height plane, the direction and

magnitude of which determine the relative importance of eddy heat flux and momentum flux.

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Figure 2.3: An illustration of Troposphere-Stratosphere interactions for weakand strong stratospheric polar vortices. Composites for periods of high and lowNorthern Annular Mode (NAM) index at 100 hPa during December–January1958–2014 from JRA-55 reanalysis. Panels a–b respectively show the zonal wind(in ms−1) composites for HIGH and LOW. Panels c–d show Eliassen-Palm (EP)flux latitude–height cross sections for the sum of zonal wavenumbers 1 to 3. Thedivergence of EP fluxes is shown as contours with blue curves as convergence.

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3. Weather Regime Detection

We introduced the large-scale circulation in Chapter 2. In this chapter wepresent an overview of flow regimes detection by providing examples for theNorth Atlantic eddy-driven jet and extratropical large-scale circulation in theNH. The North Atlantic eddy-driven jet is our main focus in Paper II and Pa-per III. The North Atlantic sector is defined as the region within the longitudes:60◦W–0◦W and the latitudes: 15◦N–75◦N.

3.1 Flow regime methods

The large-scale circulation regimes from reanalysis or model outputs can bedetected using various statistical techniques (e.g. Hannachi et al., 2017). Inorder to look for weather regimes, the system is reduced to low dimensions byapplying EOF analysis. Here we present only those methods which have beenused to explore the regimes from reanalysis and model outputs in this thesis.

1. States maximizing the probability distribution function (e.g. Hansen &Sutera, 1986)

2. Flow tendencies (e.g. Branstator & Berner, 2005; Hannachi, 1997)

Other than these two methods k-means clustering (e.g. Michelangeli et al.,1995), self organizing maps (e.g. Huth et al., 2008) and hidden Markov models(e.g. Franzke et al., 2008) are also used.

3.2 Regimes in North Atlantic eddy-driven jet

In Figure 3.1, histograms of the jet latitude index (JLI; Woollings et al., 2010) –an index to measure the latitudinal position of the North Atlantic eddy-drivenjet – are shown along with a kernel estimate and a Gaussian fit. The kernelestimation of these histograms shows three maxima which mark the trimodail-ity of the jet PDF. The atmospheric conditions associated with these preferred

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Figure 3.1: Detection of regimes by means of PDF, for North Atlantic eddy-driven jet latitude index (JLI; Woollings et al., 2010) during winter 1958–2001.Blue curve represents a Gaussian and the black line is a smooth kernel fitted tothe daily December to February jet latitude index time series.

latitudinal positions of the jet are shown in Figure 3.2. These states respec-tively, represent, negative NAO (Figure 3.2c), a low-pressure system over theNorth Atlantic (Figure 3.2b), and a high-pressure system over the North At-lantic (Figure 3.2a).

3.3 Example from flow tendencies

The flow tendencies approach (Branstator & Berner, 2005; Hannachi, 1997)is simply a finite difference trajectory evolution in the reduced phase space.In simple terms, an EOF analysis is applied to the model output and only fewleading (low-order) EOFs are retained. Then the flow tendencies are computedusing any two EOFs. An example of this technique is presented in Figure3.3. The first panel shows the direction of tendencies towards the center andthe magnitude close to the center is minimal. The circular or elliptical ten-dencies correspond to linear dynamics (no multiple solutions of the system),whereas non-elliptical tendencies correspond to non-linear dynamics (Bransta-tor & Berner, 2005; Franzke et al., 2007; Hannachi, 1997; Kondrashov et al.,2011).

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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

Figure 3.2: Spatial patterns associated with three preferred latitudinal positionsof the North Atlantic eddy-driven jet. The shaded is the JRA-55 reanalysis 500hPa geopotential height anomalies (in gmp) for the states close the northern mode(a), central mode (b) and southern mode and (c), of the North Atlantic eddy-driven jet. Stippling indicates the areas where the geopotential height anomaliesare different from the climatological values at 5% significance level using a Stu-dent’s t-test.

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(a) Original

PC2

-2 0 2

PC

3

-3

-2

-1

0

1

2

3

0

0.1

0.2

0.3

0.4(b) Linear

PC2

-2 0 2

PC

3

-3

-2

-1

0

1

2

3

0

0.1

0.2

0.3

0.4

(c) Non-linear

PC2

-2 0 2

PC

3

-3

-2

-1

0

1

2

3

0

0.1

0.2

0.3

0.4

Figure 3.3: Local mean phase space tendencies in EOF2–EOF3 plane, (a) Orig-inal tendencies, (b) Linear tendencies and (c) Non-linear tendencies. The magni-tude expressed in 1 standard deviation day−1, is in shaded and arrows denote thedirection of the tendencies. Non-linear tendencies are the difference between theoriginal and the linear tendencies (i.e. a-b).

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4. Dynamical Systems Theory

As Galileo said, "Nature is written in mathematical language". Therefore, inorder to understand Nature we need its language, i.e. Mathematics. The atmo-spheric models, either weather or climate are basically a set of mathematicalequations which can be transformed and interpreted by employing the con-cepts from dynamical system theory. Such an illustration is presented in PaperIV. Here, for the convenience of the reader, we provide a brief overview of theterminology relevant to this thesis.

A dynamical system is a system that changes its state in time. As de-scribed by Strogatz (1994), there are two types of dynamical systems: differ-ential equations and iterated maps. The differential equations deal with theevolution of a system in continuous time, whereas in the latter case the timeis discrete. The mathematical models for the atmosphere are presented in theform of partial differential equations, which can be transformed by projectionmethods to iterated maps i.e. dynamical system of second type. The benefit isthat the system dynamics can be qualitatively understood and interpreted with-out actually solving the system explicitly. Equation 4.1 represents a dynamicalsystem:

dxdt

= f (x), (4.1)

where f (x) represents a vector function that specifies the time-dependence ofx, "living" in a real m-dimensional space Rm.

Trajectory: a curve or path showing the evolution of the system dynamicsstarting from one point to another in a space. Phase space: a space where allpossible solutions are presented. This is also called state space or phase por-trait. For example, the EOF2/EOF3 plane shown in Figure 3.3, is an exampleof a phase space. Fixed points or stationary solutions: points in phase spacefor which the system dynamics do not change. A fixed point is said to be a sta-ble fixed point if the trajectory converges when it starts in its neighbourhoodand if the flow is away from that point, it is designated as an unstable fixedpoint.

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Figure 4.1: A schematic for two types of dynamical behaviour in dynamicalsystems. An unstable dynamics where the neighboring trajectories diverge aftersome time (a) and a stable dynamics where the two far-apart initial trajectoriesconverge after some time (b). Adapted from Kalnay (2003).

Periodic orbit: closed trajectories which repeat themselves after sometime. Unstable Periodic Orbit (UPO): dynamically unstable periodic orbits.The least unstable UPOs are important because the system trajectories in thephase space spend most of the time in their neighbourhood. Lyapunov expo-nent: The rate of convergence/divergence of two neighbouring trajectories ismeasured by Lyapunov exponent. A positive exponent means that the neigh-bouring trajectories diverge and the underlying system has a sensitive depen-dence to small changes in the initial condition, like our atmosphere. LyapunovSpectrum: the set of all Lyapunov exponents, usually represented in descend-ing order. The spectrum is used to compute important invariant measures ofthe dynamical system.

Since the discovery of Chaos by Lorenz (1963), the concepts from dy-namical system theory have been applied to weather and climate studies morefrequently. The atmosphere is sensitive to initial conditions, this characteris-tics in model is analyzed by computing the Lyapunov exponents. The negativeLyapunov exponents provide asymptotic stability. The use of UPOs in fullycoupled models has not been achieved yet, but results from the reduced loworder models suggest that important statistical characteristics can be recon-structed from UPOs. In paper IV we demonstrate the application of UPOs tothe results from a three-level QG baroclinic model.

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5. Summary of Papers

Paper I

Regional Climate Model (RCM) simulations provide detailed climate informa-tion for a region. Therefore, RCM output is useful for impact assessment andadaptation studies. The World Climate Research Program (WCRP) initiatedCoordinated Regional climate Downscaling Experiments (CORDEX) for 13domains around the globe. One among these domains is South Asia, where weexperience the South Asian Summer Monsoon (SASM) phenomenon whichhas vast regional and global societal impacts. In Paper I, the objective is toevaluate the performance of RCA4, a regional climate model from the RossbyCenter of the Swedish Meteorological Hydrological Institute (SMHI), over theCORDEX South Asia domain, with an emphasis on the jet streams in summerand winter.

The simulations at a 50 kilometer horizontal resolution were analyzed forthe period 1980–2005. We show that the model has good skill to reproducethe climatology. However, the surface temperature simulated by model wasunderestimated over complex topographic regions. The two simulations onederived by ERA-Interim reanalysis and the other one by EC-Earth GCM, wereable to reproduce the extent of SASM reasonably well but winter precipitationwas under-estimated in EC-Earth driven simulations.

The role of the Somali jet for stronger SASMs, is to enhance the moisturesupply from the Arabian Sea, resulting in heavy precipitation. This dynami-cal feature was reproduced by RCA4 simulations. The Tropical Easterly jet inwet summers is also stronger in both RCA4 simulations. The underestimationof winter rainfall from the EC-Earth driven simulation is consistent with theweakening of the Sub-tropical jet. We finally concluded that RCA4 provides areasonable climatology over South Asian CORDEX domain. The cold biasesresult from the deriving data set.

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Paper II

General circulation models provide an invaluable tool for studying the large-scale dynamics. The initiative from the WCRP in collaboration with the mod-elling communities, started the Coupled Model Inter-comparison Project (CMIP).This has massive amount of data freely available to researchers, the resultsfrom these CMIP studies are later assessed in the IPCC reports. Although someGCMs are good at representing the temperature and precipitation patterns, thevariability of the jet streams remains a challenge for majority of them. PaperII is a continuation study of Hannachi et al. (2013), where they used CMIP3GCMs to explore the dynamical behavior of the North Atlantic eddy-driven jet.We analyzed the same available GCMs from CMIP5 simulations to see if im-provements could be achieved in simulating the North Atlantic eddy-driven jet.

We show that the jet statistics (latitude and speed) from the historicalCMIP5 simulations are comparable to ERA-40 reanalysis data. However, inwinter months when the jet is stronger, CMIP5 GCMs show even stronger jetspeed compared to ERA-40. The ensemble mean of jet latitude biases in thehistorical simulations of CMIP3 and CMIP5 indicate that overall CMIP5 havereduced the mean difference from reanalysis data which was higher in CMIP3GCMs. The future projections from CMIP5 GCMs suggest a poleward-shiftedjet. The important feature of the North Atlantic eddy-driven jet is, its tri-modaility (three regimes), which was not observed in CMIP3 simulations. TheCMIP5 GCMs show no improvements in reproducing this trimodal feature ofthe eddy-driven jet.

Paper III

This paper examines the relation between the North Atlantic eddy-driven jetregimes and the major Sudden Stratospheric Warmings from a reanalysis dataset. We analyze the jet variability in the Japanese Reanalysis data set (JRA-55)and compare it to that of ERA-40 reanalysis as well. The results reveal that thetwo reanalyses are in good agreement regarding the variability and trimodalityof the North Atlantic eddy-driven jet.

These three modes of the jet are then analyzed with thirty major SSWevents from 1958–2014 winters (December to February). We find that theupward wave activity and the trimadolatiy of the jet are closely related. Thestratospheric polar vortex experiences significant changes via upward wavepropagation associated with the jet positions. It is found that when the jet is

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located close to its central mode the wave propagation of zonal wave number 2(WN2) from the troposphere to the stratosphere is significantly high. Eliassen-Palm (EP) fluxes from all waves and zonal wave number 1 (WN1) depict decel-eration of the stratospheric polar vortex for the eddy-driven jet with latitudinalposition close to the northern mode. Plumb wave activity variations originatemainly over the Atlantic sector for the North Atlantic eddy-driven jet states.These significant links between the North Atlantic eddy-driven jet latitudinalpositions and the stratospheric dynamics may lead to improved predictability.

Paper IV

The nonlinear nature of weather and climate has received a considerable atten-tion from the scientific community in order to address the issue of the atmo-spheric predictability. Weather predictability for low frequency variability canbe explored using the concept of regime behavior. The techniques from dy-namical system theory, provide useful tools for climate studies, like Lyapunovexponents, the attractor dimension etc. The unstable periodic orbit (UPO) is animportant dynamical tool that can be employed to reconstruct the probabilitydistributions of the atmospheric circulations.

A similar approach has been applied here to explore the dynamical behav-ior from a T21 QG three-level baroclinic model, appropriate for the NorthernHemisphere winter climatology. The model has been run for more than onemillion days and the results are analyzed for the middle level (500 hPa) stream-function. The model is capable of reproducing the climatology and major pat-terns of the variability. There are 71 positive Lyapunov exponents, showingthe chaotic nature of the system. Due to computational limitations, a total of29 UPOs have been analyzed with time-periods varying from 2 to 6 days. Theprojection of UPOs on the complex empirical orthogonal functions reveal theperiodic motion. These results provide insights from a baroclinic model forthe UPOs which can further be applied in future predictability studies.

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34

Acknowledgements

First all I would like to thank my supervisor Abdel Hannachi, who gave me theopportunity to work with him. I am grateful to him for his continuous supportand guidance during these four years of my PhD.

I would like extend thanks to my co-supervisor Peter Lundberg for alwaysbeing there; and his kind support regarding visa letters and administrative mat-ters. Thanks to Raymond T. Pierrehumbert for inspiring discussions and co-supervision during first year of my PhD. Thanks to my PhD committee mem-bers Annica Ekman and Johan Nilsson for their support.

I would like to express my gratitude to MISU for hosting me and providingan awesome research atmosphere. Everyone at MISU from administration andresearch staff has been super nice. I wish to extend a huge thank you to ev-eryone at MISU. Thanks to all current and former PhD students. Some specialwords of gratitude go to Lena, Aitor, Tongmei, Xiang-Yu, Maartje, Ettiene,Anna, Jakob Svenson, and Dipanjan. Special thanks to Sara Broomè and Evafor Swedish translation of the abstract. Lena and Aitor many thanks for prac-tically introducing me to a lot of new stuff. Tongmei thanks for the badmintonlessons, it was fun and refreshing.

Thanks to Laurant, Saeed Falahat and Susanna (x2) for their support. Thanksto Leon and Fabian for nice discussions. Thanks to CL Franzke and A Gritsunfor fruitful collaboration.

I acknowledge the International Meteorological Institute (IMI) for providingme the opportunity to meet and work with the expert scientists. Special thanksto Toshihiko Hirooka for hosting me at the Kyushu University, Fukuoka, Japan.I would also like to thank the Bolin Climate Center for funding my visits toattend AGU 2016 and EGU 2017.

I would like to thank the Lillvalch program for funding my visit to OxfordUniversity. Thanks to Tim Woollings and Lesley Grey for their hospitality andinspiring discussions. Thanks to Qiong for her continuous support and fundingmy visit to China.

I would also like to pay my gratitude to Syed Faisal Saeed for always beingthere.

I would like to express my sincere thanks to all my teachers especially RafiqMalik for being an inspiration. I admire your teaching and your passion forMathematics.

I am lucky to have so many friends, my appreciation is beyond expression forall of you! Tariq & Naeem I owe you one.

Words are inadequate to express my gratitude and respect, to my late uncleSultan Ahmad. Your memories will always be with me.

Finally, I would like to thank my parents, siblings, cousins: Shafiq, Rafiq andNaveed. I couldn’t have done this without you. Thanks to my in-laws as wellfor their support.

Last but not least, I would like to thank my wife Maida for her unconditionaland constant support.

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