Atmospheric & Oceanic Applica-tions of Eulerian and LagrangianTransport Modelling

Joakim Kjellsson

Abstract

This thesis presents several ways to understand transports of air and water masses inthe atmosphere and ocean, and the transports of energy they imply. It presents workusing both various kinds of observations and computer simulations of the atmosphereand oceans. One of the main focuses is to identify similarities and differences betweenmodels and observations, as well as between different models.

The first half of the thesis applies Lagrangian methods to study flows in the atmo-sphere and oceans. Part of the work focuses on understanding how particles follow thecurrents in the Baltic Sea and how they disperse. It is suggested that the commonlyused regional ocean model for the Baltic Sea, RCO, underestimates the transport andthe dispersion of the particles, which can have consequences for studies of e.g. bio-geochemistry as well as for operational use. A similar methodology is used to studyhow particles are transported between the tropics and mid-latitudes by the large-scaleatmospheric circulation. It is found that the mass transport associated with north-bound and southbound particles can cancel in the zonally averaged circulation, and itis proposed that the degree of cancellation depends on the method of averaging.

The latter half of the thesis focuses on Eulerian stream functions and specificallya thermodynamic stream function that combines the zonal and meridional circulationsof the atmosphere into a single circulation. The stream function is used as a diagnosticto study the inter-annual variability of the intensity and thermodynamic properties ofthe global atmospheric circulation. A significant correlation to ENSO variability isfound both in reanalysis and the EC-Earth coupled climate model. It is also shownthat a set of models from the CMIP5 project show a slowdown of the atmospheric cir-culation as a result of global warming and associated changes in near-surface moisturecontent and upper-level radiative cooling.

Cover image: Plume of ash from the Eyjafjallajökull volcano seen by the Envisat Medium Resolu-tion Imaging Spectrometer on 11 May 2010. Forecasts of ash clouds are often done by Lagrangianmodels. Photo: ESA

c©Joakim Kjellsson, Stockholm 2014

ISBN 978-91-7447-823-5

Printed in Sweden by US-AB, Stockholm 2014

Distributor: Department of Meteorology, Stockholm University

Till min mor Eva som föreslog att jag skullestudera meteorologi vid Stockholms universitet, och

dessutom stöttade mig hela vägen . . .

Vi satte båtarna i bäcken

såg dom flyta in i tunneln

kanske vidare mot Vättern

och kanalen ut till Nordsjön

över vågorna mot Irland

ut på havet och sen blåsa

iväg och aldrig komma tillbaka

mer till bäcken

där det började

ur “Söndermarken” av Lars Winnerbäck

List of Papers

The following papers, referred to in the text by their Roman numerals, are included inthis thesis.

PAPER I: Surface drifters and model trajectories in the Baltic Sea,Kjellsson J. and Döös K. (2012), Bor. Env. Res., 17, 447–459.

PAPER II: Lagrangian decomposition of the Hadley and Ferrel Cells,Kjellsson J. and Döös K. (2012), Geophys. Res. Lett., 39, L15807.DOI: 10.1029/2012GL052420

PAPER III: The Atmospheric General Circulation in Thermodynamical Coor-dinates,Kjellsson J., Döös K., Laliberté F. and Zika J. (In press.), J. Atmos. Sci.DOI: 10.1175/JAS-D-13-0173.1

PAPER IV: Slowdown of Atmospheric General Circulation with Global Warm-ing,Kjellsson J. (Manuscript),

Reprints were made with permission from the publishers Boreal Environment Re-search Publishing Board (Paper 1), John Wiley & Sons Ltd. (Paper 2), and the Amer-ican Meteorological Society (Paper 3).

Author’s contribution

Paper 1 emerged within the EU/BONUS+ project BalticWay where my task was tovalidate the upper-ocean mass transport in an ocean model using observations col-lected by Kristofer Döös. The idea came from me and Kristofer Döös. Ocean modelintegrations were provided by Markus Meier from SMHI. I processed the observa-tional data, designed and performed all trajectory simulations and all analyses. Thepaper was written by me and Kristofer Döös.

For Paper 2, the idea came from discussions between me, Kristofer Döös, Jonas Ny-cander and Rodrigo Caballero. I designed the trajectory simulations together withKristofer Döös. I performed all trajectory simulations, analyses and wrote the paperwith inputs from Kristofer Döös.

Paper 3 was an idea based on discussions with me, Kristofer Döös, Johan Nilsson,Maxime Ballarotta, Jan Zika, and Frédéric Laliberté partly during an oceanographyworkshop in Stockholm. EC-Earth integrations were provided by Laurent Brodeau.I performed all analyses and wrote the initial draft of the paper. The final paper wasimproved by me, Kristofer Döös, Jan Zika and Frédéric Laliberté.

Paper 4 was my own idea based on results from Paper 3. I collected all data, performedall analyses, and wrote the paper with inputs from Kristofer Döös and Maxime Bal-larotta.

Contents

Abstract ii

List of Papers v

Author’s contribution vii

Acknowledgements xi

1 What is Lagrangian and what is Eulerian? 13

2 The Eulerian framework 172.1 Computer models of atmosphere and ocean . . . . . . . . . . . . . . 172.2 Eulerian stream functions . . . . . . . . . . . . . . . . . . . . . . . . 19

3 The Lagrangian framework 233.1 Lagrangian observations of the world oceans . . . . . . . . . . . . . . 233.2 TRACMASS - An algorithm for Lagrangian trajectories . . . . . . . 233.3 Some Lagrangian statistics . . . . . . . . . . . . . . . . . . . . . . . 263.4 Lagrangian stream functions . . . . . . . . . . . . . . . . . . . . . . 27

4 Transports in the Baltic Sea and environmental risks 29

5 The overturning circulation of the atmosphere 315.1 Past and present . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2 Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6 Outlook 39

Sammanfattning xli

References xliii

Acknowledgements

They say that behind every successful meteorologist stands an even more successfuloceanographer. In my case, there are two: Kristofer Döös and Jonas Nycander, whodecided to hire me when others would not. Thank you for giving me the opportunityto pursue a PhD in Atmosphere and Ocean sciences! I’d also like to thank the peoplefrom the Baltic Way project for support, especially the leaders Tarmo Soomere andEwald Quak. I’m also grateful for all the help and advice from Peter Lundberg andJohan Nilsson over the years. Thank you! Also, thank you Tom Rossby and my shipmates onboard the R/V Endeavour from University of Rhode Island for teaching mehow observational oceanography is done.

I’d like to thank Fred Laliberté and Jan Zika, two brilliant young scientists fromwhom I learned a lot during the latter half of my PhD, and also Bror Jonsson (withoutthe ö. . . ) for introducing me to Princeton, being so supportive, and for all the longdiscussions of science, cold beverages and politics.

I also wish to thank the Climate Research School and the Bolin Centre for ClimateResearch for the great courses, the travel grants and the PhD conference. I’ve alsohad a lot of help from the National Supercomputer Centre at Linköping Universityand their fantastic facilities and support team. Furthermore, I thank Rune Grand Gra-versen et al. for a great CESM course in Stockholm.

Thanks to my travel companions over the years for making conferences such asEGU and AGU way more fun than they seem. Thank you Maxime (and Natalie),Magnus, Jenny, Cecilia, Marie, Cian, Abubakr, Peggy, Matthias and Henrik! Andthank you Susanne for helping me filling out the travel bills! Thanks also to the MGFsSaeed, Laurent and Cian for all the lunches. A big thanks to the innebandy team(a member list to long for the purposes of this paragraph) for making Thursdays myfavourite working day.

A very special thanks to my roommate Léon. After 11 years together in theSwedish educational system we now part ways. Your hard work has been a true inspi-ration, and I wish you all the best of luck in your future career as a scientist, marathonrunner and family man.

Moreover my family are worthy of a special acknowledgement. I would not havesurvived the undergraduate studies without the support from my mom Eva and dadTommy. Nor would it not have been this fun without my sister Sofia. The greatestthanks of all goes out to my dear girlfriend Viktoria. Thank you for putting up with

me when I try to explain my work, and thank you for supporting me when things didnot go that well.

PS. Climate-model data for Paper 4 was partly gathered during a time when mostwebsites for US research centers were down (PCMDI, GFDL, NASA, etc.), so I’d liketo “thank” President Obama, the US Congress and Senate for making data collectiona challenge.

1. What is Lagrangian and whatis Eulerian?

When you observe a fluid in motion, for instance water in a river, there are two pos-sible viewpoints: the Eulerian1 and Lagrangian2 view. In the Eulerian view the ob-server stands at a fixed point in space and observes how the flow evolves. In theLagrangian view the observer moves with the flow and observes its evolution whilemoving. A simple analogy is the various ways of seeing the “Vasaloppet”, the 90 kmcross-country skiing race between Sälen and Mora held every year in Sweden. By-standers will see the race from a fixed point in space, i.e. Eulerian, while TV camerasfollow the race by moving with the leader, i.e. Lagrangian.

Consider the temperature, T , at Observatoriekullen in Stockholm. The observer isthen taking the Eulerian view (fixed point in space), and the temperature in Stockholmdepends both on local effects (i.e. the sun warming the air) and advective effects(i.e. warm air blowing in over Stockholm). However, if the observer would take theLagrangian view (follow the air as it moves in over Stockholm) the total effect on theair mass would be observed. We summarise this into the equation

∂T∂ t

+v ·∇T︸ ︷︷ ︸Eulerian

=dTdt︸︷︷︸

Lagrangian

, (1.1)

where v = (u,v,w) is the three-dimensional wind (cf. Vallis (2006)). The La-grangian derivative is thus a sum of the local Eulerian effect (∂T/∂ t) and the advectiveEulerian effect (v ·∇T ). The word “Lagrangian” is sometimes replaced by “material”to indicate that the observer is following a piece of material, i.e. a particle or a parcel.

Observations of the atmosphere and oceans are often from an Eulerian view, i.e.weather stations, satellites, moored bouys, etc. The weather forecasts presented ontelevision is often described using the Eulerian view, i.e. “the temperature in Stock-holm will be +5C” and “the wind will be 5 m s−1 westerly”. Observations froma Lagrangian view are also used, but to a much smaller extent. An example is theGlobal Drifter Program3 which uses about 1000 satellite-tracked floating buoys in theocean which can measure temperature and air pressure every hour while drifting withthe ocean currents. Another example is Morel & Desbois (1974) who released about

1After Leonhard Euler (1707-1783)2After Joseph Louis Lagrange (1736-1813)3http://www.aoml.noaa.gov/phod/dac/index.php

13

GF

Bay St LouisGulfport Pascagoula

Mobile

Pensacola

Milton

GF

Bay St LouisGulfport Pascagoula

Mobile

Pensacola

Milton

Trajectory ForecastMississippi Canyon 252

Estimate for: 0600 CDT, Thursday, 5/06/10Date Prepared: 1300 CDT, Wednesday, 5/05/10

NOAA/NOS/OR&R

0 30 6015

Miles

UncertaintyLightMediumHeavy

Trajectory

Potentialbeached oil

Mississippi Sound

ChandeleurSound

BretonSound

MobileBay

X

This forecast is based on the NWS spot forecast from Wednesday, May 5 AM. Currents were obtained from the NOAAGulf of Mexico, Texas A&M/TGLO, and NAVO/NRL models and HFR measurements. The model was initialized fromsatellite imagery analysis provided by NOAA/NESDIS obtained Wednesday morning and a Wednesday morninghelicopter overflight. The leading edge may contain tarballs that are not readily observable from the imagery (hence notincluded in the model initialization).

Winds are forecast to be light (5 kts) and variable continuing through Thursday morning. S/SEwinds at 10 kts are expected to resume again Thursday afternoon/evening and continue throughFriday. The Mississippi Delta, Breton Sound and Chandeleur Sound continue to be threatened byshoreline contacts throughout the forecast period. All three ocean models show a westwardcurrent developing south of the Delta transporting oil to the west of the Delta.

Forecast location for oilon 06-May-10 at 0600 CDT

NextForecast:

May 6th AM

Mississippi Canyon 252Incident Location

Figure 1.1: Forecasted transport from the Deepwater Horizon oil leak calculated by theNational Oceanic and Atmospheric Administration (NOAA) using a Lagrangian transportmodel. Blue colours show the concentration of oil, and red marks show locations whereoil may reach the shore. Image courtesy of NOAA’s Office of Response and Restoration.

14

500 balloons over the Southern Hemisphere and used information about their motionto map the winds around Antarctica. Lagrangian forecasts can also be of great impor-tance. In 2010, the Deepwater Horizon oil ridge in the Gulf of Mexico sank causingthe largest oil leak in U.S. history with devastating consequences for the marine lifeand coastal areas. The National Oceanic and Atmospheric Administration (NOAA)produced daily forecasts of the oil spreading to warn the public and to plan operationsto recover or burn some of the oil still at sea.

15

16

2. The Eulerian framework

2.1 Computer models of atmosphere and ocean

Almost all computer models of the atmosphere and oceans are Eulerian, i.e. they givethe results from a fixed point of view. To represent the global atmosphere in a com-puter one must first discretise the atmosphere by dividing it into a number of boxes asin Fig. 2.1. The method is very similar to dividing a photograph into pixels. A pho-tograph on a computer is actually a digital representation of the view from the cameralens. In the same way, the global atmosphere in a computer model is a digital represen-tation of a continuous atmosphere. Similar to photography, more pixels/boxes shouldgenerally give a picture/model that is more similar to reality. However, a higher res-olution, i.e. more boxes, consumes more computer resources. As meteorologists andclimate modellers strive to produce better weather forecasts and climate predictionssome of the most powerful computers in the world are used for running atmospheric,ocean, or climate models.

Fundamentally, a computer model of the atmosphere is a computer program thatsolves a series of equations for each box (Fig. 2.1). The output from an atmosphericmodel is thus temperature, wind, humidity, pressure, etc. in each box. An oceanmodel typically outputs current velocity, temperature, salinity, density, etc. A “cli-mate” model is a coupled model, where models of e.g. atmosphere, ocean, sea-ice,land, air chemistry, marine ecosystem, etc., run at the same time and feed back oneach other. It therefore outputs a wide range of data.

A model of the atmosphere, like the Integrated Forecasting System (IFS) modelfrom the European Centre for Medium-range Weather Forecasts (ECMWF), solves anequation similar to

∂T∂ t

+v ·∇T + η∂T∂η− κTvω

(1+(δ −1)q)p︸ ︷︷ ︸dynamics

= PT +KT︸ ︷︷ ︸physics

, (2.1)

in each grid box. Similar equations for wind, humidity, etc. can be found in e.g.Kalnay (2003). In this equation, T is the temperature and the terms on the left-handside correspond to: local heating/cooling, horizontal transport, vertical transport andadiabatic expansion. These terms are often called the “dynamics” of a model sincethey represent the evolution of the flow using basic fluid dynamics. The two termson the right-hand side, PT and KT , are the “parameterisation” and “diffusion” terms,often called the “physics” of the model. These include the effect of processes that arenot resolved in computer models.

17

a)

Part IV: Physical Processes

Chapter 1

Overview

Table of contents1.1 Introduction

1.2 Overview of the code

1.1 INTRODUCTION

The physical processes associated with radiative transfer, turbulent mixing, subgrid-scale orographic drag,moist convection, clouds and surface/soil processes have a strong impact on the large scale flow of theatmosphere. However, these mechanisms are often active at scales smaller than the horizontal grid size.Parametrization schemes are then necessary in order to properly describe the impact of these subgrid-scale mechanisms on the large scale flow of the atmosphere. In other words the ensemble e↵ect of thesubgrid-scale processes has to be formulated in terms of the resolved grid-scale variables. Furthermore,forecast weather parameters, such as two-metre temperature, precipitation and cloud cover, are computedby the physical parametrization part of the model.

This part (Part IV ‘Physical processes’) of the IFS documentation describes only the physicalparametrization package. After all the explicit dynamical computations per time-step are performed,the physics parametrization package is called by the IFS. The physics computations are performed onlyin the vertical. The input information for the physics consists of the values of the mean prognosticvariables (wind components, temperature, specific humidity, liquid/ice water content and cloud fraction),the provisional dynamical tendencies for the same variables and various surface fields, both fixed andvariable.

Figure 1.1 Schematic diagram of the di↵erent physical processes represented in the IFS model.

IFS Documentation – Cy31r1 3

c)

surfacez = 0 km, p ≈ 1000 hPa

top of atm.z ≈ 40 km, p = 0 hPa

z

p

b)

Figure 2.1: The “grid” of a computer model of the atmosphere. a) The grid as seen fromabove. b) The vertical grid for a given square in a). Each box is called a “grid box”and represents a region enclosed between two longitudes, two latitudes and two verticallevels. c) Each grid box includes a set of processes that are too small to be resolved andare instead “parameterised”. Figure c) courtesy of ECMWF.

18

The letter “P” in PT denotes “Parameterisation” which means adding the effect ofa process rather than the process itself. A few examples of “parameterised” processesin the IFS atmospheric model from ECMWF is shown in Fig. 2.1c. For instance,clouds are not captured by any global weather forecasting model, but since we knowthe effect they have we can add a parameterisation that explicitly changes the humid-ity, temperature, etc. in the model in accordance with our knowledge of clouds. Theparameterisations, PT , also includes heating from short-wave radiation from the Sun,latent heat release, absorption by greenhouse gases, and more. The term KT representsmixing not captured by the model, also known as “diffusion”. In general, atmosphereand ocean models include more diffusion than what would be realistic in order to keepthe flow smooth.

Similar to the equation for temperature (eq. (2.1)) an atmospheric model also in-cludes equations for e.g. wind, pressure and humidity, while an ocean model includesequations for e.g. currents and salinity. These equations also have some specific pa-rameterisations as shown in Fig. 2.1c. For instance, atmosphere and ocean modelsalways parameterise the effect of sub-grid turbulence to some extent. By sub-grid tur-bulence, we mean motions that are too small to be resolved by the model, i.e. smallerthan the grid boxes. An example is the friction caused when air blows over the Earth’ssurface. Sub-grid turbulence is especially important in the ocean since geostrophiceddies1 can not be resolved by most global ocean models and must be parameterised.The earliest ocean models did not include such a parameterisation which meant thatthey had severe difficulties in producing a realistic global climate. Gent & McWilliams(1990) were the first to include this which greatly improved the realism of their oceanmodel. This parameterisation is nowadays known simply as “GM” and is still fre-quently used.

2.2 Eulerian stream functions

There a many ways to analyse data given in the Eulerian framework, e.g. maps oftemperature and winds in the atmosphere or currents in the ocean. A common methodto analyse the Eulerian transports of mass and energy in the atmosphere and oceansis to use stream functions. Mathematically, a stream function is a two-dimensionalfunction, Ψ(x,y), defined as

∂Ψ

∂x= v, −∂Ψ

∂y= u, (2.2)

where u and v are the east–west and north–south velocities respectively. If the flowis two-dimensional and does not change in time, then the stream lines in the streamfunction Ψ are equal to Lagrangian trajectories. However, the atmosphere and oceansare three-dimensional flows that vary in time, and must therefore be reduced to two

1similar to the low- and high-pressure systems in the atmosphere

19

dimensions. A barotropic stream function, Ψ(x,y), can be obtained by integratingvertically and averaging over time,

∂Ψ

∂x=

1t1− t0

∫ t1

t0

∫ z

0v dz dt, −∂Ψ

∂y=

1t1− t0

∫ t1

t0

∫ z

0u dz dt. (2.3)

The unit of Ψ(x,y) is [m3 s−1] which means a transport of volume. The density ofsea water is fairly constant in the ocean so a volume transport of 1 m3 s−1 is a masstransport of ≈ 1000 kg s−1. For this reason, the unit Sverdrup 1 Sv = 106 m3 s−1

is often taken as a volume transport in the ocean but as a mass transport of 1 Sv =109 kg s−1 in the atmosphere1. The case for the atmosphere is discussed further be-low.

The depth-integrated barotropic stream function, Ψ(x,y), represents the total trans-port projected onto the longitude–latitude plane. We can instead integrate over longi-tudes in which case we flow reduces to latitude–depth coordinates,

∂Ψ

∂ z=

1t1− t0

∫ t1

t0

∫ xE

xW

v dx dt, −∂Ψ

∂y=

1t1− t0

∫ t1

t0

∫ xE

xW

w dx dt, (2.4)

where xE and xW are the eastern and western integral bounds. The stream func-tion Ψ(y,z), also known as the meridional overturning stream function, is a commonlyused tool to study the north–south transports of mass and energy in the atmosphere andocean. Calculating the meridional overturning stream function for the Atlantic oceanshows the Atlantic Meridional Overturning Circulation (AMOC) and how warm watermasses are transported from the tropical Atlantic to the North Atlantic (cf. Kuhlbrodtet al. (2007)) which plays a large role in controlling European climate.

In the atmosphere, the meridional overturning stream function is often shown us-ing pressure instead of height as a vertical coordinate, i.e. Ψ(y, p). Using pressurecoordinates and multiplying the velocity by 1/g where g = 9.81 m s−2 is the grav-itational acceleration gives the stream function in units [kg s−1]. It is thus a masstransport rather than a volume transport as in the ocean. Several recent studies havegeneralised the meridional overturning stream function so that any variable can beused as a vertical coordinate but still yield the result as a mass transport (Döös & Nils-son, 2011; Pauluis et al., 2008). The meridional overturning stream function with ageneralised vertical coordinate, Ψ(y,χ), is

∂Ψ(y,χ)∂ χ

=1

t1− t0

∫ t1

t0

∮x

∫ ps

0δ [χ−χ

′(x,y, p)]g−1v d p dx dt, (2.5)

where the Dirac function, δ [χ−χ ′] is a function where δ = 1 if χ ′ = χ and δ = 0otherwise. Note that we integrate over all longitudes. Multiplying the velocity by theDirac function and integrating is thus a way to “search” all longitudes and pressuresat y and only “select” velocities where χ ′(x,y, p) = χ . The solution for Ψ(y,χ) is

1Density of sea water is ρ ≈ 1000 kg m−3 so 1 m3 s−1 ≈ 1000 kg s−1

20

Ψ(y,χ) =1

t1− t0

∫ t1

t0

∮x

∫ ps

0µ[χ−χ

′(x,y, p′, t)]g−1v d p dx dt, (2.6)

where µ is a Heaviside function which is the integral of the Dirac function andthus µ = 1 when χ ′ ≤ χ and µ = 0 otherwise. Examples of meridional overturningstream functions calculated using eq. (2.6) are shown in Fig. 5.2.

A further generalisation of eq. (2.6) is to use two generalised coordinates. This hasbeen done recently to study the atmospheric circulation from a purely thermodynamicperspective (Kjellsson et al., 2013; Laliberté et al., 2013). This generalisation is doneby taking eq. (2.5) and using λ as a second general coordinate.

∂Ψ(λ ,χ)∂ χ

=∫

Ω

δ [χ−χ′(x,y, p)]δ [λ −λ

′(x,y, p)]g−1~v dΩ, (2.7)

where integrating over Ω is equal to integrating over the full three-dimensionalglobal atmosphere. Multiplying by two Dirac functions allows for a “selection” ofthe three-dimensional velocities where λ ′ = λ and χ ′ = χ . To calculate the streamfunction, Ψ(λ ,χ) and taking temporal variations into account, we get

Ψ(λ ,χ) =1

t1− t0

∫Ω

δ [λ −λ′(x,y, p, t)]µ[χ−χ

′(x,y, p, t)]g−1~v dΩ. (2.8)

This method was used in Papers 3 and 4 of this thesis to define the hydrothermalstream function which uses latent heat and dry static energy as coordinates. The dis-cretised form of eq. (2.8) is shown in Fig 11 of Paper 3 of this thesis.

21

22

3. The Lagrangian framework

3.1 Lagrangian observations of the world oceans

As briefly mentioned in the first chapter, the Global Drifter Program gathers data fromsome 1000 satellite-tracked buoys in the world oceans. These buoys float in the up-permost layer of the ocean and drift freely with the horizontal currents. Hence, thename surface drifters. The WOCE1 standard design of a surface drifter is a float atthe surface containing a battery, GPS chip and in some cases a thermometer and/ora barometer (Sybrandy et al., 2009). Attached to the float is a 12 meter tether linethat connects to a hollow drogue. The drogue is 6 meter long and the drogue thus sitsbetween 12 and 18 m depth. This design ensures that the float at the surface actuallyfollows the currents at 12−18 m depth to a high accuracy. An overview of the designis given by Niiler et al. (1995) and Lumpkin & Pazos (2007).

Each surface drifter transmits its position and, if possible, sea-surface temperature(SST) and air pressure once every hour to a satellite. The positions can then be usedto calculate the velocity of near-surface currents in the world oceans. Several stud-ies have compared the surface-drifter data to ocean-model simulations to evaluate therealism of the models. Some studies have used the drifter data to obtain gridded Eu-lerian fields of velocity, eddy kinetic energy and other metrics (Garraffo et al., 2001;Rupolo, 2007). Others have used an algorithm to simulate Lagrangian trajectories us-ing the ocean model velocity fields (Döös et al., 2011; Lumpkin et al., 2002; McCleanet al., 2002) and compared the trajectories and their statistics.

In Paper 1 of this thesis, surface drifter data from the Baltic Sea is used to evalu-ate the realism of the near-surface currents in the widely used Rossby Centre regionalOcean climate (RCO) model for the first time ever.

3.2 TRACMASS - An algorithm for Lagrangian trajecto-ries

Paper 1 and Paper 2 of this thesis applies the TRACMASS Lagrangian trajectory codeto solve atmospheric and oceanic problems. A description of the TRACMASS algo-rithm and other trajectory codes is therefore presented here.

1World Ocean Circulation Experiment

23

CHAPTER 1. TRACMASS TRAJECTORY THEORY 8

1.1 Trajectory solution for rectangular grids

This section is here only for pedagogical reasons, since it is only valid for rectangularCartesian grids. The TRACMASS code is written in a more general way in order toenable TRACMASS to work with curvilinear grids, which are used by most GCMs, andwill be presented in the next section.

Most finite difference GCMs uses B or C grids (Mesinger and Arakawa, 1976) asshown in Fig. 1.1, where i, j, k denote the discretised longitude, latitude and modellevel, respectively. The zonal velocity ui,j,k and meridional velocity vi,j,k are locateddifferently in these two grids, while the vertical velocity wi,j,k is located in the middleat the top of the box in both grids (Figs. 1.2, 1.3a). Both these types of grids can beused in TRACMASS. The velocities in TRACMASS are set on a C-grid, which makes itstraightforward when using a C-grid model. Although B-grid velocities just need to beprojected on the C-grid by making a meridional average of two zonal velocities (uC

i,j,k =0.5(uB

i,j,k +uBi,j1,k)) and a zonal average of two meridional velocities (vC

i,j,k = 0.5(vBi,j,k +

vBi1,j,k)) for each grid box.

xi-1 xiyj-1

yj

Longitude

Latitude

vi,j

ui-1,j ui,j

vi,j-1

(x1,y1)

(x0,y0)

Figure 1.2: Illustration of a trajectory [x(t), y(t)] through one grid box. The modelvelocities are defined at the walls of the grid box.

In a finite difference model there is no information of scales below the grid size. Thetracers are regarded as homogeneous within each grid box and the velocities are onlydefined on the grid side walls. It is, however, possible to define the velocity inside agrid box by interpolating linearly between the discretised velocity values of the opposite

Figure 3.1: The trajectory of a TRACMASS particle passing through a grid box similarto those depicted in Fig. 2.1. The grid box is seen from above where v j and v j−1 are themeridional velocities at the northern and southern walls, and ui and ui−1 are the velocitiesat the eastern and western walls.

To calculate the path of a particle, e.g. as done by NOAA in Fig. 1.1, we mustknow the flow velocity and the origin of the particle. The path along which the particlemoves is called a Lagrangian trajectory. The principle is to use the fact that velocityis the time-derivative of the position, i.e.

u =dxdt

, (3.1)

which means that the position, x, of a particle at time t can be found by

x = x0 +∫ t

t0u dt. (3.2)

Numerically, the velocity at time step n, un, is used to calculate the displacementfrom xn to xn+1,

xn+1 = xn +un∆t, (3.3)

where ∆t is the time step, and n is the time index. This method is often called Eu-ler’s method and is common for solving Ordinary Differential Equations. The methodis however non-centered in time and is only first order accurate. The accuracy can bedoubled by using a second order Runge-Kutta scheme.

xn+1 = xn +un+1/2∆t, (3.4)

un+1/2 = u(xn +0.5un∆t, tn +0.5∆t) , (3.5)

where un+1/2 is the velocity between time step n and n + 1. A scheme similar tothis is used by NOAA’s HYSPLIT model (Draxler & Hess, 1998). A popular schemeto use is the 4th order Runge-Kutta scheme where the accuracy is again doubled

24

xn+1 = xn +16

∆t(u1 +2u2 +2u3 +u4), (3.6)

u1 = un, (3.7)u2 = u(xn +0.5u1∆t, tn +0.5∆t), (3.8)u3 = u(xn +0.5u2∆t, tn +0.5∆t), (3.9)u4 = u(xn +u3∆t, tn +∆t). (3.10)

This scheme, sometimes denoted RK4, makes several approximations of the ve-locity at time step n, n+1/2 and n+1 to calculate the next position xn+1. The TOM-CAT/SLIMCAT Chemical Transport Model (Chipperfield, 2006) as well as the modelused by Bowman & Carrie (2002) use an RK4 scheme to calculate the trajectories ofparticles.

The TRACMASS1 code (Blanke & Raynaud, 1997; Döös, 1995; Döös et al., 2013)is based on equations that look quite different. Start with the mass flux in a grid box

Ui = ui∆y∆z. (3.11)

The continuous mass flux U(x) is then found by linear interpolation

U(r) = Ui−1 +(r− ri−1)(Ui +Ui−1), (3.12)

where the position x is exchanged for r = x/∆x. Eq. (3.12) can be set up as adifferential equation

drds

+β r +δ = 0, (3.13)

where β = Ui−1 −Ui and δ = −Ui−1 − β ri−1 and time t is exchanged for s =t/(∆x∆y∆z). Eq. (3.13) has the solution to r and s,

r(s) =(

r0 +δ

β

)e−β (s−s0)− δ

β(3.14)

s1 = s0−1β

log[

r1 +δ/β

r0 +δ/β

], (3.15)

where r(s) is the position as a function of the time coordinate s, and s1− s0 is thetime it takes to travel from r0 to r1. The TRACMASS algorithm thus gives the positionand time for each trajectory by evaluating eqs. (3.14) and (3.15) which are exact for astationary flow. de Vries & Döös (2001) developed an exact solution for TRACMASStrajectories in time-varying flows. This is opposed to Runge-Kutta methods where theposition is approximated using e.g. eqs. (3.6)-(3.9).

1TRACing the water MASSes of the North Atlantic and the Mediterranean

25

3.3 Some Lagrangian statistics

Paper 1 focuses on calculating and comparing Lagrangian statistics for trajectoriesof surface drifters and model-simulated (“synthetic”) trajectories in the Baltic Sea toevaluate the realism of the model.

There exists several kinds of statistical metrics to diagnose the trajectories of par-ticles in a flow. An overview was given by LaCasce (2008). Two commonly usedmetrics are absolute and relative dispersion. Absolute dispersion, denoted D2

A(t), is ameasure of the displacement from the origin,

D2A(t) =

1M

M

∑m=1|x(t)−x(0)|2, (3.16)

where M is the number of particles. Absolute dispersion is often denoted as asquared distance with units [m2]. It can be calculated for a single particle and is thussometimes called single-particle dispersion.

Relative dispersion, denoted D2R(t), is a measure of the distance between two par-

ticles at a given time,

D2R(t) =

1Np

∑i6= j|xi(t)−x j(t)|2, (3.17)

where Np is the number of pairs of particles such that particle i is never the same asparticle j. Relative dispersion is often calculated for pairs of particles that are initiallyvery close to study how they separate. This gives information about the diffusivity ofthe flow, i.e. rate of mixing (Klocker et al., 2012; LaCasce & Bower, 2000; Salléeet al., 2008).

The variability of the flow can be diagnosed by calculating the auto-correlation,R(τ), of the “eddy” velocity, u′, defined as the total velocity minus the time-meanvelocity, u′(t) = u(x)−u. The velocity auto-correlation at time lag τ is the correlationof the eddy velocity time series u′(t) and the eddy velocity time series u′(t +τ) whichhas been shifted in time by τ . Hence,

R(τ) = limT→∞

1σ2

V T

∫ T

0u′(t + τ) ·u′(t) dt, (3.18)

where σ2V is the variance of the eddy velocity, u′. The velocity auto-correlation,

R(τ), can be said to hold the “memory” of the particle. The Lagrangian velocity timescale, TL, can be seen as a measure of how long time a particle “remembers” when ithas been and is defined as

TL =∫

∞

0R(τ) dτ. (3.19)

If the flow is highly turbulent the velocity of a particle will de-correlate quicklyand TL becomes short. If, on the other hand, the flow is less variable, the velocity will

26

be auto-correlated for a much longer time and TL will be long. When calculating TL itis common to filter out variations on short time scales e.g. inertial oscillations or tidessince they tend to dominate R(τ) otherwise. It is often impractical to evaluate the fullintegral in eq. (3.19). Lumpkin et al. (2002) noted that R(τ) often becomes noisy atlarge τ and presented a few methods of circumventing this problem. In Paper 1 of thisthesis the integral is truncated at the lowest τ where R(τ) = 0.

Using TL we can define the velocity time scale Tv and acceleration time scale Ta(Nilsson et al., 2013; Rupolo, 2007) as

Tv =TL +

√T 2

L −4 σ2V

σ2A

2(3.20)

Ta =TL−

√T 2

L −4 σ2V

σ2A

2(3.21)

Rupolo (2007) calculated both the auto-correlation time scale of the velocity, Tv,as well as the auto-correlation of acceleration, Ta. The ratio of these

γR =Ta

Tv, (3.22)

has been denoted the “Rupolo ratio” where a high γR generally indicates a highlyturbulent flow (Nilsson et al., 2013). The results in Paper 1 showed that this ratiogenerally is very low for the Baltic Sea.

3.4 Lagrangian stream functions

The concept of Lagrangian stream functions was introduced by Blanke et al. (1999).The principle is that any Lagrangian particle trajectory is a transport of mass fromone point to another. Similarly to the Eulerian case, a meridional overturning streamfunction can then be defined for the atmosphere as

∂Ψ(y, p)∂ p

=∮

xg−1v dx,

∂Ψ(y, p)∂y

=−∮

xg−1

ω dx, (3.23)

where v and ω are the meridional and vertical velocities of the Lagrangian par-ticle at latitude y and pressure p. If there are more than one Lagrangian trajectorythe velocities can be gridded onto a three-dimensional field and a Lagrangian streamfunction representing all particles can be calculated using eq. (3.23). In this case astream line in the Lagrangian stream function will represent the particle path averagedover several particles.

A Lagrangian stream function can be calculated for a selection of particle trajec-tories. By sorting them into different classes and calculating the Lagrangian stream

27

function for each class the total stream function can be decomposed into differentkinds of motion. Decomposition of Lagrangian stream functions similar to those ineq. (3.23) were used by Jönsson et al. (2011) in the Baltic Sea and by Döös et al.(2008) in the Southern Ocean to understand the transports of different water masses.The method was applied to the atmosphere in Paper 2 of this thesis to study the trans-port of air masses to and from the tropics.

28

4. Transports in the Baltic Seaand environmental risks

The Baltic Sea is a relatively small sea enclosed by a large population. The only con-nection to the world oceans are the narrow Danish straits which makes the Baltic Seaparticularly sensitive to pollution. Shipping and near-shore activities can thus posean environmental risk for the life in and around the Baltic Sea. Although oil spillsare uncommon, oil tankers carrying 100000-150000 tonnes1 of oil are continuouslycrossing the sea (HELCOM, 2010). In the case of an accident, Lagrangian trajectoriesprovide a valuable tool to model the transport of pollutants. An example was givenin Fig. 1.1 showing the forecasted destinations of oil slicks in the Gulf of Mexico. Inthe Baltic Sea, forecasts of Lagrangian particles are produced by the Swedish Mete-orological and Hydrological Institute (SMHI) using a particle tracking model and theHIgh Resolution Operational Model for the Baltic sea (HIROMB) model (Funkquist,2001). Naturally, Lagrangian trajectories can also be calculated backward in time tofind where the pollution came from.

HIROMB is an operational model that continuously produces 48-hour forecasts.For studying the circulation of the Baltic Sea it is however more common to use oceanmodels that run for a considerably longer time. One such model is the Rossby Cen-tre regional Ocean climate (RCO) model (Meier et al., 1999) which has been usedto produce hindcasts as far back as the 1960’s (Meier et al., 2003). Data from theRCO model and TRACMASS trajectories were used by Döös et al. (2004) to studythe large-scale circulation of the Baltic Sea and by Jönsson et al. (2004) and Jönssonet al. (2011) to understand the transport in and out of the Gdansk Bay and the Gulf ofFinland. Corell et al. (2012) used the RCO model with TRACMASS trajectories tostudy the transport and spreading of larvae and how Marine Protected Areas (MPAs)are connected. Soomere et al. (2010) and Soomere et al. (2011) used similar methodsto calculate the transport of future oil spills in the Gulf of Finland and used that in-formation to find the shipping routes that would represent the smallest environmentalrisk in the event of an accident.

In Paper 1 we find that TRACMASS trajectories driven by RCO model outputhave less absolute and relative dispersion (eqs. (3.16) and (3.17)) than the trajectoriesof observed SVP drifters. This implies that the currents in the RCO model are slowerand less variable than those observed, which is a result that will have impacts on futuretransport modelling in the Baltic Sea.

11 tonne = 103 kg

29

30

5. The overturning circulation ofthe atmosphere

5.1 Past and present

One of the key features of the atmospheric circulation is the way air masses are trans-ported between the warm tropics and the cold polar regions. Fig. 5.1 shows three ofthe early conceptual models of the equator-to-pole flows in the atmosphere. Halley(1686) (finder of “Halley’s” comet) and Hadley (1735) proposed that warm, moist aircan rise in the tropics because it is lighter than the surrounding air. As it rises themoisture condenses, releases latent heat and forms clouds and rain. At high altitudes,air masses flow towards the poles and radiates some of their energy to space. Hence,near the poles the air sinks as it becomes cold and dense. The loop is then closed byair near the surface flowing towards the equator. In this “Halley-Hadley” model theatmosphere acts as a heat engine that transports air masses from the warm tropics tothe cold polar regions.

The Halley-Hadley model as shown in Fig. 5.1a is, however, not correct. TheHalley-Hadley model predicts equatorward winds at the surface in the midlatitudes(∼ 60N/S) while measurements found them to be poleward on average. Ferrel (1859)and Thomson (1912) therefore, independently, “corrected” the Halley-Hadley idea byadding a cell in midlatitudes. Thomson (1912) added the cell beneath the “Hadley”cell (Fig. 5.1b) while Ferrel (1859) suggested a three-cell structure in each hemi-sphere (Fig. 5.1c). The “Ferrel” cell was based on the idea of an imbalance betweenair pressure and the Earth’s rotation causing surface winds in midlatitudes to be south-westerly on average.

The most prominent east–west flow is the Walker circulation, which comprisesseveral cells, of which the most well known is the Walker cell over the tropical PacificOcean (cf. Peixoto & Oort (1992)). Air rises over the western Pacific and sinks overthe east Pacific. The cell is closed by a westerly flow at high altitude and easterly flownear the ocean surface. It was discovered by Walker (1924) who described a surfaceair pressure gradient over the tropical Pacific Ocean and noted that the rainfall overthe west Pacific increased when the pressure gradient was strong. Bjerknes (1969) re-alised that the pressure difference was associated with a zonal overturning cell whichhe named the Walker cell. The Walker cell is linked to the sea-surface temperature(SST) gradient over the tropical Pacific Ocean (Neelin et al., 1998; Philander, 1983;Rasmusson & Carpenter, 1982). Periods of small SST gradients, known as El Niñoevents, are associated with a weaker Walker cell and periods of large SST gradients,

31

0° 90°N90°S 60°S 60°N30°N30°S

0° 90°N90°S 60°S 60°N30°N30°S

height

height

a) Halley-Hadley model

b) Thomson model

HH

H HFF

0° 90°N90°S 60°S 60°N30°N30°S

heightc) Ferrel model

H H FF PP

Figure 5.1: The equator-to-pole motion of air masses as imagined by a) Halley (1686)and Hadley (1735) and b) Ferrel (1859) and Thomson (1912). “H”, “F”, and “P”, denote“Hadley”, “Ferrel”, and “Polar” cells. The Halley-Hadley model comprises two large“Hadley” cells that span the Northern and Southern hemispheres respectively. The Thom-son model includes a shallow “Ferrel” cell in the mid-latitudes, while the Ferrel model hasa three-cell structure in each hemisphere.

32

a)

b)

c)

d)

Figure 5.2: Meridional overturning circulation of the atmosphere using various verti-cal coordinates. Positive values indicate clockwise circulation. Crosses mark the max-ima/minima of the stream functions, and dashed lines show the mean surface values. Unitsin Sverdrup (1 Sv = 109 kg s−1). Adapted from Kjellsson et al. (2013).

known as La Niña events, are associated with a more intense Walker cell.

Fig. 5.2a shows the meridional overturning stream function in pressure coor-dinates, Ψ(y, p), (eq. (2.6)) calculated from ERA-Interim reanalysis data covering1979-2009. The picture shows three distinct cells on each hemisphere, similarly to thepicture depicted by Ferrel (1859). The three cells are commonly known as the Hadley,Ferrel and Polar cells (Grotjahn, 1993).

Fig. 5.2b shows the meridional overturning stream function calculated using latentheat, l [J kg−1], as vertical coordinate, i.e. Ψ(y, l). The latent heat of an air parcel isthe heat that would be released if all the water vapour would condense. It can becalculated as l = Lvq [J kg−1] where Lv is the latent heat of condensation and q is thespecific humidity of the air. The stream function Ψ(y, l) shows that the Hadley cellshave an equatorward flow at high l and a poleward flow at low l as also found byDöös & Nilsson (2011). The opposite is true for the Ferrel cells. This indicates thatthe Hadley cells transport moisture from the subtropics into the tropics, and the Ferrelcells transport moisture from the subtropics into the midlatitudes. Furthermore, theFerrel cells have a much higher amplitude than the Hadley cells in Ψ(y, l) indicatingthat they facilitate higher moisture transport.

33

c) d)

a) b)

12

3

Figure 5.3: The hydrothermal stream function, Ψ(l,s), calculated from ERA-Interim re-analysis 1979-2009. Negative values (blue colours) indicate anti-clockwise circulation.Units are in Sverdrup, 1 Sv = 109 kg s−1. The dashed line is the 345 kJ kg−1 MSE line.The double-dashed line is the Clausius-Clapeyron relation for saturated near-surface air(eq. (5.1)). From Paper 3 of this thesis with permission from AMS.

Fig. 5.2c shows the meridional overturning stream function where dry static en-ergy is used as vertical coordinate. Dry static energy is the total energy that the airwould have if it was at rest (i.e. no wind) and dry (i.e. no humidity). It comprisestwo parts; heat, cpT , and potential energy, gz. Dry static energy, s = cpT + gz, isapproximately conserved for adiabatic processes 1. The result of Ψ(y,s) is that theHadley cells and Ferrel cells merge to form one circulation in each hemisphere withan equatorward flow at low s and a poleward flow at high s, similar to e.g. Townsend &Johnson (1985) and Held & Schneider (1999). This implies that the dry static energytransport is poleward at all latitudes.

Fig. 5.2d shows the meridional overturning stream function using moist static en-ergy as a vertical coordinate. Moist static energy, h = s+ l [J kg−1], is the total energyof air at rest 2. The stream function with moist static energy as a vertical coordinate,Ψ(y,h), shows a single circulation in each hemisphere with poleward flow at high hand equatorward flow at low h, similar to Pauluis et al. (2008) and Döös & Nilsson(2011). Note that the picture is very similar to the Halley-Hadley model in Fig. 5.1a.Fig. 5.2d implies that the moist static energy transport is poleward at all latitudes. Asshown by e.g. Döös & Nilsson (2011), the poleward energy transport attains its max-imum of ∼ 5 PW in the midlatitudes, in close agreement with estimates by Trenberth& Caron (2001).

Paper 3 and 4 of this thesis describe the global atmospheric motions from a ther-modynamic perspective by calculating a stream function where latent heat and drystatic energy act as coordinates, i.e. Ψ(l,s), as formulated in eq. (2.8). This is denotedthe hydrothermal stream function and the result when using ERA-Interim reanalysisdata 1979-2009 (same as in Fig. 5.2a-d) is shown in Fig. 5.3. The hydrothermalstream function is the sum of all mass transports in the atmosphere that are associated

1Dry static energy, s, is similar to potential temperature, θ , so that s≈ cpθ .2Moist static energy, h, is similar to equivalent potential temperature, θe, so that h≈ cpθe.

34

1800 1900 2000 2100 2200 2300 2400 2500Year

200

400

600

800

1000

1200

1400

1600

1800

2000

CO

2 c

once

ntr

ati

on [

ppm

v]

RCP4.5RCP6RCP8.5Hist.Pre-ind.

Figure 5.4: CO2 concentrations for climate-model simulations of the period 1765-2100taken from Meinshausen et al. (2011). Values are shown for the different CMIP5 exper-iments, “pre-industrial” (1765-1850), “historical” (1765-2005), “RCP4.5” (1765-2100),“RCP6” (1765-2100) and “RCP8.5” (1765-2100).

with a change in either latent heat or dry static energy. Following the outer stream linein Fig. 5.3 shows that the global atmosphere comprises three distinct processes whichare shown as arrows. The flow marked as “1” is a flow where latent heat is convertedinto dry static energy, which is similar to precipitation as in the rising branch of theHadley cells (Figs. 5.1 and 5.2). The flow marked as “2” is dry air where the drystatic energy decreases, which indicates radiative cooling at high altitude. Lastly, “3”marks a flow where latent heat and dry static energy increase. This could be due tomoistening and warming of air near the surface or by mixing with moist air in shallowconvective cells. The hydrothermal stream function combines the thermodynamic ef-fects of the Walker circulation, the Hadley circulations and the midlatitude low- andhigh-pressure systems into a single circulation in l–s space (Kjellsson et al., 2013). Itthus provides a convenient measure to study the variability of the global atmosphericcirculation.

5.2 Future

Observed CO2 concentrations and those projected by various “emission scenarios”(Meinshausen et al., 2011) of the 21st century are shown in Fig. 5.4. Emissions ofgreenhouse gases (GHG) and tiny particles known as “aerosols” have been shown tohave an effect on the global climate system (IPCC, 2013) by e.g. increasing the surfaceair temperatures globally (Estrada et al., 2013; Hansen et al., 2005, 2013). The globalwarming and its effects have been extensively studied using climate models, recentlyin the Coupled Model Inter-comparison Project phase 5, CMIP5 (Taylor et al., 2012).It has been found that warming at the Earth’s surface will in turn cause changes toe.g. the global transports of mass and energy in the atmosphere and oceans (Caballero

35

s ≈ 310 kJ/kg

q2 = q1 (1 + 0.07 T )q1

M1 M2 = M1 (1 0.05 T )

conv

ectio

n

radiative cooling

moistening

present future

P1 P2 = P1 (1 + 0.02 T )

surface surface

Figure 5.5: Schematic description of the thermodynamic processes controlling the inten-sity of the atmospheric circulation and the change from present-day to the end of the 21stcentury according to Held & Soden (2006). P is precipitation, M is convective mass fluxand q is specific humidity, related by P = Mq. Subscript 1 denotes present and 2 denotesfuture. s = 310 kJ kg−1 is a dry static energy surface that does not intersect the ground.

& Langen, 2005; Hwang & Frierson, 2010; O’Gorman & Schneider, 2008; Vecchi& Soden, 2007; Weaver et al., 2012). For instance, warming of the surface air tem-peratures are projected to warm and freshen the surface waters in the North Atlantic,which would slow down the Atlantic Meridional Overturning Circulation (AMOC).In the atmosphere, warmer air can hold more water vapour which will lead to a moremoist atmosphere in the global mean. As a result of global warming, global-mean pre-cipitation is projected to increase by about 1−2 % for each degree of warming whilethe atmospheric circulation is projected to slow down (Held & Soden, 2006; Vecchi &Soden, 2007).

It is possible to estimate the impact of global warming on the atmospheric circu-lation using some thermodynamic arguments. The Clausius-Clapeyron (Clapeyron,1834; Clausius, 1850; Wallace & Hobbs, 2006) relation gives the maximum amountof water vapour that air of a certain temperature can hold.

dqs

dT=

qsLv

RvT 2 , (5.1)

where qs [kg kg−1] is the saturation specific humidity, i.e. the amount of kilogramsof water vapour that 1 kg air of temperature T holds when the relative humidity is100%. Eq. (5.1) can be simplified by letting Lv, the latent heat of vapourisation, beconstant and evaluating how qs changes for a given amount of warming.

∆qs

qs= α(T )∆T =

Lv

RvT 2 ∆T, (5.2)

where T = 273 K yields α ≈ 7 % K−1. Eq. (5.2) thus means that the global-meanspecific humidity, q, will increase with about 7% for each degree of global warming,assuming that relative humidity is unchanged (which Held & Soden (2000) found itto approximately be). Held & Soden (2006) found that the climate models used for

36

the 4th Assessment Report of the IPCC (Solomon et al., 2007) showed an increasein column-integrated q of 7.5% K−1. They set up a simple scaling argument wherethe precipitation, P, is equal to the upward flux of moisture which is the product ofupward mass flux of air, M, and the specific humidity of that air, q, i.e.

P = Mq. (5.3)

Differencing,

∆P/P = ∆M/M +∆q/q (5.4)

The last term is equal to the left hand side of eq. (5.2) under the assumption thatrelative humidity is constant. Climate-model simulations have shown that precipita-tion increases by 2−3% per degree of global warming (Allen & Ingram, 2002; Held &Soden, 2006). Inserting numbers into eq. (5.4) thus gives: If precipitation increases by2% K−1 and specific humidity increases by 7% K−1, then the upward mass flux mustdecrease by 5% K−1. A schematic representation of the processes involved are shownin Fig. 5.5. Hence, global warming could cause the atmospheric overturning circula-tions to slow down. This has been found to be the case in most climate models used inthe IPCC reports (Bony et al., 2013; Vecchi et al., 2006). Knutson & Manabe (1995)also suggested that the atmospheric circulation could slow down since the warming ofthe upper troposphere (about 15 km height) must balance radiative cooling.

37

38

6. Outlook

The most advanced atmosphere/ocean/climate models continue to increase in com-plexity as they include more and more of the processes in the climate system. Theneed for tools to evaluate the differences between the models and the real world willtherefore also grow. This thesis has presented a set of new tools for doing just that.In the Baltic Sea, a new regional ocean model is being introduced which has yet tobe fully validated against surface-drifter observations. Knowledge of its ability to re-produce the transport and spreading of particles will have impacts for e.g. studies ofbiogeochemistry as well as operational use. The number of surface-drifter observa-tions is very limited and any additional deployed drifters may prove highly beneficialfor evaluating the currents in ocean models.

For atmospheric purposes, this thesis has also shown that the atmospheric circu-lation can be very different in different coupled climate models and reanalysis. Ithas been shown that the models and reanalysis respond to climate variability such asENSO as well as global warming in a similar way. However, the differences betweenthe models have not been discussed in any greater detail. Specific model simulationswhere parameterisations or other conditions are changed one at a time could give bet-ter insight. To fully understand the origin of these differences the hydrothermal streamfunction as presented in Papers 3 and 4 could be included in an atmospheric model asan “online”-diagnostic, i.e. be calculated at run-time. This could highlight the impactof various parameterisations, e.g. entrainment, rain auto conversion, turbulent mixingin the planetary boundary layer, etc.

The decomposition of the meridional mass fluxes done in Paper 2 can be extendedto include other models and a comparison of future and present-day climates. Themeridional transport of sensible and latent heat is projected to increase with globalwarming (Paper 4), but the question remains to what extent this is due to increasedmass fluxes or merely an increase in heat content of the air masses. Furthermore, thedependence on spatial and temporal resolution for the conclusions in Papers 3 and 4remains an open question.

39

40

Sammanfattning

Denna avhandling presenterar olika metoder för att studera rörelser av luft- och vat-tenmassor i atmosfären och haven samt den transport av energi detta innebär. Resultatkommer dels från olika typer av observationer och dels från datormodeller av atmo-sfären, haven, och det kopplade klimatsystemet. Ett övergripande tema i avhandlingenär att dels jämföra datormodeller med varandra, och dels att jämföra dem med obser-vationer av verkligheten.

Avhandlingens första hälft använder det “Lagrangeska” synsättet där ett flöde be-traktas som summan av flera individuella partiklar i rörelse. En del handlar om attförstå hur partiklar i Östersjön följer strömmarna nära havsytan och hur partiklarnasprider sig. Genom att sjösätta flöten som kan spåras med hjälp av satelliter inhäm-tas information om strömmarnas hastigheter vilket sedan jämförs med resultat frånen datormodell. Resultaten indikerar att datormodeller tenderar att underskatta delsströmmarnas hastigheter och dels hur snabbt partiklar sprids, något som kan ha im-plikationer för såväl studier av biogeokemiska kretslopp som operationella insatser.Liknande metodik appliceras därefter på atmosfärens storskaliga cirkulation för attstudera hur luftmassor rör sig mellan tropikerna och mellanbredderna (ca. 45N/S).Det visas att masstransport mot polerna kan tas ut av masstransport mot ekvatorn såatt ett medelvärde endast visar mycket små rörelser. Det föreslås att medelvärdet där-för kan variera starkt beroende på hur medelvärdet beräknas.

Avhandlingens andra hälft fokuserar på det “Eulerska” synsättet där ett flöde sessom en hastighet som varierar i tid och rum. Mer specifikt används s.k. strömfunk-tioner och en framförallt en termodynamisk strömfunktion där atmosfärens rörelseranalyseras utifrån energin i luftmassorna istället för longitud, latitud och höjd/tryck.Denna strömfunktion sammanfattar atmosfären som en värme- och fuktcykel som be-skriver bl. a. nederbörd, strålningsavkylning och omblandning i det planetära gräns-skiktet. Cykeln visas ha tydlig koppling till El Niño-fenomenet i Stilla havet samt tillglobal uppvärmning. Kopplingen innebär bl.a. att atmosfärens globala cirkulation blirlångsammare men att nederbörden ökar. Denna koppling återfinns i flera olika klimat-modeller vilket indikerar att resultaten är robusta.

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