Sensitivity of the

Quasi-Biennial Oscillationto Climate Change

Martin C. Doege

Diplomarbeit im Fach Meteorologie

angefertigt am Max-Planck-Institut fur Meteorologie,

Hamburg

Betreuer:

Dr. Marco A. Giorgetta

Gutachter:

Prof. Dr. Guy P. Brasseur

Dr. Olaf Kruger

Hamburg im Oktober 2003

False-color image of Eastern Asia and the Western Pacific in thermal infrared

taken by GOES-9 at 155 degrees East above the equator on September 21st, 2003 at

12:00 UTC. The high and thus cold cloudtops (colored in white) associated with deep

tropical convection are quite apparent in the Indonesian ”warm pool” region as well

as over the Pacific. These mesoscale systems generate internal gravity waves that

constitute a major part of the forcing driving the quasi-biennial oscillation. Heading

east-northeast along the coast of Japan is typhoon Choi-wan, showing a prominent eye.

Grayscale image decoded from the Eumetsat WEFAX transmission by the Department

of Electron Devices and Circuits at the University of Ulm.

Contents

1 Introduction 5

1.1 The QBO in observations . . . . . . . . . . . . . . . . . . . . . . 51.2 Theory of the QBO . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Simulation of the QBO with General Circulation Models . . . . . 81.4 CO2 concentration and and IPCC assessment of climate change . 91.5 The Brewer-Dobson circulation . . . . . . . . . . . . . . . . . . . 111.6 Motivation for this thesis . . . . . . . . . . . . . . . . . . . . . . 12

2 The MAECHAM5 General Circulation Model 15

2.1 The ECHAM lineage . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Modifications for middle atmosphere modelling . . . . . . . . . . 172.3 Model equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Parameterizations related to the QBO forcing . . . . . . . . . . . 17

3 Experimental setup 19

3.1 Climatological boundary conditions for SST and sea ice cover . . 213.2 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 The Control experiment 33

5 Run001 results 37

5.1 Zonal mean zonal wind . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Residual circulation and forcing by resolved waves . . . . . . . . 415.3 Derivation of the gravity wave RMS wind parameter . . . . . . . 445.4 Summary of experiment Run001 . . . . . . . . . . . . . . . . . . 47

6 Run002 and Run003 results 51

6.1 Zonal mean zonal wind . . . . . . . . . . . . . . . . . . . . . . . . 516.2 Forcing by resolved and parameterized waves . . . . . . . . . . . 546.3 Vertical and meridional structure of the QBO . . . . . . . . . . . 586.4 Extratropical effects . . . . . . . . . . . . . . . . . . . . . . . . . 66

7 Summary and conclusion 69

7.1 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

A The Transformed Eulerian Mean and the

Eliassen-Palm flux 73

3

Abstract

The period of the quasi-biennial oscillation (QBO) of equatorial strato-

spheric winds is mainly determined by the magnitude of upward momen-

tum transport by equatorial waves and the intensity of the Brewer-Dobson

circulation. The observed QBO period is an average of 28 months, but it

can range from 24 to 30 months. The purpose of this study is to find out

how sensitive the period and other characteristics of the QBO are to the

climate change caused by doubling CO2 concentration.

MAECHAM5 T42L90 experiments are conducted with initial values

and boundary conditions (sea ice cover, sea surface temperature) acquired

from the AMIP2 climatology and two lower-resolution coupled runs of

ECHAM5 and MPI-OM1 with CO2 concentrations of 348 and 696 ppmv,

respectively.

In a test experiment with unchanged gravity wave parameterization,

both a speedup of the Brewer-Dobson circulation and a significant increase

in convective precipitation variance are observed. Increased variance in

the diabatic forcing of the tropical atmosphere leads to strengthened exci-

tation of vertically propagating waves, specifically of gravity waves. Thus

two sensitivity experiments with different parameter settings of the sub-

grid scale gravity wave drag parameterization are analyzed.

A speedup of the oscillation from the control experiment value of 34

months to between 22 and 17 months is observed, where easterly (westerly)

phase durations decrease mostly at upper (lower) QBO levels. While the

Brewer-Dobson circulation also intensifies due to stronger forcing by the

breaking of extratropical planetary waves, it does not offset the enhanced

generation of both parameterized and resolved waves.

Discrimination between zonal wind forcing by resolved and parame-

terized waves reveals considerable changes in the parameterized forcing,

which extends to lower levels and intensifies, especially maximum west-

ward acceleration. Resolved wave forcing seems to increase mostly be-

tween 10 and 20 hPa.

Considerable uncertainty about the exact amount of QBO period short-

ening remains and longer runs will need to be conducted to more accu-

rately estimate the parameterized gravity wave amplification.

1 Introduction

The quasi-biennial oscillation (QBO, a term coined in Angell and Korshover1964) of equatorial stratospheric winds, discovered in the 1950s, is an oscillationwith a period of about 28 months in lower-stratospheric winds between 3 and100 hPa, in which alternating easterly and westerly wind regimes develop at thetop and then descend at a rate of about 1 km/month. Easterlies are dominatingat the upper levels, while westerlies take precedence below. Maximum QBOamplitude of about 20 m/s is attained at about 20 hPa, around 50 hPa the speedof downward propagation of easterly phases often slows considerably. Below70 hPa the QBO amplitude weakens drastically, but the signal does reach thetropical tropopause (Baldwin et al. 2001).

The upper layers of the QBO region intersect with the vertical extent ofthe Semi-Annual Oscillation (SAO), which is an oscillation of easterlies andwesterlies at the stratopause level with a period of six months, characterized byeasterlies at solstice and westerlies at equinox. In contrast to the QBO, the SAOis coupled to the annual cycle, which causes westerlies in the winter hemisphereand easterlies in the summer hemisphere. Conservation of angular momentumthen leads to zonal acceleration experienced by cross-equatorial flow. For sometime, when observational data was sparse, it was thought the QBO might becaused by the SAO, but this was later refuted on theoretical grounds.

1.1 The QBO in observations

The lack of instruments that could reach the stratosphere and the intermit-tent character of observations were responsible for two conflicting opinions onthe tropical stratospheric circulation—either westerlies at the lower layers andeasterlies above or the reverse: The first theory was based upon the so-called“Krakatau easterlies”, originating when Mount Krakatau erupted in the Pacificand its volcanic ashes entered the stratosphere, moving from east to west as wellas the “Berson westerlies”, termed after German meteorologist A. Berson, whodiscovered them in his balloon observations from 1908. However, there werealso measurements that favored the opposing view of the second theory.

For a long time this controversy could not be resolved, until 1954 whenPalmer found that the boundary between the wind regimes moved with time.This was refined by Graystone (1959), who was able to show the descendingnature of this boundary, made possible by a longer observational record. Thepapers that first introduced the idea of an oscillation were those by Ebdon(1960) and Reed et al. (1961), who had been working independently. Ebdonand Veryard (1961) later found the oscillation to be mostly zonally symmetric,with only minor delays between the setting in of a wind regime at a specific

5

level at different longitudes, meaning that generally zonally averaged fields areused to investigate the QBO.

For the time span from 1953 onwards, a dataset of lower stratospheric windsis supplied by the Stratospheric Research Group at the Free University Berlin aspart of their stratospheric data series. Observations are taken at Canton Island,Gan (Maledives), and Singapore (Labitzke and van Loon 1999). A sample 10-year period of the of the Singapore wind data is contoured in Figure 1. While thebasic QBO features can be seen during the entire period, considerable variabilityexists in the shape of the maxima and their precise timing within the cycle.Hence, the name quasi-biennial oscillation is justified.

Due to the long timescale and equatorial symmetry of the QBO, the QBOzonal winds are in thermal wind balance according to uz = −R(Hβ)−1T yy

(Andrews et al. 1987), where R is the gas constant, H is the scale height, andβ ≡ ∂f/∂y with the Coriolis parameter f ≡ 2Ωsinφ. Thus a vertical windshear is associated with a temperature anomaly, therefore a warm anomalywith sinking motion exists in westerly shear and vice versa. This secondarycirculation supplies the adiabatic warming to sustain thermal wind balance andis closed off the equator. It is visible, superimposed on the Brewer-Dobsoncirculation, in plots of the residual circulation, which approximates Langrangiantracer transport at solstice (also Andrews et al. 1987).

Figure 1: The quasi-biennial oscillation as measured by rawinsondes: zonal windin m/s. The data is supplied by the 2002 edition of the CD-ROM “The BerlinStratospheric Data Series”published by K. Labitzke’s research group at the FreeUniversity Berlin.

1.2 Theory of the QBO

Explaining the QBO proved more difficult than first imagined, and even tothis day, while the driving forces (that is, types of waves) are well known, theexact magnitude of each contribution is not firmly established. Nevertheless the

6

first theory put forth by Lindzen and Holton (1968) has only undergone minorchanges and is still considered basically valid today.

As soon as a long enough observational record of the QBO cycles was avail-able, it was clear that the QBO signal was not simply a subharmonic of the SAOor otherwise coupled to the annual cycle but an independent fluctuation, eventhough the probability of QBO phase changes are somewhat dependent on theseason. Instead, the QBO can be explained as being caused by the dissipationof equatorial gravity waves in lower stratospheric shear layers (also in Holtonand Lindzen 1968).

In the first place, there must be a wave source in the troposphere that excitesgravity waves with westerly and easterly phase speeds. The Indonesian “warmpool” region with its most intense high-reaching convection is a prime candidatefor this. Because the Coriolis parameter is so low at the equator, the individualwaves can travel upwards into the stratosphere, their wavelength decreasing asthey encounter a layer where the difference |c− u| between the background flowspeed and their phase speed vanishes. There, close to the critical layer, thewaves are absorbed and their momentum accelerates the flow even more. Thus,an existing slightly disturbed background flow will be amplified by the waves,and since wave absorption takes place in the shear layers below the criticallayers, the bands of easterlies and westerlies will propagate downward.

Later it was thought that Rossby-gravity and Kelvin waves might be the ma-jor driving force (Holton and Lindzen 1972), but in recent years at least a thirdof the forcing is attributed to gravity waves and it is clear that Rossby-gravityand Kelvin waves alone would not suffice to cause a QBO because of tropicalupwelling (Dunkerton 1997), which the QBO cycle has to act against. Thisupwelling is the equatorial branch of the global stratospheric Brewer-Dobsoncirculation, which is caused by planetary wave absorption in the mid-latitudestratosphere and accompanying descent, balanced by the ascent of air throughthe equatorial tropopause. The tropical upward motion counteracts the down-ward phase propagation of the QBO, effectively doubling the wave driving nec-essary to yield the observed QBO period. The importance of this circulation forthe QBO period has not been recognized for a long time.

The QBO has also been successfully simulated in water tank experimentsby Plumb and McEwan (1978). For this, a cylindrical tank was filled witha solution that was then mechanically excited on its bottom by a standingwave. A standing wave is the result of the superposition of two waves withopposite and equal phase speeds c1, c2 = −c1. When the fluid has been initiallyat rest, a circular current soon develops which reverses its direction with aperiod of several hours. This was the first experimental evidence that Holtonand Lindzen’s theory of the generation of the QBO by internal gravity wave

7

momentum deposition was essentially correct.

1.3 Simulation of the QBO with General Circulation Mod-

els

While 1- and 2-dimensional mechanistic models could be devised to simulate arealistic QBO, general circulation models were unable to generate a QBO au-tonomously until recently. A variety of causes were identified, first of all thehigh computational demand caused by running the models at a high enoughvertical resolution to have a vertical grid spacing of less than 1 km in the lowerstratosphere necessary to resolve the stratospheric shear layers sufficiently. An-other obstacle were too large values for the diffusion coefficient, destroying themeridional profile of the QBO.

An important contributing factor lay in the parameterizations for convec-tion employed in the models. While the convection parameterization usuallyproduced correct amounts of precipitation, the convection variances were oftentoo low, corresponding to drizzle in the tropics, rather than the actual violentconvection observed (Horinouchi et al. 2003). Correspondingly, the excitationof resolved tropical waves in the model was not sufficient. Finally, a parameter-ization for a spectrum of sub-grid scale gravity waves had to be implemented.

These kinds of model inadequacies, present in MAECHAM4 among others,prevented the formation of a spontaneous QBO, consequently an assimilatedQBO momentum source was introduced into the experiments (Giorgetta andBengtsson 1999; Giorgetta, Bengtsson, and Arpe 1999). It was then possible tocompare the easterly and westerly phases of the QBO with the QBO-less controlrun and study the effect of the QBO on, for instance, the Indian monsoon or thestratospheric secondary circulation, which is relevant for global tracer transport,in detail.

While such sensitivity experiments gave new insights into the importance ofthe QBO, a GCM capable of simulating a QBO on its own without externalprescription continued to be elusive until the late 1990s, when Takahashi (1996,1999) was the first to achieve a mostly realistic QBO in the CSSR/NIES model.However, certain model parameters such as the horizontal diffusion coefficienthad to be changed considerably from their usual values to make this possible.

Scaife et al. (2000) used the Unified Model with the Warner and McIntire(1999) as well as the Hines (1997a,b) schemes for the momentum transportby sub-grid scale gravity waves to simulate a realistic QBO. Giorgetta et al.(2002) were able to reproduce the oscillation also using the Hines scheme in theMAECHAM5 model without any tuning of parameters.

In the remainder of this section, some of the other underlying aspects touched

8

upon in this study will be briefly reviewed in no particular order. While theinformation given here is by no means exhaustive, the most important issuesthat pertain to this study are outlined.

1.4 CO2 concentration and and IPCC assessment of cli-

mate change

In the atmosphere of Earth, carbon dioxide (CO2) is one of the major green-house gases, others of which also include water vapor, methane, nitrous oxide,halocarbons, and ozone. Both the natural and anthropogenic greenhouse effectare partly caused by the heat-trapping properties of CO2 in the terrestrial partof the spectrum. As a linear molecule (i.e., its three atoms lie on a line inthe time average), it has among its modes of excitation four vibrational modes,three of which can interact with infrared radiation (Schwartz et al. 1994). Thefirst one (Figure 2b) has a wavelength of 4.26 µm, the others (Figure 2c,d) arefound at 14.99 µm. The fourth, at an energy of 7.20 µm, does not not change itsdipole moment during vibration, so it cannot gain or lose energy by exchangewith photons. The 15 µm absorption bands are lying at the edge of the “at-mospheric window”, where little absorption takes place by other atmosphericgases, and effectively close this window, trapping infrared radiation that wouldotherwise have escaped into space.

(c)

(a) (b)

(d)

Figure 2: The four vibrational modes of carbon dioxide: (a) symmetric, (b)asymmetric stretching; (c), (d) bending, where (d) is just (c) rotated by 90.In (a), there is no change in dipole moment during vibration, thus no interactionwith photons is possible.

The longest record of atmospheric CO2 concentration is from the stationatop Mauna Loa, Hawaii (Figure 3). From 1958 onwards, almost continuousmeasurements conducted with an infrared gas analyzer are available (Keelingand Whorf 2002). Hawaii is a good place to measure global CO2 levels becauseit is far away from both human (industry, esp. cement manufacture, energy,

9

land-use) and natural (wildfires, vegetation) sources and sinks of CO2. Theonly major natural sources and sinks on and around Hawaii are the ocean andthe Hawaiian volcanoes, so both of these effects have to be taken into account.

1960 1970 1980 1990 2000

Year

310

320

330

340

350

360

370

380

ppm

v

Figure 3: Atmospheric CO2 concentration in ppmv determined at Mauna Loa,Hawaii. Missing values are linearly interpolated. Data from Keeling andWhorf (2002).

Apart from the seasonal cycle, a clear increase over time is visible. How-ever, the precise shape of the function is still under debate: While Houghton etal. (1996) favored an exponential growth of CO2 concentration like the IPCCscenario IS92a, other scientists find a more linear increase like scenario IS92dprobable, pointing out the limited supply of fossil fuel in the future.

Besides the uncertainty about anthropogenic emission, the amount of uptakeby atmosphere, land, and ocean is another important source of the differences inconcentration scenarios (Cox et al. 2000). Also, different carbon cycle modelslike the Bern or ISAM models give slightly different results (Houghton et al.2001). Consequently, an increase of atmospheric CO2 concentration to 700 ppmvmay either happen within this century or within the next one, depending on themodel and scenario used. Of course, given the aim of this particular study,determining the exact year in which the CO2 concentration will double withrespect to the 1990 level is rather unimportant, however, the wide range ofmodels and the controversy around CO2 emission and concentration scenariosshould be pointed out.

10

1.5 The Brewer-Dobson circulation

The Brewer-Dobson circulation in ozone was postulated by Dobson et al. (1929)based on the observation that stratospheric ozone concentration is lower atthe equator (where it is produced by photodissociation of oxygen) than in themid-latitudes. Later Brewer (1949) recognized such a poleward circulation alsoaffected stratospheric water vapor. While such a poleward mass transport ex-plained the observations, the cause for it was debated for some time. It wassettled by Haynes et al. (1991), who explained it with mid-latitude planetarywave breaking, westward zonal acceleration and therefore poleward transport.This picture of the cause of the Brewer-Dobson circulation is also termed the“wave-driven pump”.

Figure 4: Schematic view of the tropical Hadley cell and the stratosphericBrewer-Dobson circulation at solstice. Thin lines mark Lagrangian trans-port, while bold arrows indicate predominant mixing directions for tracers.Tropopause and stratopause are depicted as dashed lines (from WMO 1985).

Figure 4 shows a schematic view of the Brewer-Dobson circulation at sol-stice with upwelling in the summer hemisphere and downwelling in the winterhemisphere. The arrows indicate the main effects of the Brewer-Dobson circu-lation on tracers: Upward and poleward transport (upwelling) of atmosphericconstituents such as water vapor, ozone, and man-made chemical tracers suchas ozone-destroying chlorofluorocarbons (CFCs) above the tropical tropopauseand sinking motion poleward of the mid-latitudes. The main ascending branchof the Brewer-Dobson circulation also has a seasonal dependence, shifting to theSummer hemisphere at solstice.

The importance of the Brewer-Dobson circulation for the QBO period was

11

first recognized by Dunkerton (1997), who pointed out that the tropical up-welling was acting against QBO phase descent, yielding a longer period thanthe one that would be found if there were no such upwelling.

Because the Brewer-Dobson is a phenomenon in tracer (i.e. Lagrangian)transport, a conventional Eulerian mean does not show it. Instead, the zonalmean residual velocities v∗ and w∗ from the Transformed Eulerian Mean equa-tions are commonly used, as they approximate the Lagrangian mean motion atsolstice (Andrews et al. 1987, also see Appendix A).

Tropical upwelling can also be seen in the stratospheric“tape-recorder”(Moteet al. 1996), i.e. the ascent of water vapor anomalies through the “cold trap” ofthe tropical tropopause, driven by the Brewer-Dobson circulation, which pro-duces an anomaly that looks like a signal written on magnetic tape, because thetemperature of the“cold trap”at the tropopause (and thus the maximal amountof water vapor mixing ratio that can pass through it) depends on the season: Inboreal winter, the tropopause is coldest, with a minimum over the warm poolregion. An alternative guess of the intensity of the Brewer-Dobson circulationcan thus also be attained by looking at the time water vapor anomalies take totravel from a level close to the tropopause to a level further up.

1.6 Motivation for this thesis

With the availability of General Circulation Models such as MAECHAM5 thatcan simulate a reasonably accurate QBO on their own, it becomes feasible toconduct experiments to assess the influence of climate change on the quasi-biennial oscillation.

Climate change experiments conducted with coupled atmosphere-ocean mod-els show an increase in equatorial sea surface temperature and consequently moreconvection in the tropics. Also, precipitation variance grows, therefore it is con-ceived that more intense gravity waves are excited by the individual convectiveturrets and mesoscale systems. Since the QBO is to a certain degree gravity-wave driven, it might be presumed that this change in precipitation would tendto change the amplitude and / or frequency of the QBO. This was already shownby Plumb (1977) in his mechanistic model of QBO, namely that the QBO cycleaccelerates when the wave momentum fluxes are increased.

At the same time, tropical upwelling might also intensify because of highermid-latitude planetary wave activity due to either increased winter land-sea tem-perature contrasts (Mokhov and Petukhov 2000) or synoptic-scale mid-latitudecyclone forcing increase (Dickson et al. 2000), thereby decreasing QBO fre-quency. Additionally, changes in the mean wind below the QBO levels couldaffect the shape of the QBO by the selectively filtering of waves.

12

If the QBO changes its dynamical characteristics under climate change thishas global repercussions, as the QBO is not only is responsible for the secondarycirculation advecting ozone and other tracers, but it might also impact the Northpolar vortex (Labitzke 1977) or modify tropical convection by influencing thecloud-top environment.

In this study, a more limited approach is chosen, where only CO2 concentra-tion is varied and all other constituents of realistic climate change experimentssuch as changes in aerosol concentration are not considered.

Experiments with MAECHAM5 coupled to the ocean model MPI-OM1 areused to produce changes in lower boundary conditions between the 1xCO2 and2xCO2 climates. Since those experiments feature a vertical resolution of only 19layers, inter- and extrapolation to 90 layers has to be performed for the changesin initial conditions. Also, because of the high computational demands imposedby the middle-atmosphere version of ECHAM, only relatively short runs of about10 years are possible at the time of writing. Initial values at 1xCO2 are suppliedby a longer 30-year MAECHAM5 run that has been conducted earlier.

The rest of this study is organized as follows:In section 2, the GCM employed in the integrations, MAECHAM5, which

in contrast to MAECHAM4 is able to generate a relatively realistic QBO, isintroduced.

Section 3 outlines how the boundary conditions and initial values are con-structed from the Control experiment, the AMIP2 boundary conditions, andthe CMIP experiments.

Section 4 gives a brief overview of the Control experiment which has beenconducted prior to this work.

In section 5, the first experiment under doubled CO2 climate conditions withunaltered gravity wave parameters is presented. This run is used to estimatechanges in the strength of parameterized gravity waves under doubled carbondioxide climate conditions and serves as a baseline for the later sensitivity ex-periments.

In section 6, the second and third experiments with adjustments in param-eterized gravity wave amplitude are presented.

Section 7 concludes this thesis by discussing the present results and puttingthem in the larger context of other QBO model sensitivity experiments.

13

14

2 The MAECHAM5 General Circulation Model

2.1 The ECHAM lineage

Figure 5: The ECHAM model family of ECHAM, MAECHAM, and HAM-MONIA and the effects taken into account by these models. HAMMONIA(HAMburg Model of the Neutral and Ionized Atmosphere, and also Latin for’Hamburg’) is a version of MAECHAM5 that extends up to 250 km height andis coupled to the MOZART3 (Brasseur et al. 1998) chemistry model.

The ECHAM (for European Centre / Hamburg) family of models werejointly developed from a 1988 version of the European Centre for Medium-Range Weather Forecasts (ECMWF) NWP model by the Max Planck Institutefor Meteorology and the Meteorological Institute of the University of Hamburg.Changes with regard to the ECMWF mostly concern the parameterizations,making the model more useful for climate modelling, and in the addition ofcloud water species qi as prognostic variables. Other prognostic variables arevorticity ζ, divergence D, temperature T , logarithmic surface pressure ln ps andspecific moisture q.

Horizontally, ECHAM, employing the spectral transform method, uses spher-ical harmonics up to the limits given by triangular truncation. In the exper-iments conducted for this study it is used at a horizontal resolution of T42,corresponding to 128 by 64 grid-points in the treatment of physical and non-linear dynamical tendencies, where the latitudinal positions of the grid pointsare the corresponding Gaussian latitudes.

Vertically, a second-order finite differencing scheme is used, with the coor-dinates following the terrain (σ-coordinate) for the lower layers, pressure levels

for the higher layers, and with the layers in between taking on a hybrid form.For the 90-layer (L90) middle atmosphere version of ECHAM, this means thatfor the 91 half-levels between the layers the bottom three half-levels are purelyσ-coordinate and the top 55 half-levels are purely pressure coordinate, with thetransition from hybrid levels to p-levels occurring at a height of about 50 hPain the lower stratosphere. The relationship between level number and height aswell as layer thickness is shown in Figure 6.

The time integration follows a filtered semi-implicit leap frog scheme witha timestep of (in the default configuration) 24 minutes for dynamics, whereasthe radiation timestep is two hours. In the experiments considered here, thetimestep for dynamics has to be decreased to 15 minutes. An Asselin time filteris used to suppress computational artifacts.

This work makes use of MAECHAM5, the successor of MAECHAM4. Im-provements in ECHAM5 over ECHAM4 include the parameterizations of radia-tion, surface fluxes, and cloud physics. This set of changes as well as the Hinesscheme for parameterized gravity wave drag is responsible for MAECHAM5’sability to simulate a QBO as opposed to MAECHAM4.

Figure 6: Vertical coordinate system absolute heights and half-level distances,showing the differences between the 39-layer (blue) and the 90-layer (red) ver-sions of ECHAM. In the 90-layer case, layer thickness stays well below 1 km upto about 40 km height.

16

2.2 Modifications for middle atmosphere modelling

The differences between the conventional, tropospheric configuration of ECHAMand the middle atmosphere configuration MAECHAM (see Figure 5) are twofold:Firstly, the model top moves up from 10 hPa in the 19-layer version to 0.01 hPain the 90-layer model and higher vertical resolutions are employed, for exam-ple L90 in the experiments considered here. Secondly, the parameterization forwave drag by gravity waves (Manzini et al. 1997) is vital for the accurate sim-ulation of the stratosphere and mesosphere and can thus not be neglected as inthe tropospheric runs that only extend vertically into the lower stratosphere.

2.3 Model equations

As stated by the ECHAM5 documentation, the underlying model equations inz-coordinate form are

dvh

dt= −1

ρ∇hp− 2(Ω× vh)h − 1

ρ

∂Jvh

∂z+ Kvh

dT

dt=

RdTv

pCp

dp

dt+

1Cp

[QR + QL + QD − 1

ρ

(∂Js

∂z− CpdT (δ − 1)

∂Jqv

∂z

)]+ KT

dqv

dt= Sqv −

1ρ

∂Jqv

∂z

dqw

dt= Sqw −

1ρ

∂Jqw

∂z

p = ρRdTv

∂p

∂z= −ρg

with the virtual temperature

Tv = T

[1 +

(1ε− 1

)qv

].

The final equations result from transitioning from the z-coordinate system tohybrid coordinates, rewriting of adiabatic terms for spherical coordinates anduse of spherical normal modes to represent the fields horizontally during thespectral representation part of the transform method.

2.4 Parameterizations related to the QBO forcing

Deep convection is parameterized following Tiedtke (1989) with improve-ments by Nordeng (1994). Basically, Tiedtke relates organized entrainmentat the cloud-base to large-scale horizontal moisture convergence. Nordeng, onthe other hand, uses vertical parcel acceleration as given by Convectively Avail-

17

able Potential Energy (CAPE). Convection is assumed to reduce CAPE valuesexponentially with an associated resolution-dependent timescale τCAPE.

Momentum flux deposition by a spectrum of gravity waves is modeledusing the Doppler spread parameterization by Hines (1997a,b). At some launch-ing height, a horizontal wind vertical wavenumber spectrum is prescribed thatis zero for m (the vertical wavenumber) larger than a cutoff wavenumber, mc.When the waves travel upward, decreasing density causes the total wind causedby them, uRMS , to increase until it reaches the horizontal phase speed of wavesthat have the cutoff wavenumber. At this point, nonlinear interaction betweenthe gravity waves of different wavenumbers sets in, which causes the spectrumto extend beyond mc, and finally beyond mm, a wavenumber that is marked bytotal dissipation of waves with higher wavenumbers.

This parameterization is somewhat complicated in the presence of meanbackground winds, as the Doppler-spreading of the launching height spectramust be accounted for. This is done by separating the spectra into azimuthalcomponents and summing their contributions to momentum flux at a givenheight.

A comprehensive overview of this and other parameterizations for momen-tum flux deposition is given in McLandress (1998).

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3 Experimental setup

The basic setups cover the following three areas: QBO-Control experiment, theCMIP experiments used to arrive at boundary conditions for the doubled car-bon dioxide climate, and the QBO experiments under the changed climate con-ditions. The setups and experiments are (with the names of the experimentersgiven in parentheses):

1. CONTROL (Run159, Giorgetta): MAECHAM 5.1.04, resolution T42, 90layers, present-day climate conditions, run length 30 years

2. CMIP (Roeckner, Esch): MAECHAM 5.0.10, resolution T42, 19 layers,coupled transient Global Warming experiment (1% CO2 concentrationincrease per year, no solar variability, volcano eruptions, or increase inaerosol concentration). The ocean model in the CMIP experiments isMPI-OM1 (formerly called C-HOPE), resolution 128*208 grid points (seeFigure 7), 23 vertical layers.

Figure 7: The MPI-OM1 coordinate grid with increased equatorial resolutionand a polar axis tilted so that the northern pole of the grid lies above Greenland.

(a) CMIP1CO2 (Roeckner, Esch): 500-year control integration with 1990CO2 concentration prescribed.

(b) TRANSIENT (Roeckner, Esch): Transient integration with 1% CO2

concentration increase per year, conducted up to about four timesthe starting level of concentration.

19

(c) CMIP2CO2 (Roeckner, Esch): 150-year integration with constantdouble CO2 concentration, started from the transient CMIP run atits 90th year.

3. QBO2CO2 (Doege, Giorgetta): MAECHAM 5.1.04, resolution T42, 90layers, doubled CO2 climate conditions, sea surface temperature (SST),sea ice climatology, and initial conditions derived from the difference ofthe CMIP1CO2 and CMIP2CO2 runs plus the AMIP2 climatology (SST,SIC) or CONTROL run monthly means (all other variables)

The relationship between the CMIP experiments is shown schematically inFigure 8. CMIP1CO2 is the Control CMIP experiment with “present-day”(348 ppmv) CO2 concentration. At some year, the TRANSIENT experiment isstarted with an CO2 atmospheric concentration increase of 1% per year. Afterabout 70 years, when the concentration has doubled (year zero in Figure 8), atime slice run is started (CMIP2CO2) which is representative of the doubled CO2

climate as simulated by MAECHAM5. This enables to consider monthly meansfor several decades instead of just the narrow timeframe when the TRANSIENTrun has about the right CO2 concentration. Moreover, it allows to study howthe climate reaches equilibrium after the CO2 increase has stopped and whatthe intrinsic fluctuations driven by oceanic response are.

SST, ice, atm.

CMIP1CO2

CMIP2CO2

TRANSIENT

0

1

2

3

−20 0 20 40 60 80 100 120

Atm

osph

eric

car

bon

diox

ide

[348

ppm

v]

Years

Figure 8: Schematic overview of the CMIP experiments.

All climatological boundary fields for the QBO2CO2 run are obtained byadding the 20-year mean changes between the CMIP2CO2 and CMIP1CO2SST and sea ice to the SST and sea ice fields of the AMIP2 climatology as usedin the Control experiment.

20

The spectral and grid-point initial conditions are prepared by adding theaverage climate change from 20-year periods of the CMIP1CO2 and CMIP2CO2runs to CONTROL run monthly mean data, yielding mean fields for the firstmonth to be integrated, which are then vertically interpolated from 19 to 90layers.

3.1 Climatological boundary conditions for SST and sea

ice cover

In the CONTROL experiment, the lower boundary conditions are supplied bythe AMIP2 climatology. This climatology is distributed by Lawrence LivermoreNational Laboratory as part of its Atmospheric Model Intercomparison Projectto ensure realistic and comparable forcing of the GCMs participating in thiseffort. It specifies monthly sea surface temperature and sea ice cover that arethe time mean of an observational dataset spanning the time period from 1956to 2000. In the GCM, these monthly values are then linearly interpolated foreach day.

In contrast to AMIP1, where simply the monthly mean values were used asthe climatology, AMIP2 boundary conditions are modified in such a way thatthe averages of all the daily values are equal to the observed time averages,which would not be the case if simply the observed averages themselves wereused. One can retrieve the observational data from the climatology by

Ot =18

(Ct−1 + 6Ct + Ct+1

)

where Ot is the time-mean observational data for month t and Ct, Ct−1, andCt+1 are the climatological fields for month t and its preceding and followingmonths, respectively (Taylor et al. 2000). In MAECHAM5 the data is interpo-lated first in time, and then only sea ice cover values between 0% and 100% areretained: If the computed value is larger than 100% it is set to 100%, if it issmaller than 1% it is set to 0%.

Figure 9 displays AMIP2 climatological SST and sea ice cover for annualmean, DJF, and JJA conditions. Sea surface temperature is dominated by alarge maximum that extends from the Indian Ocean to Indonesia to the WesternPacific. Particularly in the Indonesian region, northward and southward shiftsof the maximum during the course of the year are apparent. In the centralPacific, temperatures do not change much, while there is another temperaturemaximum west of Mexico and in the Gulf of Mexico. Especially in the Gulf andbeyond, temperatures rise strongly during the NH summer.

The contour levels for sea ice cover have been chosen because the 15% con-

21

Figure 9: AMIP2 climatological SST (C, shaded) and 90% (solid) and 15%(dashed) contours of sea ice cover for (a) annual mean, (b) December to Febru-ary, and (c) June to August conditions.

22

tour is taken to define sea ice extent (Gloersen 1992), while the 90% contourprominently shows the annual cycle: The Arctic maximum broadens during NHwinter, so that 90% sea ice concentration is reached at the northern edge of theEurasian and North American continents. In the Antarctic, high variability islocated in the Ross and Weddell Seas. There an almost continuous ice shieldcan be found during the SH winter season. The yearly cycle of sea ice extent (asopposed to area) is depicted in Figure 10. In comparison to other observationaldata sources (Gloersen and Campbell 1988), the values are somewhat too large,especially the maximum Arctic sea ice extent in spring.

The CMIP1CO2 experiment starts at January, 1st 1978 with initializationtaken from the reanalysis data for that day, but with a CO2 level of 348 ppmvprescribed. It needs to be kept in mind that model evolution in the CMIP ex-periments does not represent an approximation of the past or future states ofthe real atmosphere. Instead, the CMIP runs should be regarded a GCM sen-sitivity studies without a direct relationship to current state-of-the-art globalwarming experiments. All the same, model years are given here for easier refer-ence. The transient CMIP experiment branches of from the control experimentafter 90 years (model year 2068), and after the 70 years it takes CO2 to dou-ble, CMIP2CO2 is started (model year 2138). For the extraction of boundaryconditions, the periods 2010 to 2029 and 2140 to 2159 were selected from theCMIP1CO2 and CMIP2CO2 runs, respectively.

A comparison of real and simulated climate can be drawn from Figures 9 and11. The most obvious problem in simulated SST is the equatorial “cold tongue”

J F M A M J J A S O N D J

month

0

10

20

30

sea

ice

exte

nt [m

illio

n km

²]

NH+SHNHSH

Figure 10: Monthly mean sea ice extent from the AMIP2 climatology for theentire globe as well as for the Northern and Southern Hemisphere separately.

23

Figure 11: As in Figure 9 but for the 2010-2029 period of the CMIP1CO2 run.

24

Figure 12: As in Figure 9 but for the 2140-2159 period of the CMIP2CO2 run.

25

in the Eastern Pacific. Temperatures are also too high in the Indonesian regionand off the western coast of Mexico with the greatest differences in the latterplace occurring during NH summer. Sea ice cover is simulated in agreementwith AMIP2 dataset, with the exception of sea ice concentration in the Arcticdropping too low in NH summer, so that no 90% isoline is visible there in Figure11.

Another difference between the AMIP2 and CMIP runs concerns modelsetup: The land sea masks differ in some regions with complex land-sea dis-tributions. The largest differences are located in the Indonesian region wherethe CMIP land sea mask defines far more land points than the AMIP2 LSM. Itis therefore necessary to interpolate / extrapolate the SST for these points.

As shown in Figure 13, all missing points are either singular points or lieon straight lines. Therefore higher order interpolation did not seem necessary.Instead, a simple iterative interpolation method was employed: On each step,the value of an as of yet undefined point is assigned the interpolated average ofits adjacent points to the North, South, East, and West, if at least two of thesepoints are either defined in the original data or have been calculated in one ofthe previous iterations.

This scheme is repeated until no more points can be added. Then it isrepeated for points with only one neighbor, which then obviously assume thetemperature of that very neighbor. This simple procedure (a two-dimensionalcellular automaton, see Packard and Wolfram 1985) gives sufficiently smoothinterpolated fields for change of SST. Of the 126 points that need values suppliedto them, 121 are covered by the algorithm. The five remaining points (twoin Canada, two in the Persian Gulf, and one in the Baltic Sea) are assignedmanually to nearby values, for instance the two points in the Persian Gulf take

Figure 13: Differences between the AMIP2 (grey) and CMIP (red) land seamasks. For the red points, SST must be interpolated.

26

on the SST of a point at the exit of the Persian Gulf into the Gulf of Oman.In the CMIP2CO2 experiment (Figure 12), SST increases in the tropics by

about 2C, while the temperature patterns stay more or less the same. For acloser look, the average differences between the CMIP1CO2 and CMIP2CO2runs are depicted in Figure 14. SST increases almost everywhere with a maxi-mum in the Barents Sea, where there is also the largest decrease in sea ice coverunder both DJF and JJA conditions. Other maxima of this kind are situatedin the Denmark Strait north of Iceland and the Okhotsk Sea.

Maximum tropical warming occurs in the equatorial Pacific between Indone-sia and Middle America, exceeding 3C in Indonesia. However, warming in thisregion is not uniform, notably temperatures in the South China Sea betweenMalaysia and Vietnam just increase by 1 to 1.5C. In the Southern Pacific ataround 60 southern latitude and in the North Atlantic there are large areaswhere the temperature anomaly does not pass a two-sided t test at the 5% level,so the SST tendency there remains unclear.

Sea ice cover decreases between the 1xCO2 and 2xCO2 climates on bothhemispheres (Figure 15). This is also evident when comparing the AMIP2 andthe doubled carbon dioxide climatology for sea ice under doubled CO2 conditions(Figure 16), which show a clear decrease in sea ice cover, particularly in theAtlantic.

When constructing the climatology for doubled CO2 conditions, a few ad-ditional steps have to be taken for the SST data: Firstly, the differences inland-sea mask are accounted for by the method described above. Secondly, 9-point-smoothing as described in the GrADS documentation is employed twice toreduce some of the unrealistic small-scale structures in the isolines, particularlyin the Pacific, where the model might react sensitively to local disturbances inthe SST field. Thirdly, the minimum SST is set to 271.38 K where it falls belowthat value, mirroring the approach taken in the AMIP2 dataset.

These differences are added to the observational monthly means Ot of theAMIP2 dataset as determined from the formula given above. The adjusteddifferences are then added to these fields, effectively transforming the AMIP2dataset into a new, AMIP1-style climatology, because no backtransformation tothe Cts is done. This seems justified because of the relatively low amplitude andsmoothness of the seasonal cycle of tropical Pacific SST, as well as the relativelyinsignificant role of sea ice in establishing tropical convection and precipitationpatterns.

Figure 17 shows the finished SST and sea ice cover climatologies. MaximumSST can be found off the coast of New Guinea, while there is a noticeably coolerregion between Sumatra and Borneo. In the mid-latitudes, a major increase inNorth Atlantic temperatures and an almost complete absence of sea ice south

27

Figure 14: Average differences between the CMIPCO2 runs for (a) annual mean,(b) December to February, and (c) June to August conditions, with ∆SSTshaded and the −50% (solid) and −25% (dashed) contours of ∆SIC. Blankareas did not pass a t test at the 5% level.

28

of Spitsbergen can be observed.

3.2 Initial conditions

In order to reduce the spinup time that the model needs to adapt to its bound-ary conditions and produce a stable climate, the atmospheric restart fields aretreated similarly, that is the average 20-year difference between two Januariesin the CMIP experiments is added to the December 2019 restart file from theCONTROL run. Since the CMIP runs only had a vertical resolution of 19 layers,linear interpolation to 90 layers is used, with differences regarded as constantabove the 19-layer top level of 1 hPa.

Figure 18 shows the zonal mean temperature and zonal wind for the CON-TROL run restart file (a), the resulting 2xCO2 restart file, as well as theirdifference. Since these fields just represent a snapshot of the model at its firsttimestep, they can only be seen as an approximation to the differences betweenthe 1xCO2 and 2xCO2 climates. This is exemplified by the apparent triple jetin (c), which in all likeliness is an artifact. However, the contrasting temper-ature changes of a warming troposphere versus a cooling stratosphere seem inaccordance with prior knowledge of atmospheric behavior under global warmingconditions.

J F M A M J J A S O N D J

month

0

10

20

30

sea

ice

exte

nt [m

illio

n km

²]

AMIPCMIP1CO2CMIP2CO2

Figure 15: Monthly sea ice extent from the two CMIP runs in comparison tothe AMIP2 climatology.

29

Figure 16: Decrease in sea ice cover between the AMIP2 climatology andthe modified 2xCO2 climatology: Annual mean 75% sea ice cover for AMIP2(shaded) and 2xCO2 (black contour line) for the northern (top) and southern(bottom) hemisphere.

30

Figure 17: Resulting climatology for SST and sea ice cover as derived fromthe CMIP1CO2 and CMIP2CO2 runs: SST (C, shaded) and 90% (solid) and15% (dashed) contours of sea ice cover for (a) annual-mean, (b) December toFebruary, and (c) June to August conditions.

31

Figure 18: Zonal mean zonal wind (m/s, black contours) and tempera-ture (K) for experiments (a) QBO, (b) QBO2CO2, and (c) their difference,QBO2CO2−QBO.

32

4 The Control experiment

The Control run is an extension of the 17 year L90 experiment documented inGiorgetta et al. (2002). It was conducted before this body of work by M. A.Giorgetta as part of the ongoing effort to modify MAECHAM5 in such a waythat the simulated QBO is as realistic as possible. The integration spans 30years under the normal (i.e. AMIP2) climate conditions for SST and sea iceand is started from an atmospheric state without a QBO.

In Figure 19, zonal wind for the ten year period that is covered in Giorgettaet al. (2002) is shown (neglecting the seven-year spinup time), while in Figure20 the entire 30 year period of the extended run is contoured.

After an initial phase of irregular wind patterns in the Hovmoller diagram,a regular QBO with a period of about 32 months sets in. The QBO signal doesnot reach the tropical tropopause but is strongly dampened around 70 hPa. Thewesterlies have an amplitude of about 15 m/s, while the easterlies exceed 30 m/sin amplitude above 20 hPa. The model simulations also feature a considerablysmoother QBO signal than the one in the observational record, as even at a90-layer resolution, the complexity, particularly of the westerly wind maxima,cannot be entirely duplicated.

Forcing by resolved waves (Figure 21a) is strong above 3 hPa. Between 3and 10 hPa parameterized gravity waves (Figure 21b) effect most of the westerlyacceleration while contributing somewhat less to easterly acceleration. Below10 hPa, the forcing by resolved and unresolved waves at the zero wind con-tours mostly matches the acceleration needed to drive the QBO wind pattern.Examples of resolved waves accelerating the wind in the opposite direction aresporadic and are mostly located around 20 hPa.

Figure 19: Monthly and zonal mean zonal wind (m/s) at the equator in Exper-iment L90 (from Giorgetta et al. 2002).

33

Figure 20: Monthly mean time-height section of zonal mean zonal equatorialwind in m/s for the Control run, the extension of the L90 experiment.

Figure 21: Monthly and zonal mean tendency of zonal wind in ms−1d−1 at theequator by resolved waves (a) and by parameterized gravity wave dissipation(b). The zero contour of the zonal mean wind is shown in black (from Giorgettaet al. 2002).

34

To illustrate how the forcing of the QBO propagates upwards from the trop-ical tropopause, the absolute single-zonal-wavenumber contribution to the tem-perature field for waves with zonal wavenumber two is shown in Figure 22. Overthe course of the sixty days from the run depicted here, two such events wherestrong wave excitation causes wave trains to travel into the lower stratospherecan be seen. In the region of strong easterly shear at and above 30 hPa thewaves become quickly attenuated because their phase speeds are easterly.

Some of the remaining challenges surrounding the accurate simulation of theQBO by MAECHAM5 are quite evident in the Control experiment in compar-ison to the observed QBO, namely the period, which at 32 months is aboutfour months too long, and the failure of the QBO signal to reach the tropicaltropopause. Other sensitivity experiments outside the scope of this study willhave to be conducted to identify the reasons for these shortcomings and improvethe realism of the QBO as simulated in MAECHAM5.

Figure 22: Individual wave trains emanating from the tropical tropopause vi-sualized as the absolute daily mean temperature anomaly caused by the k = 2wave averaged between 5N and 5S. Upward-propagating Rossby-gravity wavesare absorbed in a strong easterly shear around 30 hPa.

35

5 Run001 results

In this first experiment, the model was run with the initial values as well as SSTand sea ice climatologies for the 2xCO2 conditions over an eleven-year periodand parameterized gravity wave forcing was left unmodified. This experimentallows to assess the changes in model parameters necessary to complete thetransition from the 1xCO2 to the 2xCO2 climate and serves to test whether themodel will reach a stable climate from the initial values and under the imposedboundary conditions.

5.1 Zonal mean zonal wind

As Figure 23 shows, after about two years where there is a hint of a descendingeasterly QBO phase, a two-to-three-year oscillation with easterly and westerlyphases that remain more or less fixed in height sets in. The cycle starts witheasterlies becoming westerlies at around 50 hPa, followed about three monthslater by an intensification of easterlies between 10 and 20 hPa. Between 80and 90 hPa there is another easterly phase that shows little temporal variation,while between 100 and 300 hPa, there are prominent super-rotating westerliesat a speed of about 5 m/s.

Close to the end of the model integration time (year 10/11), there is aninstance of descending easterlies and westerlies that look vaguely like the QBOof the control experiment. However, downward movement stops at about 50 hPa(the level of the time-mean westerly jet), and more importantly, another twoyears of model integration time showed that this QBO cycle was in all likelinessan episodic event—perhaps caused by an overly intensive generation of resolvedequatorial waves by the model in comparison to other years—and not a sign ofthe model climate transitioning to a new regime.

If the zonal mean zonal wind minus the annual mean zonal mean zonal windis considered (Figure 24), it becomes apparent that downward propagation ofthe QBO signal also takes place in this experiment, even though a systematicshift of the vertical wind profile masks this propagation somewhat in the zonalmean zonal wind. This figure shows a westerly jet between 1 and 10 hPa, fromwhich westerly QBO phases descend at fairly regular intervals. Prompted bythe absorption of westerly wave momentum, easterly wind maxima develop, e.g.in spring of years 6, 8, and 10. It is beyond the aim of this study to ascertainthe cause of this mean wind shift and its disappearance in later experiments.

The differences between the QBO in Control and the QBO in Run001 canbe shown in a wavelet power spectrum of 48.13 hPa zonal wind. Wavelets area technique similar to windowed Fourier spectra in that they show how thefrequency distribution of variance of a time series changes over time (Torrence

37

Figure 23: Run001 monthly mean zonal mean equatorial zonal wind in m/s. Aregular QBO does not develop, instead there a layers of fluctuating westerliesand easterlies at and below 50 hPa and only sporadic downward propagation ofwesterlies between 10 and 20 hPa.

Figure 24: As in Figure 23 but with the annual mean zonal mean values foreach level removed.

38

and Compo 1998). In contrast to the Fourier transform, the wavelet transformhowever uses basis functions (so-called “mother wavelets”) that are localized intime. This makes it possible to investigate non-steady spectra with decidedlynon-sinusoidal basis functions.

In practice, the time series is first zero-padded so that its length is an integerpower of two and then Fourier-transformed. The mother wavelet is scaled for theparticular frequency (and is then called a daughter wavelet) and also Fourier-transformed, and the wavelet transformation is computed as the convolution ofthe two transforms. When the point where the wavelet is centered on is so closeto one of the ends of the data set that the wavelet has nonzero amplitude beyondthe confines of the time series, this point is said to be in the “cone of influence”,where spectral power is diminished due to the influence of the zero-paddingregion. This area is usually indicated in wavelet power spectra by hatching.

The mother wavelet used here is the Morlet wavelet (shown on the top rightin Figure 25), because it is the product of a sine and a Gaussian that canrepresent slowly varying sinusoidal components like those likely to be foundboth in the QBO signal, and annual and semiannual components that resultfrom the seasonal cycle.

Figure 25: Wavelet power spectrum for the Control experiment 48.13 hPa zonalmean zonal wind monthly means.

Both for the Control (Figure 25b) and Run001 (Figure 26b) experiments,

39

there is a maximum of power in the QBO frequency range (26-30 months). ButRun001 also has additional power over all frequencies in the cone of influenceat the beginning of the time series due to initial tendencies, visible in the timeseries (Figure 26a) itself as an almost linear decrease from 13 m/s to −8 m/sduring the first year of the experiment. Naturally, this linear shape requiresmany daughter wavelets of different periods to be represented accurately, thusaccounting for the broad spectral peak. This first year is the period of initialadjustment where the model has not reached a balanced climate state. Thus,the first year of integration time is disregarded and only the ensuing ten yearsare considered in the following analyses.

Another interesting difference is found in between the contributions of annualand semi-annual components in the two experiments: In Control, there is aperiod component of about 1.5 years that is almost continually present, whileat a period of 0.5 years there is very little power. In Run001, there is verylittle variability on the 1.5 year time scale, while the semiannual component ismuch more prominent, even though intermittent over time. This latter pointcan also be inferred from the global wavelet spectrum of Run001 (i.e. the sumover time of the power spectrum, Figures 25c, 26c), which shows a pronouncedsecondary maximum at a period of 0.5 years for the Run001 experiment which

Figure 26: As in Figure 25 but for the Run001 experiment.

40

is not present in the Control experiment.Finally, from looking at the QBO-induced maximum in variance, it seems

that the maximum power in this frequency range is reached toward the end ofthe run for experiment Run001—the maximum in power lies close to the edge ofthe trailing cone of influence. This is also visible in the time series (Figure 26a),which shows an increase in the 2-year component amplitude. For Control, it issomewhat similar, maxima are reached around the years 12, 20 and 30. Thissuggests that the QBO in MAECHAM5 does have some decadal variabilitybeyond the spinup phase. Of course, the length of the conducted experimentsdo not suffice to investigate this point quantitatively.

5.2 Residual circulation and forcing by resolved waves

To study the forcing of the mean zonal wind by resolved waves and their inter-action with the zonal mean circulation, a Transformed Eulerian Mean analysis(Figure 27, see Appendix A) is carried out for three OND (October-December)time periods in which the 50 hPa westerly jets are intensifying. The TEM anal-ysis shows that the z-divergence of the vertical Eliassen-Palm flux component(Figure 27e) plays a major role in supporting both the 50 hPa westerly and the15 hPa easterly jets. The y-divergence of horizontal E-P flux (Figure 27d) onthe other hand counteracts the jets and seeks to reverse them.

The thermal wind relationship requires that downward (upward) movementsets in in westerly (easterly) shear to raise (lower) temperature by adiabaticwarming (cooling). Therefore, a meridional circulation develops that transportsmomentum downward out of the westerly jets, as can be seen in the v∗ andw∗ residual circulation (Figure 27c) . The figure also indicates an off-equatorialclosing of the secondary circulation. As a final observation, the forcings areclearly not symmetrical about the equator, resulting in small meridional shiftsof the QBO jets also found in observations.

Tropical upwelling, i.e. the tropical branch of the Brewer-Dobson circulation,is caused in the mid-latitude stratosphere by the breaking of planetary wavesfrom the winter hemisphere that induces descent of air in the mid-latitudes andan associated ascent dictated by continuity in the tropical stratosphere. Sincethis upwelling causes individual air parcels (in the Lagrangian sense) to rise, theQBO downward phase movement is hindered by a speedup of this backgroundmotion.

For some time, this upwelling was disregarded in idealized QBO simulations,until it was pointed out by Dunkerton (1997) that considerably higher wave mo-mentum deposition was needed to achieve the observed period of the QBO. Asthe forcing by planetary waves in the mid-latitudes has supposedly changed (the

41

Figure 27: Forcings of ∂u/∂t in cm/(sd) averaged over the NH winters of years2/3, 4/5, and 7/8: (a) advection by v∗, (b) advection by w∗, (c) total advectionby residual circulation, (d) y -divergence of Fy , (e) z -divergence of Fz, and(f) total E-P flux divergence. Selected contours of zonal mean zonal wind aredrawn in blue.

42

Lorenz cycle will show this for the later experiments), the Brewer-Dobson circu-lation is modified, probably accounting for the lack of downward propagation inthis experiment. Indeed the minimum value of upwelling (defined as the zonalmean w∗ at 70 hPa averaged from 12N to 12S) increases from 0.1 mm/s inthe Control run to 0.14 mm/s in Run001.

(a)

(b)

Figure 28: Climatological atmospheric“tape recorder”signals for (a) the Controlexperiment, (b) the Run001 experiment. Anomalous specific humidity in ppmvwith an approximate mean rate of ascent (black line).

Alternatively, upwelling can be inferred from the atmospheric tape recorder,i.e. the anomalies of water vapor concentration between 10 and 90 hPa. Aclimatological average for Run001 and the Control experiment is shown in Figure28. It is apparent that the water vapor signal is somewhat higher-reaching inthe Run001 experiment than it is in the Control run, as the 0.1 and −0.1 ppmvcontours, which extend up to about 40 hPa in the Control experiment reach upto about 25 hPa in Run001. This corresponds to a difference in height of about3.5 km.

Changes of the seasonal pattern of water vapor anomalies at 90 hPa hint ata modification of the source, i.e. the tropical tropopause. This makes it difficultto draw a direct comparison and lets the residual circulation seem a better wayto characterize changes in tropical upwelling. However, the anomalies do showan increase in vertical speed in November and December, when the maximumof the anomaly travels upward to about 40 to 50 hPa, which is expected giventhat the tropical upwelling is strongest in NH winter due to the enhanced mid-latitude planetary wave driving (Rosenlof 1995). This is also the region wherethe QBO signal comes to a standstill in this experiment.

An approximate visual assessment of the upwelling speed between two ar-

43

bitrary levels, 30 hPa and 70 hPa (see the black lines in the figure) yields aspan of 8.5 months and 8 months for the Control and Run001 experiments, re-spectively. That is to say, from the perspective of the tape recorder analysisdifferences in upwelling between the two experiments seem rather minor, eventhough a shifting of the seasonal cycle is conspicuous in the diagram.

5.3 Derivation of the gravity wave RMS wind parameter

To assess the intensity of parameterized gravity wave generation that shouldresult from the altered climate conditions, convective precipitation means andvariances were considered. The important variable that determines gravity wavegeneration by convective storms is vertical motion, since it is thought to bethe regions of upward and downward motion associated with the individualconvective cells impinging on a stably stratified layer above which are responsiblefor the generation of gravity waves by convection (Fovell et al. 1992).

Numerical experiments have been conducted with mesoscale models of con-vective storms (Alexander et al. 1995), verifying this theory, showing that indeedgravity waves are generated at the trailing edge of the storm, because up- anddowndrafts are most intense there. Another possible mechanism in the presenceof high mean background winds is the so-called obstruction effect, where theup- and downward currents block the mean flow similar to the way topographydoes. Numerical experiments can show this behavior too when the backgroundflow becomes fast enough.

In ECHAM, the parameterization for convective precipitation will generaterelatively realistic variances of precipitation (Horinouchi et al. 2003), so thatconvective precipitation variances can be taken as an indicator of up- and down-draft intensity and thus gravity wave generation.

Horizontal fields of convective precipitation means for the Control and Run001(Figure 29) experiments feature a considerable increase in maximum convectiveprecipitation in the Indonesian region. Panels a and c show how the maximumto the northeast of New Guinea grows from 17 mm/d (Control) to 22 mm/d(Run001). Another maximum centered southeast off the Philippines’ coast,which is minor in Control, has similar amplitude as the New Guinea maximumin Run001. But there are also decreases: The broad maximum in the IndianOcean flattens somewhat in the Run001 experiment with a corresponding lossof amplitude.

The temporal variances from 12-hourly data (b, d) show even more dra-matic shifts: While variance does rise markedly in the New Guinea maximum,the variance peak near the Philippines (shifted northward in relation to the peakin mean precipitation) more than doubles from 127 mm2/d2 to 277 mm2/d2.

44

Similarly, the maximum over eastern India and in the Gulf of Bengals, whichhad gained marginally in mean convective precipitation, shows a drastic increasein variance as well, rivalling the Philippine maximum in magnitude. This en-hancement is likely to be associated with an intensification of the variability ofprecipitation associated with the Indian monsoon circulation. Another spot toconsider is the Andes region, where MAECHAM5 had already simulated largevariance in the Control experiment and even more in Run001.

All the precipitation variance hotspots lie in the latitudinal band between10N and S where upward-propagating gravity waves are bound to affect theQBO.

In the zonal average, convective precipitation increased by a factor of 1.1for the grid points near the equator, while variance increased by approximatelya factor of 1.2. The Indonesian maximum in convective precipitation, bothin mean and variance, however, shows larger increases from the control run,with precipitation variance increasing to about 2.2 times the value found in theControl run.

An estimate of the factor that should be applied to the gravity wave pa-rameterization was obtained by first binning grid-point convective precipitation

(a) (b)

(c) (d)

Figure 29: Convective precipitation means (a, c) and temporal variances (b, d)for the Control (a, b) and Run001 (c, d) experiments. Units are mm/d andmm2/d2, respectively. The annual cycle has been subtracted before computingvariance.

45

values in 30-degree latitude boxes between 75N and 75S. For these boxes,the area-weighted 12-hourly data were considered. Then, means and varianceswere computed for each box for the entire year as well as for the four seasonsindividually (Figure 30).

The amplification factor for the parameterization is then defined as

α =

√σ2

Run001

σ2Control

where the σ2 are the convective precipitation variances suitably averaged overthe five latitude boxes. Table 1 shows α2 and α for the individual latitudebins. In all bins, variance increases significantly (at the 5% level) except for thesouthernmost one, where the opposite is true. Neglecting the outer two bins, avalue of α = 1.2± 0.1 seems plausible.

Other ways of determining the factor were investigated as well: If one dividesspectral power, for example as obtained from a periodogram of power versuswavenumber, for a quantity such as temperature or wind for the Run001 exper-iment by the Control experiment value, one can see how the variance for eachwavenumber increases when doubling CO2. If some sort of power law exists thatcouples resolved scales to unresolved scales of gravity waves and this increase is

(a)

75°N-45°N 45°N-15°N 15°N-15°S 15°S-45°S 45°S-75°S0

1

2

3

4

5

6

7

mm

/d

MEANMAMJJASONDJF

Control run convective precipitation mean(b)

75°N-45°N 45°N-15°N 15°N-15°S 15°S-45°S 45°S-75°S0

1

2

3

4

5

6

7

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/d

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Figure 30: Zonally averaged precipitation means (a, b) and variances (c, d) forControl run (a, c) and Run001 (b, d).

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almost the same for all wavenumbers, it is conceivable that the unresolved wavepower should be raised accordingly.

This analysis was carried out for temperature (Figure 31) and meridionalwind (Figure 32) at 200 hPa (above the region where gravity waves are gen-erated) using the same latitude boxes as in the precipitation method. Thecomputed relative spectra should be compared to the above values for α2.

The spectrum for temperature shows a remarkably flat increase for the equa-torial box, resulting in about a factor of 1.3 for the higher wavenumbers. Thelatitude bands next to the central one seem to indicate a factor of about 1.2.

The increases in meridional wind variance are quite similar for the equatorialand adjacent boxes, lying around 1.2. Notably, the northernmost and southern-most bands deviate strongly, especially in the middle wavenumber range.

5.4 Summary of experiment Run001

While the Run001 experiment is only a first approximation of the QBO under2xCO2 climate conditions, it has nevertheless given several important insightsinto effects that will have to be investigated in more detail later. For one,the QBO does become unstable when changes in parameterized gravity wavemomentum deposition are not accounted for. Still, some form of downwardpropagation of the QBO signal exists, even though it may only be visible whenthe time-mean vertical profile of zonal wind is subtracted. Another thing is theenhancement of the Brewer-Dobson circulation below about 50 hPa which isrelated to increased forcing by resolved waves in the extratropical stratosphere.Finally, tropical convective precipitation variances are a useful indicator of in-ternal gravity wave generation by convection. The somewhat limited integrationtime of 11 years, however, limits the accuracy of this method severely, puttingthe increase in source strength between about 10 and 20%.

Considering all the estimates for α, the following experiments feature anRMS gravity wave wind at the launching height that is increased to 110% and120% of the Control experiment values. The first value represents the best

Latitude bin α2 = σ2Run001/σ2

Control α = σRun001/σControl

75N-45N 1.34 1.1645N-15N 1.37 1.1715N-15S 1.69 1.3015S-45S 1.12 1.0645S-75S 0.82 0.91

Table 1: Annual mean convective precipitation variance (second column) andstandard deviation (third column) increases in regard to the CONTROL runvalues for the five latitude bins.

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Quotient of RUN001 and CONTROL periodograms for temperature (200 hPa)

Figure 31: Increase in spectral power between the Control and Run001 experi-ments for 200 hPa temperature.

0 10 20 30 40wavenumber

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Quotient of RUN001 and CONTROL periodograms for meridional wind (200 hPa)

Figure 32: As in Figure 31 but for meridional wind.

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guess, while the experiment associated with the second one shows if the changesare linear and can provide help in assessing significance of the results of the110% experiment. Furthermore, given the sizable standard deviation of the bestestimate, it is also conceivable that 120% the Control run value RMS gravitywave wind is the more realistic setting.

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6 Run002 and Run003 results

The analysis of the first experiment with unchanged specification of the sourcestrength of sub-grid scale gravity waves suggests a value of 1.2±0.1 for the ratioof convective precipitation variances under 2xCO2 and 1xCO2 conditions. Thesquare root of this factor then is taken to be a good estimate for the increasein sub-grid gravity wave forcing that should occur in the 2xCO2 climate withrespect to the 1xCO2 climate. Consequently, Run002 is conducted with 1.1 timesthe gravity wave RMS wind and Run003 with 1.2 times the control experimentvalue of 1 m/s.

Figure 33: Equatorial monthly mean zonal mean zonal wind in m/s for Run002(top) and Run003 (bottom), with 1.1 and 1.2 times the RMS gravity wave windfrom Run001 to account for more intense convection under the doubled CO2

climate conditions.

6.1 Zonal mean zonal wind

Since the model runs start from the same initial values, it makes sense to lookat the first years of the experiments and compare the varying effect of parame-terized gravity waves on the QBO (Figure 33). This is particularly obvious forthe first phase of westerlies and easterlies moving downward: In Run002, both

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phases halt at certain altitudes for a month or two, while in Run003 such ahalting at these levels is not apparent. These changes already signify that theparameterized waves may be quite important. The shortening of the QBO cyclebetween Run002 (six maxima of westerlies) and Run003 (eight maxima) is alsoapparent in a side-by-side comparison.

Figure 34: Composite of equatorial zonal mean zonal wind for the Controlrun. Individual panels show mean u [m/s] (top) and standard deviation [m/s](bottom) of the composited fields. Black contours of vanishing zonal meanzonal wind are superimposed on the standard deviation for better comparison.Composites start with winds getting westerly at 20.77 hPa.

The enhanced downward motion of QBO phases means that a fairly regularoscillation is found in the Run003 experiment with an average period of 17months at 20 hPa, as opposed to the 22 months and 34 months in the Run002and Control experiments, respectively. This is made clear by the Run002 andRun003 u-composites (Figures 35 and 36) in comparison to the u-composite forControl (Figure 34), which not only show the quicker QBO cycle in the latterexperiments but also subtle differences in the downward progression: The slighthalting of the line of vanishing mean zonal wind at around 25 hPa, which wasquite conspicuous in the other experiments, has completely disappeared in theRun003 experiment.

Between 30 and 70 hPa, the downward propagation speed of the flank ofwesterlies does not change in relation to the Control experiment, all the increaseof the downward propagation of the westerlies is located between 10 and 30 hPa.

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Figure 35: As in Figure 34 but for the Run002 experiment.

Figure 36: As in Figure 34 but for the Run003 experiment.

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This is in marked contrast to the findings of Giorgetta et al. (2002), who statedthe ineffectiveness of gravity wave drag for the layers below 20 hPa. The contraryis true for the flank of easterlies, which shows an accelerated downward motionbelow 25 hPa and little change in downward propagation speed above that level.

A change in amplitude is difficult to ascertain from the zonal mean zonalwind, but it is interesting to look at the standard deviation of the individualsamples used in the composite analysis (Figures 34 to 36). Here, the uncertaintyin the timing of the setting in of the ensuing (westerly) QBO cycle is apparent,where Run002 looks considerably different from the other experiments with amaximum in standard deviation before the winds becoming eastward at 10 hPa.

This shortening of the QBO period is consistent with the findings of Hamiltonet al. (2001), who used the GFDL SKYHI model, which simulates an equatorialoscillation with a period of 12 months, to conduct sensitivity experiments withraised and lowered SSTs. They added the term 2.5K(1 + cos θ), where θ is lati-tude, to the control experiment SST. Even though they had to use a horizontalresolution too low to generate a QBO, the model did produce a QLO, a “QBO-like oscillation”, that had a shorter period in the “warm SST” case and a longerperiod in the “cold SST” case, in relation to their control experiment outcome.

6.2 Forcing by resolved and parameterized waves

The forcing of QBO phases consists of E-P flux divergence by resolved waves(RW) and parameterized momentum deposition by sub-grid scale gravity waves(SGSGW). In Figures 37, 39, and 41, these forcings are shown (in m/s perday) for the individual experiments as diagnosed from the TEM equations andthe MAECHAM5 SGSGW parameterization scheme. Furthermore, for eachexperiment the composite SGSGW forcing is shown (Figures 38, 40, and 42)to elucidate in particular the changes in vertical structure. Composites of theresolved wave forcing did not provide significant insights because of the highlyerratic nature of the RW signal. Therefore, the time evolution of individual RWforcing phase should be considered instead.

The figures show that resolved and unresolved waves contribute with aboutsimilar strength to the QBO acceleration. The diagnosed RW forcing shows amore variable pattern than the SGSGW forcing, which changes much smootherover height. This smoothness is effected by the close coupling of the parame-terization to the zonal wind, which means that the vertical wind shear largelydetermines the SGSGW forcing and regions of little vertical wind shear experi-ence only minor SGSGW forcing.

Particularly for westward acceleration in the QBO region, RW accelerationis centered around the zero line of zonal wind, whereas the SGSGW forcing

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Figure 37: Monthly mean momentum deposition above the equator by resolved(top) and unresolved (bottom) waves in ms−1d−1 for eleven years of the Controlexperiment. The zero contour of zonal mean zonal wind is shown in black.

Figure 38: Composite of parameterized gravity wave forcing (top) and its stan-dard deviation (bottom) for the Control experiment. The units are ms−1d−1

and the composite contour of vanishing zonal mean zonal wind is drawn in black.

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Figure 39: As in Figure 37 but for ten years of the Run002 experiment.

Figure 40: As in Figure 38 but for the Run002 experiment.

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Figure 41: As in Figure 37 but for ten years of the Run003 experiment.

Figure 42: As in Figure 38 but for the Run003 experiment.

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takes place mostly after the mean wind has changed direction. Changes in RWforcing magnitude between Control and the other experiments are difficult toquantify, although it seems that between about 10 and 20 hPa periods of extremeforcing occupy a larger fraction of the total forcing at the shear zones. All inall, however, RW variability is too high to allow confident conclusions about themomentum deposition differences between 2xCO and 1xCO climates from suchshort-duration experiments.

SGSGW forcing does increase as expected from the prescribed change inparameterization. The intensity of this forcing also shows almost no dependenceon height, which is a stark contrast to the vertical gaps that can be seen be seen,e.g. above 10 hPa in the Control run. Finally, the temporal breaks in downwardpropagation of westerlies is due to RW forcing, which frequently counteracts thesetting in of the next phase at levels between 20 and 50 hPa. SGSGW forcingon the other hand always contributes positively to the QBO cycle and to thesetting in of westerlies.

If the minimum and maximum SGSGW forcings for the three runs are com-pared, it is interesting to note that the biggest changes involve forcing in thewestward direction (Figure 43), which even shows differences between Run002and Run003. Between 50 and 100 hPa, a new band of major gravity wave forcingseems to emerge, which can be seen to intensify in Run003.

Maximal eastward forcing does not look very dissimilar for the three experi-ments, even though Run003 differs considerably from the other two experimentsbetween 10 and 30 hPa. Above 10 hPa, the Control experiment appears to ex-hibit somewhat smaller values of forcing.

6.3 Vertical and meridional structure of the QBO

Interestingly, the acceleration of the QBO in MAECHAM5 is unevenly dis-tributed on the phases, as the histograms for 20.77 hPa and 48.13 hPa (Figures44 and 45) easterly and westerly phase durations clearly show. While at 20.77hPa the length of the westerly phases decreases only slightly, it is the east-erly phases that contribute almost exclusively to the decreased QBO periods inRun002 and Run003, shortening from about 21 months to 8 to 10 months. Inthe case of Run003, this drastic shortening of the easterly phases means thatthe 20.77 hPa winds will tend to be in a westerly phase slightly more often thanin the easterly phase. This asymmetric behavior might be due to an increasedabsorption of gravity waves with westerly phase speed in the region of intensewesterlies below the QBO domain.

At lower altitudes, at 48.13 hPa, it is the westerly phase which shows astrong decrease in average duration, halving from about 24 months to 9 to 12

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-5 -4 -3 -2 -1 0 1 2

Figure 43: Vertical profile of the minimum and maximum parameterized grav-ity wave drag forcings for Control (black), Run002 (red), and Run003 (blue)in ms−1d−1.

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months. Not much can be said with certainty about the easterly phase, eventhough it seems to shorten as well. The differences between Run002 and Run003are difficult to assess, however, for these short experiment durations.

The shortening of the QBO cycle and the comparatively longer time spentby the monthly mean zonal mean zonal wind in transitioning states also de-creases the lag-1 autocorrelation in relationship to the Control experiment val-ues at 20.77 and 48.13 hPa, although the decrease becomes more erratic withdecreasing height (Table 2). Closer to the tropical tropopause at 74.27 hPa, thestrengthening of sporadic westerlies reduces the autocorrelation even more.

Experiment 20.77 hPa 48.13 hPa 74.27 hPaControl 0.97 0.96 0.82Run001 0.95 0.85 0.37Run002 0.94 0.91 0.36Run003 0.91 0.86 0.48

Table 2: Lag-1 autocorrelations for monthly mean zonal mean zonal wind in allexperiments at three levels.

To investigate the meridional profile of the QBO, following the example ofDunkerton and Delisi (1985), a harmonic analysis of the 30 hPa zonal mean zonalwind is performed. For this, annual and semiannual components are subtractedfrom the time series, and then the residual is fitted to a Gaussian of the form

u(φ) = a + b exp(−φ2/c2)

where φ is latitude. Between about 20N and S the fit resembles well thelatitudinal structure of the QBO and the half-width of the function is then

φ1/2 = c√

log b− log(b/2− a/2).

Table 3 lists the fitted parameter means and standard deviations.

Parameter Control Run002 Run003a[m/s] 2.8±0.5 3.4±0.6 2±2b[m/s] 17.9±0.4 16.3±0.6 22±2c[] 13.1±0.4 12.4±0.5 14±1

Table 3: Fitted Gaussian parameters for the QBO zonal wind signals in thevarious experiments.

Half-widths for the individual experiments are (12.2 ± 0.4) for the Con-trol experiment, (12.0± 0.6) for the Run002 experiment, and (12.1± 1.4) forthe Run003 experiment. Evidently, the differences in mean are not significant,which supports the view taken by Haynes (1998) that the QBO half-width de-

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Figure 44: Histograms of QBO westerly (left column) and easterly (right col-umn) phase durations in months at 20.77 hPa for the Control, Run002, andRun003 experiments (rows). The data has been binned into three-month inter-vals around multiples of three.

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Figure 45: As in Figure 44 but for a height of 48.13 hPa.

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pends primarily on the Coriolis force and not so much on the width of the waveexcitation region. He reasons that the switch from the tropical response (ac-celeration) and the extratropical response (steady state meridional circulation)takes place at

φTrans = (σ/α)1/4(ND/β)1/2,

where σ is the frequency of applied body force, α is radiative damping, N isbuoyancy frequency, D is the depth scale of the forcing, and β = ∂f/∂y|equator.This equation is derived from the TEM equation for vertical motion. However,the increase in standard deviation, particularly in the experiment with 1.2 timesthe gravity wave RMS wind, is striking. It might be associated with barotropicinstability in this region. To verify this, following Hamilton et al. (2001), thequantity

σ = β − uyy = fy − uyy

where f is the Coriolis parameter 2Ω sin φ, with Ω being the angular frequencyof Earth rotation and the indices denoting partial derivatives, is plotted againstthe u-contours. In Figure 46, this quantity normalized by βequator = 2Ω/a,where a is the radius of Earth, is shown for the Run002 experiment at 29.08hPa in a Hovmoller diagram.

The westerly QBO jet does indeed have regions of barotropically unstableflow (σ < 0) close to the half-width latitudes, where lateral mixing of momentumtakes place. If the minimum σ for all the experiments at 30 hPa is considered,the various experiments do not show significantly different values, but the re-gions of barotropic instability near the QBO jet occur with higher frequency.This quantity is defined here as the average number of grid points at 29.08hPa between 30N and 30S that have barotropically unstable flow. While thehorizontal resolution is coarse and monthly averaging will suppress short-terminstable conditions, statistically significant numbers (in grid points / monthlymean) can be established as 0.75±0.06 for Control, 1.2±0.1 for Run002, and1.5±0.1 for Run003. So barotropic mixing does become more important in thelatter two experiments.

The values for upwelling (Figure 47), measured as the time-mean zonal meanw∗, do not change much between 10 hPa and 50 hPa but they show a clearincrease below 50 hPa. This is much more apparent in this quantity than in thetape recorder climatology. This considerable strengthening of upwelling below50 hPa explains why QBO downward movement stopped there in Run001.

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Figure 46: Non-dimensional barotropic instability parameter at 29.08 hPa forthe entire Run002 experiment. The zero contour is drawn in black. Negativevalues indicate barotropically unstable conditions.

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Figure 47: Zonal mean equatorial w∗ (averaged between 10N and 10S) inmm/s for Control (blue), Run002 (red), Run003 (green).

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6.4 Extratropical effects

The extratropical influence of the QBO has been proposed originally byHolton and Tan (1980) and relates the strength of the stratospheric wintervortex and the QBO phase. It is found that the 40 hPa QBO wind speed isrelated to the polar circulation in such a way that during the easterly phase, thespeed of the jet is decreased and the temperature in the jet region is maximal.The geopotential is also lower during the easterly phase. The opposite is foundto be true for the westerly phase, and also for higher reference points in theQBO at 20 hPa, where the effects are anti-correlated to the ones at 40 hPa.This effect is most pronounced during NH winter, because the generation ofplanetary waves is more intense there due to the distribution of land and sea(and hence, surface temperature) that is less zonally symmetric than in the SH.

The Holton-Tan effect is commonly explained with critical lines, which arethe latitudes of vanishing zonal mean zonal wind. Rossby waves that are gen-erated on the NH are reflected on this line if the QBO is easterly, so that theystay in the NH and decelerate the mean flow there. If, on the other hand, theQBO is westerly, they can extend beyond the equator and will not affect the NHas much. Thus the QBO acts as a “valve” to the planetary waves that regulatestheir momentum deposition in the polar stratosphere.

The Lorenz energy cycle separates between potential and kinetic energy ofthe mean flow and the disturbances. An extension of the common Lorenz energycycle was calculated, which discerns between stationary and transient eddies,and also gives, besides the total energy, a distribution of energy on three wave-length ranges: Planetary (wavenumber 1 to 3), synoptic (wavenumber 4 to 9),and short (wavenumber greater than 9) waves.

For the study of NH hemispheric planetary waves, variables of interest arethe kinetic energy of (A) the zonal mean flow, (B) the standing long waves, (C)the transient long waves, and (D) the transient synoptic waves. Table 4 liststhe values of the reservoirs in 105 J/m2. The analysis was conducted for eachof ten years from each experiment and then averaged.

Quantity Control Run002 Run003A 6.3±0.1 7.3±0.1 7.1±0.1B 0.75±0.07 1.0±0.1 0.99±0.09C 2.64±0.06 3.0±1.0 3.08±0.07D 3.1±0.1 3.28±0.05 3.31±0.09

Table 4: NH Lorenz energy cycle components in 105 J/m2 for Control, Run002,and Run003 with standard deviations.

Because of the low number of ten samples and the positive definiteness ofthe reservoirs, the distribution of the values was deemed to be too non-Gaussian

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to ascertain significance with a conventional t-test. Instead, a Wilcoxon-Mann-Whitney rank-sum significance test (Wilks 1995) was conducted. In it, the datais sorted into a batch that comprises the two datasets to be compared, andthe asymmetry of the sum of ranks for one or the other set is compared to thedistribution of all possible combinations. For sample sizes larger than ten, thisdistribution is almost Gaussian by the central limit theorem, but in this casethe null distribution was generated by a Monte Carlo resampling method.

Given a test level of 5%, none of the differences in the Lorenz variablesbetween Run002 and Run003 are significant. This is to be expected, sinceplanetary and synoptic waves are generated by regions of high horizontal tem-perature contrasts and should not be affected much by the change in gravitywave parameterization.

The differences between both the Control experiment and Run002 and be-tween Control and Run003, on the other hand, are all statistically significant,in that the Control run values are all significantly lower than the Run002 andRun003 values. It is also interesting to note that the standard deviations of thequantities A through C are almost the same for these two experiments.

It needs to be kept in mind that the Control experiment is three times longerthan the other two runs and that the NH winter circulation is quite variable.For the verification of an extratropical influence of the accelerated QBO in adoubled CO2 climate, longer integration times are necessary to allow comparisonof the full 30 years of the Control experiment with the other two runs.

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7 Summary and conclusion

Three experiments with MAECHAM5 under climate change, i.e. doubled CO2

levels, were conducted to study the impact of man-made global warming on thequasi-biennial oscillation, one of the major dynamical phenomena of the middleatmosphere.

The first experiment used the changed boundary conditions and initial val-ues obtained from the two coupled experiments, the AMIP2 data set, and theControl run under present-day climate. This test experiment did not producethe QBO which was not unexpected given that the additional momentum fluxesby enhanced tropical convection were not accounted for in the parameterizationsettings. Instead, waxing and waning winds at almost fixed levels were observed.In particular, around 50 hPa there seemed to be a strong blocking of downwardmotion of the QBO phase. However, close to the end of the run an event tookplace that showed marked downward propagation, but this event was singular.

All in all, this run was the baseline used to estimate the effect of CO2 dou-bling on the excitation of equatorial gravity waves, which is prescribed in theMAECHAM5 GCM. Several approaches can be utilized to arrive at the valuesfor this parameter: In this study, comparisons of convective precipitation vari-ance and spectral variance in wind and temperature fields were considered. Theidea is that (given the ability of ECHAM to reproduce a precipitation variancein good agreement with observational estimates in the tropics, see Horinouchi etal. 2003) this variance coincides with convective system updraft velocity, whichis responsible for gravity wave generation by impinging on the stratified layerabove.

The other approach assumes that there is some sort of power law governingthe increase in variance over the wavenumbers. While long wave increase iserratic and short wave increase near the truncation limit is modified by diffusion,the central part of the spectrum did show a roughly constant and linear increase,at least in the tropics.

Both these approaches suggested an amplification factor for variance of about1.2, which translates to 1.1 ≈ √

1.2 m/s for the gravity wave RMS wind settingof the MAECHAM5 Hines gravity wave momentum flux scheme. Both to assessthe linearity of response and because considerable uncertainty about the valueremained (with a high probability that the actual value should lie higher, forvarious reasons), two runs were conducted, with 1.1 and 1.2 times the Controlrun gravity wave RMS wind of 1 m/s at launching height.

Both of these experiments produced a QBO with considerably shorter peri-ods. The forcing by resolved and unresolved waves was analyzed by the Trans-formed Eulerian Mean formalism and an additional parameterization-only run

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of the model on the prognostic variable output of the experiment. It becameclear that resolved waves played not only a role in QBO amplification / down-ward propagation but also hindered the downward motion at times. The haltinglevels were explained by the increase in mean residual vertical motion, i.e. thetropical branch of the Brewer-Dobson circulation, as effected by momentum de-position by planetary waves in the winter hemisphere stratosphere. This motionlifts the whole QBO domain uniformly, necessitating increased wave driving toachieve the same downward phase speed. While the changes below about 50hPa were considerable, levels at higher altitudes showed only minor increasesand may also have been tainted by the QBO signal itself.

Parameterized waves played a considerable part in QBO forcing, as is alsoobserved in nature. Their forcing increased considerably between 1xCO2 and2xCO2 climates, becoming more pronounced and occupying a larger domainin the QBO region, as could be seen in composites of parameterized forcing.The coverage of parameterized wave forcing, which has gaps in the Controlexperiments, is continuous in the other runs. The importance of sub-grid scalewaves lies in the fact that their momentum is largely deposited in such a wayas to strengthen the QBO signal.

By compositing fields by QBO phase, additional features not apparent in theplots of time evolution can be recognized, such as the differences in parameter-ized gravity wave drag that include more intense forcing in lower layers and ahigher degree of vertical homogenization. Resolved wave momentum depositionproves difficult to assess from the comparatively short model integration times.

A comparison of the vertical structure of the QBO shows that the periodshortening does not take place evenly over the entire vertical domain for west-erlies and easterlies, respectively. In accordance with the time-mean verticalQBO wind profile, easterly phases shorten at higher levels while westerlies areresponsible for much of the period shortening at lower levels.

The meridional structure of the QBO did not show significant differencesbetween 1xCO2 and 2xCO2 climates, supporting the view that the meridionalQBO length scale is primarily a consequence of the Coriolis force.

There are also indications of extratropical effects of the faster QBO, eventhough the high natural variability of NH winter circulation is an impedimentto a precise assessment. Nevertheless statistically significant increases in annualmean kinetic energy of the zonal mean flow, standing and transient long wavesas well as synoptic waves were observed.

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7.1 Future directions

The need for longer experiments

Due to computationally intensive nature of the experiments conducted at T42L90resolution, it was only possible to integrate the model over 11 years. In com-parison to the 30 year length of the Control run, it is clear that this severelylimits the statistical significance of the results obtained. While the number ofavailable QBO phases for post-processing is larger in the later experiments andserial correlation in the lower stratospheric winds decreases, thus increasing theratio of effective sample size and sample size, ten years of data are not enoughfor some analyses. Thus one has to be cautious when making statements onthese experiments.

Therefore, longer integration times to gain more statistical confidence seemdesirable. Of course this would also allow examination of longer timescalesin these runs, namely the hint of decadal variability evident in the Controlexperiments. The improvement in certainty provided by a longer experimentcould be helpful in settling some of the questions around extratropical effects ofthe modified QBO.

Comparison with observations

Given the importance of sub-grid scale waves, a better estimate of RMS windmight be desirable. Other means of determining this parameter, e.g. band-passfiltered vertical profiles of temperature similar to diagnostics applied to satellitedata, may help to improve the accuracy of the estimate. It is unclear, however, ifthe current vertical resolution of about 1 km per layer in the lower stratosphereis sufficient for this kind of analysis.

While precipitation variance in ECHAM is comparatively lifelike (Horinouchiet al. 2003), it is conceivable the further refinements to the Tiedtke-Nordengdeep convection closure scheme will be implemented that effect a different spec-trum of resolved waves, just as the Tiedtke-Nordeng scheme is superior to theTiedtke scheme as used in ECHAM3, which, when used in MAECHAM5, gen-erates a QBO with a 60-month period.

The results achieved with MAECHAM5 can be compared to soundings orsatellite measurements, which could lead to verification of both the tropospheric(more intense tropical convection) and stratospheric (faster QBO) effects foundin the experiments. Satellite soundings in particular could also improve un-derstanding of tropical gravity wave generation and yield a better view on theintricate role of gravity waves in the QBO.

If the tendency of a faster QBO exists not just in MAECHAM5 but alsoin reality (which seems reasonable, although the experiments conducted here

71

are deliberate simplifications of the problem), the ever-growing observationalrecord of the QBO should mirror this tendency. A new generation of satellitescurrently in deployment might supply a better coupling of reality and generalcirculation models in the future.

Other model sensitivities

Finally, other sensitivities exist that may have a major impact on the outcome:Higher horizontal resolution influences QBO period by decreasing the spatiallimit for resolved waves, thus adding momentum flux to the experiment. Forexample, increasing horizontal resolution to T63 reduces the current-climateQBO period to a more realistic 27 months (M. A. Giorgetta, personal commu-nication). It remains to be seen whether this speedup influences the ratio ofControl experiment QBO period by CO2 climate QBO period or if this effect issuch that even though the individual periods are shortened, the ratio remainsmore or less the same.

The importance of the RMS gravity wave wind parameter even under normalclimate conditions for the QBO is evidenced by other sensitivity experiments un-der present-day climate conditions (M. A. Giorgetta, personal communication)that show a 48-month QBO period for rmswind=0.9 m/s, a 22-month periodfor rmswind=1.1 m/s, and a 29-month period under default (rmswind=1.0 m/s)conditions.

The Run001 experiment with its borderline, wind profile-shifted may alsobehave differently under later model revisions and / or higher horizontal reso-lutions. This would allow to draw comparisons for forcing and upwelling thatmight shed light on why the oscillation behaves somewhat unusually in theRun001 experiment as documented here.

72

A The Transformed Eulerian Mean and the

Eliassen-Palm flux

The Transformed Eulerian Mean (TEM) formalism was introduced by Andrewsand McIntyre (1976) as a means to group momentum and heat transport byeddies together in such a way that the eddy effect on the mean backgroundflow becomes apparent in the zonally averaged equations of motion. It was anextension of the work done by Eliassen and Palm (1961) a decade earlier, whohad introduced the Eliassen-Palm flux for the study of the effects of mountainlee waves.

The E-P flux is basically a vector in the meridional plane, whose componentsare related to the eddy flux of sensible heat (vertical component, Fz) and theeddy flux of momentum (horizontal component, Fy). When the E-P flux as wellas its divergence are plotted over each other, the total amount of eddy forcingof the zonal background wind can be inferred (from the divergence) and also therelative importance of the two eddy fluxes (the angle of the E-P flux vector in theplane) for causing these effects (Peixoto and Oort 1992). Furthermore the E-Pflux divergence is proportional to the northward transport of quasi-geostrophicpotential vorticity (Edmon et al. 1980).

The TEM formalism can be derived from different zonally averaged setsof equations of atmospheric motions, such as the primitive equations or thequasi-geostrophic approximation, and will look slightly different according tothe assumptions used. Andrews and McIntyre (1976) use the Boussinesq ap-proximation for the β-plane primitive equations in their derivations, while An-drews et al. (1987) employ quasigeostrophy. The so-called residual circulation,v∗ and w∗, is introduced into the zonally averaged momentum and thermody-namic equations. If in the quasi-geostrophic framework, for example, v∗ and w∗

are defined as

v∗ = v − ρ−10 ∂

[ρ0v′θ′(∂θ0/∂z)−1

]/∂z

and w∗ = w + ∂[v′θ′(∂θ0/∂z)−1

]/∂y,

(where the quantities with subscripted zeroes refer to average vertical referenceprofiles) these zonally averaged equations take on a simple form where the eddyforcing, represented by the divergence of the E-P flux F, and the nonconservativeeffects (X) impact the zonally averaged zonal momentum, while the diabaticheating term Q acts to change the zonally averaged temperature field:

∂u/∂t = ρ−10 ∂Fy/∂y + ρ−1

0 ∂Fz/∂z + fov∗ + X

∂θ/∂t = −w∗∂θo/∂z + Q.

73

If the time derivatives vanish, i.e. the atmosphere has reached a steady statein regard to these two zonally averaged properties, the residual circulation andthe other forcing terms balance. The vertical component, w∗, will then offset thelocal diabatic heating, while the meridional component, v∗, will counterbalancethe eddy momentum transport as characterized by the E-P flux divergence.

While the quasi-geostrophic framework is not applicable in the tropics, theequation for θ does reflect the observed secondary circulation of the QBO, inwhich air descends and warms in the regions where the vertical velocity sheardictates a warm anomaly to exist because of the thermal wind relation.

If the residual streamfunction χ∗ is defined from v∗ and w∗analogous to theEulerian streamfunction χ from v and w, the dependence of w∗ on Q causesχ∗to take on a one-cell shape with ascent in the tropics and descent in thesubtropics and mid-latitudes, as opposed to the three-cell structure exhibitedby the convention Eulerian-mean streamfunction, χ.

For linear, conservative, and steady waves, Dunkerton (1978) formally provedthe equivalence of residual and Lagrangian circulation. If these assumptions areviolated, the Generalized Lagrangian Mean (GLM) of Andrews and McIntyre(1978) must be used instead. However, while Dunkerton’s assumptions are rarelymet, the residual circulation still approximates the real Lagrangian motion wellenough for most purposes, because for longer time periods the diabatic warmingis by far the most important driving force while other effects tend to cancel out(Sutton 1994).

There are two important theorems about the E-P flux divergence: TheCharney-Drazin non-acceleration theorem (after Charney and Drazin 1961) statesthat linear, conservative, and steady waves do not change the zonally averageszonal wind (u) and temperature (T ) fields, that is, their E-P flux divergence,∇ · F, vanishes. The Generalized Eliassen-Palm theorem (also in Andrews andMcIntyre 1976) describes how nonlinear, nonconservative effects and a nonzeroEliassen-Palm flux act together to change the wave activity:

∂A

∂t= D −∇ · F + O

(α3

).

This equation states that the density of wave activity will change over timebecause of diabatic (i.e. heating) and nonconservative (i.e. friction) forcing(D), eddy forcing (∇ ·F), and nonlinear effects (the term related to the cube ofthe wave amplitude, α).

A more in-depth review of the literature on the TEM and GLM formalismsas well as their applications to the investigation of troposphere-stratospherecoupling is provided by Silvestre (2003).

74

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List of Figures

1 The quasi-biennial oscillation as measured by rawinsondes: zonalwind in m/s. The data is supplied by the 2002 edition of theCD-ROM “The Berlin Stratospheric Data Series” published byK. Labitzke’s research group at the Free University Berlin. . . . . 6

2 The four vibrational modes of carbon dioxide: (a) symmetric,(b) asymmetric stretching; (c), (d) bending, where (d) is just(c) rotated by 90. In (a), there is no change in dipole momentduring vibration, thus no interaction with photons is possible. . . 9

3 Atmospheric CO2 concentration in ppmv determined at MaunaLoa, Hawaii. Missing values are linearly interpolated. Data fromKeeling and Whorf (2002). . . . . . . . . . . . . . . . . . . . . . . 10

4 Schematic view of the tropical Hadley cell and the stratosphericBrewer-Dobson circulation at solstice. Thin lines mark Lagrangiantransport, while bold arrows indicate predominant mixing direc-tions for tracers. Tropopause and stratopause are depicted asdashed lines (from WMO 1985). . . . . . . . . . . . . . . . . . . 11

5 The ECHAM model family of ECHAM, MAECHAM, and HAM-MONIA and the effects taken into account by these models.HAMMONIA (HAMburg Model of the Neutral and Ionized At-mosphere, and also Latin for ’Hamburg’) is a version of MAECHAM5that extends up to 250 km height and is coupled to the MOZART3(Brasseur et al. 1998) chemistry model. . . . . . . . . . . . . . . 15

6 Vertical coordinate system absolute heights and half-level dis-tances, showing the differences between the 39-layer (blue) andthe 90-layer (red) versions of ECHAM. In the 90-layer case, layerthickness stays well below 1 km up to about 40 km height. . . . . 16

7 The MPI-OM1 coordinate grid with increased equatorial resolu-tion and a polar axis tilted so that the northern pole of the gridlies above Greenland. . . . . . . . . . . . . . . . . . . . . . . . . . 19

8 Schematic overview of the CMIP experiments. . . . . . . . . . . . 209 AMIP2 climatological SST (C, shaded) and 90% (solid) and 15%

(dashed) contours of sea ice cover for (a) annual mean, (b) De-cember to February, and (c) June to August conditions. . . . . . 22

10 Monthly mean sea ice extent from the AMIP2 climatology for theentire globe as well as for the Northern and Southern Hemisphereseparately. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

11 As in Figure 9 but for the 2010-2029 period of the CMIP1CO2 run. 2412 As in Figure 9 but for the 2140-2159 period of the CMIP2CO2 run. 25

81

13 Differences between the AMIP2 (grey) and CMIP (red) land seamasks. For the red points, SST must be interpolated. . . . . . . 26

14 Average differences between the CMIPCO2 runs for (a) annualmean, (b) December to February, and (c) June to August con-ditions, with ∆SST shaded and the −50% (solid) and −25%(dashed) contours of ∆SIC. Blank areas did not pass a t testat the 5% level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

15 Monthly sea ice extent from the two CMIP runs in comparisonto the AMIP2 climatology. . . . . . . . . . . . . . . . . . . . . . . 29

16 Decrease in sea ice cover between the AMIP2 climatology and themodified 2xCO2 climatology: Annual mean 75% sea ice cover forAMIP2 (shaded) and 2xCO2 (black contour line) for the northern(top) and southern (bottom) hemisphere. . . . . . . . . . . . . . 30

17 Resulting climatology for SST and sea ice cover as derived fromthe CMIP1CO2 and CMIP2CO2 runs: SST (C, shaded) and90% (solid) and 15% (dashed) contours of sea ice cover for (a)annual-mean, (b) December to February, and (c) June to Augustconditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

18 Zonal mean zonal wind (m/s, black contours) and temperature(K) for experiments (a) QBO, (b) QBO2CO2, and (c) their dif-ference, QBO2CO2−QBO. . . . . . . . . . . . . . . . . . . . . . . 32

19 Monthly and zonal mean zonal wind (m/s) at the equator inExperiment L90 (from Giorgetta et al. 2002). . . . . . . . . . . . 33

20 Monthly mean time-height section of zonal mean zonal equato-rial wind in m/s for the Control run, the extension of the L90experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

21 Monthly and zonal mean tendency of zonal wind in ms−1d−1 atthe equator by resolved waves (a) and by parameterized gravitywave dissipation (b). The zero contour of the zonal mean windis shown in black (from Giorgetta et al. 2002). . . . . . . . . . . 34

22 Individual wave trains emanating from the tropical tropopause vi-sualized as the absolute daily mean temperature anomaly causedby the k = 2 wave averaged between 5N and 5S. Upward-propagating Rossby-gravity waves are absorbed in a strong east-erly shear around 30 hPa. . . . . . . . . . . . . . . . . . . . . . . 35

23 Run001 monthly mean zonal mean equatorial zonal wind in m/s.A regular QBO does not develop, instead there a layers of fluc-tuating westerlies and easterlies at and below 50 hPa and onlysporadic downward propagation of westerlies between 10 and 20hPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

82

24 As in Figure 23 but with the annual mean zonal mean values foreach level removed. . . . . . . . . . . . . . . . . . . . . . . . . . . 38

25 Wavelet power spectrum for the Control experiment 48.13 hPazonal mean zonal wind monthly means. . . . . . . . . . . . . . . 39

26 As in Figure 25 but for the Run001 experiment. . . . . . . . . . . 4027 Forcings of ∂u/∂t in cm/(sd) averaged over the NH winters of

years 2/3, 4/5, and 7/8: (a) advection by v∗, (b) advection byw∗, (c) total advection by residual circulation, (d) y -divergenceof Fy , (e) z -divergence of Fz, and (f) total E-P flux divergence.Selected contours of zonal mean zonal wind are drawn in blue. . 42

28 Climatological atmospheric “tape recorder” signals for (a) theControl experiment, (b) the Run001 experiment. Anomalous spe-cific humidity in ppmv with an approximate mean rate of ascent(black line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

29 Convective precipitation means (a, c) and temporal variances (b,d) for the Control (a, b) and Run001 (c, d) experiments. Unitsare mm/d and mm2/d2, respectively. The annual cycle has beensubtracted before computing variance. . . . . . . . . . . . . . . . 45

30 Zonally averaged precipitation means (a, b) and variances (c, d)for Control run (a, c) and Run001 (b, d). . . . . . . . . . . . . . 46

31 Increase in spectral power between the Control and Run001 ex-periments for 200 hPa temperature. . . . . . . . . . . . . . . . . 48

32 As in Figure 31 but for meridional wind. . . . . . . . . . . . . . . 4833 Equatorial monthly mean zonal mean zonal wind in m/s for

Run002 (top) and Run003 (bottom), with 1.1 and 1.2 times theRMS gravity wave wind from Run001 to account for more intenseconvection under the doubled CO2 climate conditions. . . . . . . 51

34 Composite of equatorial zonal mean zonal wind for the Controlrun. Individual panels show mean u [m/s] (top) and standarddeviation [m/s] (bottom) of the composited fields. Black con-tours of vanishing zonal mean zonal wind are superimposed onthe standard deviation for better comparison. Composites startwith winds getting westerly at 20.77 hPa. . . . . . . . . . . . . . 52

35 As in Figure 34 but for the Run002 experiment. . . . . . . . . . . 5336 As in Figure 34 but for the Run003 experiment. . . . . . . . . . . 5337 Monthly mean momentum deposition above the equator by re-

solved (top) and unresolved (bottom) waves in ms−1d−1 for elevenyears of the Control experiment. The zero contour of zonal meanzonal wind is shown in black. . . . . . . . . . . . . . . . . . . . . 55

83

38 Composite of parameterized gravity wave forcing (top) and itsstandard deviation (bottom) for the Control experiment. Theunits are ms−1d−1 and the composite contour of vanishing zonalmean zonal wind is drawn in black. . . . . . . . . . . . . . . . . . 55

39 As in Figure 37 but for ten years of the Run002 experiment. . . . 5640 As in Figure 38 but for the Run002 experiment. . . . . . . . . . . 5641 As in Figure 37 but for ten years of the Run003 experiment. . . . 5742 As in Figure 38 but for the Run003 experiment. . . . . . . . . . . 5743 Vertical profile of the minimum and maximum parameterized

gravity wave drag forcings for Control (black), Run002 (red), andRun003 (blue) in ms−1d−1. . . . . . . . . . . . . . . . . . . . . . 59

44 Histograms of QBO westerly (left column) and easterly (rightcolumn) phase durations in months at 20.77 hPa for the Control,Run002, and Run003 experiments (rows). The data has beenbinned into three-month intervals around multiples of three. . . . 61

45 As in Figure 44 but for a height of 48.13 hPa. . . . . . . . . . . . 6246 Non-dimensional barotropic instability parameter at 29.08 hPa

for the entire Run002 experiment. The zero contour is drawnin black. Negative values indicate barotropically unstable condi-tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

47 Zonal mean equatorial w∗ (averaged between 10N and 10S) inmm/s for Control (blue), Run002 (red), Run003 (green). . . . . . 65

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Acknowledgments

The author would like to thank M. A. Giorgetta for his patience, guidance, andinsightfulness. His helpful comments in the final phase of this work were alsovery much appreciated.

I would also like to thank the engineers from NEC Corp. for constructing amachine powerful enough to tackle these kinds of scientific problems which werebeyond the reach of even the most powerful computers until a few years ago.

Finally, I owe thanks to Ludwig, bonvivant and lagomorph extraordinaire,whose ability to provide valuable emotional support remains unmatched.

In addition to the standard diagnostics and plotting packages, the followingsoftware was used:

• Transformed Eulerian Mean and parameterized gravity wave drag analysiscode by Marco A. Giorgetta

• Fluxes and Lorenz Energy Cycle by Frank I. Lunkeit

• Wavelet analysis code in Fortran and IDL by Christopher Torrence andGilbert P. Compo

• Numerical Recipes for Fortran-77 and C

• Stats.py by Gary Strangman

I am indebted to the respective authors for sharing their work.

85

Erklarung

Hiermit versichere ich, dass ich die vorliegende Arbeit selbstandig

verfasst und außer der angegebenen Hilfsmittel und Literatur keine

anderen Quellen und Hilfsmittel verwendet habe.

........................................................

Hamburg, den 30.10.2003