On the interaction between ice sheets and the large-scale atmospheric

On the interaction between ice sheets
and the large-scale atmospheric
circulation over the last glacial
cycle
Marcus Löfverström
c
Marcus
Löfverström, Stockholm 2014
ISBN 978-91-7649-010-5
Printed in Sweden by US-AB, Stockholm 2014
Distributor: Department of Meteorology, Stockholm University
Abstract
The last glacial cycle (c. 115 – 12 kyr BP) was the most recent in a series of
recurring glaciations of the subpolar continents. Massive ice sheets evolved
in Eurasia and North America, which, at their maximum, were of continental scale and together lowered the global sea-level by approximately 100 m.
The paleo-modelling community has focused on the last glacial maximum
(LGM, ∼ 20 kyr BP), leaving the longer period when the ice sheets evolved
to their LGM configurations largely unexplored.
In this thesis we study the mutual interaction between the time-mean atmospheric circulation and the evolution of the Northern Hemisphere ice sheets
over the build-up phase of the last glacial cycle. Experiments are conducted
with coupled atmosphere–ice-sheet models and a circulation model forced
by geologically consistent reconstructions of the ice-sheet topography at key
stages of the glacial cycle.
The main findings from these studies are that the ice evolution in North
America may have been controlled by circulation anomalies induced by the
background topography in conjunction with the ice sheets themselves. A geologically consistent pre-LGM ice sheet could only be obtained when including
the North American Cordillera. However, the ice sheets’ influence on the local climate conditions is also found to be paramount for this configuration.
We further suggest that the incipient ice sheets may have had a limited influence on the large-scale winter circulation as a result of their location relative
the westerly mean flow. The LGM Laurentide Ice Sheet (LIS) was, however,
different because of its continent-wide extent, and it may therefore have had
a large influence on the planetary-scale circulation, especially in the Atlantic
sector. We find that the planetary waves forced by the LIS were considerably
larger than at earlier times, and, as a result of a more frequent planetary wave
reflection over the Atlantic Ocean basin, an altered stationary wave field and a
zonalised winter jet.
Sammanfattning
Den senaste glacialcykeln (c. 115 – 12 kyr BP) var den senaste i en rad återkommande nedisningar av kontinenterna utanför polarområdena. De två största isarna utvecklades i Eurasien och i Nordamerika, vilka, under deras maximala utbredning, var stora som bergsmassiv och tillsammans svarade för en
sänkning av den globala havsnivån på ungefär 100 m. Modelleringsstudier av
cirkulationen under den senaste glacialcykeln har fokuserat på det senaste glacialmaximat (LGM, ∼ 20 kyr BP), vilket har lämnat den långa uppbyggnadsfasen av den senaste istiden relativt outforskad.
I detta avhandlingsarbete har växelverkan mellan den klimatologiska atmosfärscirkulationen och utvecklingen av inlandsisarna på norra halvklotet
studerats. Experiment har genomförts med kopplade is–atmosfärsmodeller, och
en atmosfärscirkulationsmodell driven av isrekonstruktioner förenliga med geologisk data under ett antal viktiga skeden under den senaste glacialcykeln.
Huvudslutsatserna från dessa studier är att isutvecklingen i Nordamerika
var styrd av cirkulationsanomalier inducerade både av bakgrundstopografin
och av inlandsisarna själva. Det visade sig att en iskonfiguration konsistent
med geologisk data enbart kunde erhållas när effekten av den Nordamerikanska Cordilleran inkluderas i beräkningen. Viktigt är dock att effekten av isen
själv är av största vikt för att sätta upp cirkulationsmönstren som ger upphov
till denna iskonfiguration. Vidare föreslår vi att de relativt sett mindre isarna som existerade innan LGM hade ett tämligen begränsat inflytande på den
storskaliga cirkulationen; detta på grund av deras läge relativt det västliga medelflödet. Emellertid, den massiva Laurentide-isen (LIS) under LGM kan ha
haft ett stort inflytande på den storskaliga cirkulationen, särskilt över Atlanten. Vi finner att de stationära planetära vågorna drivna av LIS var väsentligt
större än under tidigare skeden av glacialcykeln. Som en följd av detta ökade
frekvensen av planetärvågreflektion över oceanbassängen, vilket i sin tur förändrade det klimatologiska vågmönstret och genererade en zonalisering av den
Atlantiska jetströmmen under vintermånaderna.
The ice was here,
the ice was there,
the ice was all around:
it cracked and growled,
and roared and howled,
like noises in a swound!
The Rime of the Ancient Mariner,
Samuel Taylor Coleridge, 1798
List of Papers
The following papers, referred to in the text by their Roman numerals, are
included in this thesis:
PAPER I: Liakka, J., J. Nilsson and M. Löfverström (2011): Interactions
between stationary waves and ice sheets: linear versus nonlinear atmospheric response, Climate Dynamics, 38, 1249–1262,
DOI:10.1007/s00382-011-1004-6
PAPER II: Löfverström, M., J. Liakka and J. Kleman (2014): The North
American Cordillera – an impediment to growing the Laurentide Ice Sheet, to be submitted to Journal of Climate
PAPER III: Löfverström, M., R. Caballero, J. Nilsson and J. Kleman, (2014):
Evolution of the large-scale atmospheric circulation in response
to changing ice sheets over the last glacial cycle, Climate of the
Past, 10, 1453–1471, DOI: 10.5194/cp-10-1453-2014
PAPER IV: Löfverström, M., R. Caballero and J. Nilsson (2014): Nonlinear stationary wave reflection as a mechanism for zonalising the
LGM Atlantic winter jet, to be submitted to Geophysical Research Letters
Reprints were made with permission from the publishers.
Contents
Abstract
iii
Sammanfattning
v
List of Papers
vii
1
Introduction
11
2
Glacial climates
2.1 Evidence of past glaciations . . . . . . . . . . . . . . . . . .
2.2 The last glacial cycle . . . . . . . . . . . . . . . . . . . . . .
15
15
16
3
The large-scale atmospheric circulation
3.1 The Northern Hemisphere winter circulation . . . . . . . . .
3.2 The Northern Hemisphere summer circulation . . . . . . . .
3.3 Coupling between the atmospheric circulation and the ice sheet
evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Simulations of the atmospheric circulation at the LGM . . . .
19
19
21
4
5
22
25
Some theoretical considerations on the ice sheet-planetary wave
interaction
4.1 Planetary waves . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Mechanical forcing . . . . . . . . . . . . . . . . . . . . . . .
4.3 Thermal forcing . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Wave-activity flux and critical-layer reflection . . . . . . . . .
29
29
31
33
34
Summary of papers
5.1 Paper I . . . . .
5.2 Paper II . . . .
5.3 Paper III . . . .
5.4 Paper IV . . . .
37
37
38
39
39
Acknowledgements
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xli
References
xliii
Appendix: corrections
xlix
1. Introduction
Climate is defined as the time-mean state of the complex interactions between
the planetary boundary conditions and the chaotic motion in the atmosphere
and oceans. Simpler put, climate is the expected weather and circulation state
that results from a given set of boundary conditions; e.g. solar radiation, atmospheric composition, surface topography, thermal properties of land and
ocean, albedo effects, etc. During the most recent decades the anthropogenic
influence on the climate system has been the subject of intense research; rightly
so, as this will determine the living conditions for generations to come. However, much can be learned by studying earlier periods of the Earth’s history.
Deep time paleo-records have revealed evidence of rather remarkable climates
in the past, bracketed by “Snowball Earth” (c. 750 mya, Hoffman et al., 1998;
Kirschvink, 1992) as the cold extreme, and the early Eocene hyperthermals
(c. 50 mya, Pearson et al., 2007) when the temperatures were so high that
Crocodilian reptiles lived in the Arctic Ocean (Tarduno et al., 1998).
The Earth is currently in a relatively cold geological period known as Quaternary (initiated c. 2.6 mya, Gibbard and Kolfschoten, 2004), which is characterized by alternating cool and temperate stages – glacials and interglacials – in
which massive ice sheets expand and retreat over the subpolar continents. The
most successful explanation of the glacial-interglacial cycles is the astronomical theory proposed by Milankovitch (summarized by Loutre, 2003), which
states that the solar insolation is modulated by changes of the Earth’s orbital
parameters – eccentricity, obliquity, and axial precession – over time scales of
approximately 100,000, 41,000, and 23,000 years. Periods with low summer
insolation are cold and therefore support the expansion of ice sheets, and, similarly, in warmer periods when the summer insolation is higher, the ice sheets
stagnate or retreat.
Figure 1.1 shows a reconstruction of the ratio between heavy and light
oxygen isotopes in ocean water, using the measure δ 18 O over the last 1.8 myrs
(Lisiecki and Raymo, 2005). Temporal variations in δ 18 O mirror changes in
the global ice volume as heavy oxygen isotopes are less likely to evaporate
and the concentration therefore increases slightly in ocean water when lighter
isotopes are sequestered in ice sheets. Due to this relationship, the measure
δ 18 O can also been interpreted in terms of global temperature variations. Since
oxygen isotope ratios in the marine sediment record are extensively used to
11
PA1003
LISIECKI AND RAYMO: PLIOCENE-PLEISTOCENE BENTHIC STACK
PA1003
Figure 1.1: A record of the ratio of heavy and light oxygen isotopes (δ 18 O)
in ocean water constructed from 57 globally distributed ocean-sediment cores
dating back 1.8 myr. The horizontal axis shows time in thousands of years and
the numbers denote time periods with similar characteristics, commonly referred
to as Marine Isotope Stages (MIS). The last glacial inception is here at MIS 5 and
the last glacial maximum (LGM) is MIS 2. The figure is modified from Lisiecki
and Raymo (2005) and reused with permission from the leading author and the
American Geophysical Union.
determine changes of past climate conditions, one often refer to periods with
similar characteristics as Marine Isotope Stages (MIS), with a number attached
at the end to specify its position in the timeline (seen in Fig. 1.1). Proxy-data
records of this type show fluctuations with similar time scales as the orbital
parameters and thus give credence
to the astronomical theory. They also reveal
Figure 4. The LR04 benthic d18O stack constructed by the graphic correlation of 57 globally distributed
O records.glacials
The stack iswere
plotted using
the LR04 duration
age model described
in section
and with
new
that thebenthic
mostd18recent
of longer
(c. 100
kyr)5and
developed
MIS labels for the early Pliocene (section 6.2). Note that the scale of the vertical axis changes across
larger ice
sheets than the earlier glacials (c. 41 kyr long). The reasons for this
panels.
change remain unknown.
concentration of data used in the LR04 stack is at least twice 0.15% after 0.6 Ma), and we are currently developing a
Asymmetries in the Earth’s boundary, primarily the large-scale mountain
as high as in any previous stack or individual d18O record detailed description of regional d18O variability.
spanning and
that interval.
The stack’s
resolution is comparable
ranges
thermal
differences
between land and ocean, affect climate by exto previous stacks but is less than half that of the highest5. Age Model
resolution
records.
citing stationary Rossby waves, manifested
as planetary-scale meanders in the
[18] Because the LR04 stack is constructed by graphic
[17] The LR04 stack is simply the average of the aligned
18
time-mean
atmospheric
zonal
flow
(see the
review
by Heldfeatures
et al.,are2002).
correlation,
its stratigraphic
essentiallyThe
indeWe do not adjust
the mean
or variance
benthic d O records.
of the records, except to make species offset corrections. We pendent of any timescale. Below we describe the contopographic
forcing
of
the
Himalayan
and
Cordilleran
ranges,
in
conjunction
choose not to adjust the isotope curves based on their struction of an age model which takes advantage of the
modern bottom water temperatures because the temperature high signal-to-noise ratio of the stack and analysis of the
with
thermal forcing over the western ocean basins (Kaspi and Schneider,
differences between sites may have changed dramatically sedimentation rates at 57 sites. However, almost any age
couldair
be applied
the LR04
stack. This flexibility
over the induces
last 5.3 Myr.northwesterly
We also do not weight
the records
2011),
flow
of drymodel
Arctic
over tothe
northeastern
conbased on their spatial distribution. The majority of records allows the stack to be adapted to alternate models of d18O
response
to improvements in age
are from the
Ocean,
and the number
of sites in the over
tinents
in Atlantic
winter.
Further
downstream,
theor northwestern
sideestimates.
of the con[19] We construct the LR04 age model by aligning our
stack varies with time, changing the relative weighting of
tinents,
the winters
are
generally
milder
and wetter
at while
the
to athese
simple regions
model of iceare
volume
d18O stackas
different regions.
However, we
observe
that regional
differ- benthic
18
ences in benthic d O are typically less than 0.3% (less than considering the average (stacked) sedimentation rate of
end of the midlatitude stormtracks where the flow is predominantly southwestof 17
erly (Seager et al., 2002). The average6 winter
temperatures can therefore differ
◦
by several 10 C between the eastern and western side of the continents as a
result of forced asymmetries in the large-scale atmospheric circulation.
In this thesis we investigate the climate conditions and large-scale atmospheric circulation patterns in the most recent cold period (numbers 5 to 2 in
Fig. 1.1), generally referred to as the “last glacial cycle” (c. 115 – 12 kyr BP).
Although considerably milder and less extreme than Snowball Earth, continental12
scale ice sheets nonetheless developed in Eurasia and North America that
had a large influence on the atmospheric and oceanic circulation. The paleomodelling community has focused on the climate at the last glacial maximum (LGM); partly because it provides the largest changes of the planetary
boundary condition over the last glacial cycle, and also because the proxy-data
archives are richer from this period compared to earlier glacial stages. The
longer period when the climate system transitioned from the previous interglacial to the LGM conditions remains largely unexplored and many questions
regarding the last glacial cycle are therefore still open or only partially answered. Some of the more fundamental questions are:
- Why was the Northern Hemisphere glaciation zonally asymmetric and
centered around the Atlantic Ocean?
- What caused the Laurentide Ice Sheet to be much larger than the Eurasian
Ice Sheet at the LGM (Kleman et al., 2013)? Is there a remote influence
mediated by the large-scale circulation or is it simply a consequence of
the physiography of the continents?
- Why was the ice invasion in the western Laurentide area (prairies and
interior plains) slow and late compared to the rapid and repeated expansion of the Quebec Dome in the east?
- Why did Alaska (Clague, 1989) and northeastern Siberia (Svendsen et al.,
2004) remain largely ice-free over the last glacial cycle, whereas ice expanded to 40◦ N over the eastern North American continent?
- To what extent did the evolution of the ice sheets influence the atmospheric circulation and induce changing mass-balance patterns? Or, put
more simply: did the ice sheets create their own growing conditions?
The work presented here explores these questions using a numerical-modelling
approach with special focus on the coupling between the large-scale atmospheric circulation and the evolving ice sheets. Chapters 2-4 provide an introduction to the topics covered in Papers I to IV and chapter 5 presents a
summary of the main findings of the papers.
13
14
2. Glacial climates
2.1
Evidence of past glaciations
The δ 18 O-records in ocean sediment cores (Fig. 1.1) provide compelling evidence of cyclically recurring ice ages in past times. Although these proxy-data
archives reveal changes in the global ice volume, they say nothing about the ice
sheets’ spatial outlines over the continents. A complicating factor is that physical signs in nature are eroded over time and also obliterated by the expansion
of ice sheets in younger glacial periods. Consequently, the geological and geomorphological evidence of the last glacial cycle is more substantial than that
from earlier cold periods. It has been established that massive ice sheets covered large parts of northern Eurasia and North America (Kleman et al., 2013,
2010; Svendsen et al., 2004) between approximately 115 and 12 kyr BP, with
smaller ice sheets also in Patagonia in the Southern Hemisphere (Lamy et al.,
2004). Their enormous weight caused the Earth’s crust to deform and subside
somewhat into the mantle. When the ice sheets started to retreat the isostatic
rebound of the bedrock was initiated; a process so slow that it is still ongoing
and can be measured as variations in the Earth’s shape and gravitational field
(Peltier, 2004).
An ice sheet is a dynamic and highly viscous fluid that slowly creeps over
the land surface, primarily as a result of gravitational deformation driven from
the accumulation zones in the interior (i.e. where the mass balance is positive and snow is incorporated into the main body of ice). Regions that were
glaciated therefore reveal a large variety of signs of the expansion and retreat
of the ice sheets. Expanding ice sheets abrade (erode by friction) the landscape and leave what is known as erosional landforms. Examples are striations
(scratches and grooves) in the bedrock caused by rocks and boulders carried
underneath the ice sheets and smooth U-shaped valleys, such as the Norwegian
fjords, where the abrasion rounded out pre-existing topographic features.
Debris carried by the internal ice flow is typically deposited at the outermost ice margin, and remains of this type are therefore referred to as depositional landforms. A few examples are terminal moraines (fields of soil and
rock), eskers that are stratified ridges of silt, sand and rock with the heavier
material at the bottom, and till lineation (aligned sediments) left when the ice
15
sheets retreated.
The massive volumes of water in the ice sheets also gave rise to proglacial
lakes that were formed either in crevasses in the bedrock or as dammed lakes
from extensive moraine depositions. The largest (by volume), and still remaining lake region, formed by melting ice sheets is the North American Great
Lakes area (Larson and Schaetzl, 2001).
2.2
The last glacial cycle
The last glacial cycle was initiated about 115 kyr BP in a time period with
a relatively low summer insolation in the Northern Hemisphere (Berger and
Loutre, 2004), see Fig. 2.1. The glacial inception occurred in highland regions
in the Central Canadian Arctic, Quebec, Scandinavia, and along the coast of
the Barents-Kara Seas (Kleman et al., 2013, 2002; Svendsen et al., 2004). The
embryonic ice sheets expanded down the mountain slopes and over the adjacent lowland areas where they coalesced and formed larger ice masses with
shorter ablation (melting) zones. The temperature at the top of the ice sheets
is generally below freezing and the ablation is therefore restricted to marginal
zones at lower elevation. Snow accumulation, on the other hand, typically occurs over the whole ice surface but with higher concentrations in regions with
forced precipitation (Roe, 2005; Sanberg and Oerlemans, 1983).
Reconstructions have revealed that the global ice volume increased in a
stepwise fashion (e.g. Kleman et al., 2013; Peltier and Fairbanks, 2006; Stokes
et al., 2012) with growth burst in colder periods – stadials – centered around approximately 110, 70 and 25 kyr BP followed by warmer periods – interstadials –
with more stagnant ice sheets, see Fig. 2.1. Even though the evolution of
the global ice volume is fairly well established from the proxy-data records,
less is known about the ice sheets’ spatial developments over the continents.
To establish this spatio-temporal evolution one has to rely on geological evidence, such as listed above in Sect. 2.1, which relative age can be determined
from geo-chemical dating techniques, e.g. radiocarbon dating (14 C). A complicating factor is that growing ice sheets override and erase signs of previous glacial stages when advancing over the landscape. This means that more
is known about the ice sheets’ maximum spatial extent and their retreat than
about glacial stages prior to the LGM, as signs from these periods are more
elusive. Nevertheless, the geological evidence points to a rather different evolution of the Eurasian and North American ice sheets (Kleman et al., 2013,
2010; Svendsen et al., 2004).
The incipient Eurasian Ice Sheet is believed to have had a substantial longitudinal extension along the Arctic coast, from Scandinavia in the west to
central Siberia in the east (Fig. 2.2a). As time progressed the ice volume in16
Figure 2.1: The upper panel shows a reconstruction of the Northern Hemisphere
ice volume (sea-level equivalent in meters) over the last glacial cycle. The dashed
line is the total ice volume and the solid and dotted lines the North American
and Eurasian ice sheets respectively. The lower panel shows the variability of
the daily-mean top-of-the-atmosphere insolation at 60◦ N at the northern summer
solstice over the glacial cycle. The figure is taken from paper III with permission
from Copernicus Publications.
creased while the whole footprint of the ice sheet migrated southwestwards. It
is believed that the ice volume was at its maximum about 60 kyr BP (MIS 4,
see Fig. 2.1 and 2.2b, also Kleman et al., 2013), which is approximately halfway into the glacial cycle. At the LGM (approximately 20 kyr BP, Fig. 2.2c)
the center of mass was over Scandinavia and the ice sheet extended as far
southwest as to the British Isles (Bradwell et al., 2008; Kleman et al., 2013;
Svendsen et al., 2004). This progressive southwestward advancement implies
that the spatio-temporal evolution is fairly well documented, especially in the
east where the ice sheet retreated over most of the glacial cycle.
The North American glaciation is believed to have had a different life cycle. Separate ice sheets were initially established in the Canadian archipelago
and in Quebec (Kleman et al., 2010) that successively coalesced and formed
a massive double-domed structure in the northeastern corner of the continent
(Fig. 2.2a), comparable in size to the North American Cordillera. In time, the
ice sheet expanded but the center of mass remained in the Quebec Dome on
the northeastern side of the continent. Interestingly, the interior of the continent (the western prairies) remained largely ice-free over almost the entire
glacial cycle and it is believed that the western ice invasion occurred during
the final growth burst when the LGM Laurentide Ice Sheet (Fig. 2.2c) evolved.
17
inof
the
Northern
H
of
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in the Northern Hemisphere with the exception
the
to2 (Fig.
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5.3
Evolution
ofofice
inTibetan
in the
Hemisphere
with
the exception
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in Eurasia,
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growth
in North
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app
stage
2 in
(Fig.
7c)
t
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and size
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and elevation
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5.3
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6Eurasian
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andbeNo
Eurasian
and
sheets
the
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A
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southwest.ice
The
NorthisAmerican
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the
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tween
the
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of
the
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ice
sheets.
The
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volume
Forcing
tion leading into stage 2 is far more dramatic.6.1
Here,
the twoof
Eurasian
curve
(Fig.
3b)
curve
3b) shows
ice have
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until
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Northern-Hemisphere
ice-sheet
topography
raphy shown for reference.
North
h
North
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four times the Eurasian amount
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strong America
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5.3 Evolution
of mass
North Am
during four key periods of the last glacial cycle. The reconstructions are gensector,
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and
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6
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behaviors of the two ice sheets. The
ice
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6.1
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with permission from the leading author and Copernicus
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in
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larger
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Fig. 6. Terrain topography and modeled ice sheetFig.
surface
topogramember
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member
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typically
the
LGM
and
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1989).increases to 2, Charbit
phy for MIS 5blargely
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(b), and MIS
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(d) Holocene
this number
and byHowever,
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Charbit stage
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Langen and Vinther, 2008).
raphy shown for reference.
raphyThe
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for reference.
North
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climatic fi
mum occurred around 20 kyr BP at the end of the6 glacial
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www.clim-past.net/9/2365/2013/
www.clim-past.net/9/2365/2013/
Clim. Past, 9, 2365–2378,
2013
measured
what is referred to as the
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Mix, 2002; Peltier and Fairbanks, 2006), of which
thefields
Northern-Hemisphere
sector,
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measured or modeled climate parameters representing endFig. 6.
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topography
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surface100
topograice
sheets
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forsheet
about
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phy for MIS 5b (a), MIS 4 (b), and MIS 2 (c). (d) Holocene topogCharbit
etEurasian
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and Vinther,
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strong zonal misfits (too much ice in
the Alaska–E Siberia
www.clim-past.net/9/2365/2013/
1
reconstructions suggest that they contained approximately
80 %
20 %southern
of Scandinavia and
sector, and too little
ice and
in Quebec,
the Northern Hemisphere LGM ice volume, respectively.
www.clim-past.net/9/2365/2013/
1 https://pmip3.lsce.ipsl.fr/
18
Clim. Past, 9, 2365–2378, 2013
3. The large-scale atmospheric
circulation
To understand the spatial and temporal evolution of the Northern Hemisphere
ice sheets over the last glacial cycle one has to study changes in the largescale circulation of the atmosphere and ocean when the planetary boundary
conditions transitioned into the glacial configuration. Many of the arguments
made here are general and can be applied to both hemispheres. The discussion
is, however, restricted to the Northern Hemisphere, as this is the focus of the
papers constituting this thesis.
The zonally symmetric component of the tropospheric general circulation
is to lowest order a balance between the meridional pressure-gradient force, resulting from differential heating between low and high latitudes, and the Coriolis force due to the rotation of the planet. If the lower tropospheric boundary
was longitudinally uniform, the time-mean circulation would be zonally symmetric with two westerly jetstreams in the upper troposphere is each hemisphere; the subtropical jet at the northern terminus of the Hadley cell and the
midlatitude jet driven by momentum flux convergence induced by baroclinic
eddies. However, the lower boundary condition is not uniform and the atmospheric flows are influenced by large-scale topography and diabatic heating
that force asymmetries in the circulation known as stationary waves. The following two sections describe some characteristic features of the large-scale
circulation in present-day winter and summer seasons.
3.1
The Northern Hemisphere winter circulation
The meridional temperature and pressure gradients are large in boreal winter (DJF, December-February) as the high latitudes cool down substantially in
the long-lasting polar night. This implies that the zonal mean flow is strong
(as seen in Fig. 3.1b and c, climatologies derived from the ERA-Interim reanalysis, Dee et al., 2011) and the mechanical forcing of planetary waves is
important due to the kinematic boundary condition yielding a topographically
induced vertical velocity, w:
w = u · ∇h,
(3.1)
19
Figure 3.1: A present-day winter (DJF) climatology derived from the ERAInterim re-analysis (Dee et al., 2011). The upper left panel (a) shows the 300 hPa
eddy streamfunction [m2 s−1 ] (zonal mean removed), and the upper right panel
(b) the zonal wind speed at the same level. The shading in panel (c) represents
the precipitation [mm day−1 ] overlaid by the 850 hPa wind arrows. Panel (d)
shows the zonally asymmetric component of the 850 hPa temperature field [◦ C].
The solid black lines denote the 1000 m contour of the Northern Hemisphere
topography.
where u = (u, v, 0) is the near-surface horizontal wind and ∇h = (∂x h, ∂y h, 0)
is the topographic slope. In the linear case (a more thorough discussion is
provided in chapter 4), the mechanical stationary wave forcing is reduced to
[ū]∂x h, where [ū] is the zonal- and time-mean wind speed, and the flow impinging on a mountain is forced to ascend over the obstruction. This results in
a longitudinally aligned anticyclone-cyclone dipole over the mountain range
and a large-scale meander in the downwind flow field resulting from conservation of potential vorticity (Ertel, 1942; Rossby, 1940). The simplified linear model works reasonably well for describing the flow-interaction with the
North American Cordillera (see Fig. 3.1a), as this region is meridionally elongated and the flow is therefore forced to ascend over the topography. The
Himalayas, on the other hand, are both considerably higher and more meridionally confined and a larger part of the flow passes around the sides of the
mountain range. This gives rise to a different wave response in the vicinity of
the topography (often attributed to nonlinear eddy advection, Cook and Held,
1992; Ringler and Cook, 1997, 1999), and the stationary planetary waves are
predominantly located on the leeward side of the mountain range (Fig. 3.1a).
The total stationary planetary wave field is, however, more complicated and
consists of both mechanically and diabatically forced waves, from extratropical as well as tropical sources (Sardeshmukh and Hoskins, 1988; Ting and
Held, 1990), that influence each other in a non-trivial way (e.g. Held et al.,
2002; Nigam et al., 1986, 1988).
20
There are also other important large-scale circulation features during the
Northern Hemisphere winter. The Pacific sector presents a single well-defined
jet in the upper troposphere with a strong core and a largely zonally oriented
axis (Figs. 3.1b and c). In the Atlantic sector there is instead a conspicuous
double jet structure with a clear separation between the subtropical and eddydriven jets, the latter being comparatively weak and having a meridionally
tilted axis (suggested to be a result of topographically forced stationary planetary waves by the Cordillera, Brayshaw et al., 2009). The advection of cold
air from the continental interior over the more temperate oceans gives rise to
strong baroclinicity off the east coasts of Asia and North America and, therefore, well defined midlatitude stormtracks (Chang et al., 2002; Hoskins and
Valdes, 1990; Lee, 2000), largely guided by the jetstreams (the stormtracks are
recognized from the high precipitation over the oceans in Fig. 3.1c). Note that
the Cordillera acts as a shield for the Pacific cyclones and forces a great amount
of precipitation on the western slopes where the air ascends (Roe, 2005). The
asymmetries in the large-scale flow patterns also give rise to zonal temperature
anomalies (on the order of 10◦ C, see Fig. 3.1d) between the eastern and western sides of the continents and similarly also over the ocean basins (Kaspi and
Schneider, 2011; Seager et al., 2002).
The evolution of the large-scale winter circulation in response to changing
ice sheets over the last glacial cycle is discussed in Paper III. Paper IV investigates how the LGM Laurentide Ice Sheet may have influenced the downwind
planetary-scale circulation over the Atlantic Ocean and made the eddy-driven
jet axis more zonally oriented.
3.2
The Northern Hemisphere summer circulation
The weak westerly mean flow (Fig. 3.2b) during the Northern Hemisphere
summer (JJA, June-August) implies that the mechanical forcing of stationary
waves is limited. The asymmetric circulation is instead to a larger extent driven
by diabatic heating (Held and Ting, 1990; Ting, 1994; White, 1982).
Land surfaces are generally heated more than the surrounding oceans due
to their high thermal inertia (Fig. 3.2d), and the surface pressure is therefore
lower over the continents as the warm air rises. The thermally induced ascending flow branch yields a horizontally divergent flow (anticyclonic circulation) in the upper troposphere (Ting, 1994; White, 1982) (Fig. 3.2a), and the
stationary eddy field thus has different polarity in the upper and lower troposphere. Note that the pressure configuration is the opposite over the cooler
oceans where the flow instead is horizontally convergent (divergent) and thus
cyclonic (anticyclonic) in the upper (lower) troposphere. The weak zonal mean
21
Figure 3.2: Same as Fig. 3.1 but for the summer season (JJA).
flow also implies a fairly limited horizontal propagation of the stationary eddies as the wave energy is dissipated close to the source region.
Figure 3.2c shows that the prevailing low-level winds over the North American continent are southerly and advect warm and moist air from the Gulf of
Mexico over the continental interior (monsoon circulation). This flow pattern
is known as the Great Plains low-level jet and is known to bring heavy rainfall
as far north as the Great Lakes (Higgins et al., 1997; Wu and Raman, 1998).
It is conceivable that the summer monsoon may have been an important moisture supply when the North American ice sheet developed over the last glacial
cycle. As noted earlier, the westerly winter flow loses most of its humidity on
the western slopes of the Cordillera when ascending over the mountain range
(Roe, 2005), and the air on the leeward side is therefore comparatively dry.
The summer monsoon, on the other hand, brings precipitation to latitudes in
the continental interior that were known to be ice-covered at the LGM. The
situation is, however, complicated as the radiative heating of the continental
surface is to a large extent the driver of the monsoon circulation and at the
same time a limiting factor for the expansion of the ice sheets. In Papers I
and II we investigate how the summer circulation may have influenced the
spatial evolution of the North American ice sheet and limited the glaciation
in the continental interior over the larger part of the last glacial cycle. Paper
III investigates how the developing ice sheets may have changed the summer
circulation on a global scale.
3.3
Coupling between the atmospheric circulation and the
ice sheet evolution
It is still not fully understood why the ice sheets developed so differently on
the Eurasian and North American continents. The inception phase and the localization of the early ice sheets are, however, fairly straightforward to explain
from a lowest-order atmospheric-circulation perspective. We noted earlier that
22
the North American mountains induce a northwesterly flow over the continent in winter, and thus advection of Arctic air over eastern Canada where
the glacial inception is believed to have taken place (Fig. 2.2a, 3.1c and d).
Similarly, the glacial inception in Eurasia is believed to have occurred in the
high-elevation regions in Scandinavia and in the northwestern parts of Russia;
regions that are not as cold as eastern Canada but instead located at the end of
the Atlantic stormtrack and therefore receive precipitation from the synoptic
systems. If the summer temperatures are cool, due to anomalously low insolation, the conditions are favorable to establish perennial snow covers in these
regions that eventually form ice sheets. It is important to stress that the time
scale involved in this process is on the order of thousands of years.
According to the geologically constrained ice sheet reconstruction by Kleman et al. (2013), the ice volume on the two continents evolved in concert from
the glacial inception through the first interstadial (115–80 kyr BP, see Fig. 2.1).
In the second stadial (approximately 80–60 kyr BP), however, the North American ice volume increased much faster and at the end of the growth period it
was close to twice as large as the Eurasian Ice Sheet. The discrepancy is believed to have increased even more in the second half of the glacial cycle, and,
at the LGM, it is estimated to have been as much as 80 % versus 20 % of the
total ice volume in the Northern Hemisphere (not accounting for Greenland or
the sea-ice cover). This large imbalance suggests that there may have been a
remote influence between the two ice sheets mediated by the large-scale circulation (Beghin et al., 2014; Bonelli et al., 2009; Lindeman and Oerlemans,
1987; Roe and Lindzen, 2001).
We noted earlier that planetary wave propagation is limited in the summer
season, due to the weak westerly mean-flow, and forced atmospheric circulation anomalies are therefore largely confined to their source region. In winter,
on the other hand, the flow is generally stronger and planetary waves propagate and influence the climate far away. This suggests that a remote coupling
between the evolving ice sheets may have been most prevalent in the winter
season. However, as discussed in Paper III, the Eurasian Ice Sheet was located
at fairly high latitudes (Fig. 2.2) and with height contours largely parallel to the
westerly mean flow. The mechanical forcing of planetary waves may therefore
have been limited as this requires a westerly flow normal to the topography,
cf. Eq. 3.1. The incipient North American ice sheet had a larger equatorward
extension (Fig. 2.2) but may have suffered a similar problem due to the northwesterly flow over the continent (Fig. 3.1c). It is therefore possible that both
ice sheets had a limited ability to mechanically force planetary waves; at least
so long as the interior of the North American continent remained ice-free. This
is believed to have been the case until approximately 30 kyr BP, or close to the
culmination of the last glacial cycle (Kleman et al., 2013). Nevertheless, me23
chanical forcing of planetary waves is not the only way the ice sheets can
influence each other. Advection of cold air from the North American ice sheet
may have yielded an increased meridional extension of the sea-ice cover over
the northwestern Atlantic Ocean. This further implies a reduced moisture supply for the baroclinic systems and possibly changed properties of the North
Atlantic stormtrack. We discuss this topic at length in Paper III and we also
come back to the atmospheric circulation under LGM conditions later in this
chapter.
The large imbalance in the LGM ice volume may in fact also have been
a result of the different physiographies of the continents. The Eurasian Ice
Sheet supposedly started its life on the northwestern side of the continent and,
though it was fed by precipitation by the westerly flow (Roe, 2005; Sanberg
and Oerlemans, 1983), the Atlantic Ocean acted as a natural boundary that inhibited westward expansion. At the same time, the southward expansion may
have been limited by thermal constraints over the Eurasian continent in summer. The North American ice sheet, on the other hand, started its life in the
northeastern corner of the continent and expanded westwards over thousands
of kilometers before encountering any physical obstacles that inhibited further
progress. However, to understand the ice sheets “reluctance” to expand over
the interior of the North American continent over the larger part of the glacial
cycle (Fig. 2.2), one has to understand the atmospheric circulation and how it
couples to the evolving ice sheet. Studies have shown that the spatial evolution
of a continental-scale ice sheet can be strongly influenced by self-induced mechanically and thermally forced stationary waves (Liakka, 2012; Liakka et al.,
2011; Roe and Lindzen, 2001). One of the limiting factors in these model studies is that they used simplified flat continents that omit the importance of the
local background topography. We noted earlier that the winter precipitation is
substantial on the windward side of the North American Cordillera and consequently much lower over the continental interior (Fig. 3.1). It is therefore
possible that the winter season helped maintain the ice sheet but played a limited role for the ice growth, as this requires accumulation of snow. The season
of interests is therefore the summer because of the monsoon circulation that
brings moist air from the Gulf of Mexico over the continent (Fig. 3.2). It is
therefore possible that both the Eurasian and Laurentide ice sheets were built
by precipitation originating from the Atlantic Ocean (Oerlemans and van der
Veen, 1984). The thermally induced monsoon circulation also naturally limits
the ice expansion over the continental interior as this region needs to be heated
by the sun to drive the monsoon circulation in the first place. We discuss the
coupling between the planetary-scale atmospheric circulation and the evolution of the Laurentide Ice Sheet in Papers I and II.
24
3.4
Simulations of the atmospheric circulation at the LGM
One of the difficulties when studying past climates is that reliable proxy-data
records are sparse and often geographically confined as they are for the most
part based on point measurements in ice and sediment cores, tree-rings, etc.
Synthesis maps of the LGM SSTs (sea-surface temperatures) (e.g. CLIMAP,
1981; MARGO, 2009, and QUEEN1 ) and sea-ice cover (De Vernal et al., 2006,
2005) have been constructed and can be used to evaluate the climates produced by experiments with atmosphere and ocean general circulation models
(GCMs). The three generations of the Paleoclimate Modelling Intercomparison Project (PMIP 1, 2, and 3) are to date the most ambitious and comprehensive modelling enterprises of past climates ever undertaken. The idea is that
the participating modelling institutes simulate a particular time-slice in Earth’s
history (e.g. the LGM), using identical and strictly controlled forcing protocols (Braconnot et al., 2012, 2007). The simulated climates are then compared
with proxy-data and the model spread is thought to provide an indication of
the uncertainties in the obtained circulation features.
It turns out, however, that there are considerable model-to-model (Braconnot et al., 2007; Kageyama et al., 2013a; Li and Battisti, 2008; Otto-Bliesner
et al., 2009; Ullman et al., 2014) (see Fig. 3.3) and model–proxy-data discrepancies (Kageyama et al., 2006, 2013b; Otto-Bliesner et al., 2009). Nevertheless, the LGM is generally depicted as a cold climate state (typically 3-6◦ C
colder than the present in a global-and annual-mean sense, Braconnot et al.,
2012) with many circulation features substantially different from the present.
The large-scale atmospheric circulation in the North Atlantic sector in winter (DJF) shows a particular sensitivity to the generation of the models and the
forcing protocols. In PMIP 1 and 3, the models generally produced a meridionally tilted Atlantic jet (Kageyama et al., 2013a; Li and Battisti, 2008; Ullman
et al., 2014) similar to the present atmosphere (Brayshaw et al., 2009). Some
of the PMIP 2 models, on the other hand, showed larger stationary planetary
waves and a considerably more zonal and less variable Atlantic jet, see Fig. 3.3
(e.g. Kageyama et al., 2013a; Li and Battisti, 2008; Ullman et al., 2014). These
apparent discrepancies raise several important questions: Was the real Atlantic
winter jet tilted or zonal at the LGM? Why does only the PMIP 2 models generate a zonal jet axis, is this an artefact of the models or is it a result of the
forcing?
1 Quaternary
Environment of the Eurasian North,
http://queen.pangaea.de/
25
Figure 3.3: Three PMIP 2 LGM simulations with identical forcing protocols showing the 200 hPa (DJF) eddy streamfunction [m2 s−1 ] and zonal wind
[m s−1 ]. The models used are: CCSM3 (Community Climate System Model version 3) in (a, b), MIROC 3.2 (Model for Interdisciplinary Research on Climate
version 3.2) in (c, d), and IPSL-CM4 (Institut Pierre-Simon Laplace model version 4) in (e, f). The solid black lines denote the 1000 m contour of the Northern
Hemisphere topography and the outer edge of the ice sheets, respectively. Even
though the models agree reasonably well on the general structure of stationary
planetary waves and the zonalisation of the Atlantic jet, there are large discrepancies in the strength and spatial extension of the circulation features.
We have focused on the latter of the two questions in order to gain an
understanding of the winter jet dynamics under LGM conditions. Decomposition exercises have shown that most of the circulation changes obtained in
the Atlantic sector at the LGM result from the topographic influence of the
Laurentide Ice Sheet (LIS) (Broccoli and Manabe, 1987; Pausata et al., 2011).
Recently, Ullman et al. (2014) suggested that the height of the LIS is a key
factor for the orientation of the Atlantic jet axis. They conducted two experiments with the same model using a high (the ICE-5G reconstruction, Peltier,
2004, used in PMIP 2) and a low reconstruction of the LIS, all else being the
same. The results showed that the almost 4500 m high PMIP 2 LIS produced
a zonalised jet, whereas the jet axis with the lower LIS had a more meridional
tilt. It should be noted that the updated PMIP 3 LIS is only about 3500 m high,
which is close to a kilometer lower than in PMIP 2 reconstruction. However,
the mechanism or interaction that is responsible for zonalising the jetstream
when the LIS is high remains unknown. The fact that the ice-sheet topography
is an important source of planetary waves suggests that this may be a good
starting point for further investigations. In Paper IV we discuss how nonlinear
planetary wave reflection may help zonalising the jet axis, see also the theoretical discussion in chapter 4.
26
Finally, the orientation of the Atlantic jet is important as it acts as a guide
for the synoptic systems associated with the stormtrack that are the primary
sources of precipitation in western Eurasia. A zonal jet implies that the larger
part of the precipitation falls south of the ice sheet. In Paper III we discuss
how the orientation of the Atlantic jet axis may have changed in response to
the evolving ice-sheet topography over the build-up phase of the last glacial
cycle.
27
28
4. Some theoretical considerations on the ice sheet-planetary
wave interaction
The following sections present some simplified theoretical considerations on
the dynamic influence of topography and thermal forcing on the planetaryscale atmospheric flow. This discussion is for the most part general and can
be applied equally well to the present-day atmosphere and to a glaciated state
with a different topographic outline. Examples are given with connection to
the work presented in Papers I to IV.
4.1
Planetary waves
Planetary waves, or Rossby waves, are planetary-scale meanders in the atmospheric flow that exist due to the latitudinal variations of the Coriolis parameter
(Rossby et al., 1939). In a barotropic atmosphere (where the pressure and density gradients are parallel), each fluid column satisfies the relation for potential
vorticity conservation (Rossby, 1940):
D f +ζ
= 0,
(4.1)
Dt
H
where H is the fluid depth, D/Dt = (∂t + v · ∇) the material derivative, v =
(u, v, 0) the horizontal velocity vector, and ∇ = (∂x , ∂y , 0) the horizontal gradient operator. Further, f is the Coriolis parameter and ζ ≡ ∇2 ψ the relative
vorticity defined as the Laplacian of the geostrophic streamfunction, ψ. Alternatively we can define the relative vorticity from the curl of the horizontal velocity field ζ = k·(∇×v), which thus relates the wind field and the geostrophic
streamfunction as v = k × ∇ψ, where k = (0, 0, 1) is the vertical unit vector.
Equation 4.1 can be extended to a more general conservation law for a baroclinic atmosphere describing the potential-vorticity-conserving motion along
an isentropic surface (P = −g( f + ζθ )∂ p θ , Ertel, 1942).
However, all relevant dynamics needed for this part of the discussion are
captured by the barotropic Eq. 4.1. Linearizing around a zonal-mean quasi29
geostrophic westerly flow (u > 0) with constant depth H at a midlatitude β plane ( f = f0 + β y, β = ∂y f , u = [u] + u∗ , v = v∗ , where u∗ ∼ v∗ [u], |ζ ∗ | f0 , here [·] and ()∗ denote the zonal mean and zonal perturbation respectively),
the following relation can be derived:
∂
∂ ψ∗
∂
∇2 ψ ∗ + β
+ [u]
= 0.
∂t
∂x
∂x
(4.2)
Assuming wave solutions of the form ψ ∗ = Re(ψ0 ) exp [i(kx+ly−ωt)], where
k and l are the zonal and meridional wave numbers, respectively, and solving
for the frequency (ω) of the oscillation, we obtain the zonal phase speed (subscript x) from the dispersion relation as
ω/k = cx = [u] − β /K 2 ,
(4.3)
where K 2 = k2 + l 2 is the total wave number. Note that β /K 2 > 0 for all K 2 ;
the zonal phase speed relative the ground depends thus both on the wavelength
(inversely proportional to the total wave number) and the strength of the zonal
mean flow. Thus, for waves with
K 2 = β /[u] ≡ Ks2 ,
(4.4)
the zonal phase speed is equal to and opposite the westerly mean flow and
the waves become stationary relative the ground. Note that Eq. 4.3 shows
that planetary waves can only exist so long as the zonal-mean flow is westerly
([u] > 0).
Equation 4.2 describes the temporal evolution of free (unforced) planetary
waves since these waves have no spatially localized source. In this case the stationary component has no “preferred” location and the time-mean wave field
is therefore precisely zero. Expressed differently, the superposition of all free
waves over a significant amount of time will interfere destructively and cancel out. In the real atmosphere, however, there are many different sources of
stationary planetary waves such as the Himalayan and Cordilleran mountain
ranges and both external and internal large-scale diabatic heat sources from
the land-ocean temperature contrasts as well as latent heat release in the midlatitude stormtracks and in the tropics. In glacial climates the topographic and
diabatic influence of the massive ice sheets also act as sources of atmospheric
planetary waves. These forcing agents excite planetary waves of slightly different length scales, some slowly varying and propagating away from the source
region and others stationary with respect to the surface. The following sections
will discuss how these forcing agents excite stationary planetary waves.
30
4.2
Mechanical forcing
We can use a slightly modified version of Eq. 4.1 to describe the midlatitude
stationary planetary waves forced by topography. We now assume, following
Charney and Eliassen (1949), that the height of the lower boundary (hT ) is
varying, but always small compared to the total fluid depth (hT H), and, as
above, linearize around a time-independent quasi-geostrophic flow at a midlatitude β -plane with an additional weak linear damping parameter (r = τ −1 ),
Eq. 4.1 can then be extended as
∂
∂ ψ∗
f 0 ∂ hT
[u] + r ∇2 ψ ∗ + β
= − [u]
.
(4.5)
∂x
∂x
H
∂x
Note that the kinematic boundary condition (Eq. 3.1), i.e. the mechanically
forced vertical velocity is on the right hand side of this equation. Assuming that
the perturbation streamfunction and the topography are in the form (ψ ∗ , hT ) =
Re(ψ0 , h0 ) exp [i(kx + ly)] we obtain
ψ0 =
h0
f0
.
2
H K − Ks2 − iR
(4.6)
Here K = (k2 + l 2 ) is again the total wave number and Ks2 the stationary wave
number defined in Eq. 4.4. Note that the damping parameter (R = rK 2 /k[u]) is
necessary as it removes the singularity in the denominator when the total wave
number is equal to the stationary wave number (K = Ks ), and thus ensures
bounded solutions for all wave numbers.
Figure 4.1 shows the linear wave solution (Eq. 4.6) for interglacial (preindustrial) and LGM climates, respectively, compared with the (DJF) 500 hPa
eddy geopotential height field derived from simulations with a sophisticated
atmospheric general circulation model (GCM), the National Center for Atmospheric Research Community Atmospheric Model version 3 (NCAR CAM3),
(Collins et al., 2004, 2006), see Paper III. We use the zonal-mean wind averaged between 800 and 150 hPa from the GCM simulations: i.e. 18 m s−1
and 24 m s−1 for the interglacial and LGM, respectively, and the original settings presented by Charney and Eliassen (1949): f0 = f (45◦ N), H = 8 km, a
meridional wave number (l) with half-wavelength 35◦ in latitude, a damping
time-scale r−1 = 5 days, and the topographic profiles (hT ) at 45◦ N. The wave
solution from this highly simplified model is in remarkable agreement with
the GCM. Both models yield a dominant wave number 3 anomaly in the interglacial case and a wave number 2 anomaly, with greater amplitude, in the
LGM case. The lower panel (Fig. 4.1e) shows that the linear model resonates
for almost exactly the same wind speeds despite the topographic forcing, but
the LGM topography gives more weight to the resonant wave number. For
31
400
200
Interglacial
LGM
(a)
(b)
(c)
(d)
0
−200
−400
3 km
2 km
1 km
0
0
90 ◦ E
180 ◦
800
σ
600
90 ◦ W
0
0
0
5
180 ◦
90 ◦ W
0
(e)
400
200
90 ◦ E
5
10
4
2
3
15
[u]
20
1
25
30
Figure 4.1: The upper panels (a, b) show a comparison of the midtropospheric
eddy geopotential field [m] computed by the linear model (Eq. 4.6) in black,
and in red by a comprehensive atmospheric general circulation model (the National Center for Atmospheric Research Community Atmospheric Model version 3, NCAR CAM3, Collins et al., 2004, 2006). The settings are the same as in
Charney and Eliassen (1949) but we use the zonal wind speed from GCM simulations of the interglacial (pre-industrial) and LGM winter (DJF) climates, respectively. The middle panels (c, d) depict the corresponding topographic profiles
[m], and the lower panel (e) show the standard deviation of the wave response
(σ = [ψ02 ]1/2 ) as a function of the zonal wind speed [m s−1 ]. In this panel we
have used a weaker damping time scale of r−1 = 20 days for display purposes.
The figure is taken from Paper III with permission from Copernicus Publications.
a wind speed of 20 m s−1 the LGM topography yields amplitudes larger by
almost a factor of two than the pre-industrial correspondence.
Despite these encouraging results it is important to note that the linear
model has some rather apparent limitations and its predictive skill may in fact
be a fortuitous coincidence of the parameter choice (Held, 1983). Stationary waves in the real atmosphere propagate not only in the horizontal plane
but also upwards into the stratosphere (Charney and Drazin, 1961). They
also follow great-circle paths rather than latitude circles (Hoskins and Karoly,
1981), and refract into the tropics where they typically break and dissipate
their energy (Held et al., 2002). Moreover, studies have shown that thermal
forcing may be as important as topography for maintaining the midlatitude
32
stationary wave field (see e.g. Hoskins and Karoly, 1981; Sardeshmukh and
Hoskins, 1988; Smagorinsky, 1953; Ting and Held, 1990) and nonlinear flowinteractions (eddy advection by the eddy winds) can also yield large changes
in the stationary wave field (Cook and Held, 1992; Ringler and Cook, 1997;
Valdes and Hoskins, 1991). In Paper I we discuss how nonlinear interactions
may influence and change the stationary-wave field.
4.3
Thermal forcing
It was first noted by Smagorinsky (1953) that large-scale diabatic heat sources
may yield stationary circulation anomalies of the same order of magnitude as
the midlatitude mountain ranges. Although latent heat release in e.g. synoptic
systems is important for the planetary-scale circulation, we limit the discussion
to the temperature anomalies dynamically induced by topography as this is of
high relevance for this thesis work.
Following Cook and Held (1988), linearizing the time-independent thermodynamic equation (in spherical–height coordinates) around an inviscid westerly quasi-geostrophic zonal-mean flow ([u] > 0) yields
[u] ∂ θ ∗ v∗ ∂ [θ ]
∂ [θ ]
+
= −w∗
,
a cos φ ∂ λ
a ∂φ
∂z
(4.7)
where θ is the potential temperature, w the vertical velocity, v the meridional
velocity, a the radius of the Earth, and φ and λ denote latitude and longitude,
respectively. Assuming that the first term on the left-hand side (LHS) is of
leading order, and using Eq. 3.1 to replace the vertical velocity, we obtain
θ ∗ ∼ −h
∂ [θ ]
.
∂z
(4.8)
In a stably stratified atmosphere (∂z [θ ] > 0) there is thus a dynamically induced
negative temperature anomaly over a topographic obstacle. In the case of a
continental-scale ice sheet this further means that the high static stability in
the lower troposphere (due to the diabatic cooling of the surface) enhances the
temperature anomaly that extends away from the surface.
If we instead assume that the second term on the LHS is dominant, we
have
[u] ∂ h ∂z [θ ]
v∗ ∼ −
.
(4.9)
cos φ ∂ λ ∂φ [θ ]
In the real atmosphere ∂φ [θ ] < 0, hence v∗ ∼ ∂λ h and the adiabatic cooling
(warming) of the ascending (descending) air on the western (eastern) side of a
topographic obstacle is thus balanced by poleward (equatorward) temperature
33
advection. It has been shown that the diabatic cooling of an ice sheet induces
an anticyclonic circulation that acts to amplify the mechanical stationary-wave
forcing (Liakka, 2012; Ringler and Cook, 1999). This further implies that
diabatic cooling is an important factor for the simulation of glacial climates
as it affects the planetary waves that influence the climate far away from their
source region.
4.4
Wave-activity flux and critical-layer reflection
The leading-order momentum balance in the subtropical upper troposphere is
between the Coriolis acceleration associated with the Hadley cell and deceleration of the mean flow by momentum-flux divergence due to (mostly) equatorwards propagating extratropical eddies. This balance is such that it supports
a westerly mean flow – the subtropical jet – and thus a meridional potentialvorticity (PV) gradient that is crucial for the maintenance and propagation of
planetary waves.
At lower latitudes, however, the winds are weaker (there are even easterlies
in certain regions) and the wave propagation is inhibited when the phase speed
exceeds the mean background flow. This condition marks what is known as
a “critical layer”. For stationary waves, a critical layer occurs when the mean
flow is precisely zero, as these waves have no phase speed relative the surface
of the Earth. Planetary waves with small amplitudes encountering the subtropical critical layer are absorbed and the wave energy is dissipated by radiative
damping. Larger-amplitude waves, on the other hand, tend to break and mix
the PV field. If the wave amplitude is large enough and the ambient atmospheric conditions are right (e.g. a strong Hadley circulation counteracts wave
breaking, Magnusdottir and Walker, 2000; Walker and Magnusdottir, 2002),
the breaking waves homogenize the PV-field and thus neutralize the meridional
PV gradient (McIntyre and Palmer, 1983). The critical layer is then transformed from absorbing the incident waves to reflecting the planetary waves
back into midlatitudes (Brunet and Haynes, 1996; Killworth and McIntyre,
1985) with the opposite phase tilt (SE-NW instead of the SW-NE). Planetary
wave reflection is found to be a fairly common feature in the atmosphere and
re-analysis data reveals that it may occur as often as during every third wave
breaking event in the Northern Hemisphere (Abatzoglou and Magnusdottir,
2004, 2006a,b).
To diagnose the propagation of stationary planetary waves, it may be useful to derive a conservation equation describing the wave-activity flux in three
dimensions (essentially a generalization of the EP-flux, Andrews and McIntyre, 1976; Edmon et al., 1980; Eliassen and Palm, 1961). Defining the quasi34
Figure 4.2: The 300 hPa (DJF) eddy streamfunction [m2 s−1 ] and horizontal
wave activity flux vectors in the Atlantic sector derived from (a) the ERA-Interim
re-analysis (Dee et al., 2011) and (b) a LGM climatology used in Paper IV. The
outer edge of the ice sheets and the 1000 m contour of the Northern Hemisphere
topography are shown by solid black lines.
geostrophic potential vorticity at a midlatitude β -plane as
∂ 2ψ ∂ 2ψ
f2 ∂
q = f +βy+ 2 + 2 +
∂x
∂y
p ∂z
p ∂ψ
N2 ∂ z
,
(4.10)
(where N is the buoyancy frequency and p the pressure), Plumb (1985) showed
that the balance equation takes the form
∂A
+ ∇ · Fs = D,
∂t
(4.11)
where D represents non-conservative quantities (e.g. dissipation and diabatic
heating) and
1 q∗ 2
A= p
(4.12)
2 ∂y [q]
is the wave activity density. Note that ∂y [q] > 0 is a requirement for this to be
valid. Fs = cg A in Eq. 4.11 is the wave activity flux and cg = ∂k,l,m ω defines
the group velocity as the partial derivatives of the wave frequency (ω, obtained
from the dispersion relation) with respect to the directional wave numbers. In
the WKBJ-limit (a linear approximation requiring a slowly varying flow and
35
weak dissipation) the wave activity flux can be written in spherical coordinates
as
!

∗ 2
2 ∗
1
∂ψ
∗∂ ψ
−ψ
 2a2 cos2 φ
∂λ
∂λ2 



∗



∗
2
∗
∂ψ ∂ψ
∂ ψ
1
.
Fs = p cos φ 
(4.13)
− ψ∗
 2

 2a cos φ ∂ λ ∂ φ
∂λ∂φ 


2 ∗ 
 2Ω2 sin2 φ ∂ ψ ∗ ∂ ψ ∗
∗∂ ψ
−ψ
N 2 a cos φ ∂ λ ∂ z
∂λ∂z
The wave activity flux is thus a vector quantity almost parallel to the local
group velocity that points in the direction of the energy propagation of the
quasi-stationary planetary waves and normal to their phase lines.
Figure 4.2 shows the upper tropospheric eddy streamfunction field and
wave activity flux in re-analysis data and a GCM simulation of the LGM climate. There are apparently large differences in the stationary planetary wave
field, and the LGM simulations shows a conspicuous reflection of wave activity over the east-central Atlantic Ocean, a feature that is not present in the
modern re-analysis data. Paper IV discusses how reflection of planetary waves
over the Atlantic may help to explain the zonalised jet structure seen in many
simulations of the LGM, especially when using the PMIP 2 forcing protocol
with the high LIS.
36
5. Summary of papers
5.1
Paper I
Paper I examines the mutual interaction between mechanically-forced stationary waves and the evolution of a continental-scale ice sheet. Simulations
are conducted using the three-dimensional thermo-mechanical ice-sheet model
SICOPOLIS (Simulation Code for Polythermal Ice Sheets) asynchronously
coupled to a linear as well as a fully-nonlinear dry atmospheric primitiveequation model on a sphere. The coupled models use a simplified geometry
with a flat rectangular representation of North America. Precipitation is here
parameterized from the vertical velocity induced by the kinematic boundary
condition (cf. Eq. 3.1) and the atmospheric climatology is updated every 500
years until the ice sheet is in equilibrium. These experiments can be regarded
as a continuation of the study by Roe and Lindzen (2001) where a similar, but
more idealized approach was taken using purely linear β -plane dynamics.
We find that the linear and nonlinear atmospheric models yield quite different shapes of the equilibrium ice sheet as a result of the location and strength
of the mechanically forced temperature anomalies. The nonlinear atmospheric
response yields a warm anomaly over the northwestern ice sheet and a cold
anomaly in the southeast. This configuration has a small influence on the shape
of the ice sheet, as the warm anomaly is located in a region where the temperature is well below freezing and the ablation is therefore negligible. The ice
sheet is thus largely zonally symmetric and closely resembling a control case
where the stationary-wave feedback is omitted.
The linear stationary-wave response yields a repeated high-amplitude
“warming–cooling” pattern in the zonal direction that gives the ice sheet an
equatorward (poleward) extension (retreat) over the central (eastern) continent.
This ice sheet is structurally different from the “east-heavy” equilibrium state
in Roe and Lindzen (2001), even though our linear model comprises similar
dynamics as that in their study. We explain this discrepancy from the ratio
between the zonal extent of the continent (Lx ) and the zonal wavelength of the
stationary waves (λx ). In our experiment this ratio is Lx /λx ≈ 1 whereas Roe
and Lindzen (2001) have longer stationary waves, which yields Lx /λx ≈ 1/2
and thus the largest meridional extension of the ice sheet at the eastern side of
37
the continent.
5.2
Paper II
The experiments presented in this paper are a natural continuation of the research reported in Paper I. Here we use a comprehensive atmospheric circulation model (the National Center for Atmospheric Research Community Atmospheric Model version 3 (NCAR CAM3), Collins et al., 2004, 2006) asynchronously coupled to the ice-sheet model SICOPOLIS also used in Paper I.
The atmospheric model includes moisture dynamics and a prognostic cloudwater parameterization. We have also updated the planetary boundary using a
triangular representation of North America, with and without the Cordilleras
to investigate its influence on the ice growth. The atmospheric state is here updated every 2 × 106 km3 change in ice volume, which implies that the coupling
frequency is dynamic and depending on the growth rate of the ice sheet instead
of on a fixed time interval.
In the first experiment we use a flat continent, similar to the one used by
Liakka (2012); Liakka et al. (2011); Roe and Lindzen (2001). The ice sheet
evolves fairly zonally symmetric with a double-dome structure emerging with
the highest points located on the southwestern and southeastern sides of the
ice sheet. In the later stages of the simulation the center of mass is shifted
to the central parts of the continent and the ice sheet equilibrates as a largely
symmetric monodome with a structural similarity to modern reconstructions
of the Laurentide Ice Sheet (see Fig. 2.2). We explain the ice sheet’s structural
evolution as a change in the stationary-wave response. In the first half of the
simulation the mechanical stationary-wave forcing is limited and the diabatic
cooling forces an anticyclonic circulation located over the ice sheet. When
the ice sheet expands into the westerly flow at lower latitudes the mechanical
stationary-wave forcing becomes more important. The low-level wind field
then changes its characteristics into a more “nonlinear” flow-regime with cold
air advection over the ice-sheet topography.
The ice evolution when including the Cordillera is quite different. The
ice sheet rapidly obtains an “east-heavy” disposition that persists through the
simulation and the interior of the continent remains ice-free also in the equilibrium state. This structural disposition resembles the geologically determined
ice margin in MIS 4 (Fig. 2.2) (Kleman et al., 2013) and is believed to originate from the arid conditions in the lee of the Cordillera. The ice sheet itself is
shown to help maintain this asymmetric shape by inducing an anticyclonic circulation with a reduced cloudiness and warm air advection over the continental
interior.
38
5.3
Paper III
In this paper we investigate the evolution of the large-scale atmospheric circulation over the build-up phase of the last glacial cycle. We use the geologically
consistent ice sheet reconstruction presented by Kleman et al. (2013) as a firstorder topography at three key stages of the last glacial cycle: MIS 5b, MIS 4,
and the LGM, which corresponds to approximately 88, 66, and 20 kyr BP.
The simulations are conducted using the NCAR CAM3 atmospheric circulation model coupled to a mixed-layer ocean with prescribed heat flux convergence derived from equilibrated simulations of the interglacial (pre-industrial)
and LGM (Brandefelt and Otto-Bliesner, 2009) climates with the fully coupled
Community Climate System Model version 3 (NCAR CCSM3). These ocean
heat fluxes are thought to represent end members of the ocean circulation over
the glacial cycle. By running all simulations with both heat-convergence fields
we obtain an estimate of the importance of the ocean for the simulated climate.
The main conclusions from this study are that the pre-LGM ice sheets appear to have been located in regions where their mechanical forcing of stationary planetary waves was limited in the winter season (DJF). The North
American ice sheet was located in the lee of the Cordillera where the westerly mean-flow is circumventing the ice margin and the Eurasian Ice Sheet
was located to the north of the strongest westerly winds and with height contours largely parallel to the flow. However, the continent-wide Laurentide Ice
Sheet at the LGM forced much larger stationary planetary waves that resulted
in a zonalisation of the North Atlantic winter jet. In the summer season (JJA)
we find that the anticyclonic circulation forced by the ice sheets induce warm
temperature anomalies in Alaska and east-central Siberia as a result of reduced
cloudiness and advection of warm air. This may help explain why these regions
remained ice-free over the entire glacial cycle.
5.4
Paper IV
Paper IV investigates the importance of the height of the Laurentide Ice Sheet
on the planetary wave field over the Atlantic Ocean. The study is motivated by
the fact that the three generations of the Paleoclimate Modelling Intercomparison Project (PMIP 1, 2, and 3) tend to disagree on the axial tilt of the North
Atlantic jet in winter (DJF). Simulations with comparatively low representations of the Laurentide Ice Sheet (PMIP 1 and 3) show an Atlantic jet axis
retaining much of the meridional tilt familiar from the present (see Fig. 3.1).
However, simulations with the considerably higher PMIP 2 ice sheet yield a
more zonally oriented jet structure (see Fig. 3.3). A zonalised winter jet was
also obtained in Paper III when using the LGM forcing.
39
We explore this issue by simulating the LGM climate with successive increases of the height of the ice sheets. We find that the jet axis is indeed
meridionally tilted when using low ice sheets. However, when the height of
the Laurentide Ice Sheet exceeds approximately 3300 m, planetary wave reflection in the east-central Atlantic Ocean becomes sufficiently prevalent that
a poleward-directed wave-activity flux appears in the climatological stationary
wave field. It is precisely when this flux becomes apparent in the climatology that the phase lines of the stationary-planetary waves shift from having
a southwest–northeast tilt to being zonalised, which is then imparted to the
orientation of the jet axis.
40
Acknowledgements
I would like to express my sincere thanks to everyone that has contributed to
this thesis work over the years. First and foremost my supervisors: Rodrigo
Caballero and Johan Nilsson, as well as my former supervisor Heiner Körnich.
I owe you a lot of gratitude for all the guidance, inspiration and stimulating
discussions that have made this work possible. I would also like to thank
Johan Kleman who has not only contributed with an immense expertise on
glacial climates, but also financial support and a fruitful collaboration that I
hope will continue in the future. My next thanks goes to my dear friend and
colleague Johan Liakka. I hope our endless discussions about everything from
the genius of “Curb” to nonlinear stationary wave dynamics will continue for
many years to come. Johan, rock on!
I am also thankful to the Department of Meteorology and the many people
working there that made it feel joyful to go to work every day; my officemates over the years: Jenny, Magnus, and Rune, as well as all the other coworkers: Henrik, Saeed, Susanne, Peter, Anna, Joe, Maxime, Frida, Jenny,
Jonas, Sebastian, Filippa, Anders, Malin, Johannes, Abubakr, Leon, Marie,
Mondheur, Francesco, Jocke, Wing, Gabrielle, and Raza, to mention a few.
On a personal level I also express my love and thankfulness to my parents,
my brother and my sister, as well as all friends, most notably Sofia and Sara,
that stood by my side in the darkest of hours. Without your mental support this
would not have been possible.
Finally, I would also like to acknowledge my old high school teacher
in physics and mathematics Håkan Lodin. Your encouragement and support
when I attended the evening class in number theory and cryptography at the
university was really the turning point when I decided to study physics at a
higher level. Keep up the good work and continue inspiring new generations
of students!
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Appendix: corrections
The relative ages of the ice sheet reconstructions reported in section 2.4 in
paper III are wrong by a factor of 1000. The correct numbers are: MIS 5b,
∼ 88 kyr BP; MIS 4, ∼ 66 kyr BP; and MIS 2, ∼ 20 kyr BP.