Tropical Cyclone Response to Greenhouse and Solar Forcing

MCGILL UNIVERSITY
MASTER THESIS
Tropical Cyclone Response to
greenhouse and solar forcing
Author:
Flora VIALE
Supervisor:
Dr. Timothy MERLIS
A thesis submitted to McGill University in partial fulﬁllment
of the requirements
for the degree of Master
in the
Department of Atmospheric and Oceanic Sciences
August 11, 2016

iii
© 2016
Flora VIALE
All Rights Reserved

v
Abstract
The response of tropical cyclone (TC) activity and frequency in differ-
ent perturbed climates is investigated with an aquaplanet configura-
tion of a Global Climate Model with 50-km horizontal resolution. To
understand the differences between solar and carbon dioxide (CO2)
forcing, the direct response to the forcing, sea surface temperature
(SST) changes, and the combined response in slab-ocean model sim-
ulations are compared. The increased solar constant simulations and
the 4xCO2 simulations have the same global-mean radiative forcing
(about 7.7 Wm−2
), but the TC frequency changes are greater in mag-
nitude for CO2 forcing than for solar forcing. Quadrupling CO2 also
leads to a greater response of environmental variables that influence
TC activity.
TC frequency and intensity increase in a warmed climates, though
not as a direct response to radiative forcing. The increase in TC ac-
tivity is consistent with changes in environmental variables such as
potential intensity, absolute vorticity, and convergence zone latitude,
and is not accounted for by other previously discussed environmen-
tal variables such as moist entropy deficit, vertical wind shear, and
vertical velocity.
The direct response to radiative forcing for most of the environ-
mental variables is opposite to the response to SST changes. The
simulations have departures from linear additivity of the combined
response to forcing and SST in isolation, which suggests that time-
dependent SST fluctuations may need to be prescribed in fixed-SST
simulations in order to better reproduce TC changes.

vi
Résumé
Nous avons étudiés sur une planète déau, avec un modèle cli-
matique global de 50-km de résolution horizontale, les changements
induit par des perturbations climatiques sur láctivité et la fréquence
des cyclones tropicaux (CT). Pour comprendre les différences entre
le forçage radiatif solaire et le forçage radiatif du dioxyde de carbone
(CO2), les résultats des simulations avec forçage radiatif, des sim-
ulations avec forçage radiatif et températures de surface de lócéan
augmenté et les simulations avec lócéan à couche de mélange "en
dalle" sont examinées. Les simulations avec la constante solaire la
plus élevée (1450 Wm−2
) et les simulations avec la concentration en
CO2 la plus élevée (1200ppm) ont le même forçage radiatif global (en-
viron 7,7 Wm−2
), mais les résultats suggèrent que les changements
de fréquence des CT sont plus influencés par le forçage radiatif du
CO2 que par le forçage radiatif de la constante solaire. Quadrupler
la concentration de CO2 mène à des changements plus significatif,
sur les variables environnementales et sur les variations des CT, que
láugmentation de la constante solaire.
La fréquence et líntensité des CT augmentent dans un climat plus
chaud sauf quand le forçage est seulement radiatif. Láugmentation
de láctivité des CT est cohérente avec les changements des vari-
ables environnementales tels que líntensité potentielle, la vorticité
absolue et la fonction de courant, mais ne parviennent pas à être ex-
pliquée par d’autres changements des variables environnementales
tels que le déficit de léntropie humide, cisaillement vertical du vent,
le vent vertical.
Les simulations avec forçage radiatif induisent pour la plupart des

vii
variables d’environnementales un changement opposé quand com-
paré aux simulations avec changement des températures de surface
de lócéan. De plus, les résultats suggèrent que la dépendance tem-
porelle des fluctuations de température de surface de lócéan de-
vraient probablement être prescrit pour les simulations avec les tem-
pératures de surfaces de lócéan fixées afin de mieux reproduire les
changements des CT.

ix
Acknowledgements
I would ﬁrst like to express my very profound gratitude to my
thesis advisor Prof. Timothy Merlis. He consistently provided me
with direction and it was through his, persistence, understanding
and kindness that I have been able to complete my graduate degree.
Although this thesis is my own work it would not have been possible
without his immense passion and knowledge on the subject.
A very special thanks goes out to Prof. David Straub, without
whose motivation and encouragement I would not have been able
to ﬁnish this thesis.
Also I would like to thank Prof. Yi Huang for taking the time to
examine this thesis.
My sincere thanks also goes to Julie M. Thériault from UQÁM for
offering me two summer internship opportunities in her group and
leading me working on diverse exciting projects. She made a differ-
ence in my life by encouraging me to apply for a graduate master
thesis at McGill University.
Finally, I would also like to thanks my parents, my partner and my
friends for providing me with unfailing support and continuous en-
couragement throughout my years of study and through the process
of researching and writing this thesis. This accomplishment would
not have been possible without them.
Thank you.

xi
Contents
Abstract v
Acknowledgements ix
List of Figures xiii
List of Tables xv
1 Introduction 1
1.1 Tropical Cyclones . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Literature review . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 TCs and climate change . . . . . . . . . . . . . . 6
Genesis and TCs tracks . . . . . . . . . . . . . . 9
1.3.2 TCs and aerosols . . . . . . . . . . . . . . . . . . 11
1.3.3 Hydrological response . . . . . . . . . . . . . . . 12
2 Method 15
2.1 Model description . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Storms Tracker description . . . . . . . . . . . . . . . . . 17
2.3 Simulations description . . . . . . . . . . . . . . . . . . 18
3 Tropical Cyclone Response to greenhouse and solar forcing 23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 TC Frequency . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Changes in Circulation and Precipitation . . . . . . . . 28
3.3.1 Hydrological cycle . . . . . . . . . . . . . . . . . 28
3.3.2 Hadley Circulation . . . . . . . . . . . . . . . . . 31
3.4 Changes in Genesis and the Tropical Environment . . . 33
3.4.1 Genesis Potential Index . . . . . . . . . . . . . . 33
3.4.2 Vorticity . . . . . . . . . . . . . . . . . . . . . . . 35
3.4.3 Moist entropy deﬁcit . . . . . . . . . . . . . . . . 36
3.4.4 Potential Intensity . . . . . . . . . . . . . . . . . 39
3.4.5 Vertical Wind Shear . . . . . . . . . . . . . . . . . 41
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Conclusions 47
A Additional Figures 49

xiii
List of Figures
1.1 Figure from Emanuel, 2003 illustrating the structure of
a mature tropical cyclone . . . . . . . . . . . . . . . . . . 2
2.1 Net Radiation at TOA in slab ocean solid line, prescribed
SSTs dashed line, and dash-dot line experiments, with So
= 1400 Wm−2
. . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 Number of TCs per year against global-mean surface
temperature in Kelvin for all sets of simulations . . . . 24
3.2 Difference in zonal mean SSTs between simulations
and reference simulation in the slab-ocean experiment . 27
3.3 Probability of TC and Number of TCs per year against
maximum wind speed. Upper panel is for solar while
lower panel is for 4xCO2 . . . . . . . . . . . . . . . . . . 28
3.4 Precipitation in mm/day against latitude for all exper-
iments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Evaporation in mm/day against latitude for all exper-
iments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.6 Maximum value of streamfunction at 600-hPa . . . . . 32
3.7 GCM genesis, solid line, versus GPI2010, dashed line for pF 34
3.8 Moist entropy deﬁcit against latitude for all simula-
tions. Dashed lines in the third panel are for the BOTH
experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.9 Potential intensity against latitude for all simulations.
Dashed lines in the third panel are for the BOTH ex-
periment . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.10 Fractional change of mean TC genesis weighted pre-
cipitation (P), minimal potential pressure (Pmin), po-
tential intensity (PI), environmental shear (S), upward
vertical wind at 500-hPa (ω500), relative vorticity at 850-
hPa (ζ850) and global number of TCs per year (TC). . . . 44
3.11 Fractional change of mean TC genesis weighted pre-

xiv
A.1 Precipitation minus Evaporation in mm/day for each
simulations with high CO2 concentration (upper panel)
and high solar constant (lower panel) . . . . . . . . . . 50
A.2 Streamfunction differences from reference simulation
in pF experiment, for S1450 and 4xCO2 simulations . . 50
A.3 Genesis Potential Index (equation 3.1) against latitude
for each experiment. Upper panel for climate altered
by solar constant and panel below for climate altered
by GHG. . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
A.4 Genesis Potential Index against latitude for all simula-
tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
A.5 Genesis against latitude for all simulations . . . . . . . 52
A.6 Genesis and GPI against latitude for SOM simulations . 52
A.7 Vertical Wind Shear against latitude for all experiments 53
A.8 Fractional change of mean TC genesis weighted pre-

xv
List of Tables
2.1 ∆( ¯R), with ¯R the global mean of net TOA radiation . . 21
3.1 Number of TCs per year for all sets of simulations . . . 26
3.2 % change of number of TCs per year for all sets of sim-
ulation. T4K and BOTH experiments use pF reference . 26
3.3 % change of the maximum value of the streamfunc-
tion. T4K and BOTH percentages are compared to pF
reference simulation. . . . . . . . . . . . . . . . . . . . . 32

1
Chapter 1
Introduction
Humans have always been interested in predicting complex and
dangerous atmospheric phenomena such as hurricanes. After World
War II, measurement and reconnaissance with aircraft and radar started
to develop and be used by meteorologists as tools to understand and
observe strong phenomena. Now not only radar and satellites can
provide us with high-resolution imagery, but numerical model sim-
ulations can help us understand physical atmospheric phenomena.
The purpose of this thesis is to examine the response of tropical
storm activity and frequency in different perturbed climates with a
Global Climate Model of 50-km horizontal resolution on an aqua-
planet. I will introduce some of the major physical properties of
tropical storms, provide a review of literature on the subject, and
motivate for the research performed for this thesis.
1.1 Tropical Cyclones
Tropical storms are incredible phenomena driven by heat transfer
from the tropical ocean where they develop. Theses rotating systems
are known to arise in tropical regions during summer or autumn.
Their existence requires a few necessary conditions such as :
• warm sea surface temperature (usually exceeding 26◦
Celcius)

2 Chapter 1. Introduction
FIGURE 1.1: Figure from Emanuel, 2003 illustrating
the structure of a mature tropical cyclone
• pre-existing atmospheric disturbance waves of 1000-3000 km in
horizontal scale
• non-zero convergence and large cyclonic vorticity (in lower tro-
posphere) for low-level inﬂow to develop
• little vertical shear
• non-zero Coriolis force (Gray, 1968)
• high relative humidity in the mid-troposphere (Emanuel, 1995)
These necessary conditions were developed from observations of Earth
(Gray, 1968). Due to strong observational systems and extensive
analysis, the structure of tropical cyclones (TCs) is now well known.
In the center of the most intense and mature storm, a well-deﬁned
cloud-free region can develop. ’The eye’ is known to be the quietest
area in the storm, which corresponds to a region of subsidence where
downward wind reach a speed of ≈ 5 to 10 cm/s. As shown in Figure
1.1., it is surrounded by ’the eyewall’, which corresponds to a region

1.1. Tropical Cyclones 3
of deep convection and the inner part of the axisymmetric vortex,
in which strong surface wind flow cyclonically1
. The formation of
clouds extending from 20 to 50 km outward of the eyewall is due
to the deep convection, while strong winds are due to the low pres-
sure at the center. However, the top of the storm shows a weaker
anti-cyclonic flow, which is focused in few ’outflow jets’.
The horizontal wind’s intensity is greater near the ground at about
10-100km from the center. It starts decaying from its most intense
area at a rate of about r−1/2
, where |r| is the radius of the storm, which
makes the decay faster for a storm of larger radii (Emanuel, 2003).
The vertical wind’s intensity, however, is stronger within the eyewall
of the system in the mid-troposphere and are approximately 5 to 10
m s−1
.
TCs intensify rapidly after saturation of the core, and die rapidly
because of intensification’s feedback. The intensification corresponds
to the strengthening of the surface wind speed, through among other
processes stronger surface turbulent fluxes (NB: heat transfer increase
as wind increases, so it is a positive feedback). However, this positive
feedback is not endless due to finite potential intensity. More over,
intensification leads to greater dissipation (dissipation ≈ wind speed to
the cube).
Surfaces fluxes drive the eyewall’s frontogenesis, which in turn in-
fluence the strong gradient of angular momentum in that region of
the TC. In that same region, a strong radial gradient and the max-
imum value of specific entropy are found. Stronger wind tends to
occur just outside of the eyewall, where stronger gradient of entropy
is located.
1
"In the same sense as the local vertical component of the earth’s rotation"
(Kerry Emanuel, 2003)

Emanuel (2003) has shown that an ideal closed Carnot engine can
be a good representation of mature TC. Indeed, air parcels moving
inward see their pressure and angular momentum decreasing as well
as their entropy increasing from surface fluxes. Also, air parcels
moving upward see their pressure drop while their entropy and an-
gular momentum is conserved.
Because TCs are cyclonically rotating systems on the earth’s rotat-
ing surface, TC propagation is affected by differential rotation. The
air is advected equatorward at their right and poleward at their left
in the northern hemisphere which carries different planetary vor-
ticity. The air moving equatorward get cyclonic vorticity while the
air moving poleward get anticyclonic vorticity, and this provides a
"push" that moves storms to the north-east of themselves. In addi-
tion to this TC vortex ’self advection’, the track of a TC is affected by
larger scale winds.
Tropical storms are usually divided in tree groups based on inten-
sity (depressions, storms, hurricanes or typhoons), but can also be
defined as warm or cold core.2
1.2 Motivation
Since it has been demonstrated that high sea surface temperatures
(SSTs) and little vertical wind shear (VWS) are a necessary condi-
tion for the development of TCs, climate variability, such as El Niño
or North Atlantic Oscillation (NAO), can impact the development
of TCs (Camargo, Emanuel, and Sobel, 2007). More over, climate
variability is not the only factor influencing TC activity. Increases in
greenhouse gases leads to a warming climate in which the energy
2
Another category has been defined by Kerry Emanuel as "hypercanes" a theo-
retical hurricane rising over ocean warmer than 50◦
C.

1.2. Motivation 5
balance will be out of equilibrium. Both the changing SSTs and en-
ergy balance would increase TC intensity (Emanuel, 2003). Over the
past decades, the influence of climate change on TCs has generated
substantial concern, both within the scientific community and polit-
ically.
Increasing greenhouse gases in our atmosphere is well-known to
induce warming temperature. In addition, there are radiative forcing
agents, such as aerosols, that reflect solar radiation (e.g., the volcanic
eruption of Mount Pinatubo in 1991 produced stratospheric aerosol
that led to a global mean cooling). This has led to the consideration
of artificial modification of our climate through "solar radiation man-
agement" as a solution to greenhouse gas-forced climate changes.
However, this geoengineering could lead to even more unknown cli-
mate response if CO2 forcing and solar forcing lead to different cli-
mate responses. Many unresolved questions about geoengineering
remain.
Therefore this study focuses on comparing the change in tropical
storms and hurricanes frequency in climates perturbed by altered
solar constant (So) and by altered CO2 concentration. We have seen
that TCs are usually divided in three groups (depressions, storms,
hurricanes or typhoons) and for this study we mainly focus on trop-
ical storms with surface wind speed greater than 17 m s−1
and hurri-
canes which have surface wind speed above 29.5m s−1
. Some of the
main question that motivated this study are listed here:
• which environmental variables are the best predictor for changes
in TC activity in altered climates?
• is a change in TC from altered CO2 similar to change from al-
tered solar constant (So)?

• can we separate radiative forcing from SST forcing, or is the
combined effect different from the sum of individual effects?
Other concerns regarding changes in storm intensity will also be dis-
cussed. Since Emanuel has suggested the possibility of an increase
of the most intense storm (increase of potential intensity, Vmax) in
a warmer climate using the following approximation3
: |Vmax|2
≈
Ck(Ts−T0)
Cd(T0)
(k∗
0 − k) . This happens because surface thermodynamic dis-
equilibrium is a source for turbulent heat transfer and the net long-
wave emission at the surface should decrease, in a climate forced by
anthropogenic GHG, leading to stronger thermodynamic disequilib-
rium (Emanuel and Sobel, 2013).
1.3 Literature review
1.3.1 TCs and climate change
What might be the response of tropical storms activity (intensity,
frequency, rainfall, etc.) to climate changes (i.e., global warming)?
Literature suggests that TC frequency will either decreases or remain
unchanged, while the frequency of most intense hurricanes will in-
crease, with more robust result for the southern hemisphere than
for the northern hemisphere (Emanuel, 2003; Knutson et al., 2010).
However results remain uncertain, since major hurricanes (category
4 and 5, with maximum wind higher than 65m s−1
) are not well re-
produced by standard climate models and need higher resolution
(Knutson et al., 2010). Furthermore, regional projections have poor
3
where Ck and Cd are dimensionless coefﬁcients for, respectively, momentum
and enthalpy transfer, Ts and T0 are, respectively, SST and mean temperature of the
cold source, k∗
0 and k are, respectively, speciﬁc enthalpy of the air near the surface
and enthalpy of the air in contact with the ocean

1.3. Literature review 7
agreement between models, leading to uncertainty in the projected
regional patterns of climate changes.
On the one hand, TC intensification could be due, among other fac-
tors, to the observed increased SSTs over main development region
for TCs over the past decades due to GHG-induced warming. For ex-
ample, Emanuel (2005) correlated Atlantic SST with hurricane power
dissipation. A difficulty with using observed relationships between
SSTs and TC activity is that there may be multiple relationships that
fit the observations well but have different behaviours in future cli-
mates. As a matter of fact, Vecchi, Swanson, and Soden (2008) have
shown that two linear relations4
can account for the relationship be-
tween the power dissipation index (PDI) and SSTs. Indeed, not only
absolute SSTs but also relative SSTs5
are found to have a linear re-
lation with PDI. Since variation of relative SSTs cannot be yet phys-
ically separate from internal climate variability, Atlantic hurricane
activity changes recently observed cannot be explained by GHG forc-
ing only. Zhao et al. (2009) examined if simulated change in TC and
hurricane statistics are due to SST fluctuations, and if this destabi-
lization of SST is due to GHG effect or internal variability. The in-
teranual variability of hurricane frequency in their model is more
correlated with observations in the Atlantic Basin than in the east,
west or south Pacific or in the Indian Ocean. In agreement with the
results of Knutson et al. (2008), they suggest a decrease in hurricane
frequency in response to the 21st century warming.
On the other hand, the decrease in TC frequency might be due to
a weakening deep convection in the tropics (decrease in the upward
4
found for the period 1946?2007
5
relative SSTs are defined in (Vecchi, Swanson, and Soden, 2008) as SST in the
tropical Atlantic main development region relative to the tropical mean SST. Ab-
solute SSTs are SSTs in the main development region

mass flux, as well as a weakening of the tropical circulation) or to an
increase in the saturation deficit of the middle troposphere. In fact,
Zhao et al. (2013) have confirmed that the decrease of TC frequency is
well correlated with the weakening of the upward convective mass
flux. Their results suggest negative values of perturbation convec-
tive mass flux 6
for nearly all models and all experiments in response
to SST warming or CO2 forcing. This intermodel comparison built
on the study of Held and Zhao (2011), who showed the tropical deep
convective activity, measured as the genesis-weighted averaged of
upward mass flux, decreased in perturbation simulations. This de-
crease of the convective mass flux would lead to an increase in en-
trainment (dry environmental air advection) and less TC genesis.
In a warmer climate, the atmospheric water vapor content increases,
and there will be an associated increase in TC rainfall rate. Knut-
son et al. (2010) confirmed this hypothesis using high-resolution dy-
namical models, however results suggest those changes may not be
the same in all basins where tropical cyclone tends to form; it is
likely that those changes may be greater in the Atlantic Basin. Pro-
jections for rainfall rate are also likely to increase by approximately
20% within 100 km of TC center. Nevertheless, uncertainties remain
in climate models, and understanding of climate variability. For ex-
ample, nowadays attribution of the observed increase in PDI can be
explained by both anthropogenic forcing and natural variability and
the time period with high-quality TC data is too short to provide
conclusive information about climate decadal variability versus an-
thropogenic changes.
TCs and hurricanes response to climate change have been studied
6
the convective mass flux is measured as the annual mean divergence at 500hPa
spatially averaged

in a GHG-induce warmed climate through change in SSTs. However,
to understand the direct or "fast" effect of an increase in CO2 concen-
tration on the global TC frequency, Held and Zhao (2011) and Zhao
et al. (2013) have separated the forcing of the CO2 from SSTs, in the
following series of prescribed-SST simulations:
• SSTs are uniformly increased by 2k (P2K), leaving CO2 unchanged
• SSTs are unchanged and CO2 concentration is double (2xCO2)
• SSTs are increased and CO2 concentration is double (BOTH)
In addition to the annual global TC frequency decrease, their results
suggest that geographic TC frequency distribution decrease consis-
tently over the main development region (MDR), when SSTs are in-
creased and CO2 is doubled. Furthermore, the global decrease in
TC number in BOTH experiment (≈ 20%), is similar to the a linear
combination of the decrease in 2xCO2 and P2K experiments (≈ 10%
each). However, the increase in global TC intensity is only seen to
the P2K experiment, suggesting than doubling the atmospheric con-
centration of CO2 has no or little weakening effect on TC intensity.
Genesis and TCs tracks
Many studies have examined on the response of TC activity to cli-
mate change, focusing on the change in frequency, intensity and pre-
cipitation. However, few studies have focused on the impact of a
warmer climate on changes in TC genesis area and track.
Daloz et al. (2015) have investigated the ability of different climate
models to represent TCs tracks in the North Atlantic and examined
it under different climate scenarios (2K SSTs, 2xCO2 or both com-
bined). Southernmost TCs seem to reach landfall with higher inten-
sity than northernmost TCs, and simulations indicated they will be

less affected by climate change (Daloz et al., 2015). Thus, northern-
most cyclones are the leading cause of frequency changes in future
climates. It has also been suggested by literature (Murakami and
Wang (2010), Colbert et al. (2013)) that straight moving storm will
decrease while recurving moving storms will increase, hence lead-
ing to an increase in central Atlantic landfall.
Southernmost tropical cyclones are also mostly inﬂuenced by the
intertropical convergence zone (ITCZ) latitude (φ). Merlis, Zhao,
and Held (2013) shows in a climate with radiatively forced by in-
creased solar constant and increase CO2 concentration, warming is
more important in the Northern Hemisphere. Results suggest that,
in both climates, TC genesis will increase and shift poleward due
to a more spread ITCZ also shifting toward northern latitudes, de-
spite the fact that TC frequency would decrease in a warmer climate
with unchanged ITCZ position (−10%K−1
). This is due, on the one
hand, to the fact that in a water climate, the ITCZ would shift pole-
ward, which increased hurricane frequency by 40%◦
lat−1
. Indeed
Ballinger et al. (2015) results suggest that when maximum SSTs are
shifted toward higher latitude, ITCZ follows hence precipitation shift
also northward but tends to decrease while frequency of TCs tends
to increase. More over, Ballinger et al. (2015) results suggest that in-
creasing heat ﬂux also leads to a northward shift of warmer SSTs, as
well as a northward shift of the ITCZ, with an increase in the TCs
and hurricane genesis frequency.
As discussed by (Tang and Neelin, 2004), a disequilibrium state
where North Atlantic tropospheric temperature (NAtl-T) is warmer
(cooler) relative to its normal relationship to the North Atlantic sea
surface temperature (NAtl-SST) induces anomalous small (large) mean
disequilibrium principle component or potential intensity over the

tropical Atlantic. This lead to large-scale environment less (more)
conductive to tropical cyclogenesis. Hence, onsetting El Nino/La
Nina events seems to be greatly correlated with TC activity has re-
sults shown in (Tang and Neelin, 2004), since the disequilibrium (de-
parture of SST and tropospheric temperature anomalies from they
typical relationship) is consistent with NAtl-SST not having had time
to adjust to the teleconnected upper tropospheric warming or cool-
ing of onsetting ENSO or La Nina event.
1.3.2 TCs and aerosols
Sulfate aerosols have a negative (cooling) radiative forcing because
they reﬂect solar radiation. In addition, aerosols can provoke a fast
response in cloud properties (such as cloud droplet effective radius,
cloud fraction, cloud albedo), and hence further modify downward
shortwave radiation and SSTs. There is still a lot of uncertainties
since understanding of aerosol-cloud interactions is limited, and avail-
able data does not constrain aerosol cloud effects over the past decades.
This lead to difﬁculty in simulating the effect of anthropogenic aerosol
in climate models.
Literature (Vecchi, Swanson, and Soden, 2008; Dunstone et al.,
2013) suggest that possible reduction in aerosol loading may have
been provoked the observed decrease in TC frequency over the 20th
century. Mann and Emanuel (2006) suggest that aerosol forcing seems
to compensate the global warming, and be very important for SSTs
in the North Atlantic MDR. Even if most of the SST variability can
be explained by the global mean SST, the residual (which includes
aerosol-forcing) cannot be ignored. Results from Mann and Emanuel
(2006) show that net SST variations can explain more than 50% of

the total decadal variance in annual TCs counts, while the residual
explains roughly 4% of it.
Results from Dunstone et al. (2013) suggest that TC variability is
mostly affected by aerosols even though during the late twentieth
century the observed frequency decrease of TCs is associated with
the GHG increase. Since anthropogenic aerosol forcing leads to a fast
response in the climate, its variation leads to TCs decadal variabil-
ity. During inactive periods, in which there is a depletion in aerosol
loading (mostly because of socio-economic reasons), there is a shift in the
Hadley circulation southward, toward warmer SST, due to the tem-
perature drop in the MDR and extratropical east Atlantic.
TC frequency is highly correlated with SSTs variability, to under-
stand whether or not aerosols are the primary source for the NA SSTs
and sea surface salinity (SSS) variability Zhang et al. (2013) have
compared observations to model which has a strong aerosol effect.
While aerosols have a cooling effect, Zhang et al. (2013) argue that
HadGEM2-ES has too strong an aerosol effect, and this is the GCM
used by Dunstone et al. (2013). Thus, it is not clear whether aerosol
effect is important or not in the NA SSTs variability.
1.3.3 Hydrological response
The global hydrological cycle shows two responses to climate changes:
a fast and a slow response. The fast adjustment is dependent on the
adjustment of the radiative forcing and the slow response is depen-
dent on temperature-dependent changes. Bala, Caldeira, and Ne-
mani (2010) have shown that fast changes in the hydrological cycle
are dominated by the radiative forcing rather than alteration of evap-
otranspiration by CO2 fertilization. They found the slow adjustment

of the hydrological cycle to doubled CO2 and to increased solar con-
stant by 1.8% had the same response. A substantial percent of the
total response (40%) can be explained by fast adjustment by the cli-
mate system in their simulations. Results reviewed by O’Gorman et
al. (2012) show that, for the slow response of the system, CO2, solar
and sulfate aerosols force the precipitation response in the same way.
The complexities of simulating anthropogenic aerosols in climate
models leads us to pursue an examination of the climate response to
a change in the solar constant. This allows for a comparison of solar
and greenhouse gas forcing, using perturbations that have compara-
ble global spatial scales.

15
Chapter 2
Method
2.1 Model description
We have used a high-resolution general circulation model devel-
oped by the Geophysical Fluid Dynamics Laboratory (GFDL) called
High-Resolution Atmospheric Model (HiRAM), described in Zhao
et al. (2009). Also, these authors have shown that HiRAM captures
and simulates well-tropical cyclone climatology, frequency, seasonal
cycle, and interannual variability. Hence, it has also been used to
simulate tropical cyclone frequency in future climates. This GCM
has 50-km horizontal resolution with a ﬁnite-volume core using a
cubed-sphere grid topology with 180x180 grid points on each face of
the cube and 32 vertical levels. Because storms are sensitive to upper
tropospheric conditions, the discretization has higher vertical reso-
lution near the tropopause. More over, the use of aquaplanet climate
model allows shorter integration, as longitudes can be averaged to-
gether.
In this study the insolation is independent of time and chosen to
be similar to Earth’s annual mean insolation. The dependence on
latitude (φ) is given by: STOA = S0
4
[1 + ∆s
4
(1 − 3 sin2
φ)], with ∆s =
1.2. So there is no seasonal or diurnal cycle. The model includes
no aerosols or trace greenhouse gases others than CO2. The ozone

16 Chapter 2. Method
concentration is prescribed and symmetric in both hemispheres. Two
sets of experiments with different lower boundary conditions have
been performed.
First, a set of simulations with a slab ocean model (SOM) was run.
Surface boundary condition having a slab ocean means that sea sur-
face temperatures are able to change concordantly with turbulent
surface enthalpy fluxes and surface radiative fluxes. In addition to
the radiative and turbulent fluxes, an ocean heat flux convergence is
also prescribed. This is the only aspect of the forcing boundary con-
ditions that is asymmetric about the equator. It is set as a sinusoidal
function of latitude (Ballinger et al., 2015):
Q(φ) =



Qosin(φ+40
50
π) if − 90◦
< φ < −40◦
0 if − 40◦
≤ φ ≤ 40◦
Qosin(φ−40
50
π) if 40◦
< φ < 90◦
,
where Q0 represent the maximum value of the flux convergence and
is set as a reference to be 40W m−1
which corresponds to a 2.35 PW
northward ocean heat flux at the equator. Heat capacity of the sur-
face is equivalent to a water depth of 20 m. This GCM uses a constant
surface albedo of 0.08. At high latitudes, SSTs are able to go below
the freezing point of water, thus eliminating the possibility of sea ice
formation in this model.
Second, a set of simulations with prescribed-SST were run. SSTs
are prescribed from the equilibrium phase of the slab ocean simu-
lations. Since prescribed-SST simulation used the time-mean SSTs
from the corresponding slab-ocean simulation, results can differ be-
tween the two simulations. Both the slab-ocean and prescribed-SST

2.2. Storms Tracker description 17
simulations were perturbed by altered CO2 and solar constant, de-
scribed in what follows. All experiments have a run-time length of
10 years. For experiments with prescribed SSTs, all years are used
in calculations ; for slab-ocean experiment only the last 5 years are
used, due to a longer time needed to reach an equilibrium climate
state.
2.2 Storms Tracker description
All tropical storms are detected and tracked by an algorithm de-
scribed in Zhao et al. (2009) but based on Vitart, Anderson, and Stern
(1997) and Knutson et al. (2007). The tracking algorithm is split in
three steps.
First, it finds an area where minimum of sea level pressure are no
farther than 2◦
latitude or longitude from an area where anomaly of
relative vorticity at 850-hPa is higher than 3.5−5
s−1
. While Zhao et
al. (2009) have shown strong TCs are less sensitive to this parame-
ter, greater value of the parameter can make the TC tracking more
efficient. From the center of identified warm-core vortices anomaly,
local maximum values of 10-m surface wind speed are recorded us-
ing 6-hourly output interval.
Second, if identified anomalies (i.e. warm-core vortices, minimum
sea level pressure, and measure of the upper-tropospheric temper-
ature anomaly) last for a minimum of 6 hours within a distance of
400km of those in the preceding 6-hours. These storms are con-
sidered detected if the track has a duration of more than 3 days ;
since the International Best Track Archive for Climate Stewardship
(IBTrACS) observations show the majority of TCs have a duration
greater than 3 days.

Third, storms are categorized as tropical cyclones or hurricanes de-
pending of the wind speed value. If 10-m over the surface maximum
wind speed reach or exceeds, respectively, 17m s−1
and 29.5m s−1
,
storms are referred as tropical cyclones and hurricanes. Hurricane
minimum wind speed value is chosen over the standard criteria,
vsfc > 33m s−1
, due to limited horizontal resolution, as proposed in
Walsh et al. (2007). Note that the absolute number of tropical cy-
clones and hurricane depends of wind-speed threshold that has been
chosen, as well as GCM ability to simulate the full tropical cyclone
intensity distribution (as 50-km horizontal resolution does not simu-
late storms with very high wind speed, vsfc > 45m s−1
).
2.3 Simulations description
For all simulations the reference climate has a solar constant of
1400 Wm−2
, a CO2 concentration of 300 ppm and a maximum ocean
heat ﬂux convergence of 40 Wm−2
, consistent with the control sim-
ulation (Merlis, Zhao, and Held, 2013). In order to investigate the
relative importance of direct and temperature-dependent solar forc-
ing to greenhouse gases forcing on tropical cyclone frequency and
intensity, a set of perturbation experiments are run for all simula-
tions. Therefore, we have carried out simulations with perturbed
solar constant and perturbed greenhouse concentration from refer-
ence. The climate is perturbed by 50 Wm−2
, hence the lowest solar
constant is chosen to be 1350 Wm−2
, the highest is 1450 Wm−2
. The
climate simulations forced by GHG concentration is run with a con-
centration of 1200 ppm, which is a 4 times CO2 forcing compared

2.3. Simulations description 19
-100 -50 0 50 100
Latitude
2
4
6
8
10
12
14
∆R
TOA
net
[Wm
-2
]
pF
S1450 - S1400
4xCO
2
- S1400
FIGURE 2.1: Net Radiation at TOA in slab ocean solid
line, prescribed SSTs dashed line, and dash-dot line ex-
periments, with So = 1400 Wm−2

to the climate reference. This forcing has been chosen, so it corre-
sponds to the same forcing as the highest solar constant. The differ-
ence in global mean of net radiation at the top of the atmosphere for
each perturbation simulation with their respective reference simula-
tion (i.e. radiative forcing) is listed in Table 2.1 and the spatial pat-
tern is shown in Figure 2.1. The radiative forcing is close to 8 Wm−2
for both 1450 Wm−2
and 4xCO2 simulations. The global-mean TOA
radiation change is closer to 1 Wm−2
for the slab-ocean simulations
with increased radiative forcing. This indicates that these simula-
tions are close to equilibrium, but a 5-year spin up is not sufﬁcient to
obtain a true equilibrium.
Three prescribed-SST experiments were run :
1. pF simulations have ﬁxed SSTs from the reference SOM simu-
lation and perturbed radiative forcing. This allows the direct
change in TCs from radiative forcing to be examined.
2. T4K experiment is a set of simulations which have prescribed
SSTs from the equilibrium state of S1450 SOM simulation (S4K)
and 4xCO2 SOM simulation (C4K). This experiment is analo-
gous to the uniform plus 2K simulation of Zhao et al. (2013) but
includes the patterned of SST change simulated by slab-ocean
GCM.
3. BOTH have prescribed SSTs from the equilibrium state of S1450
and 4xCO2 SOM simulation and the climate is perturbed by 50
Wm−2
(high solar + S4K, hereafter SS4K) and 1200 ppm (4xCO2
+ C4K, hereafter CC4K) respectively.
The next chapter presents the tropical climate changes in this set of
simulations, including the changes in tropical cyclone frequency and
the mean climate changes that underlie the TC changes. The use
of aquaplanet climate model will allow us to investigate the role of

2.3. Simulations description 21
Solar SOM pF
1350 -0.9 -7.9
1450 1.1 7.9
CO2 SOM pF
1200ppm 1.1 7.6
TABLE 2.1: ∆( ¯R), with ¯R the global mean of net TOA
radiation
patterned SST change between solar and CO2 forcing.

23
Chapter 3
Tropical Cyclone Response to
greenhouse and solar forcing
3.1 Introduction
In this section, our goal is to understand if the solar forcing has
more or less of an impact on tropical storms and hurricanes activ-
ity than does greenhouse gas forcing (CO2 only). In addition, some
of the most important environmental variables will be examined to
understand their impact on TC activity.
3.2 TC Frequency
Figure 3.1 shows global TC frequency varies for each simulation.
It has been shown in Chapter 2 that the highest solar constant (1450
Wm−2
) has about the same radiative forcing as the radiative forcing
when quadrupling CO2 concentration (8 Wm−2
). Figure 3.1 shows
that the global-mean surface temperature for theses simulations, in
the SOM experiment, are the same (i.e., 288 K). However, tropical
sea surface temperature changes do not have the same pattern for
the highest solar constant and quadrupling CO2 in the SOM exper-
iment (see Figure 3.2). Comparing these simulations should give

24
Chapter 3. Tropical Cyclone Response to greenhouse and solar
forcing
280 281 282 283 284 285 286 287 288 289 290
Ts
(K)
280
300
320
340
360
380
400
420
440
N(numberstormperyear)
S1350
S1400
S1450
4xCO2
SOM
pF
T2K
BOTH
FIGURE 3.1: Number of TCs per year against global-
mean surface temperature in Kelvin for all sets of sim-
ulations
an understanding of how radiative forcing from CO2 affects TC fre-
quency differently than solar radiative forcing. While comparing the
response simulated in BOTH with the combined responses from T4K
and pF leads to an understanding of the linear additivity of these two
changes. The response in BOTH can also be compared to the cor-
responding SOM simulations to see if the prescribed-SST boundary
condition introduces biases in the simulated changes.
The simulations suggest a non-linear decrease of TCs with increas-
ing radiative forcing for prescribed SSTs experiments. Plus symbols,
which represent fixed SSTs simulations, have greater TCs per year
for the lowest solar constant and fewer for higher solar constant and
high CO2 concentration. As shown in Table 3.2, the direct effect of
radiative forcing is a decrease in TC frequency, with 6.5% less TC
when quadrupling carbon dioxide, while only 0.8% decrease when
the solar constant is increased by 50Wm−2
. A change of this magni-
tude may not be statistically significant but suggest a TC frequency
changes are more influenced by GHG forcing than solar forcing.

3.2. TC Frequency 25
1
<N>
∂<N>
∂So
≈ −0.8%
1
<N>
∂<N>
∂CO2
≈ −6.5%
The T4K experiment (S4K and C4K simulations) shows increasing
SSTs in insolation increases TC frequency (respectively, +6% and +12%,
for S4K and C4K).
Finally, in SOM experiments, x symbols in Figure 3.1, there is an
increase of the number of TCs per year with the combined effect of in-
creased radiation and mean sea surface temperatures. TC frequency
are respectively +9% and +16% higher for high solar and 4xCO2 in
SOM simulations. Hence, increased solar constant and altered GHG
forcing do not lead to the same response in global TC frequency.
As stated in Chapter 1, results from Held and Zhao (2011) and
Zhao et al. (2013) suggests a global decrease in TC number (≈ -20%)
which is explained by the linear additivity of the 10% decrease in
TC number when CO2 is doubled and the 10% decrease in TC num-
ber when SSTs are increased by 2 K. However, our results suggest
that when studied separately the direct radiative forcing and the SST
forcing cannot explain the increase in TC frequency as the climate
warms. From Figure 3.1 and Table 3.1, CC4k and 4xCO2 slab-ocean
simulations have almost the same TC number per year. Also from Ta-
ble 3.2, CC4K result is the sum of C4K and pF4xCO2 . However, SS4K
has ≈ 4% more TC frequency and the 1450 Wm−2
slab-ocean simu-
lation has ≈ 9% increase. The separated effect on TC frequency of
SSTs and radiative forcing, when combined (BOTH), is greater than
from the slab-ocean. This suggests that the time-dependent SST ﬂuc-
tuations in the SOM simulations would also need to be prescribed,
in addition to the time-mean SST, to more precisely reproduce the
simulated TC changes.

26
forcing
Solar SOM pF S4K
1350 263 405.8
1400 364.4 397 420.5
1450 397.8 393.9 411.8
CO2 SOM pF C4K
300ppm 364.4 397 445.6
1200ppm 421.4 371 422.5
TABLE 3.1: Number of TCs per year for all sets of sim-
ulations
Solar SOM pF S4K
1350 -27.8 2.2
1400 0 0 5.9
1450 9.2 -0.8 3.7
CO2 SOM pF C4K
300ppm 0 0 12.2
1200ppm 15.6 -6.5 6.4
TABLE 3.2: % change of number of TCs per year for all
sets of simulation. T4K and BOTH experiments use pF
reference
It has been shown in Chapter 2 that the highest solar constant (1450
Wm−2
) has a similar radiative forcing to the radiative forcing when
quadrupling CO2 concentration (about 7.7 Wm−2
globally). Figure
3.1 shows that the global-mean surface temperature for theses simu-
lations, in the SOM and T4K experiments, are the same (i.e., 288 K).
However, Figure 3.2 that the zonal-mean SSTs are different.
Merlis, Zhao, and Held (2013) have shown that ITCZ location change
can affect the frequency sensitivity of TCs. They found a 24% in-
crease in hurricane frequency for a one degree latitude shift in the

3.2. TC Frequency 27
0 2 4 6 8 10 12 14 16 18 20
Latitude
3
3.5
4
4.5
5
5.5
∆Ts
S1450 - S1400
4xCO
2
- S1400
FIGURE 3.2: Difference in zonal mean SSTs between
simulations and reference simulation in the slab-ocean
experiment
ITCZ. Consistent with those results, the CO2 has greater shift than
So, as shown in the next section.
In Figure 3.3, the direct effect of radiative forcing shows, for cli-
mate warmed by solar constant forcing, an increase (decrease) in
number of TCs per year with estimated maximum sustained 10-m
wind speed (MWS) smaller (greater) than 22 ms−1
. However, there
is less TCs in all MWS category when climate is forced by GHG. In
SOM experiments, results are a lot different from pF experiments.
Indeed, there is an increases TCs per year in all MWS category when
climate is warmed whether it is by solar or CO2 forcing. This result is
consistent with the greater TC frequency in a warmer climate. How-
ever, Figure 3.3 shows that BOTH experiment results are similar to
T4K experiments but does not capture well SOM experiments.

28
forcing
15 20 25 30 35 40 45 50
Maximum surface wind [m s-1
]
0
0.1
0.2
0.3
0.4
Probability
SOM
pF
T4K
BOTH
15 20 25 30 35 40 45 50
'Maximum surface wind [m s -1
]
0
0.1
0.2
0.3
0.4
Probability
15 20 25 30 35 40 45 50
]
0
50
100
150
200
N[#TCyr-1
]
15 20 25 30 35 40 45 50
]
0
50
100
150
200
N[#TCyr-1
]
FIGURE 3.3: Probability of TC and Number of TCs per
year against maximum wind speed. Upper panel is for
solar while lower panel is for 4xCO2
3.3 Changes in Circulation and Precipitation
3.3.1 Hydrological cycle
Figure 3.4 shows the response of precipitation against latitude for
all experiments. Direct response of precipitation when radiatively
forced is a decrease. Indeed, the direct effect of 50 Wm−2
solar forcing
leads to a ≈ 2% decrease while direct effect of quadrupling CO2 leads
to ≈ 6% decrease of the maximum precipitation. When forced by
SSTs, direct response of precipitation is an increase of ≈ 3.5% and 2%
in S4K and C4K simulations respectively (when compared against
reference prescribed-SSTs simulation; pFS1400). However, T4K ex-
periment captures well the northward shift of the maximum value
of precipitation. In slab-ocean simulations the shift is bigger when
the climate is radiatively forced by CO2 rather than solar constant.
T4K simulations also show, as in slab-ocean simulations, 4% greater

3.3. Changes in Circulation and Precipitation 29
0 5 10 15 20
Latitude
0
5
10
15
20
25
precip(mmday
-1
)
Slab-Ocean
0 5 10 15 20
Latitude
0
5
10
15
20
25
pF
S1350
S1400
S1450
4xCO2
0 5 10 15 20
Latitude
0
5
10
15
20
25
30
T4K and BOTH
C4K
S4K
SS4K
CC4K
FIGURE 3.4: Precipitation in mm/day against latitude
for all experiments
northward shift when CO2 is quadrupled. Similar results between
T4K and BOTH experiments suggest that radiative forcing has a greater
impact on precipitation rate than SST forcing. Indeed, the maximum
value for S4K, SS4K are ≈ 25 mm/day. In slab-ocean simulations,
precipitation is greater for higher solar constant, however there is a
large decrease when CO2 is quadrupled. However, SST forcing has a
greater impact on the location of maximum precipitation.
Figure 3.5 shows the response of evaporation against latitude for
all experiments. Results suggest less evaporation in response of di-
rect radiative forcing. Evaporation changes as precipitation changes
in a climate radiatively force leads to the same ≈ 2% and 6% decrease,
when forced respectively by high solar constant and high CO2 con-
centration. Slab-ocean simulations show an increase in evaporation
as climate warms, in opposition with the direct effect of radiative
forcing. T4K experiments correspond to changes in SSTs when cli-
mate is forced by high solar constant and high CO2 concentration,
we have not performed experiments for colder SSTs, but T4K exper-
iments suggest an increase of evaporation as climate gets warmer,

30
forcing
0 5 10 15 20
Latitude
3
3.5
4
4.5
5
5.5
6
6.5
E[mm/day]
Slab-Ocean
0 5 10 15 20
Latitude
3
3.5
4
4.5
5
5.5
6
pF
S1350
S1400
S1450
4xCO2
0 5 10 15 20
Latitude
4
4.5
5
5.5
6
6.5
T4K and BOTH
C4K
S4K
SS4k
CC4K
FIGURE 3.5: Evaporation in mm/day against latitude
for all experiments
consistent with intuition from the temperature dependence of the
turbulent ﬂux formulae. BOTH experiments are consistent with the
combined response of the direct forcing (pF) and SST only (T4K) per-
turbation simulations.
However, as the climate warms, we have seen that direct response
of precipitation and evaporation when the climate is radiatively forced
is opposite to the response of it in slab-ocean simulations. This sug-
gests the relative contribution of radiative forcing and SST forcing are
not the same. Indeed, A.1 shows SSTs might have a greater impact on
changes in precipitation minus evaporation. Moreover, BOTH simu-
lations is slightly different than slab-ocean simulations. Hence lead-
ing to the conclusion that although the direct effect of radiative forc-
ing and SST forcing on precipitation and evaporation could be ex-
amined separately to explain slab-ocean, it has to be reminded than
these two forcing do not have the same contribution.

3.3. Changes in Circulation and Precipitation 31
3.3.2 Hadley Circulation
Hadley circulation is the mass transport by southward compo-
nent of the trade wind flow in the lower troposphere leading to a
convection zone at the equator and poleward mass transport in the
upper troposphere, with a new sinking branch 30◦
N and S. Know-
ing the mass divergence in the meridional plane is zero because of
mass conservation, the streamfunction (ψ) is a scalar representing a
volumetric flux. It is a representation of the time-mean atmospheric
circulation. Figure 3.4 shows the maximum value of the streamfunc-
tion at 600-hPa and Table 3.3 shows the % change of the maximum
value of the streamfunction in altered climate.
The maximum value decreases as the net radiative forcing increases
for all experiments. The direct effect of radiative forcing on the Hadley
circulation is negligible, but the direct effect of SST forcing is sub-
stantial (≈ -30%, see Table 3.3). Moreover, in the SOM experiment
the maximum value is shifting northward. This northward shift is
well captured by T4K (and BOTH) experiments.
δφSo ≈ 2.9%
δφCO2 ≈ 3.7%
Results (Figure A.2 and others not shown) also suggest that north-
ward mass flux from -5 to 10◦
is greater when radiatively forced by
CO2 compared to solar constant. Thus, circulation within the tropics
is reduced in altered climates.
Finally, differences in circulations between BOTH and slab-ocean
simulations lead to the conclusion that there is a combined effect in
SOM that is not capture in BOTH. Thus, the time-dependent SST
fluctuations in the SOM simulations contributes to simulated circula-
tion changes. To capture well these changes, time-mean SST used in

32
forcing
13 14 15 16 17 18 19 20
Latitude
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Maxstreamfunctionvalue
×10
11
S1350
S1400
S1450
4xCO2
SOM
pF
T4K
BOTH
FIGURE 3.6: Maximum value of streamfunction at 600-
hPa
the BOTH experiment should be time-dependent to best reproduce
the simulated circulation changes.
Solar SOM pF S4K
1350 29.8 0.25
1400 -31.5
1450 -30.1 -2.9 -31.9
CO2 SOM pF C4K
300ppm -36.1
1200ppm -35.8 -3.6 -38.2
TABLE 3.3: % change of the maximum value of the
streamfunction. T4K and BOTH percentages are com-
pared to pF reference simulation.

3.4. Changes in Genesis and the Tropical Environment 33
3.4 Changes in Genesis and the Tropical En-
vironment
3.4.1 Genesis Potential Index
To understand how genesis is going to change in altered climates
and why, we have computed the genesis rate from the GCM and the
genesis potential index. The genesis potential index (GPI) is based on
the environmental requirement for TC to form, described in Chapter
1. It can be computed by two different methods both developed by
Kerry Emanuel:
GPI2010 = |η|3
χ−4
3 max((PI) − 35m s−1
), 0)2
× (25m s−1
+ Vshear)−4
(3.1)
GPI2004 = |105
η|
3
2 (RHmid/50)3
(
PI
70
)3
(1 + 0.1 × Vshear)−2
(3.2)
In GPI2010, η is the absolute vorticity, χ the moist entropy deficit,
PI the potential intensity and Vshear the vertical wind shear. GPI2004
uses the relative humidity of the mid-troposphere (RHmid) instead of
the moist entropy deficit. Each of these environmental variables will
be further described later on in this chapter.
High values of the GPI can be due to greater potential intensity
(PI), relative humidity and absolute vorticity, as well as low values of
saturation deficit of mid-troposphere and vertical wind shear. While
the GPI captures relatively well the genesis in prescribed SSTs exper-
iments, it does not in the SOM experiment (see Appendix A, Figures
A.3 to 6).
Figure 3.7 compares only high solar to high CO2 simulations for

34
forcing
0 2 4 6 8 10 12 14 16 18 20
Latitude
0
10
20
30
40
50
60
70
80
90
100
#TCyr-1
lat-1
S1400
S1450
4xCO
2
FIGURE 3.7: GCM genesis, solid line, versus GPI2010,
dashed line for pF
the pF experiment. GPI seems to represent well genesis in the ref-
erence climate and in altered climates, when multiplied by a con-
stant chosen to give a similar genesis rate as in the control simulation
(genesis ≈ GPI ∗ 1018
).
However, in SOM experiments GPI does not capture magnitude
or changes in genesis. For the GPI to ﬁt with the genesis in reference
climate, the constant is not the same as in pF experiment. Also, GPI
does not capture the genesis changes in altered climate. Figure A.4
and A.6 show that increasing solar constant or GHG concentration
lead to substantially greater GPI, with a maximum index for 4xCO2
simulation, however, actual genesis does not show an increase of
that magnitude. GPI also overestimates the northward shift of the
genesis in these climates. Results (see Appendix A) show that an in-
crease by 4 K in SSTs lead to a ≈ 4◦
N shift (with greater shift for the
C4K simulation). This northward shift is consistent, and of the same
magnitude, with the northward shift of the maximum value of the
streamfunction. The direct effect of increasing radiation by 50 Wm−2
is a decrease in the genesis, with greater decrease when GHG induce.

In all experiments the genesis peak is greater for the high solar simu-
lations compared to high CO2 concentration. However, results show
a broader genesis range in the T4K and SOM experiments, which
could explain greater TC frequency for 4xCO2 simulations. It seems
that SSTs have a bigger impact on TC frequency than the direct re-
sponse from a change in radiation.
While the GPI does not capture the simulation results well, and
could potentially be improved by recalibrating the parameters. Rather
than pursuing this, we simply examined individual environmental
factors that comprise the index.
3.4.2 Vorticity
We know that TCs do not develop spontaneously. Indeed, TCs
need great absolute vorticity to have synoptic low-level convergence
and the associated convective to be able to form. Gray (1968) showed
that upward motion of air from low-level is important for the pro-
duction, by condensational heating, of an anomalously warm vortex.
The absolute vorticity, η, is calculated as the sum of relative vor-
ticity, ζ, and Coriolis parameter, f, as follows : η = ζ + f. The rel-
ative vorticity ζ = ∂v
∂x
− ∂u
∂y
. The Coriolis parameter is deﬁned as
f = 2Ωsinφ, Ω = 7.292 ∗ 10−5
rad s−1
is the angular speed of rota-
tion of the earth and φ the latitude in radians. In SOM experiments,
most of the genesis happens between 10◦
and 15◦
N. Results show in
that region an increase in relative and absolute vorticity as radiative
forcing increases as well as a northward shift of the maximum value.
Results of direct effect of radiative forcing are not conclusive when

36
forcing
we look at the zonal mean, indeed, changes are quite small. How-
ever, values from genesis weighted absolute vorticity show a clear in-
crease as the forcing increases, with lower value when CO2 is quadru-
pled compared to the highest solar forcing. Temperature-dependent
change of +4 K in SSTs also leads to an increase in genesis weighted
values of absolute vorticity, with 5% lower value for S4K (and SS4K)
compared to C4K (and CC4K) that is consistent with the more mod-
est ITCZ shift.
In all experiments, result from mean genesis weighted η suggest
direct increase of CO2 forcing has more impact than solar forcing on
vorticity.
3.4.3 Moist entropy deficit
As stated in Chapter 1, TCs need high relative humidity in the mid-
troposphere to form, hence dry air in the middle troposphere restrain
low-level moisture. The χ parameter used in the GPI, is a measure of
the saturation deficit of the moist entropy in the middle troposphere,
so that it quantifies the relative importance of subsidence across the
boundary-layer top as compared to the effect of surface fluxes on the
boundary layer entropy. χ is the moist entropy deficit of the middle
troposphere and is computed as a ratio : χ = h −hm
ho −h
or χ = Sm −Sm
So −Sb
Where, h and Sm are, respectively, the saturation moist static en-
ergy of free troposphere and entropy at 600 hPa; hm and Sm are, re-
spectively the actual moist static energy and entropy of middle tro-
posphere; ho and So are, respectively, the saturation moist static
energy and entropy at sea surface ; Sb is the entropy of the boundary
layer.
High value of χ means the term above has higher value or the

term below has lower value. High value of h −hm and Sm −Sm
means mid-troposphere levels are relatively dry and for convection
to moisten it, sub-saturated mid-levels require relatively longer in-
cubation periods. Additionally, lower value of ho −h and So −Sb
indicates a reduction in ocean-to-air fluxes, diminishing boundary
layer support for convective inflow (Rappin, Nolan, and Emanuel,
2010)
For our calculation I have chosen to calculate χ with the moist
static energy (MSE) instead of entropy. MSE is defined as follows1
: h = cpT + gz + Lvq, where for h , T is the temperature of free tro-
posphere, z is the height of free troposphere, qs is saturation mixing
ratio and for sea-surface ho , T is the SST and z is 0. Since the moist
static energy depends strongly on the surface temperature, in fixed-
SST experiments changes cannot be important.
In SOM experiment, in the mid-troposphere MSE increases slightly
and linearly, by ≈ 4%, as the forcing increases, by 50Wm−2
leading
greater static stability in the atmosphere. When high solar and high
CO2 are compared, MSE is ≈ 0.3% greater for CO2 forcing. In pF ex-
periments, MSE increases even more slightly, and non-linearly. Di-
rect effect of +4 K on SSTs also shows a slight increase, greater for
C2K. Thus, as the climate warms, through radiative or SSTs forcing,
there is less favorable conditions for upward motion.
In pF experiment, as climate warms both of the numerator and
denominator of χ work together to have higher value of the moist
entropy deficit : there is less boundary layer MSE source (hence less
convective inflow since So −Sb decreases), even more for 4xCO2
simulation (-2%) and drier air in mid-troposphere level (even more
1
Cp is the specific heat at constant pressure, Lv is the latent heat of vaporization,
T is the absolute temperature, z is the height and g is the gravitational acceleration

38
forcing
0 5 10 15 20
Latitude
0.2
0.4
0.6
0.8
1
1.2
1.4
χ
SOM
0 5 10 15 20
Latitude
0.7
0.8
0.9
1
1.1
1.2
1.3
χ
pF
S1350
S1400
S1450
4xCO
2
0 5 10 15 20
Latitude
1.1
1.15
1.2
1.25
1.3
1.35
1.4
χ
T4K and BOTH
C4K
S4K
SS4K
CC4K
FIGURE 3.8: Moist entropy deficit against latitude for
all simulations. Dashed lines in the third panel are for
the BOTH experiment
for 4xCO2, while solar change is really small). The effect of increas-
ing SSTs lead to more ocean to air fluxes, and there is a larger in-
crease where the genesis happens when CO2 is quadrupled. There is
slightly longer incubation period so a drier mid-troposphere in the
T4K experiment. In SOM experiments, there is more convective in-
flow and drier mid-tropospheric air as the warmer altered climates.
However changes in the numerator are less significant. In all simula-
tions, as the climate gets warmer, the mid-troposphere have greater
saturation deficit, hence leading to a less favorable environment for
TC to form. It can be seen again that the BOTH experiment does not
have the same value as the SOM experiment, thus supporting the
idea that forcings cannot be separated. Nonetheless, SSTs seems to
have a greater contribution for changes in χ since T4K experiment
show closer value to SOM than pF does.

3.4.4 Potential Intensity
The maximum potential hurricane intensity (PI) has been devel-
oped by Dr. Kerry Emanuel and described in Bister and Emanuel
(1997). Based on thermodynamics state of atmosphere and ocean, it
corresponds to the maximum sustainable intensity (maximum winds
and minimum central pressure) of a tropical cyclone or hurricane.
The PI theory considers TC as a closed system in which heat energy
is converted to mechanical energy, thus the TC acts as a Carnot heat
engine, using the ocean as a source of its energy. Schematically, it as-
sumes an isothermal inflow of near-surface air, which is kept isother-
mal due to sensible heat flux from the underlying water (since pres-
sure is dropping towards TC center, and it is cooled due to evapora-
tion). In the eyewall air rises on the moist adiabat, along constant an-
gular momentum surfaces, which outflows at the top of the "Carnot
TC", near the tropopause. Since it is a closed system, it is assumed
that far from the TC center, cooled air sinks and return adiabatically
to the TC environment.
Maximum sustainable wind is defined in Bister and Emanuel (2002)
as V 2
max = Ts
T0
Ck
Cd
[CAPE −CAPE]m ; where Ts is the SST, T0 the out-
flow layer temperature and CAPE are, respectively, the convective
available potential energy of lifted surface saturated air, in reference
to the environment, and convective available potential energy of air
from boundary layer at the radius of maximum winds (RMW).
Beside some critiques (Smith, Montgomery, and Vogl, 2008; Camp
and Montgomery, 2001) others have suggested good agreement be-
tween PI theory and observations (Tonkin et al., 2000). Potential in-
tensity is sensitive to the ratio of the enthalpy transfer coefficient to

40
forcing
drag coefficient. As I have computed the potential intensity with dif-
ferent values for Ck
Cd
ratio, results suggest that an increase by 0.1 unit
of the value of Ck
Cd
, leads to greater maximum predicted wind speed
Vmax by ∼ 5% because higher drag coefficient leads to lower the ra-
tio, physically causing more resistance. I have chosen the ratio to be
Ck
Cd
= 0.6 since it is the value used in GCM. The potential intensity, as
well as CAPE, shows opposite behaviour when comparing SOM and
pF experiments (Figure 3.9).
1. In SOM experiments, PI and CAPE increase when solar con-
stant increases. There is little difference between S1450 simula-
tion and 4xCO2 simulation.
2. pF experiment results show that the direct change of PI to ra-
diative forcing is a decrease, and this decrease is greater when
radiatively forced by GHG than solar forcing.
3. T4K experiments show that the temperature-dependent change
of PI is an increase, with greater values between 0 and 12◦
N
for S4K and greater value northward for C2K. So the north-
ward shift of the maximum value is more influenced by SSTs
when climate is altered by CO2 than solar. Since PI values from
T4K simulations are closer to BOTH than PI values from pF
simulations. This suggests SST changes contribute more than
radiative forcing changes to PI changes. More over, PI values
and changes in BOTH simulations are similar to SOM simula-
tions, hence leading to the conclusion that changes in PI can be
understood by considering separately the individual contribu-
tions from the change in radiative forcing and change in SSTs.

0 5 10 15 20
Latitude
35
40
45
50
55
60
65
70
PI[ms-1
]
Slab-Ocean
0 5 10 15 20
Latitude
40
45
50
55
60
65
pF
S1350
S1400
S1450
4xCO2
0 5 10 15 20
Latitude
54
56
58
60
62
64
66
68
T4K and BOTH
C4K
S4K
SS4K
CC4K
FIGURE 3.9: Potential intensity against latitude for all
simulations. Dashed lines in the third panel are for the
BOTH experiment
3.4.5 Vertical Wind Shear
As described in Chapter 1, the vertical wind shear is unfavourable
for TC genesis and intensiﬁcation (Zeng, Wang, and Chen, 2010).
Vertical wind shear (VWS) can tilt and destroy the storm’s core struc-
ture. There are both thermodynamic and dynamic reason for it. As
stated before, TCs are heat engines using warm ocean as a heat and
moisture source. Gray (1968) showed that vortex must be anoma-
lously warm throughout the troposphere hence large value of wind
shear can prevent TCs to develop due to unfavourable conditions
for warm and moist surface ocean’s air to be dragged in by the TC
and ventilation of upper-air heat anomaly present. Also, shear is un-
favourable to convection.
The wind shear is the change of the wind’s speed or direction in
the atmosphere and is usually deﬁned as the difference between 850
hPa and 200 hPa. The magnitude of the difference between the wind

42
forcing
vector at those two levels is given by:
Vshear = (u200 − u850)2 + (v200 − v850)2 (3.3)
where u represent the zonal wind and v the meridional wind.
All results (see Figure A.7) show minimum values of shear is lo-
cated with the maximum value of TC genesis in latitude. The mini-
mum value is decreasing as climate warms, in SOM and pF exper-
iments. While in SOM this result is in agreement with increased
TC frequency, in pF this result is inconsistent with decreased TC fre-
quency.
1. In SOM experiment, at 200 hPa and 10◦
N, zonal component of
the wind is positive only for the lowest solar simulation (1350Wm−1
)
hence blowing from the west, while negative for all other simu-
lations, hence blowing from the east. At 850 hPa, only 1350 and
1400 Wm−2
simulations show easterly wind while in warmer
climate wind blows from west. The magnitude of u200 − u850
decreases as climate gets warmer in upper troposphere while
increases in lower troposphere (≈ at 400 hPa). The magnitude
of v200 −v850 shows the same pattern but the changes happen at
lower level (≈ at 850 hPa).
2. prescribed SSTs experiment does not show any consistent trend
when climate warms.
Vertical wind shear does not seem to be a good predictor for TC fre-
quency. Since the height of the tropopause is not ﬁxed and changes,
it is possible that VWS could be a better predictor when computed
with an upper-tropospheric level that changes with climate.

3.5. Summary 43
3.5 Summary
The overall increase, as climate warms, in global TC frequency
seen in SOM simulations in altered climates cannot be explained as
a linear combination of direct radiative forcing and direct SST forc-
ing. Also climate altered by solar or GHG do not lead to the same
response for TC activity. Each environmental variable have been
studied separately in altered climate. Also, to examine the relative
importance of each physical variable on TC frequency, I have com-
puted their fractional change (Figure 3.10, 3.11 and A.8). Each vari-
able is genesis weighted, as followed : ([field]×genesisfrequency)
(genesisfrequency)
; with
[field] the time, zonal latitudinal mean of the variable.
For ω500 positive values are ignored, so that only ascending mo-
tion is taken into account. In Held and Zhao (2011) paper ω500 is well
correlated with TC changes. Held and Zhao (2011) have used ﬁxed
sea surfaces temperatures to compare the direct effect of doubling
CO2 and increase 2 K SSTs alone. They suggest a decrease in as-
cending air motion, consistent with the decrease in TC frequency. pF
experiments agree with Held and Zhao (2011) results. While −ω500
decreases in all experiments when climate is warmed, it seems cor-
related only in the pF experiment (see Figure 3.11).
The vertical shear index in Held and Zhao (2011) paper shows a
negative factional change in both hemisphere when genesis-weighted
averaged (with a higher, although still small, negative value for the
Southern Hemisphere). Our results suggest VWS does not seem to be
a good predictor for TC frequency since changes of shears in altered
climates are inconsistent with TC frequency change. Thus, we con-
clude that VWS index cannot be used to explain the future changes
in TC activity.

44
forcing
P -χ PI -S -ω
500
η TC
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
FractionalChange
Slab-Ocean
S1350
S1400
S1450
4xCO2
FIGURE 3.10: Fractional change of mean TC genesis
weighted precipitation (P), minimal potential pressure
(Pmin), potential intensity (PI), environmental shear
(S), upward vertical wind at 500-hPa (ω500), relative
vorticity at 850-hPa (ζ850) and global number of TCs
per year (TC).
P -χ PI -S -ω
500
η TC
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
FractionalChange
SOMS1450
SOM4xCO
2
pFS1450
pF4xCO
2
C4K
S4K
SS4K
CC4K
FIGURE 3.11: Fractional change of mean TC genesis
per year (TC).

3.5. Summary 45
The moist entropy deﬁcit also seems to be well correlated with TC
change in pF experiments, while uncorrelated or negatively corre-
lated in other experiments, as shown by Figure 3.10 and A.8.
The genesis-weighted globally averaged of PI is well correlated
with the TC frequency. The direct effect of radiative forcing on PI is
a decrease while the direct effect of SST forcing on PI is an increase.
These results are consistent with Held and Zhao (2011) that suggest
a positive fractional change for PI when SSTs are increased and when
both SST and CO2 are increased. Contrary to Held and Zhao (2011)
results that suggest a decrease in TC frequency in all their experi-
ments, our results suggest only a decrease in TC frequency when cli-
mate is radiatively forced (pF experiments). PI depends on temper-
ature, pressure and relative humidity, these environmental variables
changes in altered climate could be good predictors for TC changes.

47
Chapter 4
Conclusions
The purpose of this thesis was to examine the response of tropical
storm activity and frequency in different perturbed climates, and to
understand the difference between direct solar forcing, SST changes,
and greenhouse gas forcing (CO2 only) on TC activity. Also, we have
examined differences between results from direct forcing, added forc-
ing and slab-ocean model, to understand the relative importance of
each forcing and if there is linear additivity, as suggested by Held
and Zhao (2011). To the best of our knowledge, this is the ﬁrst anal-
ysis of the TC response to closely compare different single radiative
forcing agent changes in a TC-permitting GCM.
Results leave evidence of greater TC frequency, intensity and pre-
cipitation in warmer climate (except when radiatively forced only).
Environmental variables changes such as PI, η and streamfunction
can explain changes in TC frequency in all experiments. However
a lot a environmental variables changes in altered climates are not
consistent with TC frequency changes. Among these variables, χ
which is detrimental to TC genesis, shows an increase when climate
is warmed, which should lead to a decrease in TC genesis. VWS and
ω500 also failed to explain TC changes in altered climate. Implying
there might be other factors inﬂuencing TC genesis.

48 Chapter 4. Conclusions
However, the direct effect of radiative forcing on χ and ω500 is con-
sistent with TC frequency changes in pF experiments.
We have shown that solar forcing and greenhouse gas forcing leads
to different TC activity changes. Figure 4.1 summarizes these changes
for each environmental variable playing a role in TC activity. Results
suggest both the direct and the temperature dependent responses are
different for solar forcing and greenhouse gas forcing.
It has been shown that quadrupling CO2 usually leads to a greater
response of environmental variables and TC changes than increasing
the solar constant. These simulations have about the same amount of
global-mean radiative forcing. However, the spatial pattern of these
forcing is different, and this difference is potentially important in ex-
plaining differences in both the tropical circulation and TC genesis
response between radiative forcing agents.
The direct effect of radiative forcing shows an opposite response
to SST changes for most of environmental variable. While BOTH
experiments’ results are distinct from the comprehensive boundary
condition simulations in Held and Zhao (2011). Here, we suggested
there can be departures from linear additivity of the forcing and SST
changes. Comparison with the SOM experiment suggests that time
dependence of SST ﬂuctuations may need to be prescribed in T4K
and BOTH experiments in order to better reproduce TC changes.

49
Appendix A
Additional Figures

50 Appendix A. Additional Figures
0 2 4 6 8 10 12 14 16 18 20
-10
-5
0
5
10
15
20
25
P-E[mmday-1
]
4xCO2
SOM
pF
C4K
BOTH
0 2 4 6 8 10 12 14 16 18 20
Latitude
-10
-5
0
5
10
15
20
25
P-E[mmday-1
]
High Solar
FIGURE A.1: Precipitation minus Evaporation in
mm/day for each simulations with high CO2 concen-
tration (upper panel) and high solar constant (lower
panel)
S1450 - S1400
-30 0 30
Latitude
200
800
Pressure(hPa)
-4
-3
-2
-1
0
1
2
3
4
5
4xCO2
- S1400
-30 0 30
Latitude
200
800
Pressure(hPa)
-5
-4
-3
-2
-1
0
1
2
3
4
5
FIGURE A.2: Streamfunction differences from ref-
erence simulation in pF experiment, for S1450 and
4xCO2 simulations

Appendix A. Additional Figures 51
6 8 10 12 14 16 18 20
Latitude
0
0.5
1
1.5
2
2.5
3
GPI
×10
-16
SOM
pF
C4K
BOTH
6 8 10 12 14 16 18 20
0
1
2
3
4
GPI
×10-16
SOM
pF
SK4
BOTH
FIGURE A.3: Genesis Potential Index (equation 3.1)
against latitude for each experiment. Upper panel for
climate altered by solar constant and panel below for
climate altered by GHG.
0 2 4 6 8 10 12 14 16 18 20
Latitude
0
50
100
150
200
250
300
350
400
GPI
S1400
S1450
4xCO2
SOM
pF
T4K
BOTH
FIGURE A.4: Genesis Potential Index against latitude
for all simulations

52 Appendix A. Additional Figures
0 2 4 6 8 10 12 14 16 18 20
Latitude
0
10
20
30
40
50
60
70
80
90
100
#TCyr-1
lat-1
S1400
S1450
4xCO
2
SOM
pF
T4K
BOTH
FIGURE A.5: Genesis against latitude for all simula-
tions
0 2 4 6 8 10 12 14 16 18 20
Latitude
0
50
100
150
200
250
#TCyr-1
lat-1
S1400
S1450
4xCO
2
GPI
Genesis
FIGURE A.6: Genesis and GPI against latitude for
SOM simulations

Appendix A. Additional Figures 53
0 10 20
Latitude
0
5
10
15
20
25
VWS[ms
-1
]
Slab-Ocean
0 10 20
Latitude
0
5
10
15
20
25
pF
S1350
S1400
S1450
4xCO2
0 10 20
Latitude
0
2
4
6
8
10
12
14
16
18
20
T4K and BOTH
C4K
S4K
SS4K
CC4K
FIGURE A.7: Vertical Wind Shear against latitude for
all experiments
P -χ PI -S -ω
500
η TC
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
FractionalChange
pF
S1350
S1400
S1450
4xCO2
FIGURE A.8: Fractional change of mean TC genesis
per year (TC).

55
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