Download ESTIMATION OF HEAT WAVE INDICES FROM CLIMATE MODEL

UNIVERSITÀ DEGLI STUDI DI CATANIA
FACOLTÀ DI SCIENZE MATEMATICHE, FISICHE E NATURALI
CORSO DI LAUREA IN FISICA (V.O.)
ANDREA FRANCESCO MARCHESE
ESTIMATION OF HEAT WAVE INDICES FROM
CLIMATE MODEL DATA
TESI DI LAUREA
Relatore: Chiar.ma Prof.ssa G. IMMÈ
Correlatore: Dott. S. RUSSO
ANNO ACCADEMICO 2010−2011
.
.
Dedicated to Graziella e Nino
.... for their tireless patience and great love for me.
Contents
Introduction
4
1 Physics of Climate
8
1.1 Climate system. . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.2 Earth’s energy balance. . . . . . . . . . . . . . . . . . . . . . .
9
1.2.1
Greenhouse effect . . . . . . . . . . . . . . . . . . . . . 11
1.2.2
The warming due to greenhouse effect. . . . . . . . . . 11
1.2.3
Clouds and aerosols. . . . . . . . . . . . . . . . . . . . 12
1.3 Energy circulation. . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Human-induced forcing. . . . . . . . . . . . . . . . . . . . . . 15
1.4.1
Human fingerprint on GHGs . . . . . . . . . . . . . . . 16
1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 The Intergovernamental Panel on Climate Change (IPCC) 20
2.1 The IPCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 The IPCC Organization . . . . . . . . . . . . . . . . . . . . . 21
2.3 The emission scenarios . . . . . . . . . . . . . . . . . . . . . . 22
2.4 GHGs emissions and projected temperatures based on SRES . 25
3 The ECHAM5/MPI-OM model and the ESSENCE
29
3.1 Mathematical simulation of climate . . . . . . . . . . . . . . . 29
3.1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 The ECHAM5/MPI-OM . . . . . . . . . . . . . . . . . . . . . 30
3.2.1
The ECHAM5 atmospheric component . . . . . . . . . 31
3.2.2
The equations used by the model . . . . . . . . . . . . 31
3.2.3
Model grids and resolution . . . . . . . . . . . . . . . . 42
Contents
2
3.2.4
Solution of model equations . . . . . . . . . . . . . . . 43
3.2.5
Parameterizations . . . . . . . . . . . . . . . . . . . . . 43
3.2.6
The MPI-OM ocean component . . . . . . . . . . . . . 44
3.2.7
Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 The NCEP reanalysis data . . . . . . . . . . . . . . . . . . . . 45
3.4 The ESSENCE project . . . . . . . . . . . . . . . . . . . . . . 46
4 Climate Indices and Statistical Methods
52
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 Climate Indicators . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1
Index Selection and Definition . . . . . . . . . . . . . . 55
4.3 On the definition of Heat Wave indicators . . . . . . . . . . . 58
4.4 Threshold definition
. . . . . . . . . . . . . . . . . . . . . . . 58
4.4.1
Stationary threshold . . . . . . . . . . . . . . . . . . . 59
4.4.2
No-Stationary threshold . . . . . . . . . . . . . . . . . 61
4.5 Heat Wave indices definition . . . . . . . . . . . . . . . . . . . 63
4.5.1
The HWD-nth index . . . . . . . . . . . . . . . . . . . 63
4.5.2
The HWI-nth index
4.5.3
The HWI5-nth index . . . . . . . . . . . . . . . . . . . 63
4.5.4
The HWF-nth index . . . . . . . . . . . . . . . . . . . 64
. . . . . . . . . . . . . . . . . . . 63
5 Results
65
5.1 Model Output Evaluation . . . . . . . . . . . . . . . . . . . . 65
5.2 Results: General Considerations . . . . . . . . . . . . . . . . . 69
5.3 Will the probability of HW occurrence increase in the future?
72
5.4 Will the HW frequency increase in the future? . . . . . . . . . 77
5.5 Can we expect longer future Heat-Waves? . . . . . . . . . . . 80
5.6 Can we expect more intense future Heat-Waves? . . . . . . . . 83
Conclusion
90
A Characteristics of SRES scenario
93
B R script function to compute HW indeces.
95
C HW1 and HW2 example.
99
Contents
3
D Software
101
E List of Acronyms
102
Bibliography
105
Acknowledgements
109
Introduction
”True morality consists not in following the beaten track,
but in finding out the true path for ourselves
and in fearlessly following it.”
- Mahatma Mohandas Karamchand Gandhi -
Global and regional climate patterns have changed throughout the history
of our planet. Prior to the Industrial Revolution, these changes occurred due
to natural causes, including variations in the Earth’s orbit around the Sun,
volcanic eruptions, and fluctuations in the Sun’s energy, etc...
Since the late 1800s, the atmospheric concentrations have made an increase
of carbon dioxide and other trace greenhouse gases (GHG) as a result of
human activities, such as fossil-fuel combustion and land-use change.
Changes in the atmospheric concentrations of GHGs and aerosols, land cover
and solar radiation alter the energy balance of the climate system and are
drivers of climate change. They affect the absorption, scattering and emission
of radiation within the atmosphere and at the Earth’s surface.
The observed widespread warming of the atmosphere and ocean, together
with ice mass loss, support the conclusion that it is extremely unlikely that
global climate change of the past 50 years can be explained without external
forcing and very likely that it is not due to known natural causes alone [14].
It is very clear that human activities have altered the atmosphere and that
if we continue to realease CO2 and other GHGs we can produce a significant
change in the global climate [10].
The development of this process is uncertain and depend on economic and
social decision that society has yet to make. Economically recoverable fossil
fuel reserves are uncertain, but are sufficient to sustain today’s growth of
energy consumption for many years into the future. Using coal to maintain
Introduction
5
future growth in energy consuption would probably lead to a doubling of
atmospheric CO2 by the middle of the twenty-first century. This effect when
combined with the probable increases in other GHGs, would produce a major
change in Earth’s climate. [10]
Only since the World War II the systematic study of the atmosphere and
oceans become feasible on a global scale, mainly through the increase of
in situ observations and by means of General Circulation Climate Models
(GCCM) to predict climate change future scenario.
The simulations obtained with current climate models are in reasonable
agreement with observations of the present climate for a variety of key dynamic and thermodynamic climate variables. This agreement is highly encouraging, but it does not by itself mean that climate models are capable of
accurately predicting the response of climate to a natural or human-induced
perturbation [10].
Simulations with global coupled ocean-atmosphere general circulation models
(AOGCMs) forced with GHG and aerosol emission scenarios are the primary
tools for studying possible future changes in climate mean, variability and
extremes [19].
Changes in extreme weather and climate events have significant impacts and
are among the most serious challenges to society in coping with a changing
climate [27], [19]. Climate change has many different adverse impacts, with
melting ice caps and rising sea levels being probably the most severe ones in
the very long run. In the short run, weather-related disasters such as heat
waves, droughts, floods, and storms play an important role. Worldwide, the
number of disaster losses in monetary terms (both insured and uninsured)
has increased in recent years but it is still debated whether (and, if yes, to
what extend) climate change has contributed to this increase [21].
Infact many extremes and their associated impacts are now changing. For
example, in recent decades most of North America and Europe have been
experiencing more unusually hot days and nights, fewer unusually cold days
and nights, and fewer frost days. Heat Waves (in a simple way, heat, or
anomalously hot weather, that lasts for several days) have become more
frequent and intense and droughts are becoming more severe in some regions.
Summer 2003 has been perceived as exceptionally hot, especially in most of
Introduction
6
Western Europe. As an example, in Spain the Heat Wave was characterised
mostly by the persistence of very high temperature values. The Spanish (and
European) absolute record (50.0 o C in Seville in 1881) was not broken but,
according to the Spanish National Institute of Meteorology 1 , 19 observatories (weather stations) recorded daily maximum temperatures higher than or
equal to 40o C. Besides an unusually large number of extensive forest fires,
which occurred in Portugal, Spain and France, the other main impact of the
Heat Wave was increased mortality, especially in south-western Europe [7].
One of the most recently drastic events was the Heat Wave recorded in the
Russian region during summer 2010. During that time, extensive fires across
western Russia killed 53 people and made 3500 people homeless, and Moscow
suffered a devastating rise in mortality, smoke fire, and air pollution [3].
Heat Wave future scenario is estimated to be more drastic with respect to
the past and present periods. Accordingly with the results of most of the
GCCMs, more intense, frequent and longer Heat Waves will occur during the
21th century. In the present study we use output from the 17 runs of the
ESSENCE project (Ensemble SimulationS of Extreme weather events under
Nonlinear Climate changE) to calculate Heat Wave intensity and duration
indicators in order to quantify the impact of future Heat-Waves and to answer
to the following questions:
1. Will the probability of Heat-Wave occurrence increase in the future?
2. Under future climate change scenarios can we expect more frequent
Heat-Wave events?
3. The Heat-Waves will be more intense and longer and how much the
main parameters (intensity frequency and duration) characterizing an
Heat Wave are changing?
The thesis is structured in 5 chapters each addressing to different aspect
of the changing climate to finally answer to three question listed above. In
Chapter 1 are given mention about the Physics of Climate, focusing on the
greenhouse effect and the human contribute to climate change.
Chapter 2 deals with the emission Scenarios released by Intergovernmental
Panel on Climate Change (IPCC), the leading international institution for
1
http://www.inm.es
Introduction
7
the assessment of climate change. The scenarios are used for driving Global
Circulation Model(GCM).
Chapter 3 comprises mention about the GCM, focusing on the ECHAM5/MPIOM coupled climate model. Hence, the chapter deals with the atmospheric
temperature data from the ECHAM5/MPI-OM performed by the ESSENCE
project, including a mention about NCEP reanalysis data.
In Chapter 4 we describe the most common climate indices defined by Frich
et al. (2002) and revised by the Expert Team on Climate Change Detection
and Indices (ETCCDI) mainly focusing on Heat Wave indices. Additionally,
we define some new indices measuring the intensity of a summer Heat Wave
event.
Chapter 5, at first, deals with the model output evaluation, then the materials
and methods used to compute the indeces characterizing a Heat Wave have
been explained. At the end of Chapter, each section is an answer to the
questions posed above.
In Conclusion we indicate that over most of the world Heat-Wave Occurrence
and Frequency will increase in the future. Moreover the future scenario will
prensent more intense longer Heat-Wave with extremly warmer climate in
the tropics.
The elaborations and valutations of the indicators are executed by using
the program R software for statistical computing and CDO (Climate Data
Operators) software (see Appendix D).
All graphycs and maps refer to data computing are made with R software
[24].
The result of this thesis is in preparation for publication.
Chapter 1
Physics of Climate
”If I have ever made any valuable discoveries,
it has been owing more to patient attention, than to any other talent.”
- Isaac Newton -
1.1
Climate system.
The climate system consists of the atmosphere, land surface, snow and ice,
oceans and other water sources, and everything that is alive within them.
Many physical, chemical and biological interaction processes occur among
the various components of the climate system on a wide range of space and
time scales, making the system extremely complex. Although its components
are very different in their composition, physical and chemical properties,
structure and behaviour, they are all linked by fluxes of mass, heat and
momentum.
The climate system evolves in time under the influence of its own internal
dynamics and due to changes in external forcings that affect climate.
External forcings include natural phenomena such as volcanic eruptions and
solar variations, as well as human-induced changes in atmospheric composition. There are three fundamental dipendences that affect the radiation
balance of the Earth:
1. the incoming solar radiation (e.g., changing in Earth’s orbit or the Sun
itself);
1.2. Earth’s energy balance.
9
2. the fraction of solar radiation that is reflected, called ”albedo” (e.g.,
changing in cloud cover, atmospheric particles or reflection properties
of the terrestrial surfaces); and
3. the longwave radiation that goes back from towards space (e.g., changing of greenhouse gas concentrations).
Climate, in turn, responds directly and indirectly to such changes in these
dependences through a variety of feedback mechanisms.
1.2
Earth’s energy balance.
The amount of energy emitted by the Sun during daytime reaching the top of
Earth’s atmosphere each second on area of 1m2 surface is the solar constant
S0 = 1.370W m−2, and the amount of energy m2 × sec averaged over the
entire planet is 1/4 of this (see figure 1.1).
About 30% of the sunlight that reaches the top of the atmosphere is reflected
back to space without being absorbed. Roughly 2/3 of this reflectivity is due
to clouds and small particles in the atmosphere known as ”aerosols”. Areas
of Earth’s surface at high reflectivity, mainly snow, ice and deserts reflect the
remaining 1/3 of the sunlight. This fraction is called albedo (αp ).
The energy that is not reflected back to space is absorbed by the Earth’s
climate system. This amount is approximately 240 W m−2 .
To balance the incoming energy, the Earth itself must radiate, on average,
the same amount of energy back to space. The Earth emits outgoing longwave radiation. Thus the emission temperature of the Earth is the blackbody
temperature with which it needs to emit in order to achieve energy balance.
1.2. Earth’s energy balance.
10
Figure 1.1: Estimate of the Earth’s annual and global mean energy balance [20]. Over the long term, the
amount of incoming solar radiation absorbed by the Earth and atmosphere is balanced by the Earth and
atmosphere releasing the same amount of outgoing longwave radiation. About half of the incoming solar
radiation is absorbed by the Earth’s surface. This energy is transferred to the atmosphere by warming
the air in contact with the surface (thermals), by evapotranspiration and by longwave radiation that is
absorbed by clouds and greenhouse gases. The atmosphere in turn radiates longwave energy back to Earth
as well as out to space.
Assuming the terrestrial emission as a blackbody emission, its dependence
on temperature follows the Stefan-Boltzmann law
EB = σT 4
(1.1)
where EB is the blackbody emission flux density (W m−2 )
and σ = 5.67 × 10−8 W m−2 K −4
If we equate the absorbed solar flux with the emitted terrestrial flux, we
obtaine the terrestrial energy balance:
S0
(1 − αp ) = σTe 4
4
(1.2)
where Te is the emission temperature.
Hence, a surface emitting 240 W m−2 , would have a temperature of around
−19o C. This is much colder than the conditions that actually exist at the
Earth’s surface. Infact the global mean surface temperature is about 14o C.
Instead, the necessary −19o C is found at an altitude about 5 km above the
surface.
1.2. Earth’s energy balance.
11
The reason for this warming is the presence of GHG, which act as a partial
blanket for the longwave radiation coming from the surface. This blanketing
is known as the natural greenhouse effect.
1.2.1
Greenhouse effect
The Earth’s dry atmosphere is composed mainly of nitrogen (N2 , 78.1% volume mixing ratio), oxygen (O2 , 20.9% volume mixing ratio), and argon (Ar,
0.93% volume mixing ratio). These gases have only limited interaction with
the incoming solar radiation and they do not interact with the infrared radiation emitted by the Earth.
However there are a number of trace gases, such as carbon dioxide (CO2 ),
methane (CH4 ), nitrous oxide (N2 O) and ozone (O3 ), which absorb and emit
infrared radiation. These so called GHGs, with a total volume mixing ratio
in dry air of less than 0.1% by volume, play an essential role in the Earth’s
energy budget.
Moreover the atmosphere contains water vapour (H2 O), which is also a natural GHG. Its volume mixing ratio is highly variable, but it is typically in
the order of 1%.
Because these GHGs absorb the infrared radiation emitted by the Earth and
emit infrared radiation up and downward, they tend to raise the temperature
near the Earth’s surface. Water vapour, CO2 and O3 also absorb solar shortwave radiation.
1.2.2
The warming due to greenhouse effect.
The greenhouse effect may be explained by using the energy balance. The
atmosphere is assumed to be a blackbody for terrestrial radiation, but is
trasparent to solar radiation. The energy balance at the top of the atmosphere
in this scenario is the same as in the basic energy balance that defined the
emission temperature (eq: 1.2). Since the atmospheric layers absorb all of the
energy emitted by the surface below it and emits like a blackbody, the only
radiation emitted to space is from the atmosphere.
The energy balance at the top of the atmosphere is
S0
(1 − αp ) = σTA 4 = σTe 4
4
(1.3)
1.2. Earth’s energy balance.
12
S0/4 (1 − αp )
σTA 4
Atmosphere
σTA 4
σTs
4
Surface
Figure 1.2: Scheme of energy fluxes for the Earth with an atmosphere that is trasparent for solar
radiation but opaque to terrestrial radiation.[10]
where TA is the atmosphere temperature.
Therefore we see that the temperature of the atmosphere in equilibrium must
be the emission temperature in order to achieve energy balance. The surface
temperature is much warmer, however, as we can see by deriving the energy
balance for the atmosphere and the surface. The atmospheric energy balance
gives
σTs 4 = 2σTA 4 ⇒ σTs 4 = 2σTe 4
(1.4)
where Ts is the terrestrial surface temperature and the surface energy balance
is consistent:
S0
(1 − αp ) + σTA 4 = σTs 4 ⇒ σTs 4 = 2σTe 4
4
(1.5)
We can see from the scheme in Figure 1.2 and the surface energy balance
equation 1.5, that the surface temperature is increased because the atmosphere does not inhibit the flow of solar energy to the surface, but augments
the solar heating of the surface with its own downward emission of longwave
radiation.
The atmospheric greenhouse effect warms the surface because the atmosphere
is relatively trasparent to solar radiation and yet absorbs and emits terrestrial
radiation very effectively[10].
1.2.3
Clouds and aerosols.
Clouds consist of liquid water droplets or ice particles suspended in the atmosphere. They are formed by the condensation of atmospheric water vapor
1.2. Earth’s energy balance.
13
when the temperature falls below the saturation temperature.
Clouds do exert a blanketing effect similar to that of the GHGs; however,
this effect is offset by their reflectivity, such that on average, clouds tend to
have a cooling effect on climate (although locally one can feel the warming
effect: cloudy nights tend to remain warmer than clear nights, because the
clouds radiate longwave energy back down to the terrestrial surface).
An other important atmospheric component is the aerosol. It is a suspension
of liquid or solid particles in air.
Also the clouds are composed of water aerosols, but the distinction of clouds
and nonclouds aerosols is the fact that the first are at equilibrium in air with
relative humidities in excess of 100%, while the second can be in equilibrium
at relatively low humidity.
The surface area of aerosols is important both for their role as clouds condensation nuclei (CCN) and also for their direct effect on radiation. Stratosferic
aerosols interact with both solar and terrestrial radiation and may both scatter and absorb radiation.
The aerosols that are most important for climate have radii in the range of
about 0.1 − 1µm. Aerosols can be injected directly into the atmosphere or
be formed by the condensation or chemical trasformation of vapors.
A source of direct emission of aerosols is the bursting of bubbles on the
ocean surface, which produces small droplets that evaporating leave a seasalt aerosol.
Others natural sources are the elevation by wind of mineral dust from dry
land surfaces, injection of ash and rock from vulcanoes, soot from forest fire,
and biological emission.
Aerosols can be formed to conversion by gas to particle producting sulfates,
nitrates, and hydrocarbons. Infact most stratospheric aerosols consist of a
mixture of 75% of sulfuric acid(H2 SO4 ) and 25% water. Its source is for
example the carbonyl sulfide (COS), produced in soils, which is mixed into the
stratosphere where it encounters ultraviolet radiation or atomic oxygen. Then
it is oxidized to form sulfur dioxide (SO2) and then sulfuric acid. Hence, in
the low stratosphere, it condenses to form aerosols and is ultimately removed
when the aerosols become large enough to precipitate or when the air in which
they reside returns to the troposphere.
1.3. Energy circulation.
14
The most dramatic change in aerosol-produced reflectivity comes when major
volcanic eruptions eject material into the high layers of the atmosphere. Rain
typically clears aerosols out of the atmosphere in a week or two, but when
material from a violent volcanic eruption is projected far above the highest
clouds, these aerosols typically influence the climate for about a year or
two before falling into the troposphere and being carried to the surface by
precipitation. Major volcanic eruptions can thus cause a drop in mean global
surface temperature of about half a degree celsius that can last for months
or even years.
Some man-made aerosols also significantly reflect sunlight (we will discuss
later in Subsection 1.4.1).
1.3
Energy circulation.
The Earth can be approximated to a sphere and then solar energy has a
different distribution for a given surface area in the tropics rather than at
higher latitudes, where sunlight strikes the atmosphere at a lower angle.
Energy is transported from the equatorial areas to higher latitudes via atmospheric and oceanic circulations, including storm systems.
Energy is also required to evaporate water from the sea or land surface, and
this energy, called latent heat, is released when water vapour condenses in
clouds (see Figure 1.1). The release of latent heat is the most important cause
of atmospheric circulation and the last one in turn drives much of the ocean
circulation through the action of winds on the surface waters of the ocean,
and through changes in the ocean’s surface temperature and salinity through
precipitation and evaporation.
Due to the rotation of the Earth, the atmospheric circulation patterns tend
to be more east-west than north-south. In the mid-latitude, westerly winds
constitute large-scale weather systems transporting heat toward the poles.
These weather systems are the migrating low- and high-pressure systems and
their associated cold and warm fronts. The circulation system on planetaryscale of air masses tends to be geographically anchored by continents and
mountains, although its amplitude can change with time. This fact is due to
the land-ocean temperature contrasts and obstacles such as mountain ranges
1.4. Human-induced forcing.
15
and ice sheets.
Changes in various aspects of the climate system, such as the size of ice
sheets, the type and distribution of vegetation or the temperature of the
atmosphere or ocean will influence the large-scale circulation features of the
atmosphere and oceans.
Thus we can understand that there are many feedback mechanisms in the
climate system that can either amplify or diminish the effects of a change in
climate forcing.
For example, as rising concentrations of GHGs warm climate of Earth, snow
and ice begin to melt, revealing darker land and water surfaces that absorb
more of the Sun’s heat, causing more warming, which causes more melting,
and so on, in a self-reinforcing cycle [16].
1.4
Human-induced forcing.
The geologic record indicates that dramatic changes in climate occurred in
the past, most of them for natural causes, such as solar changes and volcanic
eruptions.
Since the start of the industrial era (about 1750), the overall effect of human activities on climate has been a global warming. The human impact on
climate during this era greatly exceeds that due to natural changes.
Human activities contribute to climate change by causing changes in atmosphere of Earth in the amounts of GHGs, aerosols, and cloudiness.
These activities result in emissions of four principal GHGs: carbon dioxide
(CO2 ), methane (CH4 ), nitrous oxide (N2 O) and the halocarbons (a group
of gases containing fluorine, chlorine and bromine). As shown in Fig. 1.3,
where concentration trends of GHG are reported, significant increases in all
of these gases started to occurre in the industrial era, so they are attributable
to human activities.
Humankind, also, has dramatically altered the nature of land cover over
the globe, principally through changes in croplands, pastures and forests, so
modifying the reflective properties of the Earth surface.
1.4. Human-induced forcing.
16
Concentrations of Greenhouse Gases from 0 to 2000
2000
400
1800
Methane (CH4)
350
1600
Nitrous Oxide (N2O)
1400
1200
CH4 (ppb)
CO2 (ppm), N2O (ppb)
Carbon Dioxide (CO2)
300
1000
800
250
0
600
500
1000
Year
1500
2000
Figure 1.3: Atmospheric concentrations of important long-lived greenhouse gases over the last 2000
years. Increases since about 1750 are attributed to human activities in the industrial era. Concentration
units are parts per million (ppm) or parts per billion (ppb), indicating the number of molecules of the
greenhouse gas per million or billion air molecules, respectively, in an atmospheric sample [16].
1.4.1
Human fingerprint on GHGs
Most of GHGs have very long lifetimes in the atmosphere so that the amounts
released into the atmosphere today will remain there for up 2 centuries,
depending on the gas.
Carbon dioxide has increased from fossil fuel use in transportation, building
heating and cooling and the manufacture of cement and other goods.
Deforestation releases CO2 and reduces its uptake by plants. Carbon dioxide
is also released in natural processes such as the decomposition of plants.
CO2 is cycled between ocean, atmosphere and land. The time required for
atmospheric CO2 to achieve a new equilibrium in response to a perturbation
such as fossil fuel burning is much longer, because the carbon is exchanged
between the surface waters and deep ocean in a slow rate. To achieve a new
steady state the atmospheric CO2 concentration requires 50-200 years.
1.4. Human-induced forcing.
17
Methane has increased as a result of human activities related to agriculture, natural gas distribution and landfills. Methane is also released from
natural processes that occur, for example, in wetlands. The primary removal
mechanism is oxidation by hydroxyl (OH) in the atmosphere. Methane concentrations have more than doubled since the preindustrial era (see Fig. 1.3),
but they are not currently increasing in the atmosphere because growth rates
decreased over the last two decades. The reasons of this behaviour are not
known.
Nitrous oxide is also emitted by human activities such as fertilizer use and
fossil fuel burning. Natural processes in soils and the oceans also release N2 O.
It has an atmospheric lifetime of about 150 years. Its primary sinks are in
the stratosphere, where it is removed by photolysis and by reaction with
electronically excited oxygen atoms.
Halocarbon gases such as chlorine, bromine, and iodine have a variety of industrial applications. Principal halocarbons include the chlorofluorocarbons
(e.g., CFC-11 and CFC-12), which were used extensively as refrigeration
agents and in other industrial processes before their presence in the atmosphere was found to cause stratospheric ozone depletion. They have a strong
absorption in the 8-12 µm wavelength region where the terrestrial emission
is large, while the natural atmosphere is relatively trasparent. Fully halogenated compounds are extremely unreactive and have very long lifetimes
in the atmosphere. They are photodissociated by ultraviolet radiation in the
stratosphere, where the chlorine and bromine released participate in the catalytic destruction of ozone. The abundance of chlorofluorocarbon gases is
decreasing as a result of international regulations designed to protect the
ozone layer (see ”Montreal Protocol on Substances that Deplete the Ozone
Layer” 1 ).
Ozone is a greenhouse gas that is continually produced and destroyed in the
atmosphere by chemical reactions. In the troposphere, human activities have
increased ozone through the release of gases such as carbon monoxide, hydrocarbons and nitrogen oxide, which chemically react to produce ozone.
As mentioned above, halocarbons released by human activities destroy ozone
in the stratosphere and have caused the ozone hole over Antarctica. The re1
http://ozone.unep.org/new_site/en/Treaties/treaty_text.php?treatyID=2
1.5. Conclusions
18
duction of ozone in the stratosphere also allows more solar energy to reach
the troposphere, which partially offsets the effect of the decreased ozone
greenhouse effect.
Water vapour is the most abundant and important GHGs in the atmosphere.
However, human activities have only a small direct influence on the amount
of atmospheric water vapour. Indirectly, humans have the potential to affect
water vapour substantially by changing climate. For example, a warmer atmosphere contains more water vapour. Human activities also influence water
vapour through CH4 emissions, because CH4 undergoes chemical destruction
in the stratosphere, producing a small amount of water vapour.
Aerosols containing sulphur compounds, organic compounds and black carbon (soot) are increased from fossil fuel and biomass burning. Human activities such as surface mining and industrial processes have increased dust
in the atmosphere. The period between the release of an aerosol precursor
gas (such as SO2 ), its conversion to sulfate aerosols and final precipitation
in solution within a raindrop (acid rain), is generally only a few days. Thus
it has a short lifetime and tends to be highest near the sources of aerosols or
their precursor gases.
1.5
Conclusions
The changes in climate that result from human activities occur gradually in
response to steadily increasing climate forcing by GHGs increases, aerosols
production, and land surface modification.
The transient response of the climate system to the anthropogenic shift in
climate forcing may be very different from the equilibrium response, and an
equilibrium may never be achieved since it is unlikely that the anthropogenic
forcing of climate will remain constant for the many century required for a
steady state to be established. The response of the climate system to changed
thermal forcing will be delayed by the large heat capacity of the ocean. In
addiction, the ocean currents and their slow response to this thermal forcing
may yield geographic variations in the temperature change that are different
from those of an equilibrium calculation [10].
The magnitude and timing of global climate change are both uncertain and
1.5. Conclusions
19
also depend on economic and social decision that society has yet to make.
If we continue to alter the atmosphere in the future at the actual accelerating
rate then within a century we would produce a climate on Earth that would
be warmer than any in more than a million years. Moreover, the rate of
temperature increase would be very large by natural standards and would
make it difficult for plants, animal, and humans to adapt. Because of the long
lifetime of GHGs in atmosphere, delays in the response of climate system,
and natural variability, by the time a large climate change in response to
GHGs could be demonstrated from observations, we would be submitted to
that climate change for a long time into the future. For this reason long-term
planning for global climate change will require accurate predictions of future
climates that can withstand an extremely critical evaluation [10].
Chapter 2
The Intergovernamental Panel
on Climate Change (IPCC)
”The beginning of knowledge
is the discovery of something we do not understand.”
- Frank Herbert -
2.1
The IPCC
The Intergovernmental Panel on Climate Change (IPCC) is the leading international institution for the assessment of climate change. It was established
in 1988 by the United Nations Environment Programme (UNEP) and the
World Meteorological Organization (WMO).
The initial task for the IPCC as outlined in the UN General Assembly Resolution 43/53 of 6 December 1988 1 , was to prepare a comprehensive review
and recommendations with respect to the state of knowledge of the science
of climate change; social and economic impact of climate change, possible response strategies and elements for inclusion in a possible future international
convention on climate.
The scientific component of IPCC reviews and assesses the most recent scientific, technical and socio-economic information produced worldwide relevant
to the understanding of climate change. It does not conduct any research nor
does it monitor climate related data or parameters. Thousands of scientists
1
http://www.un.org/documents/ga/res/43/a43r053.htm
2.2. The IPCC Organization
21
from all over the world contribute to the work of the IPCC on a voluntary
basis. The IPCC is open to all member countries of the United Nations (UN)
and WMO. Currently 194 countries are members of the IPCC. Because of
its scientific and intergovernmental nature, the IPCC embodies a unique opportunity to provide rigorous and balanced scientific information to decision
makers.
Today the IPCC’s role is , as defined in Principles Governing IPCC Work, ”...
to assess on a comprehensive, objective, open and transparent basis the scientific, technical and socio-economic information relevant to understanding the
scientific basis of risk of human-induced climate change, its potential impacts
and options for adaptation and mitigation... ” [Approved at the Fourteenth
Session (Vienna, 1-3 October 1998) on 1 October 1998, amended at the 21st
Session (Vienna, 3 and 6-7 November 2003) and at the 25th Session (Mauritius, 26-28 April 2006)].
2.2
The IPCC Organization
The IPCC is currently organized in 3 Working Groups and a Task Force.
They are assisted by Technical Support Units (TSU), which are hosted and
financially supported by the Government of the developed country co-chair
of that Working Group/Task Force. The Working Groups and the Task Forse
deal with:
• The Physical Science Basis of Climate Change (Working Group I).
• Climate Change Impacts, Adaptation and Vulnerability (Working
Group II).
• Mitigation of Climate Change (Working Group III).
• Develop and refine a methodology for the calculation and reporting of
national GHG emissions and removals (Task Force).
In addition to the Working Groups and Task Force, further Task Groups
and Steering Groups may be established for a limited or longer duration to
consider a specific topic or question.
2.3. The emission scenarios
2.3
22
The emission scenarios
In 1992 the IPCC released emission scenarios to be used for driving Global
Circulation Models (GCM) to develop climate change scenarios. The so-called
IS92 scenarios were pathbreaking. Scenarios are alternative images of how
the future might unfold and are an appropriate tool with which to analyse
how driving forces may influence future emission outcomes and to assess the
associated uncertainties. They assist in climate change analysis, including
climate modeling and the assessment of impacts, adaptation, and mitigation.
The IS92 scenarios were the first global scenarios to provide estimates for
the full suite of GHGs. Since 1992 much has changed in the knowledge of
possible future GHGs emissions and climate change.
Therefore the IPCC decided in 1996 to develop a new set of emissions scenarios [13] 2 .
Four qualitative storylines, yield four sets of scenarios called ’families’: A1,
A2, B1, and B2, were developed to describe consistently the relationships
between emission driving forces and their evolution and add context for the
scenario quantification. Each storyline assumes a distinctly different direction
for future developments, such that the four storylines differ in increasingly
irreversible ways. Together they describe divergent futures that encompass a
significant portion of the underlying uncertainties in the main driving forces.
Moreover they represent different demographic, social, economic, technological, and environmental developments, as shortly depicted below:
• The A1 storyline and scenario family describes a future world of very
rapid economic growth, global population that peaks in mid-century
and declines thereafter, and the rapid introduction of new and more
efficient technologies. Major underlying themes are convergence among
regions, capacity building, and increased cultural and social interactions, with a substantial reduction in regional differences in per capita
income. The A1 scenario family develops into three groups that describe alternative directions of technological change in the energy system. The three A1 groups are distinguished by their technological
2
http://www.ipcc.ch
2.3. The emission scenarios
23
emphasis: fossil intensive (A1FI), non-fossil energy sources (A1T), or
a balance across all sources (A1B).
• The A2 storyline and scenario family describes a very heterogeneous
world. The underlying theme is self-reliance and preservation of local
identities. Fertility patterns across regions converge very slowly, which
results in continuously increasing global population. Economic development is primarily regionally oriented and per capita economic growth
and technological change are more fragmented and slower than in other
storylines.
• The B1 storyline and scenario family describes a convergent world with
the same global population that peaks in mid-century and declines
thereafter, as in the A1 storyline, but with rapid changes in economic
structures toward a service and information economy, with reductions
in material intensity, and the introduction of clean and resource-efficient
technologies. The emphasis is on global solutions to economic, social,
and environmental sustainability, including improved equity, but without additional climate initiatives.
• The B2 storyline and scenario family describes a world in which the
emphasis is on local solutions to economic, social, and environmental
sustainability. It is a world with continuously increasing global population at a rate lower than A2, intermediate levels of economic development, and less rapid and more diverse technological change than in the
B1 and A1 storylines. While the scenario is also oriented toward environmental protection and social equity, it focuses on local and regional
levels.
For each storyline 3 , several different scenarios were developed using different modeling approaches to examine the range of outcomes arising from a
range of models that use similar assumptions about driving forces. Six models were used which are representative of integrated assessment frameworks
in the literature. One advantage of a multi-model approach is that the resultant 40 SRES (Special Report on Emission Scenarios) scenarios together
encompass the current range of uncertainties of future GHG emissions arising from different characteristics of these models, in addition to the current
3
http://www.ipcc.ch/ipccreports/sres/emission/index.php?idp=92
2.3. The emission scenarios
24
knowledge of and uncertainties that arise from scenario driving forces such
as demographic, social and economic, and broad technological developments
that drive the models, as described in the storylines. Thirteen of these 40
scenarios explore variations in energy technology assumptions. Each storyline assumes a distinctly different direction for future developments, such
that the four storylines differ in increasingly irreversible ways. Together they
describe divergent futures that encompass a significant portion of the underlying uncertainties in the main driving forces. They cover a wide range
of key ”future” characteristics such as demographic change, economic development, and technological change. For this reason, their plausibility or
feasibility should not be considered solely on the basis of an extrapolation of
current economic, technological, and social trends.
Fig. 2.1 shows a schematic illustration of scenarios developed in Special Report on Emission Scenarios (SRES).
Four qualitative storylines yield four sets of scenarios called ”families”: A1,
A2, B1, and B2. Altogether 40 SRES scenarios have been developed by
six modeling teams. All are equally valid with no assigned probabilities of
occurrence. The set of scenarios consists of six scenario groups drawn from
the four families: one group each in A2, B1, B2, and three groups within
the A1 family, characterizing alternative developments of energy technologies: A1FI (fossil fuel intensive), A1B (balanced), A1T (predominantly
non-fossil fuel). Within each family and group of scenarios, some share ”harmonized” assumptions on global population, gross world product, and final
energy. These are marked as ”H S” for harmonized scenarios. ”OS” denotes
scenarios that explore uncertainties in driving forces beyond those of the
harmonized scenarios. Two additional illustrative scenarios for the groups
A1FI and A1T are also provided and complete a set of six that illustrates
all scenario groups.
To have more detailed informations about the 40 SRES, in Appendix A are
shown the characteristics of SRES scenario quantifications and the Harmonization Criteria. In Table A.1, for each scenario are listed the name of the
storyline and scenario family, full scenario name (ID), descriptive scenario
name, and which of the driving forces are harmonized at the global and regional level, and on the global level only, respectively. The listed harmonized
2.4. GHGs emissions and projected temperatures based on SRES
25
driving forces are population (POP), gross domestic product (GDP), and
final energy (FE). In Table A.2 are indicated the harmonization criteria in
terms of the maximum deviation (%) from the specified common population,
gross world product, and final energy development at the global and regional
levels.
SRES
A1
Storyline
A1 Family
A1F1
B1
Storyline
A2
Storyline
A2 Family
A1T
A1B
B2
Storyline
B2 Family
B1 Family
A2
B1
B2
Illustrative
Marker
Scenario
Illustrative
Marker
Scenario
Scenario Groups
Illustrative
Scenario
OS
HS
Illustrative
Marker
Scenario
Illustrative
Scenario
OS
HS
OS
HS
Illustrative
Marker
Scenario
OS
HS
OS
HS
OS
HS
Figure 2.1: Schematic illustration of SRES scenarios.
2.4
GHGs emissions and projected temperatures based on SRES
As we have seen in Chapter 1, each factor that alters the radiation received
from the Sun or lost to space, or that alters the redistribution of energy
within the atmosphere and between the atmosphere, land, and ocean, can
affect climate.
Observations have documented the changes that have occurred in agents that
can cause climate change. Most notable among these are increases in the
atmospheric concentrations of GHGs (see Fig. 1.3), aerosols and variations
in solar activity, both of which can alter the Earth’s radiation budget and
then climate. These observational records of climate-forcing agents are part
of the input needed to predict what climate changes could lie ahead.
2.4. GHGs emissions and projected temperatures based on SRES
26
Any human-induced changes in climate will be embedded in a background of
natural climatic variations that occur on a whole range of time- and spacescales.
In Fig. 2.2[13] the models make projections of anthropogenic emissions of
GHGs, based upon emissions scenarios from the IPCC (SRES). In all six
illustrative scenarios, the emissions of CO2 increase during the first decades of
the 21st century. This trend continues up to 2100 in three scenarios, while the
emissions peak between 2030 and 2050 and then decrease in scenarios A1T,
B1 and A1B. SRES scenarios also provide estimates for future emissions and
concentrations of other GHGs (such as N2 O and CH4 ), as well as emissions
of sulphur dioxide (SO2 ) which leads to production of sulphate aerosols in
atmosphere. In contrast to CO2, SO2 emissions reach their maximum in
all the scenarios during the first half of the 21st century and then decrease
thanks to policies devoted to reduce air pollution.
26
Scenarios
Scenarios
20
A1B
A1T
A1FI
A2
B1
B2
IS92a
24
N2O emissions (TgN)
CO2 emissions (Gt C)
25
15
22
A1B
A1T
A1FI
A2
B1
B2
IS92a
20
18
10
16
5
2000
2020
2040
2060
2080
2000
2100
1000
150
A1B
A1T
A1FI
A2
B1
B2
IS92a
SO2 emissions (Tg S)
CH4 emissions (Tg CH4)
Scenarios
800
2020
2040
2060
2080
2100
2020
2040
2060
2080
2100
Scenarios
A1B
A1T
A1FI
A2
B1
B2
IS92a
100
50
600
2000
2020
2040
Year
2060
2080
2100
2000
Year
Figure 2.2: Anthropogenic emissions of CO2 , CH4 , N2 O and SO2 for the six illustrative SRES scenarios,
A1B, A2, B1 and B2, A1FI and A1T. For comparison the IS92a scenario is also shown.
2.4. GHGs emissions and projected temperatures based on SRES
27
The Fig. 2.3 shows the projected temperature over 110 years, based upon
emissions scenarios from the IPCC (SRES). The ”several models all SRES envelope” show the temperature for the simple model when tuned to a number
of complex models with a range of climate sensitivities. All SRES envelopes
refer to the full range of SRES scenarios. The ”model average all SRES envelope” shows the average from these models for the range of scenarios. Global
mean temperature projections for the six illustrative SRES scenarios using a
simple climate model tuned to a number of complex models with a range of
climate sensitivities. Also for comparison, following the same method, results
are shown for IS92a. The darker shading represents the envelope of the full
set of SRES scenarios using the average of the model results (mean climate
sensitivity is 2.8 o C). The lighter shading is the envelope based on all seven
model (see Appendix A) projections (with climate sensitivity in the range
1.7 to 4.2 o C). The bars show, for each of the six illustrative SRES scenarios,
the range of simple model results in 2100 for the seven Atmosphere Ocean
General Circulation Models (AOGCMs) model tunings.
The globally averaged surface temperature is projected to increase by 1.4 o C
to 5.8 o C over the period 1990 to 2100. These results are for the full range of
SRES scenarios, based on climate models. Temperature increases are projected to be greater than those in the IPCC Second Assestment Report
(SAR)[12], which were about 1.0 o C to 3.5 o C, based on IS92 scenarios.
The higher projected temperatures and the wider range are due primarily to
the lower projected SO2 emissions in the SRES scenarios relative to the IS92
scenarios. The projected rate of warming is much larger than the observed
changes during the 20th century and is very likely to be without precedent
during at least the last 10,000 years, based on palaeoclimate data.
The relative ranking of the SRES scenarios in terms of global mean temperature changes with time. In particular, for scenarios with higher fossil fuel
use (hence, higher carbon dioxide emissions, e.g., A2), the SO2 emissions
are also higher. In the near term (till around 2050), the cooling effect of
higher sulphur dioxide emissions significantly reduces the warming caused
by increased emissions of GHGs in scenarios such as A2. The opposite effect is seen for scenarios B1 and B2, which have lower fossil fuel emissions
as well as lower SO2 emissions, and lead to a larger near-term warming. In
2.4. GHGs emissions and projected temperatures based on SRES
28
the longer term, however, the level of emissions of long-lived GHGs such as
CO2 and N2 O become the dominant determinants of the resulting climate
changes. By 2100, differences in emissions in the SRES scenarios and different climate model responses contribute similar uncertainty to the range of
global temperature change. Further uncertainties arise due to uncertainties
in the radiative forcing. The largest forcing uncertainty is that due to the
sulphate aerosols.
6
Scenarios
Temperature change (°C)
5
4
Several models
all SRES
envelope
A1B
A1T
A1FI
A2
B1
B2
IS92a
Several ensemble
all SRES
envelope
All
IS92
3
2
1
Bars show the
range in 2100
produced by
several models
2000
2020
2040
2060
2080
2100
Year
Figure 2.3: Projected temperature over 110 years, based upon emissions scenarios from the IPCC (SRES)
Chapter 3
The ECHAM5/MPI-OM model
and the ESSENCE
”Make everything as simple as possible,
but not simpler.”
- Albert Einstein -
3.1
3.1.1
Mathematical simulation of climate
Introduction
As described in chapter 1 and 2, the atmospheric concentrations of CO2 ,
CH4 and other so called GHGs have increased rapidly since the beginning
of the industrial revolution, leading to an increase of radiative forcing of
2.4 W m−2 up to the year 2000 [11], moreover under the predicted IPCC
scenarios (see chapter 2) the GHG atmospheric concentrations will increase
during the 21st century by following approximately a linear trend. Simultaneously, long term climate trends are observed everywhere on the Earth. Among
others, the global mean surface temperature has increased by 0.6 ± 0.2o C
over the 20th century, there has been a widespread retreat of non-polar
glaciers, and patterns of pressure and precipitation have changed [15]. To
determine the causal chain between the increase in radiative forcing and observed climate change, climate models are essential. Simulations with global
coupled ocean-atmosphere general circulation models (CGCMs), forced with
3.2. The ECHAM5/MPI-OM
30
projected GHGs and aerosol emissions are the primary tools for studying
possible future changes in climate mean, variability and extremes [19]. The
climatic processes involve various feedback mechanisms whose effects are not
always known. Also the equations expressing the physical laws are very complex, and the boundary conditions are not always sufficiently defined, because
they are based on observational data which are sometimes incomplete or inaccurate enough. All these factors lead the climate research to introduce
simplifications and specializations for the climate models, which are developed on physical and mathematical bases. The General Circulation Models
(GCMs) of the atmosphere and ocean incorporate the principles of physics,
chemistry, and biology into a mathematical model of climate. These models
are designed to derive the climate from first physical principles such as the
conservation laws of angular momentum, energy and mass.
GCM is a mathematical model of the general circulation of a planetary atmosphere or ocean and based on the Navier-Stokes equations on a rotating
sphere with thermodynamic terms for various energy sources (radiation, latent heat). By solving, by means of complex computer programs, the NavierStokes equations for atmosphere or ocean we will have respectivelly an atmospheric GCMs (AGCMs) and oceanic GCMs (OGCMs). An AGCM and
an OGCM can be coupled together to form an atmosphere-ocean coupled
general circulation model (CGCM or AOGCM). With the addition of other
components (such as a sea ice model or a model for evapotranspiration over
land), the AOGCM becomes the basis for a full climate model. Within this
structure, different variations can exist, and their varying response to climate
change may be studied [30].
3.2
The ECHAM5/MPI-OM
In this study, in order to detect global warming under A1B IPCC scenario (see
chapter 2), we use atmospheric temperature data from the ECHAM5/MPIOM simulation model outputs. It is a coupled climate model with two components, the ECHAM5 for the atmosphere and MPI-OM for the ocean.
3.2. The ECHAM5/MPI-OM
3.2.1
31
The ECHAM5 atmospheric component
ECHAM5 is the fifth-generation atmospheric general circulation model developed by the Max Planck Institute for Meteorology (Hamburg), one of
the research organizations of the Max Planck Society [25]. It was created by
modifiying global forecast models developed by European Centre for Medium
Range Weather Forecasts (ECMWF) to be used for climate research. To the
model was given its name as a combination of its origin (the ’EC’ being short
for ’ECMWF’) and the place of development of its parameterization package,
Hamburg.
3.2.2
The equations used by the model
To derive the governing equations used by the model ECHAM5 [25], we
take start from the unparametrized equations for a mixture of dry air, water
vapour, liquid water and ice, and work for convenience in a Cartesian coordinate system.
An individual component is denoted by a subscript j, where j = d, v, l, or i
for dry air, water vapour, liquid water or ice, respectively. The specific mass
of component k, denoted by qk , is defined by
mk
ρk
qk =
=
m
ρ
(3.1)
where
mk
is the mass of component k in a small material volume
moving with the local velocity of the atmosphere,
m=
ρk
ρ=
P
P
mk
ρk
is the total mass of the material volume,
is the density of component k, and
is the density of the atmosphere.
The rate of change of mk is denoted by ṁk . This change occurs because of
1. internal phase changes,
2. rainfall, snowfall, and surface exchanges.
The rate of change due to (1) alone is denoted by mk1 , and that due to (2)
by mk2 . Then
ṁk = ṁk1 + ṁk2
(3.2)
3.2. The ECHAM5/MPI-OM
32
and for dry mass
ṁd1 = ṁd2 = 0.
(3.3)
X
(3.4)
ṁkj = 0.
j
The rate of change of total mass is given by
X
X
ṁ =
ṁk =
ṁk2
k
(3.5)
k
The rate of change of density of component k satisfies the equation
ρk =
ρ
ṁk
m
(3.6)
provided (as is reasonable) volume changes due to precipitation or phase
changes are neglected. The net rate of change of density, ρ, is then given by
ρ
ρ X
ṁk = ṁ.
ρ̇ =
(3.7)
m k
m
The advective form of the unparameterized equations
The material derivative is denoted by d/dt. Its definition is
∂
d
=
+ ~v · ∇
dt
∂t
(3.8)
where ~v here denotes the three-dimensional velocity vector, and ∇ the usual
three-dimensional vector operator. Horizontal vectors and operators will subsequently be denoted by a subscript h.
Equation of state
We consider a volume V of atmosphere, of which dry air and water vapour
occupy a volume Vd+v . The equations of state for dry air and water vapour
are
pd Vd+v = md Rd T
(3.9)
pv Vd+v = mv Rv T
(3.10)
and
3.2. The ECHAM5/MPI-OM
33
where pd and pv are partial pressures. Dalton’s law then shows that the total
pressure p is given from (3.10) by
p=
md Rd T + mv Rv T
Vd+v
(3.11)
Introducing the specific volumes of liquid water vl , and ice vi ,
Vd+v = V − ml vl − mi vi =
m
(1 − ρ(ql vl + qi vi ))
ρ
(3.12)
and (3.11) becomes
p = ρT
Rd qd + Rv qv
.
1 − ρ(ql vl + qi vi )
(3.13)
Mass conservation
Conservation of mass for element k leads to the equation
ρṁk
dρk
+ ρk (∇ · ~v ) = ρ̇k =
.
dt
m
(3.14)
Summing over k then gives
dρ
ρṁ
+ ρ(∇ · ~v) =
= ρ̇.
dt
m
(3.15)
In addition, by definition
dmk
= ṁk .
dt
(3.16)
which gives
dqk
ṁk mk ṁ
1
=
−
=
(ṁk − qk ṁ).
dt
m
m2
m
(3.17)
The velocity equation
The advective form of the equations for the horizontal components of velocity is unaltered by mass changes. The horizontal velocity components thus
satisfy the equation
d~vh
1
~ × ~vh ) .
= − ∇h p − 2(Ω
h
dt
ρ
(3.18)
3.2. The ECHAM5/MPI-OM
34
~ is the earth’s rotation vector. Changes due to molecular stresses are
where Ω
neglected.
The thermodynamic equation
The first law of thermodynamics may be written
X
δQ + αdp = d1 H = d1
mk hk .
(3.19)
where H is the henthalpy, hk are specific enthalpies, α = 1/ρ is the specific
volume and the subscript 1 denotes changes independent of the mass changes
due to precipitation. As molecular diffusion is neglected, δQ represents the
heat received by the atmospheric element due to radiation and to heat exchange with falling rain or snow. Under the usual assumptions of perfect
gas behaviour for dry air and water vapour, and neglecting variations of the
specific enthalpies of water and ice with pressure, we can write the specific
henthalpy till the first order:
hk = hk 0 + Cpk T.
(3.20)
where Cpk is the specific heat with constant pressure and T the temperature,
eq.(3.19) becomes
mCp dT = αdp + δQ −
X
hk d1 mk
(3.21)
k
where
Cp =
X
Cpk qk
(3.22)
k
Thus considering a material volume of the atmosphere, we obtain the thermodynamic equation
Cp
X ṁki
dT
1 dρ
=
+ QR + QM −
hk
dt
ρ dt
m
k
(3.23)
where QR and QM are the heating rates due to respectively radiation and
the heat transferred from falling rain or snow.
3.2. The ECHAM5/MPI-OM
35
Flux equations
It is convenient to define the differential operator
D
Dt
by
dX
∂
D(X)
=
+ X(∇ · ~v ) =
+ ∇ · (X~v )
Dt
dt
∂t
(3.24)
Note that
ρ=
D(ρx)
dx
=
dt
Dt
if ρ̇ = 0
(3.25)
Equations (3.17), (3.18) and (3.23) may then be written
D(ρ)
ρ
= ṁ = ρ̇
Dt
m
(3.26)
ρ
D(ρqk )
= ṁk = ρ˙k
Dt
m
(3.27)
D(ρ~vh )
~ × ~vh )
= ρ̇~vh − ∇h p − 2ρ(Ω
h
Dt
(3.28)
Cp
X m˙ki
D(ρT )
dp
= Cp ρ̇T +
+ρ
hk
Dt
dt
m
k
(3.29)
From the definition (3.22) of Cp we obtain
D(Cp ρT )
D(ρT )
d X
Cpk qk
= Cp
+ ρT
Dt
Dt
dt k
(3.30)
and the use of (3.22) and (3.29) gives
X
D(Cp ρT )
dp
= Cp ρ̇T +
+ ρ(QR + QM ) − ρ
(h0k +
Dt
dt
k
X
ṁki
ṁk qk ṁ
+ ρT
Cpk
+
+Cpk T )
m
m
m
(3.31)
k
Using (3.2), (3.7) and (3.22), we obtain from (3.31):
X ṁki
X
dp
ṁke
D(Cp ρT )
=
+ ρ(QR + QM ) − ρ
h0k
+ ρT
Cpk
(3.32)
Dt
dt
m
m
K
k
Diffusive fluxes
We now introduce a separation of dependent variables into components that
3.2. The ECHAM5/MPI-OM
36
will be explicitly resolved in the model and components the effect of which
will require parameterization. If the bar operator represents an average over
unresolved scales in space and time, then we write:
′
X = X + X′
with X = 0
X = X + X ′′
with X = 0
and
′′
where
ρX
ρ
is a mass weighted average. It follows that
D ρX
D (ρX)
=
− ∇ · ρ~v ′′ X ′′
Dt
Dt
X=
dx
dX
=
− ~v ′′ · ∇X
dt
dt
ρXY = ρXY = ρX Y + ρX ′′ Y ′′
Using these results, equations (3.25) - (3.27) and (3.31) become
!
D (ρ)
ṁ
= ρ̇ = ρ
Dt
m
D ρ qk
= ρ̇k − ∇ · ρ~v ′′ qk′′ = ρ
Dt
D ρ ~vh
Dt
=ρ
ṁ
m
ṁk
m
!
− ∇ · ρ~v ′′ p′′k
(3.33)
(3.34)
~ × ~vh − ∇ · ρ~v ′′~v ′′ =
= ρ̇~vh − ∇h p − 2ρ Ω
h
!
′′
ṁ
ρ
~vh′′
m
h
~ × ~v ′′ − ∇ · ρ~v ′′~v ′′ −
~vh − ∇h ρ − 2ρ Ω
h
h
h
(3.35)
3.2. The ECHAM5/MPI-OM
37
and
dp
X
D ′′
′′
+ ρ QR + QM − ρ
ρCp T + ρCp T =
h0k
Dt
dt
k
+ρT
X
ṁke
m
Cpk
k
+
X
Cpk
ρT ′′
k
!
ṁke
m
+ ~v ′′ · ∇p − ∇ · ρ~v ′′ Cp T ′′ +
ṁki
m
!
+
(3.36)
′′
The equation of state (3.13) can be written
p = ρRT
(3.37)
where
R = (Rd qd + Rv qv )/[1 − ρ(ql vl + qi vi )]
whence
ρ = ρRT = ρR T + ρR′′ T ′′
P
Using Cp = Cpk qk , eq. (3.34) and (3.36) may be written
Cp
D ρT
Dt
X
dp
hk
=
+ ρ QR + QM − ρ
dt
k
+~v ′′ ∇p − ∇ · ρ~v ′′ (Cp T )′′ + T
X
X
D
−
ρCp′′ T ′′ +
Cpk ρT ′′
Dt
k
k
ṁ
m
Cpk ∇ · ρ~v ′′ qk′′ +
ṁke
m
!
(3.38)
+
(3.39)
′′
Approximations and definitions
At this stage, we make two approximations. The first is to neglect the higherorder correlations
ρT ′′
ṁke
m
′′
3.2. The ECHAM5/MPI-OM
in (3.39), the term
38
D
ρCp′′ T ′′
Dt
ρT ′′ R′′
in (3.38) and the term
ρ
ṁ
m
′′
~vh
in (3.35).
This is equivalent to assume that higher-order terms are important only when
eddy velocities and derivatives are involved.
The second approximations is to neglect the term in the equation of state, or
equivalently to neglect the volume occupied by liquid water and ice compared
with that occupied by dry air and water vapour. In addition we introduce
the following notation:
1. The vertical flux of a variable X, ρw ′′ X ′′ , is denoted by JX . Here w is
the vertical velocity component.
2. The term v ′′ · ∇p is added to the term
ing sum is expressed as the derivative
∂
ρw ′′ (Cp T )′′ and
∂z
∂JS
of the vertical
∂z
the resultflux of dry
static energy (static refers to sub-grid scale processes), plus a term
which is written ρQD and regarded as representing unorganized transfers between enthalpy and sub-grid scale kinetic energy. The latter is
parametrized by the heating implied by the dissipation of kinetic energy
due to the parametrized vertical momentum fluxes J~vh .
3. The net effect of horizontal fluxes is represented only by their contribution KX to the tendency
of variable X.
P
4. The term −ρ k hk ṁmki representing the latent heat release associated with internal phase changes is written ρQL .
Return to the advective form
With the above approximations and definitions, we obtain from the equations
of ”Diffusive fluxes”, omitting the bar operators
dρ
ṁ
+ ρ∇ · ~v = ρ
dt
m
(3.40)
3.2. The ECHAM5/MPI-OM
where
39
dqk
1 ∂Jqk
= Sqk −
+ Kqk
dt
ρ ∂z
(3.41)
1
1 ∂J~vh
d~vh
~
= ∇h p − 2 Ω × ~vh −
+ K~vh
dt
ρ
ρ ∂z
h
(3.42)
dT
1 dp
1
(QR + QL + QM + QD +
=
+
dt
ρCp dt Cp
"
#
X
∂Jqk
1 ∂JS
Cpk
) + KT
−T
−
ρ ∂z
∂z
k
(3.43)
Sqk =
ṁk
ṁ
− qk
m
m
(3.44)
In addition we have the equation of state
p = ρT (Rd qd + Rv qv )
(3.45)
and the hydrostatic equation
∂p
= −gρ
∂z
(3.46)
The model equations.
The model equations are finally obtained by neglecting density changes due
to precipitation or evaporation, setting ṁ = 0 in (3.40). This approximation
is traditionally made, although it is open to question. In addition, QM is set
to zero, an approximation of the same order as the assumption of no variation of latent heat with temperature that is made in the parametrizations.
The governing equations are
- momentum equations
d~vh
1
~ × ~vh ) − 1 ∂J~vh + K~v
= − ∇h p − 2(Ω
h
h
dt
ρ
ρ ∂z
(3.47)
- thermodynamic equation
dT
Rd Tv dp
1
=
+
(QR + QL + QD +
dt
pCp dt Cp
∂Jqv
1 ∂JS
) + KT
− Cpd T (δ − 1)
−
ρ ∂z
∂z
(3.48)
3.2. The ECHAM5/MPI-OM
40
- continuity equations for atmospheric constituents
1 ∂Jqi
dqi
= Sqi −
dt
ρ ∂z
(3.49)
- equation of state
p = ρRd Tv
(3.50)
- hydrostatic equation
∂p
= −gρ
∂z
(3.51)
1
− 1 qv
Tv = T 1 +
ǫ
(3.52)
with
In this case
Cp = Cpd (1 − qv ) + Cpv q
(3.53)
which is written
Cp = Cpd (1 + (δ − 1)qv )
where δ =
(3.54)
Cpv
.
Cpd
The model equations then follow from a change from z - to η-coordinates,
the formalism for which is given by Kasahara (1974)[18], and from rewriting
the adiabatic terms in their usual form for a spherical geometry.
Hence, it is convenient to introduce the equations and their spectral representation for a general pressure-based from terrestrial surface vertical coordinate
η(p, ps), which must be a monotonic function of the pressure p, and depends
as well on the surface pressure ps , in such a way that
η(0, ps) = 0 and η(ps , ps ) = 1
For example the continuity equation in η - coordinates is
∂ ∂p
∂p
∂
∂p
+ ∇ · ~vh
+
η̇
=0
∂η ∂t
∂η
∂η
∂η
(3.55)
Integrating equation (3.55), using the boundary conditions
η̇ = 0 at η = 0 and η = 1:
Z 1
∂ps
∂p
dη
=−
∇ · ~vh
∂t
∂η
0
(3.56)
3.2. The ECHAM5/MPI-OM
41
and
∂p
∂p
=− −
η̇
∂η
∂t
∂ ln ps
1
=−
∂t
ps
Z
η
0
Z
1
0
∂p
dη
∇ · ~vh
∂η
∂p
dη
∇ · ~vh
∂η
(3.57)
(3.58)
In order to apply the spectral method, some equations are written in terms
of vorticity and divergence. Thus, the basic prognostic variables of the model
are vorticity (V), divergence (D), temperature (T) , mass mixing ratios of
water vapor, cloud liquid water, cloud ice (qi ) , and log of surface pressure
(ln ps ) . While qi are represented in grid point space, the other variables, are
represented in the horizontal plane by truncated series of spherical harmonics:
X(λ, µ, η, t) =
N (M )
M
X
X
Xnm (η, t)Pnm (µ)eimλ
(3.59)
m=−M n=m
where X is any variable, m is the longitude wave number and n is the latitude
index. The Pnm are the Associated Legendre Functions of the first kind. The
variables λ, µ refer to the formalism given by Kasahara (1974)[18], η is the
monotonic function of the pressure p and t is the time.
The standard truncations used in ECHAM5 are at wave numbers 21, 31,
42, 63, 85, 106, or 159. Then, a grid of points covering the sphere is defined. Starting from the basic definition of the spectral expansions (3.59),
values of the prognostic variables are calculated at the gridpoints. The grid
on which the calculations are performed is chosen to give an exact contribution to spectral tendencies from quadratic non-linear terms. They may
thus be computed exactly using Gaussian quadrature, with points located at
the (approximately equally-spaced) latitudes which satisfy PNG (µ) = 0, for
sufficiently large integer NG . These latitudes form what are referred to as
the Gaussian latitudes. The associated number of Gaussian latitudes with
respect to the given spectral resolution in ECHAM5 is given in Table (3.1):
In this study we make use of ECHAM5 temperature output at a horizontal
resolution of T63 (see Table 3.1), which corresponds to a horizontal grid
spacing of approximately 140x210 km grid spacing at mid-latitudes (a grid
3.2. The ECHAM5/MPI-OM
42
Truncation
No. of Longitudes
No. of Latitudes
T21
64
32
T31
96
48
T42
128
64
T63
192
96
T85
256
128
T106
320
160
T159
480
240
Table 3.1: Truncation and associated number of Gaussian latitudes (and longitudinal number of gridpoints).
size of 1.875 degrees in longitude and roughly similar in latitude) and 31
vertical hybrid levels.
3.2.3
Model grids and resolution
Typical atmospheric GCM resolutions are between 1 and 5 degrees in latitude
or longitude. The number of vertical levels is usually on the order of 10 to
20, with variable spacing ranging from a few 100 m’s in the surface boundary
layer to a few km’s in the free atmosphere.
For having an idea of the complex solution of the equations, we can consider
how many degrees of freedom for the system we are dealing with. If the total
number of horizontal gridpoints is given by A/∆2 , where A is the area of the
globe and ∆ the average horizontal grid distance, and n is the number of
variables necessary to define the state of the atmosphere at each point, then
the total number of variables is n × k × A/∆2 .
For a standard finite difference model, uniform gridlines converge towards
the poles. This would lead to computational instabilities (CFL condition [5])
and so the model variables must be filtered along lines of latitude close to
the poles. Ocean models suffer from this problem too, unless a rotated grid
is used in which the North Pole is shifted onto a nearby landmass.
In mathematics, the CFL condition is a necessary condition for convergence
while solving certain partial differential equations numerically by the method
of finite differences. It arises when explicit time-marching schemes are used
3.2. The ECHAM5/MPI-OM
43
for the numerical solution. As a consequence, the time step must be less
than a certain time in many explicit time-marching computer simulations,
otherwise the simulation will produce incorrect results.
For one-dimensional case, the CFL has the following form:
u∆t
≤C
∆x
where u is the velocity of a generic constituent of climate system (for example
air mass), ∆t is the time step (whose dimension is Time), ∆x is the length
interval (whose dimension is Length), C is a dimensionless constant which
depends only on the particular equation to be solved. Hence, the CFL condition can be a very limiting constraint on the time step ∆t, when the grid
point separation is reduced, the upper limit for the time step also decreases.
3.2.4
Solution of model equations
Hence, the solutions of model equations are classified in three categories. The
first refers to ”Dry dynamics” which are vorticity (V), divergence (D), temperature (T) and log of surface pressure (ln ps ). For each components horizontal, vertical and temporal are used respectively spectral transform method,
finite differences (sigma-pressure) and semi-implicit leap-frog scheme with
time filter.
The second category refers to ”Advection of atmospheric constituents” and a
flux form semi-Lagrangian transport scheme (Lin& Rood, 1996) [22]has been
used.
The third categories is made up of ”Parameterized physics” on Gaussian
transform grid.
3.2.5
Parameterizations
Parameterization in a weather or climate model within numerical weather
prediction refers to the method of replacing processes that are too smallscale or complex to be physically represented in the model by a simplified
process. The dimensions of the spatial grid determine the minimum scale of
phenomena that can be resolved by the equations. The scales smaller than the
3.2. The ECHAM5/MPI-OM
44
minimum ones represent the so-called subgrid-scale processes. Thus, through
parameterization it is possible to describe the effects of all subgrid-scale eddies on the large-scale phenomena using appropriate diffusion schemes.
The ”Parameterized physics” category mentioned above for the ECHAM5
model refers to radiation, convection, stratiform clouds, vertical and horizontal diffusion, gravity wave drag and land surface processes.
The amount of solar radiation reaching ground level in rugged terrain, or due
to variable cloudiness, is parameterized as this process occurs on the molecular scale. In ECHAM5 the radiation process is characterized by two patterns.
The shortwave pattern is made up by the processes: gaseous absorption,
Rayleigh scattering and scattering and absorption by aerosols and clouds.
Thus, the atmospheric components are considered with respect their optical
properties. Infact for the gaseous absorption are considered the H2 O, CO2 ,
CH4 , N2 O, CF C ′ s, O3 and their respectively spectral ranges of absorption.
For the clouds optical properties, are considered the single scattering properties such as mass extinction coefficent (droplets, ice), single scattering albedo,
asymmetry factor, all parameterized in terms of the effective radii for cloud
droplets and ice crystals.
The longwave pattern is made up by the processes: emission, line absorption,
continuum absorption, scattering and absorption by aerosols and clouds. The
spectral resolution is fixed by 16 bands in the range of 3 - 1000 µm wavelenghts.
A typical cumulus cloud has a scale of less than 1 kilometer (0.62 mi), and
would require a grid even finer than this to be represented physically by the
equations of fluid motion. Therefore the processes that such clouds represent
are parameterized, by processes of various sophistication [25].
3.2.6
The MPI-OM ocean component
The ocean model MPI-OM is a primitive equation z-coordinate model with
a variable horizontal resolution [23]. An increased horizontal resolution is
employed between 5o S and 5o N, with a grid spacing of 0.5o in the meridional
and 2.5o in the zonal. The model has 23 vertical levels, with 10 over the upper
3.3. The NCEP reanalysis data
45
300 m. An example of the features of MPI-OM is that the primitive equations
for a hydrostatic Boussinesq fluid
1
are formulated with a free surface. The
vertical discretization is on z levels, and the bottom topography is resolved
by means of partial grid cells. The spatial arrangement of scalar and vector
variables is formulated on a orthogonal curvilinear Arakawa [2] C grid.
3.2.7
Coupling
Atmosphere, ice, and ocean are coupled by means of the Ocean-AtmosphereSea Ice-Soil (OASIS) coupler [31], which performs the interpolation between
ocean and atmosphere grids. From the atmosphere to the ocean OASIS transfers fluxes of momentum, heat and water; from the ocean to the atmosphere
it transfers sea surface temperature, sea ice thickness and sea ice concentration, snow thickness, and snow surface velocity. The coupled model includes
a river runoff scheme that treats river runoff and glacier calving interactively
in the atmosphere model, and the respective freshwater fluxes are passed to
the ocean as part of the atmospheric freshwater flux field.
3.3
The NCEP reanalysis data
Reanalysis is a scientific method for developing a comprehensive record of
how weather and climate are changing over time. In it, observations and a
numerical model that simulates one or more aspects of the Earth system are
combined to generate a synthesized estimate of the state of the system.
A reanalysis typically extends over several decades or longer, and covers
the entire globe from the Earth’s surface to well above the stratosphere.
Reanalysis products are used extensively in climate research, including for
monitoring and comparing current climate conditions with those of the past,
identifying the causes of climate variations and change, and preparing climate predictions. Information derived from reanalyses is also being used increasingly in commercial and business applications in sectors such as energy,
1
The Boussinesq fluid is incompressible (i.e., if density is independent of pressure) and
if the flow is adiabatic, the only way to change the density of a fluid parcel is through
the diffusion of heat and trace constituents through the sides of the parcel, and in most
applications the influence of such diffusion on density can be neglected.
3.4. The ESSENCE project
46
agriculture, water resources, and insurance.
The NCEP/NCAR (National Centers for Environmental Prediction / National Center for Atmospheric Research) daily maximum of 2m above the
surface temperature (T2m) reanalysis data are used in this study to evaluate
the ECHAM5 T2m outputs. The NCEP data are calculated by using a stateof-the-art analysis/forecast system to perform data assimilation using past
data from 1948 to the present. A large subset of this data is available from
the link 2 in its original 4 times daily format and as daily averages. However,
the data from 1948-1957 are a little different, in the regular (non-Gaussian)
gridded data.
3.4
The ESSENCE project
Often just one or a few transient coupled climate simulations are performed
for a given emission scenario due to the high computational demand of a
single simulation. This allows an assessment of the mean climate change
but, because of the strong internal variability, it is not possible to attribute
specific trends in model response to increased radiative forcing. To distinguish trends caused by internal variability from those induced by increased
radiative forcing, a large ensemble of climate simulations is necessary. The
usefulness of a large ensemble of simulations was demonstrated by Selten et
al. [2004] [28], who analyzed a 62-member ensemble integration over a 140
year period with version 1.4 of the CCSM climate model. In the present study
we make use of a multi-ensemble members produced within the ESSENCE
project (Ensemble SimulationS of Extreme weather events under Nonlinear
Climate changE). The ESSENCE project was performed a 17-member ensemble of runs with a state-of-the-art climate model. The model used is the
ECHAM5/MPI-OM coupled climate model. Model runs start in 1950 and
end in 2100. For the historical part (1950-2000) the concentrations of GHGs
and tropospheric sulfate aerosols are specified from observations, while for
the future (2001-2100) they follow the SRES A1b scenario [13]. The runs are
initialized from a long run in which historical GHG concentrations have been
used until 1950. Different ensemble members are generated by disturbing the
2
ftp://ftp.cdc.noaa.gov/Datasets/ncep.reanalysis/surface_gauss/
3.4. The ESSENCE project
47
initial state of the atmosphere. Gaussian noise with an amplitude of 0.1 K
is added to the initial temperature field. The initial ocean state is not perturbed. For more information about the model see Sterl et al. [2008][29].
In order to have an idea of the ESSENCE dataset and to have a preliminary
evaluation of the temperature model output data, Fig. 3.1 and Fig. 3.2 show
the daily maximum 2m-temperature (T2m) values for the 17 ensemble members (light gray open circles) their mean (black line) and NCEP observations (blue line), over the present period (decade 2001-2010) at two selected
grid points located in De Bilt-Netherlands (5o , 10′, 54′′ E; 52o, 6′ , 38′′ N) (Figure 3.1) and near Rome-Italy (15o E; 40o, 6′ , 20′′ N) (Fig. 3.2). The ECHAM5
model is able to well simulate the seasonal cycle: all the shown time series are
in phase and well synchronized with the NCEP observations. By comparing
the two selected stations the model outputs seem to fit better with NCEP
observations in De Bilt (Fig. 3.1) than in the center of Italy (Fig. 3.2) where
the daily maximum temperature values are overestimated of approximately
0.5o C with respect the NCEP data (Fig. 3.2).
The small discrepancy between NCEP model output data at the center of
Italy station is more evident by showing (Fig. 3.4) the annual-mean 2mtemperature daily maximum (T2m) for the 17 ensemble members (light gray
open circles), together with their mean (black line) and the observations
(annual mean NCEP dataset blue line) for the selected station. In De-Bilt
(Fig. 3.3) the average of the 17-ensemble annual mean is superimposed with
the NCEP annual mean, whereas at the center of Italy station (Fig. 3.4)
the model overastimates the annual mean temperature. The offset between
model and observation for the annual averaged data simulated in the center
of Italy was estimated equal to (0.5o) with a standard deviation of 0.1o C.
The annual mean of the temperature data are computed using CDO (see
Appendix D), while the average of 17-ensemble annual mean, the daily mean
in a single grid point (in the models nlon = 8, nlat = 26 for center Italy and
nlon = 4, nlat = 21 for De Bilt) and the Figures 3.4 and 3.3 are computed
using R [24].
3.4. The ESSENCE project
48
20
15
−10
−5
0
5
10
temperature (°C)
25
30
35
40
45
De Bilt − Netherlands
2001
2003
2005
2007
2009
2011
time
Figure 3.1: Daily temperatures as function of time (period 2001-2010) for the 17 ensemble members
(light gray open circles) their mean (black line) and NCEP observations (blue line) for station De Bilt
(The Netherlands) and (right panel) station close to Rome (Italy).
3.4. The ESSENCE project
49
20
15
10
5
0
−5
−10
temperature (°C)
25
30
35
40
45
Rome − Italy
2001
2003
2005
2007
2009
time
Figure 3.2: As Figure 3.1 but for station close to Rome (Italy).
2011
8
10
12
14
temperature (°C)
16
18
20
3.4. The ESSENCE project
50
time (year)
2100
2090
2080
2070
2060
2050
2040
2030
2020
2010
2000
1990
1980
1970
1960
1950
Figure 3.3: Annual-mean of T2m for the 17 ensemble members (light gray open circles), their mean
(black line) and NCEP observations (blue line) for station De Bilt (The Netherlands).
De Bilt − Netherlands
16
18
20
22
temperature (°C)
24
26
Figure 3.4: As Figure 3.3 but for station close to Rome (Italy).
51
time (year)
2100
2090
2080
2070
2060
2050
2040
2030
2020
2010
2000
1990
1980
1970
1960
1950
28
3.4. The ESSENCE project
Rome − Italy
Chapter 4
Climate Indices and Statistical
Methods
”I’m not a great programmer;
I’m just a good programmer with great habits.”
- Kent Beck -
4.1
Introduction
Emil Julius Gumbel (1891-1966), pioneer of extreme value theory, said:
”It is impossible that the improbable never happens”[9].
An extreme weather event is an event that is rare at a particular place and
time of year. As an example the impressive snowfall occurred this winter in
the center of Italy can be considered as an ”Extreme”. There is a general
consensus within the climate scientist that any change in the frequency or
severity of extreme climate events would have profound impacts on nature
and society [17]. It is thus very important to analyze extreme events. Within
a changing climate system, some of what are now considered to be extreme
events will occur more frequently. Figure 4.1 shows a stylized representation
of extremes. The most commonly used definition of extreme weather is based
on an event’s climatologically expected distribution. An event is called extreme in this sense if it is from the tails of the climatological distribution,
occurring, for example, only 5% or less of the time (4.1). The exact threshold for what is classified as an extreme varies from one analysis to another,
4.1. Introduction
53
but would normally be as rare as, or rarer than, the top or bottom 10%
of all occurrences. Figure 4.2 illustrates how the tails of the distribution of
temperature are anticipated to change in a warming world. For temperature,
both the location parameter and the tails of the distributions are expected
to move in the direction of warming. Obviously a Probability Distribution
Function (PDF) shifting in the direction of higher temperature values will
produce a temperature increasing of the same ∆T at each quantile meaning
that temperature values which were quite rare in the past will become more
common in the future. Many currently rare extreme events will become more
commonplace [17]. There are many important features of extreme events
Probability of occurrence
What is an Extreme?
Temperature
Cold
Temperature
extremes
Hot
Temperature
extremes
5%
Cold
5%
Average
Hot
Figure 4.1: Probability distributions of daily temperature. Extremes are denoted by the shaded areas.
for the present and the predicted future. The importance is related to the
impacts and adaptations by society and environment.
The most commonly considered aspect is frequency. Is the extreme occurring
more frequently? Will currently rare events become commonplace in 50 years?
Changes in intensity are as important as changes in frequency. There are
also temporal considerations, such as time of occurrence and duration. The
duration of extreme events (such as heat wave) is also potentially subject
to change. Spatial characteristics need to be considered. Is the size of the
impact area changing? In addition to the size of the individual events, the
location is subject to change.
4.2. Climate Indicators
54
probability of occurrence
Increase in Probability of
Extremes in a Warmer Climate
Temperature
Previous
Climate
Less
cold
weather
Cold
More
hot
weather
More
record hot
weather
New
Climate
Average
Hot
Figure 4.2: Simplified depiction of the changes in temperature in a warming world. Extremes are denoted
by the shaded areas.
In order to answer to the previous questions, concerning Heat Wave events as
reported in the introduction, in this chapter we describe the most common
climate indices defined by Frich et al. (2002)[8] and revised by the Expert
Team on Climate Change Detection and Indices (ETCCDI)1 mainly focusing
on Heat Wave indices. Additionally, we define some new indices measuring
the intensity of a summer Heat Wave event.
4.2
Climate Indicators
Frich et al. [2002] ([8]) produced a global data set of derived indicators to
clarify whether the frequency and severity of climatic extremes changed during the second half of the 20th century.
Later the joint World Meteorological Organization Commission for Climatology (CCl)/World Climate Research Programme (WCRP) project on Climate Variability and Predictability (CLIVAR) Expert Team on Climate
Change Detection Indicators (ETCCDI) coordinated two complimentary efforts to enable global analysis of extremes[1].
1
http://cccma.seos.uvic.ca/ETCCDMI/indices.shtml
4.2. Climate Indicators
55
One effort was the international coordination of the development of an ensemble of climate change indices which primarily focus on extremes. The
second ETCCDI effort was to coordinate regional workshops with the aim of
addressing gaps in data availability and analysis in previous global studies [8].
Finally ETCCDI has defined a core set of descriptive indices of extremes. The
indices describe particular characteristics of extremes, including frequency,
amplitude and persistence. The core set includes 27 extremes indices for temperature and precipitation. In this study we will focus only in temperature
related indices in order to select and define indices able to estimate the magnitude of the three main characteristics, duration, frequency and intensity,
of an Heat-Wave event.
4.2.1
Index Selection and Definition
The 27 indices recommended by the ETCCDI are derived from daily maximum and minimum temperature and daily precipitation. They represent
events that occur several times per season or year giving them more robust
statistical properties than measures of extremes which are far enough into
the tails of the distribution so as not to be observed during some years. The
indices can be divided into 5 different categories[1]:
Percentile-based indices: Percentile-based indices are indices with the
threshold defined by using a percentile of an empirical Probability Distribution Function (PDF). They include occurrence of cold nights (TN10p), occurrence of warm nights (TN90p), occurrence of cold days (TX10p), occurrence
of warm days (TX90p). The temperature percentile-based indices sample the
coldest and warmest deciles for both maximum and minimum temperatures,
enabling us to evaluate the extent to which extremes are changing.
Absolute indices: Absolute indices represent maximum or minimum values
within a season or year. They include maximum daily maximum temperature
(TXx), maximum daily minimum temperature (TNx), minimum daily maximum temperature (TXn), minimum daily minimum temperature (TNn).
Threshold indices: Threshold indices are defined as the number of days on
which a temperature value falls above or below a fixed threshold, including
annual occurrence of frost days (FD), annual occurrence of ice days (ID),
annual occurrence of summer days (SU), annual occurrence of tropical nights
4.2. Climate Indicators
56
(TR). These indices are not necessarily meaningful for all climates because
the fixed thresholds used in the definitions may not be applicable everywhere
on the globe.
Duration indices: Duration indices are defined as the time period in which
the data are above some threshold. The Warm Spell Duration Index (WSDI)
and Cold Spell Duration Index (CSDI) are two examples of temperature
duration indices[26].
Other indices: Other indices include indices of diurnal temperature range
(DTR), simple daily intensity index (SDII), extreme temperature range (ETR).
They do not fall into any of the above categories but changes in them could
have significant social impacts.
4.2. Climate Indicators
57
Index
Definition
Unit
TX90p
Warm days: percent (or number) of days per month with daily maximum
days
temperature over the 90th percentile of the reference period.
TN90p
Warm nights: As TX90p, but using minimum daily temperature.
days
TX10p
Cold days: percent (or numbers) of days per month with daily maximum
days
temperature below the 10th percentile of the reference period.
TN10p
Cold nights: As TX10p, but using minimum daily temperature.
days
ITX90p
Intensity of warm spells: Degree-days above 90% threshold[26].
degree-days
ITN10p
Intensity of cold spells: Degree-days below 10% threshold[26].
degree-days
WSDI
Warm spell duration: Maximum period with more than 5 consecutive days
days
with maximum temperature above the 90th percentile of the reference
period.
CSDI
Cold spell duration: Maximum period with more than 5 consecutive days
days
with minimum temperature below the 10th percentile of the reference period.
ETR
Intra-annual extreme temperature range: difference between the highest
days
temperature observation for any given calendar year and the lowest temperature reading of the same calendar year.
Table 4.1: An example of temperature’s indices listed by index, definition and unit [26].
Table 4.1 shows a list of some temperature’s indices selected from the ETCCDI with their definitions and units. For example, the Warm Spell Duration
Index (WSDI) is defined as maximum period with more than 5 consecutive
days with maximum temperature above the 90th percentile of the reference
period [26].
4.3. On the definition of Heat Wave indicators
4.3
58
On the definition of Heat Wave indicators
The list of climate indicators defined by the ETCCDI does not include any
index characterizing the intensity and duration of an Heat Wave.
Frich et al. 2002 [8] have defined the Heat Wave duration index (HWDI) as
the maximum period more than 5 consecutive days with daily temperature
maximum exceeding 5o C above the 90th percentile, where this percentile is
calculated for each day from 1961-1990 data for a 5-day window centered on
a fixed date (see sec 4.4.2).
The HWDI index, due to the fixed threshold of 5o C above climatology, is
difficult to apply in places where day-to-day variability in temperature is
very small, such as tropical regions ([1],[26], [32]). Moreover the index does
not characterize at all an Heat Wave event, since it detects only the duration
without giving any information about intensity, occurrence and frequency.
In this section, in order to overcome the limitations of the HWDI index discussed above and to detect the other foundamental features of a Heat Wave,
such as intensity and frequency, we define four new Heat Wave indicators
called as: Heat Wave Duration (HWD-nth), Heat Wave Intensity (HWInth), Heat Wave 5 days maxima Intensity (HWI5-nth) and Heat Wave
Frequency (HWF-nth).
All these are percentile based indices with n representing the level of the
selected percentile. In this study, in order to detect moderate or intense ”Extremes”, we have chosen three values of n corresponding to the 90th, 95th,
98th percentile threshold. Moreover the indices are defined twice with respect
a stationary and no-stationary threshold. We want to test if the two sets of
indicators (4 for each set for a fixed n) give us significantly different information on future changes of Heat Wave events.
Before to define the indicators a brief description of the stationary and nostationary threshold is reported below.
4.4
Threshold definition
The thresholds are computed, as usually done, from a common base period
1961-1990 at each grid point.
4.4. Threshold definition
4.4.1
59
Stationary threshold
The stationary threshold is defined as a fixed percentile of the summer season.
The daily maximum temperature data for the reference period (1961-1990)
are split by seasons in order to select the boreal and austral summer respectively for the Northern and Southern hemisphere. Hence the value at one
grid point of the stationary threshold is the nth percentile of the following
set of data:
AStat =
1990
[
Ty,d
(4.1)
y=1961
where ∪ denotes the union of sets, Ty,d is the value of temperature of the y
year and d is a day within the summer season, June-July-August (JJA) and
December-January-Febrary (DJF) respectively for the Northern and Southern hemisphere.
As an example Figure 4.3 shows, for a selected grid point located in the center of Italy, the temperature values of the AStat set of data as function of
time and the relative stationary thresholds respectively for the 90th , 95th and
98th percentiles represented by the black, blue and green lines.
60
1961
1970
time
1980
1990
4.4. Threshold definition
15
20
25
30
35
40
45
temperature (°C)
Figure 4.3: Temperature values of the AStat set of data as function of time (open gray points), releaved
in center of Italy (lon = 15o E, lat = 40o 6′ 10′′ N ) and the relative stationary thresholds respectively for
the 90th , 95th and 98th percentiles represented by the black, blue and green lines.
4.4. Threshold definition
4.4.2
61
No-Stationary threshold
The daily threshold for the reference period 1961-1990 is defined as the nth
(in this case n = 90, 95, 98) percentile, centered on a 5-day window.
We use the so-called five consecutive days (5CD) centered on the day of
interest. So for a fixed day d, the threshold is the nth percentile of the set of
data Ad defined by
Ad =
1990
[
y=1961
d+2
[
Ty,d′
(4.2)
d′ =d−2
where ∪ denotes the union of sets, Ty,d′ is the value of temperature of the y
year and d′ is a day within the five days window centered on the fixed day d.
By following the definition above the moving threshold can be defined for
each day of the year.
For this study we only use the moving threshold related to the summer season.
Figure 4.4 shows a graphical example of the moving threshold calculated at a
selected grid point in the center of Italy for each day of the year. The summer
moving threshold used for the calculation of our indices is represented by the
points between the two vertical black dashed lines.
62
days
1
90
180
270
365
4.4. Threshold definition
−5
0
5
10
15
20
25
30
35
40
temperature (°C)
Figure 4.4: Temperature values of the Ad (1 ≤ d ≤ 365) set of data as function of time (open gray
points), releaved in center of Italy (lon = 15o E, lat = 40o 6′ 10′′ N ) and the relative no-stationary thresholds
respectively for the 90th , 95th and 98th percentiles represented by the black, blue and green lines. The
points between the two vertical black dashed lines represent the summer moving threshold used for the
calculation of our indices.
4.5. Heat Wave indices definition
4.5
63
Heat Wave indices definition
The definition of the Heat Wave indices used in this study is reported below.
4.5.1
The HWD-nth index
HWD-nth - Heat Wave Duration: maximum period with more than 5 consecutive days with maximum temperature above the nth percentile threshold.
Figure 4.5 shows graphical examples of HWD-90th calculation both for stationary and no-stationary threshold. The index is represented by the black
full points connected by black lines. We can note that for the two thresholds
of the same 90th percentile (black thick lines), HWD-90th is different, infact
in a) is 8 days, while in b) is 5 days.
4.5.2
The HWI-nth index
HWI-nth - Heat Wave Intensity: the sum of the temperature’s differences
from threshold of each day into a Heat-Wave based on the nth percentile
threshold. Figure 4.5 shows graphical examples of HWI-90th calculation both
for stationary and no-stationary threshold. The shaded gray area shows the
temperature’s differences from the 90th percentile threshold with each daily
temperature into the Heat-Wave.
4.5.3
The HWI5-nth index
HWI5-nth - Heat Wave Intensity 5 days: the sum of the temperature’s
differences from threshold of the first 5 maximum temperatures into a Heat
Wave based on nth percentile threshold. Elementary, if HWD-nth = 5 days,
HWI-nth = HWI5-nth. Figure 4.5 shows a graphical examples of HWI5-90th
calculation both for stationary and no-stationary threshold. The dashed black
lines represent the temperature’s differences from 90th percentile threshold
with each first five maximum daily temperatures into the Heat-Wave.
4.5. Heat Wave indices definition
4.5.4
64
The HWF-nth index
HWF-nth - Heat Wave Frequency: number of Heat Waves based on nth
percentile threshold in a year.
40
35
25
30
35
25
30
Temperature (°C)
40
45
b) Heat Wave for no−stationary threshold
45
a) Heat Wave for stationary threshold
200
210
220
Days of a year
230
240
200
210
220
230
240
Days of a year
Figure 4.5: A graphical representation of a Heat Wave placed in center Italy (lon = 15o E, lat =
40o 6′ 10′′ N ) for year 2016. It represents a Heat Wave for: stationary threshold and. Thresholds are related
to 90th percentile and are shown in black thick line. HW Duration for at least 5 consecutive days above
the threshold is shown in black full points. The shaded gray area is related to HW Intensity and the dashed
black lines represent the Intensity for each five maximum temperatures into the Heat-Wave (HWI5-90th).
Chapter 5
Results
”Any fool can write code that a computer can understand.
Good programmers write code that humans can understand.”
- Martin Fowler -
5.1
Model Output Evaluation
For the model output evaluation the median of the 50th percentile and maximum of temperatures are computed for the summer season over the reference period between 1961 and 1990 for the ESSENCE project output and
the NCEP data (see section 3.3). Median and extreme summer temperatures as derived from ECHAM5 model outputs and NCEP data are shown
in Figures 5.1. In order to calculate the ESSENCE-NCEP differences the
NCEP daily maximum temperature data were interpolated (using CDO, Appendix D) onto the ECHAM5 grid (T63). For each of the 30 years of the evaluation period we calculate the 50th percentile and maximum for the summer
season (DJF and JJA respectively in the southern and northern hemisphere)
from both ECHAM5 and NCEP and compute their median. (Figures 5.1).
Qualitatively, observations and model outputs match very well. The hot and
cold patterns, for both summer medians and extremes, are well reproduced
(Figures 5.1, first and second column). Quantitatively, the differences (Figures 5.1, 3rd row) over 70-80% of ocean is within the range of -2o C and 2o C,
whereas over the land in almost the entire world the absolute value of the
differences do not exceed 3o C. In general, the model shows a fair degree of
5.1. Model Output Evaluation
66
correspondence with the observations.
A further comparison between ECHAM5 model and NCEP data is done at
global scale. Figure 5.2 shows the annual-mean 2m-temperature (T2m ) averaged globally for the 17 ensemble members (light gray open circles), together
with their mean (black line) and the NCEP observations (blue line).
Although the ensemble-spread of the global-mean T2m is fairly small (∼ 0.4o
C), differently with respect to Sterl et al. 2008a [29] who have demostrated
that the ECHAM5 T2m global mean encompasses the HadCRUT3 dataset
([4]) observations, a small offset of 0.5 ± 0.15 o C is detected here comparing
ECHAM5 and NCEP dataset. Between 1951 and 2011 the observed globalmean temperature increased by 0.61 o C, while the ensemble-mean gives an
increase of 0.72 o C. Observed and modelled temperature trends are nearly
identical. This gives confidence in the model’s sensitivity to changes in GHG
concentrations. The global-mean temperature increases by 4o C between 2000
and 2100, and the statistical uncertainty of the warming is extremely low
√
(0.4o C/ 17 ∼ 0.1o C). Thus within this particular climate model, i.e., ne-
glecting model uncertainties, the expected global warming of 4o C in 2100 is
very robust and the estimation of Heat-Wave events from model outputs can
be considered significantly realistic.
5.1. Model Output Evaluation
67
Median
Maximum
0
−60
NCEP
60
60
40
20
(°C)
0
−20
−40
0
−60
30
10
5
4
3
2
−2 (°C)
−3
−4
−5
−10
−30
0
−60
Differences
60
ESSENCE
60
60
40
20
(°C)
0
−20
−40
−150
−50
0
50
100
−150
−50
0
50
100
Figure 5.1: Median of 50th percentile (left column) and maximum (right column) temperature (o C) for
summer season over the period 1961-1990 for NCEP (1st row) and ESSENCE data (2nd row). The 3rd
row show ESSENCE-NCEP absolute differences expressed as Celsius degrees.
68
time (years)
1950
1960
1970
1980
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
5.1. Model Output Evaluation
15.0
15.5
16.0
16.5
17.0
17.5
18.0
18.5
19.0
19.5
20.0
temperature (°C)
Figure 5.2: Annual-mean Earth’s surface temperature for the 17 ensemble members (light gray open
circles), their mean (black line) and NCEP observations (blue line) for the global average.
5.2. Results: General Considerations
5.2
69
Results: General Considerations
The Heat-Wave indicators defined in Section 4 are calculated yearly for each
model run for the period between 1951 and 2100. The Heat-Wave indicators
are calculated using R. We used RNetCDF package[24] to export and open
the NetCDF
1
Dataset (T2m of the ESSENCE and NCEP) into R. We ela-
borate R-Scripts to compute the indicators. The Heat Wave function script
elaborated is shown in Appendix B.
In order to detect the evolution of the indeces, we considered median, 90th
and 99th percentile calculated by splitting each run of data into fifteen consecutive periods of 10 years. Then we associated 90th and 99th percentile
respectively to 10 years and 100 years return value.
Figure 5.3 show rispectively, the time evolution, in a fixed grid point located
in the center of Italy, of the HWD-98th, HWI-98th and HWI5-98th, for the
17 ensemble members (gray open circles), together with their mean (black
line). The cyan, blue and black circles are respectively median, 10-years return value and 100-years return value calculated by splitting each run of data
into fifteen consecutive periods of 10 years. During each 10 years the climate
change signal is not-significant, hence, we can treat 10 years as stationary.
Furthermore the 17 realizations are independent as their pairwise correlations
are small, and year-to-year values are independent as the autocorrelation decay time is shorter than 1 year.
Each sample for all the parameters (median, 90th and 99th percentile) estimated for an Heat Wave event is a set of 17(ensembles)*10(summer seasonal
data)=170 events defined as follows:
HWi =
17
[
ymax,i
[
HW E(e, y),
(5.1)
e=1 y=ymin,i
for i = 1, . . . , 15, with (ymin,1 , ymax,1 ) = (1951, 1960), . . . , (ymin,15 , ymax,15 ) =
(2091, 2100). Here ∪ denotes the union of sets, e the model ensemble member,
and HWE denote a single Heat Wave event calculated for summer season.
1
NetCDF (Network Common Data Form) is a set of software libraries and self-
describing, machine-independent data formats that support the creation, access, and sharing of array-oriented scientific data.
5.2. Results: General Considerations
70
The parameters defined in this study to detect Heat-Wave changes in a changing climate are calculated for all the previous set of data, but are shown only
for three selected sets: HW4 , HW9 , HW14 corresponding respectively to the
periods: 1981-1990 (past), 2031-2040 (near-future) and 2081-2090 (future)
marked by dashed gray vertical lines in the Figure 5.3. Moreover Figure 5.4
show the relative differences expressed as % between median, 90th-percentile
and 99th percentile of the HWD-90th, HWI-90th and HWI5-90th calculated
with respect the no-stationary threshold and the corresponding parameters
of the indicators with stationary threshold.
The differences, referring only to the past period, in almost the entire world
are within the range of −25% and 25% meaning that no additional informa-
tion are given if we use stationary trheshold with respect the no-stationary
threshold indicators and viceversa.
In this study, in order to consider summer day-to-day variability we will
show only results for the parameters defined above calculated only for the
no-stationary threshold indicators.
71
30
10
20
HWD−98th (n. days)
40
50
5.2. Results: General Considerations
1961
1971
1981
1991
2001
2011
2021
2031
2041
2051
2061
2071
2081
2091
150
100
0
50
HWI−98th (°C)
200
250
1951
1960
1970
1980
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
1950
1960
1970
1980
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
45
30
0
15
HWI5−98th (°C)
60
75
1950
Figure 5.3: Time evolution, in a fixed grid point located in the center of Italy (lon = 15o E, lat =
40o 6′ 10′′ N ), of the HWD-98th, HWI-98th and HWI5-98th indeces for the 17 ensemble members (gray
open circles), together with their mean (black line). The cyan, blue and black circles are respectively
median, 10-years return value and 100-years return value, calculated by splitting each run of data into
fifteen consecutive periods of 10 years.
5.3. Will the probability of HW occurrence increase in the future?
90th
99th
0
−60
0
0
−60
HWI5−90th
60
−60
HWI−90th
60
HWD−90th
60
median
72
−150
−50
0
50
100
−150
−100
−75
−50
−50
−25
0
25
50
100
50
−150
75
−50
0
50
100
100
relative difference (%)
Figure 5.4: Relative differences calculated as ((no-stationary - stationary)/stationary)*100 and expressed
as % for the time period 1981-1990. Differences of the medians, 90th and 99th percentiles are represented
in the left, middle and right panels respectively.
5.3
Will the probability of HW occurrence
increase in the future?
While many studies have demostrated that in a future climate we will have
more intense and longer Heat-Waves ([1, 3, 8, 32]) not much has been said
about their future occurrence and frequency. In this study the Heat-Wave
occurrence is defined as the probability to have at least an event once a year
whereas the frequency is calculated as the number of Heat-Waves in a year.
Heat-Wave occurrence can be considered as a logic variable which assume
value 1 and 0 respectively when Heat-Wave occurres and does not occurre.
As discussed in Section 5.2 this variable is random within each set HWi for
i = 1, . . . , 15 and distribuited by following a Bernoulli’s distribution.
The Bernoulli distribution is a discrete probability distribution, which takes
value 1 with success probability p and value 0 with failure probability q =
5.3. Will the probability of HW occurrence increase in the future?
73
1 − p, where 0 < p < 1. It therefore has Probabily Density Function :
(
1 − p for k = 0
P (k) =
p for k = 1
The probability mass function f of this distribution
f (k, p) = pk (1 − p)1−k for k ∈ {0, 1}.
(5.2)
By means of maximum likelihood estimator we have fit with a Bernoulli
distribution the HWi set in order to estimate the probability coefficient k.
If k = 0 it means that yearly we have a null probability of occurrence of a
Heat-Wave, whereas if k=1 at 100% we will have a Heat-Wave in a year.
Figures 5.5, 5.6 and 5.7 show the estimated k probability coefficient over the
entire world for a Heat Wave calculated with respect to the 90th (HW90th,5.5),
95th (HW95th, 5.6), 98th (HW98th, 5.7) percentiles for the selected periods
past, near future and future respectively upper, middle and lower panels. An
increasing trend is evident from past to future with a probabiltiy coefficient
equal 1 in the future over the tropical regions for both the three indicators
HW90th, HW95th and HW98th. In the past the probability coefficient estimated for the HW90th does not exceed the value of 0.4 in almost the entire
world. There are only small region localized in the southern subtropics and
extra-tropics where a higher probability of occurrence of a Heat-Wave has
been detected. In the same period while the HW95th shows the same patterns
of the HW90th with lower k values the probability coefficient estimated for
the HW98-th does not exceed the value of 0.1 and in many regions, mainly
located between −45o N and 45o N, any Heat-Wave has occurred. The same
regions show a high probabilty of Heat Wave occurrence in a future climate
with k approximately equal 1.
In general we can conclude that under A1B IPCC scenario in the future if
we count an Heat-Wave event with respect the 90th percentile threshold over
the 80 % of the globe we will have a Heat Wave once a year. In the case of
the 98th percentile the scenario seems to be more drastic in the tropical and
subtropical regions than the extratropics.
5.3. Will the probability of HW occurrence increase in the future?
74
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
HW 90th
−150
0.0
−50
0.2
0.4
0
50
0.6
100
0.8
1.0
Probability
Figure 5.5: Probability of occurrence of an Heat Wave with respect to the 90th percentile no-stationary
threshold. Upper, middle and lower panels are related respectively to the three different selected periods:
1981-1990 (past), 2031-2041 (near future), 2081-2090 (future). White areas represent areas with no HeatWaves.
5.3. Will the probability of HW occurrence increase in the future?
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
HW 95th
−150
0.0
−50
0.2
0.4
0
50
0.6
100
0.8
1.0
Probability
Figure 5.6: As Figure 5.5 but for 95th percentile no-stationary threshold.
75
5.3. Will the probability of HW occurrence increase in the future?
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
HW 98th
−150
0.0
−50
0.2
0.4
0
50
0.6
100
0.8
1.0
Probability
Figure 5.7: As Figure 5.6 but for 98th percentile no-stationary threshold.
76
5.4. Will the HW frequency increase in the future?
5.4
77
Will the HW frequency increase in the
future?
In Chapter 4 HWF-nth index is calculated by counting the number of HeatWave events occurring in a year. Figures 5.8 and 5.9 show past and future
projections of 10-years (90th percentile) and 100-years (99th percentile) return values calculated for the HWF-98th. In the past period (upper panel
Fig. 5.8), 10-years return values are everywhere equal to 1, whereas in 100years (upper panel Fig. 5.9) in some small tropical region (i.e. Africa and latin
America) the Heat-Wave frequency is more than once a year. The HWF98th scenario is different in the future (middle and lower panels Fig. 5.8
and Fig. 5.9), the 10-years and 100-years return values of the HWF-98th are
strongly increasing under climate change with 100-years HWF-98th return
value exceeding 1 everywhere. The higher increasing are detected over the
tropics, in particular, the Sahel Region (Burkina Faso, Chad, Mali, Mauritania, Niger, Senegal etc...) shows a drastic scenario with not less than six
Heat-Waves per year. A strong climate change impact is also detected in
other subtropical and tropical regions as the Mediterranean Basin, Eastern
Latin America, Southern United States and Northen Australian.
5.4. Will the HW frequency increase in the future?
78
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
Ret. Val. 10−years
−150
1
2
−50
3
4
0
5
50
6
7
100
8
9
10
HWF−98th
Figure 5.8: 10-years return values of the HWF-98th no-stationary threshold, over the 17 ESSENCE
ensembles. Upper, middle and lower panels are related respectively to the three different selected periods:
1981-1990, 2031-2041, 2081-2090. White areas represent areas with no Heat-Waves.
5.4. Will the HW frequency increase in the future?
79
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
Ret. Val. 100−years
−150
1
2
−50
3
4
0
5
50
6
7
100
8
HWF−98th
Figure 5.9: As Figure 5.8 but for 100-years return value.
9
10
5.5. Can we expect longer future Heat-Waves?
5.5
80
Can we expect longer future Heat-Waves?
The values of the HWD-98th index are expected to increase in a changing
climate over the entire globe. The increasing order is higher over the tropical
area than the extratropical where HWD-98th 10-year and 100-year return
values do not exceed 30 days (Figures 5.10 and 5.11).
As for the frequency in the tropics the future scenario will be extremely
warmer with very long Heat-Waves. The 100-year HWD-98th return values
in some part of the Sahel and Arabian peninsula are detected above the value
of 60 day.
In general in 2081-2090 all the regions located between 40o S and 40o N will be
extremely drier [27]. There is in the future, some probability to have a year
in which all the summer days are above the 98th percentile moving threshold
defined for the reference period (1961-1990). As showed in the upper panels
of Figures 5.10 and 5.11 a Heat-Wave with a duration of 10 days was really
an extreme event in the past, whereas in the near future and future it will
be the normality.
In summary longer Heat-Wave are spreading everywhere in the next near
future and future under A1B climate change scenario.
5.5. Can we expect longer future Heat-Waves?
81
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
Ret. Val. 10−years
−150
5
7
−50
9
13
0
17
50
100
21
60
days
Figure 5.10: 10-years return value of the HWD-98th no-stationary threshold, over the 17 ESSENCE
ensembles. Upper, middle and lower panels are related respectively to the three different selected periods:
1981-1990, 2031-2041, 2081-2090. White areas represent areas with no Heat-Waves.
5.5. Can we expect longer future Heat-Waves?
82
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
Ret. Val. 100−years
−150
5
7
−50
9
13
0
17
50
100
21
60
days
Figure 5.11: AS Figure 5.10 but for the 100-years return values of the HWD-98th no-stationary threshold.
5.6. Can we expect more intense future Heat-Waves?
5.6
83
Can we expect more intense future HeatWaves?
Heat Wave Intensity index
The previous duration indices represent an empirical way to study the change
of the number of consecutive days over a threshold. However, they do not
give any information about the values above that threshold. Russo and Sterl
(2011) [26] have defined some indices in order to detect intensity of number
of days over theshold. In section 4.5 we have adapted these indices to define
the intesity of an Heat-Wave. The intensity is quite important in order to
characterize the Heat-Wave impact. It could be that the number of threshold
exceedances is increasing while the values over the threshold have no significant trend or vice versa. As an example it could be also that two Heat-Waves
HW1 and HW2 with length respectively of 5 and 20 days could have the same
intensity if all the five days of the HW1 and the twenty days of HW2 are
exceeding the threshold respectively of 1o C and 0.25o C (see Fig. C.1 in Appendix C). In this case the HWI index calculated for both HW1 and HW2
will assume the value of 5 o C. But what is the Heat-Wave event between
HW1 and HW2 affecting more the environment? Is it more drastic a long
Heat-Wave with each day having small values above threshold or a short
Heat-Wave with high threshold exceedances? We think that to have a more
effective estimation of Heat-Wave impact the Heat-Wave intensity has to
be referred to some normalized value with respect the Heat-Wave duration.
That is the reason because to investigate on Heat-Wave intensity we have
defined two indices the HWI and the HWI5. The latter can be considered as
duration independent since it is calculated by summarizing the 5 temperature maximum days during a Heat-Wave event.
Figures 5.12 and 5.13 show 10-years and 100-years return values calculated
for the HWI-98th. The HWI-90th and HWI-95th (not shown) have the same
behavior of the HWI-98th, but with lower values. In order to not be redundant we show the results only for the HWI-98th, which is, respect to the
others indices based on the 90th and 95th percentile threshold, related to
higher extreme value temperatures.
The patterns of the 10-year and 100-year HWI-98th return values follow the
5.6. Can we expect more intense future Heat-Waves?
84
spatial distribution of the corresponding return values of the HWD-98th indices both in space and time. In the tropics, as seen for the duration indices,
the Heat-Wave intensity increases more than extratropics. Even if in the near
future (2031-2040), apart small patterns with the highest HWI-98th values
over Northen Latin America and India, very high values are observed in the
northern extratropics above the latitude of 50o N. In Scandinavia, Eurasia
and Alaska we have observed points with 100-year return HWI-98th values
above 90o C, meaning that if we have an Heat-Wave duration of 30 days each
day is exceeding the 98th percentile threshold of 3o C. An Heat-Wave so long
and intense did not have any probability to occurre in the past while today
and in the near future it could happen. An example is represented by the two
Heat-Wave events, briefly descripted in the introduction, occurred in 2003
and 2010 respectively in Spain and Russian. In the future (lower panels Figures 5.12 and 5.13) what was extreme in the 2031-2040 will become normal,
in fact we see that the HWI-98th values observed for the 100-year return
values (Fig. 5.13 middle panel) are now observed as 10-year return values
(Fig. 5.12) lower panel) with higher values. The future 100-year Heat-Wave
intensity return values are really impressive and will produce a devastating
scenario. All the regions in the globe are expected to have very high intensity
Heat-Wave with HWI-98th index above the values of 90o C over more than
75% of the global area.
5.6. Can we expect more intense future Heat-Waves?
85
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
Ret. Val. 10−years
−150
0
3
−50
5
15
0
30
50
50
100
90 360
(°C)
Figure 5.12: 10-years return value of the HWI-98th no-stationary threshold, over the 17 ESSENCE
ensembles. Upper, middle and lower panels are related respectively to the three different selected periods:
1981-1990, 2031-2041, 2081-2090. White areas represent areas with no Heat-Waves.
5.6. Can we expect more intense future Heat-Waves?
86
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
Ret. Val. 100−years
−150
0
3
−50
5
15
0
30
50
50
100
90 360
(°C)
Figure 5.13: AS Figure 5.12 but for 100-years return values of the HWI-98th no-stationary threshold.
5.6. Can we expect more intense future Heat-Waves?
87
Heat Wave Intensity five days maxima index
As explained above the HWI-nth could not be enough in order to characterize the Heat-Wave intensity since it is duration dependent. The HWI5-nth
indices give information about the sum of the 5 maximum daily temperature
exceeding threshold during a Heat Wave event. If we consider the previous
HW1 and HW2 Heat-Wave events (see Fig. C.1 in Appendix C), their HWI5nth values will be 5 and 1 o C respectively. It means that from the point of
view of the HWI5-nth index the HW1 is more intense than the HW2.
Figures 5.14 and 5.15 show 10-years and 100-years return values of the HWI598th. Differently than 10-year and 100-year Heat-Wave intensity (Fig. 5.12
and 5.13) in the past and in the near future the 5 days maxima intensity
is higher in many regions of the northern extratropics than the tropics. In
the future the 10-year and 100-year HWI5-98th return values can be considered homogeneous over the entire globe. Globally the future HWI5-98th
scenario is characterized by 100-year return values exceeding 30o C over 80%
of the global area. The highest values for both 10-year and 100-year return
values are recorded over Eurasia, Central Latin America and Mediterranean
basin. In Figure 5.14 lower panel clear red patterns emerge over these areas with 100-year HWI5-98th return values exceeding 55o C, meaning that
there is some probability to have Heat-Wave in the future with at least 5 day
temperature maxima of 11o C above 98th percentile threshold.
5.6. Can we expect more intense future Heat-Waves?
88
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
Ret. Val. 10−years
−150
0
2
−50
4
8
0
12
50
20
100
35
55
(°C)
Figure 5.14: 10-years return values of the HWI5-98th no-stationary threshold, over the 17 ESSENCE
ensembles. Upper, middle and lower panels are related respectively to the three different selected periods:
1981-1990, 2031-2041, 2081-2090. White areas represent areas with no Heat-Waves.
5.6. Can we expect more intense future Heat-Waves?
89
0
−60
0
−60
0
−60
2081−2090
60
2031−2040
60
1981−1990
60
Ret. Val. 100−years
−150
0
2
−50
4
8
0
12
50
20
100
35
55
(°C)
Figure 5.15: As Figure 5.14 but for 100-years return values of the HWI5-98th no-stationary thresholds.
Conclusion
”Computers are useless.
They can only give you answers.”
- Pablo Picasso -
In this study we have investigated projected changes by mean of indices
describing Heat-Wave events, such as the occurrence, frequency, duration and
intensity of Heat-Wave. We do so by using output from the ESSENCE project
[29], in which a 17-member ensemble of runs with a comprehensive climate
model for the period 1950-2100 under the SRES A1b emission scenario was
performed.
For the period 1950-2011 we find a good correspondence between our model
results and those derived from NCEP observations at local and global scale.
Patterns of summer mean and maximum temperature are qualitatively equal
to those derived from observations, and in many cases there is even quantitative agreement.
For the future the modelled extreme temperatures and the related HeatWaves resemble those of the historical period (1981-1990), but the change is
faster. Taken together with the close resemblance of observed and modelled
temperature and Heat-Wave patterns over the historical period, this suggests
that the patterns of extreme temperature changes might already emerge from
the weather noise. The patterns of climate change appear to be independent
of the magnitude of the forcing, confirming earlier results [e.g., Cubasch et
al., 1992 [6]].
The Heat-Wave frequency, duration and intensity increase near Equators is
much larger than at high latitudes. Relatively few days with high exceedance
values (high latitudes) contribute more to the intensity indices than does a
large number of days with small exceedances (tropics). In fact the results
Conclusions
91
show differently behavior between the HWI-nth and HWI5-nth indices. The
latter in the future show homogeneus values in almost the entire globe with
the highest values in some part of the extratropics.
In summary we can say that under future A1B scenario in the next 100 year
all the areas in the globe will be warmer. There is some probability to have
some tropical areas with all the summer days over the 98th percetile threshold calculated for the reference period 1961-1990. In the extratropics the
Heat-Waves will be shorter but with very high extreme temperature values.
A limitation of indices is that they are not independent of the local climate, which can pose difficulties for global analyses. In the context of climate
change, the principal purposes of the climate indeces is to maximize the ability to detect a secular change in their occurrence, and to identify the extent
to which such changes are consistent (or inconsistent) with changes in other
variables, or changes predicted by climate models. The indices discussed in
the present study show considerable potential for use in the monitoring of
the Heat Wave events . Against this, the complex definition of the indices
makes them potentially difficult to interpret, especially for casual users of
the information.
The warming future scenario that we analyzed in this thesis, affect both the
amount and quality of water resources available for drinking, irrigation, fish
farming, power generation, shipping, recreation, and other uses. Rising temperatures are already decreasing the size of snowpack in many regions. Over
time, this reduced snowpack could affect seasonal water supplies in regions
that depend on this source of water. Moreover an increasing of Heat Wave
and Drought events can have similar effects in areas where water supplies are
already scarce.
Higher temperatures will mean a longer growing summer season in cooler
regions. This could allow farmers to diversify crops or have multiple harvests
from the same plot. In warmer regions, however, temperatures might become
too high for certain crops to grow.
In order to prevent the descripted climate change impacts a climate change
mitigation is needed. In the future more action must be taken to decrease the
intensity of radiative forcing in order to reduce the potential effects of global
warming. Mitigation is distinguished from adaptation to global warming,
Conclusions
92
which involves acting to tolerate the effects of global warming. Most often,
climate change mitigation scenarios involve reductions in the concentrations
of greenhouse gases, either by reducing their sources or by increasing their
sinks.
In addition more human intervention are needed to reduce the sources or
enhance the sinks of greenhouse gases. Examples include using fossil fuels
more efficiently for industrial processes or electricity generation, switching to
renewable energy (solar energy or wind power), improving the insulation of
buildings, and expanding forests and other ”sinks” to remove greater amounts
of carbon dioxide from the atmosphere.
The result of this thesis is in preparation for publication.
Appendix A
Characteristics of SRES
scenario
Scenario ID
Scenario Name
Harmonized
Drivers (on World
and
SRES
Regional Level)
Harmonized
Drivers (on World
Level)
A1
A1B-AIM
A1B-ASF
A1B-IMAGE
A1B-MARIA
A1B-MESSAGE
A1B- MiniCAM
A1C-AIM
A1C-MESSAGE
A1C-MiniCAM
A1G-AIM
A1G-MESSAGE
A1G-MiniCAM
A1T-AIM
A1T-MESSAGE
A1T-MARIA
A1v1-MiniCAM
A1v2-MiniCAM
A1
A1
A1
A1
A1
A1
A1 coal
A1 coal
A1 coal
A1 oil and gas
A1 oil and gas
A1 oil and gas
A1 technology
A1 technology
A1 technology
A1v1
A1v2
FE, GDP, POP
POP
POP
FE, GDP, POP
POP
FE, GDP, POP
POP
POP
FE, GDP, POP
POP
POP
GDP, POP
POP
POP
-
FE, GDP, POP
GDP, POP
GDP, POP
POP, GDP
FE, GDP, POP
POP, GDP
FE, GDP, POP
FE, GDP, POP
POP
FE, GDP, POP
FE, GDP, POP
POP, GDP
GDP, POP
GDP, POP
POP
POP
-
A2
A2-AIM
A2-ASF
A2G-IMAGE
A2-MESSAGE
A2-MiniCAM
A2-A1-MiniCAM
A2
A2
A2 gas
A2
A2
A2-A1
POP
FE, GDP, POP
FE, GDP, POP
POP
-
FE, POP
FE, GDP, POP
POP
FE, GDP, POP
POP
-
B1
B1-AIM
B1-ASF
B1-IMAGE
B1-MARIA
B1-MESSAGE
B1-MiniCAM
B1T-MESSAGE
B1High-MESSAGE
B1High-MiniCAM
B1
B1
B1
B1
B1
B1
B1 technology
B1 high
B1 high
POP
FE, GDP, POP
FE, GDP, POP
POP
FE, GDP, POP
POP
-
FE, POP
FE, GDP, POP
POP
FE, GDP, POP
POP
FE, GDP, POP
POP
-
B2-AIM
B2-ASF
B2-IMAGE
B2-MARIA
B2
B2
B2
B2
FE, GDP, POP
POP
-
FE, GDP, POP
POP
FE, GDP, POP
Storyline
B2
94
B2-MESSAGE
B2-MiniCAM
B2C-MARIA
B2High-MiniCAM
B2
B2
B2 coal
B2 high
FE, GDP, POP
-
FE, GDP, POP
GDP
FE, GDP, POP
GDP
Table A.1: Characteristics of SRES scenario quantifications. Shown for each scenario which is the name
of the storyline and scenario family, full scenario name (ID), descriptive scenario name, and which of the
driving forces are harmonized at the global and regional level, and on the global level only, respectively.
The listed harmonized driving forces are population (POP), gross domestic product (GDP), and final
energy (FE).
Population
GDP
Final Energy
1990-2020
2020-2050
2050-2100
World
5%
5%
5%
4 SRES regions
World
10%
10%
10%
10%
10%
10%
4 SRES regions
World
25%
15%
25%
15%
25%
15%
4 SRES regions
25%
20%
15%
Table A.2: Harmonization Criteria. This table indicates the harmonization criteria in terms of the
maximum deviation (%) from the specified common population, gross world product, and final energy
development at the global and regional levels.
Appendix B
R script function to compute
HW indeces.
heat_wave_ns.R<-function(T,threshold) {
index<-T>threshold
temp_ind<-index*T
time<-c(1:length(T))
v<-time*index
which(v==0)->z1
HWF<-0
HWtime<-{}
HWD<-{}
HWI<-{}
HWI5<-{}
HW<-{}
if (sum(index)>=90) {
HWD<-sum(index)
HWI<-sum(T-threshold)
HWsort<-sort((T-threshold),decreasing=TRUE)
HWI5<-sum(HWsort[1:5])
}
if (length(z1)==1) {
if (z1[1]>5)
{
HWD0<-sum(index[1:(z1[1]-1)])
96
HWF<-HWF+1
HWtime[HWF]<-(z1[1]+1)
HWD[HWF]<-HWD0
HWI[HWF]<-sum(T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)])
HWsort<-sort((T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]),
decreasing=TRUE)
HWI5[HWF]<-sum(HWsort[1:5])
}
if
(max(z1)<length(time)
&
sum(index[max(z1):length(time)])>=5)
{
HWF<-HWF+1
HWD[HWF]<-sum(index[max(z1):length(time)])
HWtime[HWF]<-(max(z1)+1)
HWI[HWF]<-sum(T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)])
HWsort<-sort(T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]),
decreasing=TRUE)
HWI5[HWF]<-sum(HWsort[1:5])
}
}
if (length(z1)>1) {
97
if (z1[1]>5)
{
HWD0<-sum(index[1:(z1[1]-1)])
HWF<-HWF+1
HWtime[HWF]<-(z1[1]+1)
HWD[HWF]<-HWD0
HWI[HWF]<-sum(T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)])
HWsort<-sort((T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]),
decreasing=TRUE)
HWI5[HWF]<-sum(HWsort[1:5])
}
for (i in 1:(length(z1)-1)) {
HWD0<-sum(index[(z1[i]+1):(z1[i+1]-1)])
if (HWD0>=5) {
HWF<-HWF+1
HWtime[HWF]<-(z1[i]+1)
HWD[HWF]<-HWD0
HWI[HWF]<-sum(T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)])
HWsort<-sort((T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]),
decreasing=TRUE)
HWI5[HWF]<-sum(HWsort[1:5])
}
}
if
(max(z1)<length(time)
&
sum(index[max(z1):length(time)])>=5)
98
{
HWF<-HWF+1
HWD[HWF]<-sum(index[max(z1):length(time)])
HWtime[HWF]<-(max(z1)+1)
HWI[HWF]<-sum(T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)])
HWsort<-sort(T[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)]+
-threshold[(HWtime[HWF]):(HWtime[HWF]+HWD[HWF]-1)],
decreasing=TRUE)
HWI5[HWF]<-sum(HWsort[1:5])
}
}
HW<-c(HWD,HWI,HWI5)
if (length(HWD)>0) {dim(HW)<-c(length(HWD),3)}
if (length(HWD)==0) {
HW<-c(-1111,-1111,-1111)
dim(HW)<-c(1,3)
}
return(HW)
}
Appendix C
HW1 and HW2 example.
25
22
23
24
Temperature (°C)
26
27
28
HW1
200
205
210
215
220
225
230
220
225
230
33
32
31
30
Temperature (°C)
34
35
HW2
200
205
210
215
Days of a year
Figure C.1
100
Example of two Heat-Waves HW1 (upper panel) and HW2 (lower panel) with
length respectively of 5 and 20 days (shown in black full points connected by
black lines). The shaded gray area is related on the HWI-nth index and shows
the temperature’s differences from the threshold with each daily temperature
into the Heat-Wave. The HWI-nth index calculated for both HW1 and HW2
will assume the value of 5 o C because all the five days of the HW1 and the
twenty days of HW2 are exceeding the threshold respectively of 1o C and
0.25o C. The dashed black lines represent the temperature’s differences from
threshold with each first five maximum daily temperatures into the HeatWave and the HWI5-nth value for the HW1 and HW2 will be 5 and 1 o C
respectively. It means that from the point of view of the HWI5-nth index the
HW1 is more intense than the HW2.
Appendix D
Software
This thesis is written with
• LATEX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian).
For the graphycal part, have been used the programs:
• Inkscape 0.48.1 r9760 (http://www.inkscape.org)
for vector graphics,
• The GIMP 2.6 (http://www.gimp.org)
for image elaborations.
The computing elaboration, calculus and graphics are make with:
• R software for statistical computing [24].
http://www.r-project.org/. R packages:
– RNetCDF : R Interface to NetCDF Datasets;
– MASS : Support Functions and Datasets for Venables
and Ripley’s MASS;
– SuppDists: supplementary distributions;
– Kendall : Kendall rank correlation and Mann-Kendall
trend test;
– rworldmap: for mapping global data;
– classInt: choose univariate class intervals;
– RColorBrewer : ColorBrewer palettes
• Climate Data Operators version 1.4.6
(http://code.zmaw.de/projects/cdo)
Appendix E
List of Acronyms
5CD
five consecutive days
A1
storyline and scenario family IPCC
A1B
scenario IPCC
A1FI
scenario IPCC
A1T
scenario IPCC
A2
storyline and scenario family IPCC
AOGCM
Atmosphere-Ocean
General
Circulation
Model
B1
storyline and scenario family IPCC
B2
storyline and scenario family IPCC
CCl
Commission for Climatology
CCN
Clouds Condensation Nuclei
CCSM
Community Climate System Model
CDO
Climate Data Operators
CFL
Courant-Friedrichs-Lewy
CGCM
Coupled General Circulation Model
CLIVAR
Climate
Variability
and
Predictability
project
CSDI
Cold Spell Duration Index
DJF
climatological winter (December, January,
February)
DTR
diurnal temperature range
103
ESSENCE
Ensemble SimulationS of Extreme weather
events under Nonlinear Climate changE
ETCCDI
Expert Team on Climate Change Detection
and Indices
ETR
extreme temperature range
FD
annual occurrence of frost days
FE
Final Energy
GCM
General Circulation Model
GDP
Gross Domestic Product
GHG
Greenhouse gases
HadCRUT3
the third major revision dataset of Hadley
Centre compiled by the Climatic Research
Unit (CRU) of the University of East Anglia
HW
Heat-wave
HWDI
Heat Wave duration index
HWD-nth
Heat Wave Duration
HWF-nth
Heat Wave Frequency
HWI5-nth
Heat Wave 5 days maxima Intensity
HWI-nth
Heat Wave Intensity
ID
nnual occurrence of ice days
iid
independent and identical distributed
IPCC
Intergovernmental Panel on Climate Change
(Fourth Assessment Report)
IS92
IPCC emission scenarios released in 1982
JJA
climatological summer (June, July, August)
NCAR
National Center for Atmospheric Research
NCEP
National Centers for Environmental Prediction
NetCDF
Network Common Data Form
OASIS
Ocean Atmosphere Sea Ice Soil
OGCM
Oceanic General Circulation Model
PDF
Probability Distribution Function
POP
Population
SAR
Second Assestment Report
104
SDII
simple daily intensity index
SRES
Special Report on Emission Scenarios
SU
annual occurrence of summer days
T2m
daily 2-meter maximum temperature
TN10p
occurrence of cold night index
TN90p
occurrence of warm night index
TNn
minimum daily minimum temperature
TNx
maximum daily minimum temperature
TR
annual occurrence of tropical nights
TSU
Technical Support Units
TX10p
occurrence of cold days index
TX90p
occurrence of cold days index
TXn
minimum daily maximum temperature
TXx
maximum daily maximum temperature
UN
United Nations
UNEP
United Nations Environment Programme
WCRP
World Climate Research Programme
WMO
World Meteorological Organization
WSDI
Warm Spell Duration Index
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Acknowledgements
I thank Andreas Sterl (KNMI) for making ESSENCE datasets available.
In poche righe è difficile ricordare tutti coloro che in questi anni mi sono
stati vicino.
Un grandissimo ringraziamento di cuore per il mio amico, collega, nonché
”maestro” Simone. L’incontro avvenuto durante una sua conferenza sugli
”Eventi estremi e i cambiamenti climatici” alla facoltá di Fisica dell’ Universitá di Catania é stato una svolta per la mia vita personale ed universitaria.
Lo ringrazio per la sua competenza, pazienza, disponibilità, onestá ed umiltá,
per il suo modo ”materno” di condurmi verso ambienti per me del tutto nuovi.
Lo ringrazio per aver speso il suo tempo, le sue capacitá e i suoi pensieri in
un momento di cambiamenti importanti per la sua vita da fisico.
Ringrazio fortemente la Prof. Giuseppina Immé per avermi dato la possibilitá e i mezzi necessari per svolgere questo lavoro di tesi nel miglior modo
possibile. La ringrazio inoltre per la sua disponibilitá, delicatezza, fiducia nei
miei confronti e per avermi sempre seguito con attenzione e affetto durante
la mia vita universitaria e la stesura di questa tesi.
Desidero ringraziare la sede ISPRA di Roma e le persone che ho conosciuto
al proprio interno per avermi ospitato ed accolto.
Grazie infinitamente a mia mamma Graziella e mio papá Nino per quello che
sono e che saró. Per tutto quello che hanno fatto e che continuano a fare
instancabilmente per me. Grazie.
Grazie a mio fratello Pietro per il suo affetto e per avermi aiutato e incoraggiato. Senza il suo aiuto non avrei mai potuto avere la possibilitá di lavorare
su questa tesi.
Grazie anche a mia Zia Pina che mi ha aiutato, incoraggiato e talvolta ”ag-
giustato”.
Desidero ringraziare due persone importanti per la mia vita, uomini di scienza
e di grande affetto, Gianni e Nino.
Grazie a Paola per il suo amore, la sua forza, pazienza e per la nostra musica.
Un ringraziamento vá a tutti quelli che sono stati partecipi della mia vita:
Salvo, Massimo, Roberto, Valentina, Davide, Gianpaolo, Nicola, Fabio, Oriano, Gaspare, Filippo, Vittorio e tantissimi altri che spero non si offenderanno
per non essere citati.
Un ultimo ringraziamento vá alla musica che mi ha permesso di vivere e
provare emozioni uniche.