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36C3 preroll music
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Herald: ... so I'm looking forward and I
hope you are, too. I am looking forward to
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be told the difference between..
laughs ... we will all be told the
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difference between an input model and a
climate model, and we are going to be told
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this difference by karlabyrinth.
There you go.
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applause
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karlabyrinth: Thank you. Hello and
welcome, everyone. I would like to see my
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slides. Are the slides ...? Ah, OK.
laughs nice. So welcome, everyone, to my
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talk about Climate Modeling - the science
behind climate reports. First of all, I
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will shortly introduce myself and what I
do. I work at the UFZ. That's the
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Helmholtz Center for Environmental
Research in Leipzig and I work for the ESM
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project, which is short for 'advanced earth
system' modelling capacity. I am also a PhD
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student at the University of Potsdam and I
am part of the developer team for the
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middle scale hydrologic model, which is an
impact model. And I'm also a scientist for
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future and an artist. So what this talk is
about? This talk is partitioned into three
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sections, mainly. First is the
introduction where I will introduce some
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nomenclature like what is weather, what is
climate and what we can say about
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predictions. For example, why we can't
tell the weather in three years but we can
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say something about the climate, and what
are climate models. Then the second part
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will be the longest, the science behind
warming graphs. I will show you a graph
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that's typically shown when people tell
you about climate change, and I will
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explain that graph in detail and what is
behind it. The third part would be
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installing an impact model to your local
PC if there is time. If there is no time I
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will skip that. And in the end, there is, as
always, a summary and conclusion. So
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starting with the introduction. Weather is
defined as the physical state of the
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atmosphere at a given time whilst climate
is averaged weather. Most of the time a
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time period of 30 years is taken for that
averaging but also other time periods
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could be taken. So, while, the main
question was, while we
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are not able to predict whether at a
specific date in a
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decade, for example, let's say the 27th of
December in 50 years or so. Why does it
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still make sense to propose general trends
for the climate? That is a question that
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often arises when... and I'll answer that.
So, first of all, it is about average.
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Average cloud coverage gives us
information on average reflection. And
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average reflection is ... has an impact on
the warmth on the earth. And the same is
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true for another scenario. For example,
average precipitation - meaning rain or snow
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and temperature - has an impact on
vegetation and vegetation influences the
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carbon cycle. And that again influences
the warming or cooling and that has an
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influence on the ice coverage. And that,
again, on the reflection. So there are
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lots of processes that are connected to
each other and if we know something about
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the average of some of these physical
state of the atmosphere, we can say
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something about the climate trends. So the
question is, what is a climate model? And
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the AR5 defines a climate model is a
numerical representation of the climate
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system. The AR5 is a source I will cite
quite often. So I have one slide
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with the whole citation. It's the fifth
IPCC report. IPCC is the
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Intergovernmental Panel on Climate Change
and the fifth assessment report is, yeah,
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so AR5 is the abbreviation for fifth
assessment report. But coming back to a
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climate model. So a climate model could,
for example, be a GCM - a general
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circulation model - which is a global
climate model that usually consists of an
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ocean and atmosphere circulation. An RCM
is not a GCM but it's a regional climate
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model, meaning a climate model at a
limited area, and mainly it has a higher
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resolution. And for it is at a limited
area, that usually means that there is
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some input and output going in because
it's not a closed system. And an impact
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model again has usually a higher
resolution in time and space and it's not
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a climate model, but it's for simulating
extreme weather events
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like floods. So if you want to build a
dam or a dike and you want to know how
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high this dike or dam should be, then you
would usually run an impact model that
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gives you information about water height
over decades or longer or so. And then
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you would decide on the height. So this is
the use for impact models. So that's for
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the introduction part. Now I come to the
main part and I will start with a
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question: is it proven? Or with a climate
graph. As that, I will show you a graph, a
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typical image people would show you when
they address climate change. This graph
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has an x-axis with a time scale and you
see it's reaching far into the future. And
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it also has three or four regions
and the first region is only in the past.
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And the y-axis is the global surface
temperature change, meaning how much
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degrees in Celsius or in Kelvin, if it's
different it's the same, we will have in
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future or we had already. And then, you
see several lines and different colors and
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with the names RCP something. And I will
explain all the numbers and everything
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about that graph because it's a pretty
important graph. So first of all, I will
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tell you... no, no. I will tell you
something about the numbers and
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uncertainties. The uncertainties are the
transparent colors behind the lines. I
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will tell you something about the
representative concentration pathways,
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which is short RCP, and so it's reflecting
the colors of the lines. I will tell you
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something about the source of the graphs.
So where does this graph actually come
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from? So I will tell you something about
the assessment report. And first of all, I
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will answer the question: is it proven or
is there scientific evidence that we will
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face that climate change? So, you will see
that graph quite often. First of all, I
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took a definition for proof, for
scientific evidence, from Wikipedia. The
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strength of scientific evidence is
generally based on the results of
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statistical analysis and the strength of
scientific controls.
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Meaning, you make an experiment over and
over again and you change basically some
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influences on the experiments where you
want to know that this does not influence
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the output. So you can narrow it down and
know what is the source of your results
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and so you can prove a physical law or
something. Yeah, I took this comic from
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xkcd because it's a nice... it's somehow
connected. So there is a person who pulls
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a trigger and then gets struck by a bolt
or some something. Something bad happens,
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for example climate change. And then,
yeah, there are two scenarios. For
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example, a person usually would decide,
okay, I would not pull the lever again.
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But scientists usually or more often would
say, okay, maybe: Does that happen every
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time if I do so? Because yeah, that's
basically how you prove something. That's
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experiments. But in case of climate
change, even scientists say you shouldn't.
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Although it's pretty interesting for us
from a scientific perspective. But the
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problem is we only have one earth. We
cannot do this experiment very often,
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except we had a time machine. Then we
could go back, but we haven't so we
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shouldn't do that experiment. And that's
something scientists before, long ago in
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1957 said already: "Human beings are now
carrying out a large-scale geophysical
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experiment of a kind that could not have
happened in the past nor be reproduced in
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the future." So another question is, yeah,
if you ask this question if it is proven
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or that it probably is not happening or so
to climate deniers, they usually would
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tell you: Okay, maybe it's not happening.
And the other side would take the position
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and ask you, okay, if you stand in front
of a road and you want to cross the road
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and there's a car approaching very fast,
would you cross that road? Because it
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could happen that the car stops or makes a
U-turn or something. But well, usually it
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doesn't. And sadly, we know lots about
this experiment, because it's done very
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often before. We know
something about traffic, and that it's
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pretty dangerous. So let's change the
factors a little so that we don't know so
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much about that situation. Let's say a
cube approaches us with a high velocity on
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something that is maybe not a road. Would
you still cross that something? The answer
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is you still probably wouldn't. And why
wouldn't you do so although you know
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nothing about this situation? Well, you do
know something. You know conservation of
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the momentum, which is a physical law you
know about. So you have a situation, you
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know not so much about. You have never had
an experience before, but you still are
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able to make some assumptions because you
know the physical laws behind it. And
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that's basically the same we do with, in
fact, in the context of climate. So we
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have, let's say, just an earth and the sun
and the sun has some radiation and that
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comes to the earth and gets partially
reflected and the earth radiates itself
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because it has some temperature. We know
something about this sun. We know the
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solar insolation. And we know parts of the
light is reflected. And the factor that is
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reflected is usually called albedo. And so
the reflected energy is albedo times the
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solar insulation and albedo is something
about 30 percent. And we know then that
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the light that is absorbed must be all the
remaining energy. So the energy of the
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surface is 1 minus albedo times the solar
insolation. Then knowing Stefan-Boltzmann
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law for energy emissions where the
temperature goes in to the power of four
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and with the Stefan-Boltzmann constant we
can actually find find out the surface
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temperature which then is derived to -19.5
degrees Celsius. Well, we know, probably
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we know, that the earth is much warmer,
and that's because our model in this case,
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which is maybe a climate model, is far too
simple. So we change something about that.
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We add atmosphere, and atmosphere has some
interesting impact. So atmosphere has some
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trace greenhouse gases,
for example CO2 but also H2O, ozone,
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methane, O2 and nitrous oxide. And these
greenhouse gases reflect the radiation of
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earth back to earth, partially. Meaning
the atmosphere has a transparency and this
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transparency we call t is something
between 15 percent and 30 percent. So it's
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not fixed. And that's another interesting
fact. The atmosphere emits energy, which
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we call j atmos, and that goes out in
space and to earth and the energy that
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goes into the atmosphere is 1 minus the
transparency times the energy. So we know
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two equations. The first is the energy
that goes into the atmosphere also goes
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out of the atmosphere. The second is that
the surface energy of the earth
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is the term we had before,
1 minus albedo times the solar
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insolation plus the one part of the energy
that is reflected by the atmosphere. And
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so we have two formulas, two equations
with two unknowns and with the Stefan-
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Boltzmann law from before we can derive
the surface temperature, which is 15
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degrees of Celsius. And that actually is
not so far from what it actually is. In
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2000 it was measured that the surface
temperature is 14.5 degrees. So, I did
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this for a specific t which is 22.5
percent but when we change that t a little
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to, for example, 20 percent, so we add
more CO2 because, for example, we would
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add a factory that would do carbon
emissions. Then the transparency goes down
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and the temperature rises to, for example,
16.6 degrees in case of 20 percent. This
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is also a very old knowledge. So this is
maybe a little much on a slide but it is
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still very interesting because it is
copied directly from a paper that was
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published from Svante Arrhenius in 1896
already. And it's on the influence of
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carbon acid in the air upon the
temperature of the ground. And carbon acid
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is the old term for carbon dioxide. So if
we have a look to the percentage... So he
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investigated: What if we change
carbon dioxide? So what is the impact of
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our behavior? Let's say carbon dioxide
in our atmosphere would
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double, so would increase by a factor of
2, then the average temperature rise in
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Leipzig in December, so I choose the
region for Leipzig, would be 6.1 degrees.
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Well, that's probably a little high, but
what we can't see is already that
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Arrhenius back then already knew that
there is a seasonal impact on
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climate... that climate change is seasonal
and also spatial. So it is not just one...
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not the average temperature is the only
interesting knowledge we get. So
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Arrhenius said something like the
temperature in case of carbon acid doubled
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would be around four to six degrees. And
the current models predict something like
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an increase of two to four degrees for
that scenario. So there is maybe overlap
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already with that simple model from back
then. So, then I come to the question...
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a climate model represents physical laws.
That's what we learned. Where do the
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uncertainties come from? So if we know all
the physics laws and we would just
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calculate everything with this physics
laws, why are there even uncertainties?
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And there are some reasons for that. For
example, the initial conditions is one
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main source of uncertainties, meaning how
is the current state of the climate system
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now? How fast does something move?
Where are the clouds exactly?
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And so on. We don't
know these precise initial
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conditions and therefore errors
occure. Second, would be the
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resolution of a model. So the
temporal and spatial step length, meaning
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we can't... always represent our
climate system with differential equations
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and we approximate everything. We have not
the movement of every molecule but we have
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some average on cells. And if we increase
the resolution then usually the
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uncertainties go down. But sometimes they
even don't for some question, for some
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questions it's better to have a lower
resolution. But mostly it's better to have
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a higher. Then, truncation, so we have
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computational limits. And lack of
understanding, for example, clouds. Clouds
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are not understood pretty well. And when I
read the fifth assessment report, I found
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a sentence a little amusing:
Climate model... Clouds in climate models
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usually tend to rain too early. Yeah, so
but if you know all these sources of
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uncertainty, why is there no such thing as
the one best climate model? Meaning, why
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can't we go to the highest resolution and
to the best... the best computer we get
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and do everything just in the best way and
then we would have our best climate model?
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And there are some reasons for that. For
example, the so-called dynamic core,
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including the method for differential
equations or something like grids.
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For example, if we have a triangular
grid or a rectangular grid. On a
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rectangular grid we usually can
calculate faster but on a triangular grid
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we could, for example, increase the
resolution locally. That might be
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differences. And both have advantages and
disadvantages. Also, the parametrization:
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parameters in our last slide were for
example the t and the albedo which will
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probably be not the final parameters
because they are derived from other
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parameters, but physical laws or something
are often represented by rules with
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parameters, and these parameters can be
estimated. And they can be calibrated with
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different error measures.
And there this is another reason for
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uncertainties and differences in climate
models and then their schemes. For
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example, there are different formulations
of physical processes, for example, that
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again, clouds. And last the truncation,
again, we can also decide how we limit due
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to our lack of computational power. So,
yeah, what do we do? We investigate all
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the models we have. So there are different
climate models that are representing our
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climate and we take all the models that
match certain conditions - I come to that
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later - and we average the output and then
we
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get a climate prediction and also that
uncertainty band you see. So what climate
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models do we investigate? They are so-
called coordinated GCMS. So climate models
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are compared in so-called coupled model
intercomparison projects in different
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phases. These coupled model
intercomparison projects are called CMIP
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4, 5 and 6. So there might have been four
earlier ones. But currently, for the AR6,
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so for the sixth assessment report CMIP6
investigated. And I showed you on the
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map the research centers which took part
in CMIP6, so which take part in the 6th
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assessment report. These research centers
are mainly specialized research centers,
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university and metereological offices, but
generally it's open for any institution to
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participate, as long as they follow a
protocol for their contribution, where
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there are some rules so you cannot just do
anything. These institutions
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need to produce variables for a set of
defined experiments and a historical
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simulation from 1850 to present. This blue
part is a link, so if you go to my slides
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afterwards, you can see these variables
you need to reproduce and then you can do
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something like this. So we have a graph
here again. On the x axis, we see again a
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timescale that reaches from 1850 to today.
And on the y axis we again see the
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temperature anomaly or the temperature
difference between.. so, exactly the
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temperature difference, so how much the
earth has warmed up. We see CMIP3 and CMIP5
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compared, which were the models that were
investigated for the AR5. So we see a
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band. This uncertainty with the yellow and
bluish and the background and then we see
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these two lines, the blue and the red one
from CMIP3 and CMIP5 and then we see the
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black one. And that is what actually was
observed. And we see that this differs
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quite a lot. And that's due to there was
only investigated the natural forces,
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meaning excluded what the human did. And
if we
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also put the human forces into it, then
it's quite matching. And that is the best
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kind of proof we can get. And again, I
said we investigate the physical laws and
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the physical laws were actually results of
scientific experiments. And so, yeah,
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there's this kind of proof. And yeah. So
maybe a little addition. There are also
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other coordinated model intercomparisons
projects that are outside of the IPCC and
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so the ones that are inside the IPCC
where the scientific focus is on a
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subtopic, on something like land surface
for example (and that's what I do). And
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they're also published work
outside from IPCC. So back to the graph.
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We talked about the part: Is it proven?
And I hope I convinced you that it is. And
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now I will talk about the sources of the
graph. So I talked a lot about the IPCC.
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The IPCC, the Intergovernmental Panel on
Climate Change, publishes reports. So for
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example, the 5th assessment report and
what you see here is part of the cover.
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But there have been 4 ones before, as the
name 5th suggests, the first assessment
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report FAR was published in 1990. The
second SAR in 1995. Then there was the TAR
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and then for the 4th assessment report
they changed the name scheme for some
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reason to AR4 and then there was AR5,
which I'm talking about. The IPCC consists
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of several working groups, including
Working Group 1 to 3, providing the
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assessment reports and I mainly focus on
the assessment report from a working group
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1, which investigates the scientific
aspects of the climate system and climate
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change. But there is also a working group
investigating on vulnerability and
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economic impact. And the third one on the
options of limiting greenhouse gas
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emissions and others. So I totally show
you a history of the climate models. In
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something like the 70s, climate models
were investigated where there was just an
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atmosphere, the sun, rain - clouds were
missing - and CO2 emissions. And
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I hope you believe that the sun is behind
the atmosphere and not in this atmosphere.
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In the mid 80s there was prescribed
ice added and already clouds and land
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surfaces and yeah, you see a nice mountain.
But actually in that time the resolution
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was so low that the Alps only had one or
two grid cells, meaning that was not so
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much about land surface, but it was added.
And for the first assessment report there
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was a swamp ocean added, meaning an ocean
was added, but it was had no depth. For
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the second assessment report, the ocean
got some depth. So it was a normal ocean
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with surface circulation and there was
added volcano activity and sulphates. For
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the third assessment report, there was
added... So this is all about which kind of
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processes were there in the climate models
that were investigated in these assessment
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reports. Meaning there were climate models
before that already had those processes
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included, but they were not investigated
in the assessment reports. So this is a
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history of which climate models or which
processes and climate models were
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investigated in assessment reports. And
the third assessment report, there was
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another circulation edit for the ocean,
the overturning circulations. And there
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were rivers added, which is interesting
because I do something with rivers and
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there were aerosols added and a carbon
cycle, meaning that the carbon that goes
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into the atmosphere also goes out. But
yeah, not everything, or that half-time is
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not so good. For the AR5, er 4, there was
chemistry added in the atmosphere and
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interactive vegetation, and for the AR5
there was ozone added and biomass burning
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emissions. And there is a history of
processes, but there is also a history of
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computer modeling that might be really
interesting. It started more or less in
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1904 with Vilhelm Bjerknes, who found
equations that could be solved to obtain
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future states of the atmosphere. And he
thought about that maybe these equations
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are really hard to
solve and that task should be split and
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distributed to many people. So he
basically mentioned a human computer and
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then Lewis Fry Richardson came in 1922 and
did actually calculate all this.
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This did a six hour forecast solving the
equations by hand, alone. And 42 days user
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time, meaning he himself calculated 42
days on it. But those 42 days were
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distributed over two years in total. So he
was a little behind the weather, only to
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find out that it didn't give the correct
answer. audience laughs That was long
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forgotten. But people said, yea, that's
not quite practical. We cannot do that.
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But then computers came. In 1950, the
first successful weather model was run on
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a computer called ENIAC, and in 1950,
weather predictions were run twice a day
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on an IBM 701. Nowadays we use
supercomputers much larger and there's a
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whole list and rank and I will shortly
introduce JEWELS to you: the Jülich Wizard
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for European Leadership Science. That's a
supercomputer in Jülich and I would have
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shown you a picture, but you are not
allowed, you are not simply allowed to
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take pictures on that campus. But since
super computers are fancy shiny cupboards
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anyway, I thought this is OK. So we have
these cupboards that look at shiny covers
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and then this covers their blades and each
blade is called a standard node and
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consists of, in case of JEWELS, 2 times 24
cores with 2.7 GHz and it's hyper-
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threaded, meaning you can actually run 96
threads or processes on one of these
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nodes. And these notes have 12 times 8 GB
of memory. And that's not quite much if
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you want to run a climate model but
I'll come to that a little later. And in
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fact, in case of JEWELS, you have like
three rows of five of these cupboards or
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something. And so there are in total 2271
standard nodes, 240 large memory nodes and
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56 accelerated nodes having something like
GPUs. And I tell you about JEWELS, not
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because it's the
fastest, actually, it's maybe the 30th,
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not even because it's the fastest in
Germany - it was when it was built but
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that's a while ago - but I told you about
that because JEWELS provides actually
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computing budget for the ESM project, the
Advanced Earth System Modelling Capacity.
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And so there are actually earth system
models run on that machine. So what I told
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you before, there is not so much memory on
each node.
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So what you need to do is you need to cut
down your problem and distribute them over
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the nodes. And then there needs to be some
communication. So usually if the task
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is so simple, you can cut down your grid
and put a number of grid cells to each
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node. And then there's communication
between the nodes on the boundaries to
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solve the differential equations. Talking
about grids, I would talk about the
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resolution. Also, again, a history of
resolution of the climate models. For the
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1st assessment report, the region
resolution was 500 kilometers times 500
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kilometers. And as I said before, you see
these two yellow yellowish cells in the
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middle that are the Alps. For the second
assessment report, the resolution already
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doubled or halved, depends on how you want
to phrase it. For the TAR, it was 180
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kilometers for AR4, it
was 120 kilometers. For the AR5, it's a
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little bit a different section I show you.
And also, I show you two resolutions.
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There's a resolution for the higher
models, which is 87, for example, 87.5
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kilometers. And for the very high
resolution, 30 kilometers. And that's
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because climate models are not just one
model, but they are different kinds of
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models that are coupled. And each model
has its own resolution. So it's more or
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less like something like this. So we have
a model for ice, we have a model for
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atmosphere, for ocean and for terrestrial.
And this is coupled. So they all sent
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their data to a coupler or something. And
that set was there as an input to the
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other model. So this is more or
less like how climate models look.
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And each of the models, again, has several
layers. For example, the terrestrial layer
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has a ground water part and the
atmosphere. And so there's some input from
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the atmosphere to the soil and plant
system. And then there's some water that
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is sinking into the groundwater and then
coming out to the rivers. And yeah. So
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then we have the runoff. So meaning rivers
get water. And then if you have a look to
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rivers and want to parallelize rivers,
then it's not so easy because we have a
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source somewhere and the water has to go
from the source or something that happens
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at the source has an impact to the sink,
meaning this has to communicate all the
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way along to the sink. And that's where I
come in. I actually do. So I show you the
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Danube, which you probably know better
with the name Donau. At a resolution of
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five kilometers and basically cut down the
Danube into sub river domains. And we
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need. If we parallelize these we need to
calculate the subriver domains that are
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farther away from the sink first and it
uses that in the first graph a little. So
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the grayish areas are calculated first and
then it goes down farther to the sink. So
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just to tell you about what I do. So now
we come back to the main question. So we
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answered where the sources of the graphs
come from. Now we answer the questions:
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What is a representative concentration
pathway? Meaning what we all did before
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was more or less telling how we get to
that black line in the first section. And
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now we concentrate on the colored part
where we have more graphs than one. So the
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working group 1 of the IPCC generally
tests the selection of coupled models, that
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is what I told you before, matching
specific conditions and investigates the
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output assuming different emission
scenarios. Meaning we have a couple of
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climate models that are somehow different,
for example in their grid. And then we
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have input data. The input scenarios would
be, for example, the first one where we
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just do business as
usual and don't reduce carbon emissions.
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The second would be we start with our way
we do it today, but we would slowly change
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to renewable energy. And the third one
would be a scenario where we do it
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spontaneously now or so. And that is an
input scenario that we put into the
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systems and then we get out a model output,
that says something about the future. So
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there is a black line that says, OK, this
was our history until today. And from that
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on, we have three scenarios and they are
represented upper to lower. So the upper,
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upper and right line represents the way
where we do nothing or so. So this is
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basically what we do with scenarios. And
the RCPs, Representative Concentration
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Pathways are scenarios that include time
series of emissions and concentrations of
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the full suite of greenhouse gases and
aerosols and chemical active gases as well
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as land use and land cover. So that is
another graph from the AR5 and it shows
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again in the X-axis the years, it's the
same timescale as before, but on the Y-
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axis we now have the rate of forcing, that
is basically having this impact on our
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climate. And so each of the RCP scenarios
has some kind of equivalent in
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radiative forcing.
Yeah. So we have a 4 of these scenarios.
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The data for the RCP scenarios is
coordinated by again the input4MIPS: input
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datasets for model and intercomparison
projects that I told you before. And most
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of it is freely available and I gave you
the link. So if you want to run your own
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climate model and test it with these
input, you can find it there. And now I
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will explain the last part. The numbers
and uncertainties.
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So first of all, again, to the graph from
before the numbers behind the RCP refer to
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the radiative forcing at the end of the
modeling period of 2100. Meaning if you
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follow one of these lines, for example,
the red one to where it crosses the 2100
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line, then the number there is 8.5. So
RCP8.5 is the name for this RCP scenario.
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But then the numbers of these different
sections are the numbers of models used
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for this scenario in this time period.
Yes. So as I said, there are lots of
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models intercompared and we even have
different models for the different time
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periods. So until 2100 there are 39 models
for the RCP8.5. And of all the all the
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rest, there are 12. And you see this
little gap, this line break at 2100. And
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that is caused by the change of numbers of
models that took took part in this
381
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project. And another interesting thing
that we see here, and maybe the most
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important, is we have quite huge model
uncertainties. So if we compare all the
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models, there's a huge band where we can't
exactly say, OK, it's like this or that.
384
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But this band is still... About human
uncertainties are more important, than this
385
00:43:05,980 --> 00:43:13,460
model uncertainties. We see tiny overlap,
but mainly we can say how will the human
386
00:43:13,460 --> 00:43:22,930
behave derives our future. And that there
will be this climate change we are talking
387
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about. So that was the main part about
this three parts. And it's also it is also
388
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the most important part. Now, I could
probably show you how you can install an
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impact model to your local PC, but
probably I will have maybe something like
390
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three minutes left. So we'll switch to the
conclusion. And yeah, maybe if it's
391
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arising as a question, I can do it. So
what have we learned? Weather is the
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physical state of the atmosphere at a
given time, while climate is average weather
393
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over 30 years. A climate model as a
numerical representation of the climate
394
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system. And we learned that the main
uncertainty is the way we solve a
395
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differential equations. I would probably
have told you what a differential equation
396
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is in particular, but that would have
taken maybe another lecture. Climate
397
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change is not proven throughout repeating
one real experiment over and over again.
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00:44:42,690 --> 00:44:45,490
So there is only one earth it is said. But
models simulate our
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past climate pretty, well based
on physical laws that were proven in real
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experiments. And then maybe the most
important message. Human behavior
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is the primary source of climate change.
Therefore, we talk about projections and
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not predictions. Meaning if we wanted to
predict the climate, then we needed to
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simulate all human minds. And what we will
decide on future. But we don't. That would
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be another talk again. We take what humans
will decide in future as an input
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scenario, and with these input scenarios
we create different output scenarios. So
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with different inputs scenarios, we get
these different output scenarios. Where we
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can tell, OK, when we behave like that,
this is the output. And human behavior
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scenarios dominate model uncertainties,
meaning the question is what do we want?
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And if you go to a demonstration, the
answer is usually climate justice. And I
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think that's a good answer. Thank you.
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