Whilst you're all sitting down. I think I will just start the introduction.
So I think Miles Allen is somebody that probably doesn't need any introduction to almost all of you.
I think it's fair to say he's pretty much a home-grown product having done his Ph.D. here.
And I think apart from his spell at the Rutherford Appleton and the post-doc at MIT, he has had much of his career here in Oxford.
He's currently the professor of Geo System Science.
So I write this down to a system, science and school of environment, geography and the environment,
but also head of the Climate Dynamics Group here in physics, uh, a post which he's had for, for some years previously full time post.
So Miles, very much straddles physics and environmental science, but also very much straddles, I think, the public face of science and climate change.
I think if you switch on the TV and there's a climate change topic,
there's a fair probability Myles will be saying something about it if it is part of the economy.
I think many of us know that one of the really innovative things that Milo Miles has led is
the is harnessing the world's PC computer power to run phenomenal ensembles of integrations.
In my own research, I I'm I sort of feel lucky if we can do 50 member ensembles.
He does tens of thousands of member ensembles, as I say, harnessing the power of computers around the world.
And I think this is a remarkably innovative and important advance in our science utilising people power.
So Miles is never shy of controversy.
And today he's going to take on the economists. I don't know if any economists are in the audience or not, and they're all keeping a low profile.
But anyway, here we go. How hot will it get in a world run by economists?
A physicist take on climate policy models. Think how much?
And so I just thought it might be interesting to to colleagues in the physics departments to sort of report back from the the front line,
so to speak, in climate policy about how different how how different disciplines work on this issue.
Because I've been learning a lot. So and part of the motivation for taking up this post in geography was an excuse I was finding.
I was having to apologise more and more for things I was doing because they weren't really physics.
But I discovered there's a department not far away where nobody's quite sure what it is so you can do what you like.
And so, so, so, so. And there'll be somebody who'll define geography as saying it's consistent with it.
And so, so, so so this is what I've been learning a lot of economics.
I haven't actually got a sort of things slide. I realised that in the sort of inevitably as I was fiddling with my slides before this, I should have,
I should have I think like so I've learned a lot of economics, some Cameron Hepburn is a sort of key, key person I should, I should think in this.
But before then I've been working a lot with Dave Frame, who's now in New Zealand.
Ric Van de PLU is also an excellent economist based here in Oxford, and Bob Hahn has also been very helpful sort of talking about these ideas.
And I'm sure none of these people would agree with what I'm going to tell you, but they've all been very helpful in understanding these things.
And so but the real inspiration of this is somebody I've never met, Bill Nordhaus,
who's a very well-known economist based in Yale, and he's he's written a book.
So I was hoping to wave around, but I've obviously given it to somebody.
So if any of my grad students and I'm looking the Climate Casino by Bill Nordhaus
and this is really the sort of inspiration of this talk because in the in this book,
which is a sort of summary of his his life's work, he talks about the integrated assessment problem,
which is where you couple the climate system with a model of the world economy and run it forward in
time and ask under certain policy scenarios what happens and his his his optimal policy scenario,
the one in which the world cooperates. We impose rational carbon taxes at the appropriate rate determined by the social cost of carbon.
I'll sort of explain this jargon a bit as I go through the talk results in a warming over the 21st century,
which peaks out above pre-industrial at sort of somewhat below three degrees between two and three degrees,
where the impacts of climate change are a few percent of global outputs, which to put this in context,
this is in a world which is still growing at that point by a couple of.
Percent per year in terms of economic output and population has by then stabilised in this scenario.
So a few percent loss due to climate change is in this scenario really only a few years
delay in achieving the same level of per capita output and temperature stabilise.
And as I say, above two degrees above that sort of magic two degree number which so a lot of environmentalists,
three things that bill know what I'm saying what his scenario doesn't achieve two degrees so.
So that's bad. On the other hand if you look at if you look at it in the context of its own assumptions, it does look pretty rosy.
So so the sort of brief answer to my to the to the question posed in front of you is, well, if you believe some economists,
not that whole, then you can take some other economists come on to that and it could get a little warmer than that.
But what I really like to understand is why what's what's what's going on here?
Why why does temperature pick out in that way?
And so it's sort of to help me understand this, I've been sort of learning a bit about these integrated assessment models.
And I'm going to tell you a bit about the sort of idealised calculations that you can do to understand what drives what in the system.
Part of my motivation for this, of course,
coming back to the the the physics behind it is looking at the physical components of integrated assessment models.
So, so every integrated assessment model will have a climate system components as well as the economics and so on.
And the simplest thing you can do,
something we've been doing since the 1980s with the climate system model is just to double CO2 and see what happens.
And these figures behind me are the top right.
And the bottom two panels are three of these integrated assessment models that were
actually used in the US government's assessment of the so-called social cost of carbon.
This is the environmental damage done by releasing a tonne of CO2 into the atmosphere,
which the US being what it is actually now has legal weight in the US and people are suing each other over this.
So it sort of suddenly it matters what? Well, it matters for Americans how these calculations are done.
And so as a couple of Americans in the audience, Judy gets them but some.
But but and so there's a lot of scrutiny at the moment on these calculations.
And so so it sort of helps us. This is, by and large, physicists haven't been that much involved.
Right. But of course, there's an exception to this who gets involved in absolutely everything.
And he has got involved in the integrated assessment problem.
And I'm not showing you the model that that raised working on, which is actually which would look rather better on this comparison.
But but the model which raised worked on was not used in the Environmental Protection Agency's calculation of the social cost of carbon.
So these are sort of like the three quotes from long standing integrated assessment models here that the
top left panel is a sort of an assessment of what more typical climate models would would behave like.
And the crucial thing you'll see here is if I compare these responses, so focus on, as I say,
top, top right and the bottom two panels and compare these to the red lines and these plots,
which is what much more complex models which actually have fully coupled atmospheres and oceans, how they behave.
When you make a sudden change in CO2 concentration and you notice the red lines here,
there are very different shape to the to the curves in the integrated assessment models, the horizontal scales, you may not be able to read them.
They're about the same, but the integrated assessment models are adjusting rather sluggishly to the sudden input of CO2.
Whereas in the in the more complex models we see a more interesting behaviour,
which is a very rapid adjustment within a decade or so, and then a very slow adjustment.
So it's almost like a sort of bent L-shape rather than this very gradual problem,
this very gradual adjustment you see in the climate components of using these integrated assessment models.
And this is a a concern because, you know, if these things are misrepresenting the climate system, then, you know, it's they're getting that wrong.
And what, you know, what are the knock on implications of that? So it's sort of this is just motivation for why as as physicists,
I think we need to get more engaged with this whole process of integrated assessment and and talk more to the economists.
So to to to understand what the what they are assuming, how that how the models are working.
But I'm just that's just sort of motivation for why physicists need to get involved.
We'll get on to what people actually use these models for.
And I'm assuming that was sort of the apologies to many economists in the audience, I find.
Going over the basics here, but some but this is the basics that I had to learn.
So I'm going to you can share the pain with me. Okay. So,
so so the key assumption in these economic models is that there is an instantaneous equilibrium that can be found
between the increasing costs of the damage done by CO2 emissions and the increasing cost of avoiding those emissions.
So the green curve here is d damage by the emission and in case of the marginal cost of damage of putting one more tonne of CO2 into the atmosphere,
the blue curve is the marginal cost of sorry, the blue curve is the marginal cost of damage and the green curve is the marginal cost of abatement.
Obviously the more you reduce emissions, the more expensive it gets to cut out that extra tonne.
And this is a schematic diagram which was actually included in this interagency report explaining how they calculated the social cost of carbon.
An interesting thing about this diagram, which I thought was quite symptomatic and we'll come back to in the course of this to notice the green curve.
GREENHOUSE So the the the horizontal line here is reducing emissions as you move in this direction.
Okay. So, so the cost of cutting out one more time of carbon goes up steadily as you've got rid of the easy stuff, as you've, you know,
replaced your light bulbs and you've got to replace your power stations and then you've got to actually stop flying and stuff like that.
Okay. So sort of that's why this curve sort of goes up measures is pretty symptomatic.
It doesn't actually hit the the vertical axis.
And a lot of these, if you read textbooks on these things, these curves very seldom hit the vertical axis.
And that's actually going to be quite important. So we're going to be coming back to that.
Okay. So the so this is one of the sort of fundamental assumptions here that we're trying to balance
costs and costs and benefits in order to find a least cost path through the 21st century.
Obviously, as part of this, we need to know what climate change actually costs.
How much does human how much is human welfare impacted by global warming?
And again, this is an ingredient which goes into all of these integrated assessment exercises.
Here are three representative curves and before is sitting there looking really, really annoyed.
But I'm just showing what people are doing. Okay. And here are three possibly indefensible curves.
I'm showing. I'm showing how in these three sort of official models, what official,
in the sense they've been used in this calculation of the social cost of carbon represent the cost of of climate change.
So the vertical axis here is fractions of global economic output.
So notice somewhat extraordinarily here that a sort of a six degree warming so which is sort
of well on my way back to the Cretaceous is only a 10% loss in global economic output.
And bearing in mind in at least two of these models,
growth is still clipping along at 2% per year at the time at the time you reach those sort of temperatures again,
you know, a transition back most of the way to the Cretaceous is only ten years of economic growth.
So. So so that's the. So that should make you stop and think about does this does this does this make.
And I think it's important. You know, it's important.
On the other hand, it's easy to to to snipe at these things and and and to and I think that the authors of these models and I mean,
certainly, Bill Nordhaus, they're very clear that these curves really only make sense for relatively small temperature perturbations.
And as soon as we get to, you know, multiple degrees of warming,
it's some it's easy to to question whether these estimates of economic damage make any sense.
I mean, six degrees of warming would be an unrecognisable world.
And trying to quantify that in terms of a few years of economic growth, I mean, the the the global financial crisis peak to trough.
I probably should have that number in my head. But it was it was a it was a couple of years of of of of economic growth.
So. So six degrees of warming is just three or four.
Global financial crisis. Yeah. Again, isn't it helpful to think of these things in terms of orders of magnitude?
Just to get a feel for whether or not. So I think when you get out to multiple degrees of warming, it's problematic, by the way.
And there is another interesting feature of these models, the green one that the so-called sun model is actually positive, up to three degrees.
That means that in that model, in the version of that model that was used here, it's actually since been updated and moved up a bit.
The the personalisation effects of CO2 on crops actually outweighs the impacts of CO2,
the negative impacts of climate change in the up to up to about three degrees of warming now.
So so so so this is these these are relatively optimistic estimates.
I'm going to come back to this. But these are what these models use.
So given so is this sort of optimism in the damage, the reason we see these very benign futures coming out of this integrated?
And so this is one one sort of area that one might immediately think, oh,
maybe this is the reason we have this very benign future coming out of this integrated assessment process
into thinking that some of the climate change can be solved without really causing too much pain.
Another key ingredient, by the way, just to spoil the punchline, it turns out this isn't the crucial point.
Okay, so what will work through this is kind of a detective story.
We're trying to trying to find out what's going on here.
So the other aspects of this, which is tend to be very more important, very important, is the fact that in all of these models,
global consumption goes up exponentially or near exponentially through much of the century.
So we're talking about the sort of orange or red scenarios where we have rapid
growth through the century as the world economy grows from its current size,
around $75 trillion a year up to it by the end of the century, several, you know, an order of magnitude or more bigger than that.
So we can put this all together and say we've got some ingredients of the integrated assessment problem.
First of all, we've got the global consumption is going up.
That's sort of the total amount of money washing around through the system by some something which we can represent as a geometric growth.
We don't need to assume that that the growth parameter is constant over time, but we it's the geometric mean of the growth parameter over and over,
an interval that determines how wealthy the world is at the end of that interval.
Another crucial component in this is that the when we work out how much it's worth reducing an
emission or how much it's worth paying to avoid putting a tonne of carbon into the atmosphere,
we have to wait impacts over time in the future because these impacts persist.
Economists use something called discounting where they they wait in all these calculations.
They don't wait exponentially in paints going forward into the future.
There's a lot of controversy over that. Some people argue that hyperbolic discounting would make more sense.
But in the calculations that have been done here, in the standard calculations,
the discounting used is exponential, which means that the next generation gets a third.
Or, for example, if I was using, I would say that the next generation gets impacts on the next generation,
get a third of the way as impacts on our generation and impacts on the generation after that and get a ninth of the way it has.
Impacts on our generation, impacts on the generation after that really don't matter.
So so that sort of gives you a feel for how exponential discounting works.
And of course, this has been this has been heavily criticised and many,
many economists worry about the implications of exponential discounting, particularly on intergenerational problems.
What comes out as particularly important, and Bill note has also pointed this out in one of his papers is not so much the discount rate you choose,
but what he called the growth corrected discount rate or the difference between
the rate of growth of the world economy and your monetary discount rate.
So in other words, if the world economy is growing at 2% per year and you discount at 2% per year,
then you end up waiting impacts indefinitely far into the future because they carry on growing with the size of the world economy.
I should have emphasised that. You'll notice in the okay,
we'll come on to one of the key ingredients of these models is that impacts are assumed to scale with the total size of the.
World economy. In monetary terms.
So the richer we are, the more damage, the more the more in dollar terms, climate change costs, because the more stuff we've got to be damaged.
That's that's a a key component of this assessment.
And there's some justification for that. You know, it doesn't necessarily mean that that that loss matters as much,
because obviously a 1% consumption loss to a poor person can matter a great deal more than a 1% loss if,
you know, a 10% loss of consumption to a poor person, if it results in them,
dying of starvation is obviously worse than a 10% consumption loss to a rich person.
It means they just can't have two cars. So so that there's obviously a but we're only dealing here with consumption losses, monetary losses.
And so those are assumed to scale or those in these models do scale with the overall size of the world economy.
So if the world economy is growing as an exponential rate and then you're discounting at an exponential rate,
it's the difference between those two rates that determines how much weight you're going to give to impacts as you go forward into the future.
The other thing we need to know, so these are sort of just I'm just building up the key ingredients of the problem here.
The only thing we need to know is how the system responds to an injection of CO2.
And this is actually represented in various relatively complicated ways in these models.
Whereas in fact, one of the things which has emerged from climate science over the past decade
or so is actually this bit of the problem may be rather simpler than many,
many than it is represented in many of these even very simple models.
And that's illustrated by this rather complicated looking diagram, which I think the Wiggles of which conceal a very simple story.
The experiment which has been done here was one of these model and comparison projects
where they took lots and lots of earth system models of varying degrees of complexity,
dumped 100 billion tonnes of carbon into the model atmospheres on in year one of
these integrations and then just ran the model forward to see what happened. Yep.
So it's very simple experiments and it's also it's a nice experiment because it's directly
relevant to this question of what impact does adding an extra ton of carbon into the atmosphere?
What impact does that have?
And you can see that you can represent the response of many of these models quite well with a rapid adjustment and then just constant temperatures.
So an exponential adjustment to a new a new constant.
It's not an equilibrium, but it's a sort of quasi equilibrium for at least 100, 100 years or so.
Now, the Wiggles here are in the more complicated models.
Notice the scale here, because it's only 100 billion tons that's been dumped in.
The actual amount of warming is of order 2.2 degrees.
And of course, internal variability in the climate system is comparable to that, which is why you see these very large wiggles.
But if we were to run large ensembles of these models, it's actually some maybe a good thing to do at some point.
I mean, the hypothesis would be that those wiggles would just average out.
And with the possible exception of the blue one, which seems to have gone into a bit of a run away,
and that's a heavily centred model and it's quite it's quite a sensitive model.
So I think the other ones,
I think when can assume that if we did enough ensembles they would they would average out to something like that adjustment.
So we see this very simple behaviour that you put C02 into the system and it just warms up by a fixed amount.
And for many economists,
this this is sort of unfamiliar to them because they're used to the idea that every additional tonne of CO2 you put into the atmosphere
has slightly less effect on the last because they've heard about fancy Arrhenius and the logarithmic impact of CO2 on radiative forcing.
So that sort of seems to contradict the idea that actually every tonne of CO2 you put in the atmosphere has much the same impact as the last one.
And whether where that comes from is that again, this is this sort of key innovation in climate science which has come out,
is that if we look on the left, these are plots. But from from Richard Miller, I should mention,
if we look across a very large range of scenarios and the amount by which the CO2 concentration
goes up as a function of the total amount of carbon we dump into the atmosphere,
you can see it's a, it's a convex curve. It's it's it's accelerating upwards in the left.
And if we compare then with the amount of warming we get as a function of CO2 concentrations that's curving downwards.
So when you put these two together by, I think, a complete coincidence, although I'd be interested, I mean,
such coincidences are always leave you sort of wondering, but I think it is basically it can be coincidence.
You end up with something which is more or less a straight line when I plot.
The temperature induced by the total amount of CO2 dumped in the atmosphere.
The right hand handle here is when we then throw in that the left hand handle is CO2 induced warming.
The warming caused by CO2, which is a reasonably clear straight line response independent of scenario.
The many the spaghetti of red lines are all the different IPCC scenarios for the future, some which are very aggressive mitigation,
that is, they turn back on themselves, those scenarios in which we actually start pumping CO2 back out of the atmosphere.
But we still stay on this straight line relationship between CO2 and between cumulative
CO2 emissions and peak and the water and the warming you see on the right hand panel,
which is rather messier, is when you include the effect of other agents, methane sulphate,
aerosols and so forth, which obviously muddies the water slightly, but that basically you still see, broadly speaking,
this this straight line relationship, which we could, for the sake of, I believe they have a phrase in America like good enough for government work.
We can say it's good enough for government work, a sort of more or less straight line relationship of two degrees per trillion tons,
which is what we if you sort of folds your eyes and stand far enough back,
you could say that's more or less the relationship we're seeing in the right hand plot.
So here we are. We've started to we got all the ingredients we need now for an idealised integrated assessment model.
We've got we've got a damage function, which is a polynomial function of global temperature.
Remember those those curves I'm showing?
We sniped at what they would the size of them, but the overall idea that they go up and they got more steeply with time,
with temperature as temperatures rise is it's plausible at least.
So we got a polynomial function of of global temperature.
We've got this discounting convention that we consider the social cost of carbon to be the impacts,
the cost of putting an additional tonne of carbon into the atmosphere added up over time with some exponential weighting.
That's this is my. Yeah it is. Oops.
Sorry. So that's this, this term here,
I've got this exponential weighting term here and that's the incremental damage done by adding an extra tonne of carbon.
Then we've got this very nice simple response for temperature delta t is just this tcr.
It is two degrees per trillion tons and then an exponential adjustment where that is a relatively rapid adjustment time.
So that yellow curve gave me that rapid adjustment. So far so good.
And then the temperature at time t just follows really from this expression here is just the integrated
emissions up till that time again times the TCR is if I want to know what temperature I'm going to get to,
I just add up all the emissions between now and then and I multiply it by the tcr the
trans in climate response to emissions that two degrees per trillion tonnes number.
Now if I put all these things together, I actually get an analytically tractable problem.
I should say that this was largely inspired by problems for the 25 final papers,
which actually it's we put ourselves through it every year, of course,
in physics, scratching our heads and trying to work out interesting problems that can be done in 45 minutes by really bright undergraduates.
And and and oftentimes you feel at the time it's a bit of a waste of time because we very seldom do anything analytically in our professional work.
But this is so so there is there's a paper in the works, by the way, which is which comes out this.
And I'm reasonably hopeful, having seen one run of reviews on it, that you will see it at some points are making it through the works.
Touchwood But so, but it's my, my first paper which I didn't use a computer which I'm, I'm quite, quite proud of.
But so I put might well be the last paper on which I don't get to use a computer.
But so, I mean, I did use computers, made the plots, but I, but I used Excel and I don't think that counts.
I mean, so, so, so yeah.
That that doesn't count, does it?
So, so, okay, so, so let me so you can just take the system and you can I'm sure plenty of people in this room will be able to do this in their heads,
but you can solve for the conditions at the time temperatures have stabilised the ask yourself,
okay, temperatures have stabilised, what are the bounds?
You know, what's what are the the balance conditions?
And you find that at this time there's all this these rate constants here that's just
comes out of that discounting on the adjustment and so on and adding up impacts over time.
So you don't really need to worry about those. There's this term the rate of change of damage with respect to temperature.
Obviously that matters because the steeper you are on that damage curve,
the more damage adding an extra tonne of carbon into the atmosphere will will have.
We will make. And remember, at this point, temperatures have stabilised.
So this is not changing over time. It's it's it's at whatever level it's reached.
That's the tertiary, which is this magic two degrees, 4 trillion tonnes number.
And that's the size of the world economy at the time that temperatures stabilise
because this D here is expressed as percentages of global consumption.
That's a really important component of this. So we're saying that, you know, that those curves I showed you were losses in global consumption.
So 5% loss obviously goes it means more in monetary terms if the world is extremely wealthy.
So that's what that is. So I can then substitute and there's w again I just substituted in for a using today's world economic
output that exponential growth and I've just expressed time instead of expressing it in terms of time,
I've expressed it in terms of cumulative emissions up until that time.
And this gives me an expression which doesn't depend on time, just relates the social cost of carbon.
That's the cost with the expert, the ratio between the rate of growth and the average rate of emissions between now and the time of peak warming.
The peak warming temperature t one.
And that's T one again and various constants that that the don't change that that are not part of the that are not part of
the that are are not not changing over time that they're just sort of determined by the set up of the a of the problem.
And so this is what's what's nice about this. It allows us to try and identify what really matters for peak warming in this idealised setup.
And here we are.
What we see is that peak warming in the horizontal and the social cost of carbon at the time emission at the time temperatures stop rising,
which crucially, because temperatures won't stop rising until we stop putting CO2 in the atmosphere,
that has to be the cost of abatement when that blue curve hits the vertical axis.
Remember, I pointed out that it didn't hit the vertical axis in that schematic,
but it has to hit the vertical axis because we actually have to get emissions to zero if temperatures are going to stop rising.
So so you can you can equate the social cost of carbon at the time emissions peak with the cost of getting rid of that last ton,
the cost of finally getting rid of the last tonne of emissions and getting net carbon emissions to zero,
which we will need to do in order to stabilise global climate.
This is this, by the way, is what we're struggling to to get.
This has been quite widely accepted now. And one of the things if you if you're interested in such things,
one of the things you could track as you watch the progress towards the Paris talks in December
is whether the phrase net zero appears in the Paris any any communications coming out of Paris,
because although everybody acknowledges that it's true that carbon emissions have to get to net zero in order to stabilise global climate,
it'll be very interesting to see whether the United Nations Framework Convention
on Climate Change can actually bring themselves to acknowledge this formally.
But I digress slightly that okay, so what's interesting here is we've got this nonlinear relationship between the cost of
getting rid of that last ton or the social cost of carbon at the time of peak warming,
that the ratio, the growth rate and the average,
the ratio between the growth rate and average emissions between now and the time of peak warming and the temperature at the time of peak warming.
And that's shown here. And so what's interesting about this is that in this framework, if the cost of the backstop,
if there exists a technology which would allow us to get emissions to zero,
to get rid of that last tonne for only $200 per tonne, for example, then we we have a relatively optimistic future.
I can get my. I've lost my. Then we can.
Then we have this relatively optimistic future. We have quite a good chance,
provided the world economy keeps growing of being rich enough to bring emissions to
zero or to be motivated to bring emissions to zero before temperatures gets too high.
So what I like about this is that this actually explains Nordhaus results.
Because if you delve into the fine print of the book, you discover that there is a bank stock technology.
He doesn't talk about it very much, but and doesn't say what it is.
But it plays a crucial role in getting rid of that last ton.
And that's absolutely central to all of these ideas,
the existence of some technology that allows us to get emissions not just down by 20% or 80%, but actually down to zero.
What's interesting is that if we vary so this is this is sort of the picture if we assume that emissions
between now and the time of peak warming are on average more or less the same as emissions today,
which would be plausible if they go up for a bit and then come down.
I mean, that's a you know, the average would be about where we start.
If we assume that we get them down very aggressively,
obviously we can we will peak at a lower temperature for the same cost of getting rid of that last tonne.
And this is back to the sort of standard case. What's perhaps more sobering for climate physicists is we can ask ourselves,
what difference does it make if the response is high or low, the response of the climate system?
So here's the standard case where I'm assuming a two degree 4 trillion tonne
transient climate response to emissions now all increase then to three degrees.
So you go to high transit, you'll notice that there isn't a huge amount of difference.
So even though I've added 50% to the climate response, it doesn't make that much difference to the to the peak warming.
Now, why is that?
Well, because, of course, if we go back to the expression of solving here, TCR reappears in two points here that that t t carry quantity.
So it's a non-linear relationship. TCR reappears in the wealth term.
It also appears moderate are determining the value of that additional that last one.
So what's going on here is the world is getting richer and because the world is being run by economists, remember the title of the talk?
Everybody's making rational decisions about whether or not to emit that next tonne.
If the TCR is high, they will value that additional tonne higher because it'll do more damage.
Okay. But in terms of temperature, they will also get richer, slower, if you said to me so.
So that compensates. So there's a compensation effect there between the the the the additional impacts of an additional
time as a fraction of world wealth and the impact of a higher tcr on the size of the world economy.
When you get to because because in temperature terms you're getting richer slower in time
because because you're you're actually getting richer at the same rate in terms of time.
But because you're because the world economy is because the temperature is going up faster.
If you if you if you if you drew output in terms of temperature, then it would be going up slower.
So that's the sort of compensation that's going on here.
And again, if we take a low chance in climate response, this is again,
it doesn't make so much difference, a factor of two change in the climate response.
If you've got this sort of rational decision making mechanism going on,
it all sort of gets taken care of in these feedbacks between the economy and the climate.
What does make a much bigger difference is if we assume a very low damage function,
if we assume that climate change really doesn't do any harm in our calculation of whether or not to emit that extra tonne.
Not not no harm, but half the harm that that I used in the base case.
If I take that, then of course I get a much higher peak warming because you don't bother to you don't bother to stop emitting because you think,
well, climate change isn't really doing any harm. So I'll I'll carry on with just one more puff, so to speak.
And of course, if it's true that climate change isn't doing that much harm, then this is the rational thing to do.
But of course, the danger is if you just think that climate change is doing much harm and get it wrong, that's where things go wrong.
And there's another sort of rather geekier aspect of this where if you assume a higher discount rate, so if at the time of peak warming,
people decide they don't really care too much about their grandchildren and therefore they give less weight to climate impacts.
Then again, that has a big impact on what temperature we actually end up peaking to.
I'm hoping that some 70 nickels will actually sort of do all this properly with the numerical calculation.
I just thought it'd be for the sake of this, this this talk.
I sort of was quickly doing some numerical calculations just to see whether or not this was
borne out in a when I actually sort of integrate the the the integrate the model properly.
So so here we are in a sort of baseline scenario here, which is just, you know,
RCP one of these RCP scenarios where emissions just carry on up through the century and then with the standard dice like emission,
those like impacts function on the right shows you the social cost of carbon.
In in green and the impact on world consumption in blue, both sort of impact on world consumption going up by 2050 to sort of eight,
9%, by which time temperatures are sort of up at five or six degrees.
So this is this is this is the sort of pretty rosy, but not as rosy as Richard Toles,
which is an even lower damage function for the same temperature, which we'll come back to in a minute.
And let me ask. Okay. So is it true that this backstop technology matters for what temperature you peak at?
And reassuringly, it does seem to be true. This is we were putting in now numerically estimates are just sort of they're not estimates,
they're just sort of hypotheses about what the cost of reducing emissions will be as those curves reach zero.
And you can see that if I, I take a $400 per ton of CO2 estimate, I get temperatures peaking out just below three degrees.
If I'm more optimistic and assume I can get rid of CO2 for only $200 per ton, then that that saw peak temperatures drops to two degrees.
If I likewise,
the sort of intuition of the analytic set of equations also work also is borne out by asking the impact of so what happens if we assume lower growth?
So we're seeing the world doesn't grow as fast.
We see temperatures on the left here continuing to rise because we're not wealthy enough for it to be worth us reducing emissions.
That's sort of what's going on there. The world isn't growing fast enough to motivate in this cost benefit framework, reducing emissions to zero.
And then likewise on the on the right, if you take that sort of optimistic fund model estimate of the impacts,
again, you saw temperatures carrying on rising towards four degrees.
Somewhat disappointingly, the numerical calculations didn't give me quite the punch line I wanted on the impact of T series.
So I do find some, but I'm sure once somebody is finished it'll be back to where we started.
But so, you know, because when the limericks don't bear out the analytic solution, it's always the numerics that are wrong, isn't it?
I mean, that's that's kind of that's what we all believe in now.
But so but no, there is there is some logic to this.
So you can see here, this is this is a sort of hybrid.
So this is the standard response on the left and the low screen on the right, a lower response on the right.
So you can see, because you have a lower response, the some compensation there in the sense that emissions go higher because the impacts of lower.
So, you know, you're you're doing your cost benefit analysis as you go along.
You end up with balancing out with higher emissions and ending up with not as low a temperature
response as you would get if you just took a single emission profile and prompted through.
So it does there is some compensation going on there, but it's not as complete as it was in the in the analytic solution.
So there's obviously some path dependency here which we need to understand.
But what does this mean? Okay. So peak warming depends on only two variables that we can control with policy interventions today.
So this is why we're sort of getting to tell the punch line here. One is what you might call the growth productivity of carbon or the amount the rate
of growth of the world economy you can achieve with a given level of emissions.
It's the rate of growth that you can achieve with the given level emissions, not the actual output.
And that has important implications as well.
It also depends critically on this quantity the marginal cost of abatement as emissions reached zero, or the cost of getting rid of the last ton.
In the limits of slow adjustment. It does not appear to be significantly dependent on the actual climate response, which I find very interesting.
But annoyingly, when when I was looking at actual numerical integrations,
where you do have things changing over time, that that nice limit doesn't seem to work so well, so well.
So stay tuned on that one. And we do have a very strong dependence of peak warming on estimates of impacts.
So what does this actually tell us about the real world? Well, there are there are some key assumptions in here which need to be questioned.
And what the advantage of this kind of analysis is, is it brings everything out.
You can look at it and say, okay, due to all of these assumptions make sense.
One of them is that the value in dollars of impact scales with global consumption.
There's quite good arguments for that. But you also you can also, I'm sure there'll be views that can be held against it.
The other critical assumption here is that we're all rational and the world the world is
rational and we use a cost benefit analysis to decide whether to deploy abatement measures,
although we can look around with that, particularly in the in the numerical scheme and sort of try out by playing around to things like,
you know, only half the world actually bothers to abate and all that sort of thing.
But the crucial third assumption is that this backstop technology exists, that there is a technology which allows us to get emissions to zero.
And crucially, the properties of the backstop are, first of all, it doesn't increase with falling emissions.
So it's not a substitute where typically that remember that that map curve is thinking in terms of substitutes.
The mach curve goes up as you approach zero and sort of keep and they didn't actually bring it all
the way to zero because they couldn't quite bring themselves to imagine what would actually happen.
But the point is that that the if you've got to if you're trying to sort if you're if you're just relying on substitutes to reduce your emissions,
the always be, you know, another more useful use of fossil carbon that isn't quite substituted for by whatever it is you've come up with.
I would argue that the only that that although we don't know what this backstop technology is,
I would argue that it has to be an effective subtractive technology, a technology that doesn't halve emissions.
It's got to actually remove CO2 from, in effect, remove CO2 from the atmosphere.
And it's only in that way, only with a technology like that, that we can actually get emissions to zero.
And so what determines this cost, I think, is is sort of nicely illustrated by this module.
This is an actual marginal cost of abatement cost curve.
So this is the basis for these curves of how much it costs to reduce emissions.
And this is where this is a fairly old one,
but it illustrates the point where McKinsey have sort of stacked up all the different options you can take.
And sort of in the middle here, for example, that red block is nuclear.
So this is the additional cost of replacing all our coal fired power station capacity with nuclear,
and that costs $10 per tonne of CO2 avoided or something.
And we can reduce the width of that curve represents the the amount of CO2 emission
reduction potential due to that that we think we can achieve with nuclear.
So the key point about this is that if we choose not to do nuclear, for example,
if we follow the German decision and not to deploy more nuclear power stations,
it actually doesn't make a huge amount of difference to the overall form of the curve, because if you don't do nuclear,
you do something else a little bit more expensive than nuclear if you're trying to reduce emissions to a given amount.
But what really matters when you're thinking about backstops is this stuff over on the right.
And notice they all of this stuff over on the right of this curve,
although you probably can't see the little lines as the little letters CSS turn up quite a lot,
which is well, well summarised in David McCoy's book as the last thing to be.
He had a chapter on CSS called The Last Thing to Think About. And and it was a joke.
But, you know, he meant it sort of it is our last it's the technology of last resort, which is why it plays a key role in the backstop,
because the sort of elephant in the corner of the whole C02 mitigation challenge is what happens if you don't have your technology of last
resort and you discover you still need to reduce emissions or somebody somewhere is still pumping out fossil carbon into the atmosphere?
Well, the problem is that the only next option for getting rid of emissions is actually to contract consumption,
to actually to shrink the world economy.
And that's because the underlying economic productivity of carbon is so high that has an enormous economic impact.
So that's why even though CAS is the most expensive mitigation option available on many measures,
it's also the most important because it's the one of it's the it's the technology of last resort.
If you end up actually having to reduce consumption in order to reduce emissions, that's the most expensive way of reducing emissions of all.
And this is entirely consistent with the findings of the IPCC that excluding nuclear, for example,
increased the cost of meeting the two degree goal by roughly 10%, excluding solar and wind.
Again, increase the cost emissions to you.
We go by roughly 10%, excluding cars more than double it, which is another way of saying it simply won't happen.
Another way you can say fairly safely that it won't happen without CCS is if you look to where the carbon is that's lying on the ground,
the available fossil fuel reserves. This is a nice figure that Alex Otto produced showing the width of the bands in
the vertical is current production of fossil carbon and the length of the sorry,
the width of the band, the height of the bands is, is, is current production of fossil carbon.
The width of the bands in the horizontal is the number of years production at current rates.
Okay. So the area of each little block is the amount of carbon that country has available to dig up and notice that,
you know, a lot of countries, countries like Norway and Britain and so on, we really don't feature much in this.
The but the big countries like Russia, the USA and so for example, India here who has, you know, 200 years of production rates,
most of it coal and every intention of, of, of, of using it to jet to to power their their energy supplies.
So I was going to digress on on Jevons Paradox.
Well, there's a there's an interesting other there's another interesting feedback there and why,
you know, substitutes will never get us to zero because,
you know, no matter how we substitute, no matter how well we substitute or use fossil carbon more efficiently,
we always come up with new ways of using it. So what should we as physicists be concentrating on?
Well, first, one of the messages of this is that these feedbacks between the climate and the
economy partly vitiate the impact of new information on the climate response.
So we shouldn't oversell the the the our ability as physicists to say if only we could tell people exactly how the climate is going to respond,
then they'll know how to they'll know how to solve the problem of this this sort of feedback centre.
In a sense, it doesn't really matter how the climate responds because, because, you know, as,
as the impacts become clear if people are doing the rational thing and that's that's of course a big if in this that the,
the, the emissions will automatically adapt.
There's also this feedback in the in the economy, which again,
besides the impact of research into substitutes alone that there is good way of getting emissions down in the short term,
but as a way of getting emissions to zero, they're probably not they're really not the the they can't be the whole story.
One thing we definitely can help with coming out of this and I stressed in the in
the I stressed in the talk that the the impact of getting the damage function wrong,
getting the estimates of how much additional carbon dumped into the atmosphere is going to cost as as a result of it, as a result of climate change.
It would be would be extremely harmful. I mean, so if we think it's going to the climate change is going to do very much harm, and actually it does.
Then of course, you do your cost benefit analysis based on incorrect information and you end up with the worst
possible outcome because you don't mitigate enough and you end up with lots of additional harm.
And I so I was fiddling with my talk rather late in the day because a paper actually came out highly relevant.
Paper came out yesterday which looked at this, looked at sort of new estimates of climate,
of the economic impacts of climate change as a function of temperature.
It's back to those. And you can see here on the right hand panel here, those three, you can barely see them.
Those are the three lines that I was talking about really wrong from these integrated assessment models.
And this is the estimate that these authors think climate change will cost that four
or five degrees of warming will cost the world economy by the end of the century.
That's Burke et al in came out this week but this this and this is really important has a huge
would have it if correct has a huge impact on on all our estimates of the cost of climate change.
But what's worrying is that the only evidence for this is pretty and then quite frank in the paper on this,
it's pretty tentative statistical evidence based on just observations of countries.
And, you know, you can look at these regressions here and think, yeah, observations of countries.
Well, it's easy to laugh, on the other hand.
But, you know, this is a really important question, and they're using the information available as best they can and concluding that,
you know, as the world gets warmer, economic output will be negatively impacted.
What I think we can do much better at would be informing this estimate of the damage.
How much is climate change actually costing? I think that's something that we need to engage with much more as a as a climate physics community,
because rather than just having to rely on these, you know, hazy statistical relationships, we ought to be able to take the input of, you know,
the kind of models that Tim runs where where you've actually got detailed weather that actually does damage in these models and
look at the impacts of climate change within those models in order to understand quantitatively what climate change is doing.
So we're not reliant on these very hand estimates of, you know,
5% of global output in 2100 and the way that we are in this integrated assessment problem.
So I think to come back to Nordhaus, I sort of began with sort of how nought has motivated this talk.
And this is a quote from one of Nordhaus recent papers,
and he was kind of explaining why they didn't really worry too much about the costs of catastrophic,
abrupt and irreversible events and why they didn't wait on these these sort of events very heavily in his integrated assessment model.
And he kind of said this rather sort of almost peevish comment, said, well, the physicists can't actually tell us how these events are going to,
you know, what about the geophysical aspects of these events and their probabilities?
How do they expect us as economists to to to incorporate them into our integrated assessment models?
And I think it's a it's a it's a legitimate concern. I think it's something that we as physicists need to rise to to give much better
information to the economic community about not necessarily this isn't a prediction.
This is not about, you know, how climate change will look in 2100, but how much harm will climate change actually do as the world warms?
And it's something we perhaps have been devoted to, to much of our attention into the long term prediction problem and not enough of our
attention into that sort of delicate interface between weather and the economy,
which will actually allow us to quantify what harm climate change is actually doing.
So this is sort of motivated.
This this talk is motivating me to focus further on on that question about the into the interface between weather and damage.
It's a good point to stop. Thank you.