1 00:00:06,520 --> 00:00:10,239 Whilst you're all sitting down. I think I will just start the introduction. 2 00:00:10,240 --> 00:00:18,220 So I think Miles Allen is somebody that probably doesn't need any introduction to almost all of you. 3 00:00:20,920 --> 00:00:26,889 I think it's fair to say he's pretty much a home-grown product having done his Ph.D. here. 4 00:00:26,890 --> 00:00:36,520 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. 5 00:00:37,990 --> 00:00:41,209 He's currently the professor of Geo System Science. 6 00:00:41,210 --> 00:00:45,370 So I write this down to a system, science and school of environment, geography and the environment, 7 00:00:46,330 --> 00:00:54,670 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. 8 00:00:55,930 --> 00:01:06,160 So Miles, very much straddles physics and environmental science, but also very much straddles, I think, the public face of science and climate change. 9 00:01:07,390 --> 00:01:10,750 I think if you switch on the TV and there's a climate change topic, 10 00:01:10,750 --> 00:01:18,760 there's a fair probability Myles will be saying something about it if it is part of the economy. 11 00:01:21,370 --> 00:01:27,430 I think many of us know that one of the really innovative things that Milo Miles has led is 12 00:01:27,850 --> 00:01:37,870 the is harnessing the world's PC computer power to run phenomenal ensembles of integrations. 13 00:01:38,350 --> 00:01:43,990 In my own research, I I'm I sort of feel lucky if we can do 50 member ensembles. 14 00:01:44,260 --> 00:01:50,049 He does tens of thousands of member ensembles, as I say, harnessing the power of computers around the world. 15 00:01:50,050 --> 00:01:58,540 And I think this is a remarkably innovative and important advance in our science utilising people power. 16 00:01:59,530 --> 00:02:03,700 So Miles is never shy of controversy. 17 00:02:04,150 --> 00:02:10,450 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. 18 00:02:10,750 --> 00:02:17,050 But anyway, here we go. How hot will it get in a world run by economists? 19 00:02:17,140 --> 00:02:20,740 A physicist take on climate policy models. Think how much? 20 00:02:21,040 --> 00:02:29,169 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, 21 00:02:29,170 --> 00:02:39,580 so to speak, in climate policy about how different how how different disciplines work on this issue. 22 00:02:39,820 --> 00:02:46,870 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. 23 00:02:46,870 --> 00:02:50,790 I was having to apologise more and more for things I was doing because they weren't really physics. 24 00:02:51,100 --> 00:02:56,320 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. 25 00:02:57,010 --> 00:03:03,670 And so, so, so, so. And there'll be somebody who'll define geography as saying it's consistent with it. 26 00:03:04,240 --> 00:03:07,870 And so, so, so so this is what I've been learning a lot of economics. 27 00:03:07,870 --> 00:03:15,459 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, 28 00:03:15,460 --> 00:03:23,080 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. 29 00:03:23,080 --> 00:03:29,620 But before then I've been working a lot with Dave Frame, who's now in New Zealand. 30 00:03:30,070 --> 00:03:40,780 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. 31 00:03:40,780 --> 00:03:46,420 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. 32 00:03:47,140 --> 00:03:52,959 And so but the real inspiration of this is somebody I've never met, Bill Nordhaus, 33 00:03:52,960 --> 00:03:59,980 who's a very well-known economist based in Yale, and he's he's written a book. 34 00:03:59,980 --> 00:04:02,549 So I was hoping to wave around, but I've obviously given it to somebody. 35 00:04:02,550 --> 00:04:07,870 So if any of my grad students and I'm looking the Climate Casino by Bill Nordhaus 36 00:04:07,870 --> 00:04:12,609 and this is really the sort of inspiration of this talk because in the in this book, 37 00:04:12,610 --> 00:04:18,790 which is a sort of summary of his his life's work, he talks about the integrated assessment problem, 38 00:04:18,790 --> 00:04:24,729 which is where you couple the climate system with a model of the world economy and run it forward in 39 00:04:24,730 --> 00:04:32,830 time and ask under certain policy scenarios what happens and his his his optimal policy scenario, 40 00:04:32,830 --> 00:04:41,139 the one in which the world cooperates. We impose rational carbon taxes at the appropriate rate determined by the social cost of carbon. 41 00:04:41,140 --> 00:04:48,250 I'll sort of explain this jargon a bit as I go through the talk results in a warming over the 21st century, 42 00:04:48,250 --> 00:04:53,800 which peaks out above pre-industrial at sort of somewhat below three degrees between two and three degrees, 43 00:04:54,520 --> 00:05:01,540 where the impacts of climate change are a few percent of global outputs, which to put this in context, 44 00:05:01,540 --> 00:05:05,770 this is in a world which is still growing at that point by a couple of. 45 00:05:05,870 --> 00:05:11,300 Percent per year in terms of economic output and population has by then stabilised in this scenario. 46 00:05:11,600 --> 00:05:17,600 So a few percent loss due to climate change is in this scenario really only a few years 47 00:05:17,600 --> 00:05:23,330 delay in achieving the same level of per capita output and temperature stabilise. 48 00:05:24,110 --> 00:05:29,989 And as I say, above two degrees above that sort of magic two degree number which so a lot of environmentalists, 49 00:05:29,990 --> 00:05:34,160 three things that bill know what I'm saying what his scenario doesn't achieve two degrees so. 50 00:05:34,340 --> 00:05:41,840 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. 51 00:05:41,880 --> 00:05:51,050 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, 52 00:05:51,500 --> 00:05:57,470 not that whole, then you can take some other economists come on to that and it could get a little warmer than that. 53 00:05:57,740 --> 00:06:02,000 But what I really like to understand is why what's what's what's going on here? 54 00:06:02,030 --> 00:06:05,960 Why why does temperature pick out in that way? 55 00:06:06,530 --> 00:06:11,540 And so it's sort of to help me understand this, I've been sort of learning a bit about these integrated assessment models. 56 00:06:11,540 --> 00:06:19,040 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. 57 00:06:20,600 --> 00:06:22,850 Part of my motivation for this, of course, 58 00:06:22,850 --> 00:06:32,380 coming back to the the the physics behind it is looking at the physical components of integrated assessment models. 59 00:06:32,390 --> 00:06:39,230 So, so every integrated assessment model will have a climate system components as well as the economics and so on. 60 00:06:39,230 --> 00:06:40,459 And the simplest thing you can do, 61 00:06:40,460 --> 00:06:48,170 something we've been doing since the 1980s with the climate system model is just to double CO2 and see what happens. 62 00:06:48,590 --> 00:06:52,610 And these figures behind me are the top right. 63 00:06:52,610 --> 00:06:56,809 And the bottom two panels are three of these integrated assessment models that were 64 00:06:56,810 --> 00:07:03,620 actually used in the US government's assessment of the so-called social cost of carbon. 65 00:07:03,950 --> 00:07:09,140 This is the environmental damage done by releasing a tonne of CO2 into the atmosphere, 66 00:07:09,500 --> 00:07:16,250 which the US being what it is actually now has legal weight in the US and people are suing each other over this. 67 00:07:16,250 --> 00:07:23,510 So it sort of suddenly it matters what? Well, it matters for Americans how these calculations are done. 68 00:07:23,840 --> 00:07:28,040 And so as a couple of Americans in the audience, Judy gets them but some. 69 00:07:28,160 --> 00:07:32,750 But but and so there's a lot of scrutiny at the moment on these calculations. 70 00:07:32,990 --> 00:07:40,070 And so so it sort of helps us. This is, by and large, physicists haven't been that much involved. 71 00:07:41,330 --> 00:07:45,320 Right. But of course, there's an exception to this who gets involved in absolutely everything. 72 00:07:45,800 --> 00:07:47,870 And he has got involved in the integrated assessment problem. 73 00:07:48,110 --> 00:07:53,899 And I'm not showing you the model that that raised working on, which is actually which would look rather better on this comparison. 74 00:07:53,900 --> 00:08:02,150 But but the model which raised worked on was not used in the Environmental Protection Agency's calculation of the social cost of carbon. 75 00:08:02,150 --> 00:08:09,650 So these are sort of like the three quotes from long standing integrated assessment models here that the 76 00:08:09,650 --> 00:08:16,040 top left panel is a sort of an assessment of what more typical climate models would would behave like. 77 00:08:16,220 --> 00:08:22,120 And the crucial thing you'll see here is if I compare these responses, so focus on, as I say, 78 00:08:22,130 --> 00:08:27,230 top, top right and the bottom two panels and compare these to the red lines and these plots, 79 00:08:27,470 --> 00:08:33,920 which is what much more complex models which actually have fully coupled atmospheres and oceans, how they behave. 80 00:08:34,100 --> 00:08:38,600 When you make a sudden change in CO2 concentration and you notice the red lines here, 81 00:08:39,050 --> 00:08:47,120 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. 82 00:08:47,120 --> 00:08:55,250 They're about the same, but the integrated assessment models are adjusting rather sluggishly to the sudden input of CO2. 83 00:08:55,490 --> 00:09:00,379 Whereas in the in the more complex models we see a more interesting behaviour, 84 00:09:00,380 --> 00:09:05,690 which is a very rapid adjustment within a decade or so, and then a very slow adjustment. 85 00:09:05,690 --> 00:09:11,329 So it's almost like a sort of bent L-shape rather than this very gradual problem, 86 00:09:11,330 --> 00:09:16,700 this very gradual adjustment you see in the climate components of using these integrated assessment models. 87 00:09:17,000 --> 00:09:24,260 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. 88 00:09:24,260 --> 00:09:32,450 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, 89 00:09:32,450 --> 00:09:41,930 I think we need to get more engaged with this whole process of integrated assessment and and talk more to the economists. 90 00:09:42,290 --> 00:09:47,570 So to to to understand what the what they are assuming, how that how the models are working. 91 00:09:48,800 --> 00:09:52,850 But I'm just that's just sort of motivation for why physicists need to get involved. 92 00:09:53,840 --> 00:09:59,239 We'll get on to what people actually use these models for. 93 00:09:59,240 --> 00:10:05,780 And I'm assuming that was sort of the apologies to many economists in the audience, I find. 94 00:10:05,900 --> 00:10:09,890 Going over the basics here, but some but this is the basics that I had to learn. 95 00:10:10,160 --> 00:10:13,100 So I'm going to you can share the pain with me. Okay. So, 96 00:10:13,100 --> 00:10:25,790 so so the key assumption in these economic models is that there is an instantaneous equilibrium that can be found 97 00:10:26,180 --> 00:10:34,940 between the increasing costs of the damage done by CO2 emissions and the increasing cost of avoiding those emissions. 98 00:10:35,210 --> 00:10:47,540 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, 99 00:10:47,720 --> 00:10:57,410 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. 100 00:10:57,920 --> 00:11:05,180 Obviously the more you reduce emissions, the more expensive it gets to cut out that extra tonne. 101 00:11:06,500 --> 00:11:15,800 And this is a schematic diagram which was actually included in this interagency report explaining how they calculated the social cost of carbon. 102 00:11:16,400 --> 00:11:24,680 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. 103 00:11:25,970 --> 00:11:36,170 GREENHOUSE So the the the horizontal line here is reducing emissions as you move in this direction. 104 00:11:36,170 --> 00:11:44,840 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, 105 00:11:44,900 --> 00:11:50,780 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. 106 00:11:50,960 --> 00:11:55,790 Okay. So sort of that's why this curve sort of goes up measures is pretty symptomatic. 107 00:11:56,000 --> 00:11:59,690 It doesn't actually hit the the vertical axis. 108 00:11:59,690 --> 00:12:06,319 And a lot of these, if you read textbooks on these things, these curves very seldom hit the vertical axis. 109 00:12:06,320 --> 00:12:09,620 And that's actually going to be quite important. So we're going to be coming back to that. 110 00:12:10,010 --> 00:12:15,020 Okay. So the so this is one of the sort of fundamental assumptions here that we're trying to balance 111 00:12:15,020 --> 00:12:20,960 costs and costs and benefits in order to find a least cost path through the 21st century. 112 00:12:22,310 --> 00:12:27,620 Obviously, as part of this, we need to know what climate change actually costs. 113 00:12:28,070 --> 00:12:34,790 How much does human how much is human welfare impacted by global warming? 114 00:12:35,600 --> 00:12:40,220 And again, this is an ingredient which goes into all of these integrated assessment exercises. 115 00:12:40,940 --> 00:12:48,169 Here are three representative curves and before is sitting there looking really, really annoyed. 116 00:12:48,170 --> 00:12:55,700 But I'm just showing what people are doing. Okay. And here are three possibly indefensible curves. 117 00:12:55,970 --> 00:13:01,640 I'm showing. I'm showing how in these three sort of official models, what official, 118 00:13:01,640 --> 00:13:07,770 in the sense they've been used in this calculation of the social cost of carbon represent the cost of of climate change. 119 00:13:07,770 --> 00:13:11,570 So the vertical axis here is fractions of global economic output. 120 00:13:11,780 --> 00:13:18,229 So notice somewhat extraordinarily here that a sort of a six degree warming so which is sort 121 00:13:18,230 --> 00:13:26,390 of well on my way back to the Cretaceous is only a 10% loss in global economic output. 122 00:13:26,690 --> 00:13:28,910 And bearing in mind in at least two of these models, 123 00:13:29,720 --> 00:13:38,240 growth is still clipping along at 2% per year at the time at the time you reach those sort of temperatures again, 124 00:13:38,690 --> 00:13:43,730 you know, a transition back most of the way to the Cretaceous is only ten years of economic growth. 125 00:13:45,310 --> 00:13:51,220 So. So so that's the. So that should make you stop and think about does this does this does this make. 126 00:13:51,430 --> 00:13:53,080 And I think it's important. You know, it's important. 127 00:13:53,290 --> 00:14:06,009 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, 128 00:14:06,010 --> 00:14:16,059 certainly, Bill Nordhaus, they're very clear that these curves really only make sense for relatively small temperature perturbations. 129 00:14:16,060 --> 00:14:19,450 And as soon as we get to, you know, multiple degrees of warming, 130 00:14:20,050 --> 00:14:27,370 it's some it's easy to to question whether these estimates of economic damage make any sense. 131 00:14:27,370 --> 00:14:30,609 I mean, six degrees of warming would be an unrecognisable world. 132 00:14:30,610 --> 00:14:40,390 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. 133 00:14:41,480 --> 00:14:50,620 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. 134 00:14:50,640 --> 00:14:55,310 So. So six degrees of warming is just three or four. 135 00:14:55,490 --> 00:15:02,930 Global financial crisis. Yeah. Again, isn't it helpful to think of these things in terms of orders of magnitude? 136 00:15:03,170 --> 00:15:07,940 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. 137 00:15:07,940 --> 00:15:14,450 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. 138 00:15:15,080 --> 00:15:21,200 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. 139 00:15:22,470 --> 00:15:29,120 The the personalisation effects of CO2 on crops actually outweighs the impacts of CO2, 140 00:15:29,120 --> 00:15:35,390 the negative impacts of climate change in the up to up to about three degrees of warming now. 141 00:15:36,060 --> 00:15:40,620 So so so so this is these these are relatively optimistic estimates. 142 00:15:40,650 --> 00:15:44,580 I'm going to come back to this. But these are what these models use. 143 00:15:44,600 --> 00:15:56,169 So given so is this sort of optimism in the damage, the reason we see these very benign futures coming out of this integrated? 144 00:15:56,170 --> 00:15:59,420 And so this is one one sort of area that one might immediately think, oh, 145 00:15:59,480 --> 00:16:04,430 maybe this is the reason we have this very benign future coming out of this integrated assessment process 146 00:16:05,180 --> 00:16:13,160 into thinking that some of the climate change can be solved without really causing too much pain. 147 00:16:14,150 --> 00:16:21,260 Another key ingredient, by the way, just to spoil the punchline, it turns out this isn't the crucial point. 148 00:16:21,440 --> 00:16:26,230 Okay, so what will work through this is kind of a detective story. 149 00:16:26,240 --> 00:16:28,160 We're trying to trying to find out what's going on here. 150 00:16:29,000 --> 00:16:35,780 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, 151 00:16:36,350 --> 00:16:44,209 global consumption goes up exponentially or near exponentially through much of the century. 152 00:16:44,210 --> 00:16:48,650 So we're talking about the sort of orange or red scenarios where we have rapid 153 00:16:48,890 --> 00:16:53,540 growth through the century as the world economy grows from its current size, 154 00:16:53,540 --> 00:17:03,500 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. 155 00:17:04,460 --> 00:17:11,180 So we can put this all together and say we've got some ingredients of the integrated assessment problem. 156 00:17:11,840 --> 00:17:15,320 First of all, we've got the global consumption is going up. 157 00:17:15,410 --> 00:17:23,690 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. 158 00:17:23,690 --> 00:17:31,759 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, 159 00:17:31,760 --> 00:17:35,690 an interval that determines how wealthy the world is at the end of that interval. 160 00:17:36,980 --> 00:17:44,540 Another crucial component in this is that the when we work out how much it's worth reducing an 161 00:17:44,540 --> 00:17:51,080 emission or how much it's worth paying to avoid putting a tonne of carbon into the atmosphere, 162 00:17:51,380 --> 00:17:54,950 we have to wait impacts over time in the future because these impacts persist. 163 00:17:55,340 --> 00:18:01,300 Economists use something called discounting where they they wait in all these calculations. 164 00:18:01,310 --> 00:18:06,320 They don't wait exponentially in paints going forward into the future. 165 00:18:06,530 --> 00:18:10,700 There's a lot of controversy over that. Some people argue that hyperbolic discounting would make more sense. 166 00:18:11,000 --> 00:18:14,420 But in the calculations that have been done here, in the standard calculations, 167 00:18:15,200 --> 00:18:21,259 the discounting used is exponential, which means that the next generation gets a third. 168 00:18:21,260 --> 00:18:25,819 Or, for example, if I was using, I would say that the next generation gets impacts on the next generation, 169 00:18:25,820 --> 00:18:31,309 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. 170 00:18:31,310 --> 00:18:34,280 Impacts on our generation, impacts on the generation after that really don't matter. 171 00:18:35,150 --> 00:18:39,890 So so that sort of gives you a feel for how exponential discounting works. 172 00:18:40,760 --> 00:18:46,280 And of course, this has been this has been heavily criticised and many, 173 00:18:46,280 --> 00:18:52,970 many economists worry about the implications of exponential discounting, particularly on intergenerational problems. 174 00:18:53,600 --> 00:19:02,990 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, 175 00:19:03,800 --> 00:19:07,250 but what he called the growth corrected discount rate or the difference between 176 00:19:07,250 --> 00:19:10,880 the rate of growth of the world economy and your monetary discount rate. 177 00:19:11,210 --> 00:19:17,510 So in other words, if the world economy is growing at 2% per year and you discount at 2% per year, 178 00:19:18,140 --> 00:19:25,250 then you end up waiting impacts indefinitely far into the future because they carry on growing with the size of the world economy. 179 00:19:26,450 --> 00:19:30,680 I should have emphasised that. You'll notice in the okay, 180 00:19:30,890 --> 00:19:40,580 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. 181 00:19:40,650 --> 00:19:42,890 World economy. In monetary terms. 182 00:19:42,900 --> 00:19:51,900 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. 183 00:19:52,440 --> 00:19:56,130 That's that's a a key component of this assessment. 184 00:19:56,340 --> 00:20:02,940 And there's some justification for that. You know, it doesn't necessarily mean that that that loss matters as much, 185 00:20:03,780 --> 00:20:09,600 because obviously a 1% consumption loss to a poor person can matter a great deal more than a 1% loss if, 186 00:20:10,260 --> 00:20:13,230 you know, a 10% loss of consumption to a poor person, if it results in them, 187 00:20:13,470 --> 00:20:17,120 dying of starvation is obviously worse than a 10% consumption loss to a rich person. 188 00:20:17,130 --> 00:20:27,270 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. 189 00:20:28,080 --> 00:20:36,149 And so those are assumed to scale or those in these models do scale with the overall size of the world economy. 190 00:20:36,150 --> 00:20:42,600 So if the world economy is growing as an exponential rate and then you're discounting at an exponential rate, 191 00:20:42,750 --> 00:20:49,080 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. 192 00:20:50,550 --> 00:20:54,800 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. 193 00:20:54,810 --> 00:20:58,950 The only thing we need to know is how the system responds to an injection of CO2. 194 00:20:59,370 --> 00:21:04,230 And this is actually represented in various relatively complicated ways in these models. 195 00:21:04,470 --> 00:21:09,540 Whereas in fact, one of the things which has emerged from climate science over the past decade 196 00:21:09,540 --> 00:21:14,580 or so is actually this bit of the problem may be rather simpler than many, 197 00:21:14,670 --> 00:21:19,770 many than it is represented in many of these even very simple models. 198 00:21:20,190 --> 00:21:27,540 And that's illustrated by this rather complicated looking diagram, which I think the Wiggles of which conceal a very simple story. 199 00:21:28,140 --> 00:21:32,310 The experiment which has been done here was one of these model and comparison projects 200 00:21:32,310 --> 00:21:37,560 where they took lots and lots of earth system models of varying degrees of complexity, 201 00:21:37,920 --> 00:21:43,770 dumped 100 billion tonnes of carbon into the model atmospheres on in year one of 202 00:21:43,770 --> 00:21:47,550 these integrations and then just ran the model forward to see what happened. Yep. 203 00:21:47,590 --> 00:21:52,139 So it's very simple experiments and it's also it's a nice experiment because it's directly 204 00:21:52,140 --> 00:21:56,610 relevant to this question of what impact does adding an extra ton of carbon into the atmosphere? 205 00:21:56,790 --> 00:21:58,170 What impact does that have? 206 00:21:58,500 --> 00:22:06,360 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. 207 00:22:06,870 --> 00:22:11,730 So an exponential adjustment to a new a new constant. 208 00:22:12,750 --> 00:22:18,540 It's not an equilibrium, but it's a sort of quasi equilibrium for at least 100, 100 years or so. 209 00:22:19,290 --> 00:22:22,300 Now, the Wiggles here are in the more complicated models. 210 00:22:22,320 --> 00:22:26,340 Notice the scale here, because it's only 100 billion tons that's been dumped in. 211 00:22:26,580 --> 00:22:30,210 The actual amount of warming is of order 2.2 degrees. 212 00:22:30,420 --> 00:22:34,950 And of course, internal variability in the climate system is comparable to that, which is why you see these very large wiggles. 213 00:22:35,280 --> 00:22:41,790 But if we were to run large ensembles of these models, it's actually some maybe a good thing to do at some point. 214 00:22:42,420 --> 00:22:45,870 I mean, the hypothesis would be that those wiggles would just average out. 215 00:22:46,560 --> 00:22:51,990 And with the possible exception of the blue one, which seems to have gone into a bit of a run away, 216 00:22:52,860 --> 00:22:56,460 and that's a heavily centred model and it's quite it's quite a sensitive model. 217 00:22:57,210 --> 00:23:00,630 So I think the other ones, 218 00:23:00,630 --> 00:23:06,360 I think when can assume that if we did enough ensembles they would they would average out to something like that adjustment. 219 00:23:07,260 --> 00:23:14,670 So we see this very simple behaviour that you put C02 into the system and it just warms up by a fixed amount. 220 00:23:15,480 --> 00:23:18,210 And for many economists, 221 00:23:18,540 --> 00:23:29,670 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 222 00:23:29,940 --> 00:23:37,440 has slightly less effect on the last because they've heard about fancy Arrhenius and the logarithmic impact of CO2 on radiative forcing. 223 00:23:38,220 --> 00:23:47,040 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. 224 00:23:47,280 --> 00:23:52,860 And whether where that comes from is that again, this is this sort of key innovation in climate science which has come out, 225 00:23:53,070 --> 00:23:57,510 is that if we look on the left, these are plots. But from from Richard Miller, I should mention, 226 00:23:58,120 --> 00:24:04,889 if we look across a very large range of scenarios and the amount by which the CO2 concentration 227 00:24:04,890 --> 00:24:10,410 goes up as a function of the total amount of carbon we dump into the atmosphere, 228 00:24:10,590 --> 00:24:15,510 you can see it's a, it's a convex curve. It's it's it's accelerating upwards in the left. 229 00:24:16,020 --> 00:24:25,050 And if we compare then with the amount of warming we get as a function of CO2 concentrations that's curving downwards. 230 00:24:25,410 --> 00:24:31,260 So when you put these two together by, I think, a complete coincidence, although I'd be interested, I mean, 231 00:24:31,560 --> 00:24:36,330 such coincidences are always leave you sort of wondering, but I think it is basically it can be coincidence. 232 00:24:36,690 --> 00:24:40,260 You end up with something which is more or less a straight line when I plot. 233 00:24:40,610 --> 00:24:46,790 The temperature induced by the total amount of CO2 dumped in the atmosphere. 234 00:24:47,630 --> 00:24:53,959 The right hand handle here is when we then throw in that the left hand handle is CO2 induced warming. 235 00:24:53,960 --> 00:25:00,710 The warming caused by CO2, which is a reasonably clear straight line response independent of scenario. 236 00:25:00,710 --> 00:25:07,430 The many the spaghetti of red lines are all the different IPCC scenarios for the future, some which are very aggressive mitigation, 237 00:25:07,610 --> 00:25:13,010 that is, they turn back on themselves, those scenarios in which we actually start pumping CO2 back out of the atmosphere. 238 00:25:13,250 --> 00:25:19,549 But we still stay on this straight line relationship between CO2 and between cumulative 239 00:25:19,550 --> 00:25:24,770 CO2 emissions and peak and the water and the warming you see on the right hand panel, 240 00:25:24,770 --> 00:25:32,180 which is rather messier, is when you include the effect of other agents, methane sulphate, 241 00:25:32,190 --> 00:25:38,420 aerosols and so forth, which obviously muddies the water slightly, but that basically you still see, broadly speaking, 242 00:25:38,690 --> 00:25:47,060 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. 243 00:25:47,210 --> 00:25:53,540 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, 244 00:25:54,260 --> 00:25:59,900 which is what we if you sort of folds your eyes and stand far enough back, 245 00:26:00,260 --> 00:26:04,069 you could say that's more or less the relationship we're seeing in the right hand plot. 246 00:26:04,070 --> 00:26:11,990 So here we are. We've started to we got all the ingredients we need now for an idealised integrated assessment model. 247 00:26:12,860 --> 00:26:18,200 We've got we've got a damage function, which is a polynomial function of global temperature. 248 00:26:18,320 --> 00:26:20,150 Remember those those curves I'm showing? 249 00:26:20,330 --> 00:26:27,500 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, 250 00:26:27,710 --> 00:26:31,250 with temperature as temperatures rise is it's plausible at least. 251 00:26:31,250 --> 00:26:34,760 So we got a polynomial function of of global temperature. 252 00:26:35,600 --> 00:26:41,959 We've got this discounting convention that we consider the social cost of carbon to be the impacts, 253 00:26:41,960 --> 00:26:48,590 the cost of putting an additional tonne of carbon into the atmosphere added up over time with some exponential weighting. 254 00:26:48,800 --> 00:26:52,100 That's this is my. Yeah it is. Oops. 255 00:26:52,250 --> 00:26:54,409 Sorry. So that's this, this term here, 256 00:26:54,410 --> 00:26:59,750 I've got this exponential weighting term here and that's the incremental damage done by adding an extra tonne of carbon. 257 00:27:00,170 --> 00:27:07,420 Then we've got this very nice simple response for temperature delta t is just this tcr. 258 00:27:07,430 --> 00:27:13,610 It is two degrees per trillion tons and then an exponential adjustment where that is a relatively rapid adjustment time. 259 00:27:13,610 --> 00:27:17,990 So that yellow curve gave me that rapid adjustment. So far so good. 260 00:27:18,260 --> 00:27:25,040 And then the temperature at time t just follows really from this expression here is just the integrated 261 00:27:25,040 --> 00:27:31,310 emissions up till that time again times the TCR is if I want to know what temperature I'm going to get to, 262 00:27:31,460 --> 00:27:35,960 I just add up all the emissions between now and then and I multiply it by the tcr the 263 00:27:35,960 --> 00:27:39,770 trans in climate response to emissions that two degrees per trillion tonnes number. 264 00:27:40,460 --> 00:27:46,160 Now if I put all these things together, I actually get an analytically tractable problem. 265 00:27:46,520 --> 00:27:52,999 I should say that this was largely inspired by problems for the 25 final papers, 266 00:27:53,000 --> 00:27:56,420 which actually it's we put ourselves through it every year, of course, 267 00:27:56,420 --> 00:28:02,720 in physics, scratching our heads and trying to work out interesting problems that can be done in 45 minutes by really bright undergraduates. 268 00:28:03,320 --> 00:28:13,130 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. 269 00:28:13,880 --> 00:28:17,840 But this is so so there is there's a paper in the works, by the way, which is which comes out this. 270 00:28:17,840 --> 00:28:24,530 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. 271 00:28:24,680 --> 00:28:32,540 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. 272 00:28:33,290 --> 00:28:36,440 But so I put might well be the last paper on which I don't get to use a computer. 273 00:28:36,680 --> 00:28:41,839 But so, I mean, I did use computers, made the plots, but I, but I used Excel and I don't think that counts. 274 00:28:41,840 --> 00:28:45,979 I mean, so, so, so yeah. 275 00:28:45,980 --> 00:28:47,210 That that doesn't count, does it? 276 00:28:47,450 --> 00:28:57,830 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, 277 00:28:58,490 --> 00:29:04,940 but you can solve for the conditions at the time temperatures have stabilised the ask yourself, 278 00:29:04,940 --> 00:29:08,329 okay, temperatures have stabilised, what are the bounds? 279 00:29:08,330 --> 00:29:12,200 You know, what's what are the the balance conditions? 280 00:29:12,830 --> 00:29:19,280 And you find that at this time there's all this these rate constants here that's just 281 00:29:19,280 --> 00:29:23,599 comes out of that discounting on the adjustment and so on and adding up impacts over time. 282 00:29:23,600 --> 00:29:31,100 So you don't really need to worry about those. There's this term the rate of change of damage with respect to temperature. 283 00:29:31,460 --> 00:29:35,090 Obviously that matters because the steeper you are on that damage curve, 284 00:29:35,300 --> 00:29:40,130 the more damage adding an extra tonne of carbon into the atmosphere will will have. 285 00:29:40,850 --> 00:29:46,280 We will make. And remember, at this point, temperatures have stabilised. 286 00:29:46,280 --> 00:29:51,110 So this is not changing over time. It's it's it's at whatever level it's reached. 287 00:29:51,380 --> 00:29:54,920 That's the tertiary, which is this magic two degrees, 4 trillion tonnes number. 288 00:29:55,250 --> 00:30:00,920 And that's the size of the world economy at the time that temperatures stabilise 289 00:30:01,400 --> 00:30:07,640 because this D here is expressed as percentages of global consumption. 290 00:30:08,090 --> 00:30:15,920 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. 291 00:30:16,280 --> 00:30:23,810 So 5% loss obviously goes it means more in monetary terms if the world is extremely wealthy. 292 00:30:24,680 --> 00:30:36,350 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 293 00:30:36,350 --> 00:30:42,470 output that exponential growth and I've just expressed time instead of expressing it in terms of time, 294 00:30:42,620 --> 00:30:45,680 I've expressed it in terms of cumulative emissions up until that time. 295 00:30:46,520 --> 00:30:51,710 And this gives me an expression which doesn't depend on time, just relates the social cost of carbon. 296 00:30:53,210 --> 00:31:04,040 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. 297 00:31:04,940 --> 00:31:07,040 The peak warming temperature t one. 298 00:31:08,770 --> 00:31:17,679 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 299 00:31:17,680 --> 00:31:27,370 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. 300 00:31:27,790 --> 00:31:34,570 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. 301 00:31:35,410 --> 00:31:36,310 And here we are. 302 00:31:37,090 --> 00:31:49,240 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, 303 00:31:49,840 --> 00:31:56,170 which crucially, because temperatures won't stop rising until we stop putting CO2 in the atmosphere, 304 00:31:56,860 --> 00:32:01,660 that has to be the cost of abatement when that blue curve hits the vertical axis. 305 00:32:02,080 --> 00:32:05,080 Remember, I pointed out that it didn't hit the vertical axis in that schematic, 306 00:32:05,410 --> 00:32:10,990 but it has to hit the vertical axis because we actually have to get emissions to zero if temperatures are going to stop rising. 307 00:32:11,800 --> 00:32:22,840 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, 308 00:32:23,290 --> 00:32:30,580 the cost of finally getting rid of the last tonne of emissions and getting net carbon emissions to zero, 309 00:32:31,510 --> 00:32:34,930 which we will need to do in order to stabilise global climate. 310 00:32:34,930 --> 00:32:39,339 This is this, by the way, is what we're struggling to to get. 311 00:32:39,340 --> 00:32:44,379 This has been quite widely accepted now. And one of the things if you if you're interested in such things, 312 00:32:44,380 --> 00:32:49,300 one of the things you could track as you watch the progress towards the Paris talks in December 313 00:32:49,570 --> 00:32:55,240 is whether the phrase net zero appears in the Paris any any communications coming out of Paris, 314 00:32:55,870 --> 00:33:03,850 because although everybody acknowledges that it's true that carbon emissions have to get to net zero in order to stabilise global climate, 315 00:33:04,030 --> 00:33:06,879 it'll be very interesting to see whether the United Nations Framework Convention 316 00:33:06,880 --> 00:33:09,940 on Climate Change can actually bring themselves to acknowledge this formally. 317 00:33:09,940 --> 00:33:19,209 But I digress slightly that okay, so what's interesting here is we've got this nonlinear relationship between the cost of 318 00:33:19,210 --> 00:33:23,320 getting rid of that last ton or the social cost of carbon at the time of peak warming, 319 00:33:23,890 --> 00:33:27,190 that the ratio, the growth rate and the average, 320 00:33:27,430 --> 00:33:34,690 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. 321 00:33:35,740 --> 00:33:44,680 And that's shown here. And so what's interesting about this is that in this framework, if the cost of the backstop, 322 00:33:45,250 --> 00:33:50,050 if there exists a technology which would allow us to get emissions to zero, 323 00:33:50,110 --> 00:34:00,640 to get rid of that last tonne for only $200 per tonne, for example, then we we have a relatively optimistic future. 324 00:34:00,970 --> 00:34:07,590 I can get my. I've lost my. Then we can. 325 00:34:07,730 --> 00:34:10,340 Then we have this relatively optimistic future. We have quite a good chance, 326 00:34:10,580 --> 00:34:15,260 provided the world economy keeps growing of being rich enough to bring emissions to 327 00:34:15,260 --> 00:34:20,750 zero or to be motivated to bring emissions to zero before temperatures gets too high. 328 00:34:21,410 --> 00:34:26,810 So what I like about this is that this actually explains Nordhaus results. 329 00:34:27,320 --> 00:34:33,750 Because if you delve into the fine print of the book, you discover that there is a bank stock technology. 330 00:34:33,750 --> 00:34:36,870 He doesn't talk about it very much, but and doesn't say what it is. 331 00:34:37,400 --> 00:34:40,760 But it plays a crucial role in getting rid of that last ton. 332 00:34:41,270 --> 00:34:44,239 And that's absolutely central to all of these ideas, 333 00:34:44,240 --> 00:34:54,230 the existence of some technology that allows us to get emissions not just down by 20% or 80%, but actually down to zero. 334 00:34:55,850 --> 00:35:04,790 What's interesting is that if we vary so this is this is sort of the picture if we assume that emissions 335 00:35:04,790 --> 00:35:11,179 between now and the time of peak warming are on average more or less the same as emissions today, 336 00:35:11,180 --> 00:35:14,419 which would be plausible if they go up for a bit and then come down. 337 00:35:14,420 --> 00:35:17,900 I mean, that's a you know, the average would be about where we start. 338 00:35:19,160 --> 00:35:21,950 If we assume that we get them down very aggressively, 339 00:35:22,250 --> 00:35:29,720 obviously we can we will peak at a lower temperature for the same cost of getting rid of that last tonne. 340 00:35:31,610 --> 00:35:40,099 And this is back to the sort of standard case. What's perhaps more sobering for climate physicists is we can ask ourselves, 341 00:35:40,100 --> 00:35:45,380 what difference does it make if the response is high or low, the response of the climate system? 342 00:35:46,010 --> 00:35:49,880 So here's the standard case where I'm assuming a two degree 4 trillion tonne 343 00:35:50,240 --> 00:35:54,870 transient climate response to emissions now all increase then to three degrees. 344 00:35:54,890 --> 00:35:59,180 So you go to high transit, you'll notice that there isn't a huge amount of difference. 345 00:35:59,900 --> 00:36:08,330 So even though I've added 50% to the climate response, it doesn't make that much difference to the to the peak warming. 346 00:36:08,540 --> 00:36:09,560 Now, why is that? 347 00:36:09,590 --> 00:36:18,140 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. 348 00:36:18,260 --> 00:36:24,140 So it's a non-linear relationship. TCR reappears in the wealth term. 349 00:36:24,350 --> 00:36:33,140 It also appears moderate are determining the value of that additional that last one. 350 00:36:33,560 --> 00:36:41,240 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? 351 00:36:41,540 --> 00:36:46,190 Everybody's making rational decisions about whether or not to emit that next tonne. 352 00:36:46,670 --> 00:36:52,710 If the TCR is high, they will value that additional tonne higher because it'll do more damage. 353 00:36:53,270 --> 00:37:04,550 Okay. But in terms of temperature, they will also get richer, slower, if you said to me so. 354 00:37:04,640 --> 00:37:12,290 So that compensates. So there's a compensation effect there between the the the the additional impacts of an additional 355 00:37:12,290 --> 00:37:20,420 time as a fraction of world wealth and the impact of a higher tcr on the size of the world economy. 356 00:37:20,660 --> 00:37:27,680 When you get to because because in temperature terms you're getting richer slower in time 357 00:37:27,680 --> 00:37:31,100 because because you're you're actually getting richer at the same rate in terms of time. 358 00:37:31,100 --> 00:37:35,300 But because you're because the world economy is because the temperature is going up faster. 359 00:37:35,660 --> 00:37:41,450 If you if you if you if you drew output in terms of temperature, then it would be going up slower. 360 00:37:42,500 --> 00:37:45,830 So that's the sort of compensation that's going on here. 361 00:37:46,220 --> 00:37:49,280 And again, if we take a low chance in climate response, this is again, 362 00:37:49,460 --> 00:37:52,970 it doesn't make so much difference, a factor of two change in the climate response. 363 00:37:53,420 --> 00:37:56,750 If you've got this sort of rational decision making mechanism going on, 364 00:37:56,990 --> 00:38:01,610 it all sort of gets taken care of in these feedbacks between the economy and the climate. 365 00:38:02,810 --> 00:38:09,530 What does make a much bigger difference is if we assume a very low damage function, 366 00:38:09,530 --> 00:38:16,070 if we assume that climate change really doesn't do any harm in our calculation of whether or not to emit that extra tonne. 367 00:38:16,100 --> 00:38:21,470 Not not no harm, but half the harm that that I used in the base case. 368 00:38:22,010 --> 00:38:29,629 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, 369 00:38:29,630 --> 00:38:35,450 well, climate change isn't really doing any harm. So I'll I'll carry on with just one more puff, so to speak. 370 00:38:36,320 --> 00:38:42,770 And of course, if it's true that climate change isn't doing that much harm, then this is the rational thing to do. 371 00:38:43,070 --> 00:38:48,830 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. 372 00:38:50,540 --> 00:39:00,110 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, 373 00:39:00,680 --> 00:39:07,520 people decide they don't really care too much about their grandchildren and therefore they give less weight to climate impacts. 374 00:39:07,820 --> 00:39:14,330 Then again, that has a big impact on what temperature we actually end up peaking to. 375 00:39:14,570 --> 00:39:19,910 I'm hoping that some 70 nickels will actually sort of do all this properly with the numerical calculation. 376 00:39:19,910 --> 00:39:23,420 I just thought it'd be for the sake of this, this this talk. 377 00:39:23,750 --> 00:39:27,500 I sort of was quickly doing some numerical calculations just to see whether or not this was 378 00:39:27,770 --> 00:39:35,930 borne out in a when I actually sort of integrate the the the integrate the model properly. 379 00:39:36,200 --> 00:39:39,400 So so here we are in a sort of baseline scenario here, which is just, you know, 380 00:39:39,410 --> 00:39:48,410 RCP one of these RCP scenarios where emissions just carry on up through the century and then with the standard dice like emission, 381 00:39:49,370 --> 00:39:53,750 those like impacts function on the right shows you the social cost of carbon. 382 00:39:55,190 --> 00:40:04,339 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, 383 00:40:04,340 --> 00:40:08,360 9%, by which time temperatures are sort of up at five or six degrees. 384 00:40:08,360 --> 00:40:14,959 So this is this is this is the sort of pretty rosy, but not as rosy as Richard Toles, 385 00:40:14,960 --> 00:40:21,230 which is an even lower damage function for the same temperature, which we'll come back to in a minute. 386 00:40:21,530 --> 00:40:27,499 And let me ask. Okay. So is it true that this backstop technology matters for what temperature you peak at? 387 00:40:27,500 --> 00:40:36,649 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, 388 00:40:36,650 --> 00:40:42,890 they're just sort of hypotheses about what the cost of reducing emissions will be as those curves reach zero. 389 00:40:43,130 --> 00:40:50,030 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. 390 00:40:50,270 --> 00:40:58,820 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. 391 00:41:00,350 --> 00:41:01,819 If I likewise, 392 00:41:01,820 --> 00:41:14,300 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? 393 00:41:14,630 --> 00:41:16,790 So we're seeing the world doesn't grow as fast. 394 00:41:17,030 --> 00:41:25,010 We see temperatures on the left here continuing to rise because we're not wealthy enough for it to be worth us reducing emissions. 395 00:41:25,250 --> 00:41:33,410 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. 396 00:41:34,940 --> 00:41:44,179 And then likewise on the on the right, if you take that sort of optimistic fund model estimate of the impacts, 397 00:41:44,180 --> 00:41:47,720 again, you saw temperatures carrying on rising towards four degrees. 398 00:41:47,960 --> 00:41:55,530 Somewhat disappointingly, the numerical calculations didn't give me quite the punch line I wanted on the impact of T series. 399 00:41:55,530 --> 00:42:00,830 So I do find some, but I'm sure once somebody is finished it'll be back to where we started. 400 00:42:01,340 --> 00:42:07,190 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? 401 00:42:07,190 --> 00:42:10,190 I mean, that's that's kind of that's what we all believe in now. 402 00:42:10,700 --> 00:42:13,970 But so but no, there is there is some logic to this. 403 00:42:14,150 --> 00:42:16,720 So you can see here, this is this is a sort of hybrid. 404 00:42:17,390 --> 00:42:22,490 So this is the standard response on the left and the low screen on the right, a lower response on the right. 405 00:42:22,760 --> 00:42:31,100 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. 406 00:42:31,340 --> 00:42:35,270 So, you know, you're you're doing your cost benefit analysis as you go along. 407 00:42:35,510 --> 00:42:41,809 You end up with balancing out with higher emissions and ending up with not as low a temperature 408 00:42:41,810 --> 00:42:47,330 response as you would get if you just took a single emission profile and prompted through. 409 00:42:47,540 --> 00:42:54,229 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. 410 00:42:54,230 --> 00:42:57,740 So there's obviously some path dependency here which we need to understand. 411 00:42:58,670 --> 00:43:07,940 But what does this mean? Okay. So peak warming depends on only two variables that we can control with policy interventions today. 412 00:43:07,940 --> 00:43:15,589 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 413 00:43:15,590 --> 00:43:19,010 of growth of the world economy you can achieve with a given level of emissions. 414 00:43:19,850 --> 00:43:24,200 It's the rate of growth that you can achieve with the given level emissions, not the actual output. 415 00:43:25,100 --> 00:43:27,170 And that has important implications as well. 416 00:43:27,800 --> 00:43:35,810 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. 417 00:43:37,360 --> 00:43:44,380 In the limits of slow adjustment. It does not appear to be significantly dependent on the actual climate response, which I find very interesting. 418 00:43:45,040 --> 00:43:49,599 But annoyingly, when when I was looking at actual numerical integrations, 419 00:43:49,600 --> 00:43:55,060 where you do have things changing over time, that that nice limit doesn't seem to work so well, so well. 420 00:43:55,420 --> 00:44:01,299 So stay tuned on that one. And we do have a very strong dependence of peak warming on estimates of impacts. 421 00:44:01,300 --> 00:44:07,390 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. 422 00:44:07,390 --> 00:44:10,750 And what the advantage of this kind of analysis is, is it brings everything out. 423 00:44:11,140 --> 00:44:14,830 You can look at it and say, okay, due to all of these assumptions make sense. 424 00:44:15,370 --> 00:44:20,230 One of them is that the value in dollars of impact scales with global consumption. 425 00:44:20,680 --> 00:44:27,340 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. 426 00:44:28,210 --> 00:44:33,310 The other critical assumption here is that we're all rational and the world the world is 427 00:44:33,310 --> 00:44:37,930 rational and we use a cost benefit analysis to decide whether to deploy abatement measures, 428 00:44:38,080 --> 00:44:45,580 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, 429 00:44:45,760 --> 00:44:48,610 you know, only half the world actually bothers to abate and all that sort of thing. 430 00:44:49,390 --> 00:44:57,580 But the crucial third assumption is that this backstop technology exists, that there is a technology which allows us to get emissions to zero. 431 00:44:58,330 --> 00:45:05,260 And crucially, the properties of the backstop are, first of all, it doesn't increase with falling emissions. 432 00:45:05,260 --> 00:45:10,300 So it's not a substitute where typically that remember that that map curve is thinking in terms of substitutes. 433 00:45:10,570 --> 00:45:17,080 The mach curve goes up as you approach zero and sort of keep and they didn't actually bring it all 434 00:45:17,080 --> 00:45:20,710 the way to zero because they couldn't quite bring themselves to imagine what would actually happen. 435 00:45:20,920 --> 00:45:31,870 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, 436 00:45:32,860 --> 00:45:40,570 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. 437 00:45:41,350 --> 00:45:46,810 I would argue that the only that that although we don't know what this backstop technology is, 438 00:45:47,230 --> 00:45:53,860 I would argue that it has to be an effective subtractive technology, a technology that doesn't halve emissions. 439 00:45:54,130 --> 00:46:00,220 It's got to actually remove CO2 from, in effect, remove CO2 from the atmosphere. 440 00:46:00,220 --> 00:46:04,330 And it's only in that way, only with a technology like that, that we can actually get emissions to zero. 441 00:46:05,950 --> 00:46:12,350 And so what determines this cost, I think, is is sort of nicely illustrated by this module. 442 00:46:12,460 --> 00:46:15,580 This is an actual marginal cost of abatement cost curve. 443 00:46:15,880 --> 00:46:20,590 So this is the basis for these curves of how much it costs to reduce emissions. 444 00:46:20,920 --> 00:46:23,649 And this is where this is a fairly old one, 445 00:46:23,650 --> 00:46:28,630 but it illustrates the point where McKinsey have sort of stacked up all the different options you can take. 446 00:46:28,960 --> 00:46:32,350 And sort of in the middle here, for example, that red block is nuclear. 447 00:46:32,350 --> 00:46:37,360 So this is the additional cost of replacing all our coal fired power station capacity with nuclear, 448 00:46:38,260 --> 00:46:43,150 and that costs $10 per tonne of CO2 avoided or something. 449 00:46:43,300 --> 00:46:49,780 And we can reduce the width of that curve represents the the amount of CO2 emission 450 00:46:49,780 --> 00:46:55,030 reduction potential due to that that we think we can achieve with nuclear. 451 00:46:55,270 --> 00:46:58,989 So the key point about this is that if we choose not to do nuclear, for example, 452 00:46:58,990 --> 00:47:03,820 if we follow the German decision and not to deploy more nuclear power stations, 453 00:47:04,090 --> 00:47:09,880 it actually doesn't make a huge amount of difference to the overall form of the curve, because if you don't do nuclear, 454 00:47:10,030 --> 00:47:14,800 you do something else a little bit more expensive than nuclear if you're trying to reduce emissions to a given amount. 455 00:47:15,460 --> 00:47:19,720 But what really matters when you're thinking about backstops is this stuff over on the right. 456 00:47:20,350 --> 00:47:23,649 And notice they all of this stuff over on the right of this curve, 457 00:47:23,650 --> 00:47:30,010 although you probably can't see the little lines as the little letters CSS turn up quite a lot, 458 00:47:30,310 --> 00:47:38,150 which is well, well summarised in David McCoy's book as the last thing to be. 459 00:47:38,150 --> 00:47:42,400 He had a chapter on CSS called The Last Thing to Think About. And and it was a joke. 460 00:47:42,400 --> 00:47:50,110 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, 461 00:47:50,440 --> 00:48:00,399 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 462 00:48:00,400 --> 00:48:08,049 resort and you discover you still need to reduce emissions or somebody somewhere is still pumping out fossil carbon into the atmosphere? 463 00:48:08,050 --> 00:48:14,500 Well, the problem is that the only next option for getting rid of emissions is actually to contract consumption, 464 00:48:14,650 --> 00:48:16,780 to actually to shrink the world economy. 465 00:48:17,320 --> 00:48:24,880 And that's because the underlying economic productivity of carbon is so high that has an enormous economic impact. 466 00:48:25,360 --> 00:48:31,000 So that's why even though CAS is the most expensive mitigation option available on many measures, 467 00:48:31,480 --> 00:48:35,980 it's also the most important because it's the one of it's the it's the technology of last resort. 468 00:48:36,380 --> 00:48:44,900 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. 469 00:48:44,900 --> 00:48:50,810 And this is entirely consistent with the findings of the IPCC that excluding nuclear, for example, 470 00:48:50,960 --> 00:48:56,240 increased the cost of meeting the two degree goal by roughly 10%, excluding solar and wind. 471 00:48:56,570 --> 00:48:58,260 Again, increase the cost emissions to you. 472 00:48:58,260 --> 00:49:03,560 We go by roughly 10%, excluding cars more than double it, which is another way of saying it simply won't happen. 473 00:49:04,010 --> 00:49:13,220 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, 474 00:49:13,370 --> 00:49:23,209 the available fossil fuel reserves. This is a nice figure that Alex Otto produced showing the width of the bands in 475 00:49:23,210 --> 00:49:29,720 the vertical is current production of fossil carbon and the length of the sorry, 476 00:49:29,720 --> 00:49:33,710 the width of the band, the height of the bands is, is, is current production of fossil carbon. 477 00:49:33,890 --> 00:49:37,640 The width of the bands in the horizontal is the number of years production at current rates. 478 00:49:37,760 --> 00:49:46,549 Okay. So the area of each little block is the amount of carbon that country has available to dig up and notice that, 479 00:49:46,550 --> 00:49:51,530 you know, a lot of countries, countries like Norway and Britain and so on, we really don't feature much in this. 480 00:49:52,240 --> 00:50:00,830 The but the big countries like Russia, the USA and so for example, India here who has, you know, 200 years of production rates, 481 00:50:01,340 --> 00:50:11,660 most of it coal and every intention of, of, of, of using it to jet to to power their their energy supplies. 482 00:50:13,160 --> 00:50:16,940 So I was going to digress on on Jevons Paradox. 483 00:50:17,030 --> 00:50:22,970 Well, there's a there's an interesting other there's another interesting feedback there and why, 484 00:50:23,420 --> 00:50:27,559 you know, substitutes will never get us to zero because, 485 00:50:27,560 --> 00:50:32,480 you know, no matter how we substitute, no matter how well we substitute or use fossil carbon more efficiently, 486 00:50:32,810 --> 00:50:37,160 we always come up with new ways of using it. So what should we as physicists be concentrating on? 487 00:50:37,640 --> 00:50:42,219 Well, first, one of the messages of this is that these feedbacks between the climate and the 488 00:50:42,220 --> 00:50:46,550 economy partly vitiate the impact of new information on the climate response. 489 00:50:47,030 --> 00:50:55,250 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, 490 00:50:55,970 --> 00:51:01,250 then they'll know how to they'll know how to solve the problem of this this sort of feedback centre. 491 00:51:01,490 --> 00:51:08,120 In a sense, it doesn't really matter how the climate responds because, because, you know, as, 492 00:51:08,120 --> 00:51:15,359 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, 493 00:51:15,360 --> 00:51:18,800 the, the emissions will automatically adapt. 494 00:51:19,280 --> 00:51:24,109 There's also this feedback in the in the economy, which again, 495 00:51:24,110 --> 00:51:30,769 besides the impact of research into substitutes alone that there is good way of getting emissions down in the short term, 496 00:51:30,770 --> 00:51:40,790 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. 497 00:51:42,320 --> 00:51:47,120 One thing we definitely can help with coming out of this and I stressed in the in 498 00:51:47,120 --> 00:51:54,440 the I stressed in the talk that the the impact of getting the damage function wrong, 499 00:51:54,770 --> 00:52:05,630 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. 500 00:52:05,960 --> 00:52:12,590 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. 501 00:52:12,770 --> 00:52:17,989 Then of course, you do your cost benefit analysis based on incorrect information and you end up with the worst 502 00:52:17,990 --> 00:52:22,400 possible outcome because you don't mitigate enough and you end up with lots of additional harm. 503 00:52:22,610 --> 00:52:29,689 And I so I was fiddling with my talk rather late in the day because a paper actually came out highly relevant. 504 00:52:29,690 --> 00:52:35,629 Paper came out yesterday which looked at this, looked at sort of new estimates of climate, 505 00:52:35,630 --> 00:52:39,990 of the economic impacts of climate change as a function of temperature. 506 00:52:40,040 --> 00:52:46,249 It's back to those. And you can see here on the right hand panel here, those three, you can barely see them. 507 00:52:46,250 --> 00:52:50,240 Those are the three lines that I was talking about really wrong from these integrated assessment models. 508 00:52:50,570 --> 00:52:56,059 And this is the estimate that these authors think climate change will cost that four 509 00:52:56,060 --> 00:53:00,170 or five degrees of warming will cost the world economy by the end of the century. 510 00:53:00,170 --> 00:53:08,450 That's Burke et al in came out this week but this this and this is really important has a huge 511 00:53:08,510 --> 00:53:15,320 would have it if correct has a huge impact on on all our estimates of the cost of climate change. 512 00:53:15,920 --> 00:53:22,400 But what's worrying is that the only evidence for this is pretty and then quite frank in the paper on this, 513 00:53:22,640 --> 00:53:29,450 it's pretty tentative statistical evidence based on just observations of countries. 514 00:53:29,450 --> 00:53:35,660 And, you know, you can look at these regressions here and think, yeah, observations of countries. 515 00:53:36,570 --> 00:53:37,940 Well, it's easy to laugh, on the other hand. 516 00:53:37,940 --> 00:53:43,430 But, you know, this is a really important question, and they're using the information available as best they can and concluding that, 517 00:53:43,700 --> 00:53:47,600 you know, as the world gets warmer, economic output will be negatively impacted. 518 00:53:47,780 --> 00:53:54,960 What I think we can do much better at would be informing this estimate of the damage. 519 00:53:54,980 --> 00:54:01,700 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, 520 00:54:01,700 --> 00:54:10,090 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, 521 00:54:10,100 --> 00:54:16,969 the kind of models that Tim runs where where you've actually got detailed weather that actually does damage in these models and 522 00:54:16,970 --> 00:54:22,940 look at the impacts of climate change within those models in order to understand quantitatively what climate change is doing. 523 00:54:22,940 --> 00:54:26,690 So we're not reliant on these very hand estimates of, you know, 524 00:54:26,690 --> 00:54:32,420 5% of global output in 2100 and the way that we are in this integrated assessment problem. 525 00:54:32,660 --> 00:54:37,550 So I think to come back to Nordhaus, I sort of began with sort of how nought has motivated this talk. 526 00:54:37,970 --> 00:54:40,730 And this is a quote from one of Nordhaus recent papers, 527 00:54:40,970 --> 00:54:47,450 and he was kind of explaining why they didn't really worry too much about the costs of catastrophic, 528 00:54:47,450 --> 00:54:54,770 abrupt and irreversible events and why they didn't wait on these these sort of events very heavily in his integrated assessment model. 529 00:54:54,950 --> 00:55:02,480 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, 530 00:55:03,560 --> 00:55:06,680 you know, what about the geophysical aspects of these events and their probabilities? 531 00:55:06,770 --> 00:55:12,260 How do they expect us as economists to to to incorporate them into our integrated assessment models? 532 00:55:12,410 --> 00:55:18,110 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 533 00:55:18,110 --> 00:55:22,399 information to the economic community about not necessarily this isn't a prediction. 534 00:55:22,400 --> 00:55:31,190 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? 535 00:55:31,190 --> 00:55:37,280 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 536 00:55:37,280 --> 00:55:42,110 attention into that sort of delicate interface between weather and the economy, 537 00:55:42,230 --> 00:55:46,010 which will actually allow us to quantify what harm climate change is actually doing. 538 00:55:46,010 --> 00:55:47,420 So this is sort of motivated. 539 00:55:47,690 --> 00:55:55,640 This this talk is motivating me to focus further on on that question about the into the interface between weather and damage. 540 00:55:56,250 --> 00:55:57,650 It's a good point to stop. Thank you.