Mathematics of the Environment (Part 4)

We’ve been looking at some very simple models of the Earth’s climate. Pretty soon I want to show you one that illustrates the ice albedo effect. This effect says that when it’s colder, there’s more ice and snow, so the Earth gets lighter in color, so it reflects more sunlight and tends to get even colder. In other words, it’s a positive feedback mechanism: a reaction that strengthens the process that caused the reaction.

Since a higher temperature leads to a higher radiation and therefore to cooling, and a lower temperature leads to a lower radiation, according to the Planck distribution, there is always also a negative feedback present in the climate system of the earth. This is dubbed the Planck feedback, and this is what ultimately protects the Earth against getting arbitrarily hot or cold.

However, the ice albedo effect may be important for the ‘ice ages’ or more properly ‘glacial cycles’ that we’ve been having for the last few ten million years… and also for much earlier, much colder Snowball Earth events. In reverse, melting ice now tends to make the Earth darker and even warmer. So, this is an interesting topic for many reasons… including the math, which we’ll get to later.

Now, obviously the dinosaurs did not keep records of the temperature, so how we estimate temperatures on the ancient Earth is an important question, which deserves a long discussion—but not today! Today I’ll be fairly sketchy about that. I just want you to get a feel for the overall story, and some open questions.

The Earth’s temperature since the last glacial period

First, here’s a graph of Greenland temperatures over the last 18,000 years:

(As usual, click to enlarge and/or get more information.) This chart is based on ice cores, taken from:

• Richard B. Alley, The Two-Mile Time Machine: Ice Cores, Abrupt Climate Change, and our Future, Princeton U. Press, Princeton, 2002.

This is a good book for learning how people reconstruct the
history of temperatures in Greenland from looking at a two-mile-long ice core drilled out of the glaciers there.

As you can see, first Greenland was very cold, and then it warmed up at the end of the last ‘ice age’, or glacial period. But there are lot of other things to see in this graph. For example, there was a severe cold spell between 12.9 and 11.5 thousand years ago: the Younger Dryas event.

I love that name! It comes from the tough little Arctic flower
Dryas octopetala, whose plentiful pollen in certain ice samples gave evidence that this time period was chilly. Was there an Older Dryas? Yes: before the Younger Dryas there was a warm spell called the Allerød, and before that a cold period called the Older Dryas.

The Younger Dryas lasted about 1400 years. Temperatures dropped dramatically in Europe: about 7 °C in only 20 years! In Greenland, it was 15 °C colder during the Younger Dryas than today. In England, the average annual temperature was -5 °C, so glaciers started forming. We can see evidence of this event from oxygen isotope records and many other things.

Why the sudden chill? One popular theory is that the melting of the ice sheet on North America lowered the salinity of North Atlantic waters. This in turn blocked a current called the
Atlantic meridional overturning circulation, or AMOC for short, which normally brings warm water up the coast of Europe. Proponents of this theory argue that this current is what makes London much warmer than, say, Winnipeg in Canada or Irkutsk in Russia. Turn it off and—wham!—you’ll get glaciers forming in England.

Anyway, whatever caused it, the Younger Dryas ended as suddenly at it began, with temperatures jumping 7 °C. Since then, the Earth continued warming up until about 6 thousand years ago—the mid-Holocene thermal maximum. The earth was about 1° or 2° Celsius warmer than today. Since then, it’s basically been cooling off—not counting various smaller variations, like the global warming we’re experiencing in this century.

However, these smaller variations are very interesting! From 6000 to 2500 years ago things cooled down, with the coolest
stretch occurring between 4000 and 2500 years ago: the Iron Age Cold Epoch.

Then things warmed up for a while, and then they cooled down
from 500 to 1000 AD. Yes, the so-called "Dark Ages" were also chilly!

After this came the Medieval Warm Period, a period from about 1000 to 1300 AD:

From 1450 AD to 1890 there was a period of cooling, often called the Little Ice Age. This killed off the Icelandic colonies in Greenland, as described in this gripping book:

• Jane Smiley, The Greenlanders, Ballantine Books, New York, 1996.

However, the term "Little Ice Age" exaggerates the importance of a small blip in the grand scheme of things. It was nowhere near as big as the Younger Dryas: temperatures may have dropped a measly 0.2° Celsius from the Medieval optimum, and it may have happened only in Europe—though this was a subject of debate when I last checked.

Since then, things have been warming up:

The subject has big political implications, and is thus subject to enormous controversy. But, I think it’s quite safe to say that we’ve been seeing a rapid temperature rise since 1900, with the Northern Hemisphere average temperature rising roughly 1 °C since then. Each of the last 11 years, from 2001 to 2011, was one of the 12 warmest years since 1901. (The other one was 1998.)

All these recent variations in the Earth’s climate are very much worth trying to understand. but now let’s back off to longer time periods! We don’t have many Earth-like planets whose climate we can study in detail—at least not yet, since they’re too far away. But we do have one planet, the Earth, that’s gone through many changes. The climate since the end of the last ice age is just a tiny sliver of a long and exciting story!

The Earth’s long-term climate history

Here’s a nice old chart showing estimates of the Earth’s average temperature in the last 150 years, the last 16,000 years, the last 150,000 years and the last million years:

Here “ka” or “kilo-annum” means a thousand years. These temperatures are estimated by various methods; I got this chart from:

• Barry Saltzman, Dynamical Paleoclimatology: Generalized Theory of Global Climate Change, Academic Press, New York, 2002, fig. 3-4.

As we keep zooming in towards the present we keep seeing more detail:

• Over the last million years there have been about ten glacial periods—though trying to count them is a bit like trying to count ‘very deep valleys’ in a hilly landscape!

• From 150 to 120 thousand years ago it warmed up rather rapidly. From 120 thousand years ago to 16 thousand years ago it cooled down—that was the last glacial period. Then it warmed up rather rapidly again.

• Over the last 10 thousand years temperatures have been unusually constant.

• Over the last 150 years it’s been warming up slightly.

If we go back further, say to 5 million years, we see that temperatures have been colder but also more erratic during this period:

This figure is based on this paper:

• L. E. Lisiecki and M. E. Raymo, A Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records, Paleoceanography 20 (2005), PA1003.

Lisieki and Raymo combined measurements of oxygen isotopes in the shells of tiny sea creatures called foraminifera from 57 globally distributed deep sea sediment cores. But beware: they constructed this record by first applying a computer aided process to align the data in each sediment core. Then the resulting stacked record was tuned to make the positions of peaks and valleys match the known Milankovitch cycles in the Earth’s orbit. The temperature scale was chosen to match Vostok ice core data. So, there are a lot of theoretical assumptions built into this graph.

Going back 65 million years, we see how unusual the current glacial cycles are:

Click to make this graph bigger; it’s from:

• Robert Rohde, 65 million years of climate change, at Global Warming Art.

This graph shows the Earth’s temperature since the extinction of the dinosaurs about 65 million years ago—the end of the Mesozoic and beginning of the Cenozoic. At first the Earth warmed up, reaching its warmest 50 million years ago: the "Eocene Optimum". The spike before that labelled "PETM" is a fascinating event called the Paleocene-Eocene Thermal Maximum. At the end of the Eocene the Earth cooled rapidly and the Antarctic acquired year-round ice. After a warming spell near the end of the Oligocene, further cooling and an increasingly jittery climate led ultimately to the current age of rapid glacial cycles.

Why is the Earth’s climate so jittery nowadays? That’s a fascinating puzzle, which I’d like to discuss in the weeks to come.

Why did the Earth suddenly cool at the end of the Eocene 34 million years ago? One theory relies on the fact that this is when Antarctica first became separated from Australia and South America. After the Tasmanian Gateway between Australia and Antarctica opened, the only thing that kept water from swirling endlessly around Antarctica, getting colder and colder, was the connection between this continent and South America. South America seems to have separated from Antarctica around the end of the Eocene.

In the early Eocene, Antarctica was fringed with a warm temperate to sub-tropical rainforest. But as the Eocene progressed it became colder, and by the start of the Oligocene it had deciduous forests and vast stretches of tundra. Eventually it became almost completely covered with ice.

Thanks to the ice albedo effect, an icy Antarctic tends to keep the Earth cooler. But is that the only or even the main explanation of the overall cooling trend over the last 30 million years? Scientists argue about this.

Going back further:

Here "Ma" or "mega-annum" means "million years". This chart was drawn from many sources; I got it from:

• Barry Saltzman, Dynamical Paleoclimatology: Generalized Theory of Global Climate Change, Academic Press, New York, 2002, fig. 1-3.

Among other things on this chart, you can sort of see hints of the Snowball Earth events that may have happened early in the Earth’s history. These are thought to have occurred during the Cryogenian period 850 to 635 million years ago, and also during the Huronian glaciation 2400 to 2100 million years ago. In both these events a large portion of the Earth was frozen—much more, it seems, than in the recent glacial periods! Ice albedo feedback plays a big role in theories of these events… though also, of course, there must be some explanation of why they ended.

As you can see, there’s a lot of things a really universal climate model might seek to explain. We don’t necessarily need to understand the whole Earth’s history to model it well now, but thinking about other eras is a good way to check our understanding of the present-day Earth.

32 Responses to Mathematics of the Environment (Part 4)

  1. adhishm says:

    It appears to me that the climate nowadays seems more jittery simply because we have more data and higher precision for their dates while for the older data they are more sparse and the dates are not as precise.
    Disclaimer: I am no mathematician, so please forgive any silly errors I may make. Thanks.

    • John Baez says:

      Other people have made the same point here on this blog, and it sounds quite plausible. It’s probaby true in general. However, it also seems that the temperature variations in the last 30 million years—as measured by oxygen isotope concentrations in foraminifera in ocean sediments—truly have been increasing:

      I don’t believe data gets sparser as we dig deeper into these sediments, at least for this time period. So, if the increasing variations are not real, but an artifact of some sort, we’d need to make up an explanation for why. It’s easy to make one up: maybe layers of sediment gradually get mixed with neighboring layers as time passes. But it’s not so easy to show it’s true, or convincing.

      It also seems to be true that the Earth is colder now that it was in previous eras: we think it didn’t always have large regions covered with ice year-round. With large icy areas whose size varies with temperature, ice albedo feedback is enhanced: melting ice makes the Earth darker and warmer, while freezing water makes the Earth whiter and colder. This might make the climate more jittery.

      For example, at the last glacial maximum, 21,000 years ago, there were ice sheets down to the Great Lakes, the mouth of the Rhine, and covering the British Isles. Now those are mostly gone. Even in the last decade, the size of the Arctic ice cap has shrunk considerably:

      Of course, we need quantitative estimates of the ice albedo feedback, and feed these into a climate model, to see how much ‘jitteriness’ it would cause. It seems there must be other less well understood forms of feedback involved in the glacial cycles, and it’s harder to know how much these have changed with time.

      • Nathan Urban says:

        I think all of these explanations are at work: older data are more highly smoothed, but there really are increases in variability, and this is most likely due to ice albedo feedback as we transitioned from a greenhouse world to an ice age. There is large temperature variability between glacial and interglacial periods, and you don’t get that variability when the base climate is too warm for glacials.

  2. Curtis Faith says:


    Phil Plait the Bad Astronomer accuses global warming deniers of doing what he himself does with respect to the above data. He doesn’t show the 18,000 year graph, only 200 years and accuses another of cherry picking data.

    It would serve the cause of science and math for you to visit the post and let him know.

    • John Baez says:

      I’ll check it out. Of course, what counts as ‘cherry picking data’ depends in part on what one is claiming to prove with the data one has chosen. Part of my goal here was to show that as we examine the Earth’s climate history on larger and larger time scales we see more and more things going on. Not all of these things will be equally relevant to what’ll happen in the next 200 years. But any good climate scientist should at least be aware of the glacial cycles that are happening with the continents in their current configuration.

    • Nathan Urban says:

      As John hints, temperatures over the last 18,000 years are not terribly relevant to the question of whether the planet is currently warming or whether there is warming due to humans, which are what Plait is talking about. They do offer a constraint, when combined with other data, on the sensitivity of the Earth’s climate to greenhouse gases, but again, that’s not Plait’s point.

      • Arrow says:

        The problem is that Phil makes a laughable statement that the graph of the linear trend during last 16 years is “terribly misleading” while the same graph for the last 35 years is “the true situation.”

        They are both true and misleading to the exact same extent. All linear trend fitting can be misleading.

        What matters for the article he is dissing is that during the last 16 years there has been no statistically significant warming or cooling trend in the data and that is a fact. The data is consistent with the hypothesis that anthropogenic global warming stopped in that period. Of course that doesn’t prove that it did, the warming could be masked by natural variability, but in the same way the 1900-now graph doesn’t prove that it was real in the first place, we could simply be experiencing another natural variation, a stronger version of medieval warm period, and the effect of man made CO2 on top of it could be completely insignificant.

        • John Baez says:

          There’s a huge scientific and statistical issue here: what can or can’t we legitimately infer from some time series data, typically together with some other assumptions about a situation. It might be help to discuss this issue separately from this particular controversial case before wading into this case.

          Of course, that would be too dull for many people… but the advantage of being dull is that only seriously committed people stay in the discussion: everyone else falls asleep!

          There’s a lot to say… and a lot of it I don’t know, but I can say one thing: from a single graph, without any extra assumptions, we can infer nothing except the values of the data points and functions of those data points.

          In particular, if someone says that restricting attention to 16 data points is “terribly misleading” while considering 35 data points reflects “the true situation”, they are either being irrational or they are making extra assumptions about the situation.

          This is also true for a person who draws any conclusions from the 16 data points other than the values of those data points and functions of those.

          For example, saying “the average of these 16 data points is 5” is fine—it’s just a computation. (If the data is wrong, so be it.) But saying “as shown by these 16 data points, the function has stopped increasing” requires extra assumptions. And so even does “there is no statistically significant increase going on in these 16 data points”! You cannot just stare at a list of 16 numbers and decide if there’s a statistically significant increase doing on without extra assumptions.

          So, if we’re getting into arguments we can’t resolve, it’s either because someone is being irrational or because we’re making different assumptions. I’d be happy to claim that the person who wrote that article for the Daily Mail is being irrational. But never mind them: among the participants here, I suspect it’s a case of different assumptions. In that case, the cure begins by making those assumptions explicit.

        • Nathan Urban says:

          As I’ve noted more than once before in my earlier responses to your claims: trying to explain 20th century warming as “natural variation” runs into a number of problems, not only due to what we know about natural variation from modeling, but also independently of the details of the models themselves (e.g., from the observed pattern of ocean heat uptake). Also, the MWP isn’t even a very good example of your point, as it was arguably externally forced in a way that demonstrably is not occurring now, and not just pure “natural variability” (which to climate scientists means unforced internal modes of variability).

          And Phil is correct to say that it is misleading to take a 16-year global surface temperature graph and use it to argue against AGW. “Consistent with the hypothesis that AGW stopped in that period” doesn’t cut it. The real point is that a short record can be consistent with all kinds of hypotheses, and therefore shouldn’t be used to argue strongly one way or the other.

          It is false equality to suggest that 16 and 35 years are exactly the same as far as attribution is concerned. It is certainly true that you have to look at longer data than 16 years to discuss attribution. Sure, you can also look longer than 35 years, but that doesn’t change the attribution of 20th century warming. In fact, paleoclimate over many time scales widely supports modern estimates of the sensitivity of climate to CO2.

        • Arrow says:

          Yes, you said similar things before but obviously I don’t find them very convincing. Try to reread your post from a skeptical point of view – you don’t offer a very persuasive case.

          Yes, a 16 year record can be consistent with all kinds of hypotheses but the same holds true for 100 year record or 1000 year record or record of any other length. For example can you prove (as you seem to hint in your post) that the 1000 year record is inconsistent with the hypothesis that 20 century warming was mostly a repeat of MWP and that warming due to man made CO2 was relatively insignificant?

          And why is 16 years too short for attribution? During those 16 years the CO2 concentration was higher than at any point during the last century and it kept rising, ice cover was also at the lowest point (or so I’ve read) so add positive albedo feedback to it, taken together this should make global temperature rise even faster than in the past yet it failed to increase at all! So tell me what happened to all this extra warming that should be present if AGW hypothesis was correct and man made CO2 was the main driver behind the 20th century warming?

          And if climate science cannot answer this question satisfactorily why should anyone believe that it can say anything reliable about the 35 year temperature record or record of any other length?

        • Nathan Urban says:

          If arguments like “The warming isn’t coming from the oceans because the oceans aren’t losing heat to the atmosphere” are not convincing, you are welcome to present your own physically plausible argument for where the warming does come from. “Natural variability” such as MWP, by itself, isn’t an answer. Try to view that from a skeptical perspective. Natural variability is an outcome of physical processes, not a cause itself. What matters is the process at work. You could also say “we warmed out of an ice age 10000 years ago, therefore the same process could be causing the Earth to warm now”. But it’s observably not the same process at work today, and therefore that analogy fails. Natural variability doesn’t come from nowhere. It comes from external forcing (solar, volcanism, etc.), or from internal atmosphere-ocean variability — on the short term typically from fluctuations in clouds, on the long term typically from fluctuations in ocean circulation (or still other processes on geologic time).

          We can’t go back and measure the energy budget of the planet during the MWP, but the behavior is what you’d expect from what we can reconstruct from the external forcings at the time. But regardless of what you think caused the MWP, if you want to posit that the 20th century surface warming is due to “natural variability”, you have to specify what that variability actually is, in a way that’s consistent with what’s been observed. From what we’ve measured of the factors I mentioned above, much of the recent warming is not coming from any of these places. This is why late-Holocene paleoclimate analogs aren’t terribly convincing as far as attribution goes; regardless of what happened in the more distant past, we have observations of what has happened historically.

          16 years is too short for attribution because you can often see 16-year periods of lower warming due to natural variability, even with the expected CO2 greenhouse effect. You seem to admit this yourself (you just claim that the greenhouse effect can’t be distinguished from natural variability on any other time scale, either.) At present, given the expected greenhouse warming and the expected levels of natural variability, it takes longer than that, typically 20-30 years, to statistically detect a departure from the expected behavior; I’ve cited relevant studies in earlier responses. This period of time will decrease in the future as the system becomes more strongly forced by greenhouse gases, so attribution will become stronger in the future than it is now. We are currently approaching that time range, which is why I said earlier it’s something climate scientists are keeping an eye on — but it’s not yet strongly inconsistent with expectations, even under the current CO2 forcing, which is why I said that climate scientists haven’t gone back to the drawing board.

          As to where the heat goes during periods of lower warming, it’s usually either reflected to space by clouds, or taken up by extra vertical transport to the deep ocean. Our observing systems haven’t usually been good enough at partitioning the energy budget to distinguish completely between these two cases. But recently, based on continued observations, a tentative consensus seems to be emerging that in this case, it’s the deep ocean.

        • Arrow says:

          But if you admit that deep ocean can suddenly take up additional heat and lead to significant global cooling on 16 year timescale, I don’t see how you can rule out the possibility that it can also stop doing that and lead to significant warming on a longer timescale of say 50 years.

          Your arguments based on plausibility, models or community consensus are not convincing to me since as a skeptic my initial hypothesis is that climate scientists are deluding themselves into thinking they know enough about climate to attribute recent warming or predict future temperatures so first I would have to see proof that your models really work.

          It’s like the situation with aether in 19th century, it was the only plausible explanation at the time and there was a consensus that it had to be present. Well, nature didn’t play along. Luckily in physics you can perform experiments which MM did and the rest is history. Sadly the same cannot be done in climate science so there really is no way to verify current models (at least in the near future, once they have track records of centuries of correctly (small error margin) predicted global temperature things will be different).

          So I don’t expect to be convinced, I post here simply to provide a balancing point of view. I wouldn’t bother if not for the fact that climate scientists advocate massive interventions into economy and lifestyles based on their unproven and quite possibly flawed understanding of global climate while not admitting the limitations of their models or the fact that climate science is no where near as reliable as other natural sciences due to it’s inability to leverage scientific method.

        • Nathan Urban says:

          Over the last 50 years, we can quite clearly see a strong signal of top-down penetration of heat from the surface over time. Over a shorter period of time, we can’t see the transfer of heat from the upper layers to the deep ocean within the noise of the system, especially since the signal itself is much weaker.

          You can believe what you like, of course, but the scientific evidence in favor of the greenhouse effect overwhelming natural variability in the long term is far stronger than the evidence against, and any reasonable risk assessment of policy options would take that into account. And please, stop with nonsense like “while not admitting the limitations of their models or the fact that climate science is no where near as reliable as other natural sciences”. This whole thread has been a discussion of those limitations, and you can be sure that climate scientists are aware of them.

        • Arrow asks:

          can you prove (…) that the 1000 year record is inconsistent with the hypothesis that 20 century warming was mostly a repeat of MWP

          Proof by reductio ad absurdum: Consider some of the northernmost commercial vineyards today:

          Eventyrvin and Lerkekåsa Vineyard, Telemark county, Norway. 59°40′N 09°19′E

          L’Esprit d’Edvard Munch, Vestfold county, Norway. 59°25′N 10°25′E

          Blaxsta Vineyard, Södermanland County, Sweden. 59°03′N 16°35′E

          Scholium: 59°N is north of Scotland (Orkney Islands). You could also examine Gotland island.

          Compare with MWP vineyards. Q.E.D.

        • Arrow says:

          Where can we see this strong signal? Are you saying we have detailed 3d maps of ocean temperatures during last 50 years?

          Also you still didn’t address the main point – how do you know that the strong signal you see is not also noise? How do you rule out low frequency noise?

          And while climate scientists might be aware that their models are untested and unreliable they never mention it in their public communications (the whole “science is settled” fiasco) and it doesn’t stop them from advocating massive interventions into global economy based on them.

          That said by climate scientists I don’t mean you or John, I admit Azimuth is very honest about various issues when they are brought up even though you do (of course) seem somewhat biased in AGW favor to me.

          As for the vineyards any arguments based on them first have to establish that we are talking about the same grape varieties.

        • Frederik De Roo says:

          Somewhat digressing from the original topic of this post, i.e. climate science, and moving toward economic sciences (with psychology involved instead of physics and chemistry):

          Are we sure that

          interventions into global economy

          are always bad?

          For example, can regulations (and control of those) save fish stocks by preventing overfishing? Belief in the invisible hand only sounds – at least to me – like belief in the aether theory.

        • As for the vineyards any arguments based on them first have to establish that we are talking about the same grape varieties.

          Usually this subtle detail gets overlooked in the “debate”. I should have added the following 2nd scholium:

          The medieval motivation to produce wine at northern latitudes was its necessity for catholic eucharist, where it transubstantiates into the blood of Christ (and not just consubstantiate as in Lutheranism). For this act of metaphysical cannibalism the wine’s taste is irrelevant. Today the motivation is pure hedonism and it needs to have sufficient taste to compete with cheap southern imports. (E.g. Blaxsta vineyard is not only growing the quite winter hardy white Vidal, but also Chardonnay, Merlot and Cabernet Franc.)

        • Nathan Urban says:

          We do have maps of ocean temperatures over the last 50 years; see the World Ocean Database. They are most accurate to the upper 700 meters, but this is where most of the signal is.

          I didn’t say that this alone rules out the possibility of noise. I said it largely rules out the possibility of the noise coming from ocean variability: it’s a top-down penetration pattern showing large integrated heat fluxes from the atmosphere.

          And don’t put words into my mouth. Climate models are not untested — they are extensively tested, though of course nobody can run the most relevant test (massively increase CO2 under present-day conditions and wait to see what happens). Nor are they generically “unreliable”. They are good at some aspects of the climate, and not as good as others. Quite frankly, you don’t even need a complex climate model to advocate interventions into global economy as a risk management approach (not that most climate scientists are policy advocates to begin with). Historical observations, paleodata, simple climate models, and complex climate models all agree on the same range of likely climate sensitivities to carbon dioxide.

        • Arrow says:

          I had some time to take a look at World Ocean Database you mentioned. I picked all datasets except surface and selected the largest rectangular ocean area i was able to find: long -180.0 to -90.5; lat 10.0 to -69.5; (thats 14.4% of the Earth surface or 20% of ocean surface area i.e. 73 353 000 km2) selecting temperature data I got a total of 93470 casts or profiles during 25 years starting in jan 1962. Now to get a feeling for how well said area is covered lets see what would be cast density if we assumed that said points form an uniform grid. First lets assume there are 12 casts per year, that seems like way too little but just for the sake of the argument, that would give us 7789 casts per 73353000 km2 or 1 cast for 9417 km2.

          Sorry, but to me such sparse data are completely inadequate to draw any firm conclusions about global ocean heat fluxes. The signal you may be seeing in one place may be completely offset by another opposite signal in another place where you simply don’t have the data. What makes you think you can get around this?

          As for models of course the test you admit nobody can run is precisely the test that is needed to verify that climate models can tell us anything useful about what hypothetical anthropogenic global warming will mean for the latter part of this century. If they were never tested on this timescale why should anyone take anything they say about it seriously? And contrary to what you say all complex models are unrealiable unless proven otherwise, especially as complex as global climate ones.

          Finally observations, paleodata, simple climate models and so on certainly do NOT agree on likely climate sensitivities, in fact sensitivities reported in the literature are all over the map, from completely harmless 0.7C to absurd 5.2C (and those are medians of reported ranges) per CO2 doubling.

        • Arrow says:

          I actually missed two even higher sensitivities in that table: 6 and 8 C degrees C per doubling!

          Also looking at the reported confidence levels I am reminded of the old saying about astrophysicists being always wrong but never in doubt, it seems to apply to climate scientists these days.

        • Nathan Urban says:

          I completely disagree that the ocean data is too sparse to see a strong downward-penetrating heat signal. The level of variability is not large enough to invalidate these conclusions; they are highly correlated over space.

          Climate models have been tested on decadal to century timescales, though of course the further back you go, the fewer constraints you have. But more than that, they have been tested extensively against base climatology, the seasonal cycle, observations of individual feedback processes (water vapor, albedo, etc.) — which dominate the variability in long-term predictions, not the natural variability you seem so concerned with — and a wide variety of dynamical atmospheric-ocean processes (as well as against paleoreconstructions like Last Glacial Maximum). It is ridiculous to claim that they are by default “unreliable”, and similarly ridiculous to claim that a physical model cannot be used for extrapolation, which is what your statements amount to. It is impossible to “prove” a model’s reliability in a new situation. This doesn’t mean that the model is inherently untrustworthy. Models are used to extrapolate all the time. This is their main function.

          In short, I completely disagree that “the test you admit nobody can run is precisely the test that is needed to verify that climate models can tell us anything useful about what hypothetical anthropogenic global warming will mean for the latter part of this century.” Assuming you’re referring to some test of past century scale variability that hasn’t already been run (e.g., with more detailed data), I don’t agree that some dramatically more stringent test is required to be informative for climate policy.

          Decision makers don’t work with “proof”. They operate with uncertainty based on physically plausible extrapolation. And frankly, the less you trust the models, the greater precaution you should take, because then you have even less grounds for ruling out the extreme outcomes that dominate the decision process. Uncertainty doesn’t work in anybody’s favor.

          Observations, paleodata, and climate models do agree on the likely range of climate sensitivity, which is generally taken to be 1.5-4.5 C. This represents +/- 50% spread over the central estimate, but all these methods cluster in that same range. You can’t pick the few outliers and argue that they are all inconsistent with each other.

        • Arrow says:

          How on earth can you find a tiny multi-year downward heat flux among the huge daily, monthly, seasonal and multi-year fluxes due to variations in local temperature, winds, currents, “ninos” etc with such an extremely sparse data??

          It’s enough that there are more probes in places where there is a local downward heat flux, while corresponding upward heat fluxes are less well sampled and you have your “signal.”

          As for models, yes, we clearly disagree, until I see correct long term global climate *predictions* repeatedly work out I will treat all climate model predictions in that regime as random numbers.

          While lawmakers do work with uncertainty judging by their actions so far they are clearly in my camp – the reliability of climate predictions is not even close to enough to warrant extreme costs associated with mitigation policies demanded by climate activists.

          Finally as for climate sensitivity to claim that the measurements agree with your preferred 1.5 – 4.5 interval is to ignore reported confidence values. The proper conclusion one should draw is that climate sensitivity is simply not constant and therefore estimates based on reconstructed paleoclimate data are not applicable to present day. Incidentally that happens to remove all the high values from consideration and you end up with a value in the range of 1-2 C. Nothing to worry about.

  3. I’ve been thinking how these graphs compare to graphs of global extinction events:

    I notice that the biggest extinction at the P-Tr boundary correlates with a pretty big swing in the temperature graphs, but that the K-T event was followed by a period of relative stability. The aftermath of the Antarctic glaciation events are also followed by periods of pretty remarkably stablity (on a smaller scale). I wonder how to incorporate one-off events like meteor strikes or tectonic shifts into a model of the global temperature, or if they are even significant enough to matter.

    In lecture we also talked about cloud cover as an important feedback mechanism. I’ve read that cloud cover over the oceans is closely linked to ocean life, which kicks up the particulate matter (dimethyl sulfide) into the air that the clouds form around. The plankton use the clouds to keep them from burning under the sun; without the plankton around, those clouds probably wouldn’t have formed at all.

    More generally, I wonder to what extent this biological activity should affect how we interpret at least some of the details of these. Obviously the global temperature is going to affect the development of life, but perhaps the reverse can also be true, and should be incorporated into a model. After all, anthropocentric climate change implies that life can have consequences on global temperatures and atmospheric composition, so it would be surprising if this kind of issue hasn’t risen before. We know that phytoplankton are largely responsible for all the oxygen in the environment, perhaps they are also part of the feedback mechanisms affecting global climate change.

    • Nathan Urban says:

      I’m not too familiar with the early extinction events, although I have gone to some talks on the role (or not) of climate change. I’d have to dig out my notes on years past. I can speak a bit to your last points. Biological feedbacks are important to include, and they are included in modern Earth system models that incorporate terrestrial and ocean biogeochemistry (and, to a limited extent, actual ecology). As for the DMS-cloud feedback, this too is known, but is thought to be relatively small compared to other climate-cloud feedbacks.

  4. nad says:

    As John hints, temperatures over the last 18,000 years are not terribly relevant to the question of whether the planet is currently warming or whether there is warming due to humans, which are what Plait is talking about.

    (rather nonjittery, smoothed out) fast temperature changes (see e.g. PETM) do especially matter and alone for this it is good to have a long time scale for comparision for understanding what happens with which change.

    • Nathan Urban says:

      I stand by my earlier statement. The PETM can be useful for understanding the sensitivity of the Earth’s climate to carbon dioxide, as I noted above. But it’s certainly not useful for detection (whether the planet is currently warming), nor even really for attribution (whether the recent warming is due to humans). Plait was talking directly about detection and indirectly about attribution.

      Yes, improving estimates of climate sensitivity to CO2 can help with attribution in principle (by providing an estimate of how much warming is expected from anthropogenic CO2). But such paleo-estimates haven’t really proven that useful to attribution in practice. For that, it’s been most important to have physics-based estimates of recent climate trends and variability (GCM hindcasts and control runs).

      The PETM is a good qualitative example, however, of the simple fact that CO2 has been influential to the Earth’s climate throughout its history.

      • nad says:

        The PETM is a good qualitative example, however, of the simple fact that CO2 has been influential to the Earth’s climate throughout its history.

        But it is not only “a good qualitative example, however, of the simple fact that CO2 has been influential to the Earth’s climate”, but also how possible ecological results of a fast climate change could look like. In the case of the PETM the result seems to have e.g. (according to wikipedia) been the mass extinction of 35-50% of benthic foraminifera (no citation though) and a reduced body size of mamals (“dwarfing”, Gingerich2003).

  5. pohjois says:

    Nice lectures indeed.

    I’ll check it out. Of course, what counts as “cherry picking data” depends in part on what one is claiming to prove with the data one has chosen.

    It seems that you are relatively new to the climate change and have not fought flame wars with climate change denialists. The “it has not warmed since 1997” meme is one of the favourite among the anti science crowd. It has been debunked many times already, the most recent ones are given by Tamino:


    as well as in the excellent post on Skeptical Science:

    Tamino (who is a top class statistician by the way) has also shown earlier in his blog posts


    that when you account for known factors influencing the surface temperatures (such as volcanic eruptions, variation of solar radiation and ENSO) the warming trend becomes much clearer. He even published these findings in the peer reviewed journal:

    This meme is so popular (number 9 on the list of 173 myths) that it deserves its own special rebuttal in the standard Skeptical Science library:

    I highly recommend consulting a Skeptical Science website

    before you start digging yourself to check claims against climate science. You have very high chance that it has been already debunked there – the 173 myths have their summaries over there:

    They are also quick in analysing the nonsense that appears in the media. You may also want to check Tamino blog – he often reacts very quickly to some new claims that gain popularity in the denialosphere.

  6. pohjois says:

    P.S. It seems that the “it hasn’t warmed since 1997” meme is popular again, so even the RealClimate has a nice post on this.

  7. We saw last time that the Earth’s temperature seems to have been getting colder but also more erratic for the last 30 million years […]

  8. […] Part 4 – History of the Earth’s climate. […]

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