Global Warming: How Fast?

Here’s the annual average temperature for the planet Earth, from 1880 to now, according to data from NASA:

[Technical note: NASA reports temperature anomaly: the difference between temperature and its value during a “baseline” period which they chose as 1951-1980. I’m more interested in how much we’ve warmed since these records began so I’ve used a different baseline period, 1880-1899, hence values show how much we’ve warmed since then. Also, 2019 isn’t over yet so I’ve shown the year-to-date value.]

Clearly, Earth got hotter. Just as clearly, it doesn’t just follow a smooth trend over time, it also fluctuates from year to year, substantially, apparently randomly. Just as clearly, the trend it has followed has not been a straight line. Sometimes it was warming slowly, or even cooling off (especially during the early years), other times it was warming rapidly (especially recently).

We can get a good statistical model of the trend by using more than just a single straight line, we can use pieces of straight line segments joined at the ends. The “optimal” such model (if we can call it that) is this one:

It’s made of four straight-line segments, with the changes from one to the other happening in 1911, 1941, and 1970. All the parameters — the line segments themselves as well as the moments at which they begin and end — were chosen to make the model fit the data best.

According to this model — and it’s just a model (a statistical model, not a computer simulation) — the solid blue line shows where the trend most likely is, and the light-blue area around it shows the range within which the trend might be. The warming/cooling rate has gone through four “episodes.”

During the first (from 1880 to 1911) the rate was negative, Earth was cooling. Then from 1911 to 1941 we warmed significantly. From 1941 to 1970, we cooled off but not by much; in fact the uncertainty in the warming rate is bigger than the warming rate itself, so we can’t really be sure it was cooling off, it may have been just levelling off. From 1970 onward, we’ve warmed rapidly.

That’s all we can really say with confidence (statistically speaking) about how fast Earth has warmed/cooled since 1880. That doesn’t mean it really follows this “four straight-line segments” model — in fact it probably doesn’t, at least not exactly — but this is all we can say about changes in the warming rate with confidence.

What we can say with confidence is that this model captures the average warming rate during each episode. The warming rate may not be constant, but the straight-lines model gives its average (and the uncertainty in the average) for each episode, with fidelity. And here is a graph of the rates themselves, i.e. how fast Earth was warming/cooling during each episode (again, solid blue showing the most likely values, light blue outlining the uncertainty range).

This clarifies how the average rate changes over time. First it’s negative (cooling), then positive (warming), then possibly negative but possibly zero (cooling/levelling off), then rapid long-lasting positive (recent warming).

The rate during the most recent interval (from 1970 to the present) is estimated at 1.83 +/- 0.13 deg.C/century. And that is one estimate of the rate of warming right now: its average rate since 1970.

We can use more complex statistical models, which allow for more changes than just the straight-lines model. We can compute a fancy smoothed estimate, and for that I like to use the LOWESS smooth. There are many choices to make, but my choices lead to this model (again, the solid line is the best estimate of the trend value, the light red area shows its uncertainty range):

This model too enables us to estimate the warming rate — but now it’s not just four episodes of contant rate. The rate is changing all the time, and the model suggests this (best estimate in solid red, uncertainty range in light red):

The central estimate right now is 2.17 +/- 1.01 deg.C/century, over 20% higher than the rate suggested by the straight-lines model. We can even compare the two models directly (smoothed estimate in red, straight-line model in blue):

So what can we say about Earth’s warming rate right now? Based on the smoothed model, I’d say it’s almost surely between 1.66 and 2.67 deg.C/century. The average rate from 1970 to now was between 1.70 and 1.95 deg.C/century. Note that the values from the straight-line model are well within the uncertainty range of the smoothed model, so we don’t have statistically significant evidence of any recent change in the warming rate since 1970. It’s certainly possible, we just don’t have solid evidence for it.

My opinion: the present warming rate is about 2.23 deg.C/century, but could be as low as 1.66 or 2.67. It might be substantially higher than its average-since-1970 value of 1.83, but then again it might not.

My other opinion: given that the uncertainty is so large, we should at least be prepared for the possibility that right now, Earth is warming substantially faster than it has for the last 50 years. If that’s true, it’s a matter of serious concern.

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52 responses to “Global Warming: How Fast?

  1. We can also look to the climate models and see we can expect an increasing trend due to the accelerating rise in the proportion of greenhouse gasses in the atmosphere.
    This gives more support to the hypothesis that we are seeing a rising trend rather than statistical noise.

  2. “I’ve used a different baseline period, 1880-1999”
    I guess you meant 1880-1899?

    [Response: Right you are. Fixed, thanks.]

  3. cicely berglund

    How do these trends align with world human population increases or rates of increase.

  4. You might consider being more precise: what you are talking about is the surface temperature of the Earth, as opposed to what you say, i.e. the “Earth”. A lot of people don’t have a good idea of what ENSO is.

  5. do you have data or graph to make linking (correlation) between temp and CO2 ?

    do you utilize ? can i make this kind of graph with this website ?


    • rtemblay
      Using NOAA MLO data for CO2 & GISTEMP LOTI for temperture, a Least Squares yields a correlation of 0.0104ºC/ppm(v) +/- 0.0004(1sd).
      We could be a bit cheeky and assume that CO2 is rising at 2.5ppm/yr. So that would suggest the global temperature rise is running at (0.0104 x 2.5 x 100 =) 2.6ºC/century. Mind, that isn’t very scientific as CO2 has a log relationship with forcing and also there are a whole lot of other forcings operating. But it does add weight to the argument that global temperatures are showing signs of acceleration. That would be significant as for the last 4 decades the warming rate has been remarkably constant (as this graphic of Hadcrut4 data demonstrates – usually 2 clicks to ‘download your attachment’.)

  6. I am not a skeptic of climate change. I AM a skeptic of climate change models. While my modeling experience is in space mission risk, the techniques and tools used to address probabilistic events are the same. I think it safe to say that the uncertainty bands depicted here are too narrow.

    First, I wonder if the epistemic or model uncertainty is really accounted for. I have read that there are effects not yet accounted for in climate change models. Think of these as known unknowns. I suspect there are unknown unknowns as well. In my experience epistemic uncertainty is always under estimated.

    I am also skeptical that the data uncertainty is accurate. Data going back 100 years or more means many different instruments used to measure and different standards for measurement.

    Overall, I think the true uncertainty may very well swamp the results and disallow any trend evaluation.

    • Any data point 1945 has a very low error bar.

    • John, I think you should be somewhat reassured that a great many good minds have addressed these issues in depth and at length (and continue to do so, since the topic is very large and very complex.) You can read probably the most authoritative summary here:

      Click to access WG1AR5_Chapter09_FINAL.pdf

      “I have read that there are effects not yet accounted for in climate change models. Think of these as known unknowns.”

      There are, but probably not crucial ones, based on model validation studies so far. If there were ‘big pieces’ missing, it’s unlikely that hindcast model experiments could capture past patterns as well as they do.

      “I suspect there are unknown unknowns as well. In my experience epistemic uncertainty is always under estimated.”

      I appreciate the latter sentence; it’s the perspective of someone who’s ‘been there and done that,’ and has brushed up against Murphy’s Law a time or two. But be aware that researchers now have 50 years of diligent search for those ‘unknowns’ behind them. The supply of new unknowns may or may not be large, but it sure isn’t infinite, and so must have been reduced quite a bit by now.

      “I am also skeptical that the data uncertainty is accurate. Data going back 100 years or more means many different instruments used to measure and different standards for measurement.”

      Again, true but not new. The original purpose of what is now “climate data” was mostly operational weather forecasting, where accuracy was considered important (though not always fully appreciated by the ‘foot soldiers’ involved), but concerns like intercomparability, replicability, and metadocumentation were not. Consequently, making this “weather data” into usable “climate data” has been an ongoing exercise for decades. Sadly, one of the ‘rewards’ for this work has been slander from the ignorant, who impute deceptive motives to data adjustments needed to reduce documented biases in the data.

    • “I think it safe to say that the uncertainty bands depicted here are too narrow.”

      My understanding of this post is that it is statistical analysis starting from the NASA GISS-loti data set and applying one of the described models. Deriving uncertainty from this is straightforward enough that it would be a safer bet to assume it has been done correctly.

      I get the sense that you want to re-litigate the correctness of GISS-loti which one might have hoped to have been settled by the Berkley Earth effort. In any case this is probably not the best place to do so if one is interested in reaching resolution.

      • “re-litigating GISS-loti”–and it’s not just GISS; there’s strong consilience with all the data sets, including the satellite ones. BEST certainly should have been something close to the last word, though.

    • Hi, John. So in space mission risk analysis, you still launch and expect payload delivered to orbit, or beyond, don’t you? It’s a different kind of modeling you do, but I’m not certain what your point is about uncertainty in climate models (since you mentioned models specifically) while there are abundant known knowns, not based on climate models, that also indicate the expected warming.

      Sea levels rise and physics shows warmed water expands and that pouring more into a container raises the level, too. There may be other ways to raise sea level, but no observed evidence of that happening on an applicable scale.

      Ice is melting and that’s not model, that’s observation worldwide. Physics was worked out over the past century-plus for IR and greenhouse gases, and the direct air measurements and ice-core sampling of the gases are tracking increases (and now finally declines in some CFCs, thank god). The data from Tyndall’s experiments in the 1860s was pretty good, and Air Force-sponsored work by Gilbert Plass and others improved knowledge. Plass is one of the contributors to my 1964 “Infrared Physics and Engineering” textbook my uncle gave me. He worked in aerospace, but it was more along the line of heat-seeking systems, where accuracy is important, too.

      So in space mission modeling, Voyager 1’s deviation from expected course, after decades, was an unexpected additional thrust from IR photons emitted around the nuclear power supply, but the effect is tiny. The unknown unknowns of earth sciences might be like that, but would you expect something bigger to have remained hidden until now? I’m curious to understand.

    • Pete Dunkelberg

      Hi John,
      Lot’s of people share your concerns, although few express them so well. Still, as others have said, these concerns have been very well explored without finding a good basis. I’d like to mention a couple points that I do not see addressed yet.

      Uncertainty is not your friend.
      Greater uncertainty means that if we do not change directions, the future could be worse than expected.

      Risk analysis and rational response.
      We risk making our planet uninhabitable for the very large human population that we now have. It is not sane to take this risk, even if you think the chance is smaller than climate science indicates. And it could get even worse. If we set off a large CO2 release from the Arctic permafrost or other source, we risk causing atmospheric O2 concentration drop to perhaps 15%.

      You did not mention your bottom line. Often the bottom line for folks saying the uncertainty is too great is: The uncertainty is too great to risk taking corrective action. This is sometimes known as the “better world for nothing” fear. (google the expression).

      Perhaps a large economic stimulus is not the worst that could happen.

    • John Turner, Great, another engineer who thinks he understands Earths climate and the data better than the experts.

      eppure riscalda

    • Others have already commented on uncertainty in the data, so I’ll only re-emphasis a couple of points.

      On the reliability of older data, I’d point to Barton’s comment and add “central tendency.” If there’s uncertainty, there are other places to look.

      On the range of the current uncertainty, I’d make two points: the first, that there is sufficient scientific understanding to indicate that most forcingss are already understood, and there’s little besides a supervolcano eruption that would reduce the warming trend, and even in that scenario it would be a relatively transient effect – several years as opposed to the several milllennia to which the planet is committed to warming.

      The second is, as you noted above, that there is a distinct skew in the distribution of uncertainty around the mean, and that skew is such that unexpected and insufficiently-quantified factors acting on the warming of the planet are likely to result in addition to the rate of warming. Cryospheric response and feedback is a good example, although we’re starting to unpick the unknowns there. Stochasticity is also a phenomenon that’s likely to mean the uncertainty lies more toward the upper boundary, with a couple of notable exceptions – global war and pandemic. Of course, if either of those kick in to somewhat ameleorate the rate of planetary warming, people might not really have much to celebrate…

  7. cicely berglund: You should ask “How do these trends align with world human population of affluent people with cars?”

    The poor and the car-less don’t cause much global warming.

  8. This is very interesting. I did also this kind of study. I tried to reconstruct temperature anmaly from anropogenetic CO2 (CO2-level minus pre-industrial level). It gave the same kind of results. In detail slightly different. I used Hadcrut 5 for temperature anomaly but the picture is more or less the same.

  9. JT: First, I wonder if the epistemic or model uncertainty is really accounted for. I have read that there are effects not yet accounted for in climate change models. Think of these as known unknowns. I suspect there are unknown unknowns as well.

    BPL: Google “analysis of variance.”

  10. The NASA data is shown incorrectly: The 2nd cooling period lasts between 1945-1980. In general the alternating periods are 30-35 years long each.
    The statistical analysis does not explain WHY we have this zig-zag pattern instead of a smooth line like CO2 concentrations.

    [Response: The NASA data is not shown incorrectly. That’s just nonsense, as is the rest of your comment.]

    • “The NASA data is shown incorrectly: The 2nd cooling period lasts between 1945-1980.”

      You can test this hypothesis yourself easily enough with the tools at the following link. Plotting a piecewise linear trend with a break at 1980 leaves a step change at that point which is unphysical:

      • If I am understanding what Tamino is saying, the fit he did was different, in as much as it was *constrained* not to have unphysical jumps. If you did such a fit and put the breakpoint at 1980, it would not have a jump, but the lines from 1940-1980 and 1980 on would both fit rather poorly to the data. That is, the 1940-1980 line would slope up rather more than the one on your graph, and the 1980-present line would start too low and slope too much. You already show a bit of warming (not cooling!) in 1940-1980, and with the constraint you would see even more.

      • Actually the graphs used to promote the idea of global warming [example include data from NASA and 3 more sources:
        – NOAA
        – MET
        – JMA .
        The 4 datasets differ, so the main 4 periods do not have identical limits.
        Yet the fact remains that we have majors changes in average temperature trends that differ substantially form CO2 concentrations trends.

      • Yet the fact remains that we have majors changes in average temperature trends that differ substantially form CO2 concentrations trends.

        That is true. Conclusion: CO2 is not the only factor determining temperature. This is one of the only things that “skeptics”–whether real or phony–and mainstreamers agree on–even if the former often accuse the latter of not believing it.

        For instance, it was only in the second or third Assessment Report by the IPCC that they said that the anthropogenic (ie., GHG-driven) “signal” had emerged from the natural climatic “noise.” They have also been at pains to quantify the radiative forcings arising from different factors, both natural and anthropogenic, as suggested, for instance, in this summary graphic from the SPM:

        So, if you think you are making some sort of ‘telling’ point, you are mistaken. Nobody thinks that CO2 is the sole driver–least of all our host here, who has published work on the role of ENSO cycles and volcanic aerosols as they affect global mean surface temperature.

      • Thank you Doc Snow for your replay and interesting graph.
        I will disagree to “Nobody thinks that CO2”. I think that the vast majority of TV-fed public is absolutely certain that we have a permanent global warming and CO2 is the culprit…

      • TNS, The correlation between ln(CO2) and warming are actually quite good, particularly given, as Doc says, that there are many other factors that cause temperature to vary on short scales.

        On longer timescales, increasing CO2 is the dominant factor.

      • TNS: I think that the vast majority of TV-fed public is absolutely certain that we have a permanent global warming and CO2 is the culprit

        BPL: CO2 IS the culprit. It accounts for 82% of the variance of temperature since 1850. All other causes account for 18%. Many things affect climate, but at the moment, CO2 is the elephant in the room.

      • TNS:

        I will disagree to “Nobody thinks that CO2”. I think that the vast majority of TV-fed public is absolutely certain that we have a permanent global warming and CO2 is the culprit…

        Well, I certainly hope they do–because that conclusion is entirely correct, if a little lacking in nuance, and is moreover vitally important to enacting sane environmental policy.

        But you appear to think that there is some sort of contradiction between the proposition that “not only CO2 causes warming” and the proposition that “the dominant forcing determining climate today is CO2.” There is not.

        Moreover, the graph I posted, and which you termed “interesting”, goes quite a long way toward explaining why that is so. If you would like further help in understanding why, I would be glad to elaborate, and I’m sure so would other commenters here.

      • My problem is that the zig-zagging graph of temperatures after 1880 does not agree with the smooth curve of CO2 in the same period.
        Why so if CO2 is the determinant force?

        As for the SPM graph, it covers the second half of that period, leaving outside the 35 years of early 20th century global warming and the cooling period before it.

      • TNS, Good Lord, are you really that dim? If you have many factors that determine temperature, and some of them oscillate while others rise steadily, what you get is not a steady rise or a pure oscillation, but rather oscillations imposed on a fairly steady rise. In other words, what we see.

        Look at the warming trends of El Nino, La Nina and ENSO neutral years separated, and it’s much easier to see.

        Just where have you been over the last 30 years?

      • Thank you for your kind, snarkrastic reply.
        It is good to see that some people are not obsessed with the absolute dominance of CO2 in interpreting climatic variations.
        Yet, snarcasm is not the best way to express an opinion, only to display arrogance.

      • TNS: My problem is that the zig-zagging graph of temperatures after 1880 does not agree with the smooth curve of CO2 in the same period.

        BPL: This is Victor or Docgee under yet another screen name, bringing up yet another of his discredited points yet again. Ignore his ignorant ass.

      • I’m sorry, TNS, but you either don’t understand what correlation is, don’t understand the climate system, or you are trolling. And there is no excuse in 2019 for any of the above.

        Anyone of at least average intelligence can learn to do the statistical analysis through on-line tutorials.

        There are literally mountains of evidence, explanations of the evidence, popularizations of the explanations… To pretend that this is still an open question is just not plausible.

        If you have an actual question, then ask it. There are plenty of folks here with the statistical chops and ability to explain the subject matter. To claim that there is any doubt that CO2 is driving the current warming is simply trumpet proudly your own ignorance.

        Forgive the tone, but those of us who have been battling denialists for 20 years or so are getting a wee bit tired of it.

      • “battling denialists” explains a lot.
        Keep the good cause and defend the only true faith of Carbonism!

      • TNS,
        Tell ya what. I’ll try to be nicer if you try to be smarter. Deal?

        You go first. Fergodsake educate your stupid self!

    • The mid 20th century dip is fairly well understood, and is at least in part attributable to the effects of the Great Depression and the second world war, together with a relatively high proportion of particulates/aerosols in combustion emissions.

      The trajectory of planetary warming reflects a complex anthropegenic story…

      Oh, and there’s an overall background of slight natural cooling as we were exiting the Holocene. That’s now been completely swamped, but it’s worth pointing out that there’s about 0.2 C of anthropogenic warming in the Industrial period prior to the commencement of these temperature records…

  11. save_ecosystems

    The degrowth movement has the most effective solutions.

  12. Over at the ASIF forum folks are thinking out loud about how soon we’ll see ol’ BOE (Blue Ocean Event or Beginning Of End, I suppose) and what that would mean. It’s also interesting to hear frustration with standard weather forecasting models in the Arctic — as if the trick of projecting forward from previous behavior is starting to wear thin as the system readjusts.

    Needless to say, many would stop what they’re doing to see what angle Tamino has devised for a new crack at the Arctic in 2019. Forgive me for presuming to suggest work assignments, it’s just you’re angle is always uniquely clear, while the Arctic prognosis seems uniquely weird.

  13. thank Al Rodger for you graph

  14. With respect to data and instrumental uncertainty with respect to temperature it’s also worth pointing out that even within the 140 year time frame under discussion here there are a number of geologicalproxies for temperature that allow us to reconstruct trends without having to rely on historical instrumental records. Isotopic data can be used to estimate temperatures in corals, stalactites and anywhere else carbonates are laid down. We can look at ice cores and tree rings, reconstruct temperature from perturbations in geothermal gradients and many other ways.

  15. Great to have you back Tamino (Grant). And kudos to Doc Snow, Pete D, Al Rodgers and others for one of more informative and insult-free post-blog post commentaries.

  16. Yvan: the calibration of the proxy may affect the steepness of the trend, but it doesn’t cause the trend in itself. So, there is imprecision, but it does confirm that the change is not from instrument error.