Forbes says the data is consistent with a doubling of CO2 raising the temperature by about 2 °C. I think the right number is around 1.6 °C or 1.7°C, rather than 2 °C. (I would welcome someone checking my math.)

I suspect that Forbes incorrectly treated the relationship as linear. The ignored the fact that exponential growth of CO2 concentration causes only linear raise in temperature. They wrongly reasoned that since a rise in CO2 of 50% caused a temperature increase of 1 °C, then a rise of another 50% (of the original base) would cause another 1 °C of warming.

Since 1880, the beginning of the temperature records, we've increased CO2 by just under 40%. Temps have increased by about 1.1C over that period. (Not sure how they get "not quite 1C"... their own graph doesn't show that.)

Linear relationship on either of those periods would put us at about 3C or 2.75C for a doubling of CO2. It doesn't look like they used a linear relationship.

A logarithmic relationship puts us at 2.39 °C per doubling (HT JoeT), but that's transient climate sensitivity. Is that what the paper was looking at? If not, then the paper underestimated by somewhat more than it appears.

1- It's not "Forbes" who wrote this. It's written by Ethan Siegel, an astrophysicist. I think he knows about logarithms.

2- Your calculation of the climate sensitivity, based on only 2 points as given the Forbes article, is too low.

3- There is no assumption in the article of the linear relationship as you state it. When you claim that a "a rise of another 50% (of the original base) would cause another 1 C of warming", I have no idea where you read this in the article.

4- You can do this problem yourself! Someone who has posted here before has a great blog that shows you how. Scroll to the June 9 post and you can see in Figure 10 a summary of results using different surface data sets: 2.0 - 2.7 for the full record, 2.2 - 2.8 since 1970. The post on June 10 has a similar range for the troposphere (except UAH LT 6.0 of course).

Just to be clear, the climategraphs blog is not mine. I would be happy if it were, but it's not. I've posted similar statements, but the blog is far more thorough than anything I've done.

Joe T -- Regarding your point #3, the article says:

According to our estimate, a doubling of the CO2 content in the atmosphere has the effect of raising the temperature of the atmosphere (whose relative humidity is fixed) by about 2 °C.

What we've seen from the pre-industrial revolution until today matches that extremely well. We haven't doubled CO2, but we have increased it by about 50%. Temperatures, going back to the first measurements of accurate global temperatures in the 1880s, have increased by nearly (but not quite) 1 °C.

In other words: Since 1880, CO2 increased 50% and temperature increased 1 °C. This is said to closely match the model, which says doubling CO2 causes a 2 °C temperature increase. I think the article made an error in this specific claim. But, I may easily have missed something. I'd love to see someone double-check this point.

Joe, I hope this explanation clarifies my prior comment.

Thank you Joe. I was not intending to question the true value of CS. Rather I was pointing out an internal inconsistency within the article. Using your equation, where the growth in CO2 was 50%, as the article states, then

1 C = CS * log2(1.5).

That gives CS = 1.71

while the article claims that CO2 growth of 50% yields CS of "about 2"

Perhaps the article made the error of treating the relationship between CO2 growth and temperature rise as linear. Or, perhaps they stretched a bit by describing 1.71 as "about 2".

AFAIK we can't calculate the climate's sensitivity to CO2 using data-to-date because cooling from aerosols is just too large. Aerosol loading is large and not measured, and, worse, its radiative forcing depends on latitude, since the amount of reflected sunlight depends on its angle.

Thanks for the kind words, JoeT and Layzej. However, I have to admit that I haven't done much with that site lately. IIRC last time I posted here JoeT had a bunch of very good critiques/comments/suggestions, none of which I've had a chance to follow up on. Things have been busy. Maybe next month...

This is the culmination of a very strange series of comments by David in Cal:

In fact, the consistent CS is slightly farther away from 2.0 than the above. The article says,

"Temperatures...have increased by nearly (but not quite) 1 °C."

So the CS consistent with a 50% increase in CO2 would be something slightly less than 1.71.

David, as you know, the numbers in the article are not reported with sufficient accuracy to support the calculation you are doing.

So rather than calculating a number for climate sensitivity that is obviously going to be wrong because it's based on inaccurate values for CO2 and TAS, let's do your same calculation using the correct numbers:

(1) As Layzej points out, CO2 has increased by 40% since 1880.

(2) Global surface temperatures have increased by approximately 1.1 C since 1880, using the three metrics that have complete global coverage (GISTEMP, Berkeley Earth, and Cowtan & Way).

Using the correct numbers for CO2 increase and temperature change with David's approved method of calculating climate sensitivity gives a value around 2.25. As noted above, a fairly comprehensively review shows that depending on what time period and data set is used, the values for this estimate of CS will range between 2 to 3.

David, since this is your own method, I assume you can confirm the math here. Using your method, the correct value for CS is in the range of 2 to 3. Right?

This is nice, because as I note elsewhere, this range is centered precisely on the reported value for CS (2.5) in Hargreaves et al. (2012)'s study of temperature change at the Last Glacial Maximum.

climate data -- My point was to show that Forbes's headline was exaggerated. I am not trying to address the true value of CS

The calculation you object to is Forbes's calculation or Ethan Siegel's calculation. The headline says "First Climate Model Turns 50, And Predicted Global Warming Almost Perfectly". The article supplies figures that supposedly show the almost perfect fit. But, due to use of the wrong model or for some other reason, the figures in the article do not demonstrate what the article claims.

The 1967 model says that a doubling of CO2 should cause 2 deg C of warming. The article says CO2 has increased by 50% since 1967. So, temperature should have risen by 2.0 * log2(1.5) = 1.17 deg C. The article then says that the actual increase of "not quite" 1 deg C fits the model almost perfectly.

climate data - your point is yet another reason why Forbes's headline is misleading. Since the numbers in the article are not reported with sufficient accuracy to support the calculation, it was never possible to say whether or not the fit is "almost perfect".

David -- I totally agree with you that there are factors other than CO2 affecting global warming.

I was criticizing the article, particularly the headline. (I don't know if the headline was written by Siegel or by a Forbes editor.) IMHO that article implicitly DID attribute all warming to CO2. The point I meant to address is the accuracy of climate model predictions. The words "almost perfect" in the headline promote the belief that climate models can make highly accurate predictions. But, that headline was not justified by the content of the article.

BTW your good point about aerosols is yet another reason why today's climate models are not yet able to make almost perfect predictions.

My point was to show that Forbes's headline was exaggerated. I am not trying to address the true value of CS

Whether it's exaggerated is a matter of opinion, depending on how strictly one chooses to interpret the phrase "almost perfectly".

More importantly, whether the headline is accurate depends on whether the headline matches reality not whether the headline matches something in the 8th paragraph of the text.

And the real problem here is that your criticism of the headline is backwards. Insofar as the prediction by Manabe & Wetherald (MW67) was "imperfect" the problem is that it underpredicted warming. But you are deliberately muddying the waters to imply that it overpredicted warming. Your criticism of the headline is intellectually dishonest.

You carefully delete the word "about" and then use the round number of 50% to compute an erroneously low value for climate sensitivity. The result of your calculation is wrong because at least one of the inputs to that calculation is wrong.

DiC concludes with:

Since the numbers in the article are not reported with sufficient accuracy to support the calculation, it was never possible to say whether or not the fit is "almost perfect".

Except that it is possible, because you can look up the actual values for CO2 and temperature. They are not hard to find!

The bottom line ...

David in Cal is arguing that Siegel's headline is wrong. There is legitimate room for disagreement about how much difference between a 1967 prediction and 2017 reality can reasonably be described as "almost perfect". However,

(1) Whether the headline is correct depends on comparing it to reality, not to something that is not reality. There has not been a 50% increase in CO2 concentration so that should not be used to evaluate the accuracy of the headline.

(2) In reality, MW67's prediction turned out to be too low. David in Cal is trying to imply that the problem with the headline is that the model was too high. In other words, this isn't a dispute over how close something needs to be to count as "almost perfect". David in Cal literally has the sign of the error reversed.

I've put together a nice demonstration of this. See here:

The graph shows the average of the six global temperature datasets (GISTEMP, Berkeley Earth, Cowtan&Way, NOAA, HADCRU, and JMA) from 1967 to the present. The X-axis is the base-2 log of CO2 concentration, so a 1-unit increase in X represents a doubling of CO2.

The blue dots are the annual observations. The blue line is the trend of observations, and the gray dashed lines are the 95% confidence intervals.

The red line represents MW67's prediction (based on 2 degrees of warming per doubling). As you can see, actual warming has been faster than predicted. (It would be nice if David in Cal would admit this, but I'm not holding my breath....)

One other point: to some extent, in this analysis it's OK to ignore other forcings. That's because two sources of error happen to more or less cancel out:

* CO2 on average has been about 56% of the total (net) forcing. * The ratio of TCR (transient climate response) to equilibrium sensitivity is about 56%.

So for this kind of back-of-the-envelope, it's reasonable to ignore non-CO2 forcings and the difference between TCR/ECS. The two factors happen (by chance) to mostly cancel out.

Ironically, the need for the update was that I had based my post on the wording in the abstract of MW67, which reports that the temperature increase from doubling CO2 is ... "about 2 C". But the actual numerical result, listed in MW67's Table 5, is that doubling CO2 raises the temperature by 2.36 C.

That's ironic because I was tripped up by exactly the thing that I criticized David in Cal for -- using a number that was reported as a rough approximation ("about") as if it were more precise.

In this case, MW67's actual calculated climate sensitivity (2.36) is even closer to the observed change in temperature per doubling of CO2 (2.57). In fact, the error is now less than 10% of the true value, based on the past 50 years of observations.

Whether a prediction of 2.36 is "almost perfect" for observations of 2.57 will be left up to the reader to decide.

FWIW, I think it's an astoundingly successful prediction. But YMMV, as they say.

## 21 comments:

Forbes says the data is consistent with a doubling of CO2 raising the temperature by about 2 °C. I think the right number is around 1.6 °C or 1.7°C, rather than 2 °C. (I would welcome someone checking my math.)

I suspect that Forbes incorrectly treated the relationship as linear. The ignored the fact that exponential growth of CO2 concentration causes only linear raise in temperature. They wrongly reasoned that since a rise in CO2 of 50% caused a temperature increase of 1 °C, then a rise of another 50% (of the original base) would cause another 1 °C of warming.

We've raised CO2 by not quite 30% since the 60s when Keeling started recording daily, and temps have raised by about 0.9C in that time.

Since 1880, the beginning of the temperature records, we've increased CO2 by just under 40%. Temps have increased by about 1.1C over that period. (Not sure how they get "not quite 1C"... their own graph doesn't show that.)

Linear relationship on either of those periods would put us at about 3C or 2.75C for a doubling of CO2. It doesn't look like they used a linear relationship.

A logarithmic relationship puts us at 2.39 °C per doubling (HT JoeT), but that's transient climate sensitivity. Is that what the paper was looking at? If not, then the paper underestimated by somewhat more than it appears.

DiC

1- It's not "Forbes" who wrote this. It's written by Ethan Siegel, an astrophysicist. I think he knows about logarithms.

2- Your calculation of the climate sensitivity, based on only 2 points as given the Forbes article, is too low.

3- There is no assumption in the article of the linear relationship as you state it. When you claim that a "a rise of another 50% (of the original base) would cause another 1 C of warming", I have no idea where you read this in the article.

4- You can do this problem yourself!

Someone who has posted here before has a great blog that shows you how. Scroll to the June 9 post and you can see in Figure 10 a summary of results using different surface data sets: 2.0 - 2.7 for the full record, 2.2 - 2.8 since 1970. The post on June 10 has a similar range for the troposphere (except UAH LT 6.0 of course).

Layzej,

Just to be clear, the climategraphs blog is not mine. I would be happy if it were, but it's not. I've posted similar statements, but the blog is far more thorough than anything I've done.

Woops! HT "climate data analysis" who also posts here.

Joe T -- Regarding your point #3, the article says:

According to our estimate, a doubling of the CO2 content in the atmosphere has the effect of raising the temperature of the atmosphere (whose relative humidity is fixed) by about 2 °C.

What we've seen from the pre-industrial revolution until today matches that extremely well. We haven't doubled CO2, but we have increased it by about 50%. Temperatures, going back to the first measurements of accurate global temperatures in the 1880s, have increased by nearly (but not quite) 1 °C.

In other words: Since 1880, CO2 increased 50% and temperature increased 1 °C. This is said to closely match the model, which says doubling CO2 causes a 2 °C temperature increase. I think the article made an error in this specific claim. But, I may easily have missed something. I'd love to see someone double-check this point.

Joe, I hope this explanation clarifies my prior comment.

DiC

In 1880 CO2 was around 290, in 2016 around 405. That's a 40% increase.

Let's use 1C as the temperature increase as stated in the article. Then

1 C = CS * log2(405/290)

where CS is the climate sensitivity and log2 is the logarithm to the base 2. That gives CS = 2.1

Thank you Joe. I was not intending to question the true value of CS. Rather I was pointing out an internal inconsistency within the article. Using your equation, where the growth in CO2 was 50%, as the article states, then

1 C = CS * log2(1.5).

That gives CS = 1.71

while the article claims that CO2 growth of 50% yields CS of "about 2"

Perhaps the article made the error of treating the relationship between CO2 growth and temperature rise as linear. Or, perhaps they stretched a bit by describing 1.71 as "about 2".

cheers

In fact, the consistent CS is slightly farther away from 2.0 than the above. The article says,

"Temperatures...have increased by nearly (but not quite) 1 °C."So the CS consistent with a 50% increase in CO2 would be something slightly less than 1.71.

AFAIK we can't calculate the climate's sensitivity to CO2 using data-to-date because cooling from aerosols is just too large. Aerosol loading is large and not measured, and, worse, its radiative forcing depends on latitude, since the amount of reflected sunlight depends on its angle.

Thanks for the kind words, JoeT and Layzej. However, I have to admit that I haven't done much with that site lately. IIRC last time I posted here JoeT had a bunch of very good critiques/comments/suggestions, none of which I've had a chance to follow up on. Things have been busy. Maybe next month...

This is the culmination of a very strange series of comments by David in Cal:

In fact, the consistent CS is slightly farther away from 2.0 than the above. The article says,

"Temperatures...have increased by nearly (but not quite) 1 °C."

So the CS consistent with a 50% increase in CO2 would be something slightly less than 1.71.

David,

, the numbers in the article are not reported with sufficient accuracy to support the calculation you are doing.as you knowSo rather than calculating a number for climate sensitivity that is obviously going to be wrong because it's based on inaccurate values for CO2 and TAS, let's do your same calculation using the correct numbers:

(1) As Layzej points out, CO2 has increased by 40% since 1880.

(2) Global surface temperatures have increased by approximately 1.1 C since 1880, using the three metrics that have complete global coverage (GISTEMP, Berkeley Earth, and Cowtan & Way).

Using the correct numbers for CO2 increase and temperature change with David's approved method of calculating climate sensitivity gives a value around 2.25. As noted above, a fairly comprehensively review shows that depending on what time period and data set is used, the values for this estimate of CS will range between 2 to 3.

David, since this is your own method, I assume you can confirm the math here. Using your method, the correct value for CS is in the range of 2 to 3. Right?

This is nice, because as I note elsewhere, this range is centered precisely on the reported value for CS (2.5) in Hargreaves et al. (2012)'s study of temperature change at the Last Glacial Maximum.

climate data -- My point was to show that Forbes's headline was exaggerated. I am not trying to address the true value of CS

The calculation you object to is Forbes's calculation or Ethan Siegel's calculation. The headline says

"First Climate Model Turns 50, And Predicted Global Warming Almost Perfectly". The article supplies figures that supposedly show the almost perfect fit. But, due to use of the wrong model or for some other reason, the figures in the article do not demonstrate what the article claims.The 1967 model says that a doubling of CO2 should cause 2 deg C of warming. The article says CO2 has increased by 50% since 1967. So, temperature should have risen by 2.0 * log2(1.5) = 1.17 deg C. The article then says that the actual increase of "not quite" 1 deg C fits the model almost perfectly.

climate data - your point is yet another reason why Forbes's headline is misleading. Since the numbers in the article are not reported with sufficient accuracy to support the calculation, it was never possible to say whether or not the fit is "almost perfect".

david, again, you cannot attribute all warming, or lack of it, to CO2, mostly because of aerosols.

Is this to hard to understand, or are you just ignoring it?

David -- I totally agree with you that there are factors other than CO2 affecting global warming.

I was criticizing the article, particularly the headline. (I don't know if the headline was written by Siegel or by a Forbes editor.) IMHO that article implicitly DID attribute all warming to CO2. The point I meant to address is the accuracy of climate model predictions. The words "almost perfect" in the headline promote the belief that climate models can make highly accurate predictions. But, that headline was not justified by the content of the article.

BTW your good point about aerosols is yet another reason why today's climate models are not yet able to make almost perfect predictions.

DiC writes:

My point was to show that Forbes's headline was exaggerated. I am not trying to address the true value of CSWhether it's exaggerated is a matter of opinion, depending on how strictly one chooses to interpret the phrase "almost perfectly".

More importantly, whether the headline is accurate depends on whether the headline matches

realitynot whether the headline matches something in the 8th paragraph of the text.And the real problem here is that your criticism of the headline is backwards. Insofar as the prediction by Manabe & Wetherald (MW67) was "imperfect" the problem is that it

underpredictedwarming. But you are deliberately muddying the waters to imply that itoverpredictedwarming. Your criticism of the headline is intellectually dishonest.You carefully delete the word "about" and then use the round number of 50% to compute an

erroneously lowvalue for climate sensitivity. The result of your calculation is wrong because at least one of the inputs to that calculation is wrong.DiC concludes with:

Since the numbers in the article are not reported with sufficient accuracy to support the calculation, it was never possible to say whether or not the fit is "almost perfect".Except that it is possible, because

you can look up the actual values for CO2 and temperature. They are not hard to find!The bottom line ...

David in Cal is arguing that Siegel's headline is wrong. There is legitimate room for disagreement about how much difference between a 1967 prediction and 2017 reality can reasonably be described as "almost perfect". However,

(1) Whether the headline is correct depends on comparing it to reality, not to something that is

notreality. There hasnotbeen a 50% increase in CO2 concentration so that shouldnotbe used to evaluate the accuracy of the headline.(2) In reality, MW67's prediction turned out to be

too low. David in Cal is trying to imply that the problem with the headline is that the model wastoo high. In other words, this isn't a dispute over how close something needs to be to count as "almost perfect". David in Cal literally has the sign of the error reversed.I've put together a nice demonstration of this. See here:

https://climategraphs.wordpress.com/2017/11/06/evaluating-the-prediction-of-manabe-and-wetherald-1967/

The graph shows the average of the six global temperature datasets (GISTEMP, Berkeley Earth, Cowtan&Way, NOAA, HADCRU, and JMA) from 1967 to the present. The X-axis is the base-2 log of CO2 concentration, so a 1-unit increase in X represents a doubling of CO2.

The blue dots are the annual observations. The blue line is the trend of observations, and the gray dashed lines are the 95% confidence intervals.

The red line represents MW67's prediction (based on 2 degrees of warming per doubling). As you can see, actual warming has been

fasterthan predicted. (It would be nice if David in Cal would admit this, but I'm not holding my breath....)One other point: to some extent, in this analysis it's OK to ignore other forcings. That's because two sources of error happen to more or less cancel out:

* CO2 on average has been about 56% of the total (net) forcing.

* The ratio of TCR (transient climate response) to equilibrium sensitivity is about 56%.

So for this kind of back-of-the-envelope, it's reasonable to ignore non-CO2 forcings and the difference between TCR/ECS. The two factors happen (by chance) to mostly cancel out.

https://climategraphs.wordpress.com/2017/02/28/first-blog-post/

climate data analysis said... "I've put together a nice demonstration of this"Very cool! On the Log2(CO2) vs Temp graph, which years did you include?

Thanks,

Layzej

I have updated the post at the first link above:

https://climategraphs.wordpress.com/2017/11/06/evaluating-the-prediction-of-manabe-and-wetherald-1967/

Ironically, the need for the update was that I had based my post on the wording in the abstract of MW67, which reports that the temperature increase from doubling CO2 is ... "about 2 C". But the actual numerical result, listed in MW67's Table 5, is that doubling CO2 raises the temperature by 2.36 C.

That's ironic because I was tripped up by exactly the thing that I criticized David in Cal for -- using a number that was reported as a rough approximation ("about") as if it were more precise.

In this case, MW67's actual calculated climate sensitivity (2.36) is even closer to the observed change in temperature per doubling of CO2 (2.57). In fact, the error is now less than 10% of the true value, based on the past 50 years of observations.

Whether a prediction of 2.36 is "almost perfect" for observations of 2.57 will be left up to the reader to decide.

FWIW, I think it's an

astoundingly successful prediction. But YMMV, as they say.Thanks, Layzej. That graph is based on CO2 and temperatures from 1967-2016 (I used annual temperatures, so couldn't include 2017, alas...)

In other words, it only used data from after the publication of MW67.

Note also that the estimate from MW67 (2.36) is well inside the 95% confidence interval of the observations (2.29-2.84).

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