## Scenarios, Scenarios: Hansen’s Prediction Part II

May 30th, 2006Posted by: Roger Pielke, Jr.

After a bit more investigation, motivated by comments on my earlier post on Jim Hansen’s 1988 predictions (thanks all), it turns out that Jim Hansen has two sets of scenarios labeled A, B, and C. This is confusing to say the least. The conclusions of the earlier post remain unchanged, however, the analysis below may help to explain some things.

The first set of scenarios A, B and C are from his 1988 paper and the details can be found in the appendix to that paper. The second set of scenarios named A, B, and C was apparently generated for his 1998 paper in order to rescale emissions projections based on the lack of realism in the 1988 projections. The earlier post of mine therefore is actually a comparison of the 1998 scenarios with what has transpired since, and in that case it is true that Scenario C (let’s call it C98) is clearly the most comparable to how things have evolved since 1998.

For his 1988 paper here then from its appendix are the relevant annual growth rates for each scenario relevant to the time period 1990-2005, which I am now labeling with the year affixed for clarity:

Scenario A88

CO2 1.5%

N2O 0.2% 1990-1999, 0.4% >2000

CH4 1.5%

Scenario B88

CO2 1% 1990-1999, 0.5% >2000

N2O 2.5% 1990-1999, 1.5% >2000

CH4 1.0% 1990-1999, 0.5% >2000

Scenario C88

CO2 1.5 ppm 1990-2000, fixed at 368 ppm after 2000

N2O 0.0%

CH4 0.5% year 1990-2000, fixed at 1916 ppm after 2000

How do these scenarios compare? From the earlier post here again are the actuals:

CH4 0.46%

N2O 0.95%

CO2 -0.52% (Annex 1 Countries 1990-2003)

CO2 >0.45% (Non-Annex 1 Countries 1990-2003) (note typo caught in earlier post)

CO2 1.5 PPM (1990-2005)

How to evaluate these scenarios?

From 1990-2000 Scenario C88 was right on target with respect to CH4 and CO2, and off with respect to N2O (The description of Scenario C88 actually doesn’t mention N2O in the appendix describing the growth rates, so I assumed that it was zero).

Scenarios A88 and B88 were off by factors of 3 and 2 respectively with respect to CO2 and CH4. With respect to N2O Scenario A88 was by a factor of 0.2 too small and B88 was a factor of 2.5 too large. These are large errors, much larger than those documented with respect to the 1998 projections, as would be expected.

So, there are several conclusions to draw from this exercise.

1. With respect to Jim Hansen’s 1988 predictions, his Scenario C88 was the most accurate with respect to emissions 1990-2000. That scenario froze time in 2000, meaning that going forward there are two evolving scenarios which both have dramatically overestimated emissions. The lower of the two is thus “more accurate” than the other. Neither is particularly accurate or realistic. *Any conclusion that Hansen’s 1988 prediction got things right, necessarily must conclude that it got things right for the wrong reasons.*

2. With respect to Hansen’s 1998 predictions C98 has been the most accurate.

3. In two sets of predictions compared with experience, Jim Hansen’s predictions of emissions have proved to be overly aggressive both times with respect to rates of emissions with his lower estimate proving most accurate.

4. When discussing Hansen’s scenarios make sure that you differentiate between 1988 and 1998 versions.

More comments welcomed!

May 31st, 2006 at 8:01 am

First, I would make the general comment that one must be very careful when comparing percentages (as is done above)

1) to ask “% of what”? (including the “size of the ‘what’”?)

2) to consider the size of the percentages involved

Having said that, I am going to compare results for total atmospheric CO2 increase (in ppm) over the period from 1990-2005 — both calculated with Hansen’s 1988 Scenario B and ACTUAL — from NOAA data here:

http://www.cmdl.noaa.gov/ccgg/trends/

Using Hansen’s assumptions for secnario B88

CO2 1% 1990-1999, 0.5% >2000

These percentages clearly reprsent the “percent change per year in the annual CO2 growth rate”

One comes up with two equations (or one equation with different constant) for “CO2 increases” over the periods 1990-1999 (I assumed this meant “end of 99″) and 2000 and on — both exponentials, but with a different “k” factor.

I = C e^(kt)

where ^ means to the power, e is the base of natural log, t is time, and “C” is the initial “annual mean CO2 growth rate” (taken as 1.5ppm per year — which is reasonable, given Hansen’s assumption of 1.5ppm for scenario C and it is also what i get uisng a box car average of a few years bracketing 1990 from the NOAA data)

For the period 1990 through end of 1999, k turns out to be about 0.0099503.

For the period 2000 and beyond, k turns out to be about 0.0049875.

Using the equation with the given numbers for snario B88, I get 25.82ppm as the predicted total change in atmospheric CO2 concentration from beginning 1990 through the end of 2005.

From the NOAA annual mean growth rate data

http://www.cmdl.noaa.gov/ccgg/trends/

covering the same years (begiining 1990 – end of 2005), the total incerase in atmospheric CO2 comes out 27.3 ppm

So ACTAUL – PREDICTED =

27.3 – 25.82 = 1.48ppm (difference between actual and calculated with Hansen senario B88)

Now, let’s compare this with the result from the simple linear model C88, which assumes a 1.5ppm increase for each of the years from 1990-end of 1999 and then NO increase beyond.

For the 10 year period from 1990-end of 1999, the predicted total CO2 concentration increase would be 15ppm.

ACTAUL – PREDICTED =

27ppm – 15ppm = 12ppm

If one continued the increase through the end of 2005, one one have a 24ppm increase.

27.3 (actual) – 24 (predicted with C88) = 3.3ppm.

So even if one used the 1.5ppm increase for the entire period, one still comes up with a difference (Actual – predicted) for the C88 scenario (3.3ppm) that is greater than that for the B88 scenario (1.48ppm)

The B88 scenario number is CLOSER to the actual than the C88 by 1.82ppm.

It is instructive to consider what we would get if we use 0.5% as the yearly increase in annual CO2 growth rate for the entire period in question (beginning 1990 to end of 2005). If we do this, we

get a predicted total CO2 concentration increase of 24.98ppm.

So, the difference betwen using 1% and 0.5% is only 25.82 – 24.98 = 0.84ppm

over the entire period from 1990-2005.

The difference is NOT very big (even though 1% is 2X 0.5%. As I said above, one must consider size of the percentage and “percent of what”? to come up with meaningful conclsuions).

So, in the early years, at least, scenario B88 is not particularly sensitive to the actual number used as the percentage change (so long as it is small, which both 1% and 0.5% certainly are).

I think the above numbers should speak for themselves. I could have waded through that reference Roger provided and tried to figure our precisely where his percentages came from

CO2 -0.52% (Annex 1 Countries 1990-2003)

CO2 >0.45% (Non-Annex 1 Countries 1990-2003) (note typo caught in earlier post)

and whether they even refers to the same thing that Hansen’s precentages refer to, but I felt better about actually comparing apples to apples.

May 31st, 2006 at 8:18 am

Note of clarification my numbers for predicted total CO2 incerases with scenrio B above actually come for an INTEGRATION of the two exponential equations above for the years in question.

May 31st, 2006 at 8:19 am

Laurence-

Thanks much for your contribution. But you might want to check this claim:

These percentages clearly reprsent the “percent change per year in the annual CO2 growth rate”

According to Hansen et al. 1988, p. 9361:

“In scenario B the growth of the annual increment of CO2 is reduced from 1.5% per year today to 1% per year in 1990, 0.5% per year in 2000, and 0 in 2010; thus after 2010 the annual increment in CO2 is constant, 1.9 ppmv per year.”

So the growth rates are expressed as annual growth rates, not as changes in the growth rate itself.

May 31st, 2006 at 9:18 am

Roger: You are correct that I misspoke, but it changes nothing in my above analysis.

Instead of

“percent change per year in the annual CO2 growth rate”

I should have said “percent change per year in the annual CO2 growth”

In other words, I should have left off the word “rate”

Substitute my words “percent change per year” for hansen’s “growth” [which, more precisely, IS a "growth rate"] and my “annual CO2 growth” for hansen’s “annual increment of CO2″ and you get the same meaning.

The years 1990 and 2000 merely reperesnt years where Hansen introduced a NEW growth rate (ie, 1.5% to 1% to 0.5%)

May 31st, 2006 at 10:09 am

In case anyone is interested (and does not want to do the integration) here are the two INTEGRATED equations I used to get the numbers above for “predicted total CO2 increases” for the period 1990-2005 using hansen’s assumptions (arrived at by integrating the above exponential equation with different constant and time period)]

(C1/k1) (e^(10k1) – 1) for increase in 10 year period from 1990-1999 (end)

(C2/k2) (e^(6k2) – 1) for increase in 6 year period from 2000-2005 (end)

where ^ means exponentiation,

with

C1 = 1.5ppm

C2 = 1.65ppm (different from C1 since annual CO2 “increment” was assumed [by Hansen] to increase 1% each year over the period 1990-1999)

k1=0.0099503

k2=0.0049875

May 31st, 2006 at 11:49 am

Incidentally, for those who want to avoid the above integration entirely, you can get almost the same result (with an approximation, though very small because of the numbers involved) by simply figuring out the “annual CO2 increment” (as Hansen terms it) for each of the years between 1990 and 2005 and then adding up all these increments (what the integration does slightly more accurately)

If you do that, here’s what you get for the increase in CO2 from 1990-2005 (end) using Hansen’s scenario B88 assumptions

(

for the years 1990-1999, start with 1.5 and multiplying by another factor of 1.01 each year

and for the years 2000-2005, the multiplier becomes 1.005

1990: 1.5

1991: 1.515 ( ie, 1.5×1.01)

1992: 1.530

1993: 1.545

1994: 1.560

1995: 1.576

1996: 1.591

1997: 1.607

1998: 1.623

1999: 1.640

2000: 1.648

2001: 1.656

2002: 1.665

2003: 1.673

2004: 1.681

2005: 1.690

Adding up the “increments” for each year, you get a grand total of 25.7ppm change from 1990-2005 (for Hansen’s scenario B88)

Note that this number 25.7ppm is a tiny bit less than the more accurate number I got above ( 25.82ppm) by actually doing the integration.

Again, the actual incerase in the atmospheric CO2 concentration for the period 1990-2005 (inclusive) obtained by adding up the NOAA yearly increments is 27.3ppm

http://www.cmdl.noaa.gov/ccgg/trends/

May 31st, 2006 at 12:02 pm

Your objections to Hansen’s paper are misconceived. Suppose I predicted the result of rolling four dice by a computer simulation. My simulation came up with 5+4+1+2=12. You roll the real dice and get 1+4+6+3=14. I say my simulation was pretty close, but you say that I got the right answer for the wrong reasons — after all I was off by four on the first die and I could not have been more wrong about the third one and I was just lucky that the errors cancelled out.

But I wasn’t just lucky — it is rather unlikely for all the errors to go in the same direction.

Same thing with Hansen — his paper was not a prediction of the changes in each individual forcing. What he was looking at was the effect of the total change in forcing on temperature, and that’s the way you should be looking at it.

And the fraud issue, it seems like an open and shut case. Look at the doctored graph. This seems to be indefensible.

May 31st, 2006 at 5:26 pm

Laurence- Hansen states very clearly in the 1988 paper that the annual increase he is using for B and C is linear, not exponential. Thanks.

June 1st, 2006 at 2:31 am

Hmmm, confusing. And I’m afraid I still don’t understand. In Hansen’s 1998 paper ( http://pubs.giss.nasa.gov/docs/1998/1998_Hansen_etal_1.pdf ), Fig 5 is based on the original 1988 scenarios, right? In which case the forcing in B and C is virtually identical up to 2000 and not too far different from reality. So, even though the components deviate from reality, the total forcing does not, and so the model has done a good job.

June 1st, 2006 at 4:14 am

Tom-

Figure 5 shows that actuak total forcing and the growth rate were best matched by Scenario C88 (through 1996), but also that even C88 was too high. This seems to have been the case up to 2000, when Scenario C88 was “frozen”, by default making B88 the least inaccurate.

All comparisons of Hansens 1988 prediction should therefore focus on the prediction of C88 which had the most realistic emissions estimates as input, which as you note is not so different than B88 during this period.

Claims that B88 was most realistic or most accurate are incorrect. Hansen called A88 “business as usual” and B88 “most likely”.

While the temperature prediction looks quite accurate, I am now convinced that its accuracy resulted despite the poor prediction of short-term emissions paths.

This is no knock on Hansen — as someone once said – prediction is hard, especially about the future. But it is clear (e.g., the Krugman op-ed) that the 1988 prediction has been mythologized to some degree.

Thanks.

June 1st, 2006 at 5:03 am

Roger, the deviation of scenario B88 from actual is about 0.1 W/m^2 for the ‘5 gases’ actual, and perhaps 0.2 W/m^2 for the ‘6 gases’. Actual actual is somewhere in between the two, so perhaps 0.15.

Assuming a standard equilibrium sensitivity of 0.8 dec C per W/m^2, that equates to a temperature difference of about 0.1 deg C. Given the long time lags in the climate system (it takes 100 yrs to get anywhere near equilibrium), coupled with inherent variability (year to year variation is >0.2 deg C), it’s impossible to distinguish the climate effects of such a small difference in one decade.

So the fact that the predicted temperature in scenario B88 looks pretty much like observations is what you would expect. The effect of the deviation in forcing you are complaining about is too small to see through the noise (In theory, B88 temperature should be perhaps 0.05 deg C above observations. Perhaps it is – who can tell?).

The model has done really rather a good job, considering its limitations. It’s good confirmation that the lag between forcing and temperature (which is largely parameterized in the GISS model) is about right.

June 1st, 2006 at 5:54 am

Tom-

Thanks. I think that we are pretty much in agreement. If you are suggesting that choice of emissions scenario does not really matter for temperature prediction from the model Hansen used over a decade or two, I agree.

But our inability to accurately predict emissions paths on a time scale as short as a decade should be of some interest, given that climate models are based on projections out to a century, at which point the differences for forcing are quite significant.

Climate models have moved on since 1988 so this discussion is largely about how to interpret various claims being made on both sides about Hansen’s 1988 forecast made before Congress, rather than an evaluation of the model itself, which I assume most climate scientists would say is ancient science.

I am convinced that claims of the accuracy of his prediction are as overblown as claims of his inaccuracy. Hansen presented some interesting science, and his claims of continued warming made in 1988, which was the scientific consensus, have borne out. However, to parse his scenarios and give him credit for precisely anticipating the exact magnitude of the increase, based on an accurate forecast of emissions paths, goes too far. If anything the inability to anticipate emissions paths is pretty interesting (and quite consistent with efforts at forecasting emissions, see, e.g., Review of Global Energy and Carbon Dioxide Projections, B Keepin, Annual Review of Energy, November 1986, Vol. 11, Pages 357-392)

Is this analysis of Hansen’s prediction earth shattering? No. But I am glad to have sorted this out so I can better evaluate claims made in the political debate that reference this history.

Thanks!

June 1st, 2006 at 7:01 am

Tim Lambert-

Thanks for your comments. But we’ll simply have to agree to disagree when you write of Hansen’s paper, “his paper was not a prediction of the changes in each individual forcing.” It surely was according to hansen’s own words in the paper.

As far as the fraud issue, I wrote, “This analysis provides no support for anyone who would cherry pick one scenario over another to evaluate their accuracy.” So no disagreement there.

Thanks.

June 1st, 2006 at 8:43 am

All,

There is a lot being made of Pat Michaels’ 1998 testimony. For those interested in reading the testinony, it is available here ( http://www.cato.org/testimony/ct-pm072998.html ). You will see that the point that Pat was trying to make in that portion of his testimony was that climate models of the late 1980s and early-1990s simply were predicting more warming than had been observed. He selected Hansen’s Scenario A run (that Hansen termed “business as usual”) as an example, he just as well could have selected any other of a large number of model runs that would have proven his point. In fact, Pat later goes on to quote from the IPCC 1995 report that concludes the same thing–models run only with GHGs tended to overpredict observed warming. Again, that was the point that Pat was trying to make in that portion of his testimony–testimony he made 8 years ago. And that point, at the time, was by and large correct. This is hardly “news.”

-Chip

June 1st, 2006 at 9:19 am

Roger:

I would like to comment with regard to two of your posts above:

“Laurence- Hansen states very clearly in the 1988 paper that the annual increase he is using for B and C is linear, not exponential. Thanks.”

and the statement from the Hansen paper in question:

According to Hansen et al. 1988, p. 9361:

“In scenario B the growth of the annual increment of CO2 is reduced from 1.5% per year today to 1% per year in 1990, 0.5% per year in 2000, and 0 in 2010; thus after 2010 the annual increment in CO2 is constant, 1.9 ppmv per year.”

So, Roger, “growth of the annual increment of CO2″, specified as a “percentage per year” does NOT mean exponential growth of the increment?

What does it mean?

Hansen specifies the growth rates in percentages for BOTH scenarios A88 and B88, but those percentages somehow refer to something different for the two cases?

If “Annual growth rate” specified as a percentage does NOT mean exponential growth of the yearly increment for case B88 , perhaps you will be so kind as to explain what it DOES mean — including what it means with regard to total CO2 increase predicted by scenario B88 for the period 1990-2005.

Perhaps you will also be so kind as to lay out YOUR calculations of the ACTUAL CO2 increase over the period in question based on Hansen’s scenario B88 (as I did above, though mistakenly, as you claim).

If you can not perform such a detailed analysis because you DON’T know what Hansen is referring to with his growth rates in percentages, then, at a minimum, you certainly should not be implying that Hansen got the right answer fortuitously.

In order to say whether the increase in CO2 predicted by any one of Hansen’s scenarios deviates significantly from the actual increase over any given time period, it is NOT sufficinet merely to compare percentages as you have done.

You have to compare the predicted total increase to the actual total increase in atmospheric CO2 concentration (in ppm) over the time period in question — NOT just percentages.

I don’t know about anyone else, but I would certainly like to see YOUR detailed analysis of scenario B88: comparing predicted CO2 increase over the period in question using Hansen’s assumptions about CO2 growth with the ACTUAL CO2 increase over the same time period.

In fact, nothing less will convince me that your conclusions regarding Hansen’s 1988 paper are valid.

June 1st, 2006 at 10:37 am

Hansen’s paper does not describe scenario A as “business as usual” but as “on the high side of reality”. Scenarios A and C were intended to bracket the possibilities with B being the “most plausible”. Michaels committed scientific fraud when he pulled scenario A from the paper and presented it as Hansen’s forecast when it was no such thing.

If you want to look at what Hansen predicted in 1988 , I think you should look for the word “predict” in his paper. Here’s his prediction:

“that within the next several years the global temperature will reach and maintain a [0.4 degrees C] level of global warming, which is obviously significant.” The model predicted that would happen in 1998. In reality it happened in …. 1998.

June 1st, 2006 at 11:49 am

Laurence-

Thanks. From Hansen’s 1988 paper (which is unfortunately not online, but if you want to pursue this on your own, I’d suggest tracking down a copy – or if you send me an email with your mailing address we can send you a copy if it is not readily available), p. 9343:

“Scenario B has decreasing trace gas growth rates, such that the annual increase of the greenhouse climate forcing remains approximately constant at the present level.”

Thus to calculate CO2 emissions under Hansen’s Scenario B, for each period, I multiplied the base ppm times the growth rate and adding to the base. From his Figure 2, if the curve for CO2 deviates from linearity, I can’t tell by looking at it. In any case, assuming a constant growth rate errs on the side of making B88 more favorable (i.e., lower) to a comparison with actuals.

But you need not believe my analysis (I’d prefer that you confirm on your own;-). Even so, have a look at Hansen’s 1998 paper for his own calculation (through 1996) of what transpired vis-a-vis his scenarios — he arrives at the same result.

And if you really want to pursue this question, have a look at this paper which is online:

Hansen, J., and M. Sato 2004. Greenhouse gas growth rates. Proc. Natl. Acad. Sci. 101, 16109-16114, doi:10.1073/pnas.0406982101.

http://www.pnas.org/cgi/content/abstract/101/46/16109

In that paper he makes the interesting observation:

“Growth rates of climate forcings in the past several years have fallen below all IPCC (2001) scenarios (Fig. 4). Forcings for observations and scenarios are calculated with the same equations (table 1 in ref. 13), so the gap between the IPCC scenarios and observations is not an artifact of calculation uncertainties. Scenarios and observations include CO2, CH4, N2O, MPTGs, and OTGs, but they do not include tropospheric O3 and stratospheric H2O. If the latter gases were included, the gap between the alternative and IPCC scenarios would widen, because these gases decrease in the alternative scenario (due to decreasing CH4) but increase in IPCC scenarios.”

So the conclsuion that Hansen’s scenarios overshot is likely not going to be surprising to anyone who actually has expertise in this area (unlike me), and is clearly well understood by Hansen. It is however not a conclusion widely appreciated or understood.

Thanks.

June 1st, 2006 at 1:04 pm

So, if you have done the “analyis” of CO2 increases based on Hansen’s scenario B88, where is it?

Show it to us.

Where are the actual numbers that you came up with using Hansen’s Scenario B for the “yearly increments” (as Hansen calls them) for the years 1990-2005? (like those that i porvided above fo each year)

I can add them up myself to get the total if you like but show me all the increments, at the very least (and preferably, show us how you got them)

That’s not asking for much, given what you have claimed in your two posts about hansen’s paper.

All I have seen so far is a comparison of “growth rate” percentages and a few hand waving arguments involving quotatations and comments like “the graph ‘looks’ linear” (which slowly increasing exponentials do over a short time span, by the way)

You are right. I SHOULD pursue this elswhere. I am all done pursuing it here, at any rate.

June 1st, 2006 at 2:39 pm

By the way, one can use the Hansen statement that you provided above to place an ABSOLUTE UPPER LIMIT on the total increase in atmospheric CO2 concentration (in ppm) over the years 1990-2005 for his scenario B88

According to Hansen et al. 1988, p. 9361:

“In scenario B the growth of the annual increment of CO2 is reduced from 1.5% per year today to 1% per year in 1990, 0.5% per year in 2000, and 0 in 2010; thus after 2010 the annual increment in CO2 is constant, 1.9 ppmv per year.”

Under this scenario, CO2 increments are assumed to start from 1.5ppm, (which is the value he gives for scenario C and is also the value gotten by averaging over a few years bracketing 1990) and ramp up until 2010. After 2010, there is no further increase. In other words, the yearly increment is assumed to have reached its max value and stops increasing (set at 1.9ppm)

If one uses this MAX value 1.9ppm for the yearly CO2 increment for EVERY SINGLE year of the years between 1990 and 2005 (16 years), one gets a grand

total CO2 increase for 1990-2005 of

30.4ppm

30.4 – ACTAUL (27.3) = 3.1ppm

Thus, even using the MAX value (which clearly OVERESTIMATES the actual CO2 increase), you get a predicted result for CO2 increase under scenario B88 that is STILL MUCH CLOSER than what you get under scenario C88, a 15ppm (10year x1.5ppm/year) increase over the years 1990-1999 , zero therafter).

Actual – scenario C88 = 27.3 – 15 = 12.3ppm

In fact, even if one assumed that the increase of 1.5ppm under scenario C kept happening beyond 2000 (between 2000-2005, 6 years) WHICH WE KNOW IT DOES NOT, the predicted CO2 increase (in ppm) for scenarioC88 over the years

1990-2005 would be 24ppm.

ACTUAL – the latter artificial number = 27.3 – 24 = 3.3

3.3 > 3.1

In other words, even if I make the compeletely artifical (and most conservative) assumptions above (which I know are CERTAINLY NOT correct) it comes out better than scenario C88

Clearly, the OUTSIDE MAX scenario above significantly OVERESTIMATES the predicted increase under Hansen’s scenario B, since it assumes that the increment immediately jumps from 1.5ppm to 1.9ppm at the very begiining of the scenario run, when in actuality, it starts at 1.5 and ramps up between there and 1.9ppm.

Whether it ramps up in a linear or slowly growing exponential manner is completely irrelevant to my bracketing argument above.

The upshot:

Scenario B88 predicted CO2 emissions closer to reality than C88.

That’s it. I’m done.

June 1st, 2006 at 6:30 pm

Laurence- I want to acknowledge your posts and I will respond. A very sick 2 year old will take precedence over going through what you have written. A little more common courtesy on your end will be much appreciated. Thanks.

June 2nd, 2006 at 5:29 am

Roger, I am sorry about your sick two year old. I hope they get better soon.

With regard to three of your statements from your posts above (the last actually your attribution from the 88 Hansen paper for the scenario B88 indicating growth in “yearly increment”)

1) “Hansen states very clearly in the 1988 paper that the annual increase he is using for B and C is linear, not exponential.”

2) “Thus to calculate CO2 emissions under Hansen’s Scenario B, for each period, I multiplied the base ppm times the growth rate and adding to the base”

and the statement from the Hansen paper in question:“In scenario B the growth of the annual increment of CO2 is reduced from 1.5% per year today to 1% per year in 1990, 0.5% per year in 2000, and 0 in 2010; thus after 2010 the annual increment in CO2 is constant, 1.9 ppmv per year.”

3) According to Hansen et al. 1988, p. 9361:

I calculated what Hansen terms the “increment” in CO2 added to the atmosphere each year from 1990-2005 with these (YOUR) 3 assumptions.

For “base”, 1.5ppm was used

For each subsequent year of the years between 1990 and 1999, another 1% of 1.5ppm = 0.015ppm was added on.

For each subsequent year of the years between 2000 and 1999, another 0.5% of 1.5ppm = 0.0075ppm was added on.

Here’s what I got:

Hansen’s yearly “ncrement”

Under scenario B88

(“Linear” growth)

1990: 1.5ppm

1991: 1.515 (1.5 + 0.015)

1992: 1.530 (1.515 + 0.015)

1993: 1.545 etc

1994: 1.560

1995: 1.575

1996: 1.590

1997: 1.605

1998: 1.620

1999: 1.635

2000: 1.6425 (1.635 + 0.0075)

2001: 1.650 (1.6425 + 0.0075)

2002: 1.6575 etc

2003: 1.665

2004: 1.6725

2005: 1.680

Adding these up, you get a grand total increase in CO2 to the atmospheric concentration under Hansen’s B88 scenario from 1990 -2005 (end) of

25.64ppm

Again, the ACTUAL CO2 increase over the same was 27.3ppm

http://www.cmdl.noaa.gov/ccgg/trends/

ACTUAL – PREDICTED (under B88) = 27.3 – 25.64 = 1.66ppm

That’s the difference between Hansen’s scenario B88 and REALITY with regard to total CO2 increase over the period 1990-2005 using a “linear” increase for the yearly increment and Hansen’s growth schema (numbers 2 and 3 above).

Again, under scenario C88, the TOTAL increase in CO2 from 1990 – 2005 was 1.5ppm times 10 years = 15ppm (since CO2 increase CEASED after the end of 1999 — ie, 2000 and beyond)

ACTUAL – Predicted (C88) = 27.3 – 15 = 12.3ppm

So, under B88, the difference between ACTUAL and PREDICTED came out 1.66ppm

under C88, the difference between ACTUAL and PREDICTED came out 12.3ppm

CLEARLY B88 WAS CLOSER TO THE ACTUAL THAN C88

over the priod in question 1990-2005 (by 10.6ppm).

Note: If you had kept incrementing the C88 scenario by 1.5ppm for each of the years through 2005(Hansen assumed it ceased 2000 and beyond), you would come up with a total increase from 1990-2005 of 24ppm, which is 3.3ppm lower than the actual increase over that period (27.3)

The scenario B88 is STILL closer to the actual (by 3.3 – 1.61 = 1.64ppm) under the latter artificial assumption and BOTH are below the actual increase over that period.

///////////////

By the way, AS AN ASIDE, I reproduced my numbers (from my previous post above) for the “exponential growth in the yearly increment” assumption (again, using Hansen’s growth percentages of 1% between 1990 and 1999, and 0.5% between 2000 and 2005).

If you compare these year by year and the total (25.7ppm) with those obtained above for the “linear” growth assumption above (TOTAL 25.64PPM) , you will see that there is VERY LITTLE DIFFERENCE FROM THE LINEAR CASE ABOVE.

In fact, the total difference is just 25.7 – 25.64 = 0.06ppm (for the whole period from 1990-2005)

This should really come as no surprise, because the exponential is slow growing and we are talking about a relatively short time period. The exponential representing “growth in the yearly increment” is VERY NEARLY linear over this time span.

“increments” for each year from 1990-2005 (for Hansen’s scenario B88) using an “exponential growth in theyarly increment

Exponential growth in increment

1990: 1.5ppm

1991: 1.515 (1.5 x 1.01)

1992: 1.530 (1.515 x 1.01)

1993: 1.545 etc

1994: 1.560

1995: 1.576

1996: 1.591

1997: 1.607

1998: 1.623

1999: 1.640

2000: 1.648

2001: 1.656 (1.648 x 1.005)

2002: 1.665 (1.656 x 1.005)

2003: 1.673 etc

2004: 1.681

2005: 1.690

As I noted in my original post above, the total of the above increments (25.7ppm) is a tiny bit less than the more accurate number I got above ( 25.82ppm) by actually doing the integration.

June 2nd, 2006 at 6:10 am

Thanks Laurence (a better night last night for everyone!). Since I compared growth rates and not ppm directly, I will have to take some time to go through this this weekend. One obvious difference between what you have done, and what I have done, is the time frame as I only compared ABC88 to 2000 (not 2005) since C88 was frozen at that time. So even beofre going through the details, I am quite happy to accept your analysis through 2005 regarding B88 and C88 (see my conclusion #1 in the main post).

I will have to confirm what value Hansen used as the “base” — 1.5 ppm seems right, but I will confirm.

Also, more rapid increases in CO2 since 2000 may make a difference here as well. Give me a few days, I’ll catch up to you. Thanks.

June 2nd, 2006 at 2:12 pm

Roger:

To begin with, your statement “Since I compared growth rates and not ppm directly, I will have to take some time to go through this this weekend” REALLY gives me reason to pause.

Though I already wondered — in no uncertain terms on this blog — about the fact that you seemed to be comparing growth rates (instead of explicitly “comparing the ppm data” on this blog as I have done), I nonetheless had to ASSUME that you had actually “compared the ppm data” off-line and had simply not included it on your blog.

Now, I find that you have actually NOT “compared the ppm data directly”?!

How then could you feel confident in making a statement like the following?

“Any conclusion that Hansen’s 1988 prediction got things right, necessarily must conclude that it got things right for the wrong reasons.”

/////////

Having said that, I would next make a few comments about the “time interval” considered.

There is NO valid scientific reason NOT to consider the longer time interval in this case. Statistically speaking, more data points is better, particularly when we are talking about a relatively short time interval and when there is “scatter” in the measured yearly CO2 increments to begin with (and undoubtedly also in the total emissions and natural uptake of emissions from year to year).

Your comment that

“That scenario [C88] froze time in 2000″

is not an accurate characterization. Scenario C88 did not “freeze time”. It imposed a cut-off on emissions. From the scenario standpoint, there is a difference. Every Hansen graph I have seen (including the one you provided on your first post about this matter) comparing temperatures going forward for the three scenarios — and the actual temperatures has clearly shown scenario C88 data points beyond 2000.

You also continued:

“meaning that going forward there are two evolving scenarios which both have dramatically overestimated emissions. The lower of the two is thus “more accurate” than the other.

This conclusion is not warranted based on the data, as I showed above.

Such a statement that B88 “dramatically overestimated” emissions (including CO2 emissions) is simply not warranted as I showed above with the example for CO2.

B88 prediction of emissions was within 1.66ppm of the ACTUAL over 1990-2005.

If we assumed (quite artifically) that emissions did not CEASE after 1999 (as Hansen assumed) under scenario C88 and that the yearly increment of 1.5ppm per year continued, this “artifial C88″ scenario would STILL provide a less accurate predicter of total accumulated CO2 added to the atmosphere (ppm) than scenario B88.

You continued: “Neither is particularly accurate or realistic. Any conclusion that Hansen’s 1988 prediction got things right, necessarily must conclude that it got things right for the wrong reasons.”

THIS STATEMENT BY YOU IS REALLY THE CRUX OF YOUR ENTIRE POST and is simply UNWARRANTED — shown by the data that I have presented above.

On the contrary, Hansen’s B88 predictions about total CO2 increase were within 1.66ppm (6% of actual 27.3) for the period 1990-2005.

“2. With respect to Hansen’s 1998 predictions C98 has been the most accurate.”

I won’t comment on number 2 because I was restricting my attention to Hansen’s 88 paper.

“3. In two sets of predictions compared with experience, Jim Hansen’s predictions of emissions have proved to be overly aggressive both times with respect to rates of emissions with his lower estimate proving most accurate.”

This conclusion (covering both papers, the other of which I did not consider here) is NOT supported by the data — since it is not supported by the data for the B88 case (which showed the predicted accumulated total CO2 within 1.66ppm of actual for 1990-2005)

June 2nd, 2006 at 5:50 pm

Laurence-

Finally a free few moments … (and my toddler is on the upswing, thanks for the well wishes;-)

Total actual ppm growth in CO2 from 1989-2000 was 18.05, or an average of 1.504 per year.

http://www.cmdl.noaa.gov/ccgg/trends/

Hansen’s Scenario C88 fixed per year growth at 1.5 ppm. This is exactly what happened over this time period.

Your analysis starts with 1990 as the base year. I accept your point that linear vs. exponential growth does not matter on this time scale. However your analysis should properly start in 1988 as Hansen’s analysis actually did using the 1.5 ppm as the base growth rate.

So for 1989-2000, starting in 1988 with the annual CO2 increment at 1.5 ppm (growth of 1.5% in 1989 and 1% in 1990-2000) results in a total growth of 20.81 ppm, or a difference of 2.76 ppm from the actual amount of 18.05.

Thus my conclusion about the accuracy of C88 over B88 stands. Through 2000 Scenario C88 was more accurate than B88, whether measured by average growth rate or total PPM (they had better lead to the same conclusion!).

I have already stated that I accept your point that after 2000 B88 is more accurate than C88. We disagree however on how to interpret this, since C88 stopped the annual increase in CO2. I understand and respect that your perspective on this is different than mine. No worries.

I also will accept that different people can evaluate how significant the differences in the scenarios in different ways. Is a difference of 2.8 ppm between the scenarios over 12 years a big deal? This answer, in part, probably depends upon how one evaluates Hansen’s claims in 1988 that A88 was “business as usual” and B88 was “most likely”.

Bottom line to all this — when you factor in that Hansen himself has accepted that the total radiative forcing from the various gases (not just CO2) undershot his lowest scenario, I think it is quite fair for me to make the exact same point.

I hope that this clarifies my perspective, and I am willing to accept that in interpreting this we may agree to disagree. I appreciate the exchange and the chance to clarify my perspectives.

Thanks!

June 4th, 2006 at 9:58 am

Roger:

While I agree that the C88 scenario gives results closer to the actual for the first 12 years (I was never even arguing that point with you), the key issue is how the scenario performs over the longest haul.

In fact, given all inherent variability in natural processes (essentially randomness) even with perfect foreknowledge of future emissions and perfect modeling of all the processes, I would not expect ANY scenario to play out precisely, especially not over the first few years when a deviation in the yearly increment of just 1 or 2ppm can throw the actual path away from the predicted significantly. With a good scenario, this difference will “made up” over time.

The key question is the following: does the scenario converge (and stays converged on) the ACTUAL emissions development? Or does it only diverege or perhaps first converge and then diverge? (as C88 seems to do if you run it out to 2005).

It appears that you and I have a basic (probably unresolvable) disagreement about how to evaluate scenarios, but I would argue that letting the secnario run for the longest time period is the most reliable gage of its performance (and hence validity). This is a direct result of the cumulative nature of emissions. Every subsequent data point has all previous data points rolled up in it (in effect).

Finally, just let me note that I never intended to argue that Hansen’s scenario B88 got it exactly right.

In fact, I’d have to wait another 5 or ten years, during which time it too may start to diverge significantly from the actual (as a fraction of the total to date). Even 16 years is a relatively short time period for judging these things.

Specific coments with regard to your last post (iimediately above)

With regard to your characterization of the deviation between B88 and C88: I would merely note that the differences between B88 and C88 and between B88 and the ACTUAL accumulated CO2 over that period are NOT as large as they might seem based on what you provided.

1) The total you gave for actual CO2 was 18.05 (as you indicated for the years 1989-2000 inclusive). I have no argument with that.

http://www.cmdl.noaa.gov/ccgg/trends/

But the 20.81 you gave for B88 accumulated was for 13 (!) years (between 1988-2000(inclusive)).

I DO have an argument with using 13 years for the ACTUAL CO2 growth and 13 for the B88 scenario and then trying to compare the results!

It’s easy to see that the latter is for 13 years just by dividing 20.81 by 12 or a value of 1.73ppm, an AVERAGE value for the interval that is greater than the value you get (based on Hansen’s assumptions) at the the very end! I don’t think so.

You must use the same number of years (and time interval) for PREDICTED and ACTUAL if you are going to compare them, of course.

If you subtract 1.5, I come up with the CORRECT value of 19.31 for the total B88 growth in CO2 (over the period 1989-2000 inclusive). That’s for the same years over which ACTUAL CO2 growth was 18.05.

This means the deviation of B88 from ACTUAL is NOT 2.76ppm as you said, but instead 19.31-18.05= 1.26ppm (which amounts to 7% of the total CO2 (18.05ppm) growth for the period.

Is 7% a “drastic” over-prediction” as you implied in your original post??

I’ll let others decide that.

By the way, I calculated the average deviation as a fraction of the total for the first 12 years for each of the scenarios. I did it for two intervals after discovering the above “issue” with you analyis. I found that the result actually depended on starting point of the actual interval. For 1989-2000(inclusive), the average fractional deviation of B88 from ACTUAL was 0.224. For C88, it was 0.178. In that regard scenarios are with 4% of one another. For 1988-1999(inclusive), average for B88 was 0.128, (ie, within 13% of actual on average), for C88, it was 0.108. Again within 4%. The fact that the results are different for the two intervals again points to the problem with using an interval that is shorter than the maximum possible.

The most valid results from a scientific (ie, statistical) standpoint are obtained with the interval from 1988-2005(inclusive).

Roger, if you intended the interval to be 1988-2000(inclusive), you will have to add an additional 2.11 (for the actual CO2 growth in 1988) to that total to give 20.16ppm.

If you do that, however, your C88 value is no longer “dead on”. It’s off by .66 and the average is no longer 1.504 but 1.55. My point is not to say this makes a big difference (C88 is still within 3% of 20.16), but merely to point out that the fact that C88 gave precisely the right result over the period was basically a fluke of the beginning and ending points. Early on, the actual time interval makes its biggest difference. In fact, if one stopped at 1998, B88 results would be within 4% of the actual (and C88 would give about 2%.)

As one goes further out in time, the actual interval makes less and less difference – and it is best to use the ENTIRE interval 1988-2005 at any rate. Because of the cumulative nature of the emissions, going out further in time becomes a more accurate gage of the validity of a scenario.

If a scenario is very close in the first few years, that may actually NOT mean much. What is MOST important is whether it remains close as more years go by. In this regard – OVER THE LONGER PERIOD (AT THE END OF 2005) (which is the most important measure of a scenario’s performance), B88 IS performing better than C88 as I indicated (and you agreed, I think). It is very unlikely that a scenario would just HAPPEN to be right (by pure luck) after 15 or 16 years. In fact, that becomes less and less likely as time progresses. In effect, each time data point for accumulate CO2 to that point is comprised of all the points before it, so, as time moves on, data points become more and more heavily weighted with regard to judging a scenarios performance.

THIS IS THE ESSENTIAL GRIEVANCE I HAD WITH YOUR ORIGINAL (“ right answer for the wrong reason”) POST, Roger.

Though C88 is a little better than B88 in the early years, the fact is, B88 gets closer and to the ACTUAL as time progresses (it is within 5% of the total accumulated CO2 in 2005) which is precisely the behavior that one would expect from a scenario that was doing what it is supposed to do. One other hand, C88 starts to diverge (andin the later years, a rather large fractional divergence is even more significant becasue of all the data points averaged in), so that it deviates by about 11% in 2005, having reached its minimum deviation around 2000, which one would expect from a scenario that is NOT the most accurate.

These scenarios were meant to run over a LONG time period, not just a few short years.

As I indicate above, to gage the deviations from the actual at any given point in time, it is best to use a “fractional deviation”, since a 1ppm difference after 10 years means much less than a 1ppm difference after 1 year because of the cumulative nature of the beast. Actually, part of the reason that BOTH b88 and C88 deviate from the actual is that the ACTUAL values for the first 5 years deviated significantly from the 1.5 that was assumed to be the best starting value. So, right out of the gate, both scenarios were down by almost 2ppm and had to play catch up to make up the difference (which they did over time, as one would expect).

Because of the cumulative nature (and a certain amount of “random errors”, it is a little like flipping a fair coin.

Early on, you might get a “run” of heads (or tails) that makes the fractional deviation from 1/2 (heads vs tails) greater than you expect. But if the assumption about their being equally likley is corrrect, the fractional deviation will tend toward zero as time increases, even though the ACTUAL deviation (difference between number of heads and number of tails) does not.

The following table shows “Fractional deviation as a function of year” (deviation of the scenario prediction given as fraction of a total accumulated CO2 to that point)

I used two different intervals (1988-2005inclusive and 1989-2005, inclusive) – labeled (a) and (b) because of the issue I found above with Roger’s analysis and to illustrate how the starting year can affect the outcome (particularly early on)

In order to compare a scenario developing with constant yearly increase (like C88) to that of B88 in 2000 and beyond, I made an artificial assumption.

For scenario C, I assumed it continued to increase in 2000 and beyond (by 1.5ppm per year), — while Hansen set the increase to zero at the BEGINNING of 2000.

Look at Hansen’s graph of the emissions here:

http://scienceblogs.com/deltoid/2006/06/hansen_et_al_global_climate_ch.php#more

The CO2 increment CEASES on Jan 1, 2000!

In other words, there should be NO increase in the year 2000 (Roger!) and beyond for the C88 scenario, (though in the above analysis, I let Roger’s assumption that there was an increase for that year slide). Also, the interpretation that one should merely “stop considering C88 beyond 1999” is not the way Hansen intended it to be interpreted. He clearly showed data points and wished to illustrate how the model played out with no increase (ie, how natural mechanisms affected the CO2 that was already within th atmosphere). I’ll let the reader look at the paper and decide what they think he meant:

I will let the reader draw their OWN conclusions about which one is better over the longer haul but I would point out that the most important gage of a scenario’s accuracy and usefulness is precisely how closely it performs over the long run (as opposed to the short run).

1988-2005inclusive

Year B88(a) C88(a)

88 0.29 0.29

89 0.11 0.12

90 0.03 0.04

91 .08 .05

92 .25 .22

93 .25 .21

94 .17 .12

95 .10 .06

96 .13 .08

97 .09 .03

98 .0006 .06

99 .04 .02

00 .03 .03

01 .04 .03

02 .0025 .07

03 .02 .10

04 .02 .09

05 .04 .12

averageof fractional deviations:

B88 .128

C88 .108

1989-2005inclusive

Year B88(b) C88(b)

89 0.19 0.17

90 0.18 0.16

91 .29 .26

92 .54 .49

93 .45 .40

94 .29 .24

95 .19 .14

96 .21 .15

97 .15 .09

98 .04 .02

99 .09 .014

00 .07 .003

01 .07 .008

02 .02 .05

03 .007 .08

04 .0001 .08

05 .03 .11

averageof fractional deviations:

B88 .224

C88 .178

June 4th, 2006 at 10:10 am

Roger: There is a typo in the above:

My comment about a comaprison you made should read thus:

“I DO have an argument with using 12 years for the ACTUAL CO2 growth and 13 for the B88 scenario and then trying to compare the results!”

In other words, you used different time spans and then compared them (12 years for the ACTUAL and 13 for the scenario calculation)

June 4th, 2006 at 6:29 pm

One further note about the “average of fractional deviations” provided above after the tables.

I neglected to say that these are the averages for the periods 1989-2000(inclusive)

B88 .224

C88 .178

and 1988-1999(inclusive)

B88 .128

C88 .108

They are NOT the averages for the full periods ending 2005. The above averages were intended specifically to compare B88 and C88 over the shorter peiod that Roger had calculated things for.

You can see this by a previous comment above, but I should have made it clear below the data as well because it looked like it was an average over all the years.

Here’s the relevant cooment repeated:

“By the way, I calculated the average deviation as a fraction of the total for the first 12 years for each of the scenarios. I did it for two intervals after discovering the above “issue” with you analyis. I found that the result actually depended on starting point of the actual interval. For 1989-2000(inclusive), the average fractional deviation of B88 from ACTUAL was 0.224. For C88, it was 0.178. In that regard scenarios are with 4% of one another. For 1988-1999(inclusive), average for B88 was 0.128, (ie, within 13% of actual on average), for C88, it was 0.108. Again within 4%. The fact that the results are different for the two intervals again points to the problem with using an interval that is shorter than the maximum possible.”

June 4th, 2006 at 8:31 pm

Thanks Laurence, good catch regarding 13 years vs. 12 years, sorry about that — you are correct, but I don’t think that changes our disagreement which is more about interpreting the scenarios than the underlying data, which thanks to your efforts we have reconciled fully.

It would be interesting to calculate a “skill score” for each scenario, which if I ever have time might be worth doing.

Nonetheless, CO2 emissions are only part of the story here. The overprediction of CH4 and CFC emissions are dramatic. Adding these to the mix makes it difficult to claim, as Hansen’s did, that the real world has evolved like B88 (which is of course why he revised them in 1998! Had they be on target he would have not changed them.)

Thanks again for the exchange.

June 5th, 2006 at 9:12 am

Scenario A88 was a high end scenario so you should have noticed that something was wrong when you decided that the N2O estimate for A88 was lower than the other ones. You have misread his paper the 0.2% number you give for A88 is not the change in the emission rate, but the actual emission rate. For A88 the change in the emission rate was 3.5%, while B88 reduced this.

June 6th, 2006 at 11:40 am

Tim- Yes, re: N2O and A88 you are correct, thanks. A88 is even farther off that I initially concluded, that now seems obvious.

FYI, If you want your comments to appear you’ll have to register with TypeKey. Sorry about that, we’re working on alternative. Otherwise they will only appear if I stumble on them in the sea of spam as I did in this case.

Thanks.

June 7th, 2006 at 11:20 am

A university professor who goes by the alias “Eli Rabett” who bears some unknown personal grudge against me (but whose angry posts have stopped once we identified him and contacted him directly) has gone to some significant effort to evaluate Hansen’s 1988 scenarios (in response to these posts) that are of high quality and worth acknowledging.

Since he is a chemistry professor and has spent far more time on this than my back-of–the envelope calculations, so I am willing to defer to his expertise on this subject. Should he wish to emerge from anonymity, his substantial efforts are likely worth a peer-reviewed publication.

His more accurate conclusions on the data are quite similar to mine (though I anticipate he may find some differences on N2O) and those published by Hansen in 1998, namely (a) Hansen’s 1988 scenarios generally overshot actual emissions, and (b) some errors in projecting individual emissions rates may have cancelled out, thereby making the total forcing projected more accurate.

I fully appreciate that different people can interpret the significance of these data differently (what constitutes a predictive error?), and such different interpretations need not reflect malice, fraud, or ill-intent, but simply the fact that people can agree to disagree. Again to be clear, my post was not about Pat Michaels and should not be construed as a defense of him, Michaels’s decision to focus on Scenario A in Congressional testimony was a mistake. At the same time, it is also appropriate to conclude that Hansen’s claim that the real world has evolved most like Scenario B seems to be an overstretch.

On the various gases “Eli Rabett” concludes:

“It looks increasingly like Scenerio C from Hansen et al, is a much the best match (except for CO2 after 2000) to the actual greenhouse gas mixing ratios up till now. If you look at the prediction, there is not much difference between those for Scenerios B and C.”

You can see his thoughtful analysis here (with particularly useful information on CH4, he promises more info on N2O): http://rabett.blogspot.com/

He is welcome to resume commenting here under his own name and if he focused on substance and not insults or threats.

Thanks.