Hypothesis test for 2C/century:
now with Monte Carlo!
now with Monte Carlo!
Sometimes, a picture is worth a thousand words.
See the blue vertical line at 2 C/century? That’s the central tendency for trends projected by the IPCC in the AR4.
See the bell-shaped curve? That’s a spread of trends due to “weather noise” that we might expect if the “weather noise” is similar to that seen on earth since 2001. (Assumptions made are described below.
See the orange vertical line hear 0.3C/century? That’s the lower ±95% confidence interval. Based on the assumed distribution of weather noise, we’d expect fewer than 2.5% of 90 month trends fit using OLS to fall below 0.3 C/century.
See the vertical green line at -0.4 C/century? That’s the trend based on merged NOAA/HadCrut/GISS Land-Ocean data.
Diagnosis: Based on this analysis 2 C/century, the central tendency for the trend projected by the IPCC in the AR4, falsifies.
Some details: The distribution shown above was generated by running a simulation of a process in which the “monthly averaged weather noise” is AR(1), with a lag 1 autocorrelation of ρmonth = 0.5044 and variability σ=0.1039 C. The trend was assumed to be 2C/century– which matches the central tendency projected by the IPCC in the AR4.
If that process describes the climate, and weather noise, the observed trend of -0.4 C/century is a result that would happen in fewer than 1 out of 40 events. So, the assumption that the underlying trend is 2C/century falsifies to a confidence level of 95%.
Discussion
That’s the major news. Rather than write an organized narrative, I’ll just answer questions I assume people will ask. Here they are:
Why use only three sources? I usually merge data from these five sources:
GISS, HadCrut, NOAA/NCDC, UAH/MSU and RSS. However, it seems many who doubt the 2C/century is falsified based on comparison to data since 2001 think I should stick to data collected on the surface. So, I eliminated the satellite data from today’s merge. (I will include the others in posts later this month.)
Why not use Gavin’s suggestion of weather noise based on models? Because
b) the properties of that weather noise falsify when tested against monthly data,
c) I think observed real earth weather noise should generally be given precedence over “model” weather and finally
d) I will never use “weather noise” that has been shown inconsistent with real weather noise.
Why these specific properties for “weather noise”? These properties reproduce the standard deviation and lag 1 for residuals to the Ordinary Least Squares fit for the observation consisting of a merged of NOAA, HadCrut and GISS from Jan 2001-June 2008. (These are lag1 correlation of ρOLS=0.458 and sT=0.102.)
What’s the conclusion based on the Monte-Carlo? The observed weather falls well outside the 95% confidence intervals for trends that might occur if the true trend is 2 C/century, while the weather variability is described by observations of weather since 2001.
How does this compare to Cochrane-Orcutt and OLS using the Tamino Recommended method for error bars? The 95% uncertainty intervals using Monte-Carlo were ±1.68 C/century. The 95% uncertainty intervals using Cochrane-Orcutt and OLS were ±1.60 C/century and 1.76 C/century respectively. So, when OLS applies, C-O rejects 2C/century at 95% confidence a bit too often and OLS with Tamino-pumped up error bars doesn’t reject often enough. The fraction of errors for each method is about equal near ρ =0.5.
What was the conclusion based on CO and OLS? Both methods rejected the 2C/century trend, just as for the Monte-Carlo.
Any caveats?
Sure.
- While assumption of red noise does account for larger amounts of weather noise at low frequencies than does white noise, there is a possibility of even greater proportions at low frequencies. If so, methods assuming Red Noise (aka AR(1) ) under-estimate the uncertainty intervals. It is also possible the Red Noise assumes too much energy at lower frequencies. If so, it will over-estimate the size of uncertainty intervals. That said, even these generalities could flip around depending on the specific distribution of the feature of the “weather noise”.
JohnV is concerned about the impact of the solar cycle, and I believe he’s planning to look at that.
- I simulated the monthly averaged data as AR(1). If the underlying weather noise is AR(1), the lag-1 correlations for the data will deviate from AR(1) somewhat. The precise effect on the computed uncertainty intervals not entirely obvious to me. I think using averaged data will tend to over-estimate the uncertainty intervals for longer trends, but I’m not sure. I plan to look at this next month when I examine red noise.
- I have reason to believe the measurements may contain some errors.
If so, the analysis must be extended to include the possibility of these errors. The precise effect on the uncertainty intervals is also not obvious to me. I’ll be doing that next month (it’s easy; so this is not just a plan.)
Are you wondering about the individual results? I’ll post those later on!
Written by lucia.Comments
lucia
(Comment#4235)
July 17th, 2008 at 12:01 pm
Thanks Erik–
Bear in mind– Creating the graph does involve some assumptions about the data. But the assumptions don’t look too bad, and I’ll be doing a few things next month to overcome them.
Steve Geiger (Comment#4236)
July 17th, 2008 at 12:25 pm
Thanks for the interesting post. I appreciate the way you write up your posts and, as in this case, include the ‘likely’ arguments that will arise. I really wish there was more of this type of exchange thoughout climate blogdom.
George Tobin (Comment#4237)
July 17th, 2008 at 12:34 pm
A real analytical tour de force!! Thank you. It looks as if the IPCC are increasingly in the position of being right only if they also assert that the chaotic swings that characterize reality are large enough to completely conceal that which they say is really happening. We are right, but you will never be able to tell, so there!! I still think they will have to opt for bar chart graphs in 50-year blocks instead of line graphs to lucia-proof future projections. The Terminator: What year do the GSMs become self-aware and start looking for lucia…
The SkyNet funding bill is passed. The system goes online on August 4th, 1997. Human decisions are removed from strategic defense. SkyNet begins to learn at a geometric rate. It becomes self-aware at 2:14am Eastern time, August 29th. In a panic, they try to pull the plug.
Sarah Connor:
And, Skynet fights back.
Joseph
(Comment#4239)
July 17th, 2008 at 1:31 pm
What if it’s not weather noise in the conventional sense? Basically, what if the effects of weather noise you see in the historic record are not applicable to the last 10 years? I actually have some data that *may* back this up, and I’ll write about that on some other occasion, but here’s the hypothesis. It’s warmer than it should normally be given the long term temperature change trend (which I think is roughly 2C/century). When there’s imbalance, I’d suggest that local variability cannot cause the imbalance to be resolved any faster or slower (assuming the local variability ends before equilibrium is reached). Therefore, the trend gets corrected sooner or later. The way it’s corrected in this case is by a real reduction of the temperature change rate, which will last until we’re back on track.
Julian Flood
(Comment#4245)
July 17th, 2008 at 3:31 pm
Re comment 4329 Yes, but… If you look at the raw SST data from Hadcrut3 (without the dubious Folland and Parker correction), you’ll see two periods of warming, 1910 to 1940 and 1965 to 2000. The rate is .14 deg/decade. If Joseph is correct then a simple ruler and pencil will indicate when warming will recommence. Searching for “Original Caption: Folland and Parker [1995] Figure 3. Annual anomalies from a 1951-80 average of uncorrected SST (solid) and corrected NMAT (dashed) for (a) northern (b) southern hemisphere, 1856-1992. Only collocated 5 deg. x 5 deg. SST and NMAT values were used.” should find the graph. Drawing a line and extending it to give rate of .14deg/decade might have saved a lot of money spent on climate models — I wonder if it falsifies? More to the point, what might be the mechanism? After all, the consensus theory has an underlying theory, more CO2 = more warming. Wheels, bus… Speaking of wheels, there was a recent paper which made an effort to simplify the temperature record by chopping out the ENSO effects. That’s like chopping off a wheel from a car and declaring it a three-wheeler. JF
JohnV (Comment#4271)
July 18th, 2008 at 11:27 am
lucia, I’ve been working on my Matlab code for doing this type of analysis. I’m running some tests before doing anything new, but I’m having a little trouble reproducing these results. I suspect the difference is in the way we define the AR1 weather noise. My code is supposed to be doing this: Y(i) = m*X(i) + E(i) where, Does that match what you’re doing? I also have a quick question about your rho and sigma for the weather noise. I see two values for (rho, sigma) in the text: Thanks.
E(0) = rand(0)
E(i) = rho*E(i-1) + rand(i)
Y(i) is the temperature at sample i
X(i) is the time at sample i
m is the assumed underlying trend (m = 0.02C/year)
E(i) is the serially correlated weather noise at time i
rho is the lag-1 auto-correlation (rho = 0.5044)
rand(i) is a random variable with a normal distribution (mean=0, sd=0.1039)
(0.5044, 0.1039) and (0.458, 0.102). Which values were used?
lucia
(Comment#4272)
July 18th, 2008 at 11:59 am
John– <r> = ρ + (1 + 4* ρ)/N + terms of order 1/N^2 The “N” is the number of data points. the ρ is the value you use to generate the data and the <r> is what you expect to get. When I generate the random values, I wrote a code. I use: E(i) = ρ E(i-1) + sqrt(1- ρ^2) u(i) Where u(i) is gaussian with the standard deviation I need for the process. If you take square both sides and take the expected value, you’ll see this gives the correct variance. After creating the function, I ran it and checked that for zillions of numbers, I get the correct autocorrelation and variance. I also checked that my ‘us’ are normal. With matlab, is rand normal? If it’s not, you need to transform.
I use the higher set of values. When I run the OLS, it results in the lower values. This is a known result for fits to cases with finite values. When you use “N” data points, the expected value of the correlation is approximately
lucia
(Comment#4273)
July 18th, 2008 at 12:18 pm
If you do this: <E(i)E(i)> = rho^2*<E(i-1)E(i-1)> + <rand(i)rand(i)> And recognize that you want the variance of E to be steady, <E(i)E(i)> =<E(i-1)E(i-1)> =<EE> you’ll see your process ends up with (1-rho^2) <EE>= <rand(i)rand(i)> So, if your variance for <rand(i)rand(i)> = σ your variance for EE will be σ/(1-ρ^2) I assumed that Gavin means we want the process where the variance for E is If I interpret it this way, I reproduce his 8 year variance for OLS trends.
σ. That’s why I have that extra term.
JohnV (Comment#4275)
July 18th, 2008 at 1:01 pm
Thanks lucia. BTW, how do I get Greek letters in here?
I’m actually using Octave’s rndnorm() function which returns a random variable from a normal distribution.
The sigma scaling seems correct to me. I’ve implemented it and can now reproduce your results.
Now that the tools are ready I can start looking at other things…
Francois O (Comment#4276)
July 18th, 2008 at 1:04 pm
Lucia, This is great work as usual. The only question I have is about the use of that specific period. It’s not like we don’t have data for prior years. Of course there’s been little warming, or rather cooling, over the past 7 years, but what happens to all this if you take a longer period, say 1979-2008, or even 1959-2008 (so that it can be correlated, or not, with CO2 data)? I know you’ve discussed this in the past but I’m too lazy to go back to the earlier posts. The precise question is: what is the trend and confidence intervals, using the same method, but taken over a longer period. Does that give us a narrower range of possible trends? Is there overlap between the range of trends you find, and that found over a longer period? In the end, given that CO2 increases more or less exponentially, and that the assumed forcing is logarithmic, there should be a linear temperature trend associated with it, so it’s only fair to look for the linear component in temperature data. That’s not to say that that linear component is equal to the effect of CO2 (or GHG’s in their totality). Other possible forcings could contribute, positively or negatively, to that linear trend. You can end up doing like Scaffeta and West, and try to disentangle the possible forcings. I think in the end, if we have enough empirical data on both temperatures and CO2, we should be able to put upper and lower bounds on the climate “sensivity” based on empirical observations alone, ie. not models. Ideally, one should use ocean heat content, though. We don’t have much data for this, but maybe your method could nevertheless give a similar range of sensitivities based on these data. All this would, in the end, help advance the debate, and our knowledge in general.
MarkR (Comment#4277)
July 18th, 2008 at 1:18 pm
Lucia. Excellent. More questions. What is the the chance that the 8 year temperature observation correlates with the observed rise in CO2 for the period? Also, is nothing to be made of the apparent fact that the merged temperature record for the last eight years actually shows a decline? Is it really the case that the allegedly overwhelming force of CO2 in driving planetary temerature has in turn been temporarily overwhelmed for the last 8 years by some other currently mysterious, but more powerful force of nature? How are “Weather” and “Noise”, both presumably random, creating a discernable long term downward trend?
MarkR (Comment#4278)
July 18th, 2008 at 1:20 pm
oops. I see Monckton has been addressing some of these issues: http://scienceandpublicpolicy......risis.html
lucia
(Comment#4284)
July 18th, 2008 at 2:47 pm
MarkR– This flatness doesn’t disprove the theory that CO2 causes warming.
The 8 year flat trend is not inconsistent with warming. It’s just not consistent with 2C/century right now. Weather does exist, and does cause variations.
lucia
(Comment#4286)
July 18th, 2008 at 2:57 pm
JohnV– BTW, although I convinced myself it doesn’t matter how I initiallize the red-noise for current purposes, I nevertheless initialize with white noise with the appropriate standard deviation. (If you subtract in the equation, it shouldn’t matter when generating data for curve fitting. But I decided: Why risk it? Looking at the 11 year solar would be good. I find I can only add one complication at a time, and I picked adding white noise first. Adding a periodic spike at different places was going to be later. (I was thinking add an “Enso Spike” at 4 years, and 11 year bulge etc. The problem we will always have with the 11 year solar effect is that many people simply don’t believe it exists. Others, of course, believe violently in it. But, it’s definitely work looking at.
Good. )
lucia
(Comment#4288)
July 18th, 2008 at 2:58 pm
Francois– First– yes. I can repeat the same thing for more years. I plan to. I anticipate getting qualitatively similar results to what I get with OLS or Cochrane-Orcutt. The uncertainty bands for the trends will generally all overlap. I spoke to someone today. I’m thinking about ocean data.
Excellent question.
John F. Pittman (Comment#4294)
July 18th, 2008 at 5:12 pm
Lucia, I wonder if you can expand on MarkR’s comment “What is the the chance that the 8 year temperature observation correlates with the observed rise in CO2 for the period?” with respect to your weather noise as indicated in the actual weather noise you have been using. Your assumption(s) as is, etc. The question is that IPCC indicates an approximate value of 2.5C per doubling of CO2. The math is .2C per eight years. I would like to keep it at this valuse since this is the value that is responsible for the claim we need to mitigate rather than adapt. If you repeat your analysis substituting the predicted increase to temperature due to this assumption, and use your weather variation, can the 8 year trend be shown to invalidate the IPCC claim at 5%, 50%, or 95%? The answer is not trivial. The section on mitigation versus adaptation relies on this. If I remember correctly, the push for mitigation over adaptation depends on the result being 2.5+1.5, no -1.5. At 1C per doubling, adaptation would take precedence. We would have weather noise variation, the 0.2C per eight years tested against the actual fractional amount of doubling. I believe it was http://wmbriggs.com/ had a great post showing the linear trend of CO2 by month of year to get rid of oscillating wave.
Francois O (Comment#4296)
July 18th, 2008 at 6:50 pm
Lucia, “I spoke to someone today.” Is that a rare event? Maybe the blog takes a little bit too much of your time?…
John F. Pittman (Comment#4302)
July 19th, 2008 at 6:25 am
Lucia, using data from wmbriggs to estimate CO2, and IPCC 2.5+-1.5, I get that the 1Cx2CO2 sensitivity to end of June 08 is +0.058C, the 2.5C 2x is +.145C, the 4.5C 2x is +.232C, assuming that Jan 1 2000 is 0.0C. I have put it in monthly format. I use the average rather than the sinsoidal actual curve. To get .2C/decade one would have to use 2.87, rather than 2.5C for 2x, assuming a steady ln rise from 2000 to 2007 CO2 data. Perhaps .2C assumes an increasing ln rise, such that the average over the time span is .2C/decade.
lucia
(Comment#4303)
July 19th, 2008 at 7:14 am
John and Mark–
The difficulty with doing the statistical test you propose is that according to the IPCC, models, and even simple theories, the earth’s climate is not supposed to be in quasi-equilibrium. The temperature is supposed to lag the response to CO2. So, I can’t just compute the correlation for the past decade or so, show there isn’t any, and decree there is no connection. The response by those who believe there is a connection (which includes me) is to explain the theory associated with the phrase “It’s in the pipeline”.
John F. Pittman (Comment#4304)
July 19th, 2008 at 7:27 am
Lucia, since the IPCC has claimed that the last part of the 20th century was due to climate forcing, just how long, and I would wonder what proof of such an extent, is this pipeline? As a self consistancy check, could you not assume that the stuff in the pipeline is approximately the same as the stuff we are recieving that was in the pipeline, and rule this pipeline stuff out as being a relevant factor?. If it is unquantifiable, or such a small difference that it can be essientally eliminated, and we are trying to quantify something, shouldn’t it be left out?
MarkR (Comment#4312)
July 19th, 2008 at 2:25 pm
Does the current 8 year period of temperature rise correlate with any previous eight year period? What is the pipeline period specified by the IPCC, the Models, or any “Simple Theory”? Surely the “pipeline period should be subject to test and verification?
Roger Pielke. Jr. (Comment#4319)
July 19th, 2008 at 5:40 pm
Lucia- Great stuff, clearly explained. You really out to write this up for publication. Of course, another “framing” of your graph is that the observed (green line) is “consistent with” 0.2 deg C/decade since it falls somewhere within the bell curve . . . 
Ninety Month Trends: IPCC AR4 2C/Century still outside ±95% uncertainty bands. | The Blackboard
(Pingback#4331)
July 20th, 2008 at 6:47 am
[...] I do, and I think that makes the model… Hypothesis test for … [...]
jc (Comment#4532)
July 29th, 2008 at 4:37 pm
Lucia, I can’t even call myself a rank amateur at this stuff, so please pardon me if this is a stupid question. I was reading elsewhere about the concept of kurtosis and I tried to imagine how it would apply to your analysis. Could you explain what would happen to your analysis if weather noise were distributed in a more extreme manner? Do you have any comments about why, or why not, you believe a more extreme distribution could be applicable to the discussion at hand? Also, were a more extreme distribution to have any validity, would that extend the length of time required to falsify within the confidence interval? Thanks for your work. I am learning a lot from you.
lucia
(Comment#4534)
July 29th, 2008 at 5:41 pm
Jc– Asking about Kurtosis is not stupid. It’s actually rather sophisticated. I’ll write something up about that later this week. In fact, I’ll address the whole question. As a general issue: The larger the variability, the more data we need to obtain a precise estimate of any mean variable. This includes the current trend.
jc (Comment#5053)
August 14th, 2008 at 9:33 pm
Lucia, just a reminder (OK, I admit it — I’m a nag) I know you have been really busy with more important things, but I am really looking forward to your discussion of kurtosis. If I missed it, please direct me to the right place. Thanks again.
bender (Comment#5059)
August 15th, 2008 at 9:46 am
How well known are the statistical properties of 1/f noise? This model is so universal it would be quite easy to justify in a published work. Gavin’s suggestion to use a GCM-based noise model is, umm, self-serving - to say the least. He readily admits that we know so little about the ocean’s state that we can not specify its state as part of the initial conditions of a typical model run. So they use random initial conditions. THAT is how ignorant we are about how the ocean functions. And THAT is the justification for a 1/f noise model. 1/f is going to blow those envelopes wide open and show that just about anything is consistent with the IPCC projection. i.e. You could not imagine a weaker hypothesis test.
Jeff (Comment#5099)
August 17th, 2008 at 11:36 am
The period 2001-2008 was marked by a general decline in solar activity, which in the absence of other factors should lead to cooler temperatures. What was the motivation for picking that particular time period?
lucia
(Comment#5100)
August 17th, 2008 at 12:26 pm
Jeff– The AR4 was published in 2007, so in some sense, one might want to start then. But, various key documents were published in 2001. In particular, the TAR was published in 2001, making any the choice of any date prior to 2001 clearly a hindcast. Model runs prior to that would have been included in the TAR. So, the choice was 2001. Jan 2001 just happened to be intermediate between a low in 2000 and a high in 2002. So, it gives somewhat intermediate slopes compared to other choices. I do, from time to time, publish “bar and whiskers” graphs showing the sorts of difference we’d get if we picked other “first years”. The dates chosen are all based on publication dates of IPCC documents.
The selelction of the time frame was discussed at length way back in February or so. But, basically, to test a “prediction/projection”, I wanted to use data that actually represents prediction, not a hindcast.
bob (Comment#6894)
November 23rd, 2008 at 2:44 am
” In the pipeline “. The radiation reemitted by CO2 is around 15 microns. At this wavelength the absorption coefficient is 5000(cm -1). Therefore virtually all the CO2 induced energy is reflected off the oceans back into space as a significant negative feedback. How can there be CO2 induced energy in the pipeline when it can`t get into the oceans by radiation( too opaque ), conduction ( too slow ), or by convection (too small an absorption layer).
bob (Comment#6895)
November 23rd, 2008 at 3:47 am
Sorry last post should have read ” At this wavelength the absorption coefficient of water is 5000 ( cm -1).
lucia
(Comment#6896)
November 23rd, 2008 at 8:07 am
Bob– If GHG’s do add insulation to prevent heat escaping, eventually, the heat will be convected down to the lower ocean. The surface will then be a bit warmer because it won’t be able to lose heat to both the ocean and the stratosphere.
“In the pipeline” is an odd term. It means that the insulation has been put in place and the temperature of the planet has yet to respond. So, it actually describes the “too slow” issue.
DeWitt Payne (Comment#6900)
November 23rd, 2008 at 1:22 pm
bob (Comment#6894) November 23rd, 2008 at 2:44 am , It’s solar radiation absorbed by the oceans and not emitted back to space that is the heat supposed to be “in the pipeline”. That’s why it is so important to get a good measure of the ocean heat content. Any change in the heat content is a direct measure of radiative imbalance between incoming solar and outgoing thermal radiation in near real time.
bob (Comment#6922)
November 26th, 2008 at 3:08 am
Lucia The IPCC position is that a doubling of CO2 will add aprox. 3.5w/m2 to the earth`s energy balance. They say that with positive feedbacks this will produce a likely temp. increase of 3.0C. The radiative forcings graph in the 4AR shows anthropogenic CO2, CH4, N2O and halocarbons to have added 2.64w/m2 to the earth`s energy balance in 2005. By simple ratios we should be 2.3C hotter today than we would otherwise have been. This is clearly not the case. The reasons given by the IPCC for this discrepancy are that the oceans have absorbed the extra energy as radiation and will release it to the atmosphere later, and that aerosols have artificially cooled the planet. The aerosol effect, I believe, has been debunked due to it being local and none of the data seems to support it. As for the oceans, all of the gases mentioned release energy at a wavelength that cannot penetrate water. Most of this energy (99.99%) is then reflected off the ocean back to space through the IR windows. This is a major negative feedback that has not been mentioned by the IPCC and is not included in their models. If the ocean lag cannot possibly be right and the aerosol idea doesn`t stack up then nearly all the extra energy from the anthropogenic GHGs should show up almost immediately in the temperature record. If we say that the temp. increase due to GHGs is aprox. 0.3C from the 2.64w/m2 already in the system then we should be able to say that a doubling of CO2 (3.5w/m2) will only increase the temp. by 0.4C proving that negative feedbacks prevail. Your hypothesis test for 2C/century appears to be supported.
Perhaps you can help me. The following has always puzzled me about the global warming debate.
The IPCC appear to be out by a factor of 10. Is this possible.
lucia
(Comment#6927)
November 26th, 2008 at 7:30 am
By simple ratios we should be 2.3C hotter today than we would otherwise have been. This is clearly not the case. You can’t use simple ratios because those are based on the assumption of pseudo-equilibrium. We aren’t at pseudo-equilibrium. The reasons given by the IPCC for this discrepancy are that the oceans have absorbed the extra energy as radiation and will release it to the atmosphere later.. . At any time, the difference between the turkey temperature and the oven temperature would be what the IPCC calls “heat in the pipeline”. I doubt the IPCC is off by a factor of 10. The difference between the current trend and the 2C/century is at least partly weather noise. But, the difference does appear statistically significant. I think it possible the ABC (Asian Brown Cloud) may not be properly counted in the SRES. Other things are also possible. Statistical tests don’t automatically provide information on attribution.
I don’t think this is the reason the IPCC gives for the discrepancy. The reason is that for systems with high heat capacity — like the ocean– there is a thermal lag.
The analogy is your Thanksgiving turkey. When you put it in a 350F oven, the turky warms up over time. If you left the oven at 350 F and left your turkey in the oven, it would eventually reach 350F.
DeWitt Payne (Comment#6928)
November 26th, 2008 at 11:38 am
lucia (Comment#6927) November 26th, 2008 at 7:30 am , Assume you didn’t have a thermostat in the oven which starts at room temperature. Apply a current to the heating coils sufficient to sustain the oven at a temperature of 350 F at equilibrium. An empty oven heats up fairly quickly. Put a turkey in the oven and it heats up much more slowly. But the total energy balance remains the same if you include the heat content of the turkey. bob (Comment#6922) November 26th, 2008 at 3:08 am , As for the oceans, all of the gases mentioned release energy at a wavelength that cannot penetrate water. Most of this energy (99.99%) is then reflected off the ocean back to space through the IR windows. This is a major negative feedback that has not been mentioned by the IPCC and is not included in their models. Your understanding of the physics of IR radiation absorption/emission is incorrect. For one thing, the neither the CO2 band at 15 micrometers nor the vast majority of the water vapor emission is in the atmospheric IR window. Only methane and ozone have strong bands in the window. You’re wrong about the IR not being absorbed as well. It is absorbed, but the penetration depth is small, on the order of microns, but that doesn’t mean that heat cannot be transferred to and from the surface to the rest of the water. Moreover, only a small fraction of the IR emitted from the surface of the ocean is in the wavelength band of the atmospheric IR window from about 8 to 12 micrometers so greenhouse theory applies to the ocean just as it applies to the rest of the planet, at least the radiation transfer part anyway.
bob (Comment#6946)
November 27th, 2008 at 3:40 pm
Lucia In other words as far as CO2 is concerned pseudo equalibrium is reached very quickly. If your saying that the ocean warms by conduction from the atmosphere then this would have a damping effect on air temp. It would mean energy was permanently lost from the atmosphere and we, therefore, wouldn`t have to worry about it. DeWitt Here is a quote from Douglas Hoyt http://www.warwickhughes.com/hoyt/scorecard.htm ” It is worth mentioning for A=5000 cm at 15 microns, the implied water emissivity is 0.9998 implying that of the incident radiation only 0.02% of it will be absorbed. The emitted radiation will closely follow a blackbody emission curve where as the incident flux from CO2 is confined to a band centred at 15 microns. The implication of this is that much of the radiation emitted will escape directly to space through the IR windows, so it is a negative feedback.”
If the turkey reflects nearly all of the energy (99.99%) from the oven elements then the turkey would heat up so slowly that the actual oven air temp. would be a good indicator of the amount of energy in the system. True, the turkey would heat up eventually but so slowly that a ratio would be an effective way of relating oven air temp. to energy.
I believe that oceans reemit as a blackbody and most of this does go through the IR windows to space.
lucia
(Comment#6947)
November 27th, 2008 at 6:39 pm
bob– If your saying that the ocean warms by conduction from the atmosphere then this would have a damping effect on air temp. It would mean energy was permanently lost from the atmosphere and we, therefore, wouldn`t have to worry about it. If, for some reason, we start with climate system that is “cold” and then begin to add heat to the upper elements (say the atmosphere and upper ocean, then the currently cold lower ocean warms by convection with the upper ocean. This does take heat from the upper layers (i.e. upper ocean and air.) So, yes, this cools the upper air. However, eventually, the lower ocean is warm. Then it no longer sucks up heat from the air, and the air temperature will end up a bit warrm. Energy is never permanently lost from anything. The general physics of this process are the same if we map “outer layers of turkey” to “atmosphere” and “the stuffing” to the ocean. During periods when the stuffing is cool, it acts as a heat sink for the outer parts of the turkey. If you stuffed the center with ice, it would take your turkey longer to cook. (You’d also have a very bad turkey day.)
DeWitt Payne (Comment#6967)
November 29th, 2008 at 2:41 pm
bob (Comment#6946) November 27th, 2008 at 3:40 pm , It is worth mentioning for A=5000 cm at 15 microns, the implied water emissivity is 0.9998 implying that of the incident radiation only 0.02% of it will be absorbed. No. Kirchhoff’s Law applies here which means that emissivity = absorptivity so only 0.02% of the incident radiation isn’t absorbed. I suggest you go to the Archer MODTRAN site and generate and look at some calculated surface and atmospheric emission spectra. Then you will see that the atmospheric IR window covers much less than half the spectra and in the end only about 10% of the radiation emitted from the surface, on average, escapes directly to space, more at high latitudes and less in the tropics. Note that the spectra are in wavenumbers (cm-1) rather than in wavelength so the CO2 emission band is centered at 667 cm-1 and the atmospheric window is at about 800 to 1300 cm-1.
Douglas Hoyt (Comment#6969)
November 29th, 2008 at 6:57 pm
See http://www.warwickhughes.com/blog/?p=87 , particularly comment 42, for my views on warming of the oceans by increased 15 micron radiation. Major points:
1. The 15 micron is absorbed in the upper 15 microns of the oceans.
2. This layer is cooler than the water below it, so it cannot be heating the bulk of the ocean by conduction (very slow), convection (suppressed), or radiation (opaque).
3. The extra 15 micron radiation will be re-radiated upwards and over all infreared wavelengths with a blackbody spectrum so that about 40% will escape directly to space. This can be viewed as a neglected negative feedback.
4. Compo (2008) has shown that the net flow of heat in recent years has been out of the ocean, not into it.
bob (Comment#6970)
November 30th, 2008 at 3:11 am
Lucia I agree the damping effect will be reduced over time but the oceans will still have a damping effect. This and the slowness of conduction from the atmosphere to the ocean means that the air temp. will be a good measure of the amount of energy CO2 puts into the system. The oven has to get hot before the turkey starts to cook and this will show up in the temp. of the air in the oven. If virtually zero CO2 reemitted radiation enters the ocean and conduction is too slow and doesn`t matter anyway then the GHG induced 2.64w/m2 already in the system should have showed up as a temp. increase of aprox. 2.3C fairly quickly. It hasn`t, therefore, there is something desparately wrong with the IPCC`s prediction of 3C warming from 3.5w/m2. DeWitt I apologise for a mistake in my last post that may have misled you. ” It is worth mentioning for A=5000cm at 15 microns…” should have read ” A=5000cm-1 “. This means only a very small amount of radiated energy from CO2 is absorbed by the oceans. It doesn`t really matter to the arguement how much of the reflected radiation makes it to space. The point is that none of the energy reemitted by CO2 enters the ocean and therefore should show up almost immediately in the air temp. record. There is virtually nothing in the pipeline. The absorption coefficient of visible light averages 10^-3 cm^-1 and therefore penetrates water to a depth of aprox. 10 metres. the oceans are almost entirely warmed by solar radiation. The IPCC (chapter 9.6 AR4) tries to quantify ocean lags from CO2 induced radiation by referring to history. Historical temp. lags are almost entirely due to solar radiation penetrating deep into the ocean and are completely different to energy reemitted by CO2.
DeWitt Payne (Comment#6971)
November 30th, 2008 at 8:52 am
bob (Comment#6970) November 30th, 2008 at 3:11 am , You clearly do not understand the physics behind the greenhouse effect. Solar energy is absorbed by the atmosphere, the ocean and the land, ~235 W/m2 on average. That energy is then, at equilibrium, radiated back to the atmosphere and eventually to space at longer wavelengths. Because the atmosphere contains molecules that absorb and emit in the thermal IR region, the surface must be warmer than the Stefan-Boltzmann equation would predict from the amount of incident solar radiation absorbed so that total energy balances at the surface. See the Kiehl and Trenberth paper for example. Increased CO2 causes less radiation to be emitted to space from the upper atmosphere at constant temperature (see the Archer link above). You can see the dip from the CO2 band in both calculated and observed IR spectra and the integrated emission drops when CO2 is increased. The surface and the atmosphere above it must then warm so that energy balance is again achieved. There is no neglected negative feedback from CO2 emission to the surface from the atmosphere as that is strictly a function of atmospheric temperature and is fully accounted for in the energy balance numbers. Unless the relative humidity is 100%, the surface of the ocean will always be cooler than the water just below the surface because of evaporation. This energy loss is also included in the energy balance numbers as sensible and latent heat transfer from the surface to the atmosphere. While I would like to believe the Argos numbers for ocean heat content, they haven’t been collecting data long enough and are still controversial. It took quite a few years to find all the major systematic errors in the satellite MSU data reduction process, for example. They are also irrelevant to the radiation transfer physics. If they are correct, they do imply that the GCM’s are wrong. But it won’t be the radiation transfer calculations, it will be how the GCM’s account for the effects of clouds, moist convection, aerosols or some other mechanism. Since even the IPCC admits that clouds, etc. are poorly understood, trying to attack the warmers on radiation transfer is worse than pointless because it just gives rational skeptics a bad reputation.
lucia
(Comment#6972)
November 30th, 2008 at 9:00 am
Dewitt–
Looks like we pretty much see eye to eye on this. The radiation physics is solid. All other things being equal, CO2 must have a warming effect, and it happens in the way you describe.
DeWitt Payne (Comment#6974)
November 30th, 2008 at 9:33 am
lucia, Thanks. It took me a while to get to where I understood how the whole radiation transfer thing worked. I did leave out another key to the greenhouse effect, the decrease in temperature with altitude. In an isothermal atmosphere, there would be no greenhouse effect, or at least it would be a whole lot smaller. I don’t think an isothermal atmosphere that can emit in the thermal IR is stable, though. The top layer would be emitting more than it received from below so it would have to cool and that cooling would then propagate downwards. I keep meaning to try to calculate this effect with a layered atmosphere model, but you can’t use a simple gray atmosphere and you do have to include water vapor mixing ratios. Messy.
lucia
(Comment#6975)
November 30th, 2008 at 9:44 am
DeWitt– (BTW. I’m pretty sure when some people incorrectly claim GCM’s assume constant humidity, it’s rooted in some past simplified non-GCM approaches where the types of models in Chapter 4 of H-S&M assumed constant relative humidity when trying to estimate feed backs. Estimates based on simplified models are totally respectable in all fields as they give a level of insight about the physics. Of course, they are estimates, but … that’s not a defect as long as one admits it’s an estimate. )
“A Climate Model Primer” by Henderson-Sellers & McGuffie” does a pretty decent job of discussing modeling concepts. The issue you are contemplating is in Chapter 4 “Radiative-Convective Models”. It’s worth getting from the library.
John Lang (Comment#6976)
November 30th, 2008 at 10:22 am
The issue I have with the warming in the pipeline explanation (and the turkey analogy is a good one) is there is no detail on how long it will really take. Hansen has said it will take 25 to 75 years to reach 60% equilibrium based on the ocean uptake in surface layers but then how long will the remaining 40% take. His 1988 temperature predictions apparently did not take this influence into account. I note we are getting farther and farther away from the expected 3.0C per doubling trendline as time goes on. If there is not an uptick in temperatures in the next 5 years or so, the warming in the pipeline timeline will have to be extended out to perhaps over 100 years (maybe more). While we might still reach the 3.0C doubling (and it is starting to look more and more debatable whether that will occurr), the modelers need to start being more specific with the public about the timelines expected here. Hansen says we will be “committed” to the doubling temperature response when we get to the doubling level but if there is another 100 years or 200 years before temps do reach those levels, there is obviously more time for solutions. Maybe they have figured out the timelines but don’t want to be more specific since this might create less urgency to the issue.
lucia
(Comment#6977)
November 30th, 2008 at 10:51 am
John– The issue of “in the pipeline” is discussed in the IPCC report. One of the ways is by illustrating what will happen if the level of GHG’s is frozen at the current level. The IPCC just don’t use the term “in the pipeline”. I don’t know who introduced the “in the pipeline” term. Each GCM model models has a slightly different parameterizations which results in somewhat different time constant. So each model would predict different amounts of heat “in the pipeline”.
I think Hansen’s 1988 calculations had a swamp ocean. If so, the computation should account for “in the pipeline”. The question is: Does it account for it correctly?
DeWitt Payne (Comment#6981)
November 30th, 2008 at 8:17 pm
lucia, I live in the hills of East Tennessee so I didn’t even bother to look in the local library. Based on your recommendation and the excerpt and table of contents I read on Amazon, I’m buying the paperback edition. It didn’t cost that much more than the Tomb Raider Underworld PC game I just bought.
bob (Comment#7023)
December 2nd, 2008 at 4:47 pm
Dewitt I`m not interested in which negative feedbacks the IPCC has missed other than to say they must have missed some. I agree with you that solar energy is radiated back off the earth at longer wavelengths with much of this being absorbed by CO2 and other gases creating a greenhouse effect. I agree with you that extra energy at around 15 microns will excite the major bonds of the manmade CO2 molecules in the atmosphere and cause those molecules to vibrate. This vibration should be and is measured as a higher temp. in the atmosphere (aprox 0.3C to date). This vibration will cause an insignificant amount of energy to be slowly transferred from the atmosphere to the ocean by conduction.(remember, if aerosols are asumed to have negligable effect, the IPCC implies that 80% of the energy trapped by extra manmade CO2 finds it`s way into the ocean). This is where your`s and the IPCC`s narative stops and where what I`m trying to say begins. You`ve stopped too early. After a short time the excited manmade CO2 molecules, mentioned above, stabilize. As they stabilize they reemit radiation in all directions at the same 15 micron wavelength. A large percentage of this radiation hits the ocean, and 99.99% of this is reflected as a blackbody back to the atmosphere and space. Virtually none of this energy is absorbed by the ocean. Water acts like a very efficient mirror at this wavelength as it has an absorption coefficient of 5000 cm^-1 at this wavelength. I believe the IPCC wrongly treats this reemitted 15 micron radiation the same way they treat solar radiation which has an absorption depth of 10 metres or more. They use historical data (solar) to calculate equilibrium temps. caused by manmade CO2.(AR4 9.6.3.2). Douglass Hoyt is well respected in this field and his link at post #6969 suports me. There is virtually no manmade CO2 induced energy in the pipeline. The question I`ve been trying to ask, although badly, and you need to answer is this; If conduction is too slow and radiation at 15 microns is almost totally repelled by water, by what mechanism do you propose the energy trapped by manmade CO2 gets transferred to the oceans to be stored and later released to the atmosphere?
I agree and have always understood and agreed with everything you say in your post ( #6971).I feel that you have replied to my posts without actually reading them or more likely, I didn`t make myself understood well enough.
DeWitt Payne (Comment#7035)
December 2nd, 2008 at 11:16 pm
bob (Comment#7023) December 2nd, 2008 at 4:47 pm , I read your posts. Your understanding of the physics is still incorrect. I’ll try a different approach. Look at it this way, the surface warms the atmosphere, not the other way around. In fact, the atmosphere can’t, on average, warm the surface because it’s colder and heat flows from warm to cold. Heat flows from the sun to the atmosphere and surface, whether land or ocean. Note that your argument applies to the land surface as well as the ocean. An increase in a ghg does not warm the surface by first increasing IR emission. CO2 absorption is saturated, i.e. the absorptivity (and emissivity by Kirchhoff’s Law) are 1 to a good approximation over the band centered at about 15 micrometers. Emission from the atmosphere to the surface can not increase in the center of the band simply with increased concentration because it’s already emitting at the Planck curve limiting rate, which is a function of only temperature and wavelength (or frequency), not concentration. Emission from the wings of the band could in principle increase, but that doesn’t amount to much at the bottom of the atmosphere because of overlap with water vapor. Emission at the top of the atmosphere can, however, decrease significantly with increasing CO2 concentration because the CO2 emission to space is from CO2 molecules that are at high altitude where the optical density finally becomes low enough that the probability of emission to space exceeds the probability of absorption by a CO2 molecule at even higher altitude. Overlap with water vapor is negligible at high altitude because there isn’t much water vapor because it’s number density decreases with both pressure and temperature and the lines for CO2 and water vapor are much narrower at the lower pressure and temperatur that exists at high altitude. The lower temperature at high altitude also lowers the Planck curve. Higher concentration causes increased absorptivity in the wings of the band which means less radiation is emitted to space from the now wider band. Only an increase in temperature of the surface and the atmosphere caused by the excess heat retained can increase the emission intensity at other wavelengths and restore the balance between incoming and outgoing radiation. In summary, the surface warms not because of increased thermal emission from the atmosphere with increasing CO2 concentration. The surface and the atmosphere warm because less heat is lost to space at any given altitude and temperature with increased CO2 concentration, all other things being equal.
DeWitt Payne (Comment#7036)
December 3rd, 2008 at 1:13 am
Here’s some numbers from MODTRAN to illustrate the point and correct a misstatement I made above. Using the 1976 standard atmosphere and a surface temperature of 288.2 K (zero offset) let’s see what happens at 280 and 560 ppm CO2 holding everything else constant, lapse rate, humidity, etc. Surface emission is 360.472 W/m2 in both cases, obviously. Note that this is less than the Stefan-Boltzmann equation would predict for that temperature with an emissivity of 0.98 because the full spectrum is not being integrated. The wavelength range is from 6.667 to 100 micrometers and about 6% of the emitted energy is outside that range. At zero altitude looking up and 280 ppm CO2, the atmospheric emission is 257.323 W/m2 and 260.526 W/m2 at 560 ppm CO2. So I was wrong about the emission intensity at the bottom of the atmosphere not changing much. Again, however, the surface emits more than it sees from the atmosphere. The heat flow is from the surface directly and indirectly to space. But the net heat flow is lower at higher CO2 and constant temperature, 103.149 W/m2 at 280 ppm and 99.946 W/m2 at 560 ppm. I am ignoring convective heat loss, which is significant, ~100 W/m2 in sensible and latent heat. But this is an all other things being equal calculation. If the surface temperature were constant at a heat loss rate of 103.149 W/m2, then what must happen at a lower heat loss rate? The surface temperature will go up. But not because the atmosphere warms the surface. The surface temperature of land or ocean goes up because the heat loss rate at the original temperature goes down. The water beneath the surface of the ocean also warms because less heat is lost, not because heat diffuses downward from the surface. That would violate fundamental thermodynamics. This is why people use the insulation, which works by lowering the heat flux at a constant temperature differential, analogy to explain the greenhouse effect.
Jorge (Comment#7042)
December 3rd, 2008 at 9:15 am
DeWitt, Many thanks for your continuing attempts to help us understand the radiation physics. I have tried to follow some of the discussions at Climate Audit and other places but I think I am missing something very basic. I think I have the hang of how lab type spectroscopy works in that one can see/measure emission lines from a hot gas against a dark/cool background or absorbtion lines from a cool gas against a light/hot background. It seems that in these cases the gas temperature is not usually affected by the presence of the radiation as any gain or loss of energy is compensated by gains or losses from the walls of the container or the thermal mass is generally too large for small amounts of radiation to have much effect. I have not really worked out what is happening with the MODTRAN simulation. Am I right to assume that the only heat source involved is the earth at some chosen temperature and that solar radiation does not show up at all? Secondly, am I right to think that the temperature/pressure/composition profile is specified in advance of the calculation? The end result being a spectral profile of the up/down radiation at a give altitude. I can see how this can show a radiative imbalance over the whole spectrum at a particular altitude but I cannot see how this imbalance is supposed to be translated into a temperature change from the originally specifed temperature profile. Is there some rule that says the temperature must change so that up/down radiation have to be equal at each altitude? Given that there is also convection and phase changes to add/subtract energy from any given layer there does not seem to be an obvious reason why radiation alone should have to be in balance. Perhaps it is at this point where we depart from rock solid radiation physics and calculating the resulting temperature changes is very dependent on whatever other atmospheric changes result from the changed radiative imbalance with extra CO2. I know there seem to be some arguments about the details of radiation calculations but these seem minor compared to knowing how to turn a changed radiation imbalance at the top of the troposphere (or anywhere else) into a new surface temperature.
DeWitt Payne (Comment#7043)
December 3rd, 2008 at 9:23 am
To finish the example, let the surface temperature increase until the emission at the top of the atmosphere (100 km for Modtran) at 560 ppm CO2, 257.166 W/m2 at 288.2 K surface temperature, equals the emission at 280 ppm CO2 of 259.992 W/m2. That requires a surface temperature offset of 0.87 C or a surface temperature of 289.07 at constant water vapor pressure. It would be higher for constant relative humidity. The temperature at any altitude above the surface also increases by the same amount, required by the assumption of a constant lapse rate. So now we have the surface emitting 364.554 W/m2 and the atmosphere emitting 263.132 W/m2 towards the surface for a difference of 101.422 W/m2. So the increase in emission required to make up for the loss of 2.826 W/m2 at 100 km comes partly from the warmer surface, 1.476 W/m2, and the rest from the warmer atmosphere.
lucia
(Comment#7045)
December 3rd, 2008 at 9:26 am
Jorge– The book starts with oversimplified models and progressively relaxes the simplifications. So, with regard to radiation, they begin by discussing radiation in an atmosphere with no conduction or radiation. The questions you ask about whether temperature must adjust so incoming radiation balances outgoing radiation at each level is discussed in the section on the radiative convective model. Convection does indeed modify things. The later chapters discuss climate models in a general framework. (Newer versions may say more. But I have a 90’s version.)
Your questions are good. I advice getting this book from the library:
DeWitt Payne (Comment#7047)
December 3rd, 2008 at 9:50 am
Jorge (Comment#7042) December 3rd, 2008 at 9:15 am , Am I right to assume that the only heat source involved is the earth at some chosen temperature and that solar radiation does not show up at all? Secondly, am I right to think that the temperature/pressure/composition profile is specified in advance of the calculation? Yes to both. The atmospheric profile can be changed by selecting a different locality, Tropical, Sub-Arctic Winter, etc. If you select save data and click on the link in the lower graph, the complete tables of pressure, temperature and composition as well as emission are displayed. Is there some rule that says the temperature must change so that up/down radiation have to be equal at each altitude? Given that there is also convection and phase changes to add/subtract energy from any given layer there does not seem to be an obvious reason why radiation alone should have to be in balance. At equilibrium, the energy in at any altitude must equal the energy out. How the energy is transferred is much more complex in the real world compared to the simplified radiation only model, which doesn’t look at energy balance either. The atmosphere absorbs some incoming solar radiation and the surface transfers absorbed solar energy by convection and conduction as well as radiation. Increased CO2 cools the stratosphere by increasing emissivity, which is also not included in the Archer Modtran program. The lapse rate is also a function of water vapor content, but that requires an explanation of moist and dry adiabats, which is outside the scope of this thread. There are resources on the web that go into much more detail about Physical Meteorology, here for example.
Jorge (Comment#7048)
December 3rd, 2008 at 9:58 am
Lucia, I live in a very small Spanish village and our local library is even smaller! It looks as though I will have to fork out some of my meager pension and buy it from Amazon. The problem at the moment is that the English pounds I receive have crashed against the euro and so it may be best to get the book from England. There are some other books I am thinking of buying and that will keep the postage costs to a reasonable level. Do you think I will be able to follow the maths? I have not had much to do with thermodynamics since I left college. Since then my maths skills have atrophied and things like integration by parts are just a distant memory.
Jorge (Comment#7050)
December 3rd, 2008 at 10:25 am
DeWitt, Thanks for your reply. You say that the energy in must equal energy out in any layer at equilibrium. Is there any reason to suppose that a layer is in equilibrium at any one time. Given the complexities you mention it seems that it may be reasonable that there is a very long term equilibrium but there does not seem to be any requirement for an exact energy balance over days, weeks or even years. I will investigate the web resources you linked to and see what I can do with them. I suspect I will find myself out of my depth rather rapidly!!!
DeWitt Payne (Comment#7063)
December 3rd, 2008 at 2:55 pm
Jorge (Comment#7050) December 3rd, 2008 at 10:25 am , There will be large daily and seasonal variations. The annual average change should be fairly small, but not true equilibrium. Still, like local thermal equilibrium (LTE for short), it’s a useful approximation for illustrative purposes with a simple model.
Comments Closed: If you would like them re-opened, Contact Lucia
erik (Comment#4234) July 17th, 2008 at 11:41 am
Beautiful picture. I appreciate all you do, but this is by far the single best visualization of the “falsifiable warming?” data I have seen. The graph conveys a much better sense of the odds than just debating a couple likelihood numbers. Very nice.