Home/BlogSince I keep getting asked about the “latest” on the ongoing debate over clouds and feedback diagnosis between myself and Andy Dessler, I decided that this would be the best way to handle it under the current circumstances:
An Open Letter of Encouragement to Dr. Dessler
Dear Andy:
Thank you for the issues you have raised in your new paper, which I was only recently made aware of after it had already been peer reviewed and accepted for publication in Geophysical Research Letters.
Even though we disagree on the subject, I am pleased you have chosen to vigorously dispute the potential role of clouds in both confounding the diagnosis of the sensitivity of the climate system, as well as in contributing to climate variability and climate change.
I just wanted to encourage you to publish that paper as soon as you can, with or without the changes I suggested on my blog.
I am very sincere in my encouragement. I am anxious for the science to progress on this important issue, and so I eagerly await the official publication.
All the best,
-Roy W. Spencer
We notice clouds a lot in Northern California. This year has been very cloudy, and foggy on the coast. And much cooler than normal, except last year was quite similar, and the preceding year wasn’t up to hoped for standards of warmth either. The grapes seem to know the weather without us telling them about it: they’re ripening fitfully, and about three weeks later than usual.
Our blackberries, usually numerous and ripe in August, are still few and bright red in mid-September. The birds that seem to always beat me to the ripest look hungry and forlorn. Serves them right.
A thousand years ago in England, during the Medieval Warm Period denied by Mann’s trees (or at least by the anointed or chosen ones among them), the grapes grew and the wine flowed, where it neither grows nor flows today.
In vino veritas!
Having followed the interchange between distinguished scholars Spencer and Dessler over the last year. . . .I agree with Roy’s open letter. I’d also like to congratulate both men on their willingness to engage at multiple levels, including the public sharing of data, on a very important, and not nearly well enough understood subject.
Yeah, sometimes it is going to be uncomfortable. Sometimes there might even be a “hard foul” or two under the backboards.
The truth is, the engagement between Spencer and Dessler is what, over many years, I had hoped to see from climate science, and almost never did.
If I were to identify the single core irreducible value of “science”, it would be “mankind wins through the engagement, iteration, and development of opposing ideas over time, defended valorously along the way.”
Good on both of you.
It is good seeing something approaching the scientific process emerging here. It is rather ironic that the true peer review of this paper seems to have taken place thanks to the internet rather than through the reviewers selected by the journal.
I hope Andy Dessler won’t have too many problems making the changes he now thinks appropriate.
Inspired by the “simple model” published here I have been looking at differentiating radiative and non radiative forcings the character of their time dependency. Radiative forcings are dT/dt non-rad are f(t). I believe this is the key to resolving the two getting at the key feedback response.
Dessler’s paper states:
” I will focus on the period from March 2000 to February 2010, during which good data exist and the primary climate variations were caused by ENSO.”
There seems to be confusion of causation and correlation in this statement. I have focused on the period 2006-2010 where this correlation is strongest.
I would encourage those interested in resolving this issue to look at the fundamental nature of the time response of the radiative and non-radiative forcings rather to dismiss the all important time component of the data and do invalid OLS regressions on scatter plots.
Dear Dr. Spencer, maybe someone should make dr. Dessler aware that he is not allowd to simply modify his paper after it has been accepted for publication in GRL. Each modifications would require a new review.
In my opinion this fact is very important: clear rules in the review process are a guarantee for good science…
That is a good letter, and it shows confidence on Dr. Spencer’s part. I like that approach.
I hope this catches your eye DR. SPENCER.
DR. SPENCER ,you should really get on board on this increase in geological activity , if for no other reason to refute the global warmers when they say the reason temperatures are going down,(if they should and volcanic activity keeps increasing) is due to an increase in volcanic activity ,independent of everything else, which is a BOLD FACE LIE. It seems to be connected,and is CORRELATED with prolong solar minimum activity, and past history and this current year lend support to this.
Again look at all of the geological activity that has followed this recent spurt of solar activity that resulted in a K 5 to K 7 INDEX on SEP 08-09.
There have been at least 6 major earthquakes since then, plus one or two volcanic eruptions. I said 1 to 25 days following spurts of activity on the sun which effect earth’s geomagnetic field ,the increase in geological activity follows.
This has verified each and every time this year with out failure.
I know correlation does not mean cause and effect, but I take correlation ,over projections any day of the week. The global warmers/models , of course trying to project warming, due to an CO2 increase. Why not take a hard look at some other factors which can strengthen your case to be made against man made global warming.
VOLCANIC ACTIVITY , is one of the items that control earth’s climatic system.
P. Solar wrote;
“Inspired by the “simple model” published here I have been looking at differentiating radiative and non radiative forcings by (sic) the character of their time dependency. Radiative forcings are dT/dt non-rad are f(t). I believe this is the key to resolving the two getting at the key feedback response.”
Although this is stated in slightly different terms than the ones I am most familiar with, I believe that this comment corresponds to my understanding of how energy (heat/visible light/IR light) travels through a complex system.
I posit again that “radiative forcings” travel though the climate system at the speed of light (with a few short side trips as backradiation). At the same time “non-radiative forcings” travel through the climate system at the “speed of heat” as determined by the materials present in the system. The speed of heat is quite a bit slower than the speed of light.
I know this is quite a bit “off the path” regarding the last several decades of climate science, but I do believe that understanding the actual effects of “greenhouse gases” on the climate MUST consider the speed at which the numerous energy flows travel through the system.
I again posit that; increases in “greenhouse gases” are displaced by decreases in “non-greenhouse gases”. I also posit that the final result is that the gases (due to their small (virtually miniscule with respect to the oceans) thermal capacity) in the climate heat up slightly faster after sunrise (or the dissipation of cloud cover) and cool down slightly faster after sunset (or the accumulation of cloud cover).
I also posit that this effect is so slight that we probably cannot afford to measure it. The historical temperature databases do not contain the necessary data (i.e. dT/dt).
Dr. Spencer is correct that it is d—m near impossible to discern the numerous individual feedbacks/forcings that occur inside a complex system by observing the external outcome (i.e. the energy leaving at TOA).
In the engineering field we resort to “breaking the closed loop” to measure how individual components of the system respond to “forcings” applied to them. Once we understand the response of components inside the system we can manipulate the “feedbacks” to optimize the performance of the total system.
But, I’m just a crackpot with no real dog in this fight.
Cheers, Kevin.
Responding to the post of KevinK of September 15, 2011 at 10:03 PM.
KevinK writes: “In the engineering field we resort to “breaking the closed loop””.
Engineers can do that because they can engineer their systems. But students of natural processes cannot, because they cannot effectively break the loop without wrecking the whole show and all its parts. That is why they have learned to use information derived from the effects of external drivers, and why they know they have to allow the two relevant internal state variables to each have its own dynamical determination. Just one dynamically determined internal state variable cannot do the job of the two. Christopher Game
Roy, have you seen that now Trenberth et al are commenting directly on Spencer and Braswell 2011 in Remote Sensing? I hope that means you are being given the customary right to respond.
I am afraid that I must doubt, however, that standard practice is going to be followed. It is quite clear that the publishing of this comment is an attempt by Remote Sensing to cover their asses embarrassed by having let a non-orthodox view slip past the radar…They wouldn’t want to muddy the waters of their making up for their “mistake” by continuing to treat you with respect. That was their “mistake” in the first place, after all.
Also worth noting that the paper was accepted the SAME DAY as it was received. An we thought Dessler’s paper got accepted quickly.
Pretty soon they will be accepting papers before they are written. Maybe that is already the case , they just post-date the acceptance date so that it is not technically impossible.
Any way this recalls Phil Jones comment “Kevin [Trenberth] and I will keep this out , even if it means redefining what peer-review means).
At least in this case they seem to have achieved that objective.
Rarely does a paper stink the place up so badly that the editor feels the need to resign.
Rarely does an editor lack so much spine and professional decorum that he not only resigns, but writes a simpering apology letter to someone who wasn’t even involved.
Back on topic, and equally rarely, two men with different ideas can discuss these different ideas with enough good professionalism that they even help each other better make their points.
Maybe you should reconsider your comment and think of how you too can turn a new leaf of professionalism and be a better man for it.
I’ve just been told that the paper is a “commentary” not a comment, and thus circumvents normal review, as well as the normal right to reply. Remote Sensing has been much diminished as a journal of science. Disgusting…
Christopher Game wrote (in part);
“Engineers can do that because they can engineer their systems. But students of natural processes cannot, because they cannot effectively break the loop without wrecking the whole show and all its parts. That is why they have learned to use information derived from the effects of external drivers, and why they know they have to allow the two relevant internal state variables to each have its own dynamical determination. Just one dynamically determined internal state variable cannot do the job of the two.”
I agree, and my point was more about the advantages engineers have in understanding (and ultimately controlling) complex systems than about the limitations that students of natural process face.
A few specific comments follow;
Christopher wrote;
“because they cannot effectively break the loop”, I posit that they CANNOT break the loop; “effectively” or in any other manner.
Christopher also wrote;
“and why they know they have to allow the two relevant internal state variables to each have its own dynamical determination.”
With all due respect, this is GOBBLEDYGOOK…
I do indeed respect your posts and in fact read and enjoy them, however my larger point was that engineers have learned (often times the hard way) that there are LIMITATIONS inherent to the use of computer models to describe a complex system.
Part of the wisdom accumulated while using computer models is knowing when they ARE applicable and when they ARE NOT applicable. In many complex engineering fields we routinely use computer models when they apply and at the same time we routinely eschew the use of models since we know they cannot (at the current state of the art) provide the needed information.
In the engineering field (I will posit that this field has had the most success using computer models to “predict” how actual physical examples of complex systems will behave) we have learned WHEN computer models HELP and WHEN computer models DO NOT HELP.
I posit that we as human beings will “likely” (a conditional statement that climate scientists are quite fond of) NEVER be able to accurately model the “climate”.
I also posit that any scientists that “believe” they can predict the weather in 100 years are so full of hubris that it amazes those of us that are a bit more grounded in the skills of making computer models agree with the actual behavior of REAL complex systems.
I know this is wearing thin by now but in the engineering field we have a saying;
If your hardware does not perform as predicted by your model, you need to improve your model.
So, I ask;
If the climate does not perform as predicted by your model, are you going to improve the climate, OR are you going to improve your model ???????
Cheers, Kevin.
Response to the post of KevinK of September 16, 2011 at 4:05 PM.
KevinK writes: ““and why they know they have to allow the two relevant internal state variables to each have its own dynamical determination.”
With all due respect, this is GOBBLEDYGOOK…”
Chistopher replies:
Well, yes, it uses some technical terms, and perhaps for this forum may count as undue gobbledygook. I very much agree with your sentiment that ordinary language is to be preferred here, whenever it will do the job.
I suppose the worst offender in what I wrote was the term “dynamical determination”. I was just trying to express briefly the idea of a member of a set of coupled ordinary differential equations.
Please let me try again.
Drs Spencer and Braswell and Dr Dessler are talking in terms of an ordinary differential equation of the first order for their discussion of cloud feedback. I am saying that they cannot make much progress with this, apart from discovering its inadequacy as a formalism for their purpose.
No less than a second-order system of coupled ordinary differential equations, endowed with an external driver function, will serve the purpose of making a mickey-mouse model of cloud feedback, which is what they are working on.
It quite likely may be, as you say, that even this will not produce a useful mickey-mouse model for this purpose, but I am saying that nothing less will do so.
KevinK writes: “are you going to improve your model?”
Christopher replies: It seems my gobbledygook has been opaque. I am urging Drs Spencer and Braswell to improve their model, by moving to a second-order system. I do not know whether there is enough suitable empirically measured data to get the job done. Christopher Game
Andrew says:
September 16, 2011 at 4:05 PM
>>
I’ve just been told that the paper is a “commentary” not a comment, and thus circumvents normal review, as well as the normal right to reply. Remote Sensing has been much diminished as a journal of science. Disgusting…
>>
That is *very* significant. Do you have a link to that information?
Keep an eye on this one as a likely candidate for use of grey literature in AR5.
Christopher, you clearly have a good understanding of the maths behind this sort of system analysis. As Kevin points out the key in using any model is understanding and respecting its limitations.
I think there is some mileage in the kind of model Dr Spencer is using for analysing and approximating climate behaviour over a short period.
In particular , I think it is useful in separating the linear plank radiation response from the d/dt response of temperature to radiation forcing (which is what all the fighting is about).
The following figure shows the lag regression variations of CERES net flux vs UAH temps for 2000-2010.
Though the OLS estimator is plotted this is in effect showing the variation of correlation of the two terms against lag.
http://tinypic.com/view.php?pic=fth5vk&s=7
I have fitted a narrow exp(-|lag|) plus an exponentially modulated sine to the data.
As you will be aware the first would represent lag response of a linear term with gaussian noise. The second a simple oscillator with a similar noisy signal driving it.
This seems to capture much of the essence of the data , though there are clearly other effects (and or simple noise and error) present as well.
Can your expert eye suggest the significance of the zero crossing at -3 months or the attenuation of the peaks on the -ve side w.r.t the fitted curve?
BTW I used the period -3mth to 33mth to fit the coeffs
There’s clearly more to this but I’ll keep it short here.
Can you provide any insight?
best regards.
Kevin wrote: “If your hardware does not perform as predicted by your model, you need to improve your model.
So, I ask;
If the climate does not perform as predicted by your model, are you going to improve the climate, OR are you going to improve your model ???????”
I had to smile when I read this, remembering that the IPCC wrote: Observations at times do not match model results and therefore either the models are incorrect or the observations are incorrect. We tend to believe the latter.
Go ahead punk make my day! 🙂
Christopher Game, has said it so well. They need a second order system with external drivers and even that won’t be the end all.
That is so correct , because nomatter how they try through the models they are not going to be able to have enough accurate data, complete data, and the interactions of all the data with one another to a degree of understanding complete enough , to get a correct result.
I am sure factors like the earth’s magnetic field, strength, the solar flux readings, the AO/NAO atmospheric circulations, cosmic ray intensity,volcanic eruptions, to name a few, are among just a few of the important data points ,one needs to do this, that are not present in the data fed to these models. I just named a few, there are many more.
This is why I say PAST CORRELATIONS, work much better in projecting what might lie ahead for the climate, then these model PROJECTIONS, which will always and forever be based on flawed and incomplete data.
I will take correlation over projection anytime, when it comes to predicting the climate.
Since the k5 -k7 event here on earth SEP.08, we have had 10,or so earthquakes with magnitude 6.0 or higher. Plus some volcanic activity, with one in RUSSIA erupting, and some 5.5 to 5.9 earthquakes. It keeps on verifying.
QUIET SUN WITH ACTIVE SPURTS, EQUALS AN INCREASE IN GEOLOGICAL ACTIVITY.
I rest my case.
P. Solar-I am just reporting what someone on the CA thread told me.
Dr Spencer, thank you so much for your open letter. I laughed aloud reading it. Wonderful. You have risen in my estimation enormously. It gives new meaning to the expression dry humor. Very, very dry….
Responding to the post of P. Solar of September 17, 2011 at 3:33 AM.
I regret that I am not an expert. That the IPCC AOGCMs’ predictions do not fit the observed data is the main current finding of Drs Spencer and Braswell and that seems to me to be rather hard to dispute, and to be very important. The more detailed question of the way cloud dynamics work is I think where you are now questioning. My limited understanding tells me that one cannot tell the “forward” from the “backward” causal efficacy for that from the kind of diagram that you link to. Perhaps someone can carefully explain to us why I am wrong about that? Christopher Game
Climate has allways changed. The drivers of climate change are:
1) Geological activity and plate tectonics. Time scale millions to thousand millions of yrs.
2) Orbital parameters of the planetary system and the Earth. Time scale thousands to hundred thousand yrs
3) The Sun (changes in solar activity) and oceans (changes in PDO, AMO, NAO etc.)and their interactivity. Time scale tens to hundred yrs
Of course they are integrated in complicated way with each other but they are the main drivers.
Christopher Game says: “My limited understanding tells me that one cannot tell the “forward” from the “backward” causal efficacy for that from the kind of diagram that you link to. ”
It is not a case of forwards and backwards, the key point is that one is a time derivative and one is a time dependant effect. They are essentially orthogonal and hence separable. The graph I linked shows how the two show up in phase space. One is a spike , the other an oscillation.
It can also be seen, without being too precise , that they are roughly equal in their degree of correlation to the temperature signal hence of comparable magnitude. This would seem to be a pretty clear refutation of Andy Dessler’s claim of a 20:1 ratio .
The other big problem with Dessler 2010 (and many similar analyses) is that he does not understand correct use of OLS regression and assumes that the “slope” at lag=0 represents the simple feedback. Since this is less than 3.3 he erroneously concludes that this shows a positive climate feedback reducing the plank response.
In fact this result is largely due to regression dilution: reduction of the ols estimator by the presence of significant other non-correlated signals (the out of phase component). This is further compounded by significant noise in the independent variable (temperature) which further reduces the slope.
Correct regression techniques would show a regression slope firmly the other side of 3.3 W/m2/K
This analysis also gives a means to get an empirical estimation of another contested parameter in this discussion. The depth of the mixed ocean.
The period of the -lambda.dT oscillator is lambda/Cp/depth
year=365.25*24*3600; cp=4180000; feed_back=3.3
deepth=3*year*feed_back/cp;
This gives ML depth= 74.75 m . similar to estimates based on the -0.5C criterion.
There are those who think it should be deeper but that would imply stronger feedback.
oops, forget that last brainwave, its the time constant (relaxation time) not the period.
@Christopher Game,
Switch off the sun and warm up the background radiation to 290 K. Now the whole earth would come to local thermal equilibrium. There would be no convection. Nothing to generate clouds. My point is that clouds are caused by convection and convection is caused by surface heating. There is no doubt in my mind about cause and effect. Now perhaps cloudiness is correlated with ENSO, PDO, etc. No matter, correlation does not prove causation as we are all tired of hearing. The mechanism is surface heating causes buoyant uplift which causes adiabatic decompression which causes clouds. Simple as that. I’m a little bothered when Dr Spencer says that causation works in both directions. Clouds cause surface heating? Or does he mean that clouds, which are caused by surface heating, act to limit surface heating? That’s different. No second law violations.
Replying to the post of pochas of September 18, 2011 at 11:37 PM.
Yes, in general you are right that clouds are formed as a result of evaporation, convection and condensation, and that convection occurs as a result of solar heating of the land-sea body (which heats the bottom of the atmosphere), and of cooling of the atmosphere by the coolth of outer space. That is causation affecting the occurrence of clouds.
Dr Spencer and Dr Dessler rightly agree that clouds also have their own effects. They reflect sunlight back to space during the day and absorb infrared terrestrial radiation that would otherwise have gone to space at night. This is causation effected by clouds. It affects the land-sea body and the atmosphere. Overall it seems generally agreed that more clouds have a cooling effect because the reflection effect outweighs the absorption effect.
So you need not in the least be bothered when Dr Spencer says that causation works in both directions. He is right there. This is a case of a system with internal dynamics, in part described by interactions between its internal state variables, in this case the extent of cloud cover and the land-sea surface temperature. This is what people mean when they talk about “feedback” in this context. The word feedback has a very wide range of meanings. Your post was feedback to me about my previous post, and this present post of mine is feedback about yours, but not of the kind that Dr Spencer means.
The climatic questions are how the 30-year time-scale global average temperature of the land-sea surface affects the 30-year time scale global average cloud cover, and how much an external driver of global average cloud cover would affect the 30-year time-scale global average land-sea surface temperature. These are the questions at issue in this debate.
You may note that there is not much said on the 30-year time scale. So far we have been hearing about instantaneous effects (which are of course not possible in physics, but have been considered by Dr Dessler) and effects on a time-scale of months (which are physically real and have been discussed by Drs Spencer and Braswell).
I think that the mathematical formalism in which the discussion has so far been conducted is inadequate for the analysis of the questions of climatic interest. Christopher Game
CORRELATION may not prove CAUSATION, but it is much better then PROJECTIONS ,when it comes to predicting the future climate.
More EXCUSES, are coming out for why the models are so pathetic in their climate forecasting, ranging from they did not expect a decline is solar activity, or stratospheric water vapor, to they did not expect an increase in stratosphere/troposphere aerosols, to they can’t time ENSO cycles, or oceanic circulations. More BS.
It just goes to my point, which is the models will never be able to forecast the climate due to incomplete and inaccurate data.
End of story.
Why isn’t the paper published yet? What happened to GRL’s fast cycle? We’re waiting here.
An Inquirer,
“I had to smile when I read this, remembering that the IPCC wrote: Observations at times do not match model results and therefore either the models are incorrect or the observations are incorrect. We tend to believe the latter.”
And of course, there is no way that the observations, even if they were “corrected”, could agree with ALL of the models, since the only way that the models can be made to agree with each other, is to calculate Multi-Model Means.
Well… things doesnt work out for the IPCC thugs!
http://www.met.reading.ac.uk/~sgs02rpa/PAPERS/Allan11MA.pdf
Cloud feddback is N E G A T I V E. There is a new “consensus that it is”. Only a minority within the field wthout any observations to back it up claim it is positive.
Responding to the post of Slabadang of September 20, 2011 at 5:57 AM.
Slabadang seems not to understand what is being debated here. If Slabadang’s ‘understanding’ were right, then Drs Spencer and Braswell would be wasting our time. But they are not wasting our time, for Slabadang’s ‘understanding’ is mistaken. Slabadang seems not to understand what Drs Spencer and Braswell mean when they write of feedback.
Slabadang is right to point out that the direct radiative effect of a primary change in clouds is to cool the system; Slabadang’s reference puts the rate at a cooling of 21 W m^-2. As Slabadang rightly writes, there is consensus about that.
But Slabadang would be mistaken to ‘understand’ that as establishing whether feedback is positive or negative. This question, as to the sign of the feedback, asks about the effect of a primary change in land-sea surface temperature on the amount of cloud. This question is not addressed by Slabadang’s reference. Nevertheless, Slabadang’s reference is interesting. Christopher Game
I would appreciate knowing what parameters are being changed by the IPCC models to try to match historical data.
Help?
Douglass Winslow Cooper-The answer to your question, simplifying things a bit, is that the models parameters are varied a great deal, resulting in a wide range for the size of responses to CO2, and then an additional input term, the negative forcing from aerosols, is put into the models with whatever value is necessary to produce a back-cast of surface temps that isn’t widely different from what observations indicate. They can do this because no one is really sure what the size of aerosol effects should be. We are sure what, absent certain feedbacks, the CO2 effect should be, but models vary a great deal about what the feedbacks should be (other than that they all have net feedbacks that result in a larger response than the value without them) and so it should be impossible for them to all produce the same amount of change if they all have the same factors determining their trends in the 20th century. Yet they do, because they don’t have the same factors influencing their trends, they have arbitrarily selected factors that make them work in back-casts.
Douglas Winslow Cooper and Andrew:
It?s not necessarily the case that aerosols are tuned to match the historical record (I?d need to know the specific model and configuration to judge if that?s the case). More typically, aerosol emissions are estimated in a ?bottom-up? fashion, injected into the atmosphere, transported and washed out. The emissions estimates are ?best-available?, and are of course highly uncertain, but generally aren?t ?tuned?. The aerosols chemistry, radiation and interaction with clouds isn?t typically ?tuned? either (again, would need to know the specific example), but, again remains highly uncertain. It?s one of the reasons why the models don?t match the historical records exactly. But a general result across models is that the more forcings accounted for, incl aerosols and GHGs, the better the agreement with the historical result.
Other free parameters (inevitable in any parameterization) are set to match a range of different measurements, but only in the mean state, not any historical trend. Things like convective relaxation time scales, supersaturation etc?. Much effort goes into understanding the sensitivity of future projections to the uncertainty associated with variation of these parameters. The climateprediction.net project is a prime example.
Ted’s answer to Dr. Cooper’s question is more accurate than Andrew’s answer, but it could leave an inaccurate impression. To be sure, the modelers do not create aerosol numbers out of thin air to insure historical fit. Yet, for the vast majority of the historical record, aerosol numbers are non-existent. We do not know what the aerosol number is over the Phillipines in 1965, and we do not have any aerosol number world wide for 1905. However, we do have aerosol number for regions of the United States, and by 2000 we have some good #s for much of the world. Therefore, the modelers use choose various studies that possess aerosol numbers and extrapolate them and make assumptions as necessary to get a sufficient data set needed to run their models. Not all aerosol studies are used, and heroic assumptions are necessary to complete the sufficient data set. A few years ago, I spent numerous weeks examining available aerosol studies and the methodologies used to develop the sufficient data set. My conclusion is this: the aerosol studies used and the methodologies used are conveniently chosen to yield the best fit for CO2 as the explanatory power. In other words, the modelers assume that CO2 (and other GHGs) are the main driver in explaining the temperature record and then choose the aerosol studies with extrapolation methodologies to yield that result.
My thanks for these replies, which I take to mean that there is some bottom-up modeling of emissions and aerosol effects, followed by some adjustment to “back-predict” the past. Presumably there are several adjustable parameters.
“Sensitivity” studies are clearly of use. Decades ago I worked on data inversion, that came down to linearizing an integral equation, then performing least-squares optimization of the coefficients of the linear equation, to find the best equation to fit the data, as a general rule (we were studying the response function of a mesurment instrument).
It turned out that some of these sets of equations were “ill-conditioned,” having large “condition numbers,” and the uncertainties in the data were multipled by these very large factors in determining the uncertainties in the coefficients being sought.
A classic example is fitting N data points, f(xi) with a polynomial of kth order. A linear model gives the usual least squares answers, f(x) = mx+b for example. Fitting a quadratic or a cubic curve can be done, with the coefficients more sensitive to errors in the independent variable. You can even fit an Nth – order curve to go through every point, matching the date pserfectly, but producing absurd results when extrapolated beyond the range of the independent variable.
I wonder if this ill-conditioning problem is cropping up, perhaps disguised, in some of these attempts to find the right parameters to match the historical data.
Comments?
Is it published yet?