Redefining Physics
Dexter Wright re-defined the radiative transfer equations in his American Thinker article “Global Warming on Trial” with these immortal words:
Clearly, H2O absorbs more than ten times the amount of energy in the IR spectrum as does CO2. Furthermore, H2O is more than one hundred times more abundant in the atmosphere than CO2. The conclusion is that H2O is more than one thousand times as potent a greenhouse gas (GHG) as CO2.With such immutable facts facing the EPA, how will they explain their stance that CO2 is a greater danger to the public than water vapor?
So far, neither Dexter, nor his enthusiastic supporters at American Thinker have got around to updating the now defunct Wikipedia article on the Radiative Transfer Equations which describe the “old school” mathematics and are slightly more complicated.. (See also CO2- An Insignificant Trace Gas? Part Three.)
But in wondering why they hadn’t, it did occur to me that non-linearity is something that most people struggle with. Or don’t struggle with because they’ve never heard of it.
I think that the non-linear world we live in is not really understood because of the grocery factor..
(And it would be impolite of me to point out that Dexter didn’t know how to interpret the transmittance graphs he showed).
Groceries and Linearities
Dexter is in the supermarket. His car has broken down so he walked a mile to get here. He has collected a few groceries but his main buy is a lot of potatoes. He has a zucchini in his hand. He picks up a potato in the other hand and it weighs three times as much. He needs 100 potatoes – big cooking plan ahead – clearly 100 potatoes will weigh 300 times as much as one zucchini.
Carrying them home will be impossible, unless the shopping trolley can help him negotiate the trip..
Perhaps this is how most people are thinking of atmospheric physics.
In a book on Non-linear Differential Equations the author commented (my memory of what he stated):
The term “non-linear differential equations” is a strange one. In fact, books about linear differential equations should be called “linear differential equations” and books about everything else should just be called “differential equations” – after all, this subject describes almost all of the real-world problems
What is the author talking about?
Perhaps I can dive into some simple maths to explain. I usually try and avoid maths, knowing that it isn’t a crowd-puller. Stay with me..
If we had the weight of a zucchini = Mz, and the weight of a potato = Mp, then the weight of our shopping expedition would be:
Weight = Mz x 1 + Mp x 100, or more generally
Weight = Mz Nz + Mp Np , where Nz = number of zucchinis and Np = number of potatoes. (Maths convention is that AB means the same as AxB to make it easier to read equations)
Not so hard? This is a linear problem. If you change the weight (or number) of potatoes the change in total is easy to calculate because we can ignore the number and weight of zucchinis to calculate the change.
Suppose instead the equation was:
Weight = (Mz Nz) Np2 + (Mp Np) Nz3
What happens when we halve the number of potatoes? It’s much harder to work out because the term on the left depends on the number of zucchinis and the number of potatoes (squared) and the term on the right depends on the number of potatoes and the number of zucchinis (cubed).
So the final result from a change in one variable could not be calculated without knowing the actual values of the other variables.
This is most real-world science/engineering problems in a nutshell. When we have a linear equation – like groceries but not engineering problems – we can nicely separate it into multiple parts and consider each one in turn. When we have a non-linear equation – real world engineering and not like groceries – we can’t do this.
It’s the grocery fallacy. Science and engineering does not usually work like groceries.
Stratospheric Water Vapor
In many blogs, the role of water vapor in the atmosphere (usually the troposphere) is “promoted” and CO2 is “diminished” because of the grocery effect. Doing the radiative transfer equations in your head is pretty difficult, no one can disagree. But that doesn’t mean we can just randomly multiply two numbers together and claim the result is reality.
A recent (2010) paper, Contributions of Stratospheric Water Vapor to Decadal Changes in the Rate of Global Warming by Solomon and her co-workers has already attracted quite a bit of attention.
This is mainly because they attribute a significant proportion of late 20th century warming to increased stratospheric water vapor, and the last decade of cooling/warming/pause in warming/statistically significant “stuff” (delete according to preferences as appropriate) to reduced water vapor in the stratosphere.
(If you are new to the subject of the stratosphere, there is more about it at Stratospheric Cooling and useful background at Tropospheric Basics ).
There is much that is interesting in this paper.
Stratospheric water vapor - SW and LW effect vs altitude, Solomon (2010)
Firstly, take a look at the basic physics. The graph on the left is the effect of 1ppmv change in water vapor in 1km “layers” at different altitudes (from solving the radiative transfer equations).
Notice the very non-linear effect of “radiative forcing” of stratospheric water vapor vs height. This is a tiny 1ppmv of water vapor. Higher up in the stratosphere, 1 ppmv change doesn’t have much effect, but in the lower stratosphere it does have a significant effect. Very non-grocery-like behavior..
Unfortunately, historical stratospheric water vapor measurements are very limited, and prior to 1990 are limited to one site above Boulder, Colorado. After 1990, especially the mid-1990′s, much better quality satellite data is available. Here is the Boulder data with the later satellite data for that latitude “grafted on”:
Stratospheric water vapor measured 40'N, 1980-2010, Solomon (2010)
And the global changes from post-2000 less pre-2000 from satellite data:
Stratospheric water vapor change, measured vs latitude, Solomon (2010)
It looks as though the major (recent) changes have occurred in the most sensitive region – the lower stratosphere.
The paper comments:
Because of a lack of global data, we have considered only the stratospheric changes, but if the drop in water vapor after 2000 were to extend downward by 1 km, Fig. 2 shows that this would significantly increase its effect on surface climate.
The calculations done by Solomon compare the increases in radiative forcing from changes in CO2 with the stratospheric water vapor changes.
Increases in CO2 have caused a radiative forcing change of:
- From 1980-1996, about +0.36 W/m2
- From 1996-2005, about +0.26 W/m2
Changes in stratospheric water vapor have caused a radiative forcing change of:
- From 1980-1996, between 0 and +0.24 W/m2
- From 1996-2005, about -0.10 W/m2
The range in the 1980-1996 number for stratospheric water vapor reflects the lack of available data. The upper end of the range comes from the assumption that the changes recorded at Boulder are reflected globally. The lower end that there has been no global change.
What Causes Stratospheric Water Vapor Changes?
There are two mechanisms:
- methane oxidation
- transport of water vapor across the tropopause (i.e., from the troposphere into the stratosphere)
Methane oxidation has a small contribution near the tropopause – the area of greatest effect – and the paper comments that studies which only consider this effect have, therefore, found a smaller radiative forcing than this new study.
Water transport across the tropopause – the coldest point in the lower atmosphere – has of course been studied but is not well-understood.
Is this All New?
Is this effect something just discovered in 2010?
From Stratospheric water vapour changes as a possible contributor to observed stratospheric cooling by Forster and Shine (1999):
This study shows how increases in stratospheric water vapour, inferred from available observations, may be capable of causing as much of the observed cooling as ozone loss does; as the reasons for the stratospheric water vapour increase are neither fully understood nor well characterized, it shows that it remains uncertain whether the cooling of the lower stratosphere can yet be fully attributable to human influences. In addition, the changes in stratospheric water vapour may have contributed, since 1980, a radiative forcing which enhances that due to carbon dioxide alone by 40%.
(Emphasis added)
From Radiative Forcing due to Trends in Stratospheric Water Vapour (2001):
A positive trend in stratospheric H2O was first observed in radiosonde data [Oltmans and Hofmann, 1995] and subsequently in Halogen Occultation Experiment (HALOE) data [Nedoluha et. al., 1998; Evans et. al., 1998; Randel et. al., 1999]. The magnitude of the trend is such that it cannot all be accounted for by the oxidation of methane in the stratosphere which also show increasing trends due to increased emissions in the troposphere. This leads to the hypothesis that the remaining increase in stratospheric H2O must originate from increased injection of tropospheric H2O across the tropical tropopause.
And back in 1967, Manabe and Wetherald said:
It should be useful to evaluate the effect of the variation of stratospheric water vapor upon the thermal equilibrium of the atmosphere, with a given distribution of relative humidity.. The larger the stratospheric mixing ratio, the warmer is the tropospheric temperature.. The larger the water vapor mixing ratio in the stratosphere, the colder is the stratospheric temperature..
Emphasis added – note that this paper was discussed a little in Stratospheric Cooling
Conclusion
The potential role of stratospheric water vapor on climate is not a new understanding – but finally there are some observations which can be used to calculate the effect on the radiative balance in the climate.
The paper does illustrate the non-linear effect of various climate mechanisms. It shows that small, almost unnoticed, influencers can have a large effect on climate.
And it demonstrates that important climate mechanisms are still not understood. The paper comments:
It is therefore not clear whether the stratospheric water vapor changes represent a feedback to global average climate change or a source of decadal variability. Current global climate models suggest that the stratospheric water vapor feedback to global warming due to carbon dioxide increases is weak, but these models do not fully resolve the tropopause or the cold point, nor do they completely represent the QBO, deep convective transport and its linkages to SSTs, or the impact of aerosol heating on water input to the stratosphere. This work highlights the importance of using observations to evaluate the effect of stratospheric water vapor on decadal rates of warming, and it also illuminates the need for further observations and a closer examination of the representation of stratospheric water vapor changes in climate models aimed at interpreting decadal changes and for future projections.
References
Contributions of Stratospheric Water Vapor to Decadal Changes in the Rate of Global Warming, by Solomon et al, Science (2010)
Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity, by Manabe and Wetherald, Journal of Atmospheric Sciences (1967)
Stratospheric water vapour changes as a possible contributor to observed stratospheric cooling, by Forster and Shine, Geophysical Research Letters (1999)
Radiative Forcing due to Trends in Stratospheric Water Vapour, Smith et al, Geophysical Research Letters (2001)
Consider the possibility that it is not the CO2 and positive feedback that cause the increased water vapor and thus warming of the surface and cooling of the upper troposphere, but rather the warming due to other causes (ocean long term cycles, cloud variation from cosmic rays, etc.) that cause both the near surface warming and upper level cooling, and this may cause the water vapor concentration to vary with altitude. Cause and effect have not been established for the source of water vapor change vs temperature change. The reversal of lower stratosphere water vapor level occurred for about the last decade even though the CO2 has continued to rise strongly. In addition, upper troposphere temperature only dropped immediately following the heat pulse from Pinatubo in the early 1990′s, and has not dropped any more since. How much more time is needed to be convincing.
“and the last decade of cooling/warming/pause in warming/statistically significant “stuff” (delete according to preferences as appropriate)” LOL
So, this “predicted” drop in stratospheric temp due co2 is an independent effect to the one above?(still got issues “getting” that one. )
OMG – those citations!
I don’t believe I’ve ever seen such extensive use of the subjunctive tense in any writing outside of – well, [ I snip myself ]
The subjunctive tense is created for the purpose of discussing things that are not. It is not even conditional. It is made for fantasy – hence it has largely vanished as a distinct verb form in English and is conspicuously labored to perform. It is also conspicuously devoid of legitimate declaration of fact vis a vis causation in the form of an argument that connects various elements in some logical pattern.
That much effort to avoid a simple declarative statement is a well remarked hallmark of unreason in masquerade demanding attention it has no right to claim.
Here’s a joke that it immediately brought to mind:
How do you get out of a locked room with only a mirror and a table?
You look into the mirror and see what you saw.
You take the saw and cut the table in half.
Two halves makes a whole and you crawl out.
The papers don’t show that the earth should do anything, sir.
They show that somebody WISHES it should, never mind the fact that it did or didn’t. They show that a man has spent a lot of time trying to create an explanation for a set of a priori assumptions and has completely failed.
It is pretty much straight up argument ad ignorantium.
It’s been around for thousands of years, of course (who do you think put all this chaos in the universe- vast impersonal forces or something!!??!! It’s got to be Goddess! How about a latter day climate chiliast?)
Maybe you could edit that and remove all the subjunctive nonsense and boil it down to a simple sentence? Like – ‘meh, dunno but I tried to play ball for the team’.
40% of something imaginary is not just a bigger pile – there’s nonlinear for you. . (Emphasis added)
I didn’t like those quotations at all. People who come by with WatchTower talk like that.
Sorry, friend. I love your work – not the ones you quoted.
Mike Ewing
Yes – in brief.
Less in brief – Each trace gas has a radiative effect. In the case of the stratosphere: ozone, CO2 and water vapor are all important and affect both the tropospheric temperatures and stratospheric temperatures.
Remember that this is “with all other things being equal” – especially important when we consider the surface and tropospheric temperatures. Less happens in the stratosphere so it is more predictable – countered by the fact that until quite recently there was a lot less measurement of the stratospheric trace gases (and temperatures).
Not wanting to make my comment go on too long, but it is important to understand that the “radiative forcing” is a real and verifiable value. The physics of calculating radiative effects are very solid and we can point a measuring instrument in the right direction and get a value which matches theory.
Temperature effects on the other hand rely on understanding radiative effects PLUS everything else in climate..
In the article on Stratospheric Cooling you can see model results (radiative transfer equations solved) for all 3 trace gases and then the combination.
That article is very much about the stratospheric effects. This article is about the surface and tropospheric effects.
We all have.
Leonard Weinstein
Everyone agrees. That’s what Susan Solomon and her co-workers are saying. No one (?) understands the mechanism behind stratospheric water vapor changes.
Great Blog. Finished slogging through the CO2 tonight, then saw this last post. You have a very good conceptual approach to laying out each issue. It used to be common knowledge that “greenhouse” warming heated the atmosphere.
I don’t yet get the stratospheric lapse rate and cooling cause yet. Will have to slog through that post more.
WRT 2000-2009 decline H2O in the stratosphere, perhaps this is where the “missing” heat went (condensation?)
The .5ppmv H20 increase from 1980 to 2000 is within the time frame of two lower stratosphere warming periods (MSU TLS) associated with major volcanic events.
Thanks again for a very educational blog.
Thanks for another great post.
“The term “non-linear differential equations” is a strange one. In fact, books about linear differential equations should be called “linear differential equations” and books about everything else should just be called “differential equations” – after all, this subject describes almost all of the real-world problems”
Another real world reality – Almost 0% of equations describing the real world are solvable analytically. I realized this about half way through a numerical analysis class way back in the mid 70s after having spent several semesters learning how to analytically solve differential and partial differential equations.
Yes, non-linearity is tricky. I have a pan of water on the stove, the gas set to ’1′. The temperature is 80C. I turn the gas up to ’2′ – the temperature goes up to 160C, right? Oh, hang on a sec. what if we’re measuring in Fahrenheit? Or Kelvin? But when we look, it seems to have gone up to 100C. I turn the gas up to ’3′. 100C. The gas goes up to ’4′ and things are looking very exiting in there. The boiling is vigorous. The temperature is… 100C.
When people speak of so many W/m^2 here and so W/m^2 many there, they expect that you can add them all up and that the total will tell you what the overall effect on temperature is going to be. If CO2 adds forcing, that difference will be added (possibly with a constant multiplier) to the total effect of all the forcings.
I have to say, I thought you kept switching direction a lot. At first I thought you was going to talk about what proportion of the greenhouse effect was caused by CO2 and H2O respectively – a questions whose complications are well worth bringing out. Then you seem to switch to non-linearity. Then to stratospheric water vapour changes. And then conclude that we don’t really understand why it has changed or what effect it will have, so we shouldn’t jump to hasty conclusions. Or maybe that we are certain it will increase warming by 40%. I wasn’t sure.
There’s a much simpler way of explaining why you can’t easily divide the greenhouse effect up amongst the component gases. Imagine we have blinds that block half the light. We put another set up in front of the first that again blocks half the light. And a third. So now we have, under the linear picture, three halves of the light blocked.
So what proportion of the blocking does the third blind really contribute? A half, because that’s what it would block on it’s own? A third, because the three blinds are identical? Or an eighth, because that’s how much adding the third blind to the other two reduced the light by?
When the blocking is unequal, and the blinds overlap across part of their range, it all gets even more difficult. And because of the non-linearity, the proportion of the effect caused by CO2 is not necessarily the same number as the proportion of the change contributed by a change in CO2.
But having introduced the question, I didn’t really see it answered by the rest of the post. Never mind. A lot of interesting stuff, nevertheless.
Nullius in Verba
You can see this explained in CO2 – An Insignificant Trace Gas? Part Five
“Therefore, guessing at the overlap effect, or more accurately, assigning the overlap equally between the two, [...]“
“guessing at the overlap effect”?!
I was wondering, should you take percentages of the total with all greenhouses gases present, or with none?
But thanks, anyway. I hadn’t seen those particular numbers before.
Nullius in Verba
On the comment regarding the relative effect of CO2 and water vapor in CO2 – An Insignificant Trace Gas? Part Five
“guessing at the overlap effect”?!
This is me pointing out that I am assuming something not quite explicit in the Ramanathan and Coakley paper.
Later papers, like Trenberth & Kiehl, and everyone else using the RTE find water vapor has around 2.5x the effect of CO2. This is done by calculating the value of radiative forcing with all the GHGs in place, then removing each in turn and recalculating the number. You can see it described in reasonable detail in the 1997 Kiehl & Trenberth paper (link in Part Five ).
Sure. But it’s a matter of understanding how/why. And what the numbers mean.
The point about discussing the complexity of the issue is to say that there are several numbers that could validly be taken to be “the” contribution of CO2.
Are you talking about absorption, radiative forcing, or temperature change? Because all three are different, and the relationships non-linear. A is 50% reduction from B and B is a 100% increase over A, is that a 50% change or a 100% change? And so on.
What I initially expected you to say was that Dexter was wrong because the question is meaningless, unless you are very specific about what question you are asking and why. And that this is because of the nonlinearity. What I didn’t expect you to say was that there was in fact a definite answer and this was 2.5x.
From a certain point of view, yes. From other points of view, not quite.
It doesn’t really matter to the AGW question, but it’s good to understand anyway.
Nullius in Verba
Radiative forcing.
It’s reasonably explicitly stated in CO2 – An Insignificant Trace Gas? Part Five :
..Longwave radiative forcing at the top of the troposphere – 3.9W/m2..
..Removing water vapor (and keeping CO2) – 25% increase in outgoing flux..
And explained in some detail in CO2 – An Insignificant Trace Gas? Part Seven
So given that this Dexter Wright was talking about energy absorbed, have you really answered the question?
He says quantity x is one in a thousand, you say no, and to prove it show quantity y is 25%. (Or rather, cite a paper that states it without showing any working.)
Now it may well be that quantity x is around 25% as well, and Wright has got it Wrong.
And I rather suspect that the amount of energy absorbed is the wrong number to look at anyway, because it depends a lot on where it is absorbed. But whatever the answer might be – it hasn’t been clearly shown, and readers could be more confused than ever over exactly what all these different percentages refer to.
With my pan on the stove, I have changed the gas setting from ’1′ up to ’4′; you could call it four times as much thermal forcing, a 300% increase, the removal of a 75% decrease from ’4′ to ’1′, a 20C temperature change, which is 25% increase in Celsius or 5% in Kelvin, or no doubt many other ways of looking at it.
Which of them is the “right” number?
Nullius in Verba:
The intent of the first part was to illustrate the conceptual difficulty of non-linearity.
The right equations to solve are the radiative transfer equations – not multiplying 2 numbers together. And solving the radiative transfer equations comes up with a very different result.
That was all on that topic for this article. Just an intro for the strong non-linearity that can be seen in stratospheric water vapor.
Why not take a read through the whole CO2 series and then post some questions or comments, either here, or on those relevant articles.
You will see that the radiative transfer equations are derived from 1st principles and can’t be solved with a pocket calculator.
You will understand then the basis for the calculations that modern climate science makes.
I pointed you to CO2 – Part Five and CO2 – Part Seven because they contain they answers you were looking for.
Now I’ll point you to CO2 – Part One through to CO2 – Part Seven
“But in wondering why they hadn’t, it did occur to me that non-linearity is something that most people struggle with. Or don’t struggle with because they’ve never heard of it.”
Non-linearity is something people on both sides of the AGW debate struggle with. Millions of articles about what happens if atmospheric CO2 is doubled.
Almost no articles pointing out that each ‘ppm’ of additional CO2 has less impact then the previous.
“The right equations to solve are the radiative transfer equations – not multiplying 2 numbers together. And solving the radiative transfer equations comes up with a very different result.”
I don’t disagree, but I think there’s a problem with the way you argue it.
To the layman, they see two different approaches come to conflicting answers. One of them clearly must be wrong, but which one? One approach is complicated, difficult, and has a lot of “trust me” in it and many steps skipped over in the presentation. The other is simple, fairly intuitive, and sounds plausible.
It’s also a valid method. In a complicated calculation it’s very easy to go wrong, and because of the complexity not be able to see the error. But it’s normal practice to do a ‘sanity check’ approximate calculation to see that the answer makes sense. 12,345×81 = 9,999,945. But ten thousand times a hundred is a million, so we seem to be an order of magnitude out. Which calculation is more likely to contain the error: the one with many complex steps in it (in which I haven’t even shown you my working), or the one with only one simple one?
“You will see that the radiative transfer equations are derived from 1st principles and can’t be solved with a pocket calculator.”
I know that. But you know that to apply them to the real atmosphere you have to interpret, approximate, measure, and model, and it isn’t always clear what “first principles” you’re supposed to be applying. Does the calculation you’ve done apply to the situation you’re interested in? The arithmetic may be perfect, but the physical interpretation wrong.
Take this term “radiative forcing”. It is the radiative imbalance at the tropopause that would result from making the change to atmospheric composition but before letting the temperature adjust. Except that in practice the temperature always does adjust. So it’s an imaginary number; a hypothetical situation.
That doesn’t stop a lot of people calculating with it as if this was the “imbalance”, the net power input going into the system that constituted the global warming. 4W/m^2 multiplied by the number of seconds in a year is 126 MJ/m^2 build up per year. I’ve seen people do it! But fairly obviously, that’s got to be wrong. Instead, the troposphere increases its output to compensate.
So it’s important to be clear on what all these different numbers mean, and why the one you’re using is the right one to use.
That said, I think the message that you’re trying to get across with the stratospheric bits of this post is an important one, and one that I think people like Dexter Wright would probably appreciate if they saw it spelled out clearly. That you can have a tiny effect in an unnoticed and poorly measured part of the climate system (like water vapour in the stratosphere) have a relatively massive effect on the final result at the surface, that could easily explain a significant chunk of observed warming or cooling without the need for your main hypothesis – this is an important thing to know when trying to decide whether the observations “prove” the hypothesis true.
I don’t know if that’s what you was trying to say. Like I said, the post seemed to jump around to me. But I hope you realise that in being critical I’m not being unappreciative.
harrywr,
“Almost no articles pointing out that each ‘ppm’ of additional CO2 has less impact then the previous.”
I’ve seen lots of articles that do. It’s true that many others don’t, but I certainly wouldn’t say ‘almost none’ do. The internet is a big place.
Science based on conjecture is fantasy and the work of authors such as Verne. Just stopped in to see what condition your condition was in. Wishful thinking appears to describe!
Solomonic esoterical studies aside, can any current instrumentation accurately measure stratospheric water vapor changes of 1 ppmv at every 1km of elevation? If so please explain how this works. If not, what in Blazes is accomplished by discussing this gibberish at all! If Solomon etal’s study can never be tested (1ppmv/1km) how can we understand whether strato-water vapor feedback means anything at this time?
Could you comment on the approaches one might take to work out cause and effect in the water vapor – temperature relationship?
There are Radiosonde data at http://weather.uwyo.edu/upperair/sounding.html
The majority seem to show INCREASING water vapour content (g/kg) with height above the Tropopause, ie increasing WV content with temperature and with decreasing air pressure.
Is there a simple explanation?
I was thinking of the nature of the problem of explaining non-linearity to someone unfamiliar with it.
First, I had to figure out that there is a reason why someone might be unfamiliar with it.
That person will have never designed a wheel, cooked a meal, or worked out the interest on a business deal.
I guess why I totally lost the thread?
Anyhow, here’s an excerpt from a nice children’s story- children my age, when we were very very young, had this sort of thing instead of Toxic Avenger.
“The humble poet declined the gold and begged to be rewarded in the following manner:
I will be content if we simply get a chess board, and have your treasurer put one grain of rice on the first square. For each turn, the treasurer will move the rice grain to the next square, but double it as he does so. In the first move, I’ll have one grain; in the second, two; in the third, four; and so on till we’ve moved through all sixty-four squares.”
The emperor was delighted, and agreed at once.
LOL – it’s the emperors and their offspring who are the ones with no clue about nonlinearity- not the poets or elephant washers.
J Solters:
It’s a very technical and (my opinion) dull field – from the rest of your comment you seem to think it can’t be measured this accurately. If you have a specific reason for believing that this can’t be done accurately, feel free to post it and I can have a look.
Satellite measurements provide a high level of geographical coverage but don’t provide as much vertical resolution. Radiosondes do provide the vertical resolution needed. The point of the paper showing the sensitivity at various levels in the atmosphere is to demonstrate the non-linear effect of different heights, and therefore why the location of water vapor changes needs to be known.
Here’s a paper which reviewed the accuracy of the HALOE measurement -Validation of measurements of water vapor from the Halogen Occultation Experiment (HALOE), Harries et al (1996). When I get the chance to read the whole paper I will post another comment:
You can also see the error bars on the graph in the body of the article for the HALOE results, which seem to be in tune with this paper on accuracy.
Here’s a very detailed paper on radiosonde accuracy – ftp://ftp.ucar.edu/pub/mmm/milo/miloshevich_JGR2006_awex.pdf
There are plenty more papers out there as well which review the accuracy of stratospheric water vapor measurements.
It’s not a field I find particularly fascinating, unlike trying to understand why the Eemian interglacial ended, for example. If you have a particular reason for believing that instruments can’t tell the difference between 4ppm and 6ppm of water vapor after taking a look at the latter paper, feel free to add another comment.
OT, but you introduced the subject into testimony.
Eyeballing the Vostok data, glacial/interglacial transitions look very much like impulse responses. If that is the case, then an interglacial will always end and decay back to glacial conditions. The end of an interglacial does not require a trigger. It’s the end of a glacial that requires a trigger and also a stored source of energy or something to magnify the rather small initial forcing, assuming Milankovitch cycles are indeed the trigger. Once the stored energy is used up, the temperature will decline and start the storage process again. The Holocene was distorted by the Antarctic Cold Reversal and the resulting Younger Dryas in the NH so the peak temperature wasn’t as high as the Eemian and the decay hasn’t been as fast. AGW may also be contributing, a la Ruddiman.
A small point. You might wish to distinguish non-linarity from recursivity. In many mathematical models of physical phenomena the terms are recursive such that, say, y = f(x,z) and x = f(z,q,r) and r = f(y,m) (purely hypothetical example). This is entirely apart from the question whether r, say, appears as r squared, or cubed, or to the 1/2, or etc.
Totally insignificant to the discussion, however:
“He has a zucchini in his hand. He picks up a potato in the other hand and it weighs three times as much. He needs 100 potatoes – big cooking plan ahead – clearly 100 potatoes will weigh 300 times as much as one zucchini.”
I suggest you rephrase for accuracy. 100 potatoes will weigh three times as much as 100 zucchini, not one zucchini.