Nature hates straight lines

In your tropical example isn’t it the radiative forcing thats changing not the climate sensitivity. Clouds and the like are blocking solar radiation to the surface?

Here’s the doom-monger argument in two sentences. It’s obvious that the sun warms the earth and there’s a nonlinear relationship of sensitivity to solar input over the course of day (same over seasons in temperate areas). But the linear relationship is from “forcing” which we define as the delta in radiative power (solar, CO2 or other) from some baseline to the new regime with greater “forcing”.
They justify this crap (mostly the ridiculous definition of “forcing”) using models which contain constant parameterized responses (e.g. parameterized convection) which produce linear responses. It also requires the mind boggling assumption that the world and its weather is somehow affected by this hypothetical world-wide average delta. Ask yourself if the tropical daytime nonlinear response described by Willis is affected by it being 0.5 degrees warmer in that location (unlikely since it is dwarfed by the daily forcing change) or 0.5 degrees warmer elsewhere (impossible).

HR: clouds are sensitivity.

I don’t like the assumption of linearity. But I don’t find the reasoning in this post very persuasive. I’m not arguing for climate linearity here; I’m arguing that sceptics need to present a well-reasoned position and that this post isn’t it. In two parts:
There are a lot of scientific laws that claim linearity, where if you look closer things don’t behave anything like what the law describes. Ohm’s law says V=IR; if you look closely, you find that electrons are jumping all over the place. Some will go backwards, some will go sideways, the majority will go in the right direction but with a wide spread of velocities. But when you zoom out a bit, the average law works quite well. Same with the kinetic theory of gasses; PV=NkT at a wide scale, but at a smaller scale you can see that actually atoms are crashing around in entirely random ways and locally concepts like “pressure,” “volume” and “temperature” don’t make a lot of sense. So you can’t point to local weather effects and claim that they disprove the aggregate average theory of linear climate sensitivity; the randomness of small-scale weather processes doesn’t disprove the overall theory of linearity any more than observing individual electron tunnelling in silicon disproves Ohm’s law.
Secondly, whether proving linearity from a model is justified depends on the details of the models and whether they do actually assume linear sensitivity. You would need to follow all those references you deleted to find out. Perhaps the model is based on some low-level empirically-derived theory that allows you to infer whether the aggregate behaviour is linear or not; we can’t tell from the text you cite. Perhaps they actually model all the thunderstorm creation processes in the tropics, and snowfall at the poles, based on observed data, and find that when you add it all up it comes out linear. The kinetic theory of gasses is again a great example, though in reverse; the aggregate gas law was developed empirically and the model of an ideal gas was developed by reasoning about what underlying processes might produce that aggregate behaviour. There was no direct evidence that gasses were made up of tiny particles when the model was developed; that didn’t make it wrong. The model agreed with the empirically-derived law, and was successful in explaining it. It turned out to in fact be pretty much right. If you followed your reasoning in the mid-19th century, you would decry the KTOG as fairy-tales that no sane man would believe and you would later look very foolish.

Here’s a classic control system with feedback.
1. Increased solar radiation heats area of planet, causing increased evaporation of ocean, lake, river, soil, whatever is down there.
2. Increased evaporation results in higher percentage of H2O in higher pressure lower layer of atmosphere. H2O is LIGHTER than the mixture of N2/O2, and tends to “want” to rise, but is prevented from doing so by boundary layer.
3. Eventually, enough H2O pools that it starts pushing through boundary layer and rising. As it cools by entering lower pressure areas, some of it condenses into droplets or crystals which cause visible clouds. These clouds block incoming sunlight, reducing incoming energy.
4. At this point, the system can achieve a level of equilibrium, where clouds control incoming radiation and manage to hold the temperature at a level appropriate for an area’s current pressure.
5. In some cases the amount of H2O is so great in a concentrated area that it bursts through the boundary layer and large amounts from the area go with it, creating massive upwellings that can exceed 100mph and carry millions of tons of moisture to areas of low enough pressure that they are in the -40C range. Welcome to a thunderstorm, or hailstorm. These types of storms haul HUGE amounts of heat high enough in the atmosphere that excess energy can radiate directly into space, eventually dragging supercooled H2O down to ground level in the form of rain or hail.
6. No matter how much cooling or heating happens during the day, then there is night. At night, all energy radiation is exactly one direction: outward. At any given moment, slightly more than 1/2 of the planet is experiencing night. At any given moment as much energy is radiated outward from the back of the planet as is being absorbed in the front.
7. Thus, it is physically impossible to achieve dramatic temperature changes from minor trace gas changes, since equilibrium is based on total mass of atmosphere and its major gas balance. Now, if the percentage of O2 and N2 were to significantly change, so would the equilibrium temperature of the planet.

So linear computer models find no evidence of non-linearity? Makes you want to weep!
The “Sunday Times” (normally a respected newspaper in the UK) yesterday had an article “2010 the warmest year on record”, but now buried on page 15 rather that the normal spot on the front page. Perhaps the MSM are now taking the hint, along with the Royal Society and all the other clowns who were taken in by this rubbish. But I notice that last week’s draconian (and necessary) spending cuts by the UK government still left billions for wind farms and carbon capture demonstration plants. Why are governments the last ones to “catch on”?

As an aside, Connolly may be gone from Wiki, but his spirit lives on!
http://motls.blogspot.com/2010/10/wikipedia-william-connolley-was-just.html
An edit by Lubos of Briffa’s page and it’s quickly erased and threats of sanctions are made!

Jerry says:
October 25, 2010 at 2:45 am

Are you comparing apples to oranges?
Is it possible the models are working on much longer time scales than say hourly at a location?
Perhaps you are both right (Wills and ‘the models’) Willis is correct on very short time scales? The models are correct on very long time scales?

Nature doesn’t work like that. You can look at the fluid motion of milk in a cup of tea and the motion of a massive gas cloud nebula in space and describe both using the same basic rules, yet the cup of tea is an event measured in seconds and the motion of that nebula is measured in millions of years. Possibly an extreme example and I’m certain someone will find a “yes, but” that they think counters the argument but bioth are governed by the same rules of fluid motion and will both behave in the same chaotic and apparently random way as a result, just over different time scales.
We live in a fractal universe. The same rules apply at the top and the bottom, the only difference appears to be the amount of time needed to observe them. Things don’t suddenly become linear after some ill-defined threshold of convenience.

While this issue is indeed a major issue , one has to be careful with the arguments .
I have to mention that any parameter Y related to a variable X will answer in a linear way (e.g Y=a.X) provided that the variation of X is small .
This is a trivial consequence of the Taylor expansion .
Sure it is necessary that the relationship between Y and X be sufficiently smooth but this is just a technical detail .
So if one considers a very small variation of a radiative flux (a couple of W/m²) compared to the overal flux (hundreds of W/m²) , then any variable , not just temperature will answer in a linear way .
Especially if you choose a variable like global temperature that has been so averaged that it almost stays constant whatever happens .
Let’s imagine that there exists an extremely highly non linear relationship F such as the Global average of temperature Tg :
Tg = F(Global radiative flux , albedo , sun activity , wind speed , polar ice surface , cloudiness , humidity , O3 concentration , microalgae mass and time) .
Now if you consider a small variation of the variable “Radiative flux” during a short time , all other variables being considered constant , the Tg response will be almost exactly linear .
One can even give easily the value of the proportionality constant (e.g climate “sensitivity”) – it is the partial derivative of F with regard to the Global radiative flux .
Of course there are at least 2 problems .
One is lethal – you don’t know F in the real world and it is not available to experimentation . So you have no clue and will never have about what the partial derivative of F are .
Second is almost lethal too . The linearity holds only for a short time as long as the system didn’t move far from the point where it was before .
As soon as any or all variables acting on F can no more be considered constant , the linearity no longer holds . In other words you can make predictions only for a very short time .
Of course in your example with thuderstorms there are no “small” variations , no “equilibriums” and no “everything else being constant” .
That’s why the Taylor development of your G (note that your G is NOT the same as the above F !) is useless and you are exposed to the full non linearity .
However this local result does not necessarily prove something about the averages .
In other words the uselesness of a Taylor development of G (e.g your thunderstorms) does not necessarily imply the uselesness of a Taylor development of F (e.g global averages) .
You will have noticed that I said “not necessarily” .
Actually the implication is often correct but the point is that it is not automatical , one has to go a bit more in depth to prove it .
Giving just the example of G is not enough .

Straightline thinkers using circular logic. How much more convoluted can that be? (Maybe they’re completely dedicated disciples of
M. C. Escher?)

“Why are governments the last ones to “catch on”?”
An easy question to answer.
The world warms and they did nothing despite being warned: they take the blame.
The world warms and they wasted billions because they were warned: they blame the scientists.

Archonix says
“Nature doesn’t work like that. You can look at the fluid motion of milk in a cup of tea and the motion of a massive gas cloud nebula in space and describe both using the same basic rules, yet the cup of tea is an event measured in seconds and the motion of that nebula is measured in millions of years.”
Nature has a lot of non-linear responses. Non-Newtonian fluids for example. The reponse of the system in that case is very dependant on the speed of application.
I suggest that daily responses to external forcings may partially mask long term changes to forcings.
I restate my question to Willis. Does your example match parameter for parameter with the models? Especially the temporal impulse and response?

Tom says:
October 25, 2010 at 2:49 am
The laws you cite have all made spectacular predictions with astoundking accuracy over an extended period of time.
The GCM’s have also made spectacular predictions, none of which have come to pass and some of which turned out to be diametrically opposed to actual observation over the past 30 years:
increasing Hurricanes,
sea-level rise,
raising temps,
etc,
etc,
etc…

The classic example of non-linearity:
The sun takes a typical path relative to the observer over a years time, and generates a sine.
The temperature lags the actual path and creates a different sine from the path.
The actual storm fronts and pressure cells that pass on by the observer create infinitely complex patterns superimposed upon the 2 sines.
The result of this non-linearity is that it is virtually impossible for the observer to live long enough to see a carbon-copy ( : of any given year.
And we have not included any other superimpostitions that nature provides to the weather.
So, what have Global Climate modelers actually achieved?
Global Climate modelers have proven that AI is impossible without non-linear equations.
They have also proven that supercomputer clusters are fundamentally linear and without AI.

“and excluding cloud-aerosol interaction effects”
Actually I found that phrase to be the most striking when I read the explanation. What they seem to be doing is making the statement, “we want to say that the relationship is linear”, then they proceed to eliminate whatever process does not provide linearity and voila, they have a linear relationship.
Would we accept an accounting statement that a company was ‘profitable’ if the accounting firm stated up front that they ‘excluded any negative transactions’ therefore the company is profitable?
It’s one reason I abandoned feedback analysis. Every ‘model’ I studied started out with the statement, “we eliminated the following processes to make the model mathematically tractable”. I could see no value in producing a model of a physical system that didn’t actually model the system.

The world warms and they did nothing despite being warned: they take the blame.
The world warms and they wasted billions because they were warned: they blame the scientists.

Haha Steven, very good. May I add that apart from politicians who majored in Philosophy (and hence have some familiarity with the argumentum ad verecundiam), most politicians are completely clueless about how science works and what the limitations of it are. Even when they are familiar, they tend to be in awe of it. Richard Dawkins has done much to promote this kind-of awe. I’m not criticising him for promoting reason over superstition, but his kind of idealism assumes each scientist has no Human frailty and the ethics of a Saint. Reading The Hockey Stick Illusion as I am at present, nothing could be further from the truth!

In the first quoted paragraph ” …could be linearly added to gauge the global mean response,but not necessarily the regional response.” Does that help,Willis?

its more non linear than we thought.
An obsession with linearity is essentially political.
I have also noticed that the same modellers who use linear assumptions, as you mention, also tend to also “average out” various datasets, such as proxy temperature reconstructions, and assume the averages of these proxies reveal some kind of meaningful trend. All these averages do is dampen and hide uncertainty in the proxies. Such is the case in Mann et al’s more recent paper about the MWP and LIA going back to about 1200 AD. Thy are using the same linear assumptions projected back into the past, as they do for the future, which is also part of the reason behind the hockey stick’s flatness back to 1000AD. ‘Averaging different uncetainties’ just doesnt work.
There is also another ‘linear- average’ that they assume. They state that if climate senstiviy is high to one variable, than it must be high for all variables. ie if climate is sensitive to eg solar variation, then it must also be just as sensitive to C02. From this they deduce that the common skeptical argument that the MWP was greater than reconstructions such as Mann 1998, only makes things worse, ie it creates more projected warming from human c02. So they have: little warming in the MWP and c02 effect is high, or high warming in the MWP and c02 effect is high. This way they get to have it both ways. A perverse example of their extreme ‘linear’ type of thinking.

Willis Eschenbach [Top Post] says:
“… I would say that their claim of linearity is an extraordinary claim that requires extraordinary evidence.”

Bingo. I would say that anything that shows up as linear is immediately suspect and will likely be quickly debunked (well, we’ll need that raw data first). That is my gut instinct and is based on a complex but abstract reason. I still cannot correctly put it into words, but I’ll try anyway …
I can vaguely remember 9th grade algebra, where you have plotting paper and pencils and rulers (there were no calculators yet and no computers). We would write some basic function and draw the graph. You would begin with x = y or x = y + 1 and so on. At this stage the results were of course nice straight lines. Later, you add exponents and degrees. (And it was no fun drawing something like x³ + 4x, of course many years later you just drop whatever function you want into a TI-xx graphing calculator and a nice graph pops on the screen, but I digress).
The point is even then I suspected something very strange and rigid and synthetic about the concept of a straight line linear graph. Studying electricity and electronics provided me the analog perspective. I believe that what has happened is that many become locked into the artificial, neat and pretty, but synthetic world that early math classes guide you into. In a sense it is the purest digital view of our purely analog world. But, I am still not explaining this right …
It is kind of like what the alphabet, vocabulary and language is versus the complete human voice, they are little pieces of the whole. Math, arbitrary numerical representations and algorithms are like the alphabet making words and languages out of pieces of the infinite number space. Linear functions can get us to little pieces of a sine wave without ever seeing it. Trees meet forest. I get a real Matrix (movie) feeling pondering this.
I have the distinct impression that most statisticians (those in the AGW cabal) are locked into this Matrix (a very simple one) where everything can and must be described with the simplicity of a 9th grade math problem. These statisticians are usually decimated once people show up with experience outside of the classroom (and their parents’ basement). I think this is why we see Meteorologists, Geologists, Physicists, Electricians, Programmers, etc, chewing them up for breakfast. (I am also starting to think I was wrong back in the early 80’s when I first used Lotus and Excel. I figured these were just fantastic steps forward, but now wonder if they are making us lazier and dumber. But I digress again, last time :-).
But my point is really a question, Is there anything that is actually linear? Can a linear graph ever represent something real? This post, particularly the title, Nature hates straight lines, really makes sense to me.

Tom says
Tom you miss the point of these laws / models; As with Newtonian physics these laws only work within the specified limits of classical physics. They are fine for everyday calculations, for ensuring that you have the right fuse in your consummer unit, etc. They cease to mimic reality at the atomic / electron level. This is where the Quantum mechanics model takes over. Climate models are so far from this level of modeling that they are no better than a playstation game.
Physical models, for that’s what the formulii are that you have quoted, are tested by physical experiments in order to find their limits and are then not used to describe the ‘observed’ events beyond those limit(s).
Climate models have not gone through this final process to my knowledge.

LazyTeenager says:
October 25, 2010 at 4:48 am
3. There is an obvious mismatch between the idealised process described for a day in the tropics and the process of global climate.
Ok This is your opportunity to stop waving your arms and explain this phrase in detail.

“Amplification of Global Warming by Carbon-Cycle Feedback Significantly Less Than Thought, Study Suggests”
http://www.sciencedaily.com/releases/2010/01/100127134721.htm
http://www.nature.com/nature/journal/v463/n7280/full/nature08769.html

I guess there are Newtonian assumptions behind the claim. ie increasing the total energy in the system will cause a linear change in the system where the system is unique. This would assume CO2 is not well-mixed, which is incorrect.

Willis,
In addition to an assumption of linearity, there is an assumption of equivalence between forcing types which is uncritically accepted as show by the mathematical formula for converting W/m^2 to its CO2 doubling equivalent. Even a basic understanding of nonlinear dynamic systems, makes it clear that it is unsafe to assume that forcings with different distributions or different coupling to the climate are equivalent. I found a refreshing acknowledge of this in Hegerl and Knutti’s review article:
“The concept of radiative forcing is of rather limited use for forcings with strongly varying vertical or spatial distributions.”
and this:
“There is a difference in the sensitivity to radiative forcing for different forcing mechanisms, which has been phrased as their ‘efficacy'”
http://www.iac.ethz.ch/people/knuttir/papers/knutti08natgeo.pdf
Unfortunately the “efficacy” is from the work of Hansen, which threw away part of the difference between solar and GHG forcing by using models with simplified oceans and no stratosphere, and coupling GHG to the whole mixing layer of the oceans, when CO2 wavelengths only penetrate microns and solar can penetrate 10s of meters.
On consequence of this assumed equivalence, is that they can try to calculate model independent estimates of climate sensitivity using solar and aerosols and then just translate it to a climate sensitivity to CO2 doubling. Their estimates for solar variability are low, even for the Maunder and Dalton minimums so their sensitivities to solar forcing ends up high and by equivalence CO2 is high. This is why light that the current solar minimum is shedding on solar variability, especially in the UV range. Those “model independent” estimates (which often use models BTW), assume all the solar coupling was purely radiative, while UV couples non-linearly, chemically through the creation of stratospheric and to a lesser extent tropospheric ozone, a greenhouse gas.
The equivalence assumption extends to the models, all they have to do is match the global average temperature and look like a climate. Models with twice the sensitivity and twice the aerosols are equivalent and “match” each other and the climate. So what if the climate produced twice the increase in precipitation (per Wentz), the climate is just one 30 year instance. The models have it out numbered.

John Day said:

Climate models have greater uncertainty, so that’s when all the fun begins in these climate blogs, sceptic or otherwise.

Come now. To say there are no “model free” measurements of nature is entirely correct. But if I make a clock from a dandelion and tell you that it measures time – one hour passes for every petal I pick off – you would be justified in questioning the efficacy of my method, notwithstanding the accuracy of my petal picking. Uncertainty isn’t the only problem with climate models, as you well know.

Moderator, apologies for the typos, please post this revision instead:
Willis,
In addition to an assumption of linearity, there is an assumption of equivalence between forcing types which is uncritically accepted as shown by the mathematical formula for converting W/m^2 sensitivity to its CO2 doubling equivalent. Even a basic understanding of nonlinear dynamic systems, makes it clear that it is unsafe to assume that forcings with different distributions or different coupling to the climate are equivalent. I found a refreshing acknowledgement of this in Hegerl and Knutti’s review article:
“The concept of radiative forcing is of rather limited use for forcings with strongly varying vertical or spatial distributions.”
and this:
“There is a difference in the sensitivity to radiative forcing for different forcing mechanisms, which has been phrased as their ‘efficacy’”
http://www.iac.ethz.ch/people/knuttir/papers/knutti08natgeo.pdf
Unfortunately the “efficacy” is from the work of Hansen, which threw away part of the difference between solar and GHG forcing by using models with simplified oceans and no stratosphere, and coupled GHG to the whole mixing layer of the oceans, when CO2 wavelengths only penetrate microns and solar can penetrate 10s of meters.
One, consequence of this assumed equivalence, is that they can try to calculate model independent estimates of climate sensitivity using solar and aerosols and then just translate it to a climate sensitivity to CO2 doubling. Their estimates for solar variability are low, even for the Maunder and Dalton minimums, so their sensitivities to solar forcing ends up high and by equivalence CO2 sensitivity is high. This is why the light that the current solar minimum is shedding on solar variability, especially in the UV range is so important. Those “model independent” estimates (which often use models BTW), assume all the solar coupling was purely radiative, while UV couples non-linearly (chemically) through the creation of stratospheric and to a lesser extent tropospheric ozone, a greenhouse gas.
The equivalence assumption extends to the models, all models have to do is match the global average temperature and look like a climate. Models with twice the sensitivity and twice the aerosols are equivalent and “match” each other and “match” the climate. So what if the climate produced twice the increase in precipitation (per Wentz), the climate is just one 30 year instance. The models have it out numbered.

Tom says:
“the randomness of small-scale weather processes doesn’t disprove the overall theory of linearity any more than observing individual electron tunnelling in silicon disproves Ohm’s law.”
==========
Ohm’s law holds only for so called ohmic materials (metals) that exhibit roughly constant resistance at roughly constant temperature, and even then it is only a good approximation.
Most materials in the real world thumb their nose entirely at Ohm’s law by showing all kinds of non-constant (i.e. voltage-dependent) resistance/conductance.
I’ve heard biologists aptly refer to Ohm’s law as “Ohm’s dream”.

Forcing is generally taken to mean downward radiation measured at the TOA (top of atmosphere). The IPCC says that when TOA forcing changes, the surface temperature changes linearly with that TOA forcing change.

Willis: Thanks for another illuminating posting… slowly, slowly the seven veils are being stripped away… only to reveal an IPCC emperor with no clothes…
The thing that makes me smile about the concept of climate sensitivity is that it means the SUN must have been responsible for driving the surface temperature up during the Medieval Warm Period and down during the Little Ice Age.
The Intergovernmental Panel of Climate Clairvoyants just make up the rules as they go along… nothing hangs together… circular logic… conflicting rules… assumptions… fudged data… bogus models… propaganda… evasion… conspiracy… deception… misdirection… and lies… my oh my… what wonders they can see in their crystal balls…. Climate Science has become an oxymoron.
The typical tropical day clearly illustrates the non-linear climate sensitivity for a specific spot on the globe.. and lets hope there is not a cold northerly wind or a hot southerly wind that will affect their observations… and when they get to the night they see temperatures fall over time… surely they know the basic science behind the non-linear Cooling Curve http://en.wikipedia.org/wiki/Cooling_curve
Even if they you managed to establish the climate sensitivity for a specific spot on the globe it would still vary up the air column (say up to tree height or beyond) and by season for that spot on the globe… and how about the local area… it can be different 100 meters away, let alone 100 kilometers… and trying to say that somehow they have established a global climate sensitivity is simply beyond comprehension… let alone that it is linear… so now they have morphed into the Intergovernmental Panel of Climate Crazies.

Willis, I applaud you on finding this particular pea in the IPCC shell game. The next step is to find an alternative explanation that better describes climate sensitivity.
I think Tom’s argument above regarding averaging of complex systems has some validity. In hydrogeology we use similar empirical rules to characterize and calculate groundwater flow when we know that at smaller scales groundwater acts quite differently.
I am not a big fan of invoking chaos as an explanation. I suspect that chaos is too often used as an explanation when something is complex and therefore too troublesome to figure out. Natural phenomena appear to me to exhibit a form of symmetry at all scales. This seems to argue against chaos.

Two centuries ago, the river Thames used to freeze over. Then it didn’t any more. What went wrong? Was it linearity? Then the warmth came, then these last winters England suffered cold snaps such as>: http://news.bbc.co.uk/2/hi/in_depth/8447023.stm < when the UK mainland was 100% covered in snow. Also, this 2009/10 winter the northern hemisphere had the largest land snow cover ever recorded. Is this linearity. Of course not. It's called climate change. The climate change deniers are not us but them; those who are playing around with multimillion dollar computer games funded by our taxes. The IPCC are the climate deniers because its them that deny that climate is continuously changing. They say it has not changed during the past except now due to my breathing out CO2.
Now the AGWers want to control the climate by reducing/adding CO2 . They want to software-design our climate but Anthropogenic Climate Design will never work.
Great post Willis.

Oh dear. All differentiable functions are linear to first order in small quantities. It doesn’t matter how convoluted and nonlinear, or even chaotic, the curve might be, or how strong the feedbacks, it is still linear for small changes. What we are talking about here are small changes in the energy balance, of a few parts per thousand (~1W/m2 in ~1kW/m2) . So the predictable or average component of the response of the global temperature to such changes cannot help but be close to linear. The only way that could fail is if the response is pathological – either about to run into the buffers or to fall off a cliff in a (mathematical, if not physical) catastrophe – which only the most absurdly alarmist would claim.
By the way, the term “forcing” is wrong; a forcing is an oscillation imposed upon a system other than at its resonant frequency.

LazyTeenager says: October 25, 2010 at 5:09 am
PolicyGuy says
——————-
nothing but models that perform as they were written to perform
——————-
You know nothing about the models and you are pretending insight where you have none. You have been fooled by your own sophistry.
Pot meet kettle, don’t know much about computers do you. I assumed those who grew up with them might understand the computers’ limitations, guess I was wrong. Or maybe the teenager part of your moniker is a fib.

Tom says:
October 25, 2010 at 2:49 am
There are a lot of scientific laws that claim linearity, where if you look closer things don’t behave anything like what the law describes. Ohm’s law says V=IR; if you look closely, you find that electrons are jumping all over the place. Some will go backwards, some will go sideways, the majority will go in the right direction but with a wide spread of velocities. But when you zoom out a bit, the average law works quite well. Same with the kinetic theory of gasses; PV=NkT at a wide scale, but at a smaller scale you can see that actually atoms are crashing around in entirely random ways and locally concepts like “pressure,” “volume” and “temperature” don’t make a lot of sense. So you can’t point to local weather effects and claim that they disprove the aggregate average theory of linear climate sensitivity; the randomness of small-scale weather processes doesn’t disprove the overall theory of linearity any more than observing individual electron tunnelling in silicon disproves Ohm’s law.
I have been discussing this often, more recently in the Spencer thread.
Physics formulations have regimes where they hold.
Meta levels. An example from everyday life is
a) the alphabet level ( or sounds if you prefer)
b)words
c) sentences with structure
b is a meta level of a and c is a meta level of b. Each is founded on the previous, but the rules are completely different.
You will not argue that a poem has too many letter “e” or needs many “a” to carry meaning.
In the same way the current frameworks of physics, which are developed with rigorous mathematics, start with quantum mechanics, go into quantum statistical mechanics, which goes into thermodynamics. A parallel line was before the 20th century, started with the atoms, goes into statistical mechanics, goes into thermodynamics.
Each level has its own rigorous mathematics There are theorems that connect the quantities from one level to the metalevel, and there are conservation laws that are strict in all levels. The mathematics is different at each level, so one could claim/show that linearity holds in a higher level while not in the lower one, but it is not for the same quantities really. It is like mixing alphabet with words.
The difference with climate modeling is that climate is not shown to be a different framework than weather. Particularly in the infamous GCMs the weather models, that cannot predict the weather reliably for more than a few days, are taken over and used for climate with averages replacing a lot of variables that weather modeling uses. There is no different mathematics, the same equations are solved .
Secondly, whether proving linearity from a model is justified depends on the details of the models and whether they do actually assume linear sensitivity. You would need to follow all those references you deleted to find out. Perhaps the model is based on some low-level empirically-derived theory that allows you to infer whether the aggregate behaviour is linear or not; we can’t tell from the text you cite. Perhaps they actually model all the thunderstorm creation processes in the tropics, and snowfall at the poles, based on observed data, and find that when you add it all up it comes out linear. The kinetic theory of gasses is again a great example, though in reverse; the aggregate gas law was developed empirically and the model of an ideal gas was developed by reasoning about what underlying processes might produce that aggregate behaviour. There was no direct evidence that gasses were made up of tiny particles when the model was developed; that didn’t make it wrong. The model agreed with the empirically-derived law, and was successful in explaining it. It turned out to in fact be pretty much right. If you followed your reasoning in the mid-19th century, you would decry the KTOG as fairy-tales that no sane man would believe and you would later look very foolish.

When one is replacing the variables of an equation by an average value, which is what the climate models are doing, one is really expanding in a perturbation series and taking the first term : constant +a*X +b*X^2+…
a is related to the average of the value of the function.
If the weather predictions are no good after N time iterations because non linearities kick in, since solutions of coupled non linear differential equations are highly non linear, more so for climate projections which have more assumed linearities.
One does not need to go to the references to know GIGO.

Robinson said:
“… if I make a clock from a dandelion and tell you that it measures time – one hour passes for every petal I pick off – you would be justified in questioning the efficacy of my method, notwithstanding the accuracy of my petal picking. Uncertainty isn’t the only problem with climate models, as you well know.”
Yes, the other major facet of a model is its _correctness_, i.e. can it consistently predict the future (or explain the past)? [We need _consistency_ because a stopped clock is accurate twice a day etc]. A third facet may be _efficiency_, with respect to resources consumed by the modeling.
So, assuming that your dandelion-clock model is correct, i.e. it can consistently measure the passage of time, my only other major concern would be the _uncertainty_ (‘error’) of each time measurement.
So, applying this to AGW, we agree that it is correct that under certain conditions CO2 can exert some positive radiative forcing, our concern should be the calculation of the _certainty_ that this forcing will (or will not) lead to catastrophic global warming.
For the record, I have not seen any convincing proofs of CAGW. If it turns out that some non-catastrophic warming can be traced to man-made activities, we will be enlightened (but not alarmed).
😐

Very interesting. Of course the answer for the IPCC team would be that they admit in the IPCC that clouds are poorly understood. I see no reason to dispute that point with them because it’s an admission of such a large lack. Unhappily few journalists are savvy enough to recognize what a large uncertainty it means for all the sensational warnings. Clouds are poorly understood and it’s not a trivial thing that they are. Stefan-Boltzmann works well in controlled laboratory conditions but why would anyone think that stepping back from earth a few thousand paces and squinting your eyes makes something like global cloud cover a stable average that can be thought of as constant. I believe it’s most likely that global albedo, because of the changeablility of cloud cover, is not anything so stable as the level of the sea.
…
According to what I read, observations of earthshine on the moon from Big Bear Solar Observatory have already established that “Earth’s average albedo is not constant from one year to the next; it also changes over decadal timescales. The computer models currently used to study the climate system do not show such large decadal-scale variability of the albedo.” http://www.universetoday.com/9611/decreasing-earthshine-could-be-tied-to-global-warming/
This result was reported in a May 28, 2004, Science article titled, “Changes in Earth’s Reflectance Over the Past Two Decades.” Interestingly the article I found reporting on this had recast things to fit into the sensational kind of global warming headline we are more familiar with: becoming – “Decreasing Earthshine Could Be Tied to Global Warming.”
I

This article reads like someone who is trying to use debating tricks to win an argument rather than someone who is trying to discuss the science.
I admire your Thermostat Hypothesis and predict it will turn out to be an important effect.
On the other hand, random sniping and potshots at the IPCC don’t move along the discussion very much. Although everything at some point ends up being non-linear, the simplifying assumption of linearity is a very useful tool when used over limited spans. Assuming a nearly linear relationship between forcing (over some period) and the resulting temperature change is not incompatible with feedback effects like your Thermostat Hypothesis.
Your argument isn’t that much different than trying to reject the global average temperature time series as being meaningless because it doesn’t reflect either day to day variations or the spatial variations across the globe. The global average temp indeed is not an accurate depiction of the temperature anywhere on the globe, but it is still a useful metric.

As an analytical chemist, I have built a career around relating mathematical models to real-world measurements, and the only place I have found the assumption of linearity to be reliable is as an approximation during interpolation between two actual measurements of knowns (standards), and even there one often finds a deviation from linearity that is revealed by careful measurements. The Beer-Lambert Law, the physical law that relates the amount of energy absorbed by a medium to the concentration of the absorbing species (think CO2 in air) is a *logarithmic* law.

@Francisco – another one who says the same as me but draws utterly the wrong conclusion. Ohm’s law works nicely at the scales encountered for general circuit design. Or does no piece of electronic equipment actually work and it’s only me who hasn’t noticed? Biologists can say what they like, I suspect referring to very small scale (intra-cell etc) processes; engineers will keep on using it for circuit design and succeeding.
@anna v – nice to have someone interact seriously with ideas. You refer to “the climate models” as though every climate model was the same, but the IPCC report refers to only two or three papers specifically to make this point. Those papers might describe models that are extremely intricate interactions of well-known, well-understood physical processes, that show that in the aggregate, simulated over a model of the earth’s surface, those processes work out to a linear (or roughly linear, or linear over the range we are likely to care about) climate sensitivity. My point is not that they do or don’t, (I am too busy/lazy to go and check) but that just saying, “OMG, Models!” doesn’t prove it either way.
@Charile A – yes, what I was trying to say, I think.

It seems to me, Willis, you have illustrated one of the great flaws in our mathematical efforts to forecast reality: In reality nothing is linear but compueter models want to predict liniar results. I have been forecasting weather for over 50 years. Hour to hour, day to day, week to week, season to season, year to year, nothing is liniar. I have been playing poker for 30 years. The cards odd are not linear. I have been aging for 76 years. It has not been a linear process. Everything is non-linear.

Nature abhors a vacuum… that’s why it’s so dusty!

Willis: A straight line may be the shortest distance between two points in 2 dimensional geometry. However, in our (at least) 3 dimensional world the great circle route is alway shorter than the rhumb line when navigating routes longer than the distance to the horizon. Straight lines are shorter only when measuring the distances inside the circumference of our planet. Curves are beautiful and reflect perfection in nature.

Tom says:
October 25, 2010 at 2:49 am
I don’t like the assumption of linearity. But I don’t find the reasoning in this post very persuasive. I’m not arguing for climate linearity here; I’m arguing that sceptics need to present a well-reasoned position and that this post isn’t it. In two parts:
There are a lot of scientific laws that claim linearity, where if you look closer things don’t behave anything like what the law describes. Ohm’s law says V=IR; if you look closely, you find that electrons are jumping all over the place. Some will go backwards, some will go sideways, the majority will go in the right direction but with a wide spread of velocities. But when you zoom out a bit, the average law works quite well. Same with the kinetic theory of gasses; PV=NkT at a wide scale, but at a smaller scale you can see that actually atoms are crashing around in entirely random ways and locally concepts like “pressure,” “volume” and “temperature” don’t make a lot of sense. So you can’t point to local weather effects and claim that they disprove the aggregate average theory of linear climate sensitivity; the randomness of small-scale weather processes doesn’t disprove the overall theory of linearity any more than observing individual electron tunnelling in silicon disproves Ohm’s law.”
Actually you have it backwards. Ohms law and the ideal gas law are linear in small ranges, not as the entire pciture. It’s when you go to extremes that the models break down. PV=nRT around STP (Standard temp and pressure) but does a poor job at low pressures or very high pressuresorks. The reason it doesn’t work is because of significant interaction terms which exist in the real world but are mostly always disregarged when scientists create models. Others have tried to come up with gas laws that take into account compressibility factors or interactions of molecules but these mostly fall to empirically derived factors.
The climate models are sorely lacking in any understanding of the important interactions between factors which I believe is a main point of Willis’ excellent article.

Are not thunderstorms in the tropics a continual occurrence as local afternoon is always happening somewhere? Where it’s hot sweaty and time for a cool tall one. And the yellow sun forever gazes down.

It’s unfair to use observations, measurements and causation in modern climatology. You have made the same mistake as Ferenc Miskolczi. We do not live in a world of physics, chemistry etc.. We are parts of superlinear computerprograms and nature is what you see on TV.

Charlie A says:
October 25, 2010 at 8:27 am
The global average temp indeed is not an accurate depiction of the temperature anywhere on the globe, but it is still a useful metric.
~~~
Why? How?
Proponents of CAGW assume this statement to be true, a priori. But, I’m not convinced it is. To me, a global average temperatures is like a global average phone number. Interesting…maybe…but useful? Hardly.
And, I’m not even going to get into the issues of accuracy (or lack thereof) of measuring average temperature (see surfacestations.org).

Hmmm… This seems to more of a semantic problem. Isn’t the whole concept of linearity a metaphore, except in pure mathematics? It’s usable to explain stuff, but doesn’t exist in the real world.
You don’t convince me this time, Willis.

Smokey says: “mRE says:
“Um, crystals have perfectly straight lines, and absolutely precise angles.”
As Willis constantly reminds everyone: don’t assume; quote what he wrote.
Willis wrote: “Very little in nature is linear, particularly in complex systems.” [my emphasis]
Crystals are not complex systems.”
And, actually, crystals are not so perfect as this guy seems to think. It is in fact typical for crystals in the real world to have irregularities and defects. And beyond that, if the position of the constituent particles of a crystal were all so predictably, perfectly arranged, they they would have to have very poorly defined momenta, by the uncertainty principle, so their velocities could be just about anything you can imagine-clearly such uncertainty in the amount of particle motion, would not make much sense for a solid object. If we conversely say that it’s a solid, so the velocities of the particles must be all very low, then we are saying that we can’t define the position of the particles precisely-how can one say that the particles are arranged in a specific, precise way with respect to one another, if the particles don’t even have well defined positions?
On the quantum level, all matter is “fuzzy” and not neat and exact in shape.

> yes, Willis missed this one badly.
Nothing enhances the credibility of an argument better than than realizing and admitting an occasional error.
I must confess that there _is_ something that is more rare than a Perfect Circle or Line in Nature.
It is the “One-Sided, Science-is-Settled Argument”, that our AGW friends have been pandering for many years. It doesn’t exist, not even close.
😐

Tom says:
October 25, 2010 at 11:21 am
dF = 5.35 ln (C/C0)
dT = S dF
Radiative forcing is a logarithmic function of CO2 concentration. Temperature change is a linear function of radiative forcing.
————————
How many Watts/m2 is required on Sun’s surface to increase its temperature by 1.0C?
= +50,000 W/m2
How many Watts/m2 is required on Earth’s surface to increase its temperature by 1.0C?
= +5 W/m2
I don’t know how much more non-linear a phenomenon can get.
The temperature does not change linearly with the forcing.

GaryW:
>calibrated measurement instruments … single physical quantity is measured in real time and read out directly.
In the mathematics of modeling, an ‘oracle’ is such an ‘ideal’ device. An oracle can read out true values without error or interpretation. Unfortunately, oracles are fictitious entities, invented solely for the sake of argument or elaborating a proof. They don’t exist in the real world.
Every measurement tool employs a model, subject to errors of implementation and interpretation.
For example, a yardstick measures extension in one dimension.
What if the markings are incorrectly applied? What if you mistook a ‘5’ for a ‘2’? Then you’ve introduced some errors into your measurements.
What if you haven’t noticed these errors? Then there is uncertainty in all the measurements made, past and future, caused by a faulty ‘model’.
The good news is that most of these instruments (note weaseling) are so reliable that we don’t worry about them. It’s the ‘clocks’ and ‘thermometers’ used for climate modeling that we should be concerned about.
😐

When you are sitting at a desk doing math you can have things be linear. When you get up and walk away from the desk into the real word you can forget hopes of things being linear.
Everything is complex. We barely know anything about everything.

Steven Mosher,
Yes, a nice effort at changing what they said to what you want them to have said (are you are lawyer by any chance? You should consider it.) Just to be sure that they said what Willis said they said:
“there is high confidence in a linear relationship between global mean RF [radiative forcing] and global mean surface temperature response.”
But perhaps they didn’t mean what they said, but meant what you said they meant. I guess anything’s possible in climate science.

Actually, Willis, you can see the greater sensitivity at lower temperatures in the DMI graphs for the Arctic circle. During the Arctic winters, the temperature varies greatly, but during the Arctic summers, the temperature is pretty consistent year in and year out.

davidmhoffer says: “In 2.8.1 they are explaining that they measure forcing and (I presume) calculate sensitivity AT THE TROPOPAUSE.”
Sorry, but even though it might make more sense to you, and make more sense physically, sensitivity is always defined with respect to the SURFACE temperature not at the tropopause. Yes, the forcing is not defined at the surface, but typically higher up (actually usually referenced to the “top of the atmosphere”) and while this may seem to imply that the sensitivity is referenced to the same layer, it never is. The sensitivity figures they talk about are ALWAYS regarding the SURFACE TEMPERATURE. So your presumption is wrong.

George said:
> and also a circular reasoning since we are trying to get a surface Temeprature
> change from a forcing that is itself a strong function of Surface Temperature.
The “dt=lambda x dF” equation is a rubric, not a law of nature. There is no conservation law for temperatures, only for energy (and momentum).
Thus the ‘flaw’ in this sensitivity rubric (as Willis correctly pointed out in his article) is that the system can absorb massive amounts of energy, without any change in temperature, so dT=0.
Article:
“Above the thunderstorm threshold temperature, little additional radiation energy goes into warming the surface. It goes into evaporation and vertical movement. This means that the climate sensitivity is near zero.”
My quibble was the apparent conflation between non-linear mappings and their cumulative effect on energy conservation, which is always linear because energy is always conserved. Linearity, in physics, translates as the the Supposition Principle. (If we could amplify energy then we could add some scalar laws too, but that would violate conservation)
http://en.wikipedia.org/wiki/Superposition_principle
I think we may be in violent agreement with Willis.

Andrew says;
The sensitivity figures they talk about are ALWAYS regarding the SURFACE TEMPERATURE. So your presumption is wrong.>>
As stated this is just an opinion. I propose that you cite the sections of AR4 and post links to the places where they SAY this. Not vague references, or cites of cites of papers behind paywalls, actually SAY it.
Then I propose you follow up by explaining how it is that they they justify their sensitivity calculations. Per their documentation, doubling CO2 = +3.7w/m2 = +1 degree of warming. Based on Stefan Boltzman equations, a body at -20C requires +3.7w/m2 to increase equilibrium temperature by one degree. A body at +15 degrees, the “average” temperature at earth surface, requires +5.5w/m2 to increase equilibrium temperature by one degree.
So which is it? CO2 doubling = +5.5w/m2, or sensitivity is calculated against effective black body temperature of -20C at the tropopause?

Willis (and Andrew)
Here is a rather in depth analysis of the IPCC’s claims in regard to sensitivity and feedback. Despite being part of Princeton’s dept of Mechanical Engineering and Aerospace, they couldn’t find the place in the IPCC report where it SAYS how sensitivity is calculated.
So they deduced it from various numbers and then show the math to arrive at a sensitivity of 0.7 degrees per CO2 doubling rather than the IPCC’s 1 degree at earth surface.
Andrew – I suppose this gives you a third option other then the two I already proposed. You could take the position that they plain simple got the calculations wrong. I’ll just chalk up the fact that if you take the equations in this paper and apply them to -20C at the tropopause, your gonna get 3.7 watts and a sensitivity of 1 degree to complete coincidence.
http://www.princeton.edu/~lam/documents/RadPhys08.pdf

Willis,
This is exactly what I’m trying to show. Due to rotation, the majority of things move in a arches or circular.
But, most of our science does not feel it so it ignores it as no existant!
Winds at different level of our atmosphere do some pretty funky things depending on what factors are given them. The slow lining up of our low level winds to the planets rotation changes how heat can discipate more slowly.

davidmhoffer-It may well be that they erred in their calculations. At the moment I am hard pressed to find where they say that they mean the sensitivity of the surface temperature. However, I know that this is what everyone seems to think they are saying, including most of the “mainstream” scientists who talk about the sensitivity.
Maybe this is a huge fluke nobody has caught. It does seem to be rather odd that they are creating an opportunity for conflation of the surface and TOA responses.
This will require further examination.
~Andrew

I’ve no problem with the anthropomorphism. My cats run for the hills whenever we get out the hoover to clean the carpet. The reason for this should be obvious to any physicist: nature abhors a vacuum!

timetochooseagain;
At the moment I am hard pressed to find where they say that they mean the sensitivity of the surface temperature… (snip) Maybe this is a huge fluke nobody has caught. It does seem to be rather odd that they are creating an opportunity for conflation of the surface and TOA responses.>>
I could point you at a couple of the places where it sorta almost not quite says it, but why should you be exempted from the hours of fruitless searching and cross referencing that were such shear joy for me. There’s one place where it makes a clear statement about forcing and surface temps, but the surface temps reffered to are contained within the six economic scenarios which each have ranges of CO2 production rates changing over time. Good luck correlating that back to degrees C versus forcing. Why the obscure references? Why not clear concise definitions? Why not produce simple graphs depicting tropopause forcing (note – they say “at the tropopause” in almost all cases, not TOA. Is there a difference? I dunno. THEY DON’T SAY) versus surface temps. You’d think there would be ONE chart or diagram showing that. Just ONE.
I shall answer that question two ways.
1. When you wish to write a report not supported by fact, be selective of the information you use, write of it in vast quantities, and in excrutiating detail. No one will notice.
2. The “climate sensitivity” discussion distracts from a discussion of how it would exhibit itself. Suppose for a moment that the effective black body temp of earth increased by 3 degrees. What would that mean at surface? 2 degrees. But that’s an average. What would that mean at say the arctic circle. (guestimates from here to illustrate but supportable guestimates) arctic circle – 6 degrees. All year? No, plus 10 in winter plus 2 in summer. Lows of -30 instead of -40 and highs of +4 instead of +2. Equator? Plus 1. All year? Pretty much, pretty stable temps there. Oh, let’s not forget night versus day. Nights +20 instead of +19 and days +30.2 instead of 30.0.
THAT is the discussion the warmists want to avoid. Let’s do a survey. Hey all you polar bears out there, listen up. No seriously, put down your Coke and pay attention. By a show of paws, how many of you think that living through winters at -30 instead of -40 is a bad thing? None? I thought not. How about summers? Can you handle +4 instead of +2? Paws up if that’s gonna kill you guys because you might not know it but you’re the climate canaries. Those clown fish at the equator are useless, I asked them about day time highs going up 0.1 degrees and they just blew bubbles at me like the answer was obvious. No, you can’t eat the clown fish. No, not the canaries either. Why? Never mind why, just vote. What? No, the seals won’t change color, they’ll still be black. No! There aren’t any half black seals either, now would you just vote- OK, I get it. Funny polar bears.
I could go with the IPCC upper estimate of 4.5 degrees, or hey, why not 8? You still come back to the same analysis. Most of the warming happens in the coldest latitudes, in the coldest seasons, and at the coldest part of the day. The high temps don’t change all that much. Not even the IPCC has argued that Stefan Boltzman doesn’t apply.
Oh great, the polar bears all shook their Cokes and are spraying me.

Jerry says:
October 25, 2010 at 2:45 am
Are you comparing apples to oranges?
Is it possible the models are working on much longer time scales than say hourly at a location?
Perhaps you are both right (Wills and ‘the models’) Willis is correct on very short time scales? The models are correct on very long time scales?
UNQUOTE
Well Jerry
– we’ll just have to wait 100 years or so to find our who’s right and who’s wrong –
Willis with his data or the experts with their programs.
In the meanwhile let’s just destroy industrialisation, based on a hunch.

The place where I live has witnessed a 3.5-degC rise in temperature, no doubt due to UHI in this megalopolis:
http://data.giss.nasa.gov/cgi-bin/gistemp/gistemp_station.py?id=210476620003&data_set=1&num_neighbors=1
Apparently nobody is tortured by this. No cataclysmic catastrophe is noted over past decades.
What are you worrying about, Mr. Eadler????

Willis, as usual another understandable post with a point. I really prefer the ones that contain lots of side thoughts and interesting life experiences but I do understand you write to inform and educate. You brought on some controversy but I did not discern where it was justified. Reading through all those comments has tired both my eyes and my brain. Goodnight

George E. Smith says:
Well in mathematics a straight line is infinitely long and has no other dimensions. There is no such thng anywhere in the universe.
Actually you are mistaken.
Quantum physics does this in a lab using lights and lazers.
And the second is every picture showing heat and air movement for this planets surface use straight lines when rotation actually makes them curve.

Dave F says:
October 25, 2010 at 1:24 pm
Actually, Willis, you can see the greater sensitivity at lower temperatures in the DMI graphs for the Arctic circle.
It is also clearly visible in individual Arctic temperature records, for instance Cambridge Bay in Arctic Canada:
http://www.wunderground.com/cgi-bin/histGraphAll?day=26&year=2009&month=10&dayend=26&yearend=2010&monthend=10&ID=CYCB&type=6&width=500
Also, just look at the temperature reconstructions from ice cores for the last glacial compared to this interglacial: During the glacial, temperatures jumped wildly.
Warm climate is stable, cold climate is unstable. There are very good reasons to believe that global warming would only be benign, while global cooling can turn into a glacial catastrophe within a very short time.

eadler said on October 25, 2010 at 7:20 pm: “Climate sensitivity relates to the change in temperature, required to restore radiative equilibrium, which is driven by a given radiative imabalance at the initial condition, caused by a change in greenhouse gases.”
How does the weather in the locality described by Willis know that that there is a worldwide radiative imbalance and that radiative equilibrium needs to be restored? Ans: it doesn’t. The weather is always local, there is no way that weather can restore a global radiative equilibrium. So eadler is right in one respect, the earth will get warmer due to CO2 radiative imbalance. But he is wrong in supporting the modeled sensitivity that includes globally positive feedback from increased (globally averaged) water vapor. That is merely a model artifact based on parameterized weather. But the real world changes in water vapor due to slight CO2 warming will cause both warming and cooling depending on local weather. The global climate model are hopelessly coarse to be able to predict that warming and cooling. Someday, maybe, when climate models have the resolution of weather models. But not right now.
Perhaps eadler would like to address the tropics and show a fine grained tropical weather model with positive feedback?

Tom,
The amount of conceptual confusion generated by something as straighforward as Ohm’s law is perplexing. The most common source of confusion seems to consist in conflating Ohm’s law with a possible definition of resistance (or even impedance or conductance). There are actually raging discussions over what this “law” might mean. The conversation below is representative of these various forms of fog, and the final paragraph sums up the matter rather well.
http://www.archimedesplutonium.com/File1994_07-08.html
>
>We have two contradictory claims regarding Ohm’s Law.
>
>vbv@… claims that the R in Ohm’s Law (V=IR) is constant, that the “law” is only an approximation for certain materials, and that this “law” does not actually apply in all situations.
>
>kheidens@… says that Ohm’s Law does indeed apply in all situations, even though Ohm never actually intended it that way.
>
>Is there some physicist out there (preferably a Ph.D.) who can help settle this issue once and for all, in a level-headed manner?
I would hope that any undergraduate physics major could answer this question. It does not require a PhD. Ohm’s law DOES NOT apply in all situations. It doesn’t come close to describing the I-V curve of a diode, for example. Even for uniform materials, it is only a phenomenological approximation of a very complex theory of electron transport, and fails all over the place to one extent or another.
Of course, if you are willing to define R(x,t,T,…) as a variable quantity such that V/I = R, then you can declare that Ohm’s “Law” works all the time. But then you have turned it into a useless definition of a time-dependent, voltage-dependent, etc., resistance — no longer a law at all.

MarkR (October 26, 2010 at 6:06 am) “We have estimates of climate sensitivity to global forcings from palaeoclimate, see e.g. Knutti & Hegerl, 2008.”
Consider the case of a forcing such as solar magnetic. Suppose solar magnetic changes caused a temperature increase some time in the past. Some hundreds of years later, CO2 followed with an increase (which fed back to the temperature increase). Since your two measurements are CO2 and temperature, you cannot determine “sensitivity” of temperature to sensitivity because part of the temperature increase came from the third factor. The real world has several more forcings beyond the one in my example.
Reading Knutti & Hegerl, 2008, I see no estimates of paleo forcings. Maybe I missed it? They prove a “water vapor feedback” in a linear model based on an ocean current response to a volcanic forcing, but the rest of the paper ignores oceans and only considers CO2->warming->CO2 feedback, which as I point out, is impossible to distinguish from other forcings.

George E. Smith says
EVERY single concept that we introduce or discuss in MATHEMATICS whether POINTS, LINES, PLANES, CIRCLES, SPHERES, is a complete fiction that we made up in our heads. Absolutely nothing in mathematics actually exists anywhere in the universe as a real object; they are all fake.
====================
Well, whether these mental entities are real or not, and in what sense, is a matter of philosophical discussion.
In any case, even basic idealized geometry does *not* suggest that nature should be linear. If anything, it suggests the exact opposite. Consider any two points in a Eucledian space. You observe that:
a) The number of curved lines between them is infinite,
b) The number of straight lines between them is exactly 1.
So the final score in that match is really, really an amazing rout. The one goal scored by the Straights may save some pride, but not much. The Curves rule.
So even if you adopt a neo-Platonic perspective, where such pure geometrical entities not only have real existence, but are the actual building blocks of a “meta-reality”, we see that straigth lines are no match for curves. Why should it be surprising that they are so awfully hard to find in phenomenal reality as well? In fact, some may tell you they cannot be found at all. I tend to agree. Nature is overwhelmingly nonlinear.

Well the concepts of mathematics and all the elements thereof, can somewhat precisely describe the behavior of our MODELS of reality; where in fact they do exist; which is why we invented them all along with the models. But the whole gamut of them are a fiction; and we can only hope to approximate with our MODELS the observed behavior of the REAL universe; which itself is far too complex to fully describe.
The distinction is important; because if we cannot separate models from reality; then we are doomed to live in a world of exclusivity. The wave-particle duality would have to be abandoned.
The purpose of models and theories is to explain to the extent we can or predict the outcome of experiments; both those we have conducted; as well as experiments that have never been conducted. The model (theory) only has value to the degree that it’s explanations are consistent with reality. To that end; they do not even have to be unique. The wave particle duality is actually two different models of the same phenomena; and sometimes one of them is easier to use, while in other circumstances the other might be better. They also don’t have to “jibe” with “commonsense”
String theory does not jibe with common sense. How can something be fundamental; a primitive building block; and yet it wriggles. Things that wriggle, common sense tells us must be built up of things that are even more basic.
But even though string theory (which I am not a fan of) may seem quite beyond common sense; it will succedd or fail only on whether or not it correctly explains or predicts the outcomes of experiments; including ones yet to be performed.

eadler, you are comparing models of climate to models of climate which of course match. The only way you can validate models with paleo data is to have measurements of the forcings that caused the warming in that paleo era. Unfortunately the authors in the paper you linked do not have measurements, they just make up some forcings.
The main reason that these models cannot calculate sensitivity is that they do not model weather at sufficient resolution to determine the distribution (the evenness, especially in the tropical troposphere) of water vapor which is their postulated positive feedback. In fact small scale convection is a parameter in the model (an input) so what they are really doing is inputting a major aspect of sensitivity itself.

George E. Smith says:
October 26, 2010 at 8:10 am
I stand corrected and admit this mistake.
Light does disipate and expand with distance.

eadler;
What has been shown using this procedure is that climate sensitivity calculated from models are in the same range as climate sensitivity deduced from paleo data.>>
OK, so you are suggesting that if a climate model and a climate simulation are in the same range, they are proof of each other. Wait. Isn’t a simulation a model? Yes it is. Two different models, same answer, they must be right. Tell me please, which models should we use? The ones that show the MWP and the LIA or the ones that don’t? Which simulations shall we use? The ones that show the MWP and the LIA or the ones that don’t? Oh I get it, choose the ones that get the same answers and VOILA! Proof! All the others must be wrong.
That being the case, I guess warming has continued unabated for the last 15 years, sea levels have gone up a meter or so, severe weather events have increased, people are dying in droves from heat but not from cold, there are way more hurricanes, crops have failed world wide due to drought and the polar bears have increased their population fourfold as a consequence of going extinct.
Yes, I see clearly now, models and simulations in agreement are proof of sensitivity in the past. Trying to correlate their predictions with actual outcomes is an experiment just not worth carrying out and we don’t need to since we aready know they are proof of each other.
new math => new science => new reality.

George E. Smith says:
October 26, 2010 at 3:12 pm
You are very much correct.
Science has been very sloppy and complacent with just generalizing and not looking for absolute accuracy.
I have a design for power generation that engineers have no problem to say that it will run. Now add a physics design on efficiency and the engineer admitted it was beyond his area to even speculate and it would have to go to a University and would probably take years to understand the motion physics I had discovered and the designs of how this new physics can very easily be recreated.
I have yet to find that University.

eadler says:
October 26, 2010 at 9:45 am
What has been shown using this procedure is that climate sensitivity calculated from models are in the same range as climate sensitivity deduced from paleo data.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.172.3264&rep=rep1&type=pdf
Climate sensitivity estimated from ensemble simulations
of glacial climate
————————–
I imagine you realize this paper is just like all the other climate model simulations of the ice ages. Not a single one outlines what Albedo they used for all that extra glacier and sea ice. In fact, it is very telling that they do not outline the single most important factor in why temperatures fell so much in the ice ages.
This paper is just as useless as all the other ones using a climate model when the biggest key assumptions used are not outlined. In fact, I am tired of reading them looking for the key assumptions to be outlined properly – they never are. Throw this one into the pile marked “another climate paper that does not use objective data – it says whatever the author wanted it to say.” That pile will be the biggest one in your office so you don’t have to search for it.

Willis Eschenbach says:
October 26, 2010 at 5:35 pm
I think I am falling in love with your specificity on sensivity, large cognitive bias though ….. tropics gal.
Looking forward to next post.
Bill Illis says:
October 26, 2010 at 7:38 pm
Please endnote that pile for future use
Spector says:
October 27, 2010 at 12:35 am
Check out what software the journalists have had supplied in the past few years- maybe they couldn’t publish curves and went for the headers with the quickest graphics?

Frank says:
October 27, 2010 at 11:13 am

Willis: Let’s think more deeply about your tropical thunderstorms. Do they always begin to limit warming when surface temperature (2 m) rises to a fixed (or roughly fixed) temperature? No. Rapid convection begins to limit warming only when radiative cooling can no longer prevent surface temperature from exceeding the lapse rate. At this point, the cooling that occurs from expansion in a region of rising air leaves that air less dense that air above it, and the region of air can continue to rise to the tropopause. So your tropical thunderstorms limit surface warming ONLY when air higher in the tropics is cool enough to make the temperature gradient from the surface to the upper atmosphere is steep enough. …

Well, yeah, kinda. Thunderstorms are first dependent on the formation of cumulus clouds. These depend upon the temperature differential between the surface and the level where condensation occurs (the “LCL”, or lifting condensation level).
However, where condensation and freezing are occurring in the clouds, energy is being released. It is this secondary energy, released by condensation and freezing, that drives the vertical circulation from the LCL to the upper atmosphere.
From there, the energy is free to radiate to space, or to be moved polewards. Because the tropical upper atmosphere is constantly radiating and moving polewards, the upper atmosphere does not warm.
Thunderstorms are huge heat engines that turn heat into mechanical work. The work that they do is to pump the working fluid (an air-water mixture) vertically and thus (eventually) poleward.
In such a situation, the speed at which the pump turns is the major variable. The energy is passing through the situation. Warm moist air starts at the tropical surface and is pumped vertically and hence polewards. There is no static “upper atmosphere” to be warmed. Instead, air in the upper atmosphere is constantly being added to and replaced. Thunderstorms are bringing air directly from the surface. The temperature can remain nearly the same, while larger masses of air are moved and a huge amount of work is done.

Abbreviated version:
Willis;
IIRC, it was recently a surprise (re-)discovery that the stratosphere is cooling, and its H2O rising.

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.

Given that the modeled changes add up to 70% on top of CO2 radiative forcing in an earlier period and then reduce CO2 radiative forcing by 40% in a later period, this is a very significant effect.

There is also the notorious Un-Hot Spot in the tropical troposphere which was hand-waved (-swatted?) away with the remarkable logic that since one radiosonde thermometer could err, so could hundreds (in unity, in the same direction), so therefore since the Hot Spot might not be missing we’ll just assume it isn’t . Oof!
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Reading the above comments inspires me to suggest a Granularity Gauge Number, to be (rule-)assigned to every formula and data set, specifying the range of precision and measurement and the scope of applicability. “It wad frae monie a blunder free us,
An’ foolish notion.”
The “uncertainty” measures now in use don’t seem to be up to the job, judging from the results and such comments as Jones’ expert assessment of 90% confidence he was entirely correct — good enough for government work.