Guest Post by Willis Eschenbach
Yeah, I know Nature doesn’t have human emotions, give me a break. I’m aware it is unscientific and dare I call it atavistic and perhaps even socially unseemly to say Nature “hates” straight lines, but hey, it’s a headline, cut me some poetic slack.
My point is, everyone is aware that nature doesn’t deal in straight lines. Natural things move in fits and starts along complex paths, not straight from point to point. Phenomena have thresholds and edges, not slow linear changes at the perimeter. Tree branches and coastlines are jagged and bent. Things move in arcs and circles, relationships are complex and cyclical. Very little in nature is linear, particularly in complex systems.
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. If there is twice the forcing change (twice the change in solar radiation, for example), the IPCC says we’ll see twice the temperature change. The proportionality constant (not a variable but a constant) that the IPCC says linearly relates temperature and TOA forcing is called the “climate sensitivity”.
Figure 1. Photo of impending change in climate sensitivity.
Today I stumbled across the IPCC justification of this linearity assumption. This is the basis of their claim of the existence of a constant called “climate sensitivity”. I quote it below.
I’ve removed the references and broken it into paragraphs it for easy reading. The references are in the original cited above. I reproduce all of the text on the web page. This is their entire justification for the linearity assumption. Having solved linearity in a few sentences, they then proceed to other matters. Here is their entire scientific justification for the assumption of linearity between forcing and temperature change (emphasis mine):
Linearity of the Forcing-Response Relationship
Reporting findings from several studies, the TAR [IPCC Third Assessment Report] concluded that responses to individual RFs [Radiative Forcings] could be linearly added to gauge the global mean response, but not necessarily the regional response.
Since then, studies with several equilibrium and/or transient integrations of several different GCMs [Global Climate Models] have found no evidence of any nonlinearity for changes in greenhouse gases and sulphate aerosol. Two of these studies also examined realistic changes in many other forcing agents without finding evidence of a nonlinear response.
In all four studies, even the regional changes typically added linearly. However, Meehl et al observed that neither precipitation changes nor all regional temperature changes were linearly additive. This linear relationship also breaks down for global mean temperatures when aerosol-cloud interactions beyond the cloud albedo RF are included in GCMs. Studies that include these effects modify clouds in their models, producing an additional radiative imbalance.
Rotstayn and Penner (2001) found that if these aerosol-cloud effects are accounted for as additional forcing terms, the inference of linearity can be restored. Studies also find nonlinearities for large negative RFs, where static stability changes in the upper troposphere affect the climate feedback (e.g., Hansen et al., 2005).
For the magnitude and range of realistic RFs discussed in this chapter, and excluding cloud-aerosol interaction effects, there is high confidence in a linear relationship between global mean RF [radiative forcing] and global mean surface temperature response.
Now, what strikes you as odd about that explanation of the scientific basis for their claim of linearity?
Before I discuss the oddity of that IPCC explanation, a short recap regarding climate sensitivity. I have held elsewhere that climate sensitivity changes with temperature. I will repeat the example I used to show how climate sensitivity goes down as temperature rises. This can be seen clearly in the tropics.
In the morning the tropical ocean and land is cool, and the skies are clear. As a result, the surface warms rapidly with increasing solar radiation. Climate sensitivity (which is the amount of temperature change for a given change in forcing) is high. High sensitivity, in other words, means that small changes in solar forcing make large changes in surface temperature.
By late morning, the surface has warmed significantly. As a result of the rising temperature, cumulus clouds start to form. They block some of the sun. After that, despite increasing solar forcing, the surface does not warm as fast as before. In other words, climate sensitivity is lower.
In the afternoon, with continued surface warming, thunderstorms start to form. These bring cool air and cool rain from aloft, and move warm air from the surface aloft. They cool the surface in those and a number of other ways. Since thunderstorms are generated in response to rising temperatures, further temperature increases are quickly countered by increasing numbers of thunderstorms. This brings climate sensitivity near to zero.
Finally, thunderstorms have a unique ability. They can drive the surface temperature underneath them below the temperature at which the thunderstorm formed. In this case, we have local areas of negative climate sensitivity – the solar forcing can be increasing while the surface is cooling.
As you can see, in the real world the temperature cannot be calculated as some mythical constant “climate sensitivity” times the forcing change. Sensitivity goes down as temperature goes up in the tropics, the area where the majority of solar energy enters our climate system.
So the IPCC claim of linearity, of the imagined slavish response of surface temperature to a given change in TOA forcing, goes against our daily experience.
Let me now return to the question I posed earlier. I asked above what struck you as odd about the IPCC explanation of their claim of linearity regarding forcing and temperature. It’s not the fact that they think it is linear and I disagree. That is not noteworthy.
Here’s what made me stand back and genuflect in awe of their claims. Perhaps I missed it, but I didn’t see a single word about real world observations in that entire (and most important) justification for one of their core positions.
I didn’t see anyone referenced who said something like ‘We measured solar radiation and downwelling longwave radiation and temperature at this location, and guess what? Temperatures changed linearly with the changes in radiation.’ I didn’t see anything at all like that, you know, actual scientific observations that support linearity.
Instead, their claim seems to rest on the studies showing that scientists looked at four different climate models, and in each and every one of the models the temperature change was linearly related to forcing changes. And in addition, another model found the same thing, so the issue is settled to a “high confidence” …
I gotta confess, that wasn’t the first time I’ve walked away from the IPCC Report shaking my head, but that one deserves some kind of prize or award for sheer audacity of their logic. Not a prize for the fact that they think the relationship is linear when Nature nature hates straight lines, that’s understandable, it’s the IPCC after all.
It is the logic of their argument that left me stammering.
Of course the model results are linear. The models are linear. They don’t contain non-linear mechanisms. And of course, if you look at the results of linear models, you will conclude with “high confidence” that there is a linear relationship between forcing and temperature. They looked into five of them, and case closed.
I mean, you really gotta admire these guys. They are so far into their models that they actually are using the linearity of the model results to justify the assumption of linearity embodied in those same models … breathtaking.
I mean, I approve of people pulling themselves up by their own bootstraps, but that was too twisted for me. The circularity of their logic made my neck ache. I kept looking over my shoulder to see if the other end of their syllogism was circling behind to strike me again. That’s why I genuflected in awe. I was overcome by the sheer beauty of using a circular argument to claim that Nature moves in straight lines … those guys are artists.
Meanwhile, back in the real world, almost no such linear relationships exist. Nature constantly runs at the edge of turbulence, with no linearity in sight. As my example above shows, the climate sensitivity changes with the temperature.
And even that change in tropical climate sensitivity with temperature is not linear. It has two distinct thresholds. One is at the temperature where the cumulus start to form. The other is at the slightly higher temperature where the thunderstorms start to form. At each of these thresholds there is an abrupt change in the climate sensitivity. It is nowhere near linear.
Like other natural flow systems, the climate is constantly restructuring to run “as fast as it can.” In other words, it runs at the edge of turbulence, “up against the stops” for any given combination of conditions. In the case of the tropics, the “stops” that prevents overheating is the rapid proliferation of thunderstorms. These form rapidly in response to only a slight temperature rise above the temperature threshold where the first thunderstorm forms. Above that threshold, most of any increase in the incoming energy is being evaporated and used to pump massive amounts of warm air through protected tubes to the upper troposphere, cooling the surface. 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.
Now it is tempting to argue that the IPCC linearity claim is true because it only applies to a global average temperature. The IPCC only formally say that there is “a linear relationship between global mean RF [radiative forcing] and global mean surface temperature response.” So it might be argued that the relationship is linear for the global average situation.
But the average of non-linear data is almost always non-linear. Since daily forcing and temperature vary non-linearly, there is no reason to think that real-world global averages vary linearly. The real-world global average is an average of days during which climate sensitivity varies with temperature. And the average of such temperature-sensitive records is perforce temperature sensitive itself. No way around it.
The IPCC argument, that temperature is linearly related to forcing, is at the heart of their claims and their models. I have shown elsewhere that in other complex systems, such an assumed linearity of forcing and response does not exist.
Given the centrality of the claim to their results and to the very models themselves, I think that something more than ‘we found linearity in every model we examined” is necessary to substantiate this most important claim of linearity. And given the general lack of linearity in complex natural systems, I would say that their claim of linearity is an extraordinary claim that requires extraordinary evidence.
At a minimum, I think we can say with “high confidence” that it is a claim that requires something more weighty than ‘the models told me so’ ...
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.
“”””” Francisco says:
October 25, 2010 at 4:21 pm
Tom says:
October 25, 2010 at 9:08 am
Ohm’s law works nicely at the scales encountered for general circuit design. “””””
Congratulations Francisco; you are without exception the very first person I have encountered in 50 years who actually knows what Ohm’s law is. That is a question I have asked every candidate for a circuit designer job I have ever interviewed; from technicians to Stanford PhDs. And I always get E= I.R or some variant.
You are the first to note that what George Simon Ohm actually discovered was that for a certain class of materials; mostly metallic conductors under all other physical conditions being held constant; the relationship between the current flow and the applied Voltage is a LINEAR one.
And as you say; very damn few materials are linear in the sense Ohm discovered.
So Ohm’s law says:- >>> R = c <<<
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????
The IPCC argument, that temperature is linearly related to forcing, is at the heart of their claims and their models. I have shown elsewhere that in other complex systems, such an assumed linearity of forcing and response does not exist.
=============================================
Well said, Willis.
Chris
Norfolk, VA, USA
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
eadler says:
October 25, 2010 at 7:20 pm
…
This argument has nothing to do with climate sensitivity at all. It doesn’t relate to any global average annual equilibrium temperature at all. It is a description of weather.
There is no way that observation of daily weather in a given locality can be used to infer anything about climate sensitivity.
eadler, thanks for your comments. First, the tropics where I described the phenomena is not a “given locality”. It is a huge and vitally important part of the climate system, so what happens there matters.
More importantly, you seem to forget that climate is the average of weather. The patterns that I describe happening every day in the tropics are what are averaged to give us the “climate”.
Finally, none of your objections are to the point. The point is that the IPCC have asserted the linearity of forcing and response. And they have offered nothing to support that but linear models. Perhaps you could comment on that, rather than trying to shift the issue to whether my ideas about sensitivity are correct or not. I could be totally wrong as you claim … but that doesn’t change the fact that they are propping up claims of linearity by using linear model results.
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.
@ur momisugly George E. Smith – Getting off topic, I suspect, but an interesting discussion all the same.
What Ohm discovered was that the ratio of voltage to current is constant. What we describe and use as Ohm’s law today is something very different. In a sense it is not a law but a definition – we define a quantity called impedance which is the ratio between voltage and current and we describe various easy ways of finding the impedance of materials and devices, often in terms derived from complex analysis. What Ohm described is not very useful in actually designing a useful circuit – what is today described as Ohm’s law is much more useful.
Of course you know this, and I am teaching you to suck eggs, and I’m sorry for that. But stating Ohm’s law as ‘R is a constant in certain materials’ is not a very good representation of the state of the field today, and judging job candidates on whether they happen to ignore the past 150 years of development in the field the same as you might be a trifle unfair.
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.
Jason Caley
I certainly may be misunderstanding things, but I believe that the linear relationship for small variations of x does not hold in chaotic systems. This is not to say that NO values of x have a linear realtionship to y, but only to point out that not ALL values of x have that linear relationship. After all, even chaotic systems have attractors and lslands of stability.
No Jason Caley .
The linearity is a very general mathematical result valid for any function (provided some regularity technicalities) .
For small variations of some variable , all systems answer almost exactly in a linear way because the function is then simply represented by only the first (linear) term of its Taylor development .
This is true for chaotic or non chaotic systems alike .
Of course on must not confuse the necessarily linear answer on small perturbations of systems in equilibrium with a full scale answer over long times .
As the chaotic systems are out of equilibrium and strongly non linear , their “linear life time” is extremely short . But it exists .
AnnaV
You are perfectly right !
It is precisely this argument that made me interested in the climate “science” for the first time 12 years ago .
There is no , absolutely NO fundamental difference between weather and climate .
Or using your analogy with letters and words , climate is not a word meta level of weather which would be the letter level .
Climate science is just about taking the honest to God fluid dynamics’ , thermodynamics’ , quantum mechanics’ equations that govern the weather and then to atrociously mutilate them so that nobody recognizes them anymore .
Pretending that a new meta level of the dynamics (!) can be found by simply averaging solutions of the original equations (that they don’t know anyway) is such an extraordinary claim that it would need more than extraordinary proofs with EXTREMELY rigorous mathematics .
It is more than clear that naive computer simulations don’t box in that category at all .
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?
John Day says:
October 25, 2010 at 12:17 pm
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.
😐
______________________________
Isn’t this the heart of the argument?
And if not, the instruments; that were recalibrated, to provide specificity? To predict and model ‘sensitivity’?
Anyone that has had the honour of observing and using [as decried]:-
● blood letting
● leeches
● mercury sphygmomanometer
● aeneroid sphygmomanometer
[● pressure bandages as an interim to direct infusion]
in observation, also the use of analogue then digital visuals [read-out] would question the basis of the argument.
Instruments used for eg Haemoglobin [Hb] presented the same dilemma, when used with practiced observation. Pathology, tax funded, titrated the goal posts.
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.
Willis, you’ve made a critical mistake here:
“‘We measured solar radiation and downwelling longwave radiation and temperature at this location, and guess what? Temperatures changed linearly with the changes in radiation.’ I didn’t see anything at all like that, you know, actual scientific observations that support linearity.”
Climate sensitivity is _global_ response to a _global_ change. You can’t do it at a single location because heat can move to and from that location from elsewhere. The simplest demonstration of this is a thought experiment with a sphere in a vacuum. Apply radiative forcing RF1 at one point of the sphere and the temperature response dT1 there.
Consider an insulating sphere of surface area 100,000 sq km. Heat up 1 sq km with RF1 sufficient to raise the temperature by 1 C. This is the actual sensitivity of the sphere to a global change in heating.
Next, consider the situation where the sphere conducts well. The heat will be conducted around the sphere until it’s isothermal and using your logic the sensitivity is therefore 0.00001 C. But it’s not, you’re wrong by a factor of a hundred thousand in this case.
This is only one of the physical mistakes in your assumption, but it’s enough to demonstrate a serious flaw.
We have estimates of climate sensitivity to global forcings from palaeoclimate, see e.g. Knutti & Hegerl, 2008.
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.
“”” Joe Lalonde says:
October 26, 2010 at 1:41 am
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. “””
No I’m not. There is no such thing as a laser beam that has zero thickness. Everybody knows that a (TE00) laser beam has a minimum beam waist dimension; which along with the wavelength determines its angular divergence; so a laser beam is a whole lot closer to a cone (which also does not exist) than it is to a line. And that divergence goes inversely as the size of the beam waist so if the even the beam waist of the “beam” was zero, the straight line beam would actually be a hemisphere (another fiction) of light extending over 90 degrees (1/2) cone angle; you would literally have a point source of light. There’s no such thing as a point source of light either. In classical Physics you cannot satisfy the boundary conditions of Maxwell’s equations for a point radiator of electromagnetic waves; and in quantum physics, Heisenberg’s principle of uncertainty would require that source to have an infinite momentum uncertainty so it would be spread infinitely in wavelength so there would be no detectable power at any wavelength you tried to observe such a thing; unless the total radiated power was also infinite. Too many zeros and infinities to satisfy and reality constraints.
I believe that one of Steven Hawking’s discomforts with the big bang theory, is the presumed singularity that exists at the instant of its creation. For guys like him everything interesting in the field of archeo-physics, happened in the first 10^-43 seconds after the big bang.
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.
“”” Tom says:
October 26, 2010 at 1:49 am
@ur momisugly George E. Smith – Getting off topic, I suspect, but an interesting discussion all the same.
What Ohm discovered was that the ratio of voltage to current is constant. What we describe and use as Ohm’s law today is something very different. In a sense it is not a law but a definition – we define a quantity called impedance which is the ratio between voltage and current and we describe various easy ways of finding the impedance of materials and devices, often in terms derived from complex analysis. What Ohm described is not very useful in actually designing a useful circuit – what is today described as Ohm’s law is much more useful.
Of course you know this, and I am teaching you to suck eggs, and I’m sorry for that. But stating Ohm’s law as ‘R is a constant in certain materials’ is not a very good representation of the state of the field today, and judging job candidates on whether they happen to ignore the past 150 years of development in the field the same as you might be a trifle unfair. “””
Well E = I.R is simply a definition of resistance; but ONLY for materials that DO obey Ohm’s Law (R= c)
For any other case you would have to use de/di = R’
For example; if you built a feedback amplifier of say a transimpedance variety; and the feedback element was a highly non linear “resistor”; and you used E= I.R to get a value for that “resistor”, you would most certainly end up with the wrong gain; and your stability analysis could also be off, and the thing might oscillate instead of be stable based on your calculation using the wrong values. As I use the term “resistor”, it is by definition (to me) both linear and frequency independent. A classical derivation of the input behavior ofa vaccuum tube amplifier; with inductance in the cathode lead (same thing works for transistors) arrives at an input circuit with a shunt “conductance” that varies as 1/f^2. That loss mechanism loads a typical input tuned circuit in say an IF amplifierand kills the Q, and limits amplifier performance.
Well anything that varies as 1/f^2 is NOT a resitor or conductor, both of which are time independent.
A correct circuit analysis of the problem shows that the correct input equivalent circuit in fact contains a SERIES reistor having a FIXED value of gm.L/C where L is the cathode lead inductance, C is the grid-cathode capacitance, and gm is of course the transconductance of the tube. The exact same parameters apply in transistor circuits; and even thoguh L and C may be very much smaller, gm is often very much higher, so it is still an important problem in high speed amplifiers. The input equivalent circuit is in fact that resistor in series with both C and L.
The result of not being pedantic is that invariably mis-communication results.
People think “climat sensitivity” is a log relationship; when maybe it is just a non-linear relationship (who knows).
But a log function is aprecisely defined mathematical function; and you can’t just slap the title on any non-linear curve; that doesn’t satisfy those strict criteria.
Mauna Loa and GISSTemp together demonstrate that cs most certainly is NOT a log function.
And I have in fact built integrated feedback amplifiers that actually did use non-linear feedback “resistors” (made from MOSFETS); and not only was the element non-linear; but it was also highly unpredictable in value in production. The final design which was in fact a very high gain integrated photo-amplifier (including photo-detector); and despite the use of non-linear unpredictable (to high accuracy) value elements; the amplifier was quite linear in its response to photo-currents; and was also of quite predictable gain. The trick was to NOT use a transimpedance feedback amplifier architecture; that whole generations of analog circuit designers (if there’s any left) can’t see beyond but to use a Currnet gain feedback architecture where the input and output signals are BOTH currents, and the current gain is determined by the ratio of two unpredictable non-linear resistors, that by virtue of the layout architecture; had exactly the same (well closely) non-linearity, and value uncertainties. Produced a 500:1 closed loop current gain from a FemtoAmp input photo current; with a 3dB bandwidth of half a megaHerz. Try doing that with your standard op amp transimpedance phot-amplifier. So far as I know it is still the highest gain bandwidth; highest sensitivity silicon photo-detector.
One of our engineers; who is a ham, actually used one as a detector in a telescope and a AA cell powered LED indicator lamp “Transmitter” to operate a voice signal transmission across the whole width of silicon valley on a ham field day. He and his mate were the only ones in the whole world to record a communication on that “band” that day; but that is getting a bit off subject.
As for judging a candidate; the idea is to identify the exceptional from the ordinary; before applying OTHER CRITERIA; and I think there is a lot of merit in knowing what scientists actually said or did; rather than what umpteen thrid party rehashes like to claim they did.
In fact a big part of theis whole climate debate; revolves around what researchers said or didn’t say or research.
For example I still haven’t been able to get from anybody who frequents this or any other site; just EXACTLY WHO it was who FIRT invented the concept of CLIMATE SENSITIVITY; and defined it as being a logarithmic relationship; which it evidently is by definition only; since no data nore basic physical theory supports such a relationship.
And I notice that Dr Lacis dismisses climate change “skeptics” as being incompetent in understanding radiative transfer Physics.
I assume that he includes Spencer, Christy, and Lindzen in that list of incompetents; and a whole host of others. Well that enables him to dismisss them; with a “find a radiation physics for dummies” advice. To give him credit; he did give some suggestions as to some books to look at. It’s always good to know what they teach in schools these days.
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.
davidmhoffer says:
October 25, 2010 at 8:10 pm
Eadler;
The fact is that we have no way to do experiments to determine whether or not climate sensitivity as defined above, is a linear function of radiative forcing. The only way to do this is by modelling. >>
You are kidding, right? For centuries science has been:
theory => model => predicted results
experiment => compare to predicted results => supports model/theory or doesn’t.
You now propose:
theory => proof of the theory. One can only shudder at the thought of the “new math” having morphed into the “new science”.
What you have said is that science is done by comparing models to prediction. This is certainly true. That doesn’t mean that the question of whether climate sensitivity is a linear function of the forcings can be determined by the data that we have available from observations of climate. The data on forcings and resulting evolution of global average temperature are too sparse to carry out such a verification.
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
………
Our study shows that the LGM climate is likely to
constrain the upper end of the DT2x range. At least
within the range of processes captured by our
model—and provided that the simulated relationship
between LGM cooling and CO2 warming covered in our
ensemble does not strongly differ from that simulated by
different GCMs (see Section 5)—a high DT2x (larger
than 5.3C) cannot be reconciled with most recent
paleo-proxy estimates of cooling between the LGM and
pre-industrial climate. ….
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.
I have read some very well-reasoned points, but most forget one thing.
The burden of proof does not lie with Willis, but the IPCC. Willis’s claims are not proof that it is non-linear, but it is sufficient to conclude that the linearity claim needs strong supporting evidence with natural observations. This is data not provided by the IPCC, and if it provided in their supporting documentation, they made no mention of it in their own text.
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.
“”” Joe Lalonde says:
October 26, 2010 at 1:37 pm
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. “””
Joe; my point is not to be argumentative; that’s not a useful game; it’s not even a game.
For a start; let’s agree that “engineering mathematics” and “pure mathematics” are not quite the same thing. Well Engineering mathematics might also be described as “Applied Mathematics”.
The engineer’s aim is to solve the problem; drain the swamp or whatever; and his attitude is that “if I can get an answer it is the right answer.”
The Pure mathematician will spend a lot of time on “existence theorems” to establish that ANY answer even exists; or if you get an answere that it is indeed the right answer.
If you ask the engineer to prove the conjecture: “An absolutely convergent infinite series converges.” you are going to get a ROFLMAO response. He’s going to laugh his head off and then say; “well if it is absolutely convergent; then of course it converges; by the way; what the hell is absolutely convergent, and why do I care ? ”
Well the pure mathematician cares; so he develops a rigorous proof of that theorem. So why does it matter ? Well the engineer figures if he adds up a number of things, it doesn’t really matter what order he sums them in; even for an infinite number of things; so he might rearrange the order to make it easier to sum them.
The Pure Mathematician will tell him; Hey you can’t do that; unless the infinite series is absolutely convergent; which means that the sequence of the absolute values of the terms in the series; is also a convergent series.
An infinite series of alternating sign terms that IS NOT absolutely convergent can be summed to ANY POSSIBLE ANSWER YOU WANT; depending on the order in which you sum the terms.
Now the engineer with his applied maths is NOT incompetent; just not complete; and he may be on very solid ground; because real life actual Physical systems almost never yield equations or mathematical descrriptions that are not well behaved; so if the engineer gets his answer, it is unlikely that it is not the correct answer (assuming he did the math properly).
The pure mathematician is likely more interested in te circumstances under which the first answer you get; might in fact not be the correct answer; but those will be pure mathematic problems rather than engineering math problems.
Same with the Ohm’s law example. Ohm’s law as in R = c is a physics problem. But as E = I.R it is a simple problem in circuit design theory; which itself is actually a model of a real system; and not the real system itself.
The circuit designer is going to use the latter; and maybe not care too much about the former unless he really does have a peculiar interest in linearity; and he may even pay attention to Ohm’s caveat; that all other physical parameters must be kept constant; like the Temperature for example.
But if we let ourselves get too sloppy in interpreting what we thought somebody did or said; as distinct from what they actually did or said; then sooner or later it will come back to bite us.
When I went to school, a BSc in Mathematics required majors in both Pure and Applied Mathematics. Today I suppose there might be 27 majors in Mathematics. A BSc in Physics on the other hand required only one major; but there were three of those to choose from:- Physics (HLSE&M etc), Radio-Physics (electronics, propagation EM theory Ionospheric physics etc), and Mathematical Physics which was all that Vector, Field theory, and Green’s Theorem kind of stuff; and you had to choose one of those in your third year.
So I did all five of those majors; in two years (3rd and 4th). And I do use more engineering math than pure; but the other keeps me honest.
Well that was then; don’t know what they teach now; my son is doing engineering now; and I’m damned if I know what they are teaching him; maybe green is cool !
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.