CENTRAL to discussion of climate change models is the concept of “forcing” and “feedback”. So, reference is made to global warming from radiative “forcing” from elevated concentrations of carbon dioxide in the troposphere and then “positive feedback from water vapour”, adding to global warming.
Everyone talks in these terms, and it is politically correct to do so. But there are two problems.
According to the United Nation’s Intergovernmental Panel on Climate Change (IPCC) formalism, their “forcing” can include any amount of internal state variable contribution, as well as external driving function contributions. And according to this IPCC formalism, there is only one dynamically distinct internal state variable, the climate temperature, that functionally determines the apparently distinct but really merely functionally dependent “feedbacks” of their formalism.
In physics, an external driving function qualifies unequivocally as a cause. But internal state functions must always be counted as effects that are themselves caused by external drivers interacting with internal state functions acting as internal causes.
This important cause-effect structure is erased in the “forcing” concept of the IPCC formalism. It follows that cause and effect will be muddled in work that uses the IPCC formalism for simplified models. The simplified models are made of ordinary differential equations as in the qualitative theory of dynamical systems including deterministic chaos originated by Henri Poincaré in the 1880s. Poincaré used the method of phase portraits, which make explicit the presence of several dynamically distinct internal state variables.
The IPCC limitation to only one dynamically distinct internal state variable makes the IPCC concept of “feedbacks” verge on nonsense.
Roy Spencer and Danny Braswell explained this in 2008: “We can see from the plotted dots that the satellite observations are consistent with errors in diagnosed model feedback from about -0.1 to -0.8 W m^-2 K^-1”.
They showed that the IPCC formalism gives wrong answers.
At Dr Spencer’s blog he comments:
“As those who have been following our work already know, our main conclusion is that climate sensitivity has been grossly overestimated due to a mix up between cause and effect when researchers have observed how global cloud cover varies with temperature. … Significantly, our new work provides a method for identifying which direction of causation is occurring … Well…at least I thought it was new way of analyzing graphs. It turns out that we have simply rediscovered a method used in other physical sciences: phase space analysis.”
Drs Spencer and Braswell are leading the field by using Poincaré’s method of phase portraits. The two steps forward they are making here are explicit recognition of the presence of several dynamically distinct internal state variables, and clearer recognition of how the IPCC “forcing” concept leads to muddling of cause and effect, when it tries to by-pass or over-ride the difference between orthodox external driving functions and internal state variables.
I hope that the flawed IPCC formalism is on its way out as a result of their work.
Christopher Game
Melbourne
*************************
Notes
June Barrow-Green, 1997/1999, Poincaré and the three-body problem, AMS
Peixoto and Oort, Physics of Climate, AIP 1992. Pg 29
Spencer and Braswell 2008 J. Climate 21: 5624-5628
Roy Spencer’s blog, http://www.drroyspencer.com/2009/03/set-phasers-on-stun/
Phase space analysis at Wikipedia, http://en.wikipedia.org/wiki/Phase_space
Image from Wikipedia illustrating the phase space of a dynamical system with focal stability, http://en.wikipedia.org/wiki/Phase_space
Jennifer Marohasy BSc PhD is a critical thinker with expertise in the scientific method.
I find the use of the idea of “forcing” an intrusion of animistic/medieval thinking into modern science.
That is why in my paper just published in the Journal of Energy and the Environment I use the long established universal scientific framework of independent and dependent variables.
The ideas of this standard practice framework are neatly set out here:
http://viswiki.com/en/Dependent_and_independent_variables
and here
http://en.wikipedia.org/wiki/Dependent_variable
Here is the Abstract of that paper:
ABSTRACT
This paper introduces this thesis:
The Sun-Earth system is electromagnetically, magneto-hydrodynamically and gravitationally coupled, dominated by significant non-linear, non-stationary interactions, which vary over time and throughout the three-dimensional structure of the Earth, its atmosphere and oceans. The essential elements of the Sun-Earth system are the solar dynamo, the heliosphere, the lunisolar tides, the Earth’s inner and outer cores, mantle, crust, magnetosphere, oceans and atmosphere. The Sun-Earth system is non-ergodic (i.e. characterised by continuous change, complexity, disorder, improbability, spontaneity, connectivity and the unexpected). Climate dynamics, therefore, are non-ergodic, with highly variable climatological features at any one time.
A theoretical framework for considering the role of the Sun in relation to the Earth’s climate dynamics is outlined and ways in which the Sun affects climate reviewed. The forcing sources (independent variables) that influence climate processes (dependent variables) are analysed. This theoretical framework shows clearly the interaction effects between and amongst the two classes of variables. These seem to have the greatest effect on climate dynamics.
Climate processes are interconnected and oscillating, yielding variable periodicities. Solar processes, especially when interacting, amplify or dampen these periodicities producing distinctive climatic cycles. As solar and climate processes are non-linear, non-stationary and non-ergodic, appropriate analytic methodologies are necessary to reveal satisfactorily solar/climate relationships.
Keywords: Climate dynamics, climate change, Sun, Moon, solar, lunar, irradiance, plasma, gravity, tides, electromagnetic, Fairbridge, clouds, global electric circuit, heliosphere, non-linear, non-stationary, non-ergodic, Ockham’s Razor.
Here are the first few paragraphs:
1. A FRAMEWORK FOR UNDERSTANDING THE SUN’S ROLE
1.1 Total solar variability
That the Sun is a major regulator of the Earth’s climate is being corroborated increasingly. Rhodes Fairbridge (Mackey, 2007) emphasised that the answer to the question: Does the Sun affect the Earth’s climate? Has to be in terms of three considerations;
•
the variations in the quantity, intensity and distribution over the Earth of the solar output, including electromagnetic radiation, matter and the Sun’s electromagnetic field;
•
the variable gravitational force the Sun exerts on the Earth, the Moon and the Moon and the Earth as a system; and
•
interactions between these processes.
In this regard, he seems to have been a relatively lone voice, then as now.
This paper introduces a framework for examining how all types of solar activity, not merely irradiance, affect climate. It is based on the ideas of Rhodes Fairbridge. This framework is used to present an outline of the main processes by means of which solar 1
activity of all types produces climate change over a wide spread of time frames and in many different ways in relation to latitude, longitude and altitude. Understanding the Sun’s role in relation to climate dynamics requires consideration of all the variables that are related to solar activity in relation to all major climate variables.
The theory of experimental design examines relationships between two classes of variables: the independent variables which the experimenter manipulates and the dependent variables the values of which vary as the values of the independent variables vary. Carefully structured observations generate measures of relationships between the two classes of variables. Theoretical analyses aim to explain observed relationships and predict the evolution of relationships over time, amongst other things.
Using the conceptual framework of the theory of experimental design, solar variables are the independent and climate variables the dependent variables. This framework shows the Sun’s significant regulatory role.
It shows that the Sun-Earth system is electromagnetically (solar radiation), magneto-hydrodynamically (Solar Wind and Coronal Mass Ejections (CMEs)) and gravitationally (lunisolar tides) coupled, dominated by significant non-linear, non-stationary interactions. The interactions vary over time and throughout the three-dimensional structure of the atmosphere, oceans and the Earth. Non-ergodic climate dynamics, with highly variable climatological features at any one time, is the result. (Footnote: 1 North (1999) introduced the idea that we live in a non-ergodic world. He explained that an ergodic phenomenon has an underlying structure so stable theory that can be applied time after time, consistently, can be developed. In contrast, the world with which we are concerned is continually changing: it is continually novel. Inconsistency over time is a feature of a non-ergodic world. The dynamics of change of the processes important to us are non-ergodic. The processes do not repeat themselves precisely. North (1999) argued that although there may be some aspects of the world that may be ergodic, most of the significant phenomena are non-ergodic. In 1993 Douglass North and Robert W. Fogel received the Nobel Prize for Economics for pioneering work which resulted in the establishment of Institutional Economics.)
1.2 A Non-ergodic world
The concept “ergodic” refers to uniformity or sameness in which any one arrangement of the elements of a system are as likely, or as unlikely, as any other. At an aggregate, or macroscopic, level this means that an ergodic system is characterised by uniformity and predictability. The patterns that characterise an ergodic system most of the time are those macroscopic ones satisfied by very large numbers of microscopic ones. An ergodic system would be characterised by monotony at the macroscopic level.
Conversely, a non-ergodic system is characterised by continuous change, novelty, surprise, common place improbable structures, unpredictable patterns, spontaneous order, creativity, patterns self similar across a wide, perhaps indefinite, range of scales. Such systems exhibit the rich complexity and diversity of the world we experience. A non-ergodic system is characterised by creativity and novelty at the macroscopic level.
In a non-ergodic system the sequence of events of which a system or subsystem is composed does not repeat itself: the system’s evolution over time is unique. The system is not deterministic but stochastic. However, unlike probabilistic sequences that are also deterministic, the events that comprise a sequence are not independent of each other: every occurrence affects future occurrences. The future of the system is to a degree predictable; the future is uncertain but not random in the sense of a roulette wheel. Novelty emerges from a non-ergodic system and creativity persists within it.
An ergodic system has a stable structure. Although the ergodic system might be probabilistic like the journey of a particle of dust in a fluid or in the air, the sequence of events repeats itself eventually: there maybe a surprise but there is no novelty, no creativity. (Footnote: See Koutsoyiannis 2005a and 2005b).
1.3 The independent and dependent variables
The set of independent variables is the:
1. Sun’s:
• output of radiation and matter,
• electromagnetic and gravitational fields,
•shape; and
2. topological structure of the heliosphere.
The set of dependent variables consists of the Earth’s:
1. atmospheric systems;
2. ocean systems;
3. coupled atmospheric-oceanic systems;
4. clouds;
5. Rossby and Kelvin waves;
6. rotation;
7. atmospheric angular momentum;
8. dynamo;
9. electromagnetic field; and
10. global electric circuit.
The independent variables’ time-lag effects range from hours to centuries; the dependent variables have time-lags, too.
The variables within each set are not functionally independent: complex interactions that amplify or dampen total solar effects occur.
The variables are not of the same logical category. Some are one dimensional such as temperature, pressure atmospheric angular momentum and measures of solar output whereas others are systems of equations or in more complex instances, best represented as mathematical models.
1.4 Non-linear and non-stationary processes
Four non-linear, non-stationary processes relating the set of independent variables (the solar variables) to the set of dependent variables (the climate variables) have been identified. They are:
o strange attractors;
o resonant amplification;
o phase synchronisation;
o complexity matching.
There are other factors relevant to our understanding of the Earth’s climate dynamics:
• climate system’s internal variability;
• Earth’s albedo;
•cosmic rays;
•Earth’s orbital geometry, including Milankovitch processes;
•planets’ gravitational effects on the Earth’s and Moon’s orbital geometry; and,
•Sun’s epitrochoid-shaped barycentric motion.
If the global climate system is a heat engine, all forms of solar activity, and these relevant factors, are its sources of energy and regulation.
The maturity and degree of corroboration of science reviewed in this paper is variable. This is indicated to some extent by reference to publications which corroborate and/or develop the specific area under consideration. However, this paper does not evaluate the overall quality and/or durability of findings drawn upon to present overall conclusions.
Christopher,
I don’t think you should so closely identify the feedback/forcing distinction with cause/effect. Feedback amplifies a forcing to provide an enhanced (or diminished) cause. The thinking behind the distinction comes from the differential equation context that you mention. In an inhomogeneous linear ode:
dS/dt = fS + F
(S a state vector) you would describe the second term as the forcing, and the first as feedback. Generally the climate version considers what happens when this ode reaches equilibrium, but it is seen most clearly conceptually in the time development.
Nor do I think Richard Mackey’s identification with dependent/independent variables is quite right, although it is true that the final equilibrium (a theoretical abstraction) is a dependent variable depending on the independent variables of the forcings – in fact, the GCM’s basically perform that functional mapping. But I’m still thinking about what he’s written.
I don’t believe the IPCC states a limitation to one state variable – do you have a source? Clearly humidity at least is another state variable.
You then cite Poincare’s deterministic chaos. In separating the feedback idea above I used a linear equation – more generally you’d write dS/dt = H(S,F,t)
and expand H as a Taylor series. To first order gives the forcing/feedback distinction, but to second order and beyond brings in all the chaos ideas. People are well aware of this, and it’s the idea behind tipping points too. But you need to start the analysis by thinking about small changes, which are what we currently have.
I’ll try to read more on Spencer’s phase space analysis reference. He seems to be saying that cloud changes are a big effect that don’t fit so well with the linear concepts, and where it isn’t clear what is driver and what is dependent effect. That’s OK so far – the general difficulty with clouds and aerosols is well acknowledged by the IPCC. Then he goes on as if to say that chaos is an independent effect (forcing). But no, it is a consenquence of the ODE with non-linearity; it’s just hard to calculate.
Christopher – you don’t seem to be aware what modern climate modelling science is up to. You could do well to acquaint yourself with what Hadley Centre are doing instead of being presumptuous.
Radiative “forcing” is what happens when you step out from a shadow and into sunlight. The sun’s rays raise your temperature and you radiate more energy as a result. That’s the reality. Fiction has it that CO2 intercepts a portion of the spectrum you’re radiating, radiates in turn, and raises your temperature even more. What makes “CO2 forcing” a fiction is that radiative transfer obeys the same rule as conductive transfer, and only the light from a hotter body (like the sun) can raise your temperature. That’s the second law of thermodynamics, that thermal energy must flow toward lesser energy, despite Roy Spencer’s lawyerly attempt to muddy the issue by arguing that the 2nd law applies only to “whole systems” rather than to each entity within a system. Technobabble cannot reverse the laws of physics; heat transfer follows a one-way path.
“Radiative “forcing” is what happens when you step out from a shadow and into sunlight. The sun’s rays raise your temperature and you radiate more energy as a result.”
That is why we like shade in the summer time.To avoid absorbing that sunlight.We KNOW why we seek shade on a hot day.This is simply stuff.Yet so many seem oblivious to the truism that sunlight radiation burns and CO2 emitted radiation does not.
Large cities that has a dedicated tree planting program can cool the region due to blocking sunlight from reaching the ground.We KNOW why having large groves of trees help cool a region.To block the sunlight from reaching the ground.
“CO2 forcing fiction” can be tested empirically by using a flashlight (a hotter heat source) cooking a dinner roll (a cooler heat source) in the oven.Surely the CO2 will help the flaslight warm up the roll.After all we KNOW that CO2 is a powerful continous long wave backradiating greenhouse gas.A marvelous concept.Where the same (“heat”) lightwave can be used repeatedly while it triies hard to escape the oven.
Luke whatever on earth are you objecting to?
“Technobabble cannot reverse the laws of physics; heat transfer follows a one-way path.”
That is exactly what is happening. The problem is your ability to understand the science. Even the scientists on your side agree, including Spencer. They just argue the size of the effect.
The problem Nick, with AGW and its promoters at IPCC, is that they only factor in increasing chaos and exponentially worsening tipping points; for this they assume static RH and increasing SH, neither of which is verified by reality; all this with the independent variable [ACO2] at best having an asymptopic contribution and more likely no relationship with temperature at all;
http://wattsupwiththat.com/2009/01/30/co2-temperatures-and-ice-ages/#more-5392
Alan Siddons you make some good points.
Christopher I’ve been expecting to see a note from you Entitled “The Meaning in the original Bode Theory …etc” apart from two minor nit picks I thought it was a well written one and explained the situation rather well.
Nick
Actually identifying cause, effect and feedback, if any is a crucial aspect of any system identification if you are to get the right equations for analysis. To that end you should realise that feedback can only provide an enhanced cause if it comes from an already amplified output from that cause. If you have a (generalised) source at Ps and effect Po where open loop (no feedback) situation Ps > Po as you would with with any dissipative system like the atmosphere. Any attempt to provide a feedback path to the source will only drain it all the more. You can model this as a system with source and load impedance Zs and Zl respectively leading to a feedback equation of Po = Zl/Zs(Pi – Po) that is a negative feedback system you can test if it works like atmophere and surface if you increase the load impedance Po will rise, might look intuitively to you like positive feedback but the equation says otherwise.
Still flogging the old runaway bunk Cohers. I enjoyed Chris Colose taking you scammers to task. http://chriscolose.wordpress.com/2009/03/31/lindzen-on-climate-feedback/#comments
Colose of course now becoming the thinking persons blog on climate.
Nick
The open loop gain of the system and the effect of feedback on the gain of the whole system is a bit more complicated than is described in that entry.
It is assumed that the negative feed back provided by infrared radiation from the earths surface is attenuated by absorption by the CO2 and other greenhouse gases on its upward journey back into space.
However a large portion of the heat arriving at the earths surface causes evaporation of water.
The latent heat of the evaporation of water is approx 1000 Btu / lb ie the amount of heat required to raise 1000 lb of water 1.0 deg F.
The water vapour can rise as high as 18 km above the surface where it condenses. the heat is thus released as infrared up to 18km through the atmosphere without being absorbed by the greenhouse gases on its journey.
Half of the heat transported in this way is thus able to be radiated back into space after having been released after traveling through the densest part of our atmosphere without attenuation by greenhouse gases.
Yeah, Colose is ok; but Lindzen had addressed the issue raised by Colose previously;
http://portaldata.colgate.edu/imagegallerywww/3503/ImageGallery/LindzenLectureBeyondModels.pdf
See p33. The point is, if there is no TOA imbalance then the pipeline has to be invented to explain why AGW is not being expressed now; where is your evidence for that?
Sid,
I don’t really understand where your latent heat argument fits in here. But LH transport is well understood, and quantified at 78 W/m2 in the K&T diagram, which is a moderate fraction of IR. That quantification is simple and robust – it is just based on total rainfall, which is well measured. And only a tiny fraction of that 78 W/m2 is released higher than 5km.
When it is released, it goes equally up and down. But it is still wrong to say that it has a clear run to space. Because the emission of IR is indirect – the condensation heats the air generally, but the IR emission only comes from molecules than can (GHG), that means that, by Kirchhoff’s Law, the emission is concentrated in the wavelengths which are maximally absorbed.
BTW, as a general observation, I think the conversation has rather rapidly fled from the original post.
“And according to this IPCC formalism, there is only one dynamically distinct internal state variable, the climate temperature, that functionally determines the apparently distinct but really merely functionally dependent “feedbacks” of their formalism.”
Your problem is you have no idea how the models work. They are far more complex than you are aware of, apparently.
Nick
Thanks for your comments
My point was that the infrared radiation from the earths surface is not the only way that heat goes upward on its way to space. The water vapour can travel up to 18km before condensing depending on the latitude etc, and even if the majority is condensed at a lower altitude of say 5 to 7 km this represents a significant proportion of the journey from the surface to free space. This distance also represents the most dense part of the atmosphere and therefore the most concentrated part of the column of greenhouse gases that absorbs the IR.
Kirchoffs law says the the resistance of a series circuit is the sum of the resistance of each element in the circuit. I feel that the resistance of the first 5, 7, or even 18km of the distance from the surface to space is greatly reduced by this transport method.
My limited knowledge of heat exchange tells me that the thermal conductivity of all components separating the two media in question may be considered in the same way as resistance in electrical circuits.
I don’t know if the IPCC includes this in their models.
I feel that the whole climate system is affected by many variables not yet fully understood, but I certainly don’t feel that we will reach a “trip” point and have a thermal runaway due to positive feedback.
As in most of nature on earth, the climate is dominated by negative (stabilizing) feedback systems.
If the temperature of the earth has increase by say 0.7 degC in the last hundred years, and we consider the temperature where I live is say 300 degK . that is 0.7/300 = 0.23% increase in temp in 100 years. That is one good thermostat we have working for us
Rain is definitely cool, The heat has gone somewhere! perhaps space !
Thanks for taking the time to address my thoughts
Sid (Retired instrument engineer)
Alright Nick, getting back to your ode; dS/dt = fS + F, where F is the forcing and f the feedback; by well established AGW principles F is ACO2 and f is the enhanced greenhouse through increasing SH and static RH [per Dessler, Minchswaner etc]; since ACO2 is asymptopic F must be close to exhaustion or just marginally more than zero; Spencer calculates f here;
http://www.drroyspencer.com/research-articles/satellite-and-climate-model-evidence/
which is to say somewhere between 6 to 8Wm-2K-1; but this is based on TOA measurements; we know that high water is declining and widening the window there and providing a decrease in feedback; lower, near surface water is increasing; is that a net +ve or -ve feedback? Let’s say neutral with increase albedo countering the increase in absorption; therefore not only is there not a new, higher equilibrium state but possibly a lower one.
Climate tipping points is simply the latter day worry about how past climate catastrophes happened, using only what is available in the closed earth system.
It rejects outright the action of any external causation, hence the obsession with CO2 linked to a sinful humanity.
It results in the surreal climate models where ajustment of some arcane parameter causes the system to tip. It isn’t so much a gigantic con-job but a mass delusion feeding on itself.
Coho,
sorry, I didn’t understand too much of that – the sentences are a bit long for me. But let me pick up on one thing – “ACO2 is asymptotic”. I presume this is a reference to the general belief that the radiative effect of CO2 depends on the logarithm of its concentration.
I’ve said before that this notion is best forgotten, because it isn’t that important, and people keep getting it wrong. It seems to be a reasonable approximation, but in the range of CO2 that we have experienced to date, there’s little difference between logarithmic and linear. A log function is not asymptotic – it goes on increasing without bound. What it means is that if CO2 is at 780ppm instead of 390ppm, an extra ppm has about half the effect at 780 (vs 390). That’s less, but not nothing.
If you want to see the ode I wrote developed much further, it’s done in Lucia’s model Lumpy, though she is not looking at positive feedback.
“by well established AGW principles F is ACO2 and f is the enhanced greenhouse through increasing SH and static RH [per Dessler, Minchswaner etc];”
No, a forcing F can be any one of a number of types, CO2 just happens to be it, at the moment. Similarly, f, the ‘enhanced greenhouse’ effect is a combination of forcings, as well as such other factors as pressure band broadening of the absorption band. AGW ‘principles’ do not exist as such, climate physics do. AGW is the result of the current state of the strongest forcing.
Coho,
Just a follow-up, I should really have written that ode as dS/dt = fS + AF, where A is some sensitivity type multiplier, and is in general a matrix. It didn’t matter for my distinction between feedback and forcing, but it does if you have specific forcings in mind.
Andrew, did you get that?
Sorry, little will, EG is water;
http://www.climateaudit.org/?p=2567
Well Nick I don’t know how there can be little difference between log and linear;
http://img511.imageshack.us/img511/1994/logwarmingillustratedeo8.png
and why would you need a “sensitivity type multiplier” at F? Wouldn’t it go at ‘f’? And the issue is why does it have to +ve. I mean the evidence for a decline in high level water vapor is pretty clear.
Coho “Well Nick I don’t know how there can be little difference between log and linear”
There’s a big difference if you take pCO2 down to zero. But that’s theoretical. We haven’t been there, and we won’t. We’ve been from 280 to 380, and on that graph, heading for 550. That range is pretty linear.
No, sensitivity multiplies F (see Lucia for corroboration). It’s just a scaling for how much W/m2 translates to in temp C. f is a feedback factor, and after you solve over time, ends up effectively amplifying or diminishing A.
Luke. Okay, throw the word scammers on people is to becoming the thinking persons, but can’t you answer sunsettommy’s question: Luke whatever on earth are you objecting to?
You did the typical reply that the one with arguments don’t understand and should get involved in the erroneous work he described. Before you answer sunsettommy’s question you are a troll. I give you the benifit of a doubt (although I guess you don’t deserve it) to answer.
Magnus – your grammar is incomprehensible. And if you think anything that sunset said made sense you’re a magician. To receive this tedious discourse on external and internal climate system states shows we’re dealing with with a fabrication based on no idea where modern climate modelling is at.
Christopher’s comments amount to a straw man argument. The one state variable that he talks about does not describe the GCM’s that model the earth’s climate. They look at a variety of variables on a complex grid of latitude longtitude as well as heights in the atmosphere and ocean to describe the state of the earth’s climate in time. These models are run repeatedly, and the relationships derived between forcing and temperature, as well as the feedback effects, are empirically derived from these complex simulations.
The variables at each gridpoint are the analog of the phase space in statistical mechanics that is being referred to. The system is indeed understood to be chaotic, which is the reason that a variety of initial conditions are being used and the results are expressed as statistical averages.
Claiming that GCM’s don’t make use of phase space, and deal with chaos, to criticise the research doesn’t make any sense. There may be some valid criticism in all that is written, but it is really hard to find. Most of it amounts to throwing around a lot of jargon to impress people who don’t know any better.
Well Nick, regardless, the effect from further increases in CO2 is downwards and theoretically or otherwise CO2’s decline begins exponential and it is therefore asymptopic; in terms of the formula; fS + F 1]
f{S/f2df < 0 hence
S + f{S/f2df fS + F < S then
dS/dt will reset at its prior equilibrium value whenever an [internal] imbalance is encountered.
then the overall effect is that either f and/or F are less than one
Eric
WHAT?
Sorry that derivation did not reproduce completely.
I’ll try again;
dS/dt = fS + F; dividing by f;
1/f dS/dt = S + 1/f x F; equating the left side by parts;
1/fds = 1/fS + S/f2 x df; equating the 2;
1/fS + S/f2 x df = S + 1/f x F
s + f S/f2 x df = fS + F
Now even if f is +ve [but less than 1] and F is a declining function
f integral S/f2 x df is less than 0 and
S + f integral S/f2 is less than S so fS + F is less than S then dS/dt will return to the old equilibrium value not a new higher one.
“The so-called water vapour feedback, caused by an increase in atmospheric water vapour due to a temperature increase, is the most important feedback responsible for the amplification of the temperature increase.”
I think that is quite clear. They mention the most important feedback, there are others. The IPCC report, despite McIntyres snide bitching, is an attempt to summarise a vast body of scientific research. If he wants to know more detail, it provides all the references to the papers.
“snide bitching”?! Shame on you little will.
”
“snide bitching”?! Shame on you little will.”
Did you read your own link. All he does is complain that he didn’t get a pony for christmas.
Luke:
“Christopher – you don’t seem to be aware what modern climate modelling science is up to. You could do well to acquaint yourself with what Hadley Centre are doing instead of being presumptuous.”
I asked you once and Magnus brought it up again.
My question you have ducked:
“Luke whatever on earth are you objecting to?”
Was my question that hard to answer?
Comment from: cohenite April 12th, 2009 at 10:49 pm
Well Nick, regardless, the effect from further increases in CO2 is downwards and theoretically or otherwise CO2’s decline begins exponential and it is therefore asymptopic; in terms of the formula; fS + F 1]
f{S/f2df < 0 hence
S + f{S/f2df fS + F < S then
dS/dt will reset at its prior equilibrium value whenever an [internal] imbalance is encountered.
then the overall effect is that either f and/or F are less than one
I’ll try again;
dS/dt = fS + F; dividing by f;
1/f dS/dt = S + 1/f x F; equating the left side by parts;
1/fds = 1/fS + S/f2 x df; equating the 2;
1/fS + S/f2 x df = S + 1/f x F
s + f S/f2 x df = fS + F
Now even if f is +ve [but less than 1] and F is a declining function
f integral S/f2 x df is less than 0 and
S + f integral S/f2 is less than S so fS + F is less than S then dS/dt will return to the old equilibrium value not a new higher one.
Cohenite,
For the benefit of those who are not as well read as you are, could you explain where you got the equations you have written, and what the variables stand for? I don’t recognize them as something I have seen before.
Coho,
Sorry, that maths is still not working. What are you trying to do – solve the inhomogoneous linear de? The result would be (with f constant)
S = exp(f x t) int ( exp( -f x t) F )
But I’m not sure where you want to go from there.
No matter how much screaming the AGW catastrophist do. The fact remains that CO2 is rising, but temperature is not….
The Climate realists(hitherto referred too as sceptics), simply sit back and nonchalantly point out that rather embarrassing point.
There may be some valid criticism in all that is written, but it is really hard to find. Most of it amounts to throwing around a lot of jargon to impress people who don’t know any better.
i agree. but it is most interesting to witness the responses by denialists in this comments: half of them deny the effect, the other half disagrees with the cause. now that is an internal contradiction worth some thought!
No matter how much screaming the AGW catastrophist do. The fact remains that CO2 is rising, but temperature is not….
the fact of the matter is, that you don t know the difference between WEATHER and CLIMATE.
The Climate realists(hitherto referred too as sceptics), simply sit back and nonchalantly point out that rather embarrassing point.
no, actually they don t. instead they had to modify their theory (there is now arming) to at least the next step (it is not caused by CO2).
and they don t sit anywhere, instead they write rubbish like this article.
Eric; the equation comes from Nick;
“I don’t think you should so closely identify the feedback/forcing distinction with cause/effect. Feedback amplifies a forcing to provide an enhanced (or diminished) cause. The thinking behind the distinction comes from the differential equation context that you mention. In an inhomogeneous linear ode:
dS/dt = fS + F
(S a state vector) you would describe the second term as the forcing, and the first as feedback. Generally the climate version considers what happens when this ode reaches equilibrium, but it is seen most clearly conceptually in the time development”
As I say F or forcing from CO2, at the very least begins exponentially, therefore must be asymptopic; the issue of f or feedback I approached from the Spencer and Braswell position which meant that, regardless of whether the effect of water is described as a feedback or a stochastic variable, that effect is arguably negative; for purposes of the Nick eqn I assumed f was +ve but < 1 given that high water is declining and increasing the TOA window [hence the Lindzen dispute] whereas low water is probably neutral; an assumption more favourable to the AGW position.
Eric, Coho
The equation dS/dt = fS + AF I used to illustrate the functional difference between a feedback term, with state dependence, and a forcing term in a linear inhomogeneous ode. It has been used in simple climate models, as in the Lucia link I gave, and I quoted it to show how the distinction wasn’t well described as cause/effect. It isn’t a particularly good starting point for thinking about, say, w/v feedback, because you aren’t then thinking about solving (in your head) the time dependent ode (although that’s what GCM’s do).
Jan,
I raise you a What as well – Eric’s explanation is going to be interesting.
Sod,
You misunderstand the sceptic position – our position is that there is no anthropogenic gklobal warming.
And CO2 has nothing to do with it.
My education may be lacking in the area of radiation, frequencies, & absorption of same. If so, will someone please explain my error. I did read, somewhere, that the only temperature increasing, when they were, was the nightly minimum, which is unlikely to have any detrimental effect, anywhere. This would agree with my theory.
I can see no way that CO2, or any other gas can absorb any X earth radaition during daytime. Surely the absorption capacity of any GHG would be flooded by the incomming radiation from the sun, & would have no capacity to absorb any of the radiation on it’s way back out, under these conditions.
In fact, these gasses should actually reduce the incoming, by absorbing, & reradiating some of it in all directions. As at least half of this would be away from the earth, this would be reducing the heat getting to the surface. So, GHGs should actually be reducing the teperature, not increasing it. There may be some interesting equations for when the atmosphere was still in full sun, but the surtace below was not.
I can not see how the interseption, & reradiation of the much lower outgoing radiation at night could have as much effect, on the overall temperature, as this interception of the higher level, incoming, from the sun.
So, why am I not right?
And that’s why we call you denialists you see.
Interestingly though your more thoughtful sceptics do believe. But hey faux-sceptics like nothing better than to make shit up. Like the UN- Greenpeace funding bit of utter nonsense. But please keep it up – the more idiotic you seem the better.
But back to Sundown – mate what we have here is a pretentious bit of non-science. The sort of bilge that E&E love to publish. Most of the asides in the lead thread are already formalised in GCM codes so Game is simply bleating on. Internal vs external processes indeed. What we have is a long winded essay which concludes with
“The maturity and degree of corroboration of science reviewed in this paper is variable. This is indicated to some extent by reference to publications which corroborate and/or develop the specific area under consideration. However, this paper does not evaluate the overall quality and/or durability of findings drawn upon to present overall conclusions.”
Well well – what an admission of a piece of nonsense.
Hasbeen,
Sshhhh, you will be put on the rack if you continue making these incovenient statements. Let’s see how the numerati explain it.
Hasbeen – this sort of comment is STUNNING in its ignorance.
“Surely the absorption capacity of any GHG would be flooded by the incomming radiation from the sun,” This means you have failed to appreciate even the most basic element of GHG 101.
You’re a total numb nuts. Get off the blog and attend Grade 8.
And given Louis signed up – take him with you. Louis actually signed up for it. HOLY COW.
OK sceptic scum – do you support Hasbo and Louis’s comments here. Come on guys – any shyness here will be seen as a lack of support. We know you’re ashamed.
Luke,
You mentioned Greenpeace, I just mentioned environmental groups, if I was that specific in the first place.
And how about some examples of your own peer reviewed publications Luke? You are technically qualified to hold your position as Chief Scientist, are you not?
Nick Stokes “I’ll try to read more on Spencer’s phase space analysis reference. He seems to be saying that cloud changes are a big effect that don’t fit so well with the linear concepts…”
Nick…Spencer OBSERVED that behavior using a satellite. I get so frustrated listening to this modeling gibberish and the implication that an actual observation doesn’t fit it. With all due respect, you’ve got to get yourself into a real atmospheric example and think the problem through. You are getting hung up on the math.
Your example, dS/dt = fS + F, in which you describe the second term as feedback is simply wrong. How can you possibly get feedback out of that equation? What you are describing in the equation is an instantaneous change in the function S (wrt time) being equal to what I presume to be the first derivative of the function plus a constant F. That in no way describes feedback.
We’ve had this discussion before in Michael Hammer’s thread. Feedback is not an additive process, it is a mutiplicative process by a fraction greater than one. It is combined with an input in such a manner that the input is amplified by an amplifying medium. If you had written S instead of F it would have made far more sense, but it still would not be feedback.
Jeffrey Glassman wrote a paper called The Acquittal of CO2, and it was rebutted by Gavin Schmidt. In his reply to the rebuttal, Glassman points out several inaccuracies in Schmidt’s understanding of physics, one of them being positive feedback. In the following paper, that is covered half way down the page.
Glassman quotes Schmidt as saying “A positive feedback occurs when a change in one component of the climate occurs, leading to other changes that eventually ‘feeds back’ on the original change to amplify it.”
Glassman replies, “Leaving room for some climate jargon, this is almost a valid and workable definition. But it omits, among other things, the necessary control system context, and the concepts of gain, ordinary feedback, open loop and closed loop”.
Glassman goes on with another quote from Schmidt, “Gavin next attempts to explain what he thinks positive feedback means: “A simple example leads to a geometric series for instance; i.e. if an initial change to a parameter is D, and the feedback results in an additional rD then the final change will be the sum of D+rD+r2D…etc.””
Glassman responds,”This explanation and Schmidt’s understanding of positive feedback, or even feedback, are fatally flawed.
First, Schmidt’s equation expresses a change in the parameter value, not the value of the amplified, closed loop output in his definition, or anything related to it. By reference to “in an additional rD”, and by the plus signs in the series, Gavin reveals that he is thinking of the change as an additive amount. By his definition, the feedback is to cause an amplification of the original parameter. Amplification is multiplicative, not additive. If the original parameter value was P, after positive feedback the value would be rP, with r greater than one, or it might be written as (1+g)P, where g is now the feedback gain, and is greater than zero for positive feedback. Schmidt’s algebraic example does not represent his verbal definition”.
****
In the same way Schmidt’s series does not describe his original statement about feedback, neither does yours. You’re describing feedback as an independent variable and it’s not. In fact, I’d like to see you solve for F given your equation. Feedback is dependent on the amplification factor of the system, which has to be greater than zero. When the input is amplified, a portion is fed back to the input and that is amplified again. With repetition, the output diverges.
Going back to Schmidt’s statement, “A positive feedback occurs when a change in one component of the climate occurs, leading to other changes that eventually ‘feeds back’ on the original change to amplify it.” It is wrong to claim that feedback causes the amplification. It merely adds to a climate variable that has to somehow be amplified. Feedback implies a loop in which one ‘amplified variable’ has part of its quantity fedback in such a way as to increase that variable.
An example of feedback in the atmosphere is supposed to be increased WV due to increased ACO2. To get an increase in WV, the surface temperature must increase, so surface temperature has to be Schmidt’s variable. The feedback has to be back-radiation from ACO2 in the atmosphere, but since that back-radiation came from a loss in surface energy (i.e. no amplification), it cannot form a positive feedback loop. Of course, the new theory is that ACO2 absorbs IR from the IR component of solar radiation, which eliminates it as a feedback.
The AGW feedback nonsense just keeps getting muddier and muddier.
But Luke, as Pikey noticed, you are the one with no position, whether scientific or philosophical. In fact the only position you seem to have is as QLD’s climate department’s Torquemada.
Luke, when the hoi polloi start working things out for themselves, much as what happened when Tyndale translated the Bible from it’s Latin to produce the Authorised King James Version, and hence the start of the Holy See’s ending of religious monopoly, it’s time for double-speaking technocratic dictators to start worrying. If you can’t explain the science to your grandmother in terms she understands, then that simply means you don’t understand it either. Hasbeen seems to have worked it out but I am sure you will, using the double-speak of mathematics, try to prove him wrong by bluster and mathemagical arcania.
Personally I would be somewhat concerned that lay people are starting to reason it out by themselves – it means they have started to recognise the bulldust you and the rest have fallen for.
Look at Sinkers go for it in reverse – you old fox – when cornered out go the flares, start laying smoke. Come up with more fabrication and diversions.
You signed up with Hasbeen. Now back it up or apologise.
And don’t lie straight in the blog’s face
13/4/09 11:48am
“You mentioned Greenpeace, I just mentioned environmental groups, if I was that specific in the first place.”
but you said …
11/4/09 9:31pm
“Your taxes fund Greenpeace etc, via the UN. provided you pay tax in the first place, so donating more doesn’t seem all that sensible.”
So apologise to Jennifer for knowingly and willfully misleading the blog. What a disgrace.
Unless you want to back it up here and now matey.
Just filing this here:
“Eric Adler comments:
Christopher’s comments amount to a straw man argument. The one state variable that he talks about does not describe the GCM’s that model the earth’s climate.
That’s why I took out the word model and put in the word formalism. My argument knows that the GCMs are not fully covered by the formalism. That’s why I attacked the formalism, which is inadequate even to describe the GCM models. Very few know exactly what is in the GCMs. But the formalism is the vehicle of the debate and propaganda, and is therefore very fair game, and no straw man.”
Gordon,
You are getting carried away with your contrarian enthusiasm. Look again at what I wrote. Christopher referred to phase portraits and referred to Spencer’s blog statement – I just said that I would try to read it. And I can’t see how what I said on clouds is in any way misrepresenting what he says.
The equation I wrote is a generic equation for time dependent processes. It’s relevant here, because that is what GCM’s resolve, and where the feedback actually enters. It was useful for that part of the discussion, because it clarifies the cause and effect issue. When a state is changing, the rate of change can depend on things independent of the state (forcing), and on things proportional to the state.
In electrical circuits, you don’t normally solve a de for the time variation, because you mostly are thinking about a sinusoid of known frequency. In other words, you take a Fourier transform. Do that to the equation I cited, and you’ll see that it has the form you expect.
I did solve for F in my comment of 4.24am. Again, you can put a sinusoid in to get a familiar feedback, with complex phase shift.
Schmidt’s statement is perfectly reasonable. He’s using “amplify” in a conventional way – the feedback makes the effect bigger than it would be without feedback.
I think acoustic feedback is a good analogy to think about. A mike, amplifier, and an acoustic connection with, say, an audible time delay. Runaway is the familiar howl. But before runaway, you know there is positive feedback because certain frequencies get unnaturally emphasised. Tap on the mike, and you’ll here an echo of diminishing taps. A true representation of the geometric series that Gavin spoke of. If you add up the total sound, it’s more than you would have without feedback. The extra is actually time-separated. Of course, the more important case is when the signal is not a tap but a sinusoid of the right frequency that the echo adds in phase.
From this, you can see the artificiality of the fussing about active components. A good echo chamber behaves in the same way as a non-howling PA system with positive feedback. You just can’t drive it into sustained oscillation, because there is no power source. But the climate system has a power source – the sun.
Luke,
Thanks, you saved me having to locate it. So I did but I’m not apologising.
You forgot to mention the etc which makes the phrase a collective one and hence not as specific as you wish it to be. Greenpeace is a tax free NGO so one’s taxes are paying it, albeit in an indirect way. In fact in the 1972 Stockholm Earth Summit managed by the UN, they paid for the newly formed Environment groups to attend the summit.
Any organisation that does not pay tax is being effectively financed by the taxpayers.
And getting a little belligerent as well are we? I must be hitting some real raw nerves in the Lukian psyche.
Nick Stokes “Schmidt’s statement is perfectly reasonable. He’s using “amplify” in a conventional way – the feedback makes the effect bigger than it would be without feedback”.
I suggested you step away from the math and look at what is going on. You came back with the feedback model, confusing reverberation with feedback. If you tap on a mic, and hear echos, you are hearing the sound bouncing off the walls, ceiling, etc. That is not positive feedback, it dies out as the walls, etc., absorb energy.
The squealing you hear when a microphone is picking up energy from the speakers, requires an amplifier. Try setting up a mic without an amplifier. You wont get squealing and you wont get echos. The squealing comes from a specific frequency, as you pointed out, and it’s usually the resonant frequency of the room. That’s why you can control it using a graphic or parametric equalizer, which serves to filter (attenuate) the frequencies going into the amplifier.
The squealing is called feedback and it is caused by positive feedback. A signal passing into the mic is amplified and the speakers pump out acoustic energy which vibrates the walls, etc. That vibration (reverberation) feeds back into the mic, and if the phase of the signal is correct, it adds to the original signal. When the combined signal and feedback are summed at the mic, they are amplified and the process repeats till the output signal runs away, producing the squeal.
Schmidt is wrong because he implies that the feedback causes the amplification. You can see that in his series because he’s holding the ‘A’ parameter constant and changing the feedback (r). As Jan has been trying to point out, and as Glassman concurs, you need a loop with an amplifier in it. In an amplifier, it is not a practice to change the feedback since it is determined by an RC network, hence is fixed. Also, the predominant feedback in an amplifier is negative feedback to smooth out the frequency response. How Schmidt proposes to change the feedback is a mystery to me. He seems to think something like back-radiation from ACO2 is the feedback and increases with increasing ACO2.
Under that model, the only way the back-radiation can increase is through increased surface emissions. But that represents a loss to surface energy. The theory put forward in this article, that GHG’s in the atmosphere absorb energy from the IR portion of solar radiation, makes more sense. ‘IF’ that was possible, the GHG’s might be seen as an independent source capable of radiating to the surface, but that would no longer be a feedback. That scenario raises other problems, however.
On a cloudless days, one might theorize that WV in the atmosphere could absorb solar IR. However, Bohren in The Fundamentals of Atmospheric Radiation describes an experiment in which he points an IR meter at the clear sky on a warm spring day when the air temperature was about 20 C. The IR meter measured about – 50 C. He then pointed it at some clouds and it rose to – 3 C. He explains the difference in IR temperature as clouds, formed from water droplets, as being equivalent to a thin layer of water, and that water has a much higher emissitivity than water vapour.
When temperatures drop more on a cloudless night, the atmosphere can be full of water vapour. Why doesn’t that WV trap heat? It is only the water droplets in clouds that trap heat and which have an ability to radiate heat at night.
I think it’s important to remember that the surface is warmed by broad-spectrum energy from the Sun and that it has a much larger area to absorb radiation than GHG’s in the atmosphere. That’s why the notion of GHG’s trapping sufficient energy to raise the mean temperature from -19C to +15C makes no sense to me. The surface is radiating broadly and the GHG’s don’t have a hope of trapping a significant amount of radiated heat from it. What makes far more sense to me is warmed air (N2, O2, etc.) acquiring heat from the surface and transporting it poleward and into the upper atmosphere, where it is radiated into space, as Lindzen claims.
Correction…I said the surface is radiating broadly. I meant it is radiating over a broad area that the 1% of GHG’s in the atmosphere could not possibly absorb significantly.
An interesting interview with Craig Bohren, co-author of the Fundamentals of Atmospheric radiation:
http://www.usatoday.com/tech/columnist/aprilholladay/2006-08-07-global-warming-truth_x.htm?csp=34
Would it not also be the case that if f can also be a stochastic cause that dS/dt = fS + F should be written dS/dt = fS + fF?
Coho,
This is just a linear inhomogeneous equation. You can think of it as the very general equation dS/dt=H(S,t) with H expanded as a Taylor series in S and truncated at first order. As such, it crops up in a lot of places. It is, as I originally wrote it, a common stochastic de with F as the random variable. It’s more unusual to have the same random variable in both terms, though it does happen with, say, Stochastic volatility models in finance. However, let’s stay away from those tumbrils.
Incidentally, if you want to focus on that de, I should define the quantities better. S should be seen as an increment of a state variable about an equilibrium – in climate terms, an anomaly. Likewise F is an increment of the driving in that state. That’s consistent with the Taylor series concept.
Sod,
You misunderstand the sceptic position – our position is that there is no anthropogenic gklobal warming.
And CO2 has nothing to do with it.
this is false. there are people posting on this very blog, who claim that there is no warming.
i would actually consider the position, that CO2 doesn t seriously effect our climate to be a fringe position among educated “sceptics”.
I can see no way that CO2, or any other gas can absorb any X earth radaition during daytime. Surely the absorption capacity of any GHG would be flooded by the incomming radiation from the sun, & would have no capacity to absorb any of the radiation on it’s way back out, under these conditions.
the in-coming radiation is slightly different from the out-going one. as Luke, i am deeply shocked by regular posters not noticing this immediately.
the denialist position is utterly unscientific, and it is, because most of the denialists don t understand the most basic science.
ps: minor warning to all denialists: i wouldn t discuss math with somebody named “Stokes” 😉
So we now know Louis forgets what bulldust he sprouts from hour to hour.
So church groups don’t pay tax. And maybe the UN has invited some of them along now and again as well too.
Sinkers. In 1972 – back to your beloved Cold War days eh? oooooo – scary.
If you’d like Greenpeace to be taxed then redneck govts in the USA and Aussie have had plenty of opportunity to change the law in recent years. Blame them not me.
You’re just sour that a vast number of thinking people want a much better world than you do and are prepared to contribute to such organisations. That’s “vast number”…
I find the notion that we should be scared of the UN utterly amazing. The UN is so divided it’s a wonder they get to do anything. Self-interest by the members rules supreme !
Nick if f is a constant, either less [-ve] or greater than 1 [+ve] seems not to have bearing on the result according to the ode; if, as you say; S=exp(fxt) int (exp(-fxt)F) then
S = eft x int e(-ft)F which is differentiated
dS/dt =ft x int e(-ft)F + eft x e(-ft)F
=fS + eft x e(-ft)F
=fS + eft(1-F) so
fS + eft(1 – F) = fS + F
-> F =eft(1 – F)
Thus as F is greater than 1 then ft(1 – F) is less than 0 so as t approaches infinity, F approaches 0.
In other words, as soon as the Forcing factor creates an imbalance, the tendency is to return to equilibrium.
Coho,
You can’t get anything new this way – it should be just verifying the solution. Here’s how it goes:
Differentiate product rule:
dS/dt = f x e(ft) x int e(-ft)F + e(ft) x e(-ft)F
= f x S + F
sod “the in-coming radiation is slightly different from the out-going one. as Luke, i am deeply shocked by regular posters not noticing this immediately”.
What you should be shocked about is that solar IR is exactly the same as terrestial IR. I don’t know where you got the notion that they were ‘slightly’ different. The only think differentiating IR from UV and the visible spectrum is frequency. It’s all electromagnetic radiation. What most people don’t understand is that the solar spectrum is 51% IR, which is longwave, which is the same IR as the surface emits.
If you look at the NASA radiation budget I posted, which SJT thinks is just a toy for kids, you’ll see that 16% of the Earth’s budget comes from solar IR and 15% from surface IR, if you can trust NASA, that is. They don’t list any IR for back-radiation, so there goes the positive feedback for WV.
You’re like a zombie Gordon – dazed, single minded (?!) – you never give up
(1) the GHG relevant part of solar IR is tiny
(2) you can measure the IR back radiation on any cloudless night (THE SAME WAY you could measure the upwelling IR from the surface) – look – no hands – no sun !
Stokesy is correct on the lead post – you’re muddled and lost.
Gordon get some instruments – like this – do some measurements and report back – http://www.kippzonen.com/?download/36152/CGR+Pyrgeometers+-+Brochure.aspx
Slide 13 Gordon http://www.nohrsc.nws.gov/~cline/clp/meetings/boulder_nov01/presentations/houser_CLPXmicromet5.ppt
THE CENTRAL SUBJECT OF CLIMATOLOGY
Dr. Gerhard Löbert, Munich
In my opinion the researchers in climatology should put aside their present work for a moment and focus their attention on the central and decisive subject of climatology. This is the extremely close correlation between the changes in the mean surface temperature and the small changes in the rotational velocity of the Earth in the past 150 years (see Fig. 2.2 of http://www.fao.org/DOCREP/005/Y2787E/y2787e03.htm or Ref.2), which has been ignored by the mainstream climatologists. Everything else in climatology follows from this one central theme.
Note that temperature lags rotation by about 6 years.
Since temperature is lagging rotation it cannot be influencing the latter. On the other hand, it cannot be envisaged how rotation should influence temperature. Hence, a third agent must be driving the two. The solution is given in http://www.icecap.us/images/uploads/Lobert_on_CO2.pdf . There it is shown that small-amplitude vacuum density waves generated by the motion of the supermassive objects located in the center of the Galaxy are constantly acting on the Sun and the Earth and are thereby producing a series of correlated physical reactions within these celestial bodies.
Remember: Everything in climatology follows from this one central theme.
References
1. Löbert, G.: A new theory of gravitation and its impact on cosmology; stellar evolution; galaxy dynamics; the power source of stars, coronas and intergalactic gases; supermassive/superdense bodies; cosmic jets; and the generation of longitudinal gravitational (vacuum density) waves and their action on the Sun and the Earth (e.g. world climate). Munich 1993.
2. http://www.icecap.us/images/uploads/Lobert_on_CO2.pdf
3. The post of Sept. 19, 2008 in Google “Gerhard, pakteahouse”
how is the cosmic flux affecting the velocity of the earth?
and is the velocity causing anarctic sub-sea volcano eruptions?
Comment from: Jennifer Marohasy April 13th, 2009 at 2:12 pm
Jennifer wrote:
Just filing this here:
“Eric Adler comments:
Christopher’s comments amount to a straw man argument. The one state variable that he talks about does not describe the GCM’s that model the earth’s climate.”
That’s why I took out the word model and put in the word formalism. My argument knows that the GCMs are not fully covered by the formalism. That’s why I attacked the formalism, which is inadequate even to describe the GCM models. Very few know exactly what is in the GCMs. But the formalism is the vehicle of the debate and propaganda, and is therefore very fair game, and no straw man.”
So what you are saying, is you edited the opening post, by Christopher Game, and substituted “formalism” for model. If Christopher is attacking GCM’s then his ideas are wrong and inappropriate, because he claims the models are neglecting internal state variables.
So now what are we to make of this post? What you call the “formalism”, is a way to think about the results of the GCM’s, and emerges from them, rather than dictates them. It is therefore incorrect to argue that the state variables are neglected by the “formalism”.
This still makes the argument incorrect and a straw man. The summary of results is not supposed to reflect the intricate operations of the internal state variables.
Comment from: Nick Stokes April 13th, 2009 at 4:24 am
Coho,
Sorry, that maths is still not working. What are you trying to do – solve the inhomogoneous linear de? The result would be (with f constant)
S = exp(f x t) int ( exp( -f x t) F )
But I’m not sure where you want to go from there..
I agree that the Cohenite’s solution method is wrong, but I am not sure your equation gives something that converges as t gets large. It does not appear that the system is approaches equilibrium as it is supposed to.
Taking your original differential equation,
dS/dt=S/f+F,
you have to divide both sides by fS+F, and multiply both sides by f*dt.
Then you can integrate the equation simple by isolating the variables on opposite sides of the equations.
The solution I get is
(S2+F/f)/(S1+F/f)=exp(f*(t2-t1))
So now we need a boundary condition. There is a problem with this equation because it predicts that as the final value of t, t2 approaches infinity, the value of S2 becomes infinite.
I thought that y if one has a climate forcing in operation, at infinite time, the temperature anomaly should approach its finite equilibrium value even if there is positive feedback.
Is your equation the wrong description of climate forcing, or did I miss something in obtaining a solution?
Eric,
First let me repeat my earlier caveat – I’m describing how you could approach a shift in equilibrium as a time-dependent process. Normally, analytically, you wouldn’t think about it, although it is what GCM’s do. But I mentioned it because I thought it helpful with the issue of causality – to show that feedback is nothing special. I’m not putting the ode forward as a way people should be thinking about climate.
I wasn’t sure what Cohenite was trying to do, so I described the solution rather briefly. To expand, the integral is from some fixed time past to time present (as a variable). It is set out here for the case where f is a function of time. The boundary (initial) condition is that the solution was zero at that fixed past time.
The problem with your approach is that the forcing F is a function of time, which hurts when you integrate.
Did you see my verification at 7.26 am above?
Eric, I think Jennifer was just passing on a note from Christopher – ie he changed the word to formalism.
Nick,
The problem with your approach is that the forcing F is a function of time, which hurts when you integrate.
Did you see my verification at 7.26 am above?
I am sorry that I missed it. However, it is still confusing because F is not explicitly a function of time in your solution. If F is supposed to represent the forcing, one would expect it to be a declining function of the difference between temperature S and the ultimate equilibrium temperature.
Comment from: Nick Stokes April 16th, 2009 at 4:07 pm
“Eric, I think Jennifer was just passing on a note from Christopher – ie he changed the word to formalism”
OK but it still is a straw man argument no matter who instituted the change.
Nick, Cohenite,
Chris Colose, who is a real climatologist, has an essay on forcing and feedback available on line which is useful for this discussion:
http://www.mathaware.org/mam/09/essays/Radiative_balance.pdf
Dear Eric Adler, As it happens, I made the change. The science lies not in who made the change, but in what I wrote. You would like me to have made a mistake so that your straw man would have legs. The reason you want it to be a straw man is that then you wouldn’t have to find a flaw in my argument; I note that you have still made no claim to find a flaw in the argument that I put. By calling it a straw man, you are saying my argument seems correct but doesn’t matter, not trying to refute it. Indeed you have not even attempted to address what I wrote; you have addressed only a mistake that you would like me to have made. Neither does the Colose paper that you cite address what I wrote. Do you really expect me to debate with you about a mistake that you wish I had made? In your dreams. Yours sincerely, Christopher Game
Eric,
OK, a few more things not so well spelt in my original. F depends on t, but not on S. Both F and S are deviations from equilibrium – like anomalies. So F does not vary with S; the term fS handles the dependence you describe. f is independent of both t and S, although the Wiki link I gave shows how it changes if f depends on t.
Chris Colose’s article is useful. His equation 11 is effectively the same as mine if H (ocean heat) is proportional to ΔT.
Eric, Christopher
I’ve now followed C’s link to Spencer’s blog and on to the paper of Spencer and Braswell. They quite explicitly use the same breakdown (as I did) in their eq 2, so I feel more confident with it. I don’t see that they make a causality argument; they do a phase space analysis to search for the factor f, and they argue that the process is biased, in that random TOA fluctuations can be interpreted as positive feedback.
I don’t at present have an opinion on whether they have done this rightly, but I don’t see that it strikes fundamentally at the orthodox climate science view of feedback. It deals with a particular technique for deducing f.
To amplify my de based argument, I think it helps to look at the time sequence, because it is then reasonable to say that effects should follow causes. In the feedback equation I wrote (and in S&B’s eq 2) the feedback and forcing are added – ie they are treated as simultaneous, so there isn’t a cause/effect distinction.
Christopher Game wrote:
Dear Eric Adler, As it happens, I made the change. The science lies not in who made the change, but in what I wrote. You would like me to have made a mistake so that your straw man would have legs. The reason you want it to be a straw man is that then you wouldn’t have to find a flaw in my argument; I note that you have still made no claim to find a flaw in the argument that I put. By calling it a straw man, you are saying my argument seems correct but doesn’t matter, not trying to refute it. Indeed you have not even attempted to address what I wrote; you have addressed only a mistake that you would like me to have made. Neither does the Colose paper that you cite address what I wrote. Do you really expect me to debate with you about a mistake that you wish I had made? In your dreams. Yours sincerely, Christopher Game
Christopher,
I pointed out the reasons I rejected your argument very early in this thread:
Comment from: Eric Adler April 12th, 2009 at 10:35 pm
Christopher’s comments amount to a straw man argument. The one state variable that he talks about does not describe the GCM’s that model the earth’s climate. They look at a variety of variables on a complex grid of latitude longtitude as well as heights in the atmosphere and ocean to describe the state of the earth’s climate in time. These models are run repeatedly, and the relationships derived between forcing and temperature, as well as the feedback effects, are empirically derived from these complex simulations.
The variables at each gridpoint are the analog of the phase space in statistical mechanics that is being referred to. The system is indeed understood to be chaotic, which is the reason that a variety of initial conditions are being used and the results are expressed as statistical averages.
Claiming that GCM’s don’t make use of phase space, and deal with chaos, to criticise the research doesn’t make any sense. There may be some valid criticism in all that is written, but it is really hard to find. Most of it amounts to throwing around a lot of jargon to impress people who don’t know any better.
Comment from: Nick Stokes April 17th, 2009 at 12:39 am
Eric, Christopher
I’ve now followed C’s link to Spencer’s blog and on to the paper of Spencer and Braswell. They quite explicitly use the same breakdown (as I did) in their eq 2, so I feel more confident with it.
Nick, there is an important difference between your equation and S & B’s equation 2. The sign of the coefficient of T on the right hand side is negative. This makes the solution converge to equilibrium as time approaches infinity instead of approaching an infinite value.
With a negative value for f, your equation would be fine.
Eric, no, this isn’t important, because f itself has a sign. I wrote the equation my way because f positive means positive feedback. S&B are using the opposite convention. I don’t know why, but it’s only a convention.
Comment from: Nick Stokes April 17th, 2009 at 8:15 am
Eric, no, this isn’t important, because f itself has a sign. I wrote the equation my way because f positive means positive feedback. S&B are using the opposite convention. I don’t know why, but it’s only a convention.
It is important.
If f>0 the solution diverges as t gets large because of a term proportional to factor exp( f*t).
Nick,
S&B equation 2 has a term on the right hand side -alpha*T. So it is explicitly made a negative term.
You are confusing the role of “f” in your equation with the role of “f” in S&B equation 2.
Alpha has the same function in S&B eq. 2 as “f” in your equation.