Feedback, Sensitivity, Cancellation and Duality

The sensitivity of a mathematical model is a measure of the effect on a certain model output from variation of certain model input data. The sensitivity to errors in data, modeling and computation directly connects to the accuracy of a model. 

Climate sensitivity is primarily concerned with the effect on the global mean temperature from increasing the CO2 concentration in the atmosphere. 

Concerning the climate sensitivity of current climate models, IPCC states:

• Spread in model climate  sensitivity is a major factor contributing to the range in  projections of future climate changes. 
• Consequently, differences in climate  sensitivity between models have received close scrutiny in all  four IPCC reports.
• Climate sensitivity is largely determined  by internal feedback processes that amplify or dampen  the influence of radiative forcing on climate. 
• (A) To assess the  reliability of model estimates of climate sensitivity, the ability  of climate models to reproduce different climate changes  induced by specific forcings may be evaluated. 
• (B) An alternative approach, which is followed here,  is to assess the reliability of key climate feedback processes  known to play a critical role in the models’ estimate of climate  sensitivity. 

Here (A) is a reasonable way of testing climate sensitivity, and gives a large spread shown in Fig 10.2, while (B) boils down to 

• To assess the reliability of model estimates of climate sensitivity, we assess the reliability of key climate feedback processes  known to play a critical role in the models’ estimate of climate sensitivity. 

In other words, assessment of climate model sensitivities, is replaced by assessment of the feedback processes built into the model. But this is an internal check which appears to be circular: You build in a certain feedback process into the model and you then test model sensitivity by testing the validity of the feedback process you have put in. But in most cases you cannot isolate and experimentally test the validity of the feedback process you have put in: If you could directly observe climate sensitivity experimentally, then climate models would serve no purpose. 

But some sensitivities can be observed experimentally, and thus can serve as reliability tests of climate models. This is done in a recent article by Richard Lindzen showing that the radiation sensitivity of current climate models with respect to surface temperature, does not fit with observations, as shown in the above figure with ERBE radiation measurements: Climate models show too small radiation. Something is apparently wrong with the climate models, and there are many things that could be wrong...

In our exploration of the secret of turbulence by computation, we have studied output sensitivity by duality techniques based on solving associated dual linearized problems, and we have found that local exponential turbulent perturbation growth is controled by effects of cancellation. 

In turbulent flow, an important charcteristic of climate atmosphere/ocean circulation,  cancellation means that the worst combination of effects does not occur: Increase in space-time is balanced by decrease in space-time so that the net effect is smaller than worst case. Duality techniques should be able to offer important information on sensitivity also in climate models, but current models lack this capability and there seems to be room for improvement...will cancellation and duality help save humanity?

Malthus is Back Again

Mathematics can be a powerful tool:  In his famous treatise An Essay on the Principle of Population first published in 1798, Thomas Robert Malthus presented a mathematical analysis predicting exponential population growth in time, while food supply would have a much slower linear growth  in time, later referred to as Malthus' Principle of Population.

Malthus thus predicted mathematically an inevitable collapse of human civilization if actions were not taken to limit population growth. 

But the mathematics of Malthus was wrong: populations did not grow exponentially and food supply not linearly: human civilization did not collapse. Not yet at least...

Nevertheless, Malthus is today back again: Based on mathematical climate models the UN International Panel of Climate Change IPCC predicts exponential growth of the global temperature caused by burning of carbonbased fuels, which will lead to a collapse of human civilization on an overheated Earth, if actions are not taken to limit CO2 emission, now. 

Exponential growth is thus feared, but our capitalistic society is driven by dreams of exponential growth at x% per year of

• GNP 
• investments 
• income
• house prices...

But steady exponential growth is not possible, because it will surpass any limit in finite time: The exponential growth of a financial bubble is eventually followed by a financial crisis until the next bubble can start to grow, exponentially. The overall growth is not exponential because of negative feed-back: The bubble is follwed by a compensating crisis.

Exponential growth represents positive feed-back: The more it grows the more rapidly it grows. A dynamical system with positive feed-back exponential growth is unstable and in order to survive without explosion has to develop a different dynamics somehow curbing the growth by stabilizing negative feed-back. This is the nature of turbulence which is a fundamental aspect of climate. Also compare with the climate feed-back analysis by Richard Lindzen:

• The earth’s climate (in contrast to the climate in current climate mocdels) is dominated by a strong net negative feed-back. Climate sensitivity is on the order of 0.3°C, and such warming as may arise from increasing greenhouse gases will be indistinguishable from the fluctuations in climate that occur naturally from processes internal to the climate system itself.
  

The mathematics of exponential growth can be captured analytically and thus is attractive to a mathematical theoretical mind, but it is too simplistic to capture the dynamics of complex systems such as human populations or turbulence. 

Similarly, the IPCC mathematical climate models are most likely too simplistic to capture the dynamics of a the complex system of global climate. Malthus' Principle of Population and the IPCC mathematical models seem to have the same degree of realism. 

In the previous blog I noted that global climate and human population now connect on the agenda of the Optimum Population Trust endorsed by Sir David Attenborough:

• World population is projected to rise from today's 6.8 billion to 9.15 billion in 2050. The World Population Clock is ticking.  We are rapidly destabilising our climate and destroying the natural world on which we depend for future life.
• The West should provide money to promote contraception in the Third World and poor countries would be denied 'carbon allowances' unless they control their numbers. 
• Progress on climate change is being seriously hampered by the widespread refusal to acknowledge the link between total greenhouse emissions and the sheer numbers of emitters. 
• It is time we abandoned this crazy taboo.

Is this also the agenda of the upcoming UN Copenhagen Climate Council? To limit the number of emitters according to Malthus' Principle of Population? To deny poor people carbon allowances unless they control their numbers. Is Malthus back again?  What do you think?

Authority vs Science: Unreason vs Reason

Leading MIT atmospheric physicist and climatologist Richard Lindzen in a talk on The Politics of  Global Warming at the International Conference of Climate Change, New York City, March 8 2009, reminds us about a few simple truths concerning science in general and the science of climate modeling in particular:

• Endorsing global warming as scientist, just makes life easier.
• Most arguments about global warming boil down to science vs authority. For much of the public authority will win, since they do not want to deal with science.
• The climate alarm movement has control of carrots and sticks; most funding for climate would not be there without alarm.
• What can be done is to better understand science, in particular the logic of science. Actually, science and logic is often not that hard to understand. 
• Current climate models have large positive feed-backs with thermal radiation decreasing under increasing seasurface temperature, while Nature most likely has negative feed-back.  Getting people including many scientistst to understand this, is crucial. 
• The Global warming issue has done much to set back climate science, in particular the notion that climate is one-dimensional totally described by some fictitious global mean temperature and some single gross forcing a la CO2 level, is grotesque in its oversimplification.

Lindzen tells us something  important: Good science and scientific logic can be understood by many. Authority cannot win against science in the long run. 

However, in the short run it can, as is illustrated in the previous blog: Evidently Sir David Attenborough has little understanding of the mathematics of climate models, and thus easily can be convinced that predictions of climate models is the truth: If climate models show global warming up to 10 degrees Celsius over the next hundred years, because the accuracy is not better than 10 degrees, then we have to take action to prevent a certainly dangerous increase of 10 degrees. But is it reasonable to keep poor people from increasing their standard of living because climate models are inaccurate? Is it?

Note that Sir David Attenborough has joined the Optimum Population Trust with the following modest proposal on its agenda:

• The West should provide money to promote contraception in the Third World and poor countries would be denied 'carbon allowances' unless they control their numbers. 
• Progress on climate change is being seriously hampered by the widespread refusal to acknowledge the link between total greenhouse emissions and the sheer numbers of emitters. 
• It is time we abandoned this crazy taboo.

The idea to limit energy consumption of poor people until they have become rich enough to have few children is amazing in its inhuman Moment22 stupidity. Is this also a result of climate models? What does Sir David Attenborough say? Maybe it is time for an interview...

Sir David Attenborough: The Truth About Climate Change

The science of climate modeling predicting global warming by anhropogenic emission of CO2 from carbonbased fuels is nicely summarized by the legendary Sir David Attenborough in the Truth About Global Warming:

• The key question is: How can we distinguish between climate variations induced by natural causes and by CO2 emission?
• The key thing that convinced me was a temperature graph prepared by climate scientist Professor Peter Cox showing that a climate model with CO2 emission included can reproduce the temperature during the 20th century better than without.
• So there you have it: It seems little doubt that this recent rise, this steep rise in temperature, is due to human activity.
• It is clear that without the action of human beings there would have been far less temperature change since the 1970s.

The science of climate change is the science of climate modeling. Sir Attenborough became convinced by looking at a graph produced by running a certain mathematical climate model with and without a certain greenhouse effect included. But Sir Attenborough did not ask the natural question: 

• How reliable and accurate are climate models?  
  

Suppose Sir Attenborough was informed that climate models are not reliable, that their accuracy is unknown, would that change his conviction based on a single graph being the output of a climate model? Suppose he was informed that climate models are constructed so as to give the result of the graphs, a graph which is the result of modeling activity of human beings. What would Sir Attenborough then say?

Compare previous blogs on climate simulation.

Swedes in the Lead of Climate Control

Swedish scientists have played a leading role in global climate modeling: Svante Arrhenius studied the greenhouse effects of CO2. Carl-Gustaf Rossby pioneered computational weather forecasting sharing Arrhenius concern about CO2. His student Bert Bolin took the issue one step further in a 500 page report of a 1985 conference leading up to the following warning:

• In the first half of the next century a rise of global mean temperature could occur which is greater than any in man's history.

Bert Bolin was the first chairman of the UN International Panel on Climate Change IPCC 1988-1998 forming the basis of the Kyoto Protocol on control of CO2 emission negociated in December 1997.

Bert Bolin passed away in January 2008, at 82. His successor is Erland Källen.

Al Gore told Bert Bolin in a written statement in December 2007: 

• Bert, you set up the framework for the IPCC and without your contributions we would not have come to where we are today. Thank you for starting the process.
  

Al Gore in the Kingdom of Denmark

Al Gore stated in his keynote address at the World Business Summit on Climate Change May 24-26 in preparation of the Copenhagen Climate Council:

• 150 years ago the scientist John Tyndall in UK discovered for the first time that CO2 intercepts infrared radiation/heat.
  
• From his discovery followed a great deal of work that led to growing concern that from the rapid accumulation of CO2 in the atmosphere, the build up of heat in the atmosphere and ocean would reach dangerous levels.
• This year an important event will take place in this hall in this city, in this Kingdom. All nations will gather in an effort to secure a treaty limiting the accumultation of greenhouse gases and the emissions that lead to this accumulation.
• We are now facing three interrelated crisis: climate, financial and energy security, all three linked by a common thread to an absurd overdependence on carbonbased fuels. If we grab hold of that thread and pull it, these crisis begin to unravel and we hold in our hands the answer to all three:
• A historic shift from expensive vulnerable polluting carbonbased to new sources of energy that are free for ever: wind, solar and earth. In Denmark now 1/4 comes from wind
• CO2 is tasteless, odorless, colorless and has no price tag. It does trap heat.
• More increases are in store because the heat built up in the oceans that will be released into the atmosphere.
• We must put top urgent priority on preventing the catastrophy that would befall us if we did not act.
• The changes that are now needed will require participation and leadership from all parts of civilization.
• It is critically important that we get the rules of the market place correct and that the signals we derive from the market, are ones that accurately reflect human values, so that we can make decisions... that will allow us to live our lives in ways that are in keeping with what we know to be right.
• There is a very simple test of what is right where the climate is concerned: If the next generation looks back at this year and sees around them the worsening catastrophies that were foretold if the world did not act....If they look back on us and ask: What were they thinking, why did they sit on their hands, why did they choose not to take action to avoid the horrendous catastrophy that the scientific community spelled out to them, and told them would happen if they did not act.
• If they instead see around them in their world millions of good green jobs, a spirit of renewal, a sense of optimism and hope, a feeling that, yes we can deal with the problems. If they look back with gratitude, this means we have done our job.
• But it is not much time; we have to do it this year, not next year. The clock is ticking, beacuse mother Nature does not do bail-outs: 
• We have already as predicted seen increasing droughts, destructive fires, stronger storms, record flooding, spread of tropical diseases...
• But there is good news: The worlds business community and leaders are beginning to respond.
• Our policies in the US are changing: President Obama within on one month passed the largest green renewable energy stimulus bill in history. 
• Every nation and business has a leadership role to play.

In short, Gore first claims that scientists have shown that:

• CO2 emission causes global warming, which will cause horrendous catastrophy,

and then makes a political call:

• The Leaders of the World have to act and limit CO2 emissions.
  

UN Secretary General Ban Ki-Moon backs up Al Gore's message in his address to the Global Environment Forum sending the scaring message:

• droughts, floods and other natural disasters... as well as mass social unrest and violence... human suffering will be incalculable... if the world’s leaders do not seal a deal  on climate change... in Copenhagen...
  
• We have just four months. Four months to secure the future of our planet.
  

But  scientists do not seem to agree on answers to the basic questions:

• How much global warming is caused by CO2 emission?
• What will be the effects of global warming?
• What will be the effects of limits of CO2 emission, for the developing world?

In order for the December meeting in Copenhagen to be meaningful, some answers seem to be required...unless everything is just politics for the Leaders of the World...

For balance listen to Ian Plimer with lecture1, lecture2, lecture3, lecture4, lecture5 and interview1, interview2, interview3.

One question naturally presents itself: Does the ambition of the World Leaders of industrial countries to limit the use of carbonbased fuels, come from self-interest to guarantee continued access to these fuels?

Modernity in Physics, Arts and Music

In the previous blog I observed that modern physics is based on assumptions which cannot be directly verified experimentally. It appears that this aspect of modernity has a parallel in non-figurative arts and atonal music, which together with modern physics emerged in the beginning of the 20th century, in what can be viewed as a preparation to the collapse of classical Western culture in the 1st World War followed by the 2nd. 

An aspect of the modernity of non-figurative art is that it is impossible to compare the painting with what is supposed to be depicted. A non-figurative painting does not depict something explicitely, if anything only implicitely, as in the above painting. 

An aspect of the modernity of atonal music is that it is impossible to decide what the key is. Atonal music does not show tonality directly,  if any only indirectly. 

The modernity of modern physics is that it is impossible to experimentally verify basic assumptions. The basic assumptions thus do not reveal their character directly,  only indirectly through traces as shown in the above picture from a particle experiment. In classical physics basic assumptions such as Hooke's law, Fourier's law and Coulomb's law, can be directly checked in experiments. But the quanta, photons and quarks of modern physics cannot be observed directly. 

Modern physics, art and music thus share a common quality of hiding to inspection, or

impliciteness and indirectness, like the shades of Platon which only vaugely indicate their origin, if any.

We can compare with the life in the modern city with the qualities of the people we meet in the street hidden to direct inspection, only available indirectly by clothing and appearance, while in the classical village everybody directly knows everything about everybody.

Logic of Penguin Science = ??

The statement A implies B means that if A is true, then B is also true. An elementary mistake in logical scientific reasoning is to conclude that if A implies B and B is observed to be true, then A is true. But this is to confuse A implies B with B implies A. 

We illustrate: Let 

• A= You bang your head into a wall. 
• B = You have a headache.

We could probably agree that there is theoretical evidence that A implies B: Head bang leads to head ache, in theory at least. Suppose now that B is true, that is suppose that you have a headache. Can we then conclude that A is true, that is that you bang your head into a wall? Not necessarily: You may get a headache from other causes, like drinking to much alcohol. It can even be that the implication that you get a headache from head bang is incorrect, so that there is no connection at all; you may have an unusually solid skull.

Yet this type of logic is a trademark of modern physics/science: 

• If we assume that a gas is in a state of molecular chaos with the velocities of two molecules before collision being statistically independent, then we can theoretically derive Boltzmann's equation, which has certain solutions which agree with certain observations. Hence the gas in a state of molecular chaos.
• If we assume that there is a smallest quantum of energy, then we can theoretically derive a formula for the spectrum of black-body radiation, which agrees with observation. Hence there is a smallest quantum of energy.
• If we assume that light consists of particles named photons, then we can theoretically derive a formula for photoelectricity, which agrees with certain observations. Hence light consists of photon particles. 
  
• If we assume Pauli's exclusion principle, then we can explain certain observed atomic electron configurations.  Hence electrons obey Pauli's exclusion principle.
• If we assume that the wave function collapses at observation, then we can theoretically explain an certain observed blips on a screen. Hence the wave function collapses at observation.
• If we assume Heisenberg's uncertainty principle for elementary particles, then we can theoretically explain an observed interaction between observer and observed particle. Hence elementary particles obey Heisenberg's uncertainty principle. 
• If we assume that a proton consists of three quarks, then we can theoretically derive a formula for the observed mass of a proton. Hence a proton consists of three quarks.
  
• If we assume that spacetime observations of different observers are connected by the Lorentz transformation of special relativity, then we can theoretically explain the observation that the speed of light is the same for all observers. Hence spacetime observations of different observers are connected by the Lorentz transformation.
• If we assume that spacetime is curved, then we can theoretically explain observed gravitation. Hence spacetime is curved.
• If we assume there was a Big Bang, then we can theoretically explain the observed expansion of the Universe. Hence there was a Big Bang.
• If we assume there is a black hole at the center of a galaxy, then we can theoretically explain the observed shape of a galaxy. Hence there is a black hole in the center of a galaxy.
• If string theory would predict an observable phenomenon, it would follow that matter consists of tiny vibrating strings.
  
• If we assume that the Earth rests on four invisible tortoises, then we can theoretically explain why the Earth does not fall down. Hence the Earth rests on four invisible tortoises.
• If we assume that CO2 is a critical greenhouse gas, then we can theoretically explain observed global warming. Hence CO2 is a critical greenhouse gas.

Do you see the possibly incorrect logic in these statements? If so, do you see the potential danger of such possibly incorrect logic? Do you think such possibly incorrect logic represents science or pseudo-science? 

Notice that in all the above cases, the fact that a certain phenomenon is observed, which can be theoretically explained from a certain assumption, is used to motivate that the assumption is not just an assumption but a true fact: There is molecular chaos and a smallest quantum of energy, electrons do respect the exclusion principle, the Lorentz transformation must connect different observations, spacetime is curved, light is photons, there was a Big Bang, there is a black hole in the center of a galaxy, a proton is three quarks, the Earth is resting on four tortoises, CO2 is a critical greenhouse gas. 

Notice also that in all cases, it is impossible to directly check if the assumption is valid, which is part of the beauty. The assumption is hidden to inspection and can only be tested indirectly: It is impossible to directly observe molecular chaos, a smallest quantum of energy, photon, electron, particle exclusion, wavefunction collapse, uncertainty, quark, spacetime curvature, black hole, tortoise, string...or that CO2 is a critical greenhouse gas. It is therefore impossible to directly disprove their existence...Clever, but there is an obvious drawback, since the existence is also impossible to verify...science or pseudo-science?

The argument is that the assumption must be true, because this is the only way a theoretical explanation seems to be possible. Our inability to come up with an alternative explanation thus is used as evidence: The more we restrict our creativity and perspective, the more sure we get that we are right. Convincing or penguin science?

Compare the same logic in a trial: If we assume X had a reason to kill Y, then we can theoretically explain the observed murder of Y. Hence X had a reason to kill Y. And thus probably did it! What if you were X?

Notice in particular that present climate politics is based on the idea that CO2 is the cause of the observed global warming, with the motivation that certain theoretical climate models show global warming from CO2. But the observed modest global warming during the 20th century of 0.7 degrees Celsius may have natural causes rather than anthropogenic burning of fossil fuels. What do you think? What does a penguin in the Antarctic think? Compare e.g. EIKE.

Interview with Erland Källen: Meteorologist

Interview with Erland Källen, Professor of Dynamic Meteorology at Stockholm University.

CJ: What is the accuracy of the climate models used in the IPCC predictions of the effects of greenhouse gases on the global climate?

Waiting for response I quote from Questions and answers on climate change DN 2008-02-14:

EK: The error margins are pretty big. The scenario showing 2 degrees warming has an error margin between 1 and nearly 4 degrees, with the upper margin bigger than the lower. All scenarios thus give a warming with the worst scenario over 6 degrees... 

CJ: Do you really mean that if the upper error margin was 10 degrees, then the worst scenario would be more than 12 degrees, so that a bigger error margin would indicate more warming?

Or do we use the term error margin differently?

EK: ??

While waiting we cite more from Questions and answers on climate change DN 2008-02-14:

EK:  Over a longer time period there is a connection between increase of CO2 and global temperature....It is impossible that natural variations only, could explain the warming the last 50 years....From a moral point of view it is very difficult to understand, why we in the rich part of the World have a right to demand birth control in developing countries, if we don't at the same time open to an increased standard of living...To explain the warming the last 50 years it is difficult to see another main reason than increase of CO2...From computer simulations we draw the conclusion that increased CO2 is the most plausible explanation of observed temperature change..

CJ: Are you gradually changing from impossible...to difficult to see...to most plausible...to...?

EK: ??

Erland Källen does not seem to be willing to be interviewed by me. But the questions remain.

Chill-Out: Climate Change??

Chill-Out -- The Truth about the Climate Bubble (in Swedish) by Lars Bern and Maggie Thauersköld,  is an important contribution to the Swedish debate on Anthropogenic Global Warming AGW. Read and think!

The key question is if the global warming of 0.7 degrees Celsius during the 20th century, is due to an increase of CO2 in the atmosphere from 0.028% to 0.038% due to anthropogenic burning of fossil fuels, and if therefore strict limitations on CO2 emissions must be imposed to save the World? 

Al Gore says YES! based on the following key statements in the 2007 Synthesis Report of the UN Intergovernmental Panel of Climate Change IPCC:

• Continued green-house-gas/CO2 emissions at or above current rates  would cause further warming and induce many changes in the global climate system during the 21st century that  would very likely be larger than those observed during  the 20th century. 
  
• Anthropogenic warming could lead to some impacts  that are abrupt or irreversible, depending upon the rate  and magnitude of the climate change. 

Chill-Out puts these statements into perspective and in particular points to the fact that the predictions of IPCC are based on computer simulations showing a better fit to measured temperature with anthropogenic warming included than without. 

Note that the IPCC statements are very cautious, which reflects a generally accepted view that the accuracy/reliability of current climate models is questionable, which I have discussed in previous blogs on climate simulation.

The next UN Climate Conference will take place in Copenhagen in December under Swedish chairmanship of EU. UN Climate chief Yvo de Boer hopes the conference will in particular reach agreements to limit the growth of emissions in developing countries, required to be necessary by predictions of catastrophical global warming.

The key question is if poor people will have to remain poor because of the scientifically vague predictions of IPCC based on certain computer simulations generally viewed to be unreliable?Fredrik Reinfeldt, Swedish prime minister and current EU president, says YES! calling for immediate global action on climate change at the opening of Nordic Climate Solutions, in Copenhagen November 27 2008:

• We must act today, in order to save tomorrow.
  

Chill-Out helps you to understand the background and meaning of this statement.

 

Also compare A man-made mortality tale: How the IPCC’s fairly sober summary of climate science has been spun to tell a story of Fate, Doom and human folly. Read and think!