This is posted on behalf of Dr. Bernd Einfeldt.

About notes from an old climate computer-model heretic (about an essay by Freeman Dyson https://www.edge.org/conversation/heretical-thoughts-about-science-and-society)

In this essay, Freeman Dyson writes: “We are lucky that we can be heretics today without any danger of being burned at the stake. But unfortunately I am an old heretic. Old heretics do not cut much ice. When you hear an old heretic talking, you can always say, “Too bad he has lost his marbles”, and pass on. What the world needs is young heretics. I am hoping that one or two of the people who read this piece may fill that role.”

I am not young either anymore and just pass it on for a discussion. Freeman Dyson is a theoretical physicist and mathematician. He is professor emeritus in the Institute for Advanced Study in Princeton, a Visitor of Ralston College, and a member of the Board of Sponsors of the Bulletin of the Atomic Scientists. So you may asked what can I, an unknown mathematician possible add if Freeman Dyson writes about climate change? Well – modern search engine allow to some extent a check of the logical consistency of thought pattern. Even the best mathematician (a Professor of physics at the Institute for Advanced Study in Princeton is likely an outstanding mathematician) can miss important parameter in his considerations.

Freeman Dyson actually starts his opinion pieces with this remark: “My first heresy says that all the fuss about global warming is grossly exaggerated. Here I am opposing the holy brotherhood of climate model experts and the crowd of deluded citizens who believe the numbers predicted by the computer models. Of course, they say, I have no degree in meteorology and I am therefore not qualified to speak. But I have studied the climate models and I know what they can do. The models solve the equations of fluid dynamics, and they do a very good job of describing the fluid motions of the atmosphere and the oceans. They do a very poor job of describing the clouds, the dust, the chemistry and the biology of fields and farms and forests. They do not begin to describe the real world that we live in. The real world is muddy and messy and full of things that we do not yet understand. It is much easier for a scientist to sit in an air-conditioned building and run computer models, than to put on winter clothes and measure what is really happening outside in the swamps and the clouds. That is why the climate model experts end up believing their own models.” …. and in section 4 “The Wet Sahara” he writes “The biosphere is the most complicated of all the things we humans have to deal with. The science of planetary ecology is still young and undeveloped. It is not surprising that honest and well-informed experts can disagree about facts.”

My dissertation was related to the stability of compressible flow and there numerical solution. Most of my remarks are related to these stability questions, which are today (three decades after my dissertation) largely unsolved in regard to the fluid dynamic equations. The other remark is related to increasing number of people living on a finite planet with finite resources, to the storage of carbon dioxide in soil, not in relation to thoughts of an naturalist or humanist, but simply in regard to the resources for an growing population.

If climate models are based on an initial value problem for the fluid dynamic equations, then the numerical results are effected by instabilities, which could make prediction very questionable. I think the flip between El Nino and La Nina1), the weakening and temporary halt of the Gulf stream during ice ages 2), costal sea ice for the North Pacific ocean circulation3),4) jet streams5) and the collapse of the west antarctic ice shields6) and likely other climate phenomenons are related to such fluid dynamic instabilities.

Mathematical models very roughly speaking relate entities, where entities itself are described by a set of physical quantities, numbers with a dimension, like kilogram for mass or Joule for energy or seconds for time. Then the computed numbers for a model can be compared with measured numbers. If these numbers do not agree with measurements, then something is missing or the model is wrong. In the first case parameters can be added to improve a theory, in the latter case the model is not correct. Freeman Dyson essentially says that the models are incomplete, they do not contain all the relevant entities to describe the changing atmosphere, this is not heresy. It is more or less in accordance with the remarks from climate scientists, asking for additional funding to add parameter to climate models.

Anyhow I think, these partial models describing some climate entities are not part of a single mathematical climate model, they are parts of a computing frame work. Thus climate models are software programs, more related to a digital framework for self driving cars. These programs work well for tested situations. But how can climate simulation validated for climate singularities. How can we possible know all climate states and singularities? I think an analog test environment for climate models is necessary.+ My second critic is even more fundamental. I think the atmosphere is not governed by the classical fluid dynamic equation, rather by equations which are related to periodic boundary-layer equations, which allow only certain stable states.++

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In regard to carbon dioxide storage Freeman Dyson writes: “The point of this calculation is the very favorable rate of exchange between carbon in the atmosphere and carbon in the soil. To stop the carbon in the atmosphere from increasing, we only need to grow the biomass in the soil by a hundredth of an inch per year. Good topsoil contains about ten percent biomass, [Schlesinger, 1977], so a hundredth of an inch of biomass growth means about a tenth of an inch of topsoil.”

Is this the process nature uses to stabilized the earth biosphere? Then we are seriously jeopardizing this balance through land conversion; see for example palm oil production7). Human land conversion results in the release of large amounts of carbon stored in the soil. I think the inventory in the atmosphere cannot remain constant as long as the population continues to grow in a globalized world striving for a higher standard of living. Population growth resulted over millenniums in an land use change and the release of climate gases. Now it may be argued that more carbon dioxide can be stored on less land. There are however tipping points which can cause irreversible changes. Understanding these tipping points is critical I think this is only possible with the help of climate models.

Freeman Dyson noted: “When I listen to the public debates about climate change, I am impressed by the enormous gaps in our knowledge, the sparseness of our observations and the superficiality of our theories. Many of the basic processes of planetary ecology are poorly understood. They must be better understood before we can reach an accurate diagnosis of the present condition of our planet. When we are trying to take care of a planet, just as when we are taking care of a human patient, diseases must be diagnosed before they can be cured. We need to observe and measure what is going on in the biosphere, rather than relying on computer models.”

… strange, not even a closed biosphere was built to benchmark climate models. Some politician even declared: The science is settled!

Freeman Dyson wrote: “In the modern world, science and society often interact in a perverse way. We live in a technological society, and technology causes political problems. The politicians and the public expect science to provide answers to the problems. Scientific experts are paid and encouraged to provide answers. The public does not have much use for a scientist who says, “Sorry, but we don’t know”. The public prefers to listen to scientists who give confident answers to questions and make confident predictions of what will happen as a result of human activities. So it happens that the experts who talk publicly about politically contentious questions tend to speak more clearly than they think. They make confident predictions about the future, and end up believing their own predictions. Their predictions become dogmas which they do not question”.

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In relation to carbon dioxide he wrote further: “Everyone agrees that the increasing abundance of carbon dioxide in the atmosphere has two important consequences, first a change in the physics of radiation transport in the atmosphere, and second a change in the biology of plants on the ground and in the ocean. Opinions differ on the relative importance of the physical and biological effects, and on whether the effects, either separately or together, are beneficial or harmful. The physical effects are seen in changes of rainfall, cloudiness, wind-strength and temperature, which are customarily lumped together in the misleading phrase “global warming”. In humid air, the effect of carbon dioxide on radiation transport is unimportant because the transport of thermal radiation is already blocked by the much larger greenhouse effect of water vapor. The effect of carbon dioxide is important where the air is dry, and air is usually dry only where it is cold. Hot desert air may feel dry but often contains a lot of water vapor. The warming effect of carbon dioxide is strongest where air is cold and dry, mainly in the arctic rather than in the tropics, mainly in mountainous regions rather than in lowlands, mainly in winter rather than in summer, and mainly at night rather than in daytime. The warming is real, but it is mostly making cold places warmer rather than making hot places hotter. To represent this local warming by a global average is misleading.”
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I think this is what we experience right now. The so called “global warming” effects most seriously relative could places like the arctic and mountain regions. These regions however are very important for the global weather system. Warmer arctic regions can change the global ocean currents8) and the jet stream.

With dramatic consequences for human societies. To understand these changes physical models are needed. I think the study of these stability question using computer models (frameworks with glue together a large number of of models describing fractions of the climate system) is questionable. Numerical instabilities or artificial dissipation interacts with natural instabilities of the governing equation. It is nearly impossible to differentiate between artifact instabilities in climate simulations and natural instabilities, if the governing equations are not known and the simulations are merely based on subroutines in an computing frame work. Who cares? Politicians believe that new scientific results are part of an large organization like climate centers or a “building in London where the Royal Navy kept a staff of scientists”. I think climate science in Europe is today completely run by governmental funding and political programs. This method effectively kills any reasonable new idea not related to a large governmental research program; read also “they don’t know after a decade of research and a few billions invested in climate research facilities?“).

Freeman Dyson writes furthermore: “There are good arguments on both sides of this question. On the one side, we know that the level of carbon dioxide in the atmosphere was much lower during past ice-ages than during warm periods, so it is reasonable to expect that an artificially high level of carbon dioxide might stop an ice-age from beginning. On the other side, the oceanographer Wallace Broecker [Broecker, 1997] has argued that the present warm climate in Europe depends on a circulation of ocean water, with the Gulf Stream flowing north on the surface and bringing warmth to Europe, and with a counter-current of cold water flowing south in the deep ocean. So a new ice-age could begin whenever the cold deep counter-current is interrupted. The counter-current could be interrupted when the surface water in the Arctic becomes less salty and fails to sink, and the water could become less salty when the warming climate increases the Arctic rainfall. Thus Broecker argues that a warm climate in the Arctic may paradoxically cause an ice-age to begin. Since we are confronted with two plausible arguments leading to opposite conclusions, the only rational response is to admit our ignorance. Until the causes of ice-ages are understood, we cannot know whether the increase of carbon-dioxide in the atmosphere is increasing or decreasing the danger.”

At the end he writes: “I will not attempt to summarize the lessons that my readers should learn from these heresies. The main lesson that I would like them to take home is that the long-range future is not predetermined. The future is in their hands.”

Well – It is very likely that changes on the global conveyor belt are not continuous. If the warming ocean destabilizes ocean currents or even halts them, then the world may change drastically. It is estimated that it can take 1,000 years or so for a “parcel” of water to complete the journey along the global conveyor belt, cause and effect may be delayed by generations. Thus if this generation tries to get the most out of the available natural resources in term of population growth and a higher standard of living, based on cheap fossile fuel energy, then it may actually initiate changes which jeopardize the living conditions of future generations. From an mathematical point of view, is it an open question if these currents are permanent, or if they change periodically, just because the flow gets unstable under temperature changes?

“The moral of this story is clear. Even a smart twenty-two-year-old is not a reliable guide to the future of science. And the twenty-two-year-old has become even less reliable now that he is eighty-two.” … anyway Freeman Dyson teaches us what is most important: Never stop questioning. Curiosity has its own reason for existing.

I think Freeman Dyson has good reason for „opposing the holy brotherhood of climate model experts“. The climate models failed again, again and again, if prediction are made in unchartered territory. Like the software for autonomous driving cars gets better and better over time, climate models improve over time. The public may start to trust climate model predictions, similar to the trust in weather forecast. We all know there will always be singular situations in which an autonomous driving car fails, in which weather forecast are wrong. The autonomous car may stop or in the worst case it crashes and the driver dies (a few thousand people die each year alone in Germany in road traffic accidents, self-driving cars may actually reduce thus number). In case of a wrong weather forecast we may only get wet, in the worst case high alpine climber may die or cities are flooded. Climate model experts claim that the uncertainty of weather forecast averages out in climate modeling and thus models are valid for a large time-frames. I am however not aware that the underlying equations support such a bold claim.

A software failure effects always only a limited number of people and we can go on and improve the software. In the article 10) it says in regard to the model “Code for running the CM2.6 experiment is available from http:// http://www.gfdl.noaa.gov/ 11) Scripts for analysing the data are available from the corresponding authors upon reasonable request.” There is no reference to the underlying mathematical equations, it just says “The CM2.6 coupled global climate model was developed by the Geophysical Fluid Dynamics Laboratory of the National Oceanic and Atmospheric Administration”, I am sure these are great sophisticated models, based on well-founded physical principles. If however the fluid dynamics of the oceans and atmosphere is related to a boundary-layer flow, then these models cannot accurately predict singularities, like a halt of the gulf stream or the antarctic ice melt.

Climate models failed in the past in uncharted territory and even if they get more and more sophisticated over time, a wrong climate forecast of a singularity does not effect only a few people, it may result in the collapse of an unprepared society. Why did they not develop an accompanying analog models to verify climate models?+ Yes, experiments cannot be performed on the actual earth, but they likely can be performed on the ISS.

However, even with these limitations in mind, climate models indicate that the climate gas emission can trigger climate instabilities. They agree on certain basic aspects of future climate change. For example, they all show rising global temperatures with amplified warming in the Arctic, enhancement of the hydrologic cycle (dry places becoming dryer and wet places becoming wetter), and rising sea level. On the other hand it is obvious. Climate gas emissions are related to the number of people, the lifestyle and industry in a country. Thus it may be asked: Are there at least verified models for the population numbers, the average climate gas emissions, the per person emissions and the industry for each country? If not – then there is no scientific basis for the implementation of a Climate Accord.

1. What are El Niño and La Niña? https://oceanservice.noaa.gov/facts/ninonina.html
2. Woods Hole Oceanographic Institution. “Atlantic Ocean Circulation at weakest point in 1,600 years.” ScienceDaily. ScienceDaily, 11 April 2018. <http://www.sciencedaily.com/releases/2018/04/180411131642.htm>
3. Latif, Barnett, Decadal Climate Variability over the North Pacific and North America: Dynamics and Predictability. In: Journal of Climate 9, (1996), see also references for in https://de.m.wikipedia.org/wiki/Mojib_Latif: Latif and Barnett noted: “Both the observation and the model results support the picture that the decadal variations in the regions of interest is based on a cycle involving unstable ocean-atmospheric interactions over the North Pacific.” In Einfeldt, ON GODUNOV-TYPE METHODS FOR GAS DYNAMICS, SIAM J. NUMER. ANAL. VOL. 25, No. 2, April 1988 was shown that any classical numerical method which assumes a sharp stationary shear-interface between gases of different densities can produce artifact instabilities. This result applies as well to the ocean-atmospheric interface. Time did not permit to study the numerical stability of the methods used by Latif, Barnett and others.

4. University of California – Santa Cruz. “Formation of coastal sea ice in North Pacific drives ocean circulation, climate: New understanding of changes in North Pacific ocean circulation over the past 1.2 million years could lead to better global climate models.” ScienceDaily. ScienceDaily, 20 October 2015. <http://www.sciencedaily.com/releases/2015/10/151020144838.htm>.
5. On the Disruption of Weather Pattern and an old Experiment in a Laboratory” in “AChangingEarth” or Google+ – A relation to the jet stream is explained in 1).
6. Discovery of recent Antarctic ice sheet collapse raises fears of a new global flood https://www.sciencemag.org/news/2018/12/discovery-recent-antarctic-ice-sheet-collapse-raises-fears-new-global-flood „If it holds up, the finding would confirm that “the West Antarctic Ice Sheet might not need a huge nudge to budge,” says Jeremy Shakun, a paleoclimatologist at Boston College.” i.e. it is unstable under climate perturbation. „If so, the world may need to prepare for sea level to rise farther and faster than expected: Once the ancient ice sheet collapse got going, some records suggest, ocean waters rose as fast as some 2.5 meters per century.”

7. “Palm Oil Was Supposed to Help Save the Planet. Instead It Unleashed a Catastrophe” in “A Changing Earth” collection.
8. The global conveyor belt – https://oceanservice.noaa.gov/education/tutorial_currents/05conveyor2.html
9. “They don’t know after a decade of research and a few billions invested in climate research facilities?” in “A Changing Earth” collection on Facebook or Google+

10. Observed Fingerprint of a weakening Atlantic Ocean Overturning Circulation, Nature 2018-04-11
11. Read also about GFDL climate modeling at https://www.gfdl.noaa.gov/climate-modeling/ “Increasing climate model accuracy involves continually improving its completeness, correctness, and resolution. This includes the addition of new processes that represent components such as land and ocean carbon cycles, interactions between cloud droplets and aerosols, and ice sheets. These components are initially developed and tested offline before they are coupled into the climate model and are allowed to interact with the other components.” … “Climate models divide the globe into a three-dimensional grid of cells representing specific geographic locations and elevations”. It can be shown, that just representing an model on a finite grid can result in numerical artifact singularities; see http://discontinuous-flow.blogspot.com/2015/09/the-carbuncle-phenomenon-in-shallow.html

+Let me know if there is a research institute interested to address this question.

++ It is principally possible to verify this assumption, it requires however resources and time not available outside research projects.